close

Вход

Забыли?

вход по аккаунту

?

Microwave radiometry of snow-covered grasslands for the estimation of land-atmosphere energy and moisture fluxes

код для вставкиСкачать
UMI
t
MICROFILMED 1996
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may
be from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margin*,
and improper alignment can adversely affect reproduction.
In the unlikely, event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g^ maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand comer and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in
reduced form at the bade of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6" x 9" black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly
toorder.
A Bell & Howell information Company
300 North Zeeto Road. Ann Arbor, Ml 48106*1346 USA
313.-761-4700 800*521 -0600
MICROWAVE RADIOMETRY OP
SNOW-COVERED GRASSLANDS FOR
THE ESTIMATION OF LAND-ATMOSPHERE
ENERGY AND MOISTURE FLUXES
by
John F. Galantowicz
A dissertation subm itted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Electrical Engineering and Atmospheric, Oceanic and Space Sciences)
in The University of Michigan
1995
Doctoral Committee:
Professor Anthony W. England, Chair
Professor Sushil K. A treya
Professor Henry N. Pollack
Assistant Professor Kama] Sarabandi
Professor Fawwaz T . Ulaby
UMI Number: 9610X24
Copyright 1995 by
Galantowics* John Francis
All rights reserved.
OKI Microfora 9610124
Copyright 1996* by OMX Coapany. All rights reserved.
This aiccofoca edition is protected against unauthorized
copying under Title 17* United States Code.
UMI
300 North Seeb Road
Ann Arbor* MI 48103
© John F. Galantowicz 1995
All Rights Reserved
To Sara
ii
ACKNOWLEDGMENTS
I thank the com m ittee members for their insightful comments and suggestions
incorporated into this thesis and for their generous support for my work. This work
owes a great deal to the guidance of my advisor, Prof. Tony England, who contributed
many of the best ideas th a t tic m y thesis together and has always been willing to let
curiosity lead.
I am grateful to the many individuals who volunteered their services and expertise
in ways th a t have enhanced this work. I thank Dr. Dave Meyer of the USGS EROS
D ata C enter for his hospitality and support of my experimental work in Sioux Falls,
South Dakota, and the staff of EROS who m ade the REBEX-1 field study possible.
Thanks goes to the staff of the Marshall Space Flight Center's Distributed Active
Archive Center in Huntsville, Alabama, for providing SSM /I data. I would especially
like to thank Mr. Ron H artikka for his assistance and ideas in the laboratory. I
also thank th e students who helped me as a part of their own studies: Ms. C ynthia
Ballard, Mr. Howard Chang, Mr. Stan Modjeski, and Mr. Eric Beaubien who assisted
in the production of SSM /I images appearing in the thesis.
T he intellectual stim ulation, camaraderie, and hard work of my current and former
fellow graduate students have both made my work less difficult and lifted my spirits
for six years. I thank Dr. Richard Austin, Mr. Paul Dahl, Ms. Jasm eet Judge, Dr.
John K endra, Mr. Ed Kim, Dr. Brian Kormanyos, Dr. Joe Landry, Mr. Yuei-an Liou,
Dr. Adib Nashashibi, Dr. Leland Pierce, Mr. Paul Siqucira, Mr. Jim Stiles, and Dr.
Brian Zucrndorfer for their technical advice and assistance. I also thank them and
the many other Radiation Lab students who have been great friends and willing
collaborators during this project.
For their financial support, 1 thank the Office of Naval Research, which funded
the first three years of my post-graduate work, and also the National Aeronautics
and Space Administration and the National Science Foundation. I also thank the
Rackham School of Graduate Studies for providing funds for travel to technical con­
ferences.
Finally, I would like to thank my wife, Sara, who, through her faith and encour­
agement, has been my fundamental inspiration.
TABLE OF CONTENTS
D ED IC A TIO N ...........................................................................................
ACKNOW LEDGM ENTS........................................................................
LIST OF TA BLES......................................................................................
LIST OF FIG U R E S...................................................................................
LIST OF A PPEN D IC ES...........................................................................
CHAPTERS
1 IN T R O D U C T IO N ...............................................
1.1
1.2
1.3
1.4
.................
Linking snovvpack, atmosphere, and rad io m e try .......................
Approach and prem ise of the thesiB
...............................................
Questions addressed by this d isse rta tio n ....................................
Format of the d issertatio n ...............................................................
2 BACKGROUND ........................................................................
2.1
2.2
2.3
Introduction
........................................................................
Great Plains sn o w p ack s..................................................................
Microwave radiom etry of s n o w p a c k s ...........................................
3 SIMULATING THE DYNAMIC SN O W PA C K ....................
3.1
3.2
3.3
3.4
In tr o d u c tio n .......................... ..........................................................
Overview of Snow flow .....................................................................
H eat flow in s o i l .......................................................................................
3.3.1 Liquid water content in sub-freezing s o il.......................
3.3.2 Enthalpy change in freezing s o i l ....................................
3.3.3 Soil therm al c o n d u c tiv ity .................................................
Snowpack formation and heat and moisture f l u x e s .................
3.4.1 H eat and vapor transfer w ithin the s n o w p a c k .............
3.4.2 Snow-soil in te ra c tio n s ........................................................
3.4.2.1 Handling an insulating layer of grass , . . .
3.4.3
3.4.4
Shortwave attenuation and a b so rp tio n ..........................
Snow-atmosphere in te r a c t io n s .......................................
3.4.4.1 Radiative energy e x c h a n g e ...............................
3.4.4.2 Latent and sensible heat e x c h a n g e ..................
3.4.4.3 Heat from p re c ip ita tio n .....................................
3.4.5 Liquid water seepage in the sn o w p a c k ...........................
3.4.6 Compaction and mass balance of snowpack layers . .
3.4.7 M etamorphism of snow g r a i n s ........................................
D is c u s s io n ........................................................................................
28
29
30
31
33
33
36
38
39
4 MODELING RADIOBRIGHTNESS OF THE SIMULATED
SNOW PACK................................................................................
40
3.5
4.1
4.2
4.3
4.4
In tr o d u c tio n .....................................................................................
Conventional radiative transfer th e o r y .......................................
Solution for the simulated sn o w p a c k ..........................................
4.3.1 The scattering phase m atrix and Mic scattering . . .
4.3.1.1 A ttenuation coefficients: Empirical scatter­
ing reduction ....................................................
4.3.2 T he method of invariant im b e d d in g ..............................
4.3.3 Air-snow and snow-soil b o u n d a rie s..................................
4.3.4 Dielectric properties of water, ice, snow, and soil . . .
D is c u s s io n .............................................
5 GROUND BASED RADIOBRIGHTNESS OBSERVATIONS
IN THE NORTHERN GREAT PLAINS: THE FIRST RA­
DIOBRIGHTNESS ENERGY BALANCE EXPERIM ENT .
5.1
5.2
5.3
5.4
5.5
In tr o d u c tio n .........................
A p p a r a t u s ........................................................................................
5.2.1 Micromctcorological Subsystem and system integration
5.2.2 Design of th e microwave radiometers and the Tower
Mounted Radiometer S y s te m ...........................................
5.2.2.1 Microwave radiom eter c a li b r a tio n .................
In sta lla tio n ........................................................................................
E x p erim en tin g
..............................................................
Correcting radiobrightncss e r r o r s .................................................
5.5.1 Removing out of range radiobrightness v a lu e s
5.5.2 Sky reflector positioning e r r o r s ........................................
5.5.3 Revision of the day 403 37 GHz radiom eter calibration
5.5.4 Estim ation of actual sky radiobrightnesses .................
5.5.5 Calibration of the 85 GHz radiom eter for days 347-403
5.5.6 An alternative calibration p a ra m ete riz a tio n .................
5.5.7 Sensitivity of radiobrightness to antenna efficiency as­
sumptions .............................................
vi
40
40
44
48
52
55
60
61
64
65
65
66
66
70
73
78
84
85
86
87
88
90
94
97
99
5.6
D is c u s s io n ........................
9!)
6 MICROWAVE RADIOMETRY FROM SPACE: THE SPE­
CIAL SENSOR M ICR O W A V E/IM A G ER....................... 100
6.1
6.2
6.3
6.4
In tr o d u c tio n .............................................................................. 100
D ata from the S S M / I .............................................................. 101
Compensating for atmospheric attenuation and emission . . . 103
6.3.1 Using the rawinsonde atmospheric profiles.................104
6.3.2 Compensation w ithout a priori in fo rm atio n ........... 109
Comparison of SSM /I and REB EX-1 radiobrightnesses . . .
114
7 COMPARING MODELS TO OBSERVATIONS.................... 124
7.1
7.2
7.3
7.4
7.5
In tro d u c tio n ..............................................................................
Model initialization and i n p u t s ..............................................
Evaluation of the snowpack S V A T .......................................
Radiobrightness co m p ariso n s.................................................
Comments on snowpack structure, grain size, and wetness .
124
124
127
133
. 149
8 CONCLUSIONS, CONTRIBUTIONS, AND RECOMMEN­
DATIONS...................................................................................... 158
8.1
8.2
8.3
Conclusions ...............................................................
158
Contributions ................................................................................ 162
R ecom m endations.................................................................... 163
A PPE N D IC E S...........................................................................................
166
BIBLIO G RA PH Y ......................................................................................... 216
vii
LIST OF TABLES
T a b le
4.1
Mic-Rayleigh scattering param eter comparison. Q tea is in units of m3.
49
5.1
Micromclcorological instrum ents and param eters. N /A indicates data
not available......................................................................................................
6S
Microwave radiometer specifications. N /A indicates d ata not available.
See Appendix B for radiometric resolution calculations...........................
70
5.3
Estim ated loss param eters.............................................................................
70
5.4
Calibration param eters used during REBEX-1 from day indicated to
day of next calibration. Some 37 and 85 GHz param eters were later
modified. Sec Sections 5.5.3 and 5.5.5..........................................................
78
5.2
5.5
Summ ary of REBEX-1 site coverage conditions and hardware problems. 86
5.6
Corrected calibration parameters for the period from days 403 to 471.
90
5.7
Reflector efficiencies from (5.18), the number of clear sky profiles used,
and the standard deviation of
Also shown are the percentage of
T s k y values from (5.19) th at were less than zero......................................
93
5.8
Revised 85 GHz calibration parameters for days 347-403.......................
97
5.9
A lternative calibration param eters..............................................................
98
6.1
SSM /I sensor specifications [59], EFOV on earth is in k m .........................101
6.2
Average, e, and standard deviation, <re, of difference between SSM /I
(7^ and T j e r ) and REBEX-1 brightnesses. All brightnesses are h-pol. 107
Comparison of T tbr from the rawinsondc and dry standard atm osphere
methods showing average, e, and standard deviation, <re, of the differencee = TYffft(rawin.)—jfy£/i(dry atm .). Also given are these statistics
for the m agnitude of the correction, th a t is e = T jbh “
All bright­
nesses arc h-pol.................................................................................................
112
Statistics of difference between REBEX-1 and SSM /I terrain bright­
nesses in January. All brightnesses arc h-pol. DR is the January
dynamic range of the REBEX-1 brightnesses.............................................
119
Comparisons of modeled snowpack variables to REBEX-1 measure­
ments. A = model - observation, <r is standard deviation, and DR is
the dynamic range of the measured d ata over the test period................
12S
Comparison of modeled brightnesses (K) to h-pol. observations from
REBEX-1 and h-pol. and v-pol. observations from SSM /I. A — model
- observation, a is standard deviation, and DR is the dynamic range
of the measured d a ta over the test period...................................................
136
Snowflow param eters set by th e user...........................................................
169
A.2 Snowflow empirical parameters and their sources.....................................
169
A.3 O ther physical param eters used in Snowflow.............................................
170
Calibration check results. Te <
xo is the tem perature of the Eccosorb
target a t the tim e the T ap were measured. There is insufficient data
to calculate 85 GHz radiometric resolution. . ........................................
172
B.2 Soil moisture sampling data. Masses are in grams and include tare
mass. Drying was first done at 70°C then a t 105°C. Gravimetric mois­
ture content is tabulated at both tem peratures and volumetric moisture
content is tabulated only at 105CC...............................................................
175
6.3
6.4
7.1
7.2
A.l
B.l
B.3
REBEX-1 day to calendar date conversion chart.......................................... 202
C .l
SSM /I operational d ata for the F08 and F l l satellite platforms [60]. . 210
C.2
Param eters for the Ml and Mb EASE-Grid projections.............................. 214
ix
LIST OF FIGURES
Figure
3.1
Schematic of the Snowflow simulated snowpack.......................................
13
3.2
Schematic of liquid water seepage through the simulated snowpack
(after [38])..........................................................................................................
34
4.1
Conventional radiative transfer.....................................................................
41
4.2
Upwelling and downwclling brightness in a snowpack layer...................
44
4.3
Scattering geometry for an isolated particle.
50
4.4
Particle scattering geometry in the snowpack coordinate system. . . .
51
4.5
(a) Normalized scattering coefficients and (b) the independent scatter­
ing reduction factor.
...........................................................................
54
4.6
Brightness balance for the k th thin snowpack layer.................................
56
4.7
Components of the layer scattering source term , T + ,..............................
57
5.1
Interior of the trailer on site sheltering data acquisition and device
control electronics and the Macintosh com puter running the FluxMon
HyperCard stack which controlled the experim ent...................................
67
T he TMRS-1 radiometer housing.
..........................................................
71
The 85 GHz radiometer. The 19 and 37 GHz radiometers have layouts
which are comparable component by com ponent......................................
72
5.4
Microwave radiometer block diagram ..........................................................
74
5.5
View of the REBEX-1 site from the east...................................................
79
5.2
5.3
x
.........................
5.6 View of the radiometer housing with its back cover removed. Inserted
into the housing arc (from th e far side) the 85 GHz radiom eter, the IR
radiom eter and video camera module, the center connector box, the 37
GHz radiometer, and the 19 GHz radiom eter............................................
80
5.7
Plan view of the REBEX-1 site.....................................................................
81
5.8
Graduated PVC pipe with alternating 1.27 cm (0.5 in) black and white
stripes used for gaging snow depth from video stills of the REBEX-1
site..................................................
82
5.9 Insertion of the soil tem perature probes. At the tim e of this picture,
1 had already inserted the probes in th e side of the trench and refilled
it, burying the 64, 32, and 16 cm probe cables. Cables leading to the
2, 4, and 8 cm deep probes protrude from the side of the trench. . . .
83
6.1
Comparisons of SSM /I antenna tem peratures and REBEX-1 terrain
brightnesses........................................................................................................
105
(Continued from previous p a g e .).................................................................
106
T ter
Variation with tim e of the difference between T t e r from SSM/1 and
from REBEX-1.......................................................................................
108
Brightness tem peratures upwelling from the atmosphere as a function
of surface water vapor density
....................................................
Ill
Simulated antenna tem peratures as a function of surface water vapor
density given terrain brightnesses of 200, 235, and 270 Iv.......................
Ill
Comparisons between SSM/1 terrain brightness estim ates, T t e r , made
with a dry standard atmosphere ( 7 / - dry atm .) and a rawinsondc
atmosphere (T a - rawin. atm .). Alt brightnesses are h-pol.....................
113
6.6
19 GHz terrain radiobrightness from SSM/1 and REBEX-1...................
115
6.7
37 GHz terrain radiobrightness from SSM /I and REBEX-1...................
116
6.8
85 GHz terrain radiobrightness from SSM/1 and REBEX-1...................
117
6.9
Difference between REBEX-1 and SSM /I terrain brightnesses
118
6.1
6.2
6.3
6.4
6.5
6.10 19 GHz SSM /I terrain brightness at vertical and horizontal polarization
and the v-h difference..............................................................................
121
6.11 37 GHz SSM/1 terrain brightness at vertical and horizontal polarization
and the v-h difference......................................................................................
122
xi
6.12 85 GHz SSM/I terrain brightness a t vertical and horizontal polarization
and the v-h difference......................................................................................
123
7.1 Schematic of th e Snowflow and Esnow inputs and products........................ 125
7.2 Modeled and observed snow depths with wet model soil..........................
128
7.3 Modeled and observed snowpack surface tem perature with wet model
soil.......................................................................................................................
129
7.4 Modeled and observed soil tem perature at 2 cm depth with wet model
soil................................................................................................................
131
7.5 Modeled and observed soil heat flux at 2 cm depth with wet model
soil. Positive values indicate heat flow into th e soil..................................
132
7.6 Modeled and observed soil tem perature at 2 cm depth with dry model
soil.......................................................................................................................
134
7.7 Modeled unfrozen soil w ater content for model soils with initial moisture volume fractions of 0.43 (top) and 0.20 (bottom ) before freezing.
135
7.8 Modeled and observed 19 GHz h-pol. terrain brightness with wet model
soil and ground-based observations...............................................................
137
7.9 Modeled and observed 37 GHz h-pol. terrain brightness with wet model
soil and ground-based observations...............................................................
138
7.10 Modeled and observed 85 GHz h-pol. terrain brightness with wet model
soil and ground-based observations...............................................................
139
7.11 Modeled and observed v-pol. terrain brightness at 19, 37, and 85 GHz
with wet model soil and space-based observations from SSM /I
140
7.12 Modeled h-pol. terrain brightness a t 19, 37, and 85 GHz with both wet
and dry model soil............................................................................................
141
7.13 Plots of modeled 19 GHz h-pol, terrain brightness, modeled soil surface
unfrozen water content, observed 19 GHz h-pol. terrain brightness,
observed 2 cm soil tem perature, and modeled and observed snowpack
depths......................................................
143
7.14 Modeled h-pol. terrain brightnesses with dielectric layering artificially
enhanced..............................
146
7.15 SSM /I 19 GHz v- and h-pol. brightnesses (top graph and overlays)
compared to model results with wet soil, dry soil, and wet soil plus *
enhanced dielectric layering............................................................................ 147
7.16 SSM /I 19 GHz v- and h-pol. brightnesses and their difference a t Langdon, North Dakota...........................................................................................
MS
7.17 Modeled and observed h-pol. 37 GHz terrain brightnesses and modeled
total snowpack liquid water content. The arrows indicate modeled
partial snowmelt events th a t correspond to observed brightness jum ps. 150
7.IS Snow liquid w ater content profiles during a cycle of partial melt and
rcfrcczc........................................................... ..................................................... 151
7.19 Snow grain diam eter profiles from the Snowflow model..........................
152
7.20 SSM /I 19 GHz h-pol. images from February 4, 1992 at 23:24 UTC
(top) and February 8, 1992 a t 12:44 UTC. Sec text for description.. .
155
7.21 SSM /I 37 GHz h-pol. images from February 4, 1992 a t 23:24 UTC
(top) and February 8, 1992 at 12:44 UTC. Sec text for description.. .
156
7.22 SSM /I 85 GHz h-pol. images from February 4, 1992 at 23:24 UTC
(top) and February 8, 1992 a t 12:44 UTC. See text for d escription.. .
157
D.l
Summary of terrain apparent radiobrightnesses a t 19, 37, and 85 GHz. 177
B.2 Summary of reflector-measured sky radiobrightnesses a t 19, 37, and 85
GHz and therm al infrared sky tem perature................................................
178
B.3 Summary of reflector-measured sky radiobrightness and estim ated sky
radiobrightness at 19 GHz..............................................................................
179
B.4 Summary of reflector-measured sky radiobrightness and estim ated sky
radiobrightness at 37 GHz..............................................................................
ISO
B.5 Summary of reflector-measured sky radiobrightness and estim ated sky
radiobrightness at 85 GHz..............................................................................
181
B.6 Summary of REBEX-1 global and net radiation, 10 m wind speed,
subsurface soil tem peratures, and soil heat flux a t 2 cm depth..............
182
B.7 Summ ary of REBEX-1 relative humidity, rainfall per experim ent cy­
cle, therm al infrared surface tem perature, air tem perature, and soil
tem perature a t 2 cm dep th.............................................................................
183
B.8 Summ ary of terrain apparent radiobrightness spectral gradients and
T P R reference load gain factors......................
184
B.9 Summary of REBEX-1 snow depths estim ated from video stills of the
site and from National W eather Service reports at Sioux Falls, S D .. .
185
B.10 October terrain (surface) apparent radiobrightnesses and reflector-mea­
sured sky radiobrightnesscs a t 19 and 37 GHz, net and global radiation,
and wind speed a t 10 m .......................................................
187
B .ll October subsurface soil tem peratures, vertical heat flux at 2 cm depth
in the soil, relative humidity, rainfall, air tem perature, and therm al
infrared Burface tem perature.........................................
188
B.12 November terrain (surface) apparent radiobrightnesses and reflectormeasured sky radiobrightnesscs a t 19 and 37 GHz, net and global ra­
diation, and wind speed at 10 m ........................................
189
B.13 November subsurface soil tem peratures, vertical heat flux a t 2 cm
depth in the soil, relative humidity, rainfall, air tem perature, and ther­
mal infrared surface tem perature..................................................................
190
B.14 December terrain (surface) apparent radiobrightncsses and reflectormeasured sky radiobrightnesscs a t 19, 37, and 85 GHz, net and global
radiation, and wind speed at 10 m ................................................................
191
B.15 December subsurface soil tem peratures, vertical heat flux at 2 cm depth
in the soil, relative humidity, rainfall, air tem perature, and therm al
infrared surface tem perature..........................................................................
192
B.1G January terrain (surface) apparent radiobrightnesscs and reflector-mea­
sured sky radiobrightncsses a t 19, 37, and 85 GHz, net and global
radiation, and wind speed a t 10 m .................
193
B.17 January subsurface soil tem peratures, vertical heat flux at 2 cm depth
in the soil, relative humidity, rainfall, air tem perature, and therm al
infrared surface tem perature..........................................................................
194
B.18 February terrain (surface) apparent radiobrightnesses and reflectormeasured sky radiobrightnesses at 19, 37, and 85 GHz, net and global
radiation, and wind speed a t 10 m ...............................................................
195
B.19 February subsurface soil tem peratures, vertical heat flux at 2 cm depth
in the soil, relative humidity, rainfall, air tem perature, and thermal
infrared surface tem perature..........................................................................
19fi
xiv
B.20 March terrain (surface) apparent radiobrightncsses and reflector-mea­
sured sky radiobrightncsses at 19, 37, and 85 GHz, net and global
radiation, and wind speed a t 10 m ...............................................................
197
B.21 March subsurface soil tem peratures, vertical heat flux at 2 cm depth
in the soil, relative humidity, rainfall, air tem perature, and therm al
infrared surface tem perature.................................................................. 198
B.22 April terrain (surface) apparent radiobrightncsses and reflector-mea­
sured sky radiobrightncsses at 19, 37, and 85 GHz, net and global
radiation, and wind speed a t 10 m ........................................................ 199
B.23 April subsurface soil tem peratures, vertical heat flux a t 2 cm depth
in the soil, relative humidity, rainfall, air tem perature, and thermal
infrared surface tem perature................................................................... 200
C .l
SSM/1 scan geometry.
..................................................................................
C.2 A section of the SSM /I swath................................................................
208
C.3 Antenna patterns: (a) 19 GHz V-pol.effective antenna pattern, (b) 37
GHz V-pol. interpolated to 19 GHz pattern a t center of scan, (c) 37
GHz V-pol. interpolated to 19 GHz pattern between edge and center
of scan, (d) 85 GHz V-pol. interpolated to 19 GHz pattern a t center of
scan, (e) 85 GHz V-pol. interpolated to 19 GHz pattern between edge
and center of scan. The contours arc at 3, 6, 12, and 24 dB ......... 212
C.3
(Continued from previous p a g e .)..........................................................
213
C.4
SSM /I 85 GHz h-pol. images from February 2, 1992 a t 12:21 UTC
dem onstrating resampling to low resolution (top) and high resolution
(bottom ) EFO V ......................................................................................... 215
205
LIST OF APPENDICES
APPENDIX
A
SNOWPLOW PARAM ETERIZATIONS................................
1G6
B
DATA FROM R E B E X -1............................................................
171
C
RESAMPLING SSM /I RADIOBRIGHTNESSES TO A COM­
MON G R ID ...................
203
xvi
CH A PTER 1
INTRO DUCTIO N
The brightness of microwave radiation em itted by snow varies measurably with the
moisture, structure, and substrate conditions of the snowpack. This feature has been
widely studied and exploited in mapping seasonal, alpine, and polar snowficlds. This
thesis employs the sensitivity of snowpack microwave emissions in a different way: as
a tool in the determ ination of energy and moisture fluxes between snow-covered land
and the atmosphere.
1.1
Linking snowpack, atmosphere, and radiome­
try
The cornerstone and m ajor contribution of the thesis is REBEX-1, the first Ra­
diobrightness Energy Balance Experim ent. REBEX-1 combined continuous measure­
ments of terrain brightness a t three microwave frequencies (19, 37, and 85 GHz)
with simultaneous monitoring of micrometeorology. The microwave radiometers sim ­
ulated the channels and observation angle of the space-borne Special Sensor Mi­
crowave/Imager (SSM /I) with the added advantage of continuity a t a single locale.
The experimental site near Sioux Falls, South Dakota, is typical of the northern
Great Plains grasslands in clim ate and vegetation cover. The experim ent lasted from
October, 1992 through April, 1993 and spanned vegetation senescence, snowpack
1
2
formation and evolution, and spring thaw.
REBEX-1 was the first experiment linking the radiobrightness of terrain to lo­
cal weather over this length of time. Terrain radiobrightness (also called apparent
radiobrightness) is the the combined intensity of microwave radiation em itted by
and reflected off of the ground and ground-covcr. The source of microwave emission
is therm al radiation in the em itting medium transm itted through the surface and
into the air. W eather conditions are linked to emission through their control of the
m oisture content and therm odynam ic state of the terrain. Because the microwave di­
electric properties of water arc strong functions of frequency, tem perature, and phase
(liquid or solid), radiobrightncss is a sensitive indicator of moisture variation. But
the relationship is complicated because moisture content and tem perature m ay vary
throughout the column of ground cover and soil th a t constitute the distributed source
of em itted radiation.
The radiobrightncss of snow-covered terrain is an extrem e example of the dis­
tributed source phenomenon. The dielectric loss factor of ice is around three orders
of m agnitude smaller than th a t of w ater at SSM /I frequencies, and the low thermal
conductivity of snow means th a t the tem perature change from soil to air through the
snowpack may be more than 30 K. Consequently, the effective tem perature of the
em itting source may have little relationship to the snowpack surface tem perature. In
addition, the inhomogeneity of the snowpack dielectric constant scatters and reflects
radiation on its way to and from the snowpack surface, modifying both th e em itted
intensity and the reflectivity of the terrain. And when w ater is present in the snow­
pack a t low volume fractions, it changes the snowpack into a dense, absorptive cloud
with emissivity approaching unity.
Formation and evolution of a snowpack are integrally tied to local meteorology, and
3
the link between snowpack radiobrightness and w eather is similarly strong. Besides
the obvious fact th a t snowpacks form from precipitation, th e evolution of snowpack
structure is a function of internal tem perature and tem perature gradients th a t arc di­
rectly related to snowpack-atmospherc energy fluxes. And snowpack characteristics—
for example, low therm al conductivity, high shortwave and low longwave reflectivity,
and high moisture availability—in turn affect th e mechanisms of land-atmosphcrc
energy and moisture transfer. In seasonal snowpacks, melt and ablation (rapid va­
porization) arc the conclusion of this process and signal the transition to a new
land-atmosphcrc transfer regime.
1.2
Approach and premise o f the thesis
This thesis presents two numerical models for use in analyzing REBEX-1 snowseason data. The first, called Snowflow, is a model of snowpack evolution and atm o­
spheric interactions, and the second, called Esnow, calculates the radiobrightncss of
the Snowflow-modclcd snowpack. Snowflow is among a class of numerical models for
soil-vcgctation-atmospherc transfer (SVAT) calculations. SVAT models are land-at­
mosphcrc interaction param eterizations th a t, when linked to an atm ospheric model,
provide a boundary condition for the vertical fluxes of latent and sensible heat a t the
bottom of the atmosphere.
Snowflow differs from most SVATs in the level of detail used in modeling th e
surface medium. Atmospheric models are com putationally intensive and m ust trade
off the need for com putation speed with vertical and horizontal spatial resolution.
For example, th e spatial resolution of Pennsylvania S tate U niversity/N ational C enter
for Atmospheric Research Mesoscale Model version 4 (MM4) is 60 km, and GCMs
(General Circulation Models) characterize th e earth ’s surface in cell sizes ranging from
4
2.5°-10° in latitude and longitude [1]. At these levels of resolution, m any processes in
the atmosphere are reduced to sub-grid scale param etcrizations—cloud formations, for
example—and the high sub-grid heterogeneity of the e arth ’s surface is best modeled
by a param eterization scaled to fit the grid-sized needs of th e atm ospheric model.
Simple SVAT param etcrizations employ both the macroscopic reduction of ccotomes into basic classes and the microscopic reduction of soil and soil cover classes into
abstract param eter sets [2][3]. A parameterized description is not designed to match
the tem perature regime or physical structure of even an idealized terrain. Instead,
term s of the param eterization correspond to the fluxes required by the atmospheric
model and the param eterized information available from it. A b a basic example, the
bucket model of soil has a threshold w ater capacity—for example, 15 cm—beyond
which runoff is generated [4]. Evaporation may be calculated as a function of the full­
ness of the bucket (soil moisture) and the potential evaporation. Although the model
is based on physical argum ents, the param eterization says little about conditions in
the soil itself.
In contrast to a simple SVAT, Snowflow m ust produce a comprehensive simula­
tion of near-surface conditions m atching the level of detail needed to estim ate terrain
radiobrightness. As discussed above, the distributed nature of th e therm al emission
source in a snowpack requires an emission model with detailed tem perature and struc­
tural information, while the fluxes of m oisture and heat between the snow surface and
the atmosphere can be parameterized using only snowpack surface conditions. Yet the
motivation for SVAT model simplicity—computational speed—remains if the SVATlinked emission model is to be used as the boundary condition for an atmospheric
model. The independent variable of a SVAT—and the atmospheric model to which
it is linked—is time, and the length of tim e modeled may be m onths and the tem ­
5
poral resolution may be ju st a few minutes. Although emission calculations are not
necessary at all SVAT mode] tim es, the SVAT-Hnked radiobrightness model needs to
evaluate emission two to six tim es per day to adequately capture th e dynamics of
land-atmosphcre interactions. Consequently, for a combined SVAT-emission model
to be useful as an experimental test-bed, its evaluation speed m ust be comparable to
th a t of the SVAT model alone.
A well-tested numerical analog to global or mcsoscale meteorology would be a
unique indoor laboratory in which climate predictions and sensitivities could be
tested. B ut verification of an atmospheric model is hindered by the lack of long-term
global scale meteorological data against which the sim ulated conditions could be com­
pared. Similarly, any atmospheric model m ust be initialized with large Bcalc d ata that
accurately describes the state of the real system. In some cases remote sensing mea­
surements have been used in both the initialization and verification stages of model
development. For example, Dickinson e t al. [5] initialized vegetation param eters for
the Biosphcre-Atmosphere Transfer Scheme (BATS) using both satellite rem ote sens­
ing data and conventional maps when linking BATS to MM4. T he BATS/M M4 model
was tested against historical remote sensing d ata including seasonal snowpack depth.
The premise of this thesis is th a t remote sensing may be used more intensively
in mesoscale clim ate model verification by exploiting the satellite-m easured radlobrightness records of large-scale seasonal snowpacks and comparing them to landatmosphere interaction model dynamics. The G reat Plains seasonal snowpack is well
suited to this use because it both responds to meteorological conditions through
structural and therm al changes and is a direct product of meteorology. The Snowflow-Esnow model described here presents a simplified bu t not simple attem pt to
verify the concept of a SVAT-linked radiom etric emission model. T he REBEX-1 data
6
set serves as a surrogate atmospheric model while providing frequent measurements
of terrain radiobrightness for comparison to the models.
1.3
Questions addressed by this dissertation
This thesis addresses the following questions:
* How does emission from snowpack-covered terrain respond to long-term atm o­
spheric conditions?
& W hat characteristics of the G reat Plains snowpack and its substrate soil m ust
be modeled to simulate dynamic emission accurately?
$ Under what conditions do microwave radiometric measurements from space
correlate to those made from ground-based instrum ents?
$ W hat SVAT processes have strong enough radiobrightness signatures th a t ra­
diometric measurements may be used to m onitor them ?
$ How can measurements of microwave radiobrightness be used in conjunction
with SVAT-linked emission model predictions to improve the SVAT model sim­
ulation?
1.4
Format of the dissertation
The dissertation is organized based on the chronology of SVAT-linked emission
model development and testing. C hapter 2 first covers background m aterial regard­
ing snowpack radiometry and land-atm osphere transfer. Then C hapter 3 describes
Snowflow, the snowpack therm al sim ulation model. Snowflow’s critical param eterizations, the governing equations, and their solutions are developed. Appendix A
includes several additional subordinate param cterizations and the model’s fixed in*
put param eter set. Chapter 4 describes the model of snowpack microwave brightness
called Esnow. The chapter explains how Esnow uses the detailed snowpack simulation
from Snowflow to calculate snowpack emission and reflection.
The experimental work of the thesis is presented in Chapters 5 and 6. C hapter 5
explains the REBEX-1 apparatus, methodology, and post-experiment d ata process­
ing. Graphical presentation of REBEX-1 d ata is included as Appendix B. C hapter G
describes d ata from SSM /I, comparing observations from the satellite to those from
REBEX-1. Processing methods for the SSM /I d ata arc included in Appendix C.
Chapter 7 brings together theory and observation. The chapter discusses the ac­
curacy of the Snowflow snowpack simulation when it is driven with atmospheric d ata
from REBEX-1. Esnow emission estim ates are compared to both th e ground-based
and satellite-acquired radiobrightnesses over a 55 day period. C hapter 8 summarizes
the conclusions, implications of the results, contributions of the thesis, and recom­
mendations for future work.
CH APTER 2
BACKGROUND
2.1
Introduction
This chapter briefly covers two background topics: (a) the role of G reat Plains
snowpacks in the clim ate system and (b) research on th e microwave radiometric prop­
erties of snow. The discussion is m eant to place this thesis in the context of previous
work, lay the groundwork for the analysis of modelled and observed radiobrightncss in
Chapters 6 and 7, and m otivate the application of land-atmosphcre transfer modeling
in microwave remote sensing.
2.2
Great Plains snowpacks
Mid-continental regions are climatically more sensitive to the land-atmospherc
boundary condition because the influence of oceanic weather systems decreases away
from coastal regions.
In particular, the G reat Plains of C anada and the United
States straddle the boundary between the wet east, which receives moisture from the
Gulf of Mexico, and the dry west, with less than 50 cm of precipitation per year
[1]. W intertim e snow usually covers the northern G reat Plains and is a factor in
springtime water availability. T he presence of a snowpack delays springtim e warming
through heat absorption during melting, and in w inter snow dram atically changes
the therm al balance—prim arily through its high albedo. In addition, the smooth
8
g
snowpack alters the aerodynamic roughness by burying vegetation, decreasing the
efficiency of energy transfer.
The net climatic effect of the seasonal snowpack is of interest in clim ate model­
ing because of the feedback response the snowpack m ay have under clim ate change
scenarios [4], Snow has a high albedo and its presence will decrease the absorption
of incident solar radiation. Snow's therm al infrared cmissivity is also high, leading
to faster cooling of the surface during cold, clcar-sky conditions and more efficient
warming when the sky is radiomctrically warm. Consequently, the clim atic effect
of snow cover may be cither net cooling or warming: higher albedo and infrared
cmissivity means an increase in radiative cooling under clcar-sky conditions but high
1R absorptivity reduces radiative cooling under cloudy skies. Depending on cloud
conditions—an uncertainty in clim ate change models—current GCMs indicate th a t
the net seasonal effect of snowcovcr on regional clim ate m ay be weakly positive to
negative net cooling [6].
2.3
Microwave radiometry of snowpacks
Observations of snowpack radiobrightncsses have been conducted with groundbased, airborne, and satellite radiometers. Early ground based studies showed th at
although r&diobrightncss is linked to the hydrologically im portant snowpack param e­
ters of depth, w ater equivalent, and wetness other factors m ust be taken into account
(7][8], The fundam ental conclusion of early studies and th e basis for further work has
been th a t radiobrightness is reduced dram atically by th e presence of a snowpack over
bare ground [7][8][9][10j. Saturation of this trend has usually been shown to occur
near the w ater equivalent depth of 25 cm (th at is, the depth of water which would
be measured if the snowpack were completely melted). Under some circumstances
10
radiobrightness has been shown to increase with w ater equivalent above 25 cm in
highly evolved snowpacks [11], In a study in which consecutive layers of a snowpack
were removed, it was found th a t the presence of a 30 cm depth hoar layer contributed
to the bulk of radiobrightness reduction in snowpacks th a t were from 64 to 83 cm
thick [12].
Dry snow is prim arily a m ixture of air and ice which has low dielectric loss at
microwave frequencies (1-100 GHz) compared to soil or water. Consequently, emission
depth in dry snow is large—from 10 to 100 wavelengths [13]. The contribution to
radiobrightncss of the medium underlying the snowpack is therefore significant except
with very thick or wet snow layers [7][14][10]. Since em itted radiation originates
at significant depths within the snowpack, cmissivity cannot be measured directly
due to the difficulty of defining the thcrm om ctric tem perature of the source. For
thin snowpacks, the substrate tem perature has been used [12] as well as the average
tem perature of the snowpack [10] to define effective cmissivity values so th a t apparent
snow radiobrightness could be corrected for the variable contribution of reflected
downwelling sky brightness.
Volume scatter darkening effects in the snowpack are a consequence of large pen­
etration depths. Since snow grain sizes range typically from 0.1-5.0 mm and may
grow up to more than 3 cm in depth hoar [15], scattering effects are increasingly
large for frequencies over 10 GHz. The presence of w ater in th e snowpack surface
layer reduces emission depth and volume scattering effects [16][17][9]. The resultant
absorbing “cloud" has a high cmissivity especially a t th e higher frequencies and its
radiobrightness is easily distinguishable from th a t of dry snow. Diurnal m elt/freeze
cycles can be recognized by the contrast between appropriately timed radiobrightness
observations [11].
11
Experim ental studies of microwave emission from snowpacks and the availability
of data from spaceborne radiometers have led to the practical use of satellite radiobrightncsses in monitoring snowpack param eters (for example, [18]). There have
been considerable obstacles to corroborating radiometrically derived snow param eters
from satellite d ata including low measurement resolutions, geolocation errors, slope
effects, vegetation effects, and atmospheric interference [19] [20] [21] [22] [23]. Several
studies of the correlation of radiobrightness or spectral gradient to snow depth or
snow water equivalent have found th a t good statistical agreement can be found but
only when seasonal or regional variation is removed [24][14][22]. T he large contrast
in radiobrightncss between wet and dry snowcovcrs has been observed from satellite
platforms as well [25][22][2G]. The mapping of hemispherical snowcovcr by radiometry has been achieved based primarily on the negative spectral gradients (usually a
function of 7^(37 GHz)-7fl(19 GH z )) characteristic of dry snowpacks [27][28][29][30].
D ata from the SSM/1 have, only recently become available but there has been some
investigation of the use of the higher frequency 85.5 GHz channel for retrieval of snow
param eters [23] and classification of snowcover [28] [23].
Several studies have noted th e need for detailed ground tru th measurements of
not only snow water equivalent, depth, moisture, and underlying soil conditions but
also crystal size distribution, stratification, and tem perature structure [31][11](32],
Techniques have been developed for retrieving detailed descriptions of snow grain
properties [33] but have not been widely used in microwave studies because they are
difficult to m aster and tim e consuming [34]. Researchers have suggested the use of
snowpack emission models which track grain size as a function of the meteorologi­
cal conditions which control metam orphism, but none have been published to date
[111132].
C H A PTER 3
SIMULATING THE DYN AM IC SNOW PACK
3.1
Introduction
This chapter presents a numerical model of snowpack development, tem perature,
m oisture movement, and atmospheric interactions called Snowflow. Snowflow is a
SVAT (soil-vcgctation-almosphcrc transfer) model whose snowpack simulation in­
cludes information necessary for radiobrightness calculations—th a t is, far more infor­
mation than is needed for energy and mass transfer alone.
Although Snowflow is a new model, I have borrowed many of its formulations from
other approaches. The solution method and m ost of the param etcrizations arc taken
from Anderson [37]. Formulations for snowpack w ater seepage, compression, and
snow-grain growth are primarily from the more comprehensive SNTHERM.89 model
by Jordan [38], who also draws on the earlier Anderson work. Snowflow differs from
these models prim arily in its treatm ents of (a) soil therm al conductivity and unfrozen
water content (section 3.3), (b) latent and sensible heat exchange (section 3.4.4.2),
and (c) an insulating grass layer (section 3.4.2.1). W here necessary, Snowflow’s param eterizations are designed to sim ulate conditions specific to the grasslands of the
northern G reat Plains. Consequently, several sections in this chapter refer to the
REBEX-1 experiment site, described in more detail in C hapter 5,
12
13
Qsw
Qw
1Qemlt
Qprcp
Qair
Qlatent
Air
Ns
Snowpack
layers
Grass
layer
®
0
Soil
layers
Ng
W
/////7 /7 7 //Z
7 7 7 ///////////////9 7 ////.
Qg = O
Figure 3.1: Schematic of the Snowflow simulated snowpack.
3.2
Overview of Snowflow
Snowflow’s model components fall into four broad categories: snowpack energy,
snowpack structure, soil tem perature, and atm ospheric interactions. Snowpack energy
(enthalpy) change includes tem perature changes and—if the snow is a t the freezing
point—phase changes. Snowpack structure includes moisture movement by gravity,
density changes, snow grain growth, and snowpack development from precipitation.
Snowflow can run without a snowpack in which case only soil tem perature and atm o­
spheric interactions are active while the model checks for new snowfall.
Figure 3.1 shows the conceptual elements of Snowflow. T he surface flux bound­
ary condition is Snowflow’s link to an atmosphere th at drives the simulation and
determines its particular locality and time. In Snowflow’s current configuration the
atmosphere is independent and may be modeled on historical d ata or be the result of
14
an atmospheric model. W ith minor modifications, Snowflow could also interact with
an atmospheric model as it operates, providing a dynamic boundary condition for the
model atmosphere.
The following energy boundary condition constrains the total enthalpy change of
the snow and soil, A Q , in a tim e interval, A t:
Qnet
“
Q»tu
+
Qtw ~ Q tm ii
4* Qair +
Qlatent
+
Qprcp
4" Qg
~ &Q
(3.1)
where Q net is the net heat added to the snow/soil system per unit area, Q ,w is heal
from solar (shortwave) radiation, Qtw is from atmospheric (longwave) radiation, Q 0(r
is from sensible heat transfer with the air, Qlatent is from latent heat transfer with
the air, Qprcp is from heat exchanged with precipitation, and Qg is from deep in the
ground. Snowflow defines a therm ally active region th a t extends down to the point
where the tem perature gradient falls below a given criterion—effectively assuming
th a t Qg — 0. By conservation of energy, the change in stored heat per unit area is
given by the sum of enthalpy changes in all the layers to the depth where Qg = 0:
A<? = £ A / / i + £ > / / „ , ,
•b O
(3.2)
isO
where A H*ti is the enthalpy change per unit area of the i ^ 1 layer of medium x, and
x is either s (snow) or g (ground). Alternatively, a lower boundary could be set a t a
depth at which Q g could be estim ated from historical d a ta or a m ulti-year model.
Snowflow divides both the soil and snowpack into discrete layers and each layer
interacts only with its im m ediate neighbors. For th e i ,h layer of snow or soil we can
define an equalization function,
based on one-dimensional heat transfer:
^*,i(ur,i+liuM(u*,i-l) = ^ ^ r ,i
Q r,i
(3.3)
where QXl1 is heat added to the layer, «r .i is the unknown variable describing a layer’s
thermodynamic state, x is s for snow or g for soil (ground). T he vector of solutions,
15
U , satisfies
£ ,..(U ) = 0
(3.4)
for all layers. In soil, the therm odynam ic variable is always tem perature, T , but in
snow it may be either T or liquid water content, W (expressed as a depth). In the
later case, the snowpack tem perature is known and is equal to the freezing point of
water, T0.
The top and bottom layers of the snow-soil system are special cases of (3.3). For
the top layer (either snow or soil), Snowflow uses the net energy balance (3.1) to
constrain the therm al state:
^r.fop(u) = f3x.nel(ur,fop) “ A (J(u)
(3.5)
where u is the vector of the unknown state variables for all the layers. The bottom soil
layer is always constrained by the condition Qg = 0 which implies th a t T,,n(+i = Tg^ t Conscquently, for the bottom soil layer:
^g,bot ~
U;_j) S A //^ g t
Qg,bot
(3.G)
Snowflow solves the set of soil and snow energy equations simultaneously using
the Newton-Raphson iteration technique. First, (3.3), (3.5), and (3.6) are expressed
by a set of first order m ultivariate Taylor series:1
Ei{ u) = £ ,(U 0) + E;t (U „)A u + . . .
(3.7)
where E |T is the transpose of the vector whose j th elem ent is:
duj
‘The medium subscript, r , is now implicit.
(3.8)
u=u.
U a is an estim ated solution for the unknown vector and A u = u — U 0. If U is the
exact solution then £ ,(U ) = 0 and:
E '(U a )A U « - E ( U . ) ,
where the (i, j ) clement of the m atrix E* is the derivative
(3.9)
Because all but the top
layer equation are dependent on only three unknowns, E fU * ) is a singly bounded
band-diagonal m atrix. A t a particular tim e step, i + A t, Snowflow solves for U ,+Al
by taking U fl = U ' initially, solving (3.9) for A U by decomposition and forward- and
back-substitution, and determining a new estim ate of the unknown vector U ,+Af =
U* -{- A U . The process is repeated until all of the elements of |A U | arc less than a
threshold value. When the unknown for any snowpack layer changes from T to W , the
process is autom atically repeated until the solution for the new unknown converges.
The remainder of this chapter details the param etcrizations th a t Snowflow uses
to specify (3.3), (3.5), and (3.6) for snow, soil, the snow-soil boundary layers, and the
boundary with the atmosphere. Appendix A includes additional formulas for physical
variables and tabulated values for Snowflow param eters.
3.3
Heat flow in soil
Snowflow models soil using the one-dimensional heat flow equation [39]:
M V(T ) _ d_ (
, d T ( z ,t ) \
dt
d z y hto ', (T ' Z> Qz )
(3-10)
where T ( z ,t) is tem perature a t tim e t and depth below th e surface z tH V(T ) is en­
thalpy per unit volume (J /m 3), and A*f0,j(7 ',j) is soil therm al conductivity (W /m K ).
We want to derive a heat transfer equation in the form of (3,3). Expanding the depth
derivative, we have:
d H v (T ,z ) _ d h \ o:, 8 T
dt
dz dz
d*T
0,1 d z 2 ’
1
*
17
We then apply (a) an implicitly formulated discrete tim e approximation using the
average heat exchange a t times t and t + A t, and (b) a finite difference approximation
for a layer of thickness
Eg,i =
Then the equalization function (3.3) for soil (ground) is:
~ Qg,i
= A H £ i ~ 0 .5 A t d g.{
m
m
*
*
®
! ,
\ l+ A i
/ f l J ,r \
* ^ * 1
. 12 )
Snowflow uses £ p , for the interm ediate soil layers in (3.9). The top soil layer is unique
because of its interaction with the snowpack and the addition of heat from shortwave
radiation. Section 3.4.2 deals with these questions after a description of snowpack
heat flow has been formalized.
Snowflow approximates the depth derivatives in (3.12) and elsewhere using the
finite difference approach:
m
V° z )
\ os2/ .
+
i
V *1 “
Z;+1 -
C,_1 \ Cl+1 — S i
* i-l
-1+1 ~ *i /
S i — C,_1 /
(3.11)
,3,4)
where V is the function of depth whose derivatives are to be found and r, is the
m idpoint depth of layer i. W ith this expansion, the derivatives of E8j with respect
to the vector of soil unknowns T , are easily found and applied in (3.9). For brevity,
this set of derivatives will not be written out here.
The following subsections describe Snowflow’s param eterizations for soil enthalpy
change and conductivity. In a freezing soil these variables depend prim arily on the
residual unfrozen water content, so we first turn to the characterization of this phe­
nomenon.
IS
3.3.1
Liquid water content in sub-freezing soil
Experimental observations have dem onstrated th a t soil w ater freezes over a broad
range of tem peratures below the freezing point of free water. W ater in soil forms weak
chemical bonds which inhibit the formation ice crystals. Some soil-water is bound
more closely to solid particles and, in very moist soils, a portion of the soil water
will behave like free water. The proportion of w ater bound in any particular state
is dependent more on the soil type—and primarily its specific surface area—than on
the total water content. T hat is, given the soil type and adequate water availability,
the am ount of unfrozen water a t some tem perature below freezing is independent of
the total water content.
Unfrozen water content can be estim ated from the empirical formula:
Xui
if
^ 1'/pd\
Xu — 1
(3.15)
otherwise,
Pvt
where x w is the volume fraction of water when the soil is above freezing, a wu and
Pwu (which is negative) are param eters of the soil type, /><, is the soil bulk (tn si/u)
density, and pw is the intrinsic density of water. Tjpj is the freezing point depression
tem perature, the lowest tem perature below freezing at which x„ = arw: ,
\ i
(
Experimental values of a w and (3WU have been tabulated for a wide variety of mineral
soils but there is scant d ata on soils with high organic contents. Soils with a large
am ount of organic m aterial are characterized by a slower decrease in the unfrozen
water content with decreasing tem perature than the more extensively investigated
mineral soils [40], Snowflow uses a wu and 0 WU values for kaolinite soil from [41]
because it also has a shallow freezing curve.
19
3.3.2 Enthalpy change in freezing soil
The enthalpy change of a soil layer, A /f A,, in (3.12) is the integral from T l to
T ,+a' of the apparent heat capacity of the soil layer per unit area, C£,:
-7'i+Ai
= JT,
C&HW
(3.17)
where
(pw{CpWXu + Cpi(xw - * „ ) ) + pbCpav - h t WUXy W)
c ? j(r)o .
v
•"
T < Tfpi
J
(3.18)
^ « *JpA*
idgti(ptoCptoXiu *t* pbCpav)
When T < Tjp4 , the first term in parenthesis is the combined specific heat capacity of
the ice and water content of the soil, Cptt„ is the average heat capacity of the dry soil
constituents, and the last term is due to freezing/melting, where 1/ is the latent heat
of fusion and /?«,„ < 0. If both integral limits arc below the freezing point depression
tem perature, then integrating (3.17) yields:
a
= i,.i (*<*,+p«.<wi»)(r'+41 - r‘)
+ h p t .° U o ar
+ 1
- « f")
J (3.19)
where 0\ = T0 —T* and 0% — T0 — 71,+A,t In general, (3.17) is integrated piecewise
across the discontinuity at T — TjP4 .
3.3.3 Soil thermal conductivity
Freezing soil is a multi-phase, m ulti-constituent m atrix whose components have
intrinsic therm al conductivities spanning three orders of magnitude. Appendix A
lists intrinsic conductivities for the minerals, ice, water, and air which constitute the
Snowflow mode) soil m atrix. To calculate the m atrix conductivity, Snowflow applies
the de Vries method with modifications to include ice in the m atrix [-12][43][44j.
20
The general form of the de Vries conductivity mixing formulation is:
f»
ZoAo d*
An
fq
i + E **.
(3 ° ’
where x„ and A„ are the volume fraction and intrinsic conductivity, respectively, of
the n ^ 1 constituent. The O^1 constituent is generally the one th a t is m ost nearly
continuous—for example, air in dry soil or w ater in very wet soil. The weighting
factor,
relates the microscopic tem perature gradient in the n ^ 1 constituent with
th at in the background:
k
=
(321)
{dTfdz) o
1 '
Assuming th a t the granules of constituent n arc ellipsoidal and randomly oriented,
dc Vries gives the weighting factors as:
(3 -22)
where, for example,
1 , f°°
ga - -a b c J o
du
+ u)3/2(6J + u)1/2tc2 + u jl/a.
tn
(3.23)
gr depends only on the ratio of the ellipsoid axes (a ,b ,c ), and ga + g t + ge = 1. For
spherical particles, ga = 9b = 9e = 1/3.
Use of the de Vries conductivity model (3.20) requires the choice of an appropriate
background medium and determ ination of the gr for th e remaining constituents. The
de Vries model is fundamentally empirical and has been shown to work well when
the gr are tuned for a particular soil type. For example, de Vries offers a correction
factor for the dry soil case when using ga = gb = 0.125 for a mineral soil with dry air
filling the voids:
L•
**
^ ne f Xvoid^voi4'im^ k nXnXn \
( ~ ^M +
)■
< **>
21
For a saturated soil, the voids are filled with water and:
A-
i
+ £ f c .* .A .
+ E U ' "
(3 ’25)
To find Ktoit over a range of moisture conditions, de Vries interpolates between the
saturated and dry cases. The following discussion uses this m ethod and extends it to
include ice as well as air, water, and solids.
In moist, freezing soil, there arc three possible background media: air, water, and
. ice. But, as discussed in Section 3.3.1, w ater bound to the skeleton of the soil m atrix—
the soil grains—exists in soils to tem peratures well below freezing. Consequently, wc
can take water to be the background medium in moist soils whether below freezing
or not, being careful to check th a t in the lim iting case of completely frozen soil the
soil conductivity reduces to th a t of an air-icc-solids m atrix.
Beginning with limiting cases, the weighting factors for two types of solid soil
constituents (to be specified later) in a background of constituent 0 are given by:
k l '°
= 5 (> + (it - 0 ** + 1+ (fc - 1) (1- 2s.,))
(3'26)
5 (> + (&-l)s..P + i + f e - 0 < 1- 2*M'>)
(3'27)
=
where g a,P is the principal size factor of the soil particles and the background medium
is either air or water. To find the weighting function for air in a w ater background,
A'atr.w* as a function of x w, consider a soil th a t is very nearly saturated with small air
inclusions th a t are approxim ately spherical in shape. In this case, g a,air(xw = x v) =
1/3 is the shape factor and the corresponding weighting coefficient is ka, w h e r e
x v is the volume fraction of voids. On the other extrem e, in a very dry soil with air
nearly filling the voids, water will coat the soil particles and the weighting factor fo r
22
water in an air background is:
rw o ‘u,<a
_ i ) ga p + i + (2 * . - i) (1 - 25a,„))
3 ( i +
(3 28)
Equation (3.21) gives us a way to exchange the background medium with the nth
constituent. Switching the background in (3.28) from air to w ater yields:
1
lim fca,w - ;r
*
limrv_+o k'w,a
2
1
H 1 + ( t ” O'/a.oiftO)
1+
\
” O t 1 ” 2& .air(°))/ (3.29)
We can then solve a quadratic equation for ga,air(xw = 0). Aa,y varies with tem perature
when the air contains water vapor which in turn is a function of the saturation state
of the soil. In Snowflow, the conductivity of the soil air is divided in to dry, Aairi</,
and vapor, Aa,yiV, regimes according to:
AaiVtd
I/H —
^
(3.30)
AqiV , A(ii>^(T) 0 ^ x w ^ xju
where x/w is the so called field capacity of soil moisture and is given Appendix A.
We can linearly interpolate between the extrem e values of 50,ofr(*w)t yielding an
expression for the size factor of air in a w ater background for the complete range of
Xu.:
J« ,o ir(® v )
< 7 a ,a ir ( 2 \u ) =
Xv
(ffa ,a ir(* u )
<7o,oir,v( 0 ) )
X f f J < X w < X„
*
ffa,air,d( 0 ) + ” ' ( S i IB i'r (l/lil)
Xv
0 ^ Xw < X y jj (3.31)
where ga,w {x v) and </a,a.v.i>(0) are solutions of (3.29) with m oist air and <7<,fa.r,<i(0) is
the solution of (3.29) with dry air.
For ice particles in a water background, Snowflow assumes th a t the shape factors
are all 1/3 and uses this value in (3.22) to calculate fc,>. Then the soil conductivity
23
as a function of tem perature and total soil m oisture content is:
I
ii ^ iit " f
X ifciA j d* X jfc jA j d" X oir^oirA air *t" X jfc/A
+ X jfci + X 2fc2 + X airk air + x.-fcf
Xu> ^ Xflj|
h'.oii(T,xw) = A*„ - ^ - ( K ir, - K m ( T , x u .))
Z u, < I , i ,(3'32)
where x aifi is the volume fraction of adsorbed (bound) w ater and x,- and A, arc the vol­
ume fraction and intrinsic conductivity of ice. Below this value, I \toii is interpolated
down to the empirically determined dry soil conductivity given by (3.24).
Dry soil particles arc of either mineral or organic composition. Of the mineral
components, quartz content is m ost critical because of its high intrinsic conductivity
(8.16 W /m K ). de Vries characterizes soil as a combination of quartz and a composite
of other minerals with a mean conductivity of 2.93 W /m K . The conductivity of
organic m atter is an order of m agnitude smaller bu t highly variable—de Vries gives
a value of 0.25 W /m K . Because scant empirical evidence is available on the m atrix
conductivity of organic soils, Snowflow simply assumes a quartz plus mineral m ixture.
The bulk (dry) density of this m ixture is given by:
pb ~ (1 -
+ 1ompm)
(3.33)
where io, is the weight fraction of quartz, pq is the intrinsic density of quartz, wm
is the weight fraction of other m atter in the dry soil, and pm is the mean intrinsic
density of th a t m atter. A typical bulk density of 1520 k m /m 3 was chosen, with the
corresponding weight fractions found from (3.33) using x v from the REBEX-1 test
site. These param eters are listed in Appendix A.
24
3.4
Snowpack formation and heat and moisture
fluxes
Snowflow handles the snowpack processes of heat transfer, compaction, liquid
water seepage, grain growth, and interaction with the atm osphere in separate but
interdependent modules. Following discussion of simulated snowpack formation, this
section examines each of these processes individually.
Snowflow evaluates each precipitation event and flags it as snow if the wet bulb
tem perature of the air, 7U , is below freezing. Snowflow determines the characteristics
of a new snow layer based solely on its initial tem perature, 71,, which is set to TwbThe initial density of new snow is (modified from Anderson [37]):
— 258.16)'6 if T, > 258.16 K
f 75 +
if r.< 258.16
"‘ “ I t s
k.
(3-!M)
The initial grain size (a diameter in m) is a function of density [38]:
ga =
0.1GE-3 + I.IE-13/jJ,
(3.35)
and the thickness of the new layer is given by:
d ,= —
P•
(3.36)
where P is the precipitation in kg/m 3. O ther param eters discussed in the following
sections are initially set to 0, including the liquid w ater content.
Snowflow adds snowfall in consecutive tim e steps to the same model layer unless
the layer has exceeded a maximum thickness. When additional snow is added, the
characteristics for the layer given above are recalculated as a weighted average of the
new snow values and the values for the existing layer. When a layer exceeds the
maximum thickness, it is divided into a layer of optim al thickness dll0pt and a layer
of thickness d, - dM)0pt,
25
3.4.1 Heat and vapor transfer within the snowpack
The Snowflow simulation treats the problem of heat transfer in the snowpack in a
manner similar to th a t for soil. In addition to conductive heat transfer through show
grains, energy is transferred through shortwave radiation, w ater vapor, and longwave
radiation. In practice, the transfer of heat by conduction through snow grains, Con­
duction through the air in voids, and longwave radiation cannot be experimentally
separated. Consequently, these mechanisms are combined into a single flux charac­
terized by an effective conductivity, I\\jj in a m anner sim ilar to (3.10) yielding the
one-dimensional heat transfer equation:
37)
is the differential enthalpy change per unit volume of snow due to conduction
alone. Equation (3.37) only applies to dry snow. If the snow is wet its tem perature
m ust be uniformly T0 and dH)[K — 0. Consequently, we can substitute dH][h
Cipt dT,,K in (3.37), where c; is the heat capacity of ice and dT,,h‘ is the differential
snow tem perature change due to conduction alone. The substitution yields:
BT..k
CIP' ~
dI\'B OT
~ ~
I 7
0>T
+ h* W
(3’38)
The effective conductivity as a function of snow density is given by [38]:
h%ff - Anir.rf + (7.75E-5 + 1.105E-6pJ)(A, - Aair,rf).
Since
A ' rJgr
(3.tl9)
is a function of p , only, it will be convenient to apply the chain rule to its
derivatives, which yields:
0T.m
dt
"
QKtg dp, 8T
&T
dp, d s d s * h t S dz*'
,
^ *
Snowflow uses Anderson’s derivation of heat transfer by the processes of vapor
diffusion and vapor transfer by tem perature gradients [37]. W ater vapor diffusion
26
is a function of the vapor density, f ( T ) — pvt—which is at its saturated value in
a snowpack—and the snowpack effective diffusion coefficient, De{T), given in Ap­
pendix A. Defining 8 f / 8 T = / ' , the snow tem perature change due to vapor diffusion.
dr,,D, is given by:
dT..D
*p,
a
Qt
*
/
. 81
l»D *d z 7 + / » 9 : d z ~~
i r
-
T ' o W . ' c
* Dt
=
Qi
<3 *4 1 )
d ( T n° ) 8 f
ds*+ , D e
8z
.8 /
8z
1 81
l*CD' T n'>
Combining (3.40) and (3.42) and noting th a t / , / ' < < q p f, we have the complete
equation for internal heat transfer in the snowpack:
8Ta,i
• v .- g f
=
8 T ,tK .
+
8T,,o
(
IA‘ ,j +I I'C
I CiD tfp T nn\]
-— [A
3
-42)
_ +i ^ _ _ j _
+CW. [/'n0 r » -’ + 7”»r] ( 5 7 )
In addition to internal heat transfer there arc two sources of external heat: (a) the
heat from shortwave radiation penetrating the snowpack and (b) the heat absorbed/re­
leased by melting/freezing. The enthalpy and tem perature change due to these ex­
terna] sources is:
r n ^ * 'E
—
/
n
* Pt~ d T " n r ~ iPwn r
/o
(
jo \
^
where Ftw is the flux of shortwave radiation at depth z in the snowpack. Combin­
ing (3.43) and (3.43) and converting to discrete tim e, we have the finite difference
27
approximation for the equalization function in snowpack layer i:
=
- T ') + tjp J U " * * ' - I V ' ) - 0 .5 A f(f,'„ , + F J + f )
+ C ih /.[y , n D r » - , + r » / * ] ®
+ (
[
*
W
+ w . [ / ' nor
Snowflow uses
3.4.2
)
+
-
+ r » / " ] ( f ) S) ' + 4 ' ] .
(344>
in a m anner comparable to Etti (3.12).
Snow-soil interactions
Snowflow parameterizes the heat exchange between th e snowpack and soil using
the steady-state heat flow equation:
g , J = 0 .5 A t
V
' ( F \ MF I M( T * - T , a )
\Flpod*o/2 + F ljodpo/2/
yta,1
/ F U F I A T * - r ri)
\F lg o d ^ /2 + F l g o d ^ / i )
^
.45)
where d,o/2 and dffo/2 arc the midpoints of the bottom snow and top soil layers,
respectively, and F I is a composite conductivity factor given in Appendix A. The
steady-state approximation is applicable here because the insulating effect of the
snowpack is likely to minimize the tem perature gradient and, consequently, tem per­
ature fluctuations at the bottom of the snowpack.
Snowflow also uses the 6teady-state formulation for heat flow between the top
and second soil layers and between the bottom and next-to-bottom snow layers. The
interm ediate layer formulations are not usable for these two interfaces because it is
not possible to calculate second derivatives there using (3.14) if either (3.12) or (3.44)
are used as the equalization functions.
28
3.4.2.1
H a n d lin g an in s u la tin g la y e r o f g ra s s
Snowflow treats the grass layer between snow and soil as a massless, therm ally
resistive thin layer which effectively reduces the snow-soil conductivity. We can gen­
eralize (3.45) as a problem of heat flow between two media with uniform tem perature
through a virtual slab:
Q.j = A | tr * ~ 7 >o)
(3.46)
‘I*#
where R t<s — Lvf A’„ is the therm al resistance of the virtual slab, A'„ is its conductivity,
and i v is its thickness. By equating (3.46) and (3.45) and assuming th a t djg = dgo =
8mm, then for typical values of F 1, and F l a the therm al resistance of the virtual
slab is R ,tS = 0.044 Iv/W . Now we can insert the grass layer as a parallel slab with
thermal resistance Rgn„ such that:
<5.4,,^... = A I
.
(3.47)
A rough approximation of the conductivity of the grass layer is as a grass-air m ixture
with 1% grass by volume. Taking conductivities of Aon,anic — 0.25 W /m K and Aa,v =
0.025 W /m K , the conductivity of the m ixture is 0.027 W /m K . Then a grass layer
about 3 cm thick has a therm al resistance of 1.06 K /W , or about 24 times greater
than the typical value for /?*,,. Snowflow implements this approxim ate correction as:
= A<(T2 5 ^ 0) = ^
3.4.3
(3’48)
Shortwave attenuation and absorption
The shortwave heat source in (3.44),
is calculated in Snowflow by [37]:
= ^ ( e - ,‘^ - < ) -
(3.49)
29
where Ztf is the height of the top of the snowpack and rj is the height of the top of
layer i. v is a single band attenuation coefficient given by:
VW
Si
Pi
(3.50)
where Uq is an experimentally determ ined constant, i/,■ is the attenuation coefficient
for solid ice, and p, is the intrinsic density of ice.
Further research since the publication of Anderson's thesis has shown th a t the
attenuation rate in the snowpack is highly frequency dependent, with near-infrared
wavelengths absorbed within the top 10 cm of the surface and shorter wavelengths
penetrating to great depths. B randt and Warren [45] suggest th a t a 10-band model
would adequately describe shortwave snowpack attenuation. Any approach for atte n ­
uation in pure snow will require some modification for the relatively shallow snowpacks and short grasses of the Northern Great Plains. Since research concerning these
conditions is unavailable, Snowflow uses the simpler, single band model as a starting
point.
3.4.4 Snow-atmospliere interactions
Fluxes between the Snowflow snowpack surface and th e atm osphere constrain
the Snowflow snowpack solution through the energy balance equation for the top
snowpack layer (3.5), T he atm osphere provides radiative fluxes from th e sun and sky
th a t add heat independent of snowpack tem perature. The remaining fluxes depend
on the surface tem perature and the flux values are determ ine as part of the solution.
The following sections describe Snowflow's param eterizations of atmospheric fluxes.
30
3.4 .4 .1
R a d ia tiv e e n e rg y e x c h a n g e
Radiative energy exchange between the snowflow snowpack and the atm osphere
has three components: absorbed longwave, absorbed shortwave, and em itted longwave
radiation. In Snowflow, the absorbed shortwave heat per unit area over a tim e interval
A t is:
Q*u> — (1 ~ A )Q tUt{ne
(3.51)
where A is the albedo (shortwave reflectivity) of th e snowpack and Q«u>,inr is the
incident shortwave radiation from the atm osphere (approxim ately wavelengths 0.3*3
pm ). Similarly, the absorbed longwave heat is:
Q iw
= (1 ”
(3.52)
where eiw is the longwave cmissivity of the snowpack and Qiw,inc is the incident long­
wave radiation from the atmosphere (3-100 pm wavelength). Longwave radiation
em itted by the snowpack goes as th e fourth power of the top snowpack layer tem per­
ature;
3™ ,, = A fe /u,< r7 ^
(3.53)
where <x is the Stefan-Boltzmann constant.
Qiw,ine is not available from REBEX-1, so Snowflow estim ates it from air tem per­
ature and relative humidity (39):
Qlw,ine ~ A iaT*ir (o .6 1 + 4.33E-3v/p Wf(7’oir)/2 //) .
(3.54)
Estim ating Qiw,ine by this method neglects th e contribution of clouds to the longwave
flux. (Clouds always increase the flux.) Although it is impossible to address the
question of clouds precisely, Snowflow avoids very low values of Qiw,i„e by setting an
artificial lower limit of 180 W /m 3.
31
3 .4 .4 .2
L a te n t a n d s e n s ib le h e a t e x ch a n g e
The only near-surface atmospheric conditions available from REBEX -1 arc air
tem perature and hum idity a t a single reference height above the ground and wind
speed at a second reference height. This strictly limitB the methods available to
estim ate the fluxes of sensible heat and moisture, many of which arc based on detailed
field measurements of wind, tem perature, an d /o r hum idity profiles. Snowflow uses
the energy balance (or Bowen ratio) m ethod for calculating these fluxes [46][47). Over
a tim e step A t, sensible heat transferred, Q0I>, and potential latent heat transferred,
Qpot are given by:
. _ a *_________ e w t o k f o t r , **' Tx)
[in
n
- t&ms] [in ( i f s j ) -
.
0
,a +
0
, i]
_ a j _________ k P r ir k f o a f o - f r ) ___________
[in ( ^ ) -
0
m8] [in ( g f j ) -
+
0
.
,i]
where k, is the von Karman constant (0.4), Cp is the specific heat of air, p0 is the
air density, U3 is the wind speed a t height
height
22,
23
above the surface, T 2 is tem perature a t
T\ is tem perature a t height zj, d ib the so-called zcro-displaccmcnt height,
z„ is the roughness length of the surface, and qj and
91
are specific humidities, k-
is either lv if the surface is at or above the freezing point and I, otherwise. The
—where x may be m for momentum, q for moisture, or h for tem perature—are
functions of the atmospheric stability and are discussed further below.
The energy balance method says little about interaction of the surface with the
atmosphere except through the roughness length param eter. Snowflow uses the energy
balance method heat transfer equations with modifications for estim ating th e fluxes
from Snowflow’s surface tem perature, T,. First, the height z\ is set at the top of the
snowpack and T\ = T„ Also, the specific hum idity at the surface of the snowpack is
assumed to be at the saturated value for Tt so Qhieni — Qpot>
32
The shear functions, <£*., and profile functions, y x, are found using an iterative
method [47]. Initially assuming neutral stability (<£m = l.ti’m = 0), th e Richardson
number, Ri is calculated as:
Ri
(3.57)
™ = l S ( f +*)
(3'58)
where z - (*i + *2 ) / 2 , Rb is the bulk Richardson number, u is the wind speed a t z ,
T is the tem perature a t f , y j is the dry adiabatic lapse rate (9.8E-3 K /m ), and g is
the acceleration of gravity. Stability is a function of Ri: R i > 0 implies stability, in
which case:
z
Ri
L
1 - 5 Ri
(3.59)
(3.60)
0m == i + 4
0m
(3.62)
0*2 _ _ 5 £Xl 1
(3.63)
(3.64)
0,1
ii
0m3 _ _ 5 £3
Cli
H i*
(3.61)
For stable conditions:
(3.65)
0
m~
(3.66)
x ( i) '
7T
i»“) - 2 ta n ” x (r) + —,
= |n ( | (
0
ms = l n Q ( l + x ( z 3)2)(l + i ( j 3))3j ^ ,3
=
21n 0
1 +
^ 1
1+ 0
-
1C
^
2
j
|
tan " 1 x (s3) + -p
(3.67)
(3.6S)
)
(3.69)
)
(3.70)
33
where
1 “ 16“ )
.
(3.71)
3.4.4.3 Heat from precipitation
When Snowflow determines th a t precipitation falling on the snowpack is unfrozen
(see th e beginning of section 3.4 for this criterion), the w ater tem perature is artifi­
cially set to T0. The w ater then interacts with the snowpack through the seepage
param eterization in section 3.4.5. In nature, when rain w ater comes in contact with
a snowpack, either some portion of precipitation is frozen or some portion of th e ice
in the snowpack 1b melted during the event. Snowflow’s approach om its the ability
of rainw ater to m elt ice in the snowpack. The omission does not affect results in
this thesis because there was little rainfall on the snowpack during the test period
described in C hapter 7.
3.4.5
Liquid water seepage in the snowpack
Liquid w ater seeps through the simulated snowpack under the pull of gravity
when the liquid water content of a layer exceeds its holding capacity. Snowflow’s
param eterization of seepage comes from Jordan [38] with some modifications. In
the numerical sim ulation, the solution of th e heat transport problem (see section 3.2)
precedes and is independent of the seepage solution. W hen the heat transport problem
is solved, the initial effective saturation, s‘ , of each layer is given by :3
4 =if*
Superscriptsinthissectionindicatethesnowpacklayer.
(3.72)
34
i = Ns
i’ = n
Row zone
i' = o
Snowpack
layers
Row zone
Figure 3.2: Schematic of liquid water seepage through the sim ulated snowpack (after
[38]).
and
y = x
Pw<t>'
(3.73)
(3.74)
Pi
7. = P[ ~ 7(
(3.75)
7/ = ^
11
di
(3.76)
where s is saturation, sr is the irreducible water saturation constant, <f>is porosity,
is bulk ice density, and
71
is the bulk density of liquid w ater. If the s* of a set
of adjacent layers is greater than zero, then there iB downward flow in the region.
Figure 3.2 shows the geometry of a snowpack with two active flow regions,
Snowflow finds the post-flow effective saturation of each layer in a flow zone by
solving a set of linear equations of the form:
4 ' 4 +I + A f e = B*'
(3.77)
35
where the coefficients arc, for the top (nth) layer in the flow zone,
<
= 0,
(3.78)
A f = c7i + Q.5Akim i„
(3.79)
B n' = —0.5(l//+l - V t) + c fs U
(3.80)
and for the interior layers of the flow zone,
A$ = -0.54Jfc,+lm i+1,
(3.81)
A i - c7* + O.S/Uk'mi,
(3.82)
B v = - 0 .5 (t / / +1 - Uj) + c7{si + 0.5Aki+1Vt+i - 0.50.5
(3.83)
The param eters A k and c7 can be calculated independent of position of the layer in
the flow zone:
A k 1«
(3.84)
c7' = Pw<t>' {^ ~ Sr)
(3.85)
A ';ox = 0.077ffs3e~OOQ78'y'.
(3.8G)
where
fti
is the dynamic viscosity of water (1.78E-3 N s/m 2) and
gs
is th e average snow grain
size (diam eter). Away from the edges of the flow region (V ^ 0, i' ^ n'), th e constants
b, and m , are given by:
= 3 (s i ) 2
(3.87)
t f = - 2 ( s i ) 3.
A t the
(3.88)
flowboundaries, b, — 0 and m , is found by first estim ating the effective
saturation, s e,e.«, by solving the cubic equation:
V,
'
c7‘
tfs j-U l+ '+ O M I
0.5/U"
0.5,U '
_
'
*
36
Then m , =
The liquid water flow rates, U j, is the final product of the flow calculations. Its
value in the equations above is estim ated from its value in the previous tim e step.
After (3.77) is solved for the effective saturation of the layers in the flow zone, then
Uj is given by;
Uj = - A k ^ y .
(3.90)
U} is always negative and represents the flow of w ater out of th e bottom of the
snowpack layer. W ater th a t flows out of the flow zone into a dry layer will freeze until
an equilibrium is reached. Appendix A describes this calculation.
3.4.6 Compaction and mass balance of snowpack layers
The compaction rate of a snowpack layer, C/2, is a function of the structure of
the layer and th e overburden of snow above [38]:
“ - i t
= C /^m et«norphlim
C/2overburden
^ g, j
- 2.778B-6c3C4e-00<«r °-T>+
Vo
where Pt is the overburden pressure, r)0 is the viscosity coefficient (at T — T„ and
pt =
0 ),
cs and cq are empirical constants, and cj and c< are given by:
C3 = C 4 = 1
if 7 ; s= 0 and 7 ,- < 150 kg/m 3
ca = e - o w®H'-16°) i f 7 i < 150 kg/m 3
C4 =2
if7 / >0 .
(3.92)
W ater and vapor movement in the snowpack change the mass of the snowpack
layers. Mass changes coupled with compression alter the layer’s density. Section 3.4.5
provides the solution for fluid the fluid flux, U\. The net fluid flow for an interior layer
37
i is U(ntt = Uf+i — U{. For the top layer (i = N t ) the net flow is:
r/Ai _ _ _ _ _ ttN ,
u l,net ~
Ul *
(3.93)
Note th a t positive tIt,net means net flow out of th e layer. The vapor flux from snowpack
layer i to layer * — 1 below is given by:
,,m -i = 'lCDeT?D}[T ? S J,i_ x{Ti - 7 j-i)
The net flux for interior layers is U lnet =
+ Ui,<+1 where
(3.94)
The
net flux of the top layer is:
- —
alent
A t/„
\( T Ni > T(01
UNt
*J v,ne< =
(3.95)
ljN, _ Qh W
A t I,
otherwise.
Then the change in the total mas 9 of the layer is given by:
A (p,d,)i = (p .d .)? * ' - (p,d,)\
(3.96)
“ “ A t ( t / / , n e | + Fv,ti(l)>
The compaction rate then gives the depth of the new layer:
(o d
( i - A t c r n , ) . 7 \ h l t N! ijk ,
I
for the toP layeri
(3.97)
\P*Q»)n ,
+ Uv,nct
d*ftI( l - A t CRi)
otherwise.
net
And the new snow density is:
P*,i =
for the top layer,
(3.98)
+ u&
dt+At
otherwise.
W ith this param eterization, the net vapor flux of the top layer changes its thickness
and not its density.
38
3.4.7 Metamorphism of snow grains
The size of grains is im portant in the determ ination of the structural stability
of a snowpack for avalanche forecasting and the support of weight. In the energy
and moisture transfer equations, grain size affects the perm eability o f the snowpack
to fluid flow (section 3.4.5) and the shortwave extinction coefficient (section 3.4.4.1).
The grain size is also of critical im portance in calculating the brightness of microwave
radiation em itted by the snowpack, discussed further in C hapter 4. Snowflow uses
(3.35) from Anderson [37] to initialize snow grain size and follows the method of
Jordan [38] for modeling growth of grains. Snow grain growth is an area o f continued
research effort and these semi*empirical param etcrizations arc interim solutions.
Snowflow calculates the change in grain size, gs,+A,—g s \ in dry snow as a function
of the water vapor flux, t/„:
(3.99)
where Ca,\ is an empirical constant and
Uv = CDtT nDf
dT
dz
(3.100)
In wet snow, grain growth is accelerated as smaller grains—whose equilibrium fusion
tem perature is sm aller than th a t of larger grains—m elt and feed the growth of larger
grains:
gst + A t ^ { x t + 0.05)
9s
0 < jti < 0.09
gs*+“ =
(3.101)
$w' + A *-2£(0.14)
x, > 0 .0 9
where C9& is an empirical constant and x\ is the volume fraction of liquid water*
39
3.5
Discussion
Chapter 7 describes the results of Snowflow’s snowpack simulation when it is
driven by the REBEX-1 atmosphere. T h at chapter discusses th e short-comings and
sensitivities of the snow and soil models and the way th at REBEX-1 data are linked
to the Snowflow parametcrizations described in this chapter.
C H A PTER 4
MODELING RADIOBRIGH TNESS OF THE
SIMULATED SNOW PACK
4.1
Introduction
This chapter describes Esnow, a snowpack emission model designed to take full ad­
vantage of th e detailed d ata available from Snowllow's snowpack simulation described
in Chapter 3. The Snowflow model provides a snowpack stratified in up to 50 layers
with tem perature, density, grain size, and wetness information in each layer. Beneath
the snowpack is a soil half-space with tem perature and moisture information. The
objective of the Esnow model is to estim ate the brightness of microwave emission and
the reflection characteristics of the terrain over a broad range of snowpack conditions
with reasonable computation speed.
4.2
Conventional radiative transfer theory
Conventional radiative transfer (CRT) theory is based on a heuristic development
of the problem of intensity transmission through attenuating media. In a medium
containing scatterers, CRT assumes th a t each particle scatters independently of the
others, that is, as if it were the only scatterer. In fact, when scatterer density ex­
ceeds about 1 % by volume, the scattered fields interact in phase, resulting in reduced
scattering by the individual particles.
40
41
dA
/Oj
tOj
Figure 4.1: Conventional radiative transfer.
This section develops the form of the differential equation of transfer th a t Es­
now uses to solve the snowpack emission problem. Section 4.3.1 .1 will account for
the inadequacies of the independent scattering assumption by introducing an em pir­
ical correction to the independent scattering extinction coefficient th a t reduces its
magnitude to the level of experim ental observations and more sophisticated models.
Figure 4.1 diagrams the process of extinction by scattering and absorption expe­
rienced by a spectral intensity, I, as it traverses an incremental length, dr, along the
ray r with a directional cosine /ij — cos 0f. A plane-parallel geometry is assumed with
sym m etry about the z-axis. The change in intensity, d l, is given by:
^
( dfj[ ) = ~ Ka^ r ” *i,ldr + K„J0dr + ti,3 ,d r
(4,1)
where /„ and /* are the vertically and horizontally polarized components of I, k „ and
k,
are the absorption and scattering coefficients (per unit length) in the medium, and
J„ and J , are the absorption and scattering source functions per unit length. The
differential optical depth, d r, is defined as:
d r - « ed r
where kc = na -f*
(4.2)
is the extinction coefficient of the medium. Substituting (4.2)
42
into(4.1):
4 - = —(1 —a)I —al + (1 —a)J„ + aJ, *= —I + (1 - a ) J 0 + aJ,
ar
(4.3)
where a = K ,/n e is the single scattering albedo and, for independent scattering, is
equal to the ratio of scattering cross section to extinction cross section for a single
particle.
The absorption source function can be deduced from IvirchhofTs Law: Under
conditions of local therm odynam ic equilibrium emission m ust be equal to absorption.
The radiation from a differential clement of the transmission medium balances th a t of
its neighbors isotropically with a spectral intensity per polarization given by Plank's
black-body radiation law:
where p is /i- or u-polarization, h is Plank’s constant, / is frequency, k is Boltzm ann’s
constant,
T
is tem perature, c is the speed of light in vacuum, and n is the index of
refraction of the medium. A t microwave frequencies, the exponent is small and the
Raylcigh-Jcans approximation can be used to linearize the formula:
, _ h/V (
ca
1________ \
( ( 1 + h //k :r+ • • • ) - 1 / *
kp n 'T
c* *
( 5)
At 85.5 GHz—the highest frequency of interest here—the error in using the RayleighJcans approximation is +0.7% at
T=
300 K. T he absorption source function is then
a function of absolute tem perature only:
p
_ k /V r(r)
c2
—
•
,...
(4»(>)
By convention, the correspondence between tem perature and the source function leads
to the definition of a convenient quantity, brightness tem perature. T he brightness
43
tem perature of a source in terms of its radiant intensity measured in vacuum is:
c3
= A>k f 2 ‘
Along a ray traveling through media of varying refractive index, a more appropri­
ate quantity is the index-normalized brightness tem perature which rem ains invariant
along a ray in lossless, homogeneous media:
Tn'V =
^2
i7 p ‘
Since the problem considered here involves radiative transfer through media with con­
tinuously varying refractive index, index-normalized brightness tem perature is used
as the propagating term . The absorption source function for index-normalized bright­
ness tem perature is:
Tw s
= r(r).
(4.9)
The scattering source function accounts for radiation from all incident directions,
(/<,•,<&), being scattered into ( p „ 0 ,):
= "fa J
(4-10)
where <j>is the azim uth angle around the z-axis and <ffl; = sin OidOidfa is the differential
B
solid angle. P , is the so-called phase m atrix and its elements determ ine the scatter­
ing transformation from polarizations p< and direction (/*,,$,•) in to p , and (p„<£,)*
Following from (4.9), define the equivalent scattering index-normalized brightness
tem perature source by:
j
2
2
Inserting (4.6) and (4.10) into the differential transfer equation, (4.3):
_
= _ l + (i _ a ) ^ L _ ^
j + __
^ ^
44
z=0
ISW)
e»
W
z = -d
Figure 4.2: Upwclling and downwelling brightness in a snowpack layer.
Replacing intensity with the definition of index-normalized brightness tem perature
using (4.8) and elim inating common term s, wc have the differential equation of ra­
diative transfer in terms of T n:
^
= -T „ + ( l - o ) T „ + aT„,.
(4.13)
where T n,„ and T n>l are given by (4.9) and (4.11), respectively.
4.3
Solution for the simulated snowpack
T he plane parallel Snowflow snowpack is naturally stratified by the spacing of
snowfall events, with some artificial limits on layer thickness as discussed in C hapter 3.
Each layer has separate values for tem perature, density, grain size, and wetness.
Consider the upwelling brightness, T+, and downwelling brightness, T “ , through a
layer as in Figure 4.2. From (4.13), the transfer equations are:
= -? M ) +
(1
"
+ a T U v t.ti)
(4.14)
45
and
where
d r ± = i — dc.
nf
(4.16)
m
T n,« alone has an azim uthal
dependence through P , in (4.11). Integrating (4.14)
and (4.15) over <j>,\
M U r t)
dr+
=
-T + W ) + ( l - “)T ^
(4.17)
+ 1 1
and
=
-T „ -(p ;) + (l-a )T „ ,„
(4.18)
where
P»o(p»IP») =
jf
$*? /^i» &)•
(4.19)
We will integrate (4.19) when the functional form of P j is given in Section 4,3.1.
%
To solve the diiTerentia) equations (4.18) and (4.19), we divide each equation by
attenuation from the appropriate boundary:
(
V
*+
+ x +(u + )) e T+<_d,*) = ^ w ( ^ « ) er ( d,,>) _ p + e-r+{-4f.*>
+ " (" ‘ V
dr+
" F"e
(4
20)
+ T " ( p 7 ) j eT~t°>*» = ,rftT n jp ;)e _T (0-*}] _ F - eT-(o.»)
(4.21)
where F* is the sum of source term s
= (1 -°)T „..
(f.22)
+ f Jo
+| j
l
and
r ± ( ^ i , s 3) =
/ ' ’ d r* .
(4.23)
Jti
Integrating (4.20) over ( - d , r ) and (4.21) over (0,z) and substituting (4.16) for d r* ,
we have:
J- d
**•
- T ;(o ,(r;)c '" < 0'°i = - /
Jo
fl.
(4.24)
dz\
(4.25)
Solving for T * ( ; ,p f ) :
T + (e,/r+ ) = T I M . / i J - J e - '* ! - '^ + f F J e - ' * ' - ' - ' ^ . - '
J-lf
/i,
T ; ( : , / 0 = T„-(0,/r;)e-’-<«'*' + / °
F - o - ^ '- ^ d z '.
/i.
(4.20)
(4.27)
Equations (4.26) and (4.27) were derived for a Snowflow snowpack layer of thick­
ness d. We can divide the Snowflow snowpack into layers of arbitrarily small thick­
nesses, <f, using interpolation from the original snowpack layer m id-points to calculate
tem perature, grain size, and densities. Then by choosing S small enough to neglect
the depth dependence of ne and F * , we can m ake the approximations:
47
T ; ( r , / i ; ) « T ; ( 0 ^ ; ) e _T“,M + F ; — c * * '* I
**•
(4.20)
Wc then solve for the upwelling brightness at th e top of the layer, T ^ (0 ,p ^ ), and
downwelling brightness at the bottom , T ~ ( —6, h 7 ):
T+(0,pJ-) « T J ( - i , (i,+)c-’, l-M' + P j ^ r^ ( l
(4.30)
Hi Kc
T ;M
, / 0
»
**• * '
o - 'i - - ) .
(4.31)
Combining terms:
T + (0,/l+ ) e= T + (-« ,p ,+)c -, , l- “ l + F + (l - e—
)
(4.32)
T - ( - i ,# i 7 ) « T ;( o ,( ,; ) c - ''" , - , >+ F~(i - c — 4'"").
(4.33)
Recall th a t the source term s (4.23) include scattering integrals over the incident
directions,
The method of Gauss-Legcndrc integration (or Gauss quadrature)
allows us to numerically evaluate these integrals using a small num ber of /ry and
a set of N weighting coefficients, Wj [48]. Gauss quadrature is accurate when the
integrand is well-approximated by a polynomial and is frequently used with radiative
transfer problems [49], Applied to (4.32) and (4.33) we have:
T + (0 ,rf) M T + ( - « ,^ ) c - '* < - « l + ( l - e - “-4'» J ) |( l - a ) T n.„
+ ! E
“ j»l
W iJT jttW j) + P „ W ; - W i l T ; ^ ) ) ]
T ” (—<T,/i7) w T - ( 0 ,/ O e - '- < ° '- 4>+
"b
a N
9 ^ n ) j ( P #0 (—
“ >=»
where the scattering directions,
tions,
(4.34)
(1
- e" 't*4A‘~)[(l _ fl)T n ,0
(4.35)
;/i|j)T j(/r,j) + P»0( ~ ^ » ! /^O")Tn (/i»j))]
m ust now include the discretized incident direc­
as well as th e direction corresponding to the observation angle of interest,
48
Hobt. In this work, N = 5 was sufficient in th a t greater N did not significantly change
the radiative transfer result.
W ith (4.35) and (4.36) for thin layers in hand, we can use the method of invari­
ant imbedding to find a solution for the whole snowpack as a stack of thin layers
(Section 4.3.2). B ut first the next section deals with th e form of th e scattering phase
matrix.
4.3.1
The scattering phase matrix and Mie scattering
Grains in the Snowflow snowpack arc modeled by a single grain size—the diame­
ter, gs—in each Snowflow snowpack layer. Although the grains in true snow arc both
indistinct and not spherical in shape, they arc usually randomly oriented. Assuming
this is the case, the Mie scattering phase function for spherical particles is an ap­
propriate approximation. If the particles were small compared to the wavelengths of
interest, then the simpler Rayleigh scattering function could be used. According to
[50], the validity criterion for Rayleigh scattering is |n rx| < 0.5 where
x —
(4.36)
is the size param eter, r is the particle radius, A0 is the free space wavelength, c[9 is the
background dielectric constant (the real part of the complex perm ittivity), and n r is
the relative index of refraction of the scatterer (1.77 for ice). Table 4.1 compares Mie
and Rayleigh scattering at two grain diam eters—0.17 mm and 2.2 m m , the largest
value from Snowflow. Although for the smaller grain diam eter the Rayleigh criterion
is satisfied at all three frequencies it is not valid even for the lowest frequency a t the
largest grain size. Here, the error in the Rayleigh scattering cross section, Qtea is
4.6% at 19 GHz and 117% a t 85 GHz.
Derivations of Mie scattering can be found in many texts (for example, [51]) and
49
19 GH z
98
0.17 mm
2 .2
mm
Method
Rayleigh
Mie
Rayleigh
Mie
Q tca
|n rx|
1.615E-14
1.615E-14
6.83E-8
7.16E-8
0.06
0.79
37 GH z
|» r*|
Q tca
2.212E-13
2.214E-13
0.94 E -6
1.03E-6
0 .1 2
1.5
Tabic 4.1: Mie-Rayleigh scattering param eter comparison.
85 GHz
|n fr |
Q tca
6.30E-12 0.28
6.35E-12
3.5
2.67E-5
1.23E-5
Q tCa
is in units of m 2.
will not be repeated here. Figure 4.3 diagrams the prim ed particle coordinate system
showing the nominal scattering plane and the perpendicular and parallel polarization
directions of the scattered radiation. If the incident fields arc polarized f> and h as
shown, the relationship between incident and scattered field components is given by:
\ El )
-ik h r
^ Si.
(4.37)
S u ) \ El )
where ktg is the propagation constant in the background medium and the Spq arc the
scattering am plitudes relating incident to scattered field at incident polarization t> or
h and scattered polarization || or X. The scattering am plitude m atrix in the particle
reference frame is given by:
P" ' “ "
"
S l¥
Su
) ~ \
S ,( /,.) c o s ^
j
(4 '3 8 )
where Sa and Si are the co-polarized and cross-polarized Mie am plitude scattering
m atrix elements in the plane of incident polarization and are functions of ft, only.
Assuming incoherent fields, we can then write the scattering phase function for a
particle in the particle's reference frame:
i% n
Q™ v
,ro/
Q ^kl
|5 u , | 3 )
(4.39)
where (M ,m) is the Stokes m atrix for th e scatterer.
Figure 4.4 diagrams the transformation of the scattering am plitudes from the
particle scattering plane polarizations, || and X, to h and v polarizations relative
50
Scattered radiation
Particle
x'
Incident radiation
Figure 4.3: Scattering geometry for an isolated particle.
51
Scattered
radiation
Incident
radiation
Figure 4.4: Particle scattering geometry in the snowpack coordinate system.
to the snowpack horizon. In the snowpack coordinate system , th e z*axis is vertical
and
the x- and y-axes are arbitrarily oriented. The angle A is the azim uthal angle
between the incident and scattering directions. T he snowpack azim uth origin (fa — 0)
is arbitrary so for convenience assume A — fa - fa. T he x'-axis from Figure 4.3 and
the v polarization are always in the sam e plane as the snowpack z-axis. The scattering
am plitude m atrix relating incident to scattered fields polarized with respect to the
snowpack horizon is:
c
l - ( Sw Svh\ _ ( casfa' sinfa1 W
tnowpaek ~ VShv Shtl ) - [ sinfa' -cos fa' ) Sparlicte
(4*40>
52
where, in term s of the snowpack scattering coordinates,
* jJ)
sm<p
= sin* 9{n . „
sm&,
((4.41)
a ji 1 \
cos <f>,r
= - cos A cos <f> + sin A sin <f>cos 0,
(4.42)
sin 0, sin A
= ----------- —
sin # '
cos#'sin 0,- —sin#, cos A
= ---------- :— ----sin O' cos 0j
.
(4.43)
. ,
sin<p
,,
cos®
cos O'
A
. . ...
(4.44)
= cos Oi cos 0,+ sin #,■sin 6, cos A
(4.45)
= <f>t —fa.
(4.46)
The scattering phase function for a particle in the snowpack reference frame is:
b
4ir •
P i(Pit^ii/*M^i) = q TJ’Sjootifieki
ST9CQ™kg
(4*47)
Recalling (4.19) for the scattering phase m atrix for the plane-parallel geometry,
b
1
f2n
P » ( ^ ii^ i) = jif jjj
1
[2*
_
^ * 2 n Jo
(4.48)
we can now elim inate one integral by z-axis sym m etry and replace the other with A:
P « (P a ;w ) = ^ I
d A P ,(/i#;/i,;A ).
(4.49)
The remaining integral can be solved numerically using Gauss-Legendre integration
as described above. The solution converges with 16 azim uthal angles.
4.3.1.1 Attenuation coefficients: Empirical scattering reduction
Laboratory experiments have dem onstrated th a t th e assumption of independent
scattering does not hold for particle densities in excess of about 1 % of the total volume
[52], Calculations applying QCA-CP-PY—th e quasi-crystalline approxim ation with
coherent potential and Percus-Yevick pair-distribution function—reflect this result
and can be used with the laboratory observations as th e basis for a heuristic cor­
rection to independent scattering [53]. Figure 4.5 shows scattering coefficients from
53
independent scattering and an empirically adjusted QCA-CP-PY fit as a function of
the volume fraction of ice (particles) in air. The normalized independent scattering
t
coefficient is given by:
Vf*eat
where
= /
(4.50)
is the scattering coefficient for independent scattering, / is the volume
fraction of scattcrcrs, Vteat is the volume occupied by a single particle, N teat is the
num ber of particles per unit volume, and Q teat is the scattering cross section of the
particle (from Mic theory). The curve in Figure 4.5(b) fits independent scattering to
empirically adjusted QCA-CP-PY results:
Ki.mrf
=
7 (1
_ /)(|0 .5 -
/ |3
+ 0.015).
(4.51)
Although experimental observations are made o f total extinction not the scattering
coefficient, variation in extinction in dry snow should be controlled by the scatter­
ing term. QCA is only slightly dependent on the background moisture content of
the snowpack and a t the frequencies of interest here attenuation by the background
medium quickly exceeds attenuation by the particles [54]. Consequently, the same
scattering reduction formula is used for wet and dry snow.
The QCA-CP-PY scattering coefficient fit in Figure 4.5 approxim ates results re­
ported in [53] and [54] for volume fractions up to 0.4. T he latter used a mean particle
radius of 1 mm and showed th a t at / = 0.4 extinction coefficients were about 6.5%
of those from independent scattering over frequencies from 35 to 140 GHz. Esnow
infers the shape of the QCA-CP-PY fit for / > 0.4 by assuming it issym m etric about
/ — 0,5.
As/ approaches 1 , scattering becomes a function of air pockets in a mostly
ice m atrix and is roughly analogous to scattering by ice grains in air.
!
54
1 .0 n
(a)
c
.2
£
a>
o
0
C7)
0 .8
~j
•g 0.6 i
©
1
« 0 .4 H
TJ
O
N
T5
0.2 -
o
Z
0.0
f
0 .0
S catterin g coefficients
Ind ep en d en t scattering
QCA-CP-PY
QCA-CP-PY (inferred)
—i-------1------ 1------ r
0 .2
0 .4
0 .6
0 .8
Volum e fraction of sc a tte re rs
1 .0
1.0
0.8
0.6 -
S catterin g reduction factor
QCA-CP-PY/lnd. scat.
0 .4 -
0.2 0.0
0 .0
0 .2
0 .4
0 .6
0 .8
V olum e fraction of s c a tte re rs
1.0
Figure 4.5: (a) Normalized scattering coefficients and (b) the independent scattering
reduction factor.
55
In summary, the Esnow attenuation coefficients are:
— NicatQabi 4" ^bg
k,
= A’. „
Ke
-
(4<d2 )
, 7(1 - / ) ( | 0 . 5 -
/ | 3
+ 0.015)
(4.53)
(4.54)
K „ = Kg
where Qait is the absorption cross section of a particle (from Mic theory),
is the
background absorption coefficient given by
=
and
2M
I - / ) Hm {fit, ) | ,
njp
(4.55)
is the complex index of refraction of the air-w ater background medium given
in Section 4.3.4.
4.3.2 The method of invariant imbedding
Equations (4.35) and (4.36) gave th e upwclling and downwclling brightness from
a thin snowpack layer in a set of discretized directions. The goal of this section is to
solve the snowpack emission and reflection problem by iteratively adding thin layers
from the bottom up and calculating upwelling emission and half-space reflectivity
concurrently. This method of solving the radiative transfer problem for a layered
medium has been called invariant imbedding [5 5 ].
Figure 4.6 diagrams the boundary conditions of the k th thin layer of the snowpack
for which T+ and T~ satisfy (4.35) and (4.36). Consider the upwelling brightness at
the top of the layer to be the following sum:
T + (**,/i.) = Q * ( ^ ) T + '( ^ - „ /i.) + T + (zk,n ,) + T + ( r* ,/i,)
(4.56)
TJ'l-'t-i./i.) = T + (n .„ p .) + f;R ,.,(,,.;p „)T „-0(.-i .^,) )
(4.57)
where
]=l
5G
Air
m :
z (k + 1 )-----------------------V --------- y f--------------- / ------------- v »
T > ) /
Snowpack
la y e r *
°
Tnl*k)
,
f M
/
l '
/ o
/
o
/»
/
„
\
/T ^ k -1 )
z(k)
---
0
Soil
►=Attenuated
Figure 4.6: Brightness balance for the k tU thin snowpack layer.
is the upwelling brightness leaving th e k — 1 layer and a* =
is the total attenuation of the k th layer independent of polarization. T+, and T “ 0
are upwelling and downwelling absorption source term s from (4.35) and (4.36). Since
H* — f i j , these term s are equivalent:
T+, = T - =
(1
- o ) T „ ( l - e— ‘'<“•) = T „ . ( a , ii,).
(4.58)
e
is the reflectivity m atrix a t the k — 1 boundary for incident radiation
at the discretized direction /i,-j and reflected/scattered radiation a t fit . In general,
s
R|t-j(/V *Pij) includes cross-polarization term s due to scattering in th e volume below
the boundary.
The last term of (4.56), T + (z * ,/it ), is the scattering source term for the layer and
is given schematically by Figure 4.7. Since th e scattering phase m atrix for the layer
is symmetric with respect to the vertical direction in the snowpack, it is convenient
57
Snowpack
layer k
-► = Attenuated
Figure 4.7: Components of the layer scattering source term , T *,.
to define:
(4.59)
(4.60)
In the schematic, P M represents scattering away from th e hemisphere of the incident
■*
radiation and P t0 represents back-scattering into the hemisphere of the incident ra­
diation. T he scattering source for the layer is a function of upwelling radiation only.
(Downwelling emission from the layer, T ^ , is reflected and included in T J',) Upwelling radiation a t all angles contributes to T+f (c*,/i,), so to simplify the notation
we can redefine the brightness vector to include all of the discretized propagation
directions, the principle observation direction, and both polarizations:
(
J S .O '.) \
T + M
T#n* =
(4.61)
»
*
♦
^ 'I'n.hif1'**)
The corresponding scattering m atrix can then include the Gauss-Legendre weighting
58
functions and other terms from (4.35):
(4.62)
4
P v v im til)fls W 1
P vv(M ^\)Q o b * m
P h K w u iM u i
4•
■
i
■
•
•
•••
Pwit*N\HN)PlW>N 0
P*(HobM‘,HN)Pob,WN 0
Ph*fa\\M)Ptv>N o
44
*
*
•
■
•
4
P L { v m h n )P nv >n o
Phvi^ob,; fiN)P0b.Ws 0
•••
•
*
4
J3(j*i;wv)0i«>jv o>
4
4
P v k iW H N ^ N m
P ^ o b t\H N ) P o b ,U } S
o
o
*
4
Pvh(t*N\lll)PNU>l •••
P*hittob»\Hl)Pob*W\ •••
•••
4
4
4
/*t)Avtvi •••
Phh(M th)Pob,u>i •••
4
4
o
4
4
4
4
4
4
AfcOwwOAvW iv o
Phhivob,lHN)Pob,u>N 0 /
where Pj = a (l —t y ) / 2 . Note th a t the zeros correspond to incident radiation in the
observation direction which do not contribute to the Gauss-Legendre approximated
59
scattering integral. Similarly, define a multi-directional volume scattering m atrix:
(4.63)
71 =
o
*
•
Rvt>[ftNif*N)
R v v iw u i)
RwiHebtWl)
RhAf*iWi)
Rvv{fiobti
0
R vviflo bti Hob§)
RhviHl'iUN)
o
Rhv[f*N\f*N)
Rhv(fiobri Hn )
0
*
«
0
RvhiHiWi)
RvhiW H N )
■
•
•
4
4
RvhiHN'iHi)
ftuh iW i P n )
Rhhif*liPt)
0
t*I )
0
Rhh(Hi\HN)
0
Rhh(PN\th)
RhhifiNWN)
0
t t hh ( V ob . \ ( l l )
Hn)
«
«
*
R-hhiHobi) Hobi) J
Additionally, we will need a diagonal m atrix, a , whose elements arc a (/ 4,) , the layer's
p
attenuation in direction p t .
W ith these definitions, if we apply (4.35) up to third order then the scattering
source term in (4.56) is:
T+t {Zk) — (P*0 + QkPk-lPt0 + K f i k - l K + Ok'Rk-l'P.oPk-l'P.o
+ P , 0T l> i- iP t< ftk - iP ,0 l
)7^+,(:*-i).
(4.64)
Similarly, the volume reflectivity m atrix for th e fc,h boundary is given by:
P'k ~ P.o + (*k'R'k-l'P,0 + Ofc^k-jafc +
(4.65)
Increasing the num ber of terms in (4.64) or (4.65) did not change th e result of the
radiative transfer solution for the snowpack significantly.
60
4.3.3 Air-snow and snow-soil boundaries
The only boundaries of significant dielectric contrast in the Snowflow snowpack
arc the soil-snow and snow-air interfaces. Section 4.3.4 discusses the calculation
of the dielectric constant for these media. At the soil-snow interface, Esnow ubcs a
specular boundary. As discussed in Chapter 3, the Snowflow soil contains a significant
am ount of unfrozen w ater even when the tem perature is below the freezing point.
Consequently, the soil !b lossy with shallow effective emission depths and it can be
modeled as a dielectric half-spacc. The soil-snow reflectivity m atrix is;
(4.66)
where
(fo.i/t/ |2
ft§nowft$oil
_
ft toil ft m
IPomI3 =
o w
(4.67)
4" U ,nouiflio il
ftto ilftso il
H m ow ft t now
(4.68)
ftioilftgoil 4* ft MOWf t MOW
The direction cosine in soil is fixed by Snell’s law and the discretized propagation
angles in the snowpack:
Jihpuj s in 0 t now
ft,o,i = COS Sm” 1 ( ^ IIIW ^ ^*noui\ |
\
«<•«
/J
(4.69)
Emission from the soil—the initial condition for the snowpack emission solution
(4.56)—is given by:
(4.70)
^n(-O tP j) ” 7*oi/(I “ ®o)
s
where I is the identity m atrix and Ttou is the soil surface tem perature.
The snow-air reflectivity m atrix is similar, with v- and h-polarized components:
3
|ro,y.v*|a =
U jnotupair ** ftgjrftsnow
(4.71)
ft*now ftair 4* Sg|V/J,niiiii
|E air,fcfc|2
=
ftsnowftgnow
fttn o w ft m
o w
fta irfta ir
4*
fta ir fta ir
(4.72)
61
When the air-snow boundary is reached using invariant embedding, Esnow calculates
the snowpack brightness iteratively in a m anner similar to (4.64). First, downwclling
sky brightness is transm itted through the air-snow boundary, reflected, and depolar­
ized by the volume, contributing to the topmost upwelling vector:
r n+'(.-n+l) =
(4.73)
Then m ultiple reflections off the boundary and scattering by the volume arc accounted
for, the upwelling brightness is transm itted through the snow-air interface, and the
sky brightness reflected off the surface is added:
( - n + l , (*»)
— ( I 4* H m & a ir
4" ' ^ n ^ a i r ^ m ' J ^ a i r 4*
** *
( * n + 1)
4 - ( ! - £ » ,> J T * '.
(4.74)
4.3.4 Dielectric properties of water, ice, snow, and soil
The complex perm ittivity of free water, cw, is well known as a function of tem ­
perature and frequency in the microwave spectrum [50]. Ice isgenerally accepted to
have dielectric constant independent of tem perature and microwave frequency:
eI- = 3.15.
(4.75)
The imaginary p art of the complex perm ittivity of ice is small (especially relative
to th a t of water) and, consequently, difficult to measure. Esnow uses the following
empirical formula from [56]:
«? = j 4- P f
(4.76)
62
where
o
o
(50.4 + 62.O0)l.OE-4e“ 221*
0 =
3 0 0 /r+ l
0
1.0EM(0.445 + 2.11E-3 T ) + ()
=
T is tem perature in °C and / is frequency in GHz. The complex perm ittivity is
U — Cf T
•
The complex perm ittivity of dry snow can be calculated from the empirical for­
mulas [50];
4
=
(1 +0.508E -3703
_
i
'pi
(4.77)
( 2 cj, + 1 )
+ 2 crf,)(ci + 2 c£)
7
(4.78)
where 7 ,- is the density of ice in situ (the snowpack density) and p ,• is the intrinsic den­
sity of ice. The background perm ittivity o f dry Bnow for Mic scattering calculations
is 1 .
The complex perm ittivity of wet snow can be found by solving the Polder-Van
Santcn mixing formula for the water-air-icc m atrix [50]:
£u/i - U* + Tr(£u. " t* ) 5 3 7 T ~ m Z — 7Y
J
u«.6.e L1 + ^«*
“ 1J J
where
(4-79)
is the volume fraction of w ater in the snowpack. T he coefficients are:
A a = /U ” 0.475 and A c = 0.05 [57]. Equation (4.79) is cubic in l wl and can be
solved using a numerical complex root finding routine. The wet snow background
dielectric is a w ater-air m atrix whose perm ittivity can be found by replacing the host
perm ittivity, c* , with 1 in (4.79):
1
Zbg = 1 +
“ 0
53
u = o ,l> ,c
l+ A .(£ -l)
(4.80)
63
Esnow calculates the soil complex perm ittivity based on a dielectric mixing of
free water, bound water, dry soil, and ice. The rotation of water molecules that arc
adsorbed (bound) to soil grains is inhibited by weak chemical attractions (39). Esnow
assumes th a t only w ater in excess of 7% by dry weight is free while the remainder is
bound. Then the soil complex perm ittivity is given by:
=
*7%
+
X/retP7%{flCw
+
(1 “
(4.81)
fl)Ci)/pw
where
17 %
— 3.3 + 1'0.4
Xu
%bound
ft
=
Xu
=
( X<
T ,ri
=
T, - (
\owupbJ
ft
0.93
XtypUf
-
Pl%
niui =
X /ree
—
Xfcound
~
2/rce
Ur
\■ otwuiTo
— Tioifl^pb/pw
'lum
i f T j o i l '^
Tfpd
otherwise
Ph "f
p7%(mw - 0.07)
pu>{\ m w)
X|y ” X j r t f
£7* is the complex perm ittivity of soil with 7% moisture by weight (from [50]); //
is the fraction of the free w ater (unbound) th a t is in liquid form; x u is the unfrozen
soil moisture volume fraction; 7 / ^ is called the freezing point depression and is the
tem perature a t which x ^ = x„; pj% is the bulk density of soil with 7% moisture by
weight; m w is the weight fraction of all w ater with respect to the moist soil; and x Jret
and Xbound are the volume fractions of free w ater (including ice) and bound water,
respectively. From Snowflow, pb is the bulk (in situ) dry soil density, pw is the intrinsic
64
density of water, x w is the total soil moisture volume fraction, and o wu and /3U,„ are
param eters for calculating unfrozen water content.
4.4
Discussion
The combined Snowflow-Esnow model operates as a responsive system with at*
mosphcric data as the driving force. Consequently, complete testing and validation of
Esnow can only be done in conjunction with Snowflow and in comparison to a natural
snowpack interacting with the sam e atmosphere. C hapter 7 discusses these compar­
isons after a description of the REBEX -1 radiobrightness experim ent in C hapter 5.
Esnow’s self-consistency can be tested independently by taking a typical Snowflow
snowpack profile and setting th e soil and snow tem peratures to J iMi, and setting the
sky brightness from alt directions a t the top of the snowpack to:
V kv = TuJ tkv
(4.82)
where t,ky represents the unit vector of T*kv. Then the Esnow snowpack brightness
m ust also be equal to 7fMr at all angles and frequencies according to KirchhofTs Law.
In fact, Esnow's brightness was within 0.02 Iv a t the observation angle of 53.1° and
frequencies of 19, 37, and 85 GHz.
CH APTER 5
GROUND BASED RADIOBRIGH TNESS
OBSERVATIONS IN THE NO RTH ERN GREAT
PLAINS: THE FIRST RADIOBRIGH TNESS
ENERGY BALANCE EXPERIM ENT
5.1
Introduction
This chapter describes the experim ental apparatus, methodology, and measure­
ments from the first Radiobrightness Energy Balance Experim ent (REB EX - 1 ). REBEX -1 was the first in a series of field studies designed to track the microwave radio­
m etric response of terrain to antecedent weather. T he purpose of REBEX -1 was to
examine the link between radiobrightncss and land-atm osphcrc energy fluxes in the
northern G reat Plains through the course of w intertim e freezing and spring thaw.
During REBEX-1, three microwave radiometers measured the apparent radio­
brightness of a grassy site at 19, 37, and 85 GHz. Augmenting these data were
measurements of sky radiobrightnesses, terrain and sky infrared radiometric tem ­
peratures, net and global radiation, soil tem peratures, soil heat flux, rainfall, air
tem perature, relative humidity, and wind speed. In addition, a video cam era and
digitization hardware acquired
100
images of the radiom eter observation area during
the experiment for later use in evaluating snowcover conditions.
REBEX-1 ran from October, 1992 through April, 1993, making 17200 observation
G5
66
cycles encompassing vegetation senescence, snowpack formation, soil freezing, and
thaw. The study site was on the grounds of the EROS D ata Center (EDC), U. S.
Geological Survey, near Sioux Falls, South Dakota a t 43°43' N latitude and 96°30' VV
longitude. This chapter describes th e experim ental apparatus, installation, and the
d ata collected and discusses post-experim ent error handling.
5.2
Apparatus
REBEX - 1 had two m ajor instrum ent subsystems: the Tower Mounted Radiome­
ter System (TM RS), with microwave radiometers designed and built as a part of this
thesis, and the micromctcorological subsystem (MMS), a collection of commercially
available instrum ents for monitoring local weather conditions. The instrum ent sub­
systems were integrated around a com puter-autom ated d ata acquisition and control
system. More detailed descriptions of these systems can be found in [58].
5.2.1 Micrometeorological Subsystem and system integration
Table 5.1 lists the specifications of each MMS instrum ent along with the parame­
ters measured. The Infrared Tem perature Transducer—hereafter referred to as an IR
radiom eter—produced a tem perature outp u t com puted from a 15° field-of-vicw ther­
mal infrared radiometric measurement and an assumed target emissivity of 0,95. The
IR radiom eter and the other MMS instrum ents were factory-calibrated. I was able to
confirm only a few of these calibrations independently. I checked the soil therm istor
calibration and signal conditioning circuitry by immersing the probes in an ice water
bath. All therm istor channels reported the ice bath tem perature to be 273.15 K to
within 0.1 K. I confirmed rain gage and anem om eter operation by manually actuat­
ing switch closures in each. During the experiment, nighttim e global radiation values
67
Figure 5.1: Interior of the trailer on site sheltering d a ta acquisition and device control
electronics and the Macintosh com puter running the FluxMon HyperCard stack which
controlled the experiment.
were between 0 and 2 W /m 2 and the maximum relative hum idity value was 101.5%,
providing indirect confirmation of the calibration accuracy of the pyranom ctcr and
humidity probe, respectively.
Figure 5.1 shows the interior of the small heated trailer (1.5 m x 2.4 in floor
dimensions) on site th at sheltered the d a ta acquisition and experim ent control elec­
tronics. An Apple Macintosh II com puter controlled all aspects of the experim ent and
provided a modem linking the experim ent to offices a t the University o f Michigan. A
custom designed program called FluxMon—operating in the H yperCard software de­
velopment environment—managed data acquisition from all devices except the video
camera, autom atically controlled power to the instrum ents and heaters, and provided
a graphical interface for control param eter adjustm ent and m anual radiom eter cal­
ibration. FluxMon communicated with the IR radiom eter via form atted character
Instrum ent
Model
REBS N et Radiom eter
Epplcy Black and
W hite Pyranom eter
T hom thw aite
Soil H eat Flow Disk
M et-One Anemometer
Texas Electronics
Tipping Bucket Rain Gage
Vaisala Relative
H um idity Probe
Cam pbell Scientific
Therm istor
Cam pbell Scientific
T herm istor
Everest Interscience Infrared
Tem perature Transducer
Q- 6
8-84
014A
525
Param eters
Net radiation 1
Global radiation
(shortwave ) 1
Soil heat flow
a t 2 cm depth
W ind speed at 10 m height 1
Rainfall
HMP35AC
Relative hum idity
107
Air tem perature at 1.8 m
107B
Soil tem peratures a t 2, 4, 8 ,
16, 32, and 64 cm depths
Therm al IR surface and
sky tem peratures
610
4000ALCS
Accuracy
N /A
± 1 .0 %
N /A
0-1400 W /m a
N /A
N/A
±1.5% or 0.11 m /s
± 1 .0 %
0.447-45 m /s
0-5.1 c m /h r
±2% RH over 0-90% RH
±3% RH over 90-100% RH
± 0 .2 K
0-100% RH
± 0 .2 K
240-321 K
± 0.5 K
243-373 K
Range
'B oth instantaneous and experiment cycle average values o f these parameters were recorded.
Table 5.1: Micrometeorological instrum ents and param eters. N /A indicates d ata not available.
240-321 K
|
69
strings transm itted through one of two Macintosh serial communications ports. A
National Instrum ents NB-MIO-16 board with an AMUX-64T m ultiplexer provided
32 differential analog to digital conversion (ADC) channels and a TTL (transistortransistor logic) counter/tim er channel. NB-D10-24 and NB-T1O-10 boards provided
TTL in p u t/o u tp u t and additional counter/tim er channels. All of th e boards fit into
internal NuBus expansion slots in the Macintosh.
The NB-MIO-16 digitized the signals from all of the instrum ents with voltage
outputs: the microwave radiometers, the internal radiom eter therm istors, and most
of the MMS instrum ents. I used therm istors in bridge circuits for all tem perature
measurements because of their accuracy and case of use. Instrum entation amplifiers
conditioned the rest of the MMS voltage signals for ADC. The NB-DIO-24 TTL
output channels controlled power relays for the radiometers, the radiom eter heaters,
the radiometer fans, the humidity probe, and the m otor th a t opened and closed the
radiometer housing door. NB-DIO-24 TTL input channels read signals from three
microswitches indicated the door's position: fully opened, fully closed, or opened to
the sky reflection position. The NB-TIO-IO counter/tim er channels generated TTL
square wave signals for setting radiom eter heater power levels. FluxMon determined
heater duty cycle settings approximately once per m inute and reset the tim er channel
outputs based on a ten second total period. Counter channels counted switch closures
from the anemometer and rain gage. FluxMon calculated wind speed as a function
of number of switch closures over an elapsed time. For the rain gage, each switch
closure was equivalent to 0.245 mm (0.1 in) of rain.
Tim buktu/R em ote software enabled rem ote control of the experim ent from Michi­
gan. Remote control procedures included trouble-shooting observations and control
software changes, data file and video image down-loading to Michigan, and manual
70
Frequency (GHz)
Wavelength in air (mm)
IF bandwidth (MHz)
Radiometric resolution (K)
Mixer operation
Polarization
Integration time
A ntenna 3 dB beamwidth
Incidence angle
(terrain brightnesses)
Nominal zenith angle
(sky brightnesses)
85.5
37.0
19.35
3.5
15.5
8 .1
10-250 1 0 0 - 1 0 0 0 100-1500
N /A
0.61
0.82
Double-sideband
Horizontal
6 8
10°
53°
45°
Tabic 5.2: Microwave radiometer specifications, N /A indicates d a ta not available.
Sec Appendix B for radiometric resolution calculations.
control of the video image acquisition software.
5.2.2 Design of the microwave radiometers and the Tower
Mounted Radiometer System
Table 5.2 lists the specifications of the TM RS microwave radiometers. The ra­
diometers simulated the observation angle, bandwidths, and three of the four fre­
quencies of the spaccborne Special Sensor Microwave/Imager (SSM /I), a Defense
Meteorological Satellite Program instrum ent. TM RS measured both terrain appar­
ent radiobrightncsses and sky radiobrightnesses a t 19, 37, and 85 GHz. I manually
calibrated the microwave radiometers a t the beginning of the experim ent using am ­
bient and liquid nitrogen tem perature microwave absorbers (Eccosorb). In addition,
the system automatically executed gain recalibration of the radiom eters during the
experiment using internal noise reference sources (m atched microwave loads).
Figure 5.2 shows the TMRS housing a t the top of the REBEX tower. T he towerbased electronics were divided into five modules; one each for the 19, 37, and 85
GHz radiometers, one for the IR radiom eter and video camera, and one in the back
of the housing’s center com partm ent for the electrical bus.
In addition, a motor
71
19 GHz Radiometer
37 GHz Radiometer
Video Cam era
85 GHz Radiometer
Infrared Radiometer
Door & S k y Reflector
Figure 5.2: T he TM RS -1 radiom eter housing.
72
Figure 5.3: The 85 GHz radiometer. The 19 and 37 GHz radiometers have layouts
which are comparable component by component.
and screw drive mechanism in the center com partm ent positioned the door for sky
brightness measurements during each experiment cycle. Figure 5.3 shows the 85 GHz
radiometer module. The 19 and 37 GHz radiometers have similar com ponent layouts.
In each radiometer module, a mixer down-converted the RF signal to IF which then
passed two amplifier stages and a bandpass filter. Three 12.2 m coaxial cables carried
the IF signals from the tower to the trailer. The three radiom eter modules differed
only in the frequencies of their R F (radio frequency) and IF (interm ediate frequency)
components and in the voltage level of the regulators for their local oscillators.
For each radiometer, a square law detector converted the IF signal from the tower
to AF (audio frequency, in this case 0-20 kHz). AF amplifiers in a tem perature
controlled com partm ent then conditioned these signals for ADC by the NB-MIO-16.
T he NB-MIO-16 sampled the AF radiom eter signals separately on three ADC
channels a t 40 ksam ples/s for 6 seconds. FluxMon then calculated radiom eter output
values in instrum ent counts depending on which of two possible radiom eter modes
was activated—total power mode or Dicke mode. In total power radiom eter (T PR )
73
mode. FluxMon calculated radiom eter outputs by simply averaging each d ata stream .
In Dicke radiom eter mode, a 1250 Hz TTL signal generated by th e NB-MIO-16
counter/tim er modulated the RF input between th e antenna and th e internal reference
load. This TTL signal also triggered ADC sampling, synchronizing it to the RF input
modulation. FluxMon calculated the Dicke-mode radiom eter output values by first
numerically demodulating the d a ta stream s and then averaging. During autom atic
radiometer operation, FluxMon used TPR-m odc for gain rccalibration measurements
off the internal reference loads and Dickc-modc for brightness measurements.
Complete manual calibration of the microwave radiometers required TPR-m odc
and Dicke-mode measurements (in ADC instrum ent counts) of (i) a microwave ab­
sorber soaked in liquid nitrogen (LN2) and (ii) an absorber at am bient tem pera­
ture. T P R measurements of the internal reference noise sources also made a t cali­
bration tim e established a baseline value for radiom eter gain drift corrections. The
radiometers were always under computer-controlled tem perature stabilization during
calibration—th a t is, FluxMon autom atically measured tem peratures and set radiome­
ter heater duty cycles about once every minute. The calibration d ata acquisition
procedures built into FluxMon also triggered measurements of the radiom eter inter­
nal reference load and antenna tem peratures with each d ata sample. A therm istor
embedded in the ambient tem perature absorber registered its tem perature. The tem ­
perature of the LN2 soaked absorber is fixed at about 80 K by the liquid-gaseous
phase change.
5.2.2.1 Microwave radiometer calibration
Figure 5,4 is a block diagram showing the components of th e microwave radiome­
ters, all of which followed the same basic design. During the experim ent, the calibra-
74
Tem perature controlled
radiom eter box (on tower)
Reference
nolle source
(matched load)
Standard gain
horn antenna
Intermediate frequency
amplifiers
Isolator
Latching
ferrite
circulator
Switch driver
Bandpass
(liter
oscillator
10.2 m IF
coaxial cable
Counter/timer
Computer
• DIcke/rPR mode
selection
40 kHz sampling
Signal processing
NB-MIO-16:
Counter/timer and
12 bit differential
analog to digital converter
Temperature controlled
compartment
Audio frequency
amplifier
DC-20 kHz
Figure 5.4: Microwave radiom eter block diagram.
Square law
detector
75
tion parameterization included estim ates of transmission line losses from the antenna
to the receiver and from the reference load to the receiver. Arbitrarily defining the
receiver as beginning a t the output port (port
1)
of the RF switch (a latching fer­
rite circulator) we have the following forward radiom eter equation for the radiometer
output signal:
VD = C.D [ f ^ A V +
- D° / l )
(5-1)
where Vd is the measured Dicke radiometer output in counts, Tap is the apparent—
or radiometric—tem perature being measured, L 21 is transmission line loss from the
antenna to the receiver, tjt is the antenna radiation efficiency, Tpa is the physical
tem perature of the antenna, and CMp and D0/ j arc the Dicke-mode gain and offset
param eters, respectively. Inverting (5.1) for apparent radiobrightness:
( 5 -2 )
C , d and D0j f were found through a two point Dicke-mode calibration:
r,
_
1 Vdo(T a p i Vi + (1 - i]i)Tpa1 ) — Vd i (T apoVi + (1 —f}t)Tpoo)
“
—
Z/21
Vbo — Vp\
U °!S — ~
T a p w /i
*D
where subscripts
1
and
0
2| +
(1
—l}l)Tpao/ L 21
(5.3)
— D o //
indicate d ata from the ambient and LN2 tem perature
sources. 1 estim ated values for Zrji, L3 1 , and »//, listed in Table 5.3, from m anu­
facturers specifications.
Precise radiometric measurements require a calibration curve established at a time
as close as possible to the tim e of measurement. This is because radiom eter outputs
are sensitive to gain variations. T he TMRS radiometers were most vulnerable to gain
76
Param eter
19 GHz
37 GHz
85 GHz
Vl
L 21
0.9
1 .1 0 0 1
£31
1.18
0.9
1.034854
1.034982
0.9
1.13186
1.13494
Tabic 5.3: Estim ated loss parameters.
drift through the inevitable change in IF coaxial cable tem perature and the com­
m ensurate change in loss through the cable. These cables were directly exposed to
weather over most of their 12.2 m lengths. IF and AF amplifiers were also subject to
gain drift over the seven m onth length of the experiment. By using the param eteri­
zation in (5.1), gain variation may be isolated to the param eter Cto- Reference load
tem perature and RF transmission line losses and tem peratures are then the primary
determ inants of the radiom eter offset param eter, D0/ j , and I assume these term s to
be constant.
To track gain drift, FluxMon autom atically made TPR-m odc measurements of
the internal reference loadB and their tem peratures during each experim ent cycle.
Assuming th a t receiver noise tem perature and DC ofTscts remained constant, the
reference load gain param eter,
is:
Ct REF - 7p— }rREF, T
J re //
(5.5)
31 + * ree
where V e e f is the TPR-m ode outp u t in counts when switched to the reference load,
Tre/ is the tem perature of the reference load, L31 is transmission line loss from the
reference load to the receiver, and Tree is the TPR-m ode receiver noise tem perature
param eter which includes DC offsets in the AF amplifier. Each manual calibration
determined
y .
_
T ree
using LN2 and ambient tem perature absorber data:
1 Va n t q { T a p \HI
+
(1 -
V i W pn i) — V a n t i ( T apq JIi + (1
- FaNTo
-
w )7 p « o )
jq
^
where the param eters are defined as in (5.3) except th at V a n t is the TPR-m ode
output in counts when the RF switch is set to the antenna input.
Dicke-mode and TPR-m ode gains differ due to the differing mismatches and losses
in the antenna and reference load transmission lines. The R F components preceding
the receiver arc passive and their losses and mismatches arc constant. Provided that
internal radiom eter tem peratures and, consequently, Trec are stable, the ratio of C ,n
to CtfiEF will remain constant in tim e. T h at is, relative gain variation in th e TPR
reference load radiometer can be used to track variation in Dicke-mode gain using
the relationship:
C ,p(t) _ CtREF(i)
C .D(0)
C .„ b H 0 )
(r ...
where t indicates the tim e of the experim ent cycle and t = 0 is the calibration time.
Figure B.8 in Appendix B is a graph of the T P R gain factors, Ct REF* measured during
each experiment cycle using (5.5). In each experiment cycle, FluxMon calculated C»p
from C , r e f using:
*
c.D (0 =
(5.8)
I manually calibrated the microwave radiometers and changed the calibration pa­
ram eters accordingly on the dates listed in Table 5.4. Appendix B contains data used
to evaluate the accuracy and precision of the microwave radiometers. In summary,
the radiometric resolutions (repeatabilities) of the 19 and 37 GHz radiometers were
0.G1 and 0.82 K, respectively, based on 20 measurements of known sources. Insuffi­
cient d ata are available to give the radiometric resolution of th e 85 GHz radiometer.
The average calibration accuracies were 0.24, -0.61, and -0.53 I< for the 19, 37, and
85 GHz radiometers, respectively.
78
Radiometer
Day
Tim e
19 GHz
279
309
403
279
288
309
403
309
403
1800
1600
0100
1800
1900
1600
0100
1600
0100
37 GHz
85 GHz
D* u
272.552
271.099
270.710
310.754
310.055
309.465
303.357
292.432
276.149
146.796
84.4456
68.48
2.76098
-10.007
-53.472
-38.874
225.183
122.348
CtojCtREF
0.91918
0.91065
0.91162
0.93106
0.93520
0.93452
0.94690
0.91427
0.92667
Tabic 5.4: Calibration param eters used during REBEX-1 from day indicated to day
of next calibration. Some 37 and 85 GHz param eters were later modified. Sec Sec­
tions 5.5.3 and 5.5.5.
5.3
Installation
Figure 5.5 shows the EDC site as seen from the cast. The TM RS radiom eter
housing is positioned atop the REBEX tower. The housing was attached to the
9.14 m (30 ft) aluminum tower via a winched shuttle. I installed and calibrated the
radiometers with the housing lowered and left it at full height during all experiment
cycles. The housing was made from alum inum sheet welded to a tube frame and
the bottom hinged door was stainless steel. Figure 5.G shows the housing with its
back cover removed, revealing the housing power bus, the protruding door motor
mechanism, and the housing’s center module. The bracket mounting th e housing to
the shuttle perm its rotation of the housing into a vertical position for servicing and
module removal.
Figure 5.7 shows th e distribution of the other instrum ents to the southeast of the
tower. The radiom eter observation area was kept undisturbed through the installation
process. I chose an observation area to the southeast o f the trailer and th e MMS
instrum ents so th a t w intertim e prevailing winds from the northwest would not cause
snow drifts on the site. A graduated 5.1 cm (2 in) diam eter PVC pipe with alternating
79
Radiometer Homing
Guy W in
Radiometer Observation Area
(4 tn i2 m )
30 a
Tower
LQ Ji
Trailer
Soil Heat Flow
Diak (Buriedl
Air Temperature &
Relative Humidity Probe*
Figure 5.5: View of the REBEX-1 site from the east.
80
Figure 5.6: View of the radiometer housing with its back cover removed. Inserted
into the housing are (from the far side) the 85 GHz radiometer, the JR radiom eter
and video camera module, the center connector box, the 37 GHz radiom eter, and the
19 GHz radiometer.
Guy wire
Trailer
* *. ►
Air temperature &
relative humidity
probes
y
#■‘
v
Guy wire
Tower
Guy wire
Net
radiometer
• Soil
temperature
probes
(buried)
Pyranomcler
•
Soil heat
flow disk (buried)
Radiometer
observation
area
4m
Figure 5.7: Plan view of the REBEX-1 site.
Figure 5.8: G raduated PVC pipe with alternating 1.27 cm (0.5 in) black and white
stripes used for gaging snow depth from video stills of the REBEX-1 site.
1.27 cm (0.5 in) black and white stripes was installed within the video camera field*
of-view, as in Figure 5.8. Video images of this gauge were used to make the snow
depth estim ates shown in Figure B.9.
I installed the soil heat flow disk a t 2 cm depth below the soil surface and the soil
tem perature therm istors at depths of 2t 4 , 8 , 1G, 32, and 64 cm, as shown in Figure 5.9.
I chose an undisturbed area under which to install the tem perature probes. Because
the soil was obscured by grass roots and litter, identifying the surface was possible to
within only about 0.5 cm. The tem perature probes themselves were 1 cm in diam eter
and were inserted into the soil through six 46 cm long horizontal holes made in the
side of a trench, which was then back-filled. I installed the soil heat flux disk under a
separate undisturbed area by cutting into the sod and soil with a knife and inserting
the disk horizontally.
83
RMSES
^ Tf t c t 3 Mm ?l|j? i
b. tfc frA*;*■* * ? f s 9 i v ^ l
»\"V \7iwnWMQ|
Figure 5.9: Insertion of the soil tem perature probes. At the tim e of this picture, I
had already inserted the probes in the side of the trench and refilled it, burying the
64, 32, and 16 cm probe cables. Cables leading to the 2, 4, and 8 cm deep probes
protrude from the side of the trench.
84
5.4
Experiment log
The REBEX-1 field data report gives a detailed account of the experiment log
[58], This section summarizes key qualitative information from the experim ent. All
experim ent dates in this thesis are given as day numbers from January 1, 1992 (day
1). For example, January 1,1993 is day 367 since 1992 was a leap year. A REBEX-1
day number vs. calendar date chart is given in Appendix B. All times arc Universal
Time (UT) which is six hours ahead of Central Standard Tim e (CST) at the site.
While the experiment was operational, FluxMon initiated measurements a t pre­
set times—initially at every 10 m inute mark of th e hour and then later every 15
minutes. D ata sets were tim e stam ped a t the end of each experim ent run which lasted
approximately 5 minutes. I acquired video images via the telephone link infrequently
at first but then almost every day when there was snow on the ground. Approximately
100 video images were recorded over th e course of th e experiment. The frontispiece
of this thesis shows one such image from day 420 (February 23,1993). The REBEX-1
field d ata report [58] contains copies of all the images.
Setup of the experiment began on day 269 and installation was completed by day
271. Several equipm ent failures forced a delay in experim ent commencement until
day 279, when d ata taking began a t 1805 UT, Chief among these were the failures
of the IR radiometer and one of th e three microwave radiom eter IF detector units
and general electrical bus noise. Rewiring the infrared tem perature transducer onto
an independent DC power supply circuit resolved th a t failure and rewiring one of the
85 GHz circuits resolved the DC problems. There were no spare IF detector units
so I left the two good detectors in the more reliable 19 and 37 GHz radiometers and
placed the faulty diode with th e 85 GHz radiom eter. Although the 85 GHz output
was unusable, I left the 85 GHz radiom eter installed to monitor the performance
85
of the complete electrical system. This was the configuration when the experiment
began.
Over the course of the experiment, cold weather periodically affected instrum ent
performance. The rain gage was not heated and so did not record snowfall accurately,
if at all, and only worked reliably in warm weather. Dew, frost, and snow interfered
with operation of the net radiom eter and pyranometer, covering the instrum ent domes
and blocking radiation. A heavy frost in early February, 1993 apparently caused the
seizure of the anemom eter lasting from day 404 to 409.
On day 289, the com puter clock stopped a t 0934 UT and did not resume until
1318 UT when a worker manually disturbed the com puter keyboard or mouse. Similar
clock stoppages occurred several tim es during th e course of the experiment and were
resolved by manual means each time. The problem seemed to be attributable to a
suspension of normal com puter time-keeping interrupt generation when large data
streams were collected from the microwave radiometers by th e NB-MIO-16. The
problem was resolved in later implementations of the software by initiating a query
of the system clock after each large data acquisition run.
Table 5.5 summarizes hardware problems th a t lasted for significant portions of the
experiment and divides the experiment into seven tim e periods by general site con­
dition. More detailed descriptions of most entries can be found in [58}. Section 5.5,5
discusses the problems with the 85 GHz radiometer and Section 5.5.2 discusses TMRS
housing door problems. T he experiment itself lasted from day 279 to day 471.
5,5
Correcting radiobrightness errors
The following sections describe post-experiment processing of the radiom eter data.
The analysis covers deletion of out of range values,-identification of sky brightnesses
86
Days
279-306
307-315
316-337
338-401
403-407
408-452
453-471
Days
279-295
295-394
279-309
309-347
347-403
403-471
350-471
415-471
404-409
Site coverage conditions
No snow, green grass cover, unfrozen ground
Snow cover
No snow, dorm ant grass cover, unfrozen ground
Snow cover
Snow cover cleared manually exposing grass over frozen ground
Snow cover
Mostly snow free, dorm ant grass cover
Hardware problems
IR radiometer: Some d ata missing due to serial communi­
cations error
IR radiometer: D ata drop-outs of tem peratures less than
249.9 K (-9.9°F)
85 GHz radiometer: Not installed due to missing IF detector
85 GHz radiometer: Installed but malfunctioning
85 GHz radiometer: Functioning bu t not manually calibrated
85 GHz radiometer: Functioning and calibrated
TMRS housing door: Frequently fails to open to sky
reflection position
TMRS housing door: Frequently fails to close past sky
reflection position
Anemometer: Not spinning due to frost
Table 5.5: Summary of REBEX-1 site coverage conditions and hardware problems.
corrupted by reflector positioning errors, 37 GHz radiom eter calibration errors on
day 403, estimation of actual sky brightnesses, 85 GHz recalibration for days 347403, an alternative calibration param eterization, and radiobrightness sensitivity to r/(
assumptions.
5.5.1 Removing out of range radiobrightness values
Both terrain and sky radiobrightnesses exhibited occasional ou t of range values,
typically near 296, 320, and 332 K for the 19, 37, and 85 GHz radiom eters, respec­
tively. The spurious points occurred singly in either the sky or terrain m easurement
and were not accompanied by spurious T P R gain factor readings. The out of range
values occurred about once every other day in each instrum ent. The spurious ra-
87
diomctric measurements were always greater than the corresponding infrared surface
tem peratures, so they were distinguishable as non-physical.
1
manually deleted these
values from the data set.
5,5.2 Sky reflector positioning errors
Sky radiobrightncss measurements suffered from two m ajor sources of error dur­
ing REBEX-1—incorrect sky reflector position and inadequate reflector size. Sec­
tion 5.5.4 discusses the later of these errors in detail. Motion of the TMRS housing
door—which also served as a sky reflector—became erratic on day 351 due to wear
in the screw drive mechanism. A t th a t tim e, only door closures were affected, with
incomplete closures occurring periodically and usually in groups. Commensurately,
sky brightness measurements were at times unusually high but I did not tic them to
the door problems until day 414. Prom day 351 to 414, if an experiment cycle began
when the door was not completely closed, FluxMon would make sky measurements
without moving the door from its current, partially closed position. Many flawed sky
brightnesses from this period were greater than the concurrent terrain brightnesses
and could be easily identified. However, th e sporadic occurrences of sky-brightening
clouds or precipitation make sky brightness inherently highly variable, complicating
the job of weeding out faulty data. Since terrain brightnesses are a combination of
em itted radiation and reflected radiation from the sky, it is possible to use terrain
brightness variation as an indicator of sky brightness validity. For example, if sky
brightness jum ps by 100 K from one measurement cycle to the next, one would expect
terrain brightness to increase by
10
K if the reflectivity of the terrain were
1 0 %.
Manual editing of sky brightnesses in the day 351 to 414 period used the following
criteria: sky brightnesses were deleted when they exceeded terrain brightnesses or
88
when a sudden, large change in sky brightness was not accompanied by a commen­
surate change in terrain radiobrightness. W hen the data were ambiguous. 1 chose to
remove the points rather than risk using bad data. In most cases, a group of removed
points would include a t least one very high value, or a group of low values would be
bounded by large jum ps not mirrored in the terrain brightnesses. It is likely that
faulty d ata remain, however, since zenith angles between
12°
and the the nominal sky
measurement angle of 45° were possible and would have yielded cold sky brightnesses
th a t were indistinguishable by our criteria from valid 45° measurements.
The door mechanism failed in a new way on day 414 when it would not open
completely. Software changes a t this time eliminated the need for subjective editing
of sky measurements. During the sky measurement, the reflector was either in the
correct sky measurement position or fully open. Erroneous sky measurements were
close to terrain measurements and easily identified. From day 414 to the end of the
experiment, I deleted a sky measurement set if both its 19 and 37 GHz sky bright­
nesses were greater than 0.95 tim es the respective terrain brightnesses, I checked
this criterion against the data from before day 350 and found no matching points,
indirectly confirming th a t no valid points from days 414-471 were removed.
5.5.3 Revision of the day 403 37 GHz radiometer calibration
Following the experiment, the 37 GHz radiom eter physical antenna tem perature
(Tpa) values recorded during the day 403 calibration were found to be erroneous. Since
no modifications had been made to the system following this calibration, the erroneous
value is likely to have persisted through the end of the experim ent. Physical antenna
tem perature affects apparent radiobrightness calculations only when it changes from
its value a t calibration time. Over the course of the experim ent, the range of 37 GHz
89
physical antenna tem perature was approximately 9 K. This variation is modified by
the factor of
{1
—
in (5.2) so the error could have a maximum effect of aboul
0.9 K on T a p FluxMon did not save the physical antenna or reference load tem peratures used
in the calculation of T ap during the experiment. In order to correct the 37 GHz
calibration for the period from day 403 to the end of the experim ent, 1 estim ated
these tem peratures using outside air tem perature. The following steps gave corrected
37 GHz data:
• Using d ata available from calibrations on days 279, 288, and 309, perform linear
regressions between the 37 GHz Trej and Tpa and air tem perature.
• Calculate Tn / and Tpa for each experim ent cycle after the day 403 calibration
using the factors from the linear regression.
• Using the erroneous Tpa value (282,73 K), the original calibration factors from
day 403, and C , r e f values saved from each experim ent cycle, estim ate the
radiometer output, Vfc, for each experiment cycle after the day 403 calibration
by applying (5.1).
• Use the raw calibration data from the day 403 calibration with the estim ate for
the correct T a p to calculate a new set of calibration factors (D 0j j , T rtct and
CtDfCtREF)*
• Calculate VfcjSF
each experiment cycle by using th e original Trte value and
solving (5.5).
• Calculate new CtpEF and Ta p values for each experim ent cycle from (5.5) and
(5,2) using the new calibration factors and previously estim ated Trtj and Tp„.
90
( Radiom eter
Day
37 GHz
403
Time
0100
D0/ f
Trec
C ,D /C tREF
305.936 | -41.7428 | 0.93759 |
Table 5.6: Corrected calibration param eters for the period from days 403 to 471.
Table 5.6 lists the corrected calibration param eters. Of the approximately 5700 ex­
perim ent cycles between day 403 and the end of the experiment on day 471 the largest
correction by this procedure was -0.914 K and th e smallest was -0.124 K. The average
correction was -0.538 K.
5.5.4 Estimation of actual sky radiobriglitnesses
High REBEX-1 sky radiobriglitnesses suggest th a t these measurements were cor­
rupted when radiation from the terrain reached the radiometers. As seen in Figure 5.2,
the 19 and 85 GHz radiometers were close to the edges of TMRS housing door. Al­
though the size of the door accommodated
10°
ficld-of-view main antenna beams,
it did not account for side lobes and ncar-fiold diffraction effects. Sky brightnesses
arc used to calculate terrain emission from apparent radiobrightness and modeled
terrain reflectivity. Since reflected sky brightness is usually small in comparison to
emission from the surface, in most cases an approxim ate sky brightness will introduce
only second order errors in terrain emission calculations. It is therefore valuable to
attem p t to estim ate sky radiobriglitnesses from the available flawed sky and terrain
measurements.
To make a sky brightness estim ate, consider the hypothesis th a t for each radiome­
ter the sky reflector had a fixed efficiency,
such that:
T r f l ~ VrJlTsh’V + (1 ~ Vr/tWTER
(5.9)
where T r f l is sky brightness measured with the reflector, T s k y is actual sky bright­
ness, and T t e r is apparent terrain radiobrightness. The hypothesis suffers from some
91
obvious flaws since it assumes th a t radiation corrupting the sky measurement originstes from the same area and a t the same incident angle as T j e r • If we assume
thfit the radiation source corrupting the sky measurements is of terrestrial origin,
then T t e r is a t least a valid surrogate. If, however, th e corrupting source is either
emission by the TMRS housing components—including the reflector itself which at
times was wet or ice covered—or radiation from angles near the horizon, then T t e r
is sit best th e same order of m agnitude as the source and the estim ate of Ts k y will be
invalid. The 37 GHz radiometer is most likely to fall into this second category since
it was positioned near the center of the TMRS housing and did not have direct line
of rite to th e terrain except at high incidence angles.
1 estim ated r;r// for each radiometer by calculating T s k y from Huron, SD rawinsondc data using radiative transfer. (Sec Section B.3 for a description of the data.)
Rawinsonde profiles from Huron were available twice daily at 1100 and 2300 UT. I
selected
20
profiles corresponding to clear sky periods as reported in both the Sioux
Falls and Huron LCD’s. T s k y >s the sum of T o n * the downwclling radiobrightness
from the atmosphere, and cosmic radiation attenuated by the atmosphere. Calcula­
tion of Tpfj is based on solution of the equation of radiative transfer [50]:
</B
— + B = J
(5.10)
where B is brightness (W /m*sr) and J is the effective total source function a t a point
r in direction r, d r is incremental optical depth defined as
dr= 5K edr,
(5-11)
and K' is th e total extinction coefficient. A t 19, 37, and 85 GHz, the atmosphere
is scatter-free
for
in the absence of clouds and precipitation,
k* = k9, the coefficient
absorption by atmospheric gases, and J = J at the isotropic absorption source
92
function. Using the Rayleigh-Jcans approximation to Plank's blackbody radiation
law, we can express Ja in terms of air tem perature, T(r):
2k
J 0 (r) = A f - T ( r )
(5.12)
where k is Boltzm ann’s constant, A is wavelength, and A / defines the bandwidth. (In
general, A is a function of r but its variance is negligible in the atm osphere.) Similarly,
we can use Raylcigh-Jeans to define apparent radiometric tem perature,
Tap,
in terms
of B:
2k
f l( r ) f = A f ^ T AP(r)i.
(5.13)
Solving for downwelling apparent radiometric tem perature, T o n , a t the surface
from zenith angle
0
in a plane-stratified atmosphere, we have:
Td n (0) = sec 0
JO
Kg(z')T(z')e-Tio'''>™0 dz'
(5.14)
where
tt'
r(0 ,c ') = I ng(z)dz
’
JO
and z
isverticalheight
dom inant absorbers in the
(5.15)
in the atmosphere. Oxygen and w ater vapor are th e pre­
microwave region so k 8 (z ) is a function of tem perature,
pressure, and atmospheric water vapor content. The semi-empirical formulations in
[50] give Kg, The solution to (5.14) can then be found by integrating numerically over
the range of altitudes available in the Huron atmospheric profiles. Before integrating,
I increased the vertical sampling density of the rawinsonde d a ta by 20 times using
cubic spline interpolation. W ithout th e denser data, the non-linearity of (5.14) pro­
duced erroneous results when tested with a modified isothermal Huron atmospheric
profile.
93
Vrlt
19 GHz
0.701
37 GHz
0.723
20
20
0 .0 2
0.06
0 .1 2
8 .1
17.7
0 .1
Number of samples
a
Percent T s k y <
0
85 GHz
0.636
«•
i
Table 5.7: Reflector efficiencies from (5.18), the num ber of clear sky profiles used,
and the standard deviation of qr/(. Also shown are the percentage of T s k y values
from (5.19) th a t were less than zero.
1
calculated T s k y for each of th e
20
profiles using:
Ts k y - T d n
+ T c o s /L { 0 )
(5.16)
where T cos is the cosmic background radiation (2.7 K) and L is the atmospheric loss
at zenith angle 0 :
(5.17)
L{0) Inverting (5.9) for
we have:
_ TfiFL ~ T t e R
tfrjt “ rp
rri
* SKY - 1 TEH
I then calculated
•
(5.1S)
using all 20 clear sky points for the 19 and 37 GHz radiometers
and only the last seven for the 85 GHz radiometer, which was not calibrated until day
403. Table 5.7 gives the resultant reflector efficiencies. Having calculated the reflector
efficiencies, I applied the following equation for estim ated sky brightness, T s k Y i to
the entire REBEX -1 d ata set:
Ts k y
= (T r f l - (1 -
j ^ T t e r )h k j i
(5.19)
For each radiometer there were a percentage—given in Table 5 .7 —of T s k y values
less than zero, a non-physical result. This percentage was greatest a t 37 GHz, sug­
gesting th at the reflector efficiency hypothesis expressed by (5.9) was least applicable
94
____
*
to the the 37 GHz radiometer. T s k y and T r f l are graphed in Figures B.3 through
B.5 of Appendix B. Figure B.4 shows th a t the negative 37 GHz T s k y values arc
mostly concentrated in the fall and spring whereas the later chapters of this thesis
focus on the winter months. The rem ainder of this thesis uses T s k y as a surrogate
for true sky brightness measurements with the knowledge th a t T s k y is a first order
approximation.
5.5.5
Calibration of the 85 GHz radiometer for days 347-403
As discussed in the experim ent log (Section 5.4), the 85 GHz radiom eter was
unused from the beginning of the experim ent until day 309 when 1 installed a new
IF detector unit and calibrated the radiometer. The instrum ent quickly drifted out
of calibration as seen in the T P R gain factor plot (Appendix B, Figure B.8 ). On day
347 the T P R gain factor d a ta reveal an apparent transition to a functioning state.
Since there is no explanation for cither the initial drift or the day 347 transition,
the day 309 calibration is not valid for the operational period after day 347. This
section describes a means of determining an 85 GHz radiom eter calibration set for
this period.
Equation (5.1) describes the forward radiom eter param eterization for Dicke-modc
output:
Vo = C .o
+
0
,
(5.20)
and (5.5) gives the TPR-m ode reference load param eterization:
Vr EF - @i REf ( “7 “^ + Tree).
"31
(5.21)
Before recalibrating the radiom eter, I first evaluated (5.20) and (5.21) to recover the
radiometer outputs originally measured during each experim ent cycle. T he 85 GHz
95
radiometer took d ata from days 347 to 403 using the day 309 calibration param eters
given in Tables 5.3 and 5.4. The remaining term s in (5.20) and (5.21)—the tem per­
ature variables Tpa and Tre/ —were derived from air tem peratures using the method
described in Section 5.5.3.
Having recovered Vi> and Vr b F i a new calibration set for the day 347-403 period
was needed to recalculate 7^/>. I assumed th a t the ratio C «p(0)/C «n^r(0) in (5.8)
remained constant between this period and th e day 403 calibration and th a t C miief
could be found for each experiment cycle by inverting (5.21) once Trte was found.
Of the remaining param eters—D0/ j and Trte—the d ata in Table 5.4 shows th a t Trtc
varied between calibrations more than Do// for the 19 and 37 GHz radiometers.
Consequently, I chose to use D0/ j from the day 403 calibration in recalibrating the
day 347-403 data, leaving Tree to be determined.
From day 347 through 403, the only possible calibration sources were the eleven
sky brightnesses, Ts k y * calculated from clear-sky Huron rawinsoudcs as described
in Section 5.5.4.
The inefficient sky reflector—also described in Section 5.5.4—
complicated the calculation of Trec using these T s k y - We can solve for Trtc •>}’
inverting the TPR-m ode reference load param eterization, (5.21):
^
Tre/
irte — „
— j
t 'j REF
1>ZI
71
(5.22)
where (from (5.8)):
C W =
(5.23)
To calculate T rec from (5.22), we m ust find C , d using T s k y values from the Huron
rawinsondes. We begin with the hypothesized formulation for reflector-measured sky
brightness, (5,9):
T r f L = Vr/lTsKY + (1 - Vr/t)TTER-
(5.24)
96
For each rawinsonde-estimated Tsky* we have Dicke-mode measurements of T r f l
and T t e r from the coincident experiment cycles th a t we can use in (5.20):
VfiFL = CiD { f ^ TRFL +
VrEit = C ,d ( j r - -T t e r +
- D.ti'j
(5.2S)
*
(5.26)
Solving (5.24), (5.25), and (5.26) for C»d , we have:
r
_______________ v n f l - (1 - T]r/i)VrEn____________
tD
W k J lT s K Y /L il
+ (1 - *1l)*lrJlTpa/ L v - VrJlDofj
and we can then calculate Trte from (5.22) and (5.23).
The average Trtc for the eleven rawinsondcs was 116.359 K with values ranging
from 92.195 to 139.247 K. T ree was 122.348 K in the day 403 calibration (Table 5.4),
for a difference of
6
K. For comparison, the 19 and 37 GHz Tree’s changed by -16
and 14.6 K, respectively, between their day 309 and 403 calibrations.
Table 5.8
summarizes the revised 85 GHz calibration param eters. I used th e new calibration
param eters and the 85 GHz radiom eter outputs—from (5.20) and (5.21)—to calculate
T t e r , T r f l , and T s k y d ata for days 347-403. Plots of these param eters appearing in
Appendix B use the recalibrated data only. Figure B . 8 of Appendix B shows both the
original and recalculated T P R gain factor, C,/tEF. between days 347 and 403. The
day 347-403 recalculated
values are on average somewhat higher than those
after day 403 but there is some crossover. Since there is no check of the recalibrated
85 GHz radiobriglitnesses except by the same mode) used to derive the calibration, the
recalibrated 85 GHz d ata should be considered approxim ate and of lesser reliability
than the 19 and 37 GHz d ata over the same interval.
97
Radiometer
Days
85 GHz
347-403
Do//
276.149
Trtc
116.359
C$o / C tnEF
0.92667
Table 5.8: Revised 85 GHz calibration param eters for days 347*403.
5.5.6 An alternative calibration parameterization
The REBEX-1 calibration param eterization UBed approxim ate values for the trans­
mission line loss factors,
£21
and £ 3 1 , and ignored the effects of mismatch differences
between the antenna and reference load radiom eter transmission lines. Because ra­
diometer output is linear in apparent radiobrightness, only two param eters need be
determined through calibration in order to make an im mediate radiobrightness mea­
surement of some unknown source. In this case a very simple param eterization for
the radiometer equation, (5.1), could be used, for example:
V = ATap + B
(5.28)
where A differs from the gain param eter, C ,d, in (5.1) by constant term s only while
B includes variable gain, physical antenna tem perature, and receiver noise terms. I
used the parameterization in (5.1) instead of (5.28) because in practice each of the
terms in B can be treated separately. This effectively isolated the most variable
factor—gain—into one term so th a t it could be corrected through experiment-time
T P R reference load measurements. It was not necessary, however, to include the
loss parameters
£ 21
and L 31 in the param eterization.
£31
may be eliminated from
the Dicke-mode calculations in (5.2) through (5.4) by redefining C[D — C , o l L n and
£>0/ / — A >//£ai. Since
£31
is constant, it has no time-varying effect on C ,d , th a t
is, the ratio Cfo(<)/C jo(0) in (5.7) will remain th e same despite the transformation.
£31
and
£31
may be similarly removed from the T P R calibration equations (5.5) and
(5.6). Because the transmission lines for the antenna and reference load were at nearly
98
Radiometer
Day
19 GHz
279
309
403
279
288
309
403
403
37 GHz
85 GHz
Tim e
1800
1600
0100
1800
1900
1600
0100
0100
D 'oII
r1
299.982
298.227
297.097
321.333
320.862
320.196
316.599
313.057
161.896
96.678
72.500
2.62806
-10.3558
-55.563
-41.7428
139.472
re t
C i n / C 'n E i r
0.9635
0.96266
0.96763
0.93155
0.93532
0.93704
0.93759
0.92653
Table 5.9: A lternative calibration param eters.
the same tem perature as the reference load itself, self emission by the transmission
lines compensated for loss of signal from the load. Consequently, th e alternative
parameterization:
C '">EF
=rJ+L
( 5
' 2 9 )
is a better model of the T P R reference load mode of the radiom eter, although the
(false) assumption is made th at Trec is the same for the antenna and reference load
radiometer modes. We may justify this assumption—made in this and the original
calibration—by taking (5.29) to be an index o f gain variation but not a true radiome­
ter equation for the T P R reference load mode.
The effect of the alternative calibration on the other calibration equations is simply
as if the values of L n and
£31
param eters were set to unity, so these equations will
not be restated here. The alternative calibration param eters were calculated from
each set of manual calibration d ata and the results are listed in Table 5.9. Applying
the alternative calibration changed the calculated value of T a p by a t most 0.016 K.
Its advantage is simplicity and the elimination of arbitrary constants.
09
5.5.7 Sensitivity of radiobrightness to antenna efficiency as­
sumptions
To examine the sensitivity of T a p to ty, 1 recalibrated and recalculated 37 GHz T a p
using alternative rji values of 0.95 and 0.85 and d ata from day 403 to day 471. W ith
tji s: 0.95, the average deviation from the 0.9 case was -0.024, the maximum deviation
was 0.165, and the minimum deviation was -0.253. W ith t// = 0.85, the average
deviation from the 0.9 case was 0.028, the maximum was 0.283 and the minimum was
•0.184. These deviations arc less than the radiometric resolution of about 1 K which
justifies the initial assumption of ty =
5.6
0 .9 .
Discussion
Appendix B contains both overview and month-by-month plots of all the REBEX-1
radiobrightness and micromctcorological measurements. Discussion of the d ata is
left to Chapter 6 , which compares REBEX - 1 radiobriglitnesses to coincident SSM/I
measurements, and Chapter 7, which uses the Snowflow and Esnow models from
Chapters 3 and 4 to analyze REBEX -1 observations of the snowpack.
C H A PTER 6
MICROWAVE RADIOM ETRY FROM SPACE:
THE SPECIAL SENSOR
M ICROW AVE/IM AGER
6.1
Introduction
The last three chapters have presented the theoretical foundations for a dy­
namic snowpack radiobrightness sim ulation and experimental observations linking
radiobrightness to atmospheric conditions.
This chapter adds a third elem ent—
observations of radiobrightness from a space-borne instrum ent, the Special Sensor
Microwave/Imager (SSM /I). It is im portant to present SSM /I observations before
comparing theory with experiment for two reasons. Firstly, the validity of any remote
sensing model m ust be confirmed for the intended instrum ent—th a t is, a space-borne
one. The SSM /I field of view encompasses a range of surface cover conditions th a t are
not necessarily well-characterized by conditions a t the REBEX -1 site. Consequently,
there will be times when differences between REBEX -1 measured brightnesses and
SSM /I brightnesses are large, and understanding these differences will help determ ine
the generality of the REBEX-1 observations and th e simulations based on them . Also,
the space-borne instrum ent measures radiation from the earth and an intervening at­
mosphere whose effects m ust be minimized in studying emission from the terrain.
Secondly, the SSM /I has both vertical and horizontal polarizations, complementing
100
101
Channel
frequency
(GHz)
Pol.
(V /H )
Pass-band
(MHz)
3 dB beamwidth (dcg)
E-plane H-plane H-plane
IFOV
IFOV
EFOV
19.35
19.35
22.235
37.0
37.0
85.5
85.5
V
H
V
V
H
V
H
10-250
10-250
10-250
1 .8 6
1 .6
1.87
1.87
1.65
1 0 0 -1 0 0 0
1 .0 0
1 .1 0
1 .8 8
1 0 0 -1 0 0 0
1 .0 0
1 .1 0
100-1500
100-1500
0.41
0.42
0.43
0.45
1.93
1.93
1.83
1.27
1.31
0.60
0.60
EFOV on earth
cross- alongscan
scan
69
43
69
43
60
40
37
28
37
29
15
13
15
13
Table 6.1: SSM /I sensor specifications [59]. EPOV on earth is in km.
the REBEX -1 radiometers which had only horizontal polarization. The addition of
the v-polarizcd channels will contribute to evaluation of the snowpack simulation in
Chapter 7.
6.2
D ata from the SSM /I
The SSM /I instrum ent is a part of the Defense Meteorological Satellite Pro­
gram (DMSP) and four DMSP platforms have carried versions of it. SSM /I dnta
arc archived for civilian use by the National Environmental Satellite, Data, and In­
formation Service, an agency of the D epartm ent of Commerce’s Nation Oceanic and
Atmospheric Administration (NOAA). Beginning in 1990, a jo in t NOAA-NASA (Na­
tional Aeronautics and Space Administration) program called Pathfinder has been
archiving the d ata for global change research a t NASA’s Marshall Space Flight Cen­
ter (MSFC) D istributed Active Archive Center (DAAC). The MSFC-DAAC is an
element in NASA’s Earth Observing System (EOS) D ata and Information System
(EOSDIS). The MSFC DAAC provided all the SSM /I d ata discussed in this thesis.
Table
6 .1
gives the characteristics of the SSM /I sensor channels. The antenna
beamwidth d ata are from antenna range measurements with the first SSM/I on the
DMSP FOS platform but apply to later instrum ents as well [60]. The SSM/1 is a
102
conically scanning instrum ent with a fixed incidence angle of 53.1° at the earth's
surface. Samples are taken in a 102° arc centered on the ground track of the satellite.
The 85 GHz radiom eter takes 128 samples in each scan and the other radiometers
take 64 samples in every other scan. The radiom eter integration tim e, r , is 7.95 ms at
19,
22,
and 37 GHz and 3.89 ms a t 85 GHz. The F08 SSM /I channels had pre-launch
radiometric resolutions of 0.45, 0.73, 0.38, and 0.73 I< at 19, 22, 37, and 85 GHz,
respectively. In Table 6 . 1 , the instantaneous field of view (IFOV) is the beamwidth
of the stationary instrum ent and the effective field of view (EFOV) on the earth 's
surface takes into account integration tim e and movement of the beam along the scan.
. The antenna H-planc corresponds to the along-scan direction.
This analysis uses d ata from th e DMSP F l l platform . During the REBEX -1
period, the F08 and F10 platforms also carried SSM /I instrum ents bu t the F08 85 GHz
channel was inoperative and the F10 was in a high-ccccntricity orbit, distorting the
SSM /I field of view. The F l l crosses the equator at 17:04 (ascending) and 05:04
(descending) local time, and measurements at Sioux Falls, SD fall in the ranges 22:3123:51 and 11:42-13:03 UTC (Universal Time). SSM/1 processing included (a) sub­
setting the data to a local region from the global d ata provided, (b) calculation of
antenna tem peratures from sensor counts, and (c) resampling of the d a ta to a common
earth-registered grid at a common spatial resolution. Appendix C gives the details of
these processes. Before satellite and ground-based measurements can be compared,
the effect of atmospheric interference m ust be accounted for. This is th e subject of
the next section.
103
6.3
Compensating for atmospheric attenuation and
emission
The SSM /I measures radiobrightnesses from above an absorbing and em itting
atmosphere whose characteristics arc continuously changing. Section 5.5.4 discussed
calculation of the downwclling brightness tem perature from the atmosphere, T dn (0).
and the expression for upwelling brightness, 7V/>(0), is similar:
Tvp( 6 ) = scc0 I ” K t i z ' m z ' ^ ' W ^ d z '
Jo
(6 . 1 )
where z is vertical height in the atm osphere, H is the effective top of the atmosphere,
and
=
(.-)* .
(0.2)
As discussed in section 5.5.4, the predom inant absorbers in a cloudless atmosphere a t
SSM /I frequencies arc oxygen and water vapor. Ulaby, ct a). [50] give the total gas ab­
sorption coefficient, n8 as a semi-empirical function of air tem perature, pressure, and
w ater vapor. (Clouds and precipitation also contribute to atmospheric attenuation
but will not be included in this analysis.) The apparent (radiom etric) tem perature,
TaP\ in the sensor field of view is given by : 1
Tap = t & ) + T v p = T a
(6-3)
where T t e r is the idealized apparent tem perature of the terrain w ithout atmospheric
interference and L„ is the loss factor of th e atmosphere:
L a(0) =
(6.4)
l The apparent temperature, T a p , is strictly defined along a ray incident upon the sensor antenna
and antenna temperature Ta is the integral of T a p over 4rr solidangle. In this analysis, assume
T ap is constant over the main beam o f the antenna and that the antenna sidelobes are negligible
such that 7 a s= T a p .
104
T
ter
of
is the quantity wc seek for rem ote sensing of the land surface. Given estim ates
T up
and L„,
T
ter
can be estim ated from SSM/I antenna tem peratures by:
f T BR
= { T A - T u p ) L a(8),
(6 .5 )
Atmospheric tem perature and water vapor pressure are param eters th at can vary
over location and tim e throughout the year, especially near the surface where high
pressure and water vapor density increase the attenuation. There are several m eth­
ods by which the atmosphere can be characterized for a particular tim e and place,
including weather balloons (rawinsondes), atmospheric models, and remote sensing
techniques. The analysis of Ton in section 5.5.4 used rawinsondes from Huron, South
Dakota to characterize 21 clear-sky atmospheres near the RBBEX-1 site. Now wc use
these same rawinsondes to estim ate T te r from SSM /I T a measurements using (6.5).
6.3.1 Using the rawinsonde atmospheric profiles
Figure 6.1 compares three types of brightness tem perature measurements—terrain
radiobrightnesses measured by the ground-based REBEX-1 radiometers (REBEX -1
T ter ) i SSM/I antenna tem peratures with no atmospheric compensation (SSM /I 7 ^),
and SSM /I antenna tem peratures with the Huron rawinsonde atm osphere removed via,
(6.5) (SSM /I T a - rawin. atm . = T ter ). All the measurements were made under clear
sky conditions within two hours of the launch tim e of the Huron rawinsonde at either
1100
or 2300 UTC. Because SSM/1 coverage is incomplete, there are ju st 12 times at
which SSM /I and rawinsonde measurements correspond. As discussed in Appendix C,
resampling of the SSM /I 85 GHz channel produces both high resolution—th at is, the
original 85 GHz EFOV given in Table 6.1—and low resolution samples approxim ating
the 19 GHz EFOV. 19 and 37 GHz resample to low resolution only. This section
examines both low and high 85 GHz resolution levels.
105
19 GHz
19 GHz
7 200
150
200
250
REBEX-1 T ^ K )
150
300
300
(b)
W
300
200
250
REBEX-1 T ^ tK )
37 GHz
37 GHz
250-
.250
7 200
200
150
S i1 5 0
150
200
250
REBEX-1 T ^ K )
(c)
300
150
200
250
REBEX-11™ (K)
300
(d)
Figure 6 . 1 : Comparison of SSM /I antenna tem peratures and REBEX -1 terrain radio­
brightnesses (on the abscissa) a t tim es coincident with rawinsonde measurements, AU
brightnesses are h-pol. (a) 19 GHz SSM /I antenna tem peratures, (b) 19 GHz SSM /I
antenna tem peratures with rawinsonde atm osphere removed ( T t e r ) (see text), (c)
37 GHz SSM /I antenna tem peratures, (d) 37 GHz SSM /I antenna tem peratures with
rawinsonde atmosphere removed (T t e r )• (Continued on following page.)
106
65 GHz, low resolution /
85 GHz, low resolution
250-
7 200
200 -
++
150-
150
200
250
REBEX-1 Tjg, (K)
150
300
<*)
300
200
250
REBEX-1 T ^ t K )
300
(0
300
85 GHz, high resolution
85 GHz, high resolution
250-
200-
eg 1 5 0 -
150-
150
200
REBEX-1
(8 )
250
(K)
300
150
200
REBEX-1
250
(K)
300
(h)
Figure 6.1: (Continued from previous page.) (e) 85 GHz low resolution SSM/1 an­
tenna tem peratures low resolution, (f) 85 GHz low resolution SSM /I antenna tem ­
peratures with rawinsonde atm osphere removed ( T t e i »). (g) 85 GHz high resolution
SSM /I antenna tem peratures, (h) 85 GHz high resolution SSM /I antenna tem pera­
tures with rawinsonde atmosphere removed (T te r ).
107
Channel
(GHz)
19
37
85 (low res.)
85 (high res.)
c
= Ta
c
-2 . 0
-0.9
7.4
2 .2
-
T ter
Ot
c = T te r
1 1 .0
-3.5
-4.4
- 1 1 .0
-16.8
1 1 .1
13.6
13.5
—
T te r
e
10.9
1 0 .8
1 2 .1
1 1 .2
Table 6.2: Average, c, and standard deviation, tr«, of difference between SSM/1 {TA
and T t e r ) and REBEX - 1 brightnesses. All brightnesses are h-pol.
Table
6 .2
gives the average difference between REBEX -1 {T t e r ) and SSM /I {T te r
or TA ) brightnesses. Note th a t T te r is always less than T a . This occurs because the
atmosphere em its in proportion to its tem perature and to its rate of absorption, while
radiation from the ground—initially scaled down from the surface tem perature by an
cmissivity factor—is absorbed in the atmosphere at an equal rate. An analogous pro­
cess explains why 7rE n(SSM /I) is often less than JYjsh(REBEX-I). T he REBEX-1
site differed from most of the surrounding farmland in th a t it was covered with a
thick m at of grass while the w intertim e farms were m ostly bare. Although perhaps
physically colder than the underlying soil, the grass layer is an absorbing cloud with
a negligible dielectric contrast to air. Consequently, radiometrically cold emission
from the REBEX-1 ground—reduced by the high ground-air dielectric contrast—is
attenuated in the grass layer while the grass em its proportionately to its tem perature
and the same attenuation/em ission function.
Table 6.2 indicates th a t, when th e atm osphere is taken into account, the terrain
is on average radiometrically colder in the SSM/1 field of view than a t the REBEX -1
site. But th e average is by no means a complete description of the difference. Fig­
ure 6 . 2 plots the difference T t e r - T t e r over the duration of REBEX- 1 . As described
above, in October and mid-December—before there is significant snowcover—grass
cover makes the REBEX -1 site radiometrically warmer than the SSM /I field of view.
108
Date
11/1/92
20 H
1/1/93
3/1/93
:
19 GHz
+
*
0
-
i
20 -
+
i
!
]
|
► +
s
I
37 GHz
+
-
+
+
CC
, -20 H
5 -4 0 $
+ .
i
3i
t
.1 20
t
\
i
|
#
I
I
£:
2* - 4 0 -
0
i
.
i
:
!
t
+
!
*
BS
OQ
LU
5/1/93
I 1 I 1 I 1 I 1 I ' I 1 I
I 1 I r 'l 1 I '
______ I_____
I_______
20 H
85 GHz
+
•H-
-20*
-40I
1
I
1
I
1
I
1
1
1
I
1
I
1
I
1
"I
1
I
1
I
1
I
1
260 280 300 320 340 360 380 400 420 440 460 480
Day from Jan. 1,1992
Figure 6.2: Variation with tim e of the difference between T t e r from SSM /I and T t e r
from REBEX- 1 .
109
But snow accumulating in the second half of December seems to create the opposite
effect—th at is, the REBEX-1 site is radiometrically colder than SSM /I—but only at
the lower frequencies (19 and 37 GHz). Section 6.4 uses additional d ata to address
these questions.
6.3.2
Compensation without
a p r io r i
information
Rawinsondes are the most reliable way to characterize the atmosphere for es­
tim ating T t e r but they are rarely available. W ithout a priori information about
the atmosphere, this section attem pts to derive a first-order correction m ethod th a t
uses only the d ata available from the SSM /I. For this purpose, the 19 and 22 GHz
v-polarizcd channels are good candidates because 22.235 GHz is a water vapor ab­
sorption line but is close enough to 19.35 GHz th a t we can assume the brightness
tem perature of the terrain, Tg, is the same for both:
7b(19,V ) = 7b(22,V ).
(6 .6 )
Applying (6.3), we have:
(T*(19f V) - TVMIQ, V ))L .(lfl, V ) - « r« fi* (l» f V)
= (7h(22, V ) - 7W (22,K ))Z. 0 {2 2 , V) - RTSKY(22, V)
(6.7)
where R T s k y is reflected sky brightness and
T b — T te r
”
RTdn<
(6.8)
Since reflected sky brightness is a second order effect, we further assume th a t R =
0,
such th a t for the true values:
A i m , = C W 9 .K ) - ^(//.(lD, V ))La(19,V )
-
(T a (2 2 ,
V) -
Tap(22, V ))L a(22, V)
«
0.
(6.9)
110
To find the unknowns in (6.9)—19 and
22
GHz T u p and La—we seek a model a t­
mosphere th a t minimizes A|g, 22 . Using approxim ate expressions for the U.S. Standard
Atmosphere from [50], we have the profiles:
TM = l r ( 0 ) “
*
\T { ll)
72
° ^ l lfcm’
llfcm < ; <
(6 10)
2 0 km ,
P (z) = P0 c~z' H\
(6.11)
p v = poC ~ ‘ ,H \
( 6 . 12 )
where 7 is the tem perature lapse rate (6.5 K /km ), P0 is sea-level atmospheric pressure
(1013 m bar), po is surface w ater vapor density, and the scale heights arc taken to
be H3 = 7.7 km and //< = 2.3 km. O f the two remaining unknowns, T(0) and po,
atmospheric attenuation is most sensitive to po a t these frequencies. Consequently, for
our simple correction set T ( 0 ) = 270K. This is a reasonable first order approximation
for wintertim e tem peratures in South Dakota.
Now the model atm osphere is characterized only by the po th a t minimizes A | 0,22
in (6.9). B ut can a minimum always be found? Figures 6.3 shows th e sensitivity of
Tup to pQ for the model atmosphere with T(0) = 270I<. As mentioned above, the
difference 7y/»(22) - Typ(19) increases with po such th a t—if T up were independently
measured—the difference could be used to infer po. Figure 6.4 shows a simulation of
what is actually measured—antenna tem peratures—given terrain brightnesses, T te r ,
of 2 0 0 , 235, and 270 K. The simple correction m ethod proposes to use the information
in the difference 7^(22) —T/i(19) to infer po, but the simulation shows th a t when T t e r
is around 235 I( the m ethod fails because 7^(22) - 7^(19) is insensitive to po—that
is, there is no information in the difference th a t can be used to determ ine po.
W ithout po information, a reasonable first order assumption is th a t po — 0. This
will yield the minimum atmospheric correction—one based on atmospheric oxygen
0
5
10
15
20
25
30
Pv(0) (gm/m )
Figure 6.3: Brightness tem peratures upwelling from the atm osphere as a function of
surface water vapor density.
270-1
2 6 0 - Tr a «270K
£
% 250k
>235 K
+ 240-
19 GHz
22 GHz
i
230h
II 220, <
»- 21 0 -
1
200-
200 K
1------------ 1----------- 1---------- 1--------------1------------1
0
5
10
15
. 20
25
30
Pv(0) (gm /m )
Figure 6.4: Simulated antenna tem peratures as a function of surface w ater vapor
density given terrain brightnesses of 200, 235, and 270 K.
112
Channel
(GHz)
A T ter
raw in.-dry atm.
e
ot
1.1
0.7
1.5
1.0
8.1
5.7
19
37
85
c = T ter - T a
(rawinsonde)
e
oe
e - T ter —TA
(dry atmosphere)
e
ot
-1.5
-3.5
-16.8
-0.35
-2 . 0
-8.7
0.33
1.8
8.5
0.33
1 .8
6.2
Table 6.3: Comparison of T t e r from the rawinsonde and dry standard atm o­
sphere methods showing average, e, and standard deviation, <re, of the difference
c = 7Y£fl(rawin.) - 7Yfifl(dry atm .). Also given are these statistics for the magnitude
of the correction, th at iB e = T t e r “ Ta- All brightnesses arc h-pol.
content only—and is unlikely to ovcr-compensate for the atmosphere. Figure 6.5
compares SSM /I
T
ter
calculated using the rawinsonde m ethod in section 6.3.1 and
the dry standard atmosphere method (T’(O) = 270K). As in section 6.3.1, each graph
has about 12 points where rawinsondes and SSM /I samples correspond. Table 6.3
summarizes the statistics of each correction.
The relative magnitudes of the rawinsonde corrections arc about 3%, 5%, and
16% of the range of
Tte r
a t 19, 37, and 85 GHz respectively. The dry atmosphere
corrections are about a factor of two smaller, th a t is, a dry atm osphere can model
about 50% of the brightness change im parted by an intervening atm osphere u n d e r
c le a r s k y c o n d i t i o n s d u r i n g w i n te r . In warmer months and when there are clouds
the dry atmosphere correction will under-estim ate the correction to a greater degree,
especially at 85 GHz. The rest of this thesis uses SSM /I
T
ter
calculated by the dry
atmosphere method with the caveat th a t the true terrain brightness may be—and
usually will be—lower.
113
300
E 250
S3 150
150
200
250
300
SSM/I TA- rawin. aim. (K)
SSM/1 Ta - dry atm. (K)
300-
37 GHz
300
85 GHz
250-
200 -
150-
(3 150
150
200
250
300
SSM/I Ta - rawin. atm. (K)
(b)
150
200
250
300
SSM/I Ta - rawin. atm. (K)
(c)
Figure 6.5: Comparisons between SSM /I terrain brightness estim ates, Tjtw?, made
with a dry standard atmosphere (T a - dry atm .) and a rawinsonde atm osphere (T a
- rawin. atm .). All brightnesses are h-pol.
114
6.4
Comparison of S S M /I and REBEX-1 radio­
brightnesses
Figures 6.6 through 6.8 compare SSM /I and REBEX-1 h-polarized terrain bright­
nesses a t 19, 37, and 85 GHz, respectively. The clear trend a t 19 GHz is for better
correspondence between REBEX-1 and SSM /I during the snow season (late Decem­
ber through March) than in spring and fall. This trend is consistent with snowfall
«
correlation lengths a t least on the order of the SSM/1 EFOV (Table 6.1) such th a t the
snow cover a t the REBEX-1 site is characteristic of th e surrounding region. In spring
and fall, when there is no snow cover, the grass-covered REBEX-1 site is brighter
than predominantly bare farmland of the SSM /I region. Section 6.3.1 described this
brightening, which is due to emission from the absorbing grass cover. Grass bright­
ening is seen to a lesser degree at 37 GHz (Figure 6.7) and not at all a t 85 GHz
(Figure 6.8), although no fall REBEX-1 d ata are available at th a t frequency.
Figure 6.9 graphs the differences between SSM /I estim ated terrain brightnesses
and REBEX-1 terrain brightnesses, 7Ve/i (SSM /I) — 7 tji/i (REBEX). Section 6.3.1
presented similar graphs for the few times a t which rawinsonde d ata were avail­
able and noted th a t the snowpack—which is well established by January—makes the
REBEX-1 site radiometrically colder than the SSM /I EFOV at 19 and 37 GHz. For
example, Table 6.4 summarizes the difference statistics for January indicating th at
the REBEX-1 site iB on average 6.6 K colder than SSM /I a t 19 GHz. The same effect
occurs briefly even in early November when snow covered the REBEX-1 site for about
5 days. Figure 6.6 showed th a t increasing snow is associated with the coldest SSM/I
brightnesses, and we know from REBEX-1 th a t the site was uniformly snow-covered
through all of January. Consequently, these observations suggest th at the SSM /I
viewed a mixed scene with less snow cover on average than the REBEX-1 site.
1 0 /1 /9 2
Date
1/1/93
1 1 /1 /9 2
4 /1 /9 3
Terrain radiobrightness (K)
280260240220-
200 -
19 GHz
SSM/I H-pol
REBEX-1 H-poI.
180-
160-
260
320
I i I i | 1 I i | » I »~1 » l~ r ; t | > I 1 I ' I 1 I 1 I 1 I
340
360
380
400
420
440
460
480
Day from Jan. 1,1992
Figure 6.6: 19 G Hz terrain radiobrightness from S S M /I and R E B E X -1.
1
1 0 /1 /9 2
1 1 /1 /9 2
1 2 /1 /9 2
Date
1 /1 /9 3
2 /1 /9 3
3 /1 /9 3
4 /1 /9 3
5 /1 /9 3
300
Terrain radiobrfghtness (K)
280260240 220 -
37 GHz
SSM/I H-pol.
REBEX-1 H-pol.
200-
180160
140260
280
300
320
340
380
360
400
Day from Jan. 1,1992
420
440
Figure 6.7: 37 GHz terrain radiobrightness from SSM /I and REBEX-1.
460
480
1 0 /1 /9 2
1 /1 /9 3
1 1 /1 /9 2
4 /1 /9 3
Terrain radiobrightness (K)
280 -
260 -
240220 -
85 GHz
SSM/I H-pol.
REBEX- 1 H-pol.
200 -
180-
160 -
1
260
I 1 | 1 I 1 | 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I » | 1 I 1 I 1 I 1 I 1 r ' | 1 T ~r 1
280
300
320
340
360
380
400
Day from Jan. 1,1992
420
440
F igure 6.8: 85 GHz terrain radiobrightness from S S M /I and R E BE X -1.
460
480
*1
i
118
Date
------
_______ _______ _______
19 GHz
40
i
i. - -
i l k
J
l / W
i
-40 - y - 1 i
2
E 40 ,
3
20
UJ
®
uj
CC
°n
iv l
i
| ■I |
i
!i 37 GHz
|
1
1
|
1
|
1
1
1
1
T"' |
• T
1
1
'
1
!
i
II
i
it
1
1
j
a
1
r
H
m
A,
“ 1— 1— 1— 1
1
1^1
1
1
85 GHz
1 1
260 280
1 I 1 1 ■ I 1 I » I 1 I ■ | '» I i |
» |■
300 320 340 360 380 400 420 440 460 460
Day from Jan. 1,1992
Figure 6.9:
Difference between REBEX-1 and SSM /I terrain brightnesses,
jfrfiflfSSM/I) — 7Y£/i (REBEX), a t 19, 37, and 85 GHz. All brightnesses are hpolarized.
119
Channel
(GHz)
19
37
85
TT e r {SSM /I) - Tteu(R E B E X )
e
6.6
1.7
1.0
<re
6.4
7.7
13.9
<7e/D R
0.08
0.09
0.12
Tabic 6.4: Statistics of difference between REBEX-1 and SSM /I terrain brightnesses
in January. All brightnesses are h-pol. DR is the January dynamic range of the
REBEX-1 brightnesses.
O ther features of Figure 6.9 include:
# Negative S S M /I-R E B E X -1 differences in February at all frequencies. Recall
from chapter 5 th a t the REBEX-1 site was cleared of all snow in early Febru­
ary, so even after new snow fell the SSM /I viewed on average a deeper—and
radiometrically colder—snowpack than th a t a t the site.
# High variance in the differences in March. March brightnesses are wildly varying
(at least on the tim e scale shown here) due to melting and rcfreezing in the
snowpack—usually on a diurnal cycle. (C hapter 2 discussed how snowpack
brightness increases with wetness.) The variation in the difference is probably
a function of m elt/freeze timing which is unlikely to be synchronized over the
entire SSM /I EFOV.
# Generally high variability in the 85 GHz difference. 85 GHz January brightness
tem peratures are usually the lowest of the three frequencies, and, consequently,
85 GHz snowpack reflectivity is commensurately high. Add to this th e natural
variability in 85 GHz upwelling and downwelling atm ospheric brightness (see
Figure 6.3) and the result is amplification of the variability seen a t th e other
frequencies.
Figures 6.10 through 6.12 a t the end of the chapter compare SSM /I brightnesses
120
a t v- and h-polarization. Since the REBEX-1 radiometers were single polarization (hpol.), SSM /I is the only source of v-pol. brightnesses available to us. The minimum
polarization difference occurs in late Septem ber as thick vegetation cover obscures
the soil surface. Polarization difference at 85 GHz is always small, suggesting that
scattering and emission by th e cover medium dom inate the signal.
Figures 6.10 through 6.12 show th a t polarization difference is always largest at
19 GHz. Wet soil dielectric constants are higher a t 19 GHz and scattering by the
cover medium is minimized by the longer wavelength. For m any terrain types, the
SSM /I incidence angle is close to the point of v-polam ation total transmission—th a t
is, the Brewster angle,
in the em itting medium. In air, the propagation angle
corresponding to the Brewster angle is:
tanf?at> = cI/3
(6.13)
where c is the dielectric constant of the em itting terrain and is equal to 1.77 for total
transmission at 53.1°. A t the SSM/I frequencies, the dielectric constant of soils may
range from 3 for frozen soils to 15 for warm, wet soils (50], for total transmission
angles of 63.4° and 75.5°, respectively. B ut even at high dielectric constants, v-pol.
emissivity a t 53.1° remains significantly higher than h-pol. The very large 19 GHz
polarization difference during the snowpack season (days 350 through about 450) is
more difficult to explain by this reasoning. The next chapter will address this issue
further when modeling results are presented.
1/1/93
1 1 /1 /9 2
4 /1 /9 3
28026024019 GHz
SSM/I V-pol.
SSM/I H-ool.
20 0 -
180160-
H (K)
Terrain radiobrightness (K)
10/1/92
JL
Difrerence (V —H)
i
!
I
>
1 I I < | 1 T 1 | 1 "I » | 1 I 1 | I I 1 | r ‘ I > | T~l 1 | 1 I 1 |
260
280
300
320
340
360
380
400
Day from Jan. 1,1992
420
I » | 1 I 1 | 1 I 1 | 1I 1
440
460
480
Figure 6.10: 19 G H z S S M /I terrain brightness at vertical and horizontal polarization and th e v-h difference.
1 0 /1 /9 2
Date
1 /1 /9 3
1 1 /1 /9 2
2 /1 /9 3
4 /1 /9 3
280260-
220 -
37 GHz
SSM/I V-pol
SSM/I H-pol
200 -
180160-
H (K)
Terrain radiobrightness (K)
±
Difference (V - H)
I
>
T
| i~l < | » I i ' |
280
300
320
1
I v-|
340
i | i |
i - 1 i | i | i j » I »~ |
360
380
400
Day from Jan. 1,1992
420
I * I 1 I * I
460
480
Figure 6.11: 37 GHz S S M /I terrain brightness at vertical and horizontal polarization and th e v-h difference.
12/1/92
1
1 1 /1 /9 2
2 /1 /9 3
5 /1 /9 3
X
4 /1 /9 3
280260240-1
220 -
85 GHz
SSM/I V-pOl
SSM/I H-pol
200 -
180160-
H (K)
Terrain radiobrightness (K)
1 0 /1/92
X
Date
1 /1 /9 3
Dlfference (V —H)
I
>
I
260
>
|
280
1
I
1
|
300
1 'l
«
|
320
1
I
»' |
340
i
l
<
i
■' l
■
|
1
l
«
|
360
380
400
Day from Jan. 1,1992
i" l
1
|
420
i
|
1
|
440
'
i
r
|
460
i -j
i
|
i
i
480
Figure 6.12: 85 G H z S S M /I terrain brightness a t vertical and horizontal polarization and th e v-h difference.
i
C H A PTER 7
COMPARING MODELS TO OBSERVATIONS
7.1
Introduction
Chapters 3 and A presented the theoretical groundwork for a SVAT-linkcd snow­
pack radiobrightness model and Chapters 5 and 6 described an observational d ata
set comprising continuous terrain brightness and micromcteorological measurements
spanning 193 days. This chapter connects model with observation and, through the
comparison, examines the physical processes th a t tie microwave emission to snowpackatmosphere fluxes.
7.2
M odel initialization and inputs
This section briefly describes how REBEX-1 d a ta drive the Snowflow snowpack
SVAT and the Esnow brightness sim ulation. Since Snowfiow’s inputs are taken di­
rectly from the REBEX-1 micrometeorological record and Esnow uses measured sky
brightness to calculate terrain brightness, it is im portant to clarify which param eters
are modeled and which measured. Some information here is repeated from Chapters 3
and A and the reader should turn to those chapters for more detail about the models.
Also, Appendix A lists fixed Snowflow constitutive param eters, their symbols, and
their values used in these simulations.
Figure 7.1 diagrams inputs to the snowpack simulation. Snowflow’s simulation
124
125
InitiaLstflifl
Soil tem perature profile
Rxed soil moisture
No Snow
Atmospheric Inputs
from REBEX-1
U3, Tair, RH, P,
Qsw, Qlw
Snowflow
SVAT fluxes
Qair, Q latent,
Qprcp, Qemlt
Snowoack profile
Ts, ps, Ws, gs, ds
Sky brightness
from REBEX-1
(TSKY)
19, 37, 85 GHz
Esnow
IerralfibfiflhtDfissgs
(TTER)
1 9 ,3 7 ,8 5 GHz
v- and h-polarizations
Figure 7.1: Schematic of the Snowflow and Esnow inputs and products.
126
always begins with no snowcover and soil tem peratures are the only input constraint
on the initial state. For the results in this chapter, Snowflow initialized soil tem per­
atures using REBEX-1 measurements at six soil depths, interpolating to the fixed
depths of the model soil layers. For layers below the deepest REBEX-1 tem perature
measurement, Snowflow extrapolated tem peratures to a maximum depth of 1.5 m.
Initializing tem peratures of deeper layers had minimal effect on surface tem peratures
in short term trials (2-3 model days.) As discussed in section 3.2, deep tem peratures
and heat flux will have an effect in th e longer term .
Of the fixed Snowflow param eters listed in Appendix A, soil moisture requires
special attention. Snowflow treats total soil moisture as an invariant constitutive
param eter of the soil when in fact it varies dynamically under th e influence of moisture
gradients, gravity, tem perature, and freezing zones. This chapter discusses Snowflow
model results with two soil moisture treatm ents th a t bracket the observed range.
“W et” soil has volumetric moisture content before freezing of x w = 0.43, which is the
highest value measured during REBEX-1 and ju st under saturation a t 0.45. “Dry"
soil has Xu, = 0.20, which is far drier than the lowest REBEX-1 moisture (0.30). This
discussion takes wet soil results to be the more realistic sim ulation and uses dry soil
results to examine soil moisture sensitivity.
In each model tim e step, Snowflow’s only inputs are a set of atm ospheric forcing
variables—wind speed, air tem perature, relative humidity, precipitation, shortwave
radiation, and longwave radiation. All of these variables are taken directly from the
REBEX-1 micrometeorology except longwave radiation which is estim ated from air
tem perature and RH (see section 3.4.4.1). When gaps in the record longer than one
hour occur, Snowflow uses micrometeorology from 24 hours before. All Snowflow
model results have a nominal 15 m inute interval.
127
O utput from the Snowflow snowpack simulation includes soil tem peratures at
the soil surface and six depths and snow density, tem perature, liquid w ater content,
average grain size, and thickness in every modeled snowpack layer. A maximum of 43
snowpack model layers were produced. Esnow uses these d ata to calculate snowpack
emission and reflectivity and then uses input REBEX-1 sky brightnesses to produce
terrain brightnesses. In this chapter, Esnow brightness results have been calculated
about every four hours.
The model-cxpcrimcnt comparisons here arc based on a Snowflow test period
running from December 2, 1992 through February 4, 1993 (REBEX-1 days 337-401).
First snowfall occurred on Dec. 3 but the snowpack was not perm anent until Dec. 14.
Terrain brightness comparisons here begin on Dee. 13. As described in C hapter 5,
snow was cleared from the REBEX-1 site on Feb. 6 so comparisons to the model are
invalid after this point. Focusing on the test period, the following sections evaluate
first the snowpack simulation then the brightness simulation—which, o f course, can­
not be analyzed independently of the model snowpack. The last section discusses the
link between radiobrightncss and snowpack structure, grain size, and wetness.
7.3
Evaluation of the snowpack SVAT
This section compares the Snowflow wet-soil snowpack sim ulation to observations
of four variables from REBEX-1, all of which are measured independently of the
Snowflow inputs. These are snow depth (from Sioux Falls, SD LCD), surface tem per­
ature (from the REBEX-1 IR radiom eter), and soil tem perature and heat flux a t 2 cm
depth. T he discussion also covers the sensitivities of soil tem perature and unfrozen
w ater content to total soil moisture.
Table 7.1 summarizes the modeled-observed difference statistics for all four com­
128
Date
1 2 /1 1 /9 2 1 2 /2 1 /9 2 1 2 /3 1 /9 2 1 /1 0 /9 3
1 /2 0 /9 3
1 /3 0 /9 3
Snow depth
Sioux Falls LCD
Snowflow model (wet soli)
0.2 E
£
:
§■ 0.1 -=
Q
:
0.0
0.1
Difference
E
'w*
f.
a)
Q
<j
0.0 ■”
:
•
:
-o.i -i
340
350
360
370
380
Day from Jan. 1,1992
390
400
Figure 7.2: Modeled and observed snow depths with wet model soil.
parison variables. Figure 7.2 compares modeled and observed snow depths.
The
average snow depth difference is 0.02 m with a standard deviation of 0.027 m. For
comparison, the measurement resolution of the LCD snow depth d ata is 0.025 m.
T he prominent feature of this comparison is the sharp difference on day 364. Before
the snowfall here, the model already has 0.05 m more snow than observed. Then the
model under-estimates the density of the new snow and diverges further from obserVariable
Snow depth (m)
Surf. tem p. (K)
2 cm soil temp. (K)
2 cm heat flow (W /m 3)
A
0.02
-5.5
-1.5
-3.6
<f£k
0.027
5.0
0.96
15.9
o&l DR
0.12
0.17
0.64
0.59
Table 7.1: Comparisons of modeled snowpack variables to REBEX-1 measurements.
A = model - observation, a is standard deviation, and DR is the dynam ic range of
the measured d ata over the test period.
129
Date
1 2 /1 1 /9 2 1 2 /2 1 /9 2 1 2 /3 1 /9 2 1 /1 0 /9 3
1 /2 0 /9 3
1 /3 0 /9 3
........................I ■ ■ * i n n i I i i i i i u i II ...............I t i l I n I i i n i i l l n n 1 I I 1 I I I 1 I I
Snowpack surface temperature
2
280
REBEX- 1
Snowflow model (wet soil)
&
E 260
i n i i i'i 1 1 1 1 1 r 1 1 1 1 1 1 1 1 1 1 1 r rT'i'i r i r i 'i i 1 1 1 i t t i i n t 1 1 1 1 1 11 i t t i i 1 1 1 1 f i
Difference
£
1 1 ) 1111
| i m f 1 1 1 1 1 1 1 1 1 1 1 1 ii i ii
340
\
350
1111111111
) | ii 1 1 1 i i 1 1 1 1 ii i [ i i n
360
370
360
Day from Jan. 1,1992
390
11
400
Figure 7.3: Modeled and observed snowpack surface tem perature with wet model soil.
vations. New snow density estim ates are based solely on air tem peratures, reaching
their minimum value at Tat> = 258 K. Figure 7.3 shows th a t the snowpack surface
tem perature on day 364 was around this value. The snow depths are in closer agree­
m ent after the snowpack deepens on day 377, with th e subsequent ablation occurring
a t comparable rates.
Figure 7.3 compares surface tem peratures from the Snowflow wet soil model to
REBEX-1 observations. T he average difference is -5.5 I< with 5.0 K standard de­
viation. The negative bias could be caused by under-estim ated values of Qiw, the
longwave radiation from the atmosphere. Since this input param eter is estim ated
from air tem perature and relative hum idity only, the warming contribution of clouds
130
is systematically neglected. The other possible source of surface tem perature error is
the latent and sensible heat transfer param eterization, but there is nothing to suggest
th at such an error would have a negative bias.
The remaining directly comparable Snowflow variables are soil tem perature (Fig­
ure 7.4) and soil heat flux (Figure 7.5), both measured a t 2 cm depth in the soil.
For soil tem perature, the average difference is -1.5 K with 0.96 K standard deviation.
Although the magnitudes of these values arc small they are significant nevertheless
because the soil tem perature is near the freezing point. As discussed in section 3.3.1,
soil w ater freezes over a range of tem peratures and this elevates the heat capacity of
the soil and its therm al inertia over th a t range. Consequently, the soil tem perature
solution is sensitive to errors in the tem perature dependence o f the model soil's heat
capacity.
The average model soil tem perature error is a direct consequence of negative bias
in the model snowpack surface tem perature, discussed above, bu t higher model vari­
ability may be caused by differences in either heat capacity or the balance of fluxes
at the soil surface. The rapid divergence of model soil tem peratures from measure­
m ents in the first model day—before REBEX-1 soil reached freezing—suggests th at
the balance of fluxes at the soil surface is the larger source of error.
Figure 7.5
compares modeled and observed heat flux at 2 cm depth and shows the components
of model flux a t the soil surface: the net flux into the soil (Fg = Ftg + Flu,j) , the
quasi-conductive flux between the snow and ground from section 3.4.2 (F #fl), and the
shortwave radiative flux absorbed by the soil surface from section 3.4.3 (F ,WlJ). The
average difference between the modeled and observed 2 cm heat flux is -3,6 W /m 3
with 15.9 W /m 3 standard deviation. The strong diurnal cycle of
is the largest
component of Fg and is the driving force behind diurnal tem perature variation in the
Date
12/11/92 12/21/92 12/31/92 1/10/93
tt
278
276
1 /2 0 /9 3 1/30/93
It H 1■I .1 t «UK l l ................i l l ............. It I-IHJUI I I I I I I «I 11I I I .. .
Soil temperature at 2 cm
REBEX-1
Snowflow model (wet soil)
274
272
270
268
266
n "| 111111111111111111111111| t t n 1111111 r r rj 11111 m i| 11111 u i i j i
6
4
Difference
2
0
-2
-4
-6
* 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 n i i i 1 1 1 1 1 1 1 1 1 1 i i 1 1 1 1 1 1 1 n 1 1 1 1 1 n n n n 1 11 n 1 1 1 1 1 1 1
340
350
360
370
380
Day from Jan. 1,1992
390
400
;ure < : Modeled and observed soil tem perature at 2 cm depth with wet model
I,
Date
12/11/92 12/21/92 12/31/92 1/10/93
i i i i i i i l l . t .111 1. . I .. . . n
n
i I . . . . «n
n
t . m
1/20/93
m
1/30/93
. .1 I ■ . ■ ■ ■ . n l . i i . .
Heat flux Into soil at 2 cm depth
REBEX-1
Snowflow model (wet soil)
60
40
20
0
•20
-40
i' i
100
80
| ‘i i
i i
i
i i
11111n
p -m
p 'T n i 1 1 1 1 1 m
1) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1
it t i
1 1111
Shortwave flux at soil surface
Snowflow model (wet soil)
60
40
20
0
40
20
TTTT 1
Snow-soll heat flux
Snowflow model (wet soil)
0
-20
-40
rjTT n
340
|ll I Ir n
350
1 I 1 I I II | I I M [I I I l | I IT I | I I I l | I I I I | I I I I | I I I I | I II ) | 1
360
370
380
Day from Jan. 1,1992
390
400
ure 1 : Modeled and observed soil heat flux a t 2 cm depth with wet model soil,
dues indicate heat flow into the soil.
♦ .4
133
model soil (Figure 7.4). As discussed in section 3.4.2.1, Snowflow accounted for the
grass m at by increasing the therm al resistance a t the snow*soil interface but it ne­
glected shortwave attenuation by grass inside and at the bottom of the snowpack. The
lack of an observable diurnal cycle in soil tem peratures suggests th a t little shortwave
radiation penetrated to the REBEX-1 soil surface.
The sensitivity of soil tem perature to m oisture content is dem onstrated in Fig­
ure 7.6 which plots 2 cm soil tem peratures from the dry soil model. The average
difference with respect to the observed tem perature is -2.8 K with a standard devia­
tion of 2.4 K. Figure 7.7 plots the wet and dry soil unfrozen w ater content calculated
as a function of tem perature as in section 3.3.1. Although dry soil tem peratures arc
up to 4.7 K colder than wet soil tem peratures, all the moisture in the drier soil re­
mains unfrozen through most of the test period. This is because the freezing point
of the soil water is reduced to 268.0 K in the dry soil while it is 272.5 K in wet
soil. Consequently, the heat capacity of the drier soil is comparatively small and its
tem perature reacts more quickly to changes in heat flux.
7.4
Radiobrightness comparisons
This section compares the radiobrightness simulations of the linked snowpack
SVAT and emission models to observed terrain brightnesses from the REBEX-1
ground-based radiometers and SSM/1, The discussion also covers brightnesses from
the wet and dry soil models, the relationship between snow wetness and brightness,
the relative effects of soil moisture and the snowpack a t 19 GHz, and the sensitivity
*
of brightness to snowpack layering.
Figures 7.8 through 7.10 compare model terrain brightnesses a t h-pol, with groundbased observations from REBEX-1. Table 7.2 summarizes the difference statistics
Date
12/11/02 12/21/92 12/31/92 1/10/93
1/20/93
i i n . i i I ««t i m i l I n i i i h i i I i i i n i i . . I i i . m
. .. I . i i m
1/30/93
i . i I. . . . .
Soil temperature at 2 cm
RE8EX-1
Snowflow model (dry soil)
276
276
274
272
270
268
266
| i i 1 1 1 1 1111 it
111
ii
11
|n n
11111111111
ii ii
11
ii n i r 1 1 1 n i i-p i n p
6
4
Difference
2
0
-2
-4
-6
•8
;ure '
!.
']n
40
1 11111
i p 1 1 1 1 1 1 1 1 | i 1 1 1 1 h i »| r 1 1 1 1 1 1 1 1 |t i i n i i 1 1 1 1 1 1 1 1 1 r 1 1 1 1
350
360
370
380
390
400
Day from Jan. 1,1992
Modeled and observed soil tem perature a t 2 cm depth with dry mode]
135
Date
12/11/92 12/21/92 12/31/92 1 /10/93
• ‘« ■“
0 .4 E,
1 ■ * ■
........ I . I I . I H
I t I H
. I IH
■ ■ I■ . .
1/20/93
l■
1/30/93
. Modeled unfrozen soil water (wet soil)
0 .3 -
? 0.2 | 0, :
o.or>
E
o
|
Modeled unfrozen soil water (dry soil)
0 .4 0 .3 . -
0 2
0.1
-
0.0 -
340
350
360
370
380
Day from Jan. 1,1992
390
400
Figure 7.7: Modeled unfrozen soil water content for model soils with initial m oisture
volume fractions of 0.43 (top) and 0.20 (bottom ) before freezing.
136
along with those for the SSM /I data, discussed below. The usefulness of a brightness
comparison in a remote sensing context is the information content of the modelobservation difference. Model brightnesses a t 19 GHz h-pol. (Figure 7.8) arc at first
colder than observed, then briefly warmer, and at the end of the test period the dif­
ference is highly variable. Since interaction with th e dry snowpack is weak a t 19 GHz.
coldness in the 19 GHz model is likely caused by the dielectric contrast at the soil
surface—th a t is, cither the contrast is too high in the model or the un-modclcd grass
cover increases the observed brightness. A sharp dip in the observed brightness around
day 370 may be the dielectric signal of wetness a t the top of the soil or the efTccl of
dielectric contrasts in the snowpack layers. Lastly, the high-variability period, which
is distinct at 37 GHz as well, is a result of partial m elt and rcfrcczing cycles in the
snowpack combined with wetness a t the top of th e model soil. These phenomena arc
all discussed in more detail below.
Figure 7.9 compares 37 GHz brightnesses from the models and REBEX-1. Except
for the middle period (days 365-385), there is little in the comparison to suggest
th a t any particular process is unmodeled, although the simulation fails a t times to
m atch the details of the processes. In the early period (days 347-364) during which
19 GHz modeled brightness were cold, 37 GHz modeled brightnesses are unbiased.
Since at 273 K the dielectric constant of w ater a t 19 GHz is about twice th at at
Channel
(GHz)
19
37
85
REBEX-1, h-pol.
A
oa
cta/D R
-11.5 22.0
0.29
8.1
14.5
0.16
10,6 14.7
0.13
SSM /I, h-pol.
A
ca
<ta/D R
•11.0 19.4
0.38
10.8 14.8
0.23
8.3
18.8
0.16
SSM /I, v-pol.
A
(ta <ta/D R
-15.1 11.6
0.72
3.4
10.7
0.20
3.7
18.8
0.17
Table 7.2: Comparison of modeled brightnesses (I<) to h-pol. observations from
REBEX-1 and h-pol. and v-pol. observations from SSM/1. A = model - observa­
tion, a is standard deviation, and DR is the dynamic range of the measured data
over the test period.
Date
1 2 /1 1/$2 1 2 /2 1 /9 2 1 2 /3 1 /9 2 1 /1 0 /9 3
■ t I ■ H
M I u. .............
260g
1 /2 0 /9 3
1 /3 0 /9 3
I i-i-l-l i 1 i II t i I . i I
m
240-
$ 220 ©
200
|
CD
s
180 H
160140
19 GHz, h pol. brightness
REB EX-1
Models (wet soil)
r 11i t 11 r r n 11 ii 11 1 1 1 rp"i 11 1 1 1 ii
11
11111111 ii i
] 1 1 1 1 1 ii
340
1111
$50
h
1 1 1 1 1 1 1 1 111111
ii ■| ■i i i 1 1 i i i p
111111
360
370
380
Day from Jan. 1,1992
1111111r
i|in
1 111
390
j i i i i 11
n |
1 1 ii
400
Figure 7.8: Modeled and observed 19 GHz h-pol. terrain brightness with wet model
soil and ground-based observations.
37 GHz, the modeled dielectric contrast at th e soil surface and sensitivity to soil
moisture are reduced a 37 GHz. From day 388 to 401, snowmelt events dom inate
the 37 GHz signature in both the simulation and th e measured data. W here the two
diverge strongly, informa tion about the tim ing of partial snowmelt may be inferred,
as discussed below.
Figure 7.10 compar^i:s 85 GHz modeled and observed brightnesses.
The best
m atch—and the least r<^sidual information—occurs between day 370 and 385 where
19 and 37 GHz brightm sses were least precisely modeled. The outstanding features
of the 85 GHz d ata are t lat brightnesses are very low and variability very high. These
138
Date
12/11/92 12/21/92 12/31/92 1/10/93
. I » 111
lit
. ... I I 1 I I
1/20/93
I 1 . t-i-i-l-l n i l ...........I l l l . l l ......
1/30/93
.......... I l l l l i m
260g
240 “
g? 220 I
200-
cn
£
37 GHz, h-pol, brightness
REBEX-1
Models (wet soil)
1 8 0 “;
160140'
1 I I | I I I H 'l I I I I n
I I I I I I I I I I I I | T 1' I 1 I I I I I |*1T I T | I I I I I I I I I I I 1 I I 1 I I I 1'P
Difference
-6 0 ~ i 111111
340
1 1 1 1 ) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ] 1 1 1 ty T V i i 1 1 1 1 1 1 m 1 1 1 m i r p
350
360
370
380
390
400
Day from Jan. 1,1992
Figure 7.9: Modeled and observed 37 GHz h-pol. terrain brightness with wet model
soil and ground-based observations.
features are related because, by KirchhoiTs law, low emissivity means high reflectiv­
ity, and the reflected source— the sky—is highly variable at 85 GHz, as discussed in
Chapter 6. Emissivity is low at 85 GHz because of scattering in the dry snowpack
th a t elevates extinction and decreases the effective depth of emission. Low emission
depths mean th a t snow thicknesses beyond a threshold value have little effect on
emission and neither do soil conditions.
Figure 7.11 uses SSM /I terrain brightnesses (Tt e r in C hapter 6) to evaluate the
v-pol. model performance, The model-SSM/I difference statistics (Table 7.2) indicate
th a t the model deviates least from observations when compared to 37 and 85 GHz v-
139
Date
12 /1 1 /9 2 1 2 /2 1 /9 2 1 2 /3 1 /9 2 1 /1 0 /9 3
1 /2 0 /9 3
1 /3 0 /9 3
260
240
2
$
220
|o>
200
£
180
160
140
60
5
-
20
■c
-20
<
-40
03
Difference
40
8©
B
.c
cn
85 GHz, h-pol. brightness
REBEX-1
Models (wet soli)
0
-60
340
350
360
370
380
Day from Jan. 1,1992
390
400
Figure 7,10: Modeled and observed 85 GHz h-pol. terrain brightness with wet model
soil and ground-based observations.
pol. SSM/1 brightnesses. In contrast, modeled 19 GHz v-pol. brightness is on average
15 K colder than SSM /I which is the worst model-observation mismatch. Since v-pol.
radiation is least sensitive to dielectric contrasts (the Brewster angle cfTect discussed
in section 6.4), the weak contrasts in dry snow due to layering are unlikely to affect
it strongly. The closest 19 GHz v-pol. model-SSM/I brightness m atch for dry snow
occurs around day 375, and this is when modeled unfrozen soil w ater content was at
its lowest value (about 25% by volume in Figure 7.7).
The sensitivity of all three frequencies to soil moisture is examined in Figure 7.12
which plots h-pol. brightnesses from the wet and dry soil models. T he plots show the
140
Date
12/11/92 12/21/92 12/31/92 1/10/93
i i «i i i i i i
£
1/20/93
1/30/93
................1.1.1 l n i i i i . n l n i n i i i i l M m i i . i l i_i_t.il i i . t
1 ■i i i .
260240-
|
220 -
§
2 0 0 -j
ai
180
£
19 QHz, v*pol. brightness
SSM/I
Models (wet soil)
I I | I I I l ' | 'I I I I | I T I I | I I I I | I I l l | I T l I | I I I T | I I I I | I I I I | I I I I | I I I l | i
ii
r p
260240-
|O)
§
220
200
160
37 GHz, v-pol. brightness
SSM/I
Models (wet soil)
I I | I I I I | I I I I | l l I I | I I IT' I' I I I I | I I I I | I I I I | ' l I I I | I I I I | I I'I I | I I I l ' | I I I I [ I
260£
240-
$ 2200)
| 200o
g
180
160-
85 GHz, v-pol. brightness
SSM/I
Models (wet soil)
140 tTi 111117 1 r i 1111 i i | ii 11"| 11 ii 11111| 11 n | 111 i|'i 11111111111111 it 1 i p
340
350
360
370
360
Day from Jan. 1,1992
390
400
Figure 7.11: Modeled and observed v-pol. terrain brightness a t 19, 37, and 85 GHz
with wet model soil and space-based observations from SSM /I.
141
Date
12/11/92 12/21/92 12/31/92 1/10/93
1/20/93
....................... I n ..................... I ......................
1/30/93
l i n n
Brightness (K)
260
✓— -n/J
240220 200 180160140
19 GHz, h-pol. brightness
Models (dry soli)
Models (wet soil)
¥ M T" l l I I | n
I I | I I I I | I I I I | I I M | I I I I | 11 1 I I I I I I I I I I I I I I I I I I I I I I I T T T | I
Brightness (K)
260240220 200
180
160
140
37 GHz, h-pol. brightness
Models (dry soil)
Models (wet soil)
) | p 1 1 n n 1 1 1 1 1 i i 1 1 11 r p
111
p
i 111 n
i i
)11 1 11111111 n
1 1 11111111111
Brightness (K)
260240220200-
180160140
65 GHz, h-pol, brightness
Models (dry soil)
Models (wet soil)
11 p'i 111 i i 11 [ 11 rr| 111 rj i i 11 ; 111111111111 n 1111111111 [ 11 i i 11111 j i
340
350
360
370
360
Day from Jan. 1,1992
390
400
Figure 7.12: Modeled h-pol. terrain brightness a t 19, 37, and 85 GHz with both wet
and dry mode) soil.
142
brightening effect of lower soil moisture and also the overall decreased influence of
soil conditions with increasing frequency. For example, the average difference between
wet and dry soil brightnesses is 15.4 K at 19 GHz but only 9.7 K at 37 GHz. The two
cases arc almost indistinguishable at 85 GHz except after day 393 when the snowpack
has thinned and the wet soil is mostly thawed.
Figures 7.13 through 7.16 present additional d ata on model-observation mis­
matches a t 19 GHz, The discussion above suggested th a t 19 GHz emission is pri­
marily a function of the am ount and state of soil m oisture. The top two graphs of
Figure 7.13 dem onstrate th a t this is in fact the case for modeled brightness, which
rises and falls in synchronization with partial freezing and thawing of the model soil.
REBEX-1 19 GHz brightness with 2 cm soil tem perature observations arc also plot­
ted and the following argum ent suggests th a t its variation is also the result of liquid
water content. On day 337 at the beginning of th e plot, the soil a t 2 cm is ju st
above freezing and 19 GHz brightness is at 270 K. Compared with the IR radiometric
tem perature (see Appendix B), the 19 GHz emissivity was 0.97 or higher from day
324—the last tim e rain was recorded at the REBEX-1 site—until day 344 when it
began to decline. Video images of the REBEX-1 site indicate light snow cover as early
as day 338 with surface tem peratures remaining below freezing from day 338 to 344.
From day 344 to 349, the surface tem perature was often a t or above freezing. These
d ata suggest th a t light sub-freezing snow fell on a dry soil on day 338 and had little
effect on emissivity until some melting occurred between day 344 to 349. On day 349
a more substantial snowpack formed covering and insulating the still warm soil from
the cold air. And as Figure 7.13 shows, the 2 cm soil tem perature rose slightly under
the snowpack from day 349 through 355. Some melting at the snowpack base likely
occurred, adding to the soil moisture.
143
Date
12/11/92 12/21/92 12/31/92 1/10/93
i i i i i i n
I . i .
...............I
t t
1/20/93
i t i i ( i i I . . <i i i i . i I i i i . n
1/30/93
■i i I i i i i i i i . n l i i t i i
260-
£■ 2 4 0 8} 220 o
| 200 o>
§ 180-
160140
«
19 GHz, h-pol. brightness
Models (wet soil)
I I 111 I I I 11 I 1 1 1 1 I I I | I I T I | I I I I | 1 1 1 I | I I I I | I I I I p i I I | I I I I | I I I I | I I I 111
Modeled unfrozen soil water (wet soil)
0.4
0.3
0.2
g
1 I l"| I I I I | M "
| II I I | I I II | I I I I | II I I | I I I I | I I 1 1 | II 1 I | I II I | II I I | I I I I | I
260
% 240
a>
220
|
CD
19 GHz, h-pol. brightness
S 200
REBEX-1
160-1 i i~p i11 n 111) T111n ii 1111 r 1111 ii-) i u» 11m i ) 11111111111 m 111 n 11
g
da 274 H
E
j© 2 7 2 - Soli temperature at 2 cm
REBEX-1
I I TpT Ii iI IH 1 1 1 H 1 1 1 1 1 1 rr i[ i n n
I»“N
E
£
a
0
a
. -
0 2
0.1
11
Snow depth
- Sioux Falls LCD
|\
Snowflow model (wet soil) ^
n
11
ii 1 1 1 1 1 1
| 1 1 1 1 1 1 1 1 111 n
111
m i 11
_ __ ____
^
■
a . 1111j 111 I'p i i 11111111111| i n rji 11ip i i i [ T i l 11i t t i 11m 111n p
. -W
T|
340
350
360
370
380
390
400
Day from Jan. 1,1992
0 0
Figure 7.13: Plots of modeled 19 GHz h-pol. terrain brightness, modeled soil surface
unfrozen w ater content, observed 19 GHz h-pol. terrain brightness, observed 2 cm soil
tem perature, and modeled and observed snowpack depths.
144
As the 2 cm tem perature dropped below freezing around day 361, some portion
of the soil moisture began to freeze. At the same time, 19 GHz brightness reached
a tem porary minimum a t 223 K, which stood until day 368. A two-day decline
111
brightness began on day 368 leading to the lowest 19 GHz brightnesses around 190 K
on day 370. Soil tem perature at 2 cm rose to a maximum of 272.9 K on day 270
commensurate with the declining brightnesses and consistent with melting at the
soil surface. If soil moisture beneath the snowpack is as dynamic a quantity as this
sequence suggests then a coupled moisture and energy transfer model for freezing soil
is required to achieve an accurate brightness simulation. Simple modification of the
fixed soil moisture in the Snowflow model would fail to match the dynamic variations
described in this scenario.
A possible alternative to th e soil moisture variation scenario is th a t snowpack
stratification is the source of observed 19 GHz dynamics. The surface of a snowpack is
subjected to compaction from wind and atmospheric conditions, and this effect is not
modeled by Snowflow. W hen surfaces are buried by new-fallen snow, interfaces may
develop with m oderate dielectric contrasts. A scries of moderately sharp contrasts
can have the same darkening effect on emission as a single strong boundary. Creation
of such boundaries and their subsequent disappearance through compression of the
snowpack could explain the variability in REBEX-1 19 GHz brightness.
Figures 7.14 and 7.15 test the enhanced layering hypothesis by comparing the
effects of enhanced dielectric contrasts to those of the dry soil model. For these graphs,
the Esnow snowpack emission model was modified such th a t th e dielectric contrast
at each snowpack layer boundary was increased by a factor of two by modifying
the greater of the two dielectric constants. The upper lim it on th e modified dielectric
constants was th a t of pure ice (3.15). Figure 7.14 shows the effect of enhanced layering
145
for h-pol. brightnesses which are reduced by about 15 K at 19 and 37 GHz. The change
is minimal at 85 GHz and when the snowpack is wet because in these cases emissions
originate near the top of the snowpack. T he effect of layering is also small at. vpol. for all frequencies because of the Brewster angle effect, with v-pol. brightnesses
decreasing by 1.4,3.1, and 3.6 K on average a t 19, 37, and 85 GHz, respectively. This
test shows th a t layering may be the cause of 19 GHz h-pol. darkening in general. But
with respect to the temporal signature of 19 GHz brightness at the REBEX-1 site
(and from coincident SSM /I measurements), the model with enhanced layering still
fails to sim ulate the initial gradual decline in brightness and the strong dip around
day 370. Figure 7.15 shows 19 GHz SSM /I brightnesses at v- and h-pol. with plots of
brightnesses from the three model treatm ents: wet soil (the baseline case), dry soil,
and wet soil with enhanced layering. W hat this d ata shows is th a t in all cases there
is dynamic information missing from the modeled brightnesses. The wet soil baseline
model matches v- and h-pol. SSM /I brightnesses simultaneously for a short period
around day 374 and the dry soil model matches some points between day 350 and
355. These results arc consistent with the hypothesis th a t soil moisture variation is
driving brightness dynamics. And since the net effect of enhanced layering is to cool
h-pol. brightnesses a t all limes, there is no indication th a t layering in the natural
snowpack is responsible for increased brightness variation.
A nother test of layering is to examine SSM /I d a ta for another site where tem ­
peratures are colder and the snowpack is deeper.
Figure 7.16 shows the 19 GHz v-
and h-pol. SSM /I terrain brightness near the Langdon Experim ent Station in North
Dakota (48.75N latitude, 98.33W longitude). Also given are the polarization differ­
ence and snow depths from Local Climatological Data, In January, the snow depth
at Langdon is up to 0.6 m deep compared to only 0.2 m at the REBEX-1 site. Yet
146
Date
12/11/02 12/21/92 12/31/92 1/10/93
1/20/93
1/30/93
I H 1 I I 1 I I I I I I I I I I I I t 1 I H I I I 1 I I 1 1 « 1 1 I I I I 1 I 1 I 1 I 1 1 1 I I I I I 1.1.11 I I I 1J.I I
19 GHz, h-pol. brightness
Models (wet soli)
Models (wet soil, layering)
2602
240-
8 220-
o
|
o>
s
200 *
100160140 i i U i i n | i ii i i i ii r p i vi-| i i n | i n r p n 111111111 ri 111111 rn 11n m i
37 GHz, h-pol. brightness
Models (wet soil)
Models (wet soil, layering)
260
2
240
8 220
|o>
200
5 100
160-
140
260
2
I I |TTf"l | H I I | r n ITH'I'I | I I I I | I I I I | I I I I | I I I I | I I I I | I I I I | I I I I | I I IT'I I
65 GHz, h-pol. brightness
Models (wet soli)
Models (wet soil, layering)
240-
g 220-
|
200 -
£
100-
o>
160-
140 <
ITTI I | I I I T'| ITTTJTI I I | I I ITj I
340
350
360
370
380
Day from Jan. 1,1692
390
400
Figure 7.14: Modeled h-pol, terrain brightnesses with dielectric layering artificially
enhanced.
147
Date
1 2 /1 1 /9 2 1 2 /2 1 /9 2 1 2 /3 1 /9 2 1 /1 0 /9 3
M 1 ...............! ■
280
g
i ■n
11 i I I I I I I I I
II i
1 /2 0 /9 3
1 /3 0 /9 3
I i ■i » ■■n i I i
■■ i * ■ n
i n i
260
jjj 240
Io> 220
19 GHz brightness
— v-pol. SSM/I
—•— h-pol. SSM/I
m 200
1 8 0 -\
t' l | I I I I | I T T * '| I I I I | I I I I | I I I I |"l I 1 1 | I 111'l'l'l I I | I I I l"| ' l I I I | I I I I T I I I I ' l l
v-pol. models (wet soil)
h-pol. models (wet soil)
280260£
2408
o 220J=
o> 2 0 0 a
VII | ii 111111111 ii 11 ii 11 111 I I | l i i i 11111 p 111 1111 1111 111l 111 111 f l »
v-pol. models (dry soil)
h-pot. models (dry soil)
5? 260
m 200tt111n
280 -i
£
260-
1 1 n 1 1 1 1 1 r p 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 p i n | ii i n
v-pol. models (wet soli, layering)
h-pol. models (wet soil, layering)
240g
g
s 220.c
CJ) 2 0 0 •ft
•
m
160-
1 1 1 1 1 1 1 1 1
’i m
1 6 0 -, ti
111
340
n '|
|m
350
1 1 1 1
11
itt
111111
| i »11111111111111 m
360
370
380
Day from Jan. 1,1992
| n i-i-p
U
] 1 111 p
390
1 1 111
if i
400
Figure 7,15: SSM /I 19 GHz v- and h-pol. brightnesses (top graph and overlays)
compared to model results with wet soil, dry soil, and wet soil plus enhanced dielectric
layering.
1
1 2 /1 /9 2
4 /1 /9 3
260240220 200-
19 GHz (Langdon, ND)
SSM/I V-pol.
SSM/I H-pol.
Difference (V —H)
0 .6 -
Snow depth (m)
1 1 /1 /9 2
280 —
V — H (K)
Terrain radiobrightness (K)
10/1/92
_L
Date
1 /1 /9 3
2 /1 /9 3
J ___________ L
Snow depth
;
0 .3 -
i i i ■ t *1 i i i i t i •[ i i i i i t » i 1 i i i * * 1 i
I • •
260
260
300
320
340
360
380
400
420
Day from Jan. 1,1992
t i r f" t
1 > 1 i »' i *
440
460
480
Figure 7.16: SSM /I 19 GHz v- and h-pol. brightnesses and their difference at Langdon, North Dakota.
149
at 20 K, the average polarization difference for the m onth is less than th a t for Sioux
Falls, which was 28 K (wet snow periods excluded). In addition, the polarization dif­
ference at Langdon decreases slightly with increasing snow depth in December as the
snow-soil boundary is obscured. Average air tem peratures a t Langdon in December
and January were well below freezing (257 and 255 K, respectively). If we assume
th a t such cold tem peratures imply very low liquid w ater content in the soil, then
these d ata suggest th a t layering contributes some to decreased h-pol. brightness but
th a t soil conditions arc the more dynamic driver.
7.5
Comments on snowpack structure, grain size,
and wetness
The strongest tem poral snowpack radiobrightncss signature is caused by partial
snowmelt. Figure 7.17 plots the correspondence between model snowpack liquid water
content and modeled and observed 37 GHz h-pol. brightness. Note th at modeled
brightness spikes on days 390, 393, and 394 each produce similar maximum brightness
tem peratures—th a t is, once a threshold am ount of moisture is present the brightness
tem perature saturates at about 265 K. The four arrows point to modeled snowmelt
events th a t correspond to observed brightness jum ps. W here model and observation
are in disagreement, the contrast may be used to adjust param eters of the snowpack
SVAT model th a t are otherwise fixed. For example, the snowmelt event on day 390
reaches a maximum wetness of 1.84 mm. A 25% reduction in the absorbed shortwave
radiation-representing, for example, an increase in the snowpack shortwave albedo—
reduces maximum wetness by 50% to 0.9 mm . Of course, more detailed study is
needed to determ ine the appropriate feedback param eters and gains but this example
dem onstrates the process.
150
Dale
12/11/92 12/21/92 12/31/92 1/10/93
I » • • ............... 1I t i
I ........I i 1 i i i n
M ■1 1 ..............
1 /20/93
m i l i . n
1/30/93
.......... l i n n
260g
240-
8 220-
I 200 H
o
§
180 H
37 GHz, h-pol. brightness
REBEX-1
160H
140
TTrrrn'i 1111111111111 r p r i >| »11 r| 111 n 111111 n ' i | i n 1111111111 n i
260g- 2 4 0 ■
8 220Q>
|
200 O)
g 180160
140
—1 1 1 1 1 1
3.0-1
E
E
£
&
Q
i
3
S
37 GHz, h-pol. brightness
ModelB (wet soil)
n - | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i i 1 1 1 1 r 1 1 1 1 1 1 n i 1 1 1 1 1 1 1 1 1 1 1 1 1 ii
1 1 1 1 1 1 11
Snowflow modeled snowpack wetness
2 *°:
i.o ;
0.0 -
350
360
370
380
Day from Jan. 1,1992
390
400
Figure 7.17: Modeled and observed h-pol. 37 GHz terrain brightnesses and modeled
total snowpack liquid water content. The arrows indicate modeled partial snowmelt
events th at correspond to observed brightness jum ps.
151
E 0.20-a
Day 392.817
Day 392.879
Day 392.941
-i— |----i— 1— r
i— |— i— |— r
£ 0.15-r
0.10
2O) 0.05 -=
I 0.00 | i I i I I
0.0
1.0
2.0
? 0.20 -a
Day 393.003
0.0
1.0
2.0
0.0
1.0
2.0
Day 393.127
Day 393.065
§ 0 .1 5 -i
0. 1 0 -
0 .0 5 I
-i
0.00
0.0
3•
[— 1---- 1---- T
1.0
2.0
Day 393.189
0.0
1.0
2.0
Day 393,251
0.0
*]
1.0
2.0
Day 393.313
•
0
“
0.10
2
0.05 :
1
0.00. =—
-J
-
j
, ,j , - i— |— «— |— i— ^
I 1~' I 1
0.0
1.0
2.0
0.0
1.0
2.0
0.0
1.0
2.0
3._3
Snow liquid water content (m /m x 100)
Figure 7.18: Snow liquid water content profiles during a cycle of partial m elt and
refreeze.
The cycle of snowpack wetting is shown in detail in Figure 7.18 which chronicles
partial m elt and refreezc on day 392-393.1 First m elt occurs a t 12:15 CST and begins
near but not at the surface of the snowpack, which is 0.18 m deep a t this time. The
maximum wetness occurs at 17:00 CST, and the snowpack is completely refrozen
by 02:00 CST on day 393. There are two implications of this d ata. T he first is
th a t satellite measurements—which for a sun-synchronous orbit have a nominal 12
hour spacing—need to be synchronized such th a t one of the daily measurements
occurs during the coldest part of the day—ideally, 04:00-06:00 local tim e. The second
'Fractional day is in Universal Tim e (UTC) which is 6 hours ahead o f local time at Sioux Falls
(CST). 393.0 fractional day corresponds to 18:00 local time on day 392.
152
0.20
Iw
•:
Day 355
015i
c 0.10 4
£ 0.05 4
u>
a
X 0.00
t—
0.0 0.5
0.2 0 -
r — i—
1.0 1.5
Day 385
Day 365
0.0 0.5 1.0 1.5
0.0
Snow grain diameter (mm)
Day 375
1— T
0.5 1.0
T
1.5
Day 365
0 .1 5 0.10 -
0.05
0.0 0.5
I
I
1.0 1.5
0.0 0.5 1.0
Snow grain diameter (mm)
I
1.5
Figure 7.19: Snow grain diam eter profiles from the Snowflow model.
implication concerns the shape of the m elt profile. If the m elt region extends to and
wets the soil surface, then residual moisture may be left a t the soil surface, which is
separated from the cold air and sky by the insulating snowpack. Consequently, when
the snow completely refreezes but the soil stays wet, the brightness after the mcltrefreeze cycle will be colder than before at frequencies which penetrate the snowpack.
Another snowpack property affected by partial melt-refreeze cycles is the grain
size. As discussed in section 3.4.7, grain growth is accelerated by the presence of liquid
water. Figure 7.19 shows example grain size profiles in 10-day intervals through the
test period. On day 375 the grain size a t all levels is about 1.0 mm or greater. A t the
same tim e, both model and REBEX-1 85 GHz brightnesses are at their lowest point
to date—around 180 K—indicating strong scattering (see Figure 7.10), Even lower
brightnesses (155 I<) were observed around day 395 after several melt-freeze cycles.
Model and observation diverge a t this point, with the 85 GHz model about 30 K
153
warmer than observations. A probable cause is th a t model grain size did not develop
as quickly as grains in the natural snowpack. In contrast, at 37 GHz (Figure 7.9 the
model m atches observations to within 5 K during the re-freeze portion of the cycle
on days 395-396 while the 19 GHz model is about 40 K too cold. Since the model
soil is almost completely thawed here (see Figure 7.7), 19 GHz model darkening is
directly attributable to the high dielectric contrast. Then the 37 GHz darkening is
probably due to separate effects: larger grains in the natural snowpack and wet soil
in the model.
Figures 7.20 through 7.22 show pairs of SSM/1 brightness images th a t dem onstrate
how the mclt-frcezc process correlates over spatial scales. The d a ta arc from days 401
and 405 near the end of the period of melt-freeze cycling which lasted from day 397
to 407.2 The day 401 image was acquired at about 17:24 local tim e and the day 405
image at about 06:44 local time and probably correspond with times of high snowpack
wetness and refreeze, respectively, at the REBEX-1 site. T he strongest mclt-frcezc
signal can be seen at 85 GHz in Figure 7.22. In the bottom image, a darkened region
extends from about 43N to 45N latitude and 95W to 97W including the REBEX-1 site
at 43.72N, 96.5W. In the top image the same region is of comparable brightness to the
surrounding terrain. The consistently brighter region to the west may have a wet snow
cover th at extends over into the REBEX-1 region during daylight on day 401, 19 and
37 GHz images in Figures 7.20 and 7.21 show the same pattern bu t with the contrast
between wet and frozen snow decreasing with frequency. This decrease is consistent
with the REBEX-1 observations of melt-freeze cycles. By day 405 the REBEX-1
site had undergone several melt-freeze cycles with com m ensurate opportunities for
accelerated grain growth.
Consequently, it is likely th a t the REBEX-1 region is
3See the figures in Appendix B for REBEX-1 data extending past day 401.
154
radiomctrically darker a t 85 GHz than other regions th at did not undergo melt-freeze
cycles.
155
-113
10 GHz Horizontal Pol (Aim. Ramoved)
1002:4O1:2324 UTC
-108
-*7
-ft
1 pixel - 0.3 deg.
160 180 200 220 240 260 300 300
Itadlebrighlnm (K)
-V i
10 GHz Horizontal Pol. (Aim. Rammed)
1002:405:13:44 UTC
-106
—07
:
-ft
160 180 200 220 240 260 280 300
RodlobrigMnm (K)
Figure 7.20: S S M /1 19 GHz h-pol. images from February 4,1992 at 23:24 UTC (top)
and February 8, 1992 a t 12:44 UTC. See text for description.
156
*»•
1
si*..
200 280 2W0
ItodtobrtflMiw* 00
&
fto m F eb^
r . 6a n d
« l$
February 8 , 19»-
£
$
£
£
*
«
for "
,
^
,0" '
-
^
U TC (t01"
157
85 GHz Horizonlol Pol. (Atm, R«mov*d), High P m .
189 J : 4 0 1 ^ 2 * UTC
*0T
\ pixel ■ 0.1 d»q
100
100
200
220
240
200
200
090
RodtobrigbtnvM 0 0
OS CM*
Horizontal P o t («">. R *™ '*4)- W«H R~
i O«3!40S:114* UTC
I pImI - 0.2
160 100 200 220 240 200 200 300
RodtobrightMW 0 0
Figure 7.22: SSM /I 85 GHz h-pol. images from February 4, 1992 a t 23:24 UTC (top)
and February 8, 1992 a t 12:44 UTC. See text for description.
CH APTER 8
CONCLUSIONS, CONTRIBUTIONS, A ND
RECOM M ENDATIONS
This chapter summarizes the m ajor results and implications of the radiobrightness d ata analysis in Chapters 6 and 7. The chapter also lists the contributions of
the thesis, discusses some lessons learned from experimental work, and makes rccom*
mendations for further study.
8.1
Conclusions
The m ajor results of this thesis come from the comparisons of simulated and
observed snowpack radiobrightncsses in Chapter 7. The principle implications of
these comparisons include: (a) 19 and 37 GHz radiobrightncsses arc sensitive to
the dynamically-varying unfrozen soil moisture beneath the snowpack, (b) snowpack
stratification may reduce these brightnesses but is not as dynamic a driver as soil
wetness, (c) dry snow 85 GHz brightness is sensitive to grain size development during
snowpack partial m elt and sky brightness is the main driver of its variability, and
(d) the sharp contrast between the brightness of dry and partially melted snowpacks
may be explained by a lossy-cloud model of wet snowpack emission. The careful
treatm ent of grass may be critical to producing a sim ulation th a t accurately models
energy exchange between the snowpack and ground—especially regarding shortwave
158
159
radiation penetration. Soil wetness modeling requires the handling of m elt-w ater from
the snowpack and a coupled moisture-heat transfer model for freezing soil.
The m easurem ent of microwave brightness by ground-based instrum ents has been
shown to be a viable way of simulating long-term space-borne monitoring, although
the large ficld-of-view of satellite instrum ents m ust be taken into account. Compar­
isons between ground-based and satellite radiobrightnesses indicate th a t brightnesses
correlate b etter when a snowpack is present than a t other times because of the relative
homogeneity of regional snowfall compared to vegetation cover. There is less agree­
m ent between ground- and space-based measurements during episodes of snowpack
partial melt and rcfreczc because of the magnitude of the w et-dry radiobrightncss
difference and the fact th at the process is not usually synchronized across the SSM/1
ficld-of-view. Also, it is likely th a t variability in atmospheric w ater vapor content
and tem perature a t times adds to the difference between ground- and space-based
measurem ents—especially a t 85 GHz. Yet with only simple atmospheric corrections
o f SSM /I brightnesses, the differences between ground- and space-based m easure­
m ents were within about 10% with respect to the January snowpack’s radiom etric
dynam ic range at all frequencies.
The use of REBEX-1 d a ta with models suggests several ways in which future
experim ents of this type may be improved,1 REBEX-1 d ata were used to drive the
snowpack SVAT in the same way th at an atmospheric model would drive its landatm osphere boundary condition param eterization. The key param eters missing in
this context were down welling longwave flux and precipitation from a heated gauge.
As for model diagnostics, the most critical missing param eter was unfrozen soil water
content, which may be measured autom atically through tim e domain reflectometry
1Some o f these lessons have already been incorporated in implementation of REBGX-3 in Alaska,
which was begun in August, 1994.
160
techniques. O ther measurements th at would have been useful—and are possible with
existing methods—include soil surface tem perature under the snowpack, tem pera­
tures inside the snowpack, albedo (shortwave reflectivity), and Bowen ratio (the ratio
of sensible to latent heat transfer rates) for closure of the land-atmospherc energy
balance. It would also aid modeling if one of the key sources of measurement error—
frost and snow obstructing radiation instrum ent domes—could be elim inated. Also.
C hapter 5 spends a great deal of tim e correcting REBEX-1 sky brightnesses for the
effects of the reflector used in their jncasurcment. The accuracy of these measure­
m ents could be improved if the brightnesses could be measured directly w ithout a
reflector.
The results presented in this thesis suggest th a t a SVAT model sim ulating radiobrightncss may be a useful diagnostic tool in atmospheric modeling. Consider an
atmospheric model with a spatial resolution comparable to th a t of the EASE-Grid
radiobrightncsses and run for a historical test period like th a t of C hapter 7—that
is, December, 1992 and January, 1993. On a grid-point by grid-point basis, modeled
brightnesses from the atmosphcre-SVAT-emission model could be evaluated against
SSM /I measurements of the actual terrain, and differences could be used to verify
aspects of the model’s performance. For example, the distinct tem poral radiobright­
ness signal of melt-freeze cycles are a sensitive indicator of th e am ount of energy
incident on and absorbed by the snowpack. Differences in the tim ing of melt-freeze
episodes between model and measurements could be used to judge the model’s net
land-atmosphere energy exchange rate. A nother possible feedback param eter is snow
grain size, Divergence between modeled and observed 85 GHz brightness would track
grain size development which is closely tied to snowpack tem perature gradients and
internal heat flux in dry snow. Lower modeled brightnesses would indicate larger
161
grain sizes and greater flux rates than in the historical record. Of course, th e model
relating grain size development to tem perature gradients would need improvement
over the one presented here to make this difference meaningful. Lastly, since the
wetness of frozen soil is closely tied to the deposition o f energy in the snow and soil,
19 GHz darkening due to increased soil wetness might also be a sensitive indicator of
energy exchange rate differences.
The link between radiative balance and snowpack state may be exploited by a
well-tuned snowpack SVAT-emission model to evaluate the shortwave and longwave
fluxes from an atmospheric model. A snowpack SVAT’s param cterizations of sensible
and latent heat flux and albedo can be tuned through extended measurements of the
complete snowpack-atmosphcrc energy balance. W ith a well-tuned snowpack SVAT,
radiobrightness would be most sensitive to radiative forcing from a model atmosphere.
As described above, 19 GHz brightness is sensitive to shortwave radiation penetrat­
ing to the soil and 37 GHz brightness is sensitive to net radiation through snowpack
melt-refrecze cycles. Both these processes are tied to time-averaged conditions so
once or twice daily satellite measurements would be adequate samples. Since radia­
tive forcing from the atmosphere is a direct function of the percent cover and height
of clouds, radiom etric monitoring of snowpacks may be a good way to determ ine the
accuracy of the cloud component of an atmospheric model. This is dem onstrated by
the example in section 7.5 th at showed th a t—on a day when the snowpack melted
partially—an artificial 25% reduction in th e total diurnal shortwave flux reduced the
m aximum snowpack wetness by 50%. Consequently, 37 GHz brightness would be sen­
sitive to cloud cover and could be used to find the percent cover range corresponding
to observed snowpack conditions.
Linking models of atmosphere, snowpack, and radiobrightness may also present
162
a way to improve the monitoring of snowpack param eters from space. Snowpack
equivalent w ater content and onset of m elt are the prim ary param eters of interest
in snowpack monitoring. W ith the aid of an atmospheric model th a t simulates the
current state o f the atm osphere (often called a “nowcast” ), a snowpack SVAT could be
used to infer snowpack history and soil conditions. Since a particular radiobrightness
signature may be indicative of multiple snowpack states, a priori information from
a measurem ent-adjusted model can help eliminate possible interpretations of new
data. For example, increasing snowpack depth and grain size both lead to darkening
of 37 GHz brightnesses. If snowpack m elt and rcfreezc occur, then grain size will
increase while snow depth decreases. If the model accurately simulates the mcltrcfrcczc cycle, then the darkened brightnesses would not be mistaken for a signal of
increased snow depth.
8.2
Contributions
This thesis presented a record of concurrent microwave radiometric and meteoro­
logical measurements a t a northern G reat Plains site (REBEX-1) and developed a
S VAT-linked microwave radiobrightncss model th a t sim ulated the observed snowpack.
The m ajor contribution was the REBEX-1 data set which includes 192 days worth of
continuous h-pol. radiobrightness measurements a t 19, 37, and 85 GHz. The snow­
pack SVAT and radiobrightness models are implementations of existing knowledge
but their combination and use with the unique REBEX-1 record represents a novel
approach in the development of radiom etric models and their testing. The thesis also
dem onstrates the resampling of a long-term SSM /I brightness record to a common
resolution at a single earth surface coordinate. Successful comparisons of this data
with terrain radiobrightnesses from REBEX-1 show th a t the resampling technique is
163
sound and useful and th a t ground-based radiometric measurements arc meaningful
surrogates for high-temporal space-based observations.
8.3
Recommendations
The successful implementation of REBEX-1 suggests the usefulness of further
long-term ground-based studies of th e link between radiobrightness and antecedent
weather. The analysis here covered only a portion of the REBEX-1 d ata set. Further
analysis of the d ata concerning th e radiobrightncss of grass-covered terrain in fall
(lasting about 60 days) and during spring thaw (about 46 days) is suggested. Also, a
repetition of the experiment with improvements to the instrum entation recommended
above would be valuable in resolving some of the ambiguities in the REBEX-1 data.
A more northerly site may be more representative of the Great Plains as a whole.
Also, the site's vegetation cover should be consistent with th a t o f the surrounding
terrain to facilitate comparisons to space-based instrum ents.
The SVAT-linked emission model may be improved by the addition of a coupled
heal and m oisture transfer model of the soil, although further empirical work on the
relationship between tem perature below freezing and the unfrozen water content of
organic soils needs to be done. Current research on the growth of snow grains and
a param eterization of new snow density accounting for wind packing should also be
incorporated. The total albedo and distribution of shortwave radiation in shallow
snowpacks with grass need to be further examined although improvements to the
snowpack SVAT may be made immediately by increasing the num ber of shortwave
absorption bands. Lastly, the empirical correction to independent scattering discussed
in C hapter 4 needs to be re-examined in the context of finding a comprehensive but
com putationally efficient solution to the problem of microwave radiative transfer and
164
scattering in snowpacks.
The usefulness of dynamic SVAT-linked radiobriglitncss models can only be ex­
ploited if satellite observations arc frequent enough to capture th e events of interest.
The minimum useful measurement periodicity for capturing events like partial melt
and refreczing of the snowpack is twelve hours. Each additional measurement could
be used to determ ine the tim ing of the m elt event. The coverage of each SSM/1 in­
strum ent is incomplete a t the latitudes of th e G reat Plains and two sun-synchronous
satellites arc required to guarantee diurnal coverage. Based on th e results in this the­
sis, the preferred tim ing of the first two satellites would be at 04:00-06:00 local equator
crossing time. The maximum benefit from additional satellites could be gained with a
12:00-14:00 local equator crossing time. In addition, a radiom eter channel a t 10 GHz
would be useful as a probe of soil surface conditions since radiation a t this frequency
would interact less with the dry snowpack and be more more responsive to soil water.
APPENDICES
u
1G5
A PP E N D IX A
SNOW FLOW PARAM ETERIZATIONS
This appendix gives formulas for variables used in Snowflow (C hapter 3). Sec­
tion A.6 lists values for the param eters used in these formulas and those in C hapter 3.
A .l
Saturation vapor pressure and density
The saturation vapor pressure, pwt, is found by solving the Clausius-Clapcyron
differential equation:
d ln p m
dr
k(T)
IU T 2
(A .l)
where /* is either lv in the ease of vaporization or /, for sublimation. Colbeck [Cl]
suggests the following solution for use in snow modeling:
(A.2)
where pwt0 is empirically determined a t T = T0, Then the saturation vapor density
is:
(A .3)
ICC
167
Snowflow requires the first, second, and third derivatives of f ( T ) and these are given
by:
f'(T ) =
rm =
f m(T) —
A.2
r jt
R JT2
t£
H ’
<a-4)
PUT)
R JT3
- ( s y ,+ f e ) T
*
(A'c>
Wet bulb tem perature
The wet bulb tem perature, 7 ^ , is given by recursive evaluation of the relationship:
T« = T.ir where
& !2<Z“*]££(1 _ RH)
Cp.airP
(A . 7)
is the latent heal of vaporization /„ or sublimation /„ p U T ) is the vapor
pressure of saturated air a t tem perature T (from (A.2), cr is the ratio of the dry air
and water vapor gas constants (/fj/tfw ), Cp,a,> is the specific heat capacity of air, p is
the air pressure, and R H is the relative humidity.
A.3
Water vapor diffusion coefficient
The effective water vapor diffusion coefficient is given by:
D,(T)
=
=
(J rY ° T"D
P \ T 0J
CDeT n®
(A.8)
where p0 is atmospheric pressure at sea-level and C ot and n o are constants.
A.4
Composite conductivity factor, FI
The composite conductivity factor is:
F 1(T ) = K + lkD ' ( T ) f ( T ) = K + fl C0 t7,nD/'( 7 ')
(A.9)
16S
where K is therm al conductivity and 4 is either /„ or
A .5
Freezing o f water flowing into dry snow
W ater a t T — Te th a t flows into a dry layer will freeze until an equilibrium is
reached. Snowflow finds the am ount of freezing by first assuming th e equilibrium
tem perature is T„. Then the water content of the equilibrium state would be (in m):
W„ = W, -
({C m + ^ r T . ) T , - {C m + ^ T ) t )
l/f t , V.
2
2
/
(A , 0)
where W0 is the depth of w ater before freezing occurs, (dgp , y is the mass of ice
in the layer, T is the tem perature of the layer before the w ater was added, and
C m and C m are coefficients of the tem perature dependent heat capacity of ice,
CicefT1) — C m + C m T . If Weq is less than zero, then all the water th a t seeped in
eventually froze and the equilibrium tem perature of the layer is found from:
m
Ttq
y / C h T E ^ - C m
----------------— ---------------
/*
,,v
(A .11)
where
Kp* (I, +{Cm + ^r.)r„) + (</./>,)'(C„, + S?T )T
■
A.6
=
(W
+ * .
•
(A a2 )
Summary o f Snowflow parameters
The following tables list Snowflow param eter values th a t are (a) set by the user,
(b) empirically determined but fixed, and (c) fundam ental physical constants. All
param eter values are given in SI units.
169
Table A .l: Snowflow param eters set by th e user.
Symbol
A
dao
dg,opt
V
Q„
Wm
W„
Description
snowpack albedo (range 0.4-0.95 [62])
top soil layer thickness
optimal initial snow layer thickness
air pressure
heat from below the bottom soil layer
weight fraction of non-quartz m atter in dry soil
weight fraction of quartz in dry soil
initial soil water volume fraction
Value
0.7
0.001 m
0.02 m
1.013E5 N /m a
0 J /m a
0.75
0.25
0.20 or 0.43
Table A.2: Snowflow empirical param eters and their
sources.
Symbol
Cpav
Cs
Cfl
Cg, |
Cg, 2
Cm
Cn a
DtOg
Description
average dry soil heat capacity
snow compaction coefficient
snow compaction coefficient
snow grain growth coefficient
snow grain growth coefficient
ice heat capacity coefficient
ice heat capacity coefficient
water vapor diffusion coefficient
in ground
water vapor diffusion coefficient
in snow
d
zero displacement height for snow
longwave emissivity of snow
Clui
size
factor of soil solids
9o,p
von Karman constant
ka
water vapor diffusion tem perature
exponent in ground
water
vapor diffusion tem perature
no,*
exponent in snow
irreducible water saturation constant
Sr
volume fraction of adsorbed soil water
2 ati$
volume fraction of w ater a t field
x/w
capacity
•Tp
volume fraction of soil voids
roughness length for snow
screen height (air tem perature)
wind speed height
•3
continued on next page
Value
900 J/kgK
0.08 1/K
0.021 m3/k g
5.0E-7 m4/k g
4.0E-12 m a/k g
92.95 J/kgK
7.369 J/k g K a
Xt,'1.61&5 m a/s
Source
(39)
[38|
[38]
|38]
[38]
[37]
[37]
[38]
0.92E-4 m a/s
[38]
0m
0.97
0.125
0.4
2.3
[48]
[38]
[42]
[48]
[38]
6
[38]
0.04
0.07
0.1
[38]
[42]
[42]
0.45
2.0E-3 m
1.8 m
10 m
REBEX-1
[46]
REBEX-1
REBEX-1
170
continued from previous page
Symbol Description
unfrozen soil moisture factor
Qtt/u
unfrozen soil moisture factor
0uw
snow
viscosity coefficient
no
therm al conductivity of dry air at T 0
Aair.rf
therm
al conductivity of ice
A,
mean therm al conductivity of
An»
minerals and organics
Aerpanie therm al conductivity of organic m atter
A,
therm al conductivity of quartz
Au,
therm al conductivity of water
soil bulk density
Pb
intrinsic density of quartz
Pi
mean intrinsic density of
Pm
non-quartz soil minerals
snow shortwave attenuation factor
V0
ice shortwave attenuation
Vi
Value
0.238
-0.360
3.6E6 N s/m 2
0.0241 W /m K
2.18 W /m K
2.93 W /m K
Source
(41]
[41]
[38]
[63]
[42]
[42]
0.25 W /m K
8.16 W /m K
0.561 W /m K
972 kg/m 3
2.6GE3 kg/m 3
2.8E3 kg/m 3
[42]
[63]
[63]
REBEX-1
[42]
[42]
0.084
1.72E3 m
[37]
[37]
Table A.3: O ther physical param eters uBcd in Snowflow.
Symbol
Cp,0ir
Cpi
Cpt»
<7
'/
/.
U
Pui*0
IU
nw
To
Id
PI
Po
Pi
Put
a
Description
specific heat capacity of dry air (at 273 K)
specific heat capacity of icc (at 273 K)
specific heat capacity of water (at 273 K)
acceleration of gravity
latent heat of fusion (at 273 K)
latent heat of sublimation (at 273 K)
latent heat of vaporization (at 273 K)
saturation water vapor pressure at 273 K
dry air gas constant
water vapor gas constant
freezing point of water
dry adiabatic lapse rate
dynamic viscosity of water
density of air a t sea level
intrinsic density of ice
intrinsic density of water
Stefan-Boltzmann constant
Value
1005 J/k g K
2106 J/k g K
4218 J/k g K
9.8 m /s 2
0.334E6 J /k g
2.834E6 J /k g
2.501 E6 J /k g
610.5 N /m 2
287.05 J/k g K
461.51 J/k g K
273.15 K
9.8E-3 K /m
1.78E-3 N s/m 2
1.225 kg/m 3
917 k g /m 3
1000 k g /m 3
5.G696E-8 W /m 2K<
171
A P P E N D IX B
DATA FROM REBEX-1
B . 1 Microwave radiometer performance evaluation
To test the calibration accuracy and radiometric resolution of the microwave ra­
diometers, I placed a known source (microwave absorber) in front of the radiometer
during regular experiment cycles. The use of the complete experiment cycle for these
tests was necessary to simulate experiment conditions including internal load TPRmodc gain factor rccalibration.
Table D.l gives the results of these tests.
Here,
radiometric resolution is the standard deviation of the errors. I did not include the
day 403 1448 and 1504 UT calibration checks in the radiom etric resolution calcu­
lations because the Eccosorb tem perature was more than 3 K over the ambient air
tem perature at th a t time. The discrepancy suggests th a t there was a tem perature
gradient between the Eccosorb surface and the therm istor embedded in it. For these
times, Table B .l compares th e 19 GHz apparent brightness to the Eccosorb therm istor
tem perature and the 37 and 85 GHz brightnesses to air tem perature as approxima­
tions to actual em itting tem peratures. In the future, the Eccosorb should be shielded
from wind and direct sunlight and should not be brought into direct contact with the
surface of the heated radiometers.
19 GHz
Day
279
Time
1813
1823
288
1743
1753
1854
1903
1913
289
1644
1658
1703
37 GHz
T ecco
296.7
296.7
297.4
297.4
279.9
279.8
279.9
279.8
281.8
281.2
296.9
295.1
297.6
296.8
281.2
280.0
280.2
280.2
281.8
280.3
A
0.2
*1.1
0.2
-0.6
1.3
0.2
0.3
0.4
0.0
-0.9
281.1
281.5
278.1
278.3
281.7
281.7
278.5
278.5
0.6
0.2
0.4
0.2
Tap
277.9 279.3
277.9 278.3
403 0238 273.4 273.5
273.7 274.5
0243 273.3 [273.3
273.6 274.3
1448 272.3 271.7
272.7 273.3
1504 273.0 271.2
273.2 273.0
Average A
Radiometric resolution
1.4
0.4
0.1
0.8
0
0.7
-0.6*
0.61
-1.81
-0.2*
0.24
0.61
85 GHz
T ecco
296.7
296.7
297.4
297.4
279.9
279.8
279.9
297.0
296.3
297.6
297.3
278.0
277.9
278.6
A
0.3
-0.4
0.2
-0.1
-1.9
-1.9
-1.3
281.8
281.2
80
281.1
281.5
278.1
278.3
277.6
277.9
277.9
273.4
273.7
280.6
279.9
80.8
280.5
281.2
276.8
276.4
277
277.2
277.3
273.7
273.9
-1.2
-1.3
0.8
-0.6
-0.3
-1.3
-1.9
-0.6
-0.7
-0.6
0.3
0.2
273.6
269.8*'
269.8*
269.8*
269.8*
273.8
266.2
269.0
267.7
268.7
0.2
-3.6*
-0.8*
-2.11
-1.1*
-0.61
0.82
Tap
T ecco
Tap
A
273.4
273.7
273.3
272.9
273.4
272.5
-0.5
-0.3
•0.8
269.8* [271.3
269,8* 271.4
269.8* 271.4
269.8* 268.6
1.51
1.6*
2.6*
-1 01
-0.53
'These data were not included in radiometric resolution calculations as noted in the text.
s Air temperature used in place of measured Eccosorb temperature.
Table B .l: Calibration check results. T ecco is th e tem perature of the Eccosorb target
at the tim e the T ap were measured. There is insufficient d a ta to calculate 85 GHz
radiometric resolution.
173
B.2
Soil and canopy moisture samples
I took soil samples from the REBEX-1 site on five days in October and November.
1992, using an 8.255 cm (3.25 in) diam eter cylindrical coring tool. A 6.35 cm (2.5 in)
high bit screwed on to the end of the coring tool, holding in place a set of rings which
lined the cylinder. From the lop of the bit, we inserted rings of 2, 2, 2, 8, 2, and 8 cm
heights. To take samples, we drove the coring tool into the soil to a depth of 12.35
cm. We twisted the tool to break the soil at th e bottom of the bit and extracted the
core. We then sliced off the soil extending from the bottom of the bit, unscrewed the
bit from the cylinder, and removed the core from the cylinder surrounded by the bit
and the three lowest 2 cm rings. We sliced between the rings and between the bottom
ring and the bit with a knife to make three samples of 2 cm thickness. We then slid
the soil remaining in the bit into a 4 cm ring and removed th e excess from the bottom .
T he soil samples then spanned 0-2, 2-4, 4-6, and 6-10 cm depths. We usually took
grass samples before coring by cutting the grass over the sampling position as close
to the soil horizon as possible.
I first dried the grass and m ost of the soil samples in a 70°C oven until the mass
had reached a constant value. The drying tim e was 9 days for the grass samples and
3-3.5 days for the soil samples. I then dried all of the soil samples a t 105°C for an
additional 24 hours, as is the usual practice, The gravim etric calculation of soil and
grass moisture as a mixing ratio to dry m atter is:
Aftwl Mdry
w = TMf dry
------ICi
— M |,re
where w stands for
wet sample,
<r, ,
(B J )
,
gravimetric moisture content, Mu,etis the measured mass of the
Mdry is the measured mass of the
dried sample, and Mtare is the container
(tare) mass. To calculate volumetric moisture content, I first estim ated the soil bulk
174
density by taking the maximum ratio of dry soil mass to core volume. By this method
the soil bulk density was 0.972 gm /cm 3, which is within the wide range of possible
organic soil densities. Volumetric moisture content, 0, is then given as:
0= —
(B.2)
Pw
where pb is the soil bulk density, and pw is the density of water. The soil and grass
d a ta arc given in Table B.2.
B.3
D ata from the National Weather Service
To augment d ata obtained by TMRS and MMS during REBEX-1, 1 acquired
two data sets from the National W eather Service: the October, 1992 through April,
1993 monthly Local Climatological D ata (LCD) for Sioux Falls, SD and selected
Radiosondc/Rawinsondc Observations and the LCD’s from Huron, SD. The LCD’s
include daily summaries of snow depth, which could only be roughly estim ated from
REBEX-1 video stills, and precipitation, which was unavailable from the REBEX-1
rain gage during cold weather. T he LCD’s also give reports of sky cover, ceiling, and
weather at six times per day. These d ata were used in conjunction with the Huron
rawinsondcs to determ ine when the sky was cloud free and to calculate the clear-sky
downwclling radiobrightncsses discussed in Sections 5.5.4 and 5.5.5. The rawinsondc
data set includes atmospheric profiles of pressure and tem perature from ground level
to about the 10 m bar level and dew point and relative humidity to th e height at which
dew point falls to about -50°C.
175
Day
Time
Depth
Tare
Mass
Wet
Mass
287
2100
Grass
0-2 cm
2*4 cm
4-6 cm
6-10 cm
Grass
0-2 cm
2-4 cm
4-6 cm
6-10 cm
Grass
0-2 cm
2-4 cm
4-6 cm
6-10 cm
Grass
0-2 cm
2-4 cm
4-6 cm
6-10 cm
Grass
0-2 cm
2-4 cm
4-6 cm
6-10 cm
Grass
0-2 cm
2-4 cm
4-6 cm
6-10 cm
0*2 cm
2-4 cm
4-6 cm
6-10 cm
12.26
8.99
9.00
8.99
9.04
12.24
9.02
9.00
9.03
9.03
12.26
9.00
8.98
9.02
9.00
12.23
8.97
9.03
9.01
9.05
12.29
9.06
9.02
9.08
8.99
12.27
9.08
9.07
9.02
8.99
7.25
7.20
7.22
7.20
22.17
152.12
110.85
100.67
260.40
20.59
126.17
122.15
124.04
237.95
26.91
141.10
127.36
119.24
223.16
35.72
117.81
121.19
130.73
234.07
25.84
138.99
126.34
129.38
239.31
32.30
101.61
120.95
123.04
227.72
125.74
127.98
133.84
233.01
288
1400
2100
289
1400
2100
290
307
1400
2100
Dry
Mass
70°C
18.12
115.75
85.75
78.77
204.55
17.88
96.90
95.07
97.36
186.79
22.06
108.73
98.42
92.39
172.34
25.64
90.37
93.93
101.51
182.88
20.68
108.36
98.38
101.55
188.64
24.89
n r i.o e
95.31
97.71
181.01
—
—
—
—
Gravimetric
Moisture
70°C | 105°C
—
—
0.69
113.01 0.341 0.376
84.69 0.327 0.346
77.89 0.314 0.331
201.81 0.286 0.304
—
—
0.48
95.65 0.333 0.352
93.89 0.315 0.333
96.25 0.302 0.319
184.42 0.288 0.305
—
—
0.49
107.27 0.325 0.344
97.15 0.324 0.343
91.34 0.322 0.339
171.02 0.311 0.322
—
—
0.75
89.15 0.337 0.357
92.59 0.321 0.342
100.32 0.316 0.333
180.42 0.294 0.313
—
—
0.62
106.72 0.308 0.330
97.00 0.313 0.333
100.21 0.301 0.320
185.78 0.262 0.303
—
—
0.59
79.95 0.285 0.306
93.92 0.297 0.319
96.48 0.286 0.304
178.08 0.272 0.294
—
89.38
0.443
—
94.87
0.378
—
100.37
0.359
—
176.43
0.334
Dry
Mass
105®C
Vol.
Mois.
105°C
—
0.365
0.336
0.322
0.295
—
0.342
0.324
0.310
0.296
—
0.334
0.333
0.330
0.313
—
0.347
0.332
0.324
0.304
—
0.321
0.324
0.311
0.295
—
0.297
0.310
0.295
0.286
0.431
0.367
0.349
0.325
Table B.2: Soil moisture sampling data. Masses are in grams and include tare mass.
Drying was first done at 70°C then a t 105°C. Gravimetric moisture content is ta b ­
ulated at both tem peratures and volumetric m oisture content is tabulated only a t
105°C.
176
B.4
Overview plots of continuously measured pa­
rameters
The graphs in this section summarize the measured param eters as well as several
derived param eters from the entire period of REBEX*1. The param eters are 19, 37.
and 85 GHz terrain apparent radiobrightncsses, reflector-measured sky radiobrighlnesses, estim ated sky radiobrightncsses (sec the main text for a description of the
estim ation process), therm al infrared sky tem perature, global radiation, net radia­
tion, wind speed a t 10 m , soil tem peratures, heat flux in the soil, relative humidity,
rainfall, therm al infrared surface tem perature, air tem perature, terrain radiobrighlness spectral gradients, T P R gain factors, estim ated 85 GHz T P R gain factor (for
the uncalibrated period discussed in the main tex t), and snow depths. These figures
contain terrain and sky radiobrightncsses edited for flawed data, with points removed
th a t were cither out of range or taken when the internal radiom eter tem peratures
drifted from their design values. Sky radiobrightncsses and IR sky tem peratures th at
were in error due to incorrect reflector positioning have also been removed. C hapter 5
describes in detail reflector position errors and the editing methodology applied to
the sky data. Because of a communications error described in Section 5.4, the IR
radiometer sky d ata also contains additional incorrect points but these have not been
removed here.
The terrain radiobrightness spectral gradients, Sgy shown in Figure B.8 are given
by:
h ~~ Ji
where f \ and / j are radiom eter frequencies and f i is less than / 3.
300 -
Apparent radiobrightness (K)
280-
260II
240-
220 -
200 -
180-
-—
ii
19 GHz
37 GHz
85 GHz
160-
1 4 0 -1
I 1 I 1 I 1 i ■ I i I » | i I » |
340
360
380
400
420
Day from J a n . 1 ,1 9 9 2 (UT = C S T + 0.25)
Figure B .i: Sum m ary of terrain apparent radiobrightnesscs a t 19, 37, and 85 GHz.
3002 8 0 -
1
Sky radiobrightness or temperature (K)
2 6 0 2 4 0 -
IR radiometer
220 2001 8 0 1 6 0 1 4 0 -
120-
00
100
19GHZ
37 GHz
85 GHz
T
320
1 I 1 I 1— i— *— I— »— I— «— I— »— i— «— |— i— i— i— |— i— i—i— |— i— i— i— j— i— r
340
360
380
400
420
440
460
D ay from J a n . 1 ,1 9 9 2 (UT = C ST + 0.25)
Figure B.2: Sum m ary o f reflector-m easured sky radiobrightnesses at 19, 37, and 85 GHz and therm al infrared sky tem perature.
300-
260240-
19 GHz sky radiobrightness
M easured
Estim ated
220 -
Radiobrightness (K)
200 -
180160140120 100 -
-
20-
1 '— I— 1— I— 1— I— 1— I— I— I— 1— I— »— I— I— |— «— I— i— j— i— I— i— j—i— I— I— j— i— I— i— j—»—i—i— j— i— r
280
300
320
340
360
380
400
420
440
460
D ay from J a n . 1 ,1 9 9 2 (UT = C ST +• 0.25)
Figure B.3: Sum m ary o f reflector-m easured sky radiobrightness and estim ated sky radiobrightncss at 19 Cillz.
300
280
37 GHz sky radiobrightness
Measured
Estimated
260
240
220
200
180
160
140
120
100
80
60
40
20
0
-20
-40
-60
30
300
320
"•— i— »— i— *— |— »— i— >— i— i— i— i— |— i— i— i— j— i— i— i— j— i— r
340
360
380
400
420
440
460
Day from J a n . 1,1992 (UT = C ST + 0.25)
igure B.4: Sum m ary o f reflector-m easured sky radiobrightncss and estim ated sky radiobrightncss at 37 GHz.
Radiobrightness (K)
85 GHz sky radiobrightness
M easured
Estim ated
-20-
I
•40 “ I
:
:
:
I
i
'
I
:
j
;
:
•
I
;
;
. ; *
;
j
I
I
■
!
:
:
|
j
' 6 0 * t — 1— i— 1— i— 1— i— 1— i— »— i— i— |— i— i— i— j— i— i— •— i— i— i— i—j— i— i—«—j— i—i— i— j— i— j— i— j— i— r
280
300
320
340
360
380
400
420
440
460
from
(U T C S T
Day
Jan. t, 1992
=
+0.25)
Figure B.5: Sum m ary o f reflector-m easured sky radiobrightncss and estim ated sky radiobrightncss at 85 G Hz.
1000-1
£600—
.2200 -
1 Iin x 1;!I.!
.»
• ■« t
»•
I?
•
•
- 200-
: !
-4 0 0 -
i
h
Wind speed at 10 m (m/s)
8 0 0 -
Global radiation
Net radiation
1 0 m wind speed
2 9 0 -1
Soil temperature
cm -------- 16 cm
4 cm -------- 32 cm
8 cm
64 cm
2 8 5 -
- 2
Heal flux (w /m 2)
2 8 0 -
g 2 7 5 -
E 2 7 0 -
2 6 5 -
w
\
Heat flux into soil at 2 cm
t — >—l—i—i—«—|—•—i—•—|—i—i—i—i—i—i— i—i—i—i—i—i—i—i—i—j—i—r
340
360
380
400
420
440
460
Day from Jan . 1,1 9 9 2 (UT = CST + 0.25)
Figure B.6: Sum m ary of REBEX -l global and net radiation, 10 m wind speed, subsurface soil tem peratures, and soil heat flux
a t 2 cm depth.
100-1
nO
*5
E
8 0 -
Rain (mm/cycle)
S'
6 0 -
3
X
4 0 -
a
>
a
a>
DC
2 0 -
QO
2 9 0 -
'2 8 0 -
g 270
Surface
2 cm depth in soil
Air
1—•—i—i—i—*—i—i— |— i— i—i—i—i—i—i—|—i—i—«—|—i—i—i— |—i—i— i—|— i—i—i— |—i—i— i—|—
280
300
320
340
360
380
400
420
440
460
Day from Ja n . 1 ,1 9 9 2 {UT = CST + 0.25)
Figure B.7: Sum m ary of REBEX-1 relative humidity, rainfall per experim ent cycle, therm al infrared surface tem perature, air
tem perature, and soil tem perature a t 2 cm depth.
Spectral gradient (K/GHz)
19 to 3 7 GHz
19 to 85 GHz
37 to 85 GHz
00
TPR gain factor
0^
Am sift
19 GHz
85 GHz (measured)
37 GHz
85 GHz (estim ated)
I—•—l—i—|—i— i— i— |—i— i— i— |—*—i— i— |—i— i— i—i—i—i—i— |— i—i— i— |—i—i—i—j—i— r
300
320
340
360
380
400
420
440
460
D ay from J a n . 1 ,1 9 9 2 (UT = C S T + 0.25)
Figure B.8: Summary of terrain apparent radiobrightncss spectral gradients and T P R reference load gain factors.
40 - ]
30-
JZ
Snow depth from gauge
Apparent height of grass
obscuring snow gauge
Snow depth at Sioux
Falls, SD
20-
10-
280
300
320
340 ,
360
380
400
420
Day from Jan. 1,1992 (UT = CST + 0.25)
440
460
Figure B.9: Sum m ary of REBEX-1 snow depths estim ated from video stills of th e site and from National W eather Service
reports a t Sioux Falls, SD.
186
B.5
M onthly plots of continuously measured pa­
rameters
The graphs in this section are monthly compilations of m ost of the physical
param eters measured during REBEX-1. Each month from October, 1992 through
p
April, 1993 is covered by two sets of graphs in consecutive figures. The param e­
ters graphed in the first set for each month arc terrain apparent radiobrightncsscs,
reflector-measured sky radiobrightncsscs (no corrections applied), global and net ra­
diation, and wind speed a t 10 m. The param eters in the second set for each month
arc subsurface soil tem peratures, vertical heat flux a t 2 cm depth in the soil, relative
humidity, rainfall, air tem perature, and therm al infrared surface tem perature. Some
terrain and sky radiobrightncss d ata have been edited out as discussed in Section B.4.
320 -
OCTOBER 1992
3 00-
£
*
3
280H
i.ftr
I 2 60-
Surface
— 19GHz
37 GHz
240S
Tm
3
« 220 H
cc
200-
180-■
i n ' 1 i »~r» i »~i i i i i » i i i ■ i i i i i i i i i i i i i i i i i i
i
i | i i > | i i < i i i i i i-[ i | t i i |
3 200
»
?
i •, , t
r iooo
- 800 _JO
- 600 ®
- <00 g
- 200 f
,i
rj ' l t ’ • l
: I
A ||’ :
;V j l fl : ;
\
I 1
» u U U- L5
i
I
■ i i i ; * :
10 m wnd speed
i
278
280
r °
1
~ *200 3„
- -400 ~
‘ V*"S*
i ) r | i | t- |- i | i I i |
276
a
282
284
286
288
290
292
294
296
Day from Jan. 1,1992 (UT a CST + 0.25)
298
T 'l 1 1 1 i 1 I T I 1 --600
302
304
306
Figure B.10: O ctober terrain (surface) apparent radiobrightnesses and reflector-m casurcd sky radiobrightncsscs at 19 and 37
G H z, net and global radiation, and wind speed a t 10 m .
290
2cm
Soa temperature:
4cm
32 cm
8cm
64 cm
- 80
Temperature
60
280
40
275
20
270-
Heat flux (W/m“)
(K)
285
265
100
‘20
Soil treat flux at 2 cm :
260
I
5
I
t
Rain (mm/cyde)
RH (%)
60
60
40
Relative humidity ■
20
“ 0
Temperature <K)
300-1
' Temperature: -— Surface
290
280
270
260
OCTOBER 1992
276
278
280
282
284
286
288
290
292
294
296
Day from Jan. 1,1992 CUT= CST ♦ 025)
298
300
302
304
306
Figure B .l l : O ctober subsurface soil tem peratures, vertical heat flux at 2 cm depth in th e soil, relative hum idity, rainfall, air
tem perature, and therm al infrared surface tem perature.
320 -
Surface
196Hz
37 GHz
Radlob rig fitness (K)
300280260240-
240-
200 -
Sky
19 6Hz
37 GHz
120 -
Wind spead (m/s)
Radtobrightness (K)
200 -
gL;*' :
600 ■
400 2
10 m wind speed
306
-200 3
I"1'! 1 I 1 1 1 I 1 < 1 I 1 » 1 I 1 I 1 1 1 I 1 I 1 I i 1 1 I i | i I i | * I i 1 i I t | I M 1 ■
308
310
312
314
316
318
320
322
324
326
328
330
332
Day from Jan. 1 .1992 (UT = CST + 0.25)
Figure B .I2: N ovem ber terrain (surface) apparent radiobrightnesses and reflector-m easured sky radiobrightncsscs at 19 and 37
G Hz, net and global radiation, and wind speed at 10 m .
Temperature
Sofl temperature:
2cm
4cm
16 cm
32 cm
285
80
280
60
40
275
20
270
0
265
-20
100
5
80
4
60
3
2
Relative humkSty
1
20
Raln (mm/cycle)
RH (%)
So9 heat flux at 2 cm
40
Heat flux (W/m*)
(K)
290
0
I
Surface
Air : '
Temperature
(K)
300
280
270
260
NOVEMBER 1992
306
308
310
312
314
316
318
320
322
324
326
Day from Jan. 1,1992 (UT = CST 0.25)
328
330
332
334
336
Figure B.13: N ovem ber subsurface soil tem peratures, vertical heat flux at 2 cm depth in th e soil, relative hum idity, rainfall, air
tem perature, and therm al infrared surface tem perature.
320-
Radiobrightness (K)
300-
DECEM
BER1992
Surface
— 19 GHz
37 GHz
— 85 GHz
280260- '
240220 200 -
240200-
160 -
| i i i \ t t i j i t
Sky
19 GHz
37 GHz
B5GHz
120-
Radiation (W
/m )
Wind «peed (m/s)
Rsdfobrightnssa (K)
1B0- . 1 I | - l 1 I 1 I 1 t ' 'I ' I i | i 1 i | i I i~f i I i i i i i ) i i i | i | i | i i i | i | i | i H
10 m wind speed
% ;V
336
j l I i | » |-r-1 i I I 1 i I « | i I l | I 1 l | I 1 ' | I I i | l I i i 1 I 1 I 1 I 1 I »1 | I I i | i I i | i
338
340
342
344
346
348
350
352
354
356
358
360
362
364
366
Day from Jan. 1,1992 fUT = CST + 025)
Figure B.14: D ecem ber terrain (surface) apparent radiobrightncsses and reflector-m easured sky radiobrightncsscs at 19, 37, and
85 G H z, n et and global radiation, and wind speed at 10 m .
290
Sofl temperature:
2 cm
4cm
8cm
18 cm
32 cm
-64 cm
285
80
2BO
CO
40
C 275-
I
I *™ i
265-;
-20
Soa heal flux at 2 cm :
260
! m
100
- S
4
*
u
- A
80
g
60
20
«
; I
; jTemperature:
280
t
Surface —
Air
i
I
4
360
362
260
y~ 250
DECEMBER 1992
240
336
338
340
342
344
346
348
350
352
354
358
Oay from Jan. 1,1992 (UT « CST + 0.25)
358
364
366
Figure B.15: D ecem ber subsurface soil tem peratures, vertical heat flux a t 2 cm depth in th e soil, relative hum idity, rainfall, air
tem perature, and therm al infrared surface tem perature.
280 -
Radiobrightness (K)
280-
JANUARY 1993
Surface
— 19 GHz.
37 GHz
65 GHz
240*
220200-
180160-
Radiobrightness (K)
140-
T ' n i i i
t~,~l ■ I > l I I I I » | » I I I I t » | i t
i
I »t I i I i i
i i ( 11I i I I
i
I I I
Sky
240-
- 19GHz:
37 GHz]
- 85 GHz
200 -
160-
!y :
;
120-
80-
a
s «
I
40-
i~i 1 i i i * i i i i i i r «'m i i i • i i i » i i t i i i i i i i i t i »■i i i i t i t i i i i i p i t i i » i i t i i
Radiation:
Global
-
Net
1000
- 800
- 600
4030-
- 200
20 -
10-
0-
10 m wind speed
- -200
.4
1 » 1"H » r n
376
T
11i 1111111) 11111111»1111111111
37fl
380
382
384
386
386
Day from Jan. 1. 1992 (UT = CST ♦ 025)
390
392
394
396
Radiation (W
/m )
Wind speed (m/s)
50-
r ~*°°
398
Figure B.16: January terrain (surface) apparent radiobrightnesses and reflector-m easured sky radiobrightnesses at 19, 37, and
85 G Hz, net and global radiation, and wind speed a t 10 m .
Sot) temperature;
2 ere
4 cm
8cm
32 cm
16 cm
64 cm
285
80
280
60
40
275
20
270
Heat flux (W/me)
Temperature (K)
290
265
20
Soil heal flux at 2 cm
260
100
Raln (mm/cycle)
RH (%)
80
60
40
20
1
Temperature:
Surface
Air
:
(K)
280
Temperature
270
260
250
JANUARY 1993
240
368
370
372
374
376
378
380
382
384
386
388
Day from Jan. 1,1992 (UT * CST + 025)
390
392
394
396
398
Figure B.17: January subsurface soil tem peratures, vertical heat flux a t 2 cm depth in th e soil, relative hum idity, rainfall, air
tem perature, and therm al infrared surface tem perature.
280
Surface
19 GHz
37 GHz :
85 GHz
260
240
220
200
180
160
140
Sky
19 GHz
37 GHz
85 GHz
240
200
160
L
120
n|
80
vivM
ii W i f
40
50
Racfiation:
Global
40
30
20
10
0
'1 1 I i | » M | i I i | i I i | i I i i i | i | i | i i i | i | i i i | i i-T-j i | i | n
18
400
402
404
406
408
410
412
414
416
418
Day from Jan. 1,1992 (UT = CST + 025)
420
422
/V S s /
■I M i
424
42
uary terrain (surface) apparent radiobrightnesses and reflector-m easured sky radiobrightnc
;1obal radiation, and wind speed at 10 m .
290
So9 temperature:
2cm
4cm
8cm
16cm
32 cm
- 64 cm
80
60
280
40
275
20
270
0
265
— Soil heat flux at 2 cm
260
;
5
t
J
80
4
60
3
40
2
Relative humidity
1
20
Raln (mm/cyde)
RH {%)
•20
: i
100
Heat flux (W/m8)
Temperature (K)
285
0
1
Temperature
Temperature (K)
280
Surface
t
Air
270
260
250
FEBRU A RY 1993
240
398
400
402
404
406
408
410
412
414
416
418
Day from Jan. 1.1992 (UT = CST + 025)
420
422
424
426
Figure B.19: February subsurface soil tem peratures, vertical heat flux at 2 cm depth in th e soil, relative hum idity, rainfall, air
tem perature, and therm al infrared surface tem perature.
280
MARCH 1993
Surface
19 GHz
37 GHz
85 GHz
260
240
220
200
160
V M
160
[;U i i ;
:
140
240
19 GHz
200
160
120
to
—J
80
40
50
40
5561943299
600 ®
30
20
10
200 3
10 m wind speed
I 1( »111 1I 1| 1m
!6
428
430
432
434
» I i -f i > » 1 T i 1 ■ l~> 1 > t I T 1 t M 1
436
438
440
442
444
446
Day from Jan. 1.1992 (UT ®CST +■025)
448
450
452
454
ch terrain (surface) apparent radiobrightnesses and reflector-measured sky radiobrightncsses at 19, 37, and 85
bal radiation, and wind speed at 10 m .
290
2cm
4cm
Bern
16cm
64 cm ■:
32 cm
60
280
40
275
20
270
0
265
•20
Soil heat fhrx a t 2 cm
260
100
i
5
t
RH (%)
4
3
40
2
20
t
0
1
1
Temperature (K)
Surface
Air ;
l
1
i
t
t
454
456
Rain (mm/cyde)
80
290
Heat flux (W/ma)
Temperature (K)
80
270
260
M ARCH 1 9 9 3
250
426
428
430
432
434
436
438
440
442
444
446
Day from Jan. 1 .1992 (UT = CST + 025)
448
450
452
Figure B.21: March subsurface soil tem peratures, vertical heat flux at 2 cm depth in th e soil, relative hum idity, rainfatl, air
tem perature, and therm al infrared surface tem perature.
3 20 -
A PR IL 1 9 9 3
300- 280-
s
|
Surface
— 19 GHz
37 GHz
— 85 GHz
I-V TTA
260- f ;
:v
£ 2402
a 2 20 -
tL
200-
180
i |- r I r ;■! I i I i I i I i 1 i | > M I i I i 1 i 1 i | i r r - | i I i | i I »'| i 1 > | i 1 i | i | i | r ] i | i (
240-i
s9
200 H
Sky
- 19 GHz
37 GHz
- 85 GHz
c
£ 160
?a 1 2 0 * ;
2
T3
to
to
80-;
* . ■■ < ! i !
40 \
m
i i i"i
<i <i ■i i i m
i i i i
■i
»-i i i
<i
i i
i
i i i
> i"i i i r>
i i i
t*i i i > t » i
i i ~»-i
>i
50-
-
j Radiation;
I
5
6n
•o
40-
Global
Net
1000
T 800 D
r 600 |
- 400 a
30-
- 200 i
20
-o
?
7 -200 3^
1 0 -1
— ~ 10 m wind speed
0 _ 1 i j i I i | i I i | i l i~r
458
460
462
464
I I | i I » H
466
7-400
I 1 I r "l 1 I 1 f™1 I 1 M | 1 I 1 | i I i | » I M U ' I ' i - r j - r ■--600
468
470
472
474
476
478
Day from Jan. 1.1992 (UT = CST + 0.25)
480
482
484
486
Figure B.22: April terrain (surface) apparent radiobrightnesscs and reflector-m easured sky radiobrightncsscs at 19, 37, and 85
G H z, net and global radiation, and wind speed at 10 m .
290
; Sofl temperature:--------2 cm
4cm
8cm
18cm
32cm — • 6 4 cm j
80
60
280
40
275
20
270
0
265
•20
Sofl heat flux at 2 cm
260
100
5
r
4
3
40
2
Relative humidity
20
1
Raln (mm/cycle)
80
RH (%)
Heat flux (W/m*)
Temperature (K)
285-
O
Temperature (K)
300
J
Temperature
Surface
Air
i
i
280
270
260-
A PR IL 1 9 9 3
458
460
462
464
466
468
470
472
474
476
478
Day from Jan. 1.1992 (UT = CST + 0.25)
480
482
484
486
Figure B.23: April subsurface soil tem peratures, vertical h eat flux a t 2 cm depth in th e soil, relative hum idity, rainfall, air
tem perature, and therm al infrared surface tem perature.
201
B.6
REBEX-1 day to calendar date conversion
Use Tabic B.3 to convert REBEX-1 day numbers to calendar date. The REBEX-1
day number is equivalent to Julian day for 1992 dates and is 366 plus the Julian day
for 1993 dates (1992 was a leap year). Calculate fractional day by adding tim e of day
to the day number. For example, 1200 UT on January, 1 1992 becomes fractional
day 1.5.
202
1
2
3
4
5
G
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
OCT
275
276
277
278
279*
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
1992
NOV
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
DEC
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
JAN
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
1993
FEB MAR
426
398
399
427
428
400
429
401
402
430
431
403
432
404
433
405
434
406
407
435
436
408
409
437
410
438
411
439
412
440
441
413
414
442
415
443
444
416
417
445
418
446
419
447
420
448
449
421
422
450
451
423
424
452
425
453
454
455
456
APR
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471a
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
1First day or experiment.
3 Last day o f experiment.
Table B.3: REBEX-1 day to calendar date conversion chart.
203
A PPE N D IX C
RESAM PLING S SM /I RADIOBRIGHTNESSES
TO A COMMON GRID
This appendix describes the how th e SSM/1 brightnesses in C hapter 6 were re­
sampled to the geographically fixed coordinates of the Equal-Arca SSM /I Earth Grid
(EASE-Grid). The resampling process lakes two steps: (a) Identification of a set
of 16 SSM /I borcsight loci th a t surround a grid point, and (b) interpolation of the
SSM /I brightnesses to the closest of a set of predeterm ined interpolation loci in the
sensor reference frame. The set of interpolation loci arc dense enough th a t the error
in re-mapping by nearest neighbor selection is reduced below the gcolocation error of
the data. Interpolating to points th a t are fixed with respect to the satellite reference
frame enables the use of time-saving interpolation coefficients calculated once for a
particular sensing geometry.
The advantages of this process over conventional mapping techniques are two-fold.
First, brightness variation with tim e can be somewhat removed from spatial variation
since the earth grid is fixed for all times and sensors. Secondly, the interpolation
process can include the simulation of arbitrary sensor patterns. T he antenna pattern
of the SSM /I varies with the frequency of its channels, with the 19 GHz channel
viewing the largest area of earth (see Table 6.1). To make inter-channel comparisons
measurements m ust represent the brightness of the same geographical area. This can
204
be achieved by choosing a single optim al interpolated pattern and using it for all the
channels. Here, the chosen pattern is th at of the 19 GHz V-polarizcd channel.
The first section of this appendix details the optimizing interpolation scheme for
geophysical d ata first developed by Stogryn [64] and first adapted for SSM/1 by Poe
[65]. Section C.1.1 describes implementation of the m ethod for th e available SSM/I
data stream . Section C.1.2 discusses the use of a common interpolated pattern and
section C.2 describes remapping to the EASE^Grid system.
C .l
Optimal interpolation
An interpolation filter for geophysical d a ta may be described as optim al if inter­
polation to a particular location gives the same value as would have been measured
had the sensor borcsight been pointed there. Poc [65] presents a m ethod for closely
approximating this optimal interpolation for SSM /I d ata based on the application of
Qackus-Gilbcrt inversion methodology [66][64].
The SSM /I views the earth with a conical scanning geometry as shown in Fig­
ure C .l.
In term s of an instantaneous antenna gain function, Q (so(t'),s(t')), the
antenna tem perature measured in the direction
t*Va) = £
is given by:
~ dl'l‘C) //<ms(i0(O.a(O)W,i(!V')
(c.i)
where s o ( 0 is the instantaneous boreslght direction of the antenna, s[t’) is the unit
vector from the antenna in the direction of th e solid angle dSl, p is the position
vector of a spherical earth surface coordinate system , and h is the impulse response
of the radiom eter receiver low-pass filter. T b ( p , a(t'), t') stands for the brightness
tem perature at a point p, tim e
and in the direction s (t'). The region of integration,
E , encompasses the entire surface of the earth intercepted by s(f'). Note th a t both h
and Q are normalized such th at
dt h = 1 and f E dU Q = 1, The antenna boresight
Figure C .l: SSM /I (F08 platform ) scan geometry showing earth and satellite coordi­
nate system reference vectors, p and p \ are normal to the earth 's surface. The F I 1
platform 's geometry differs only in th e direction of the ground track. (Modified from
206
pointing direction, S4 , is given by:
/
+0O
1
f+ t/2
dt'h{t')s0{t') = 1 /
T J-rf 2
■00
d/'io(0
(C.2)
where /i has been replaced by integration over r , the characteristic tim e of the receiver
filter.
The differential solid angle, dfi, can be replaced by the corresponding differential
area of the earth ’s surface according to:
- W - f l dA.
sHV)
(0.3)
Exchanging the tim e and space integration, we can rewrite (C .l) as:
T a (? a ) = T a {s a )
(C.4)
where the vector p& points from th e center of th e earth to the intersection of the
borcsight with the e arth ’s surface.
For simplicity, assume th a t the brightness tem perature upwclling from an area
dA is both independent of direction and, on average, independent of time. This
assumption constitutes a lim itation in the analysis only if the T b a t a particular dA
changes significantly over the range of directions or tim es at which th e overlapping
measurements view it. Nevertheless, for practical purposes, the functional dependence
of T b is reduced to:
(C.5)
Then T b comes out of the tim e integral in (C.4) and we can define an effective antenna
gain function:
1 /,+T/ J
G(PA,P) = ~T J - t //2 < /< '0(3o(*V (O )
- s ( f ') •
p
(C.G)
207
Combining (C.4), (C.5), and (C.6) yields this expression for the measured antenna
temperatures:
T a Ip
a
)
= J J <!Ag[j>M r iT B{p).
(C.7)
E
Note th a t (C.7) is the forward equation for TA(pA) when p \ is the geolocation of an
SSM /I sensor measurement.
We seek a way to use the information in (C.7) to optimize the interpolation of Ta
to an arbitrary p within the swath. W ithout a loss of generality, wc can constrain
the set of desired interpolation loci, p j, to fall along arcs offset from th e scans and
along lines parallel to the ground track as shown in Figure C.2. An estim ate of the
antenna tem perature TA(pd) th a t would have been measured by the sensor had it
been pointed a t pd is given by a weighted linear combination of a set of neighboring
sensor measurements:
f A(Pd) = ' t o iTA(pAi)
(C.8)
i=l
where {a,} is a set of N weighting coefficients to be determined and {TA(pAi)} »s the
set of corresponding sensor measurements,
Substituting (C.7) into (C.8) yields:
Ta ( M = / / « £ ; a & p A ,p )T B{ fi.
E
(C.9)
isst
Comparison of (C.9) to (C.7) leads to the definition of an interpolated effective an­
tenna gain function as:
N
Gl(pdip) = J 2 a&(PAi'Pl'
(C.10)
1=1
To determ ine the {a,}, we would like to minimize the error, e, in the estim ate of
208
Scan Angle
Along View
12.5 km
12.5 km
Along Scan (j)
Along Track (I)
Figure C.2: A section of the SSM /I swath showing parts of five scans. The section
is about 27° past the subsatellitc track along the arc of the scans. The circles ap ­
proxim ate the 3 dB extent of each measurem ent’s effective field of view. The dashed
box delineates the set of 16 measurements used to interpolate to any of th e points in
the center of the box. For example, an idealized interpolated antenna pattern for the
point marked with an X is shown as a dashed ellipse. The separation between rows
and samples is 12.5 km for 85 GHz sampling and 25 km for other SSM /I channels.
209
T a {pa)'
e = |Ta ( M - t A& ) \
=
|J
\Q{pt,p) - S m ,P ) ] T B { p )|.
jd A
(C .! 1)
E
It is clear from (C .ll) th a t e is minimized if Q is closely approxim ated by the interpo­
lated pattern, Qj—which is, at the same tim e, a desirable condition in th a t antenna
pattern information remains consistent in the resampling process. From [64], the
solution for the weighting coefficients, {a,}, is obtained by minimization of Q j
Qj =
2
[//<M
- ' £ oA pa,, p )
(C.12)
E
where the function J[p j,p ) can be used, for example, to reduce the sidclobe levels in
Qi but is set to unity in this analysis.
Using Backus-Gilbert inversion theory [66], Stogryn [64] gives the {a,} th a t min­
imize Qdi
. ( l - u Tg~lv ) :
a = g~x v H------rrjprrp:— u
u 'g *u
(C.13)
where the elements of the m atrix g and the vectors u and v are:
OH
=
JJ
d A Q ( p A i ,p ) Q { p A j ,p )
(C.14)
E
Ui = jjd A Q { p A u P )
(C.15)
E
Vi S I J d A g ( p Au m p d%f i '
(C.16)
E
Since this analysis does not take system noise into account, the variance in the
resulting interpolated antenna tem peratures should be examined to insure th a t it
does not exceed acceptable levels. We assume th a t the sensor antenna tem perature
m easurement noise is uncorrelated between samples and th a t the variance of the
210
Launch date
Viewing direction
Ascending equator crossing
tim e (local time)
Maximum altitude
DMSP Platform
F ll
F08
28 Nov. 1991
19 June 1987
Aft looking
Forward looking
17:04
06:15
882 km
878 km
Tabic C .l: SSM /I operational d ata for the P08 and F l l satellite platforms [60].
noise is the same for all samples. The resulting variance in the interpolated antenna
tem perature is given by:
( & f Ay = a r Ea = { b T A), ' £ ' ‘l
is]
(C.17)
where E is the covariance m atrix of measurement noise for the samples contributing
TA(pd)*
to
In practice, A
Ta
*
is often less than
ATa
because m any noisy samples are
combined in the interpolation process.
C.1.1
Implem entation
Calculation of interpolation coefficients—the {a,} in (C.8)—requires the instru­
m ent antenna patterns which were acquired from Hollinger [67]. These antenna p at­
terns were measured from the SSM /I instrum ent aboard th e F08 DMSP platform.
Because the 85 GHz channel of the F08 SSM /I failed in 1990, this thesis presents data
from the F l l platform. The sensor differences are negligible for the purposes of this
work. Table C .l compares param eters for the F08 and F l l platforms. (Param eters
for the individual channels can be found in Table 6,1.)
I acquired global NESDIS Level lb Form at SSM /I d ata for the period of REBEX-1
from the Marshall Space Flight Center (M SFC) Distributed Active Archive C enter in
Huntsville, Alabama. MSFC provided com puter programs for extracting d ata for a
particular geographical region (ssmillblatlon.c) and for converting raw sensor counts
211
to antenna tem peratures (ssm illb ta .f),
The interpolation coordinates in the satellite reference frame were based on a
four-times increase in scan and sample frequency. T h at is, the num ber of samples
per scan was increased from 64 to 256 for the low frequency channels (19, 22, and 37
GHz) and from 128 to 512 for the 85 GHz channel.
C.1.2
Resampling to a common resolution
The above derivation assumes in (C.12) th a t th e optimal antenna pattern is th a t of
the channel th a t sampled T a ( p m )- But the need for multi-channel brightness compar­
isons suggests th a t a single pattern is desirable for all polarizations and frequencies. If
the chosen pattern is Gd(pd,p}i then the minimized function Qd from (C.12) becomes:
Qd - |JJ dAIGd{pd,p) " J2 aMpA" P)
■E
2
J{pd,p)
(C.18)
<Bl
and the param eters of (C.13) are exactly the same except for u,, which is now given
by:
=
JJ dAG[pAiip)Gd[pd,p)-
(C.19)
E
In this thesis, the common pattern is th a t of the 19 GHz V-potarizcd channel of the
SSM /I.
The 19GHz pattern has the largest footprint of the four SSM/1 frequencies,
and the interpolated patterns of the other channels are
able to fit it w ithout high
side-lobes. If the 19 GHz pattern were interpolated to a significantly smaller desired
pattern—th a t is, either the 37 GHz or 85 GHz pattern—then the best achievable
interpolated pattern would be distorted and have high side-lobe levels.
Figure C.3 shows example interpolated antenna patterns for the 37 and 85 GHz
channels compared with the optim al 19 GHz pattern.
Because samples are more
closely distributed near the scan edges, the degree to which the interpolated pattern
212
U
Figure C.3: A ntenna patterns: (a) 19 GHz V-pol. effective antenna pattern, (b) 37
GHz V-pol. interpolated to 19 GHz pattern at center of scan, (c) 37 GHz V-pol.
interpolated to 19 GHz pattern between edge and center of scan, (d) 85 GHz V-pol.
interpolated to 19 GHz pattern a t center of scan, (e) 85 GHz V-pol. interpolated to
19 GHz pattern between edge and center of scan. The contours are a t 3, 6, 12, and
24 dB.
213
□
(d)
(<0
Figure C.3: (Continued from previous page.)
matches the optimal pattern depends upon where in the scan the interpolation occurs.
Figure C.3 shows this effect in the 37 GHz patterns. A t th e scan edge, the pattern
closely matches the elliptical shape of the optimal pattern while at th e the center
of the scan the interpolated pattern is more rectangular. The 85 GHz patterns arc
distinctly rhomboidal a t all scan angles because the antenna pattern a t 85 GHz is
more than three times smaller than the 19 GHz pattern and th e density of samples is
four times greater (see Table 6.1). To b etter approxim ate a 19 GHz optimal pattern,
interpolation could be performed with more than 16 85 GHz samples. This is a
subject for future investigation.
C.2
Remapping to the Equal-Area S S M /I Earth
Grid
As discussed above, the interpolation loci are defined in th e satellite reference
frame relative to the sample points of the SSM /I sensors. This yields a nominal
sample spacing of 6.25 km (or 3.125 km for 85 GHz high-resolution resampling).
Consequently, nearest neighbor re-registration to fixed coordinates on the earth has
214
a maximum error of about 3.125 km (1.563 km for 85 GHz), which is 7% of the 19
GHz field of view.
Fixed earth coordinates are defined by the Equal-Area SSM/1 E arth Grid (EASEGrid), used by the National Snow and Ice D ata Center (NSIDC) for global SSM/I
d ata archiving [68]. This thesis uses two EASE-Grid projections: Ml (low resolution
m ercator) and Mh (high resolution m crcator, for 85 GHz only). Column num ber (r)
and tine num ber (s) of the projections arc based on a cylindrical equal-area map true
at 30° N /S latitude:
r = j^Acos 30 + rO
(C.20)
V
R
s= -
sintf)
c
^
,
_
+!°
(C-21)
where R is the radius of the earth (6371.288 km), C is the nominal cell size, A is the
latitude in radians, and <f>is the longitude. The projection origin (r0,s0) is the point
in the projection where A = 0 and <£ = 0. Table C.2 lists the param eter values for
the Ml and Mh grids.
Grid
Ml
Mh
C
25.067525
12.5337625
r0
691.0
1382.0
sO
292.5
585.0
Table C.2: Param eters for the Ml and Mil EASE-Grid projections.
Figure C.4 shows example images made from EASE-Grid d ata in both the Ml and
Mh formats. The d ata are displayed in a conical projection but the coordinates of
each pixel are at EASE-Grid locations. Note th a t the four-times increase in sample
density of the Mh grid and the smaller EFOV highlight variation not visible in the
low resolution image. The displayed d ata was subset to the region bounded by 41 N
latitude, 51 N latitude, 89 W longitude, and 110 W longitude. Note th a t the. edge of
the swath is to the east of 110 \V.
215
65 GHt Hortsontol Pafw totlon, Low R tt.
12:21 UTC
160
180
200
220
240
260
280
300
RodlobrtQMntw (K)
6 5 O H t H o rfro n la l P o lo riio tlo o ,
High R m l
1993399:12:21 UTC
160 180 200 220 240 280 280 300
RodtoWgMiww (K)
Figure C.4: SSM /I 85 GHz h-pol, images from February 2,1992 a t 12:21 UTC demon­
strating resampling to low resolution (top) and high resolution (bottom ) EFOV.
BIBLIOGRAPHY
[1] Giorgi, P., and Mcarns, L. 0 ., “Approaches to the Simulation of Regional Cli­
m ate Change: A Review,11 Rev. Gcophys., Vol. 29, No. 2, pp. 191-216, 1991.
[2] Dickinson, R. E., Hcndcrson-Scllcrs, A., Kennedy, P. J., and Wilson, M. F..
Biosphere'Atmosphere Transfer Scheme (B A T S) fo r the NCAR. Community Cli­
mate Model, NCAR Technical Note, NCAR/TN -275+STR, December, 1986.
[3] Sellers, P .J., Mintz, Y., Sub Y.C., and Dalchcr, A., “A Simple Biosphere Model
(SiB) for use within general circulation models,11 J , A tm . Sci., Vol. 43, No. 6,
pp. 505-531, 1986.
[4] Peixoto, J. P., and Oort, A. H., Physics o f Climate, American Institute of
Physics, New York, 1992.
[5] Dickinson, R. E., Errico, R. M., Giorgi, F., and Bates, G. T ., “A regional climate
model for the Western United States,11 Climate Change, Vol. 15, pp. 383-422,
1989.
[6] Cess, R. D., Potter, G. L., Zhang, M.-H., Blanchct, J.-P., C halita, S., Colman, R.,
Dazlich, D. A., Del Genio, A. D., Dymnikov, V., Galin, V., Jcrrett, D., Kcup, E.,
Lacis, A. A., Lc Treut, H,, and others “Interpretation of Snow-Climatc Feedback
as Produced by 17 General Circulation Models,” Science, Vol. 253, pp. 888-892,
1991.
[7] Edgerton, A. T., Stogryn, A., and Poe, G., Microwave radiometric investigations
o f snowpacks, Final Report, 1285R-4, Aerojet-General Corporation, July, 1971.
[8] Schmugge, T ., Wilheit, T . T ,, Gloerson, P., Meier, M. F., Frank, D., and
Dirmhirn, I., “Microwave signatures of snow and fresh w ater ice,” Presented
at the Interdisciplinary Symposium on Advanced Concepts and Techniques in
the Study of Snow and Ice Resources, Goddard Space Flight C enter, Greenbelt,
MD, Nov. 1, 1973.
[9] Stiles, W. H., and Ulaby, F. T ., “The active and passive microwave response to
snow param eter 1. Wetness,” X Geophys, Res., Vol. 85, No. C2, pp. 1037-1044,
1960.
216
217
|10] Stiles, W. H., and Ulaby, F. T., “The active and passive microwave response to
snow param eter 2. W ater equivalent of dry snow,” J. Gcophys. Res., Vol. 85. No,
C2, pp. 1045*1049, 1980.
[11] M atzler, C., Schanda, E., and Good, W ., “Towards the definition of optim um
sensor specifications for microwave remote sensing of snow,” IE E E Trans. Gcosci.
Rem. Sens., Vol. GE*20, No. 1, pp. 57-66, 1982.
[12] Sturm , M., Grenfell, T. C., and Perovich, D. K., “Passive microwave measure­
m ents of tundra and taiga snow covers in Alaska, U.S.A.,” Annals Glaciology.
Vol. 17, pp. 125-130, 1993.
[13] Zwally, H. J., “Microwave cmisslvity and accumulation rate of polar firn,” J.
Glaciol., Vol. 18, No. 79, pp. 195-215, 1977.
[14] Foster, J . L., Rango, A., Hall, D. K., Chang, A. T. C., Allison, L. J., and
Dicscn, B. C., “Snowpack monitoring in North America and Eurasia using passive
microwave satellite data,” Rem ote Sens. Environ., Vol. 10, pp. 285-298, 1980.
[15] Hall, D. K., Sturm , M., Benson, C. S., Chang, A. T. C., Foster, J. L., Garbcil,
H., and Chacho, E., “Passive microwave rem ote and in situ measurements of
arctic and subarctic snow covers in alaska,” Remote Sens. Environ., Vol. 38, pp.
161-172, 1991.
[16] Hofer, R., and Good, W., “Snow param eter determ ination by multichannel mi­
crowave radiom etry,”Remote Sens. Environ., Vol. 8, pp. 211-224, 1979.
[17] Hofer, R., and Shanda, E,, “Signatures of snow in the 5 to 94 GHz range,” Radio
Sci., Vol. 13, No. 2, pp. 365-669, 1978.
[18] Goodison, B. E., “Determination of areal snow water equivalent on the Canadian
praircs using passive microwave satellite d ata,” in Proceedings o f IG ARSS89,
Vancouver, Canada, July 10-14, 1989.
[19] Hall, D. K., Foster, J. L., and Chang, A. T. C., “M easurement and modeling of
microwave emission from forested snowfields in Michigan," Nord. Hydrol., Vol.
16, pp. 129-138, 1982.
[20] Chang, A. T. C,, Foster, J. L., and Hall, D. K., “Nimbus-7 SMMR derived global
snow cover param eters,” Anna/s Glaciology, Vol. 9, pp. 39-44, 1987.
[21] Chang, A. T . C., Foster, J. L., and Rango, A., “Utilization of surface cover
composition to improve the microwave determ ination of snow w ater equivalent
in a m ountain basin,” Int. J , Remote Sens., Vol. 12, No. 11, pp. 2311-2319, 1991.
[22] Rango, A., Chang A. T , C., and Foster, J. L., “The utilization of spaceborne
microwave radiometers for monitoring snowpack properties,” Nord, Hydrol., Vol.
10, pp. 25-40, 1979.
218
[23] Wang, J. R., Chang, A. T. C., and Sharm a, A. Iv\, “On the estim ation of snow
depth from microwave radiometric measurements," IE E E Trans. Geosci. Rem.
Sens., Vol. 30, No. 4, pp. 785*792, 1992.
[24] Kunzi, K. F., P atil, S., and R ott, H., “Snow*covcr param eters retrieved from
Nimbus-7 Scanning Multichannel Microwave Radiom eter (SMMR) D ata,” IE E E
Trans. Geosci. and Remote Sensing, Vol. GE-20, No. 4, pp. 452-467, 1982.
[25] Chang, T. C., Glocrsen, P., and Schmuggc, T., “Microwave emission from snow
and glacier icc,” J. Glaciol., Vol. 16, No. 1, pp. 23*39, 1976.
[26] McFarland, M. J., Wilke, G. D., and Harder, P. H. Ill, “Nimbus 7 SMMR
investigation of snowpack properties in the northern great plains for the winter
of 1978-1979," IE E E Trans. Geosci. and Remote Sensing, Vol. GE-25, No. 1, pp.
35-46, 1987.
[27] Grody, N. C., “Surface identification using satellite microwave radiome­
ters," IE E E Trans. Geosci. and Remote Sensing. Vol. 26, No. 6, pp. 850-859,
1988.
[28] Grody, N. C., “Classification of snow cover and precipitation using the Special
Sensor Microwave Imager," J. Gcopkys. Res., Vol. 96, No. D4, pp. 7423-7435,
1991.
[29] Fiore, J . V. jr., and Grody, N. C., “Classification of snow cover and precipitation
using SSM /I measurements: case studies,"Int. J. Remote Sens., Vol. 13, No. 17,
pp. 3349-3361, 1992.
[30] Neale, C. M. U., McFarland, M. J., and Chang, K,, “Land-surface-type clas­
sification using microwave brightness tem peratures from the special sensor mi­
crowave/imager," IE E E Trans. Geosci. Rem. Sens., Vol. 28, No. 5, pp. 829-838,
1990.
[31] Stiles, W. II., Ulaby, F. T., and Rango, A., “Microwave measurements of snow­
pack properties,"Nord. Hydrol., Vol. 12, pp. 143-166, 1981.
[32] Chang, A. T . C., Foster, J. L„ and Rango, A „ “The role of passive microwaves
in characterizing snow cover in the Colorado river basin," GeoJoumal, Vol. 36,
No. 3, pp. 381-388, 1992.
[33] Davis, R. E,, Dozier, J., and Perla, R., “M easurement of snow grain properties,"
in Seasonal Snowcovers: Physics, Chemistry, Hydrology, D. Reidel, p. 63-74,
1987.
[34] Shi, J., Davis, R. E., and Dozier, J., “Stereologica! determ ination of dry-snow
param eters for dicrete-scatterer microwave modeling," Anna/s Glaciology, Vol.
17, pp. 295-299, 1993.
219
[35] Brun, E., M artin, E., Simon, V., Gendrc, C., and Colcou, CM “An energy and
mass model of b o o w cover suitable for operational avalanche forecasting,” J.
Glaciol., Vol. 35, No. 121, pp. 333-342, 1989.
[36] Loth, B., Graf, H. F., and Oberhuber, J. M., “Snow cover model for global
clim ate simulations,” J. Geophys. Res., Vol. 98, No. D6, pp. 10451-10464, 1993.
[37] Anderson, E. A., A Point Energy and Mass Balance Model o f a Snow Cover, A
dissertation subm itted to the Dept, of Civil Engineering and the committee on
graduate studies of Stanford University, December 1, 1975.
[38] Jordan, R., A one-dimensional temperature model fo r a snow cover: Technical
documentation fo r SN TH ERM .89, U.S. Army Corps of Engineers, Cold Regions
Research and Engineering Laboratory, Special Report 91-16, 1991.
[39] England, A. W ., “Radiobrightness of Diurnally Heated, Freezing Soil,” IE E E
Trans. Geosci. Rem. Sens., Vol. 28, No. 4, pp. 464-476, 1990.
[40] Nakano, Y., and Brown, S., “M athematical modeling and validation of the ther­
mal regimes in tundra soils, Barrow, Alaska,” Arctic and Alpine Res,, Vol. 4, No.
1, pp. 19-38, 1972.
[41] Anderson, D. M., Tice, A. R., and McKim, H. L., “The unfrozen w ater and the
apparent specific heat capacity of frozen soil,” in Permafrost: North American
contributions [to the] Second International Conference, Yakutsk, Siberia, pp. 289295, 1973.
[42] De Vries, D. A., “Thermal properties of soils” , in Physics o f Plant Environment,
W. R. Van Wijk, ed., North-Holland, A m sterdam , pp. 210-235, 1963.
[43] de Vries, D. A., and Philip, J. R., “Soil heat flux, therm al conductivity, and the
null-alignment m ethod,” Soil Sci. Soc. A m . J ., Vol. 50, pp. 12-18, 1986.
[44] de Vries, D. A., and Afgan, N. H., Heat and Mass Transfer in the Biosphere
1. Transfer Processes in Plant Environment, John Wiley and Sons, New York,
1975,
[45] B randt, R. E., and W arren, S. G., “Solar-heating rates and tem perature profiles
in A ntarctic snow and ice,” J. Glaciol., Vol. 39, No. 131, pp. 99-110, 1993.
[46] Panofsky, H. A., and D utton, J. A., Atmospheric Turbulence, John Wiley, New
York, 1984.
[47] Sm ith, E. A ., Crosson, W, L„ and Tanner, B. D., “Estim ation of surface heat and
m oisture fluxes over a prairie grassland 1. In situ energy budget measurements
incorporating a cooled m irror dew point hygrom eter,” J. Geophys. Res., Vol. 97,
No. D17, pp. 18557-18582, 1992.
220
[48] Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vettcrling, YV. T.. A'umcricat Recipes: The Art o f Scientific Computing, Cambridge University Press.
Cambridge, 1986.
[49] Chandrasekhar, S., Radiative Transfer, Dover Publication, Inc., New York. 1960.
[50] Ulaby, F. T., Moore, R. K., and Fung, A. K., Microwave Remote Sensing: Active
and Passive, Vol. /, Addison Wesley, 1981.
[51] Bohrcn, C. F., and Huffman, D. R., Absorption and Scattering o f Light by Small
Particles, John Wiley & Sons, New York, 1983.
[52] Ishimaru, A., and Kuga, Y., “A ttenuation constant of a coherent field in a dense
distribution of particles,’1 J. Opt. Soc. A m ., Vol. 72, No. 10, pp. 1317-1320, 1982.
[53] Tsang, L., M andt, C. E., and Ding, K. H., “Monte carlo simulations of the
extinction rate of dense media with randomly distributed dielectric spheres based
on solution of Maxwells equations
Optics Letters, Vol. 17, No. 5, pp. 314-316,
1992.
[54] Kuga, Y., Ulaby, F. T., Haddock, T. F,, and DcRoo, R. D., “Millimeter-wave
radar scattering from snow: 1. Radiative transfer model,11 Radio Sci., Vol. 2G,
No. 2, pp. 329-341, 1991.
[55] Tsang, L., Kong, J. A., and Shin, R. T ., Theory o f Microwave Remote Sensing,
John Wiley k Sons, New York, 1985.
[56] Hufford, G., “A model for the complex perm ittivity of ice at frequencies below
1 THz,” Int. J. IR and M M Waves, Vol. 12, No. 7, pp. 677-682, 1991.
[57] John Kendra, personal communication, 1995.
[58] Galantowicz, J.F .
brightness Energy
Sioux Falls, South
RL-913, February,
and England, A.W., Field data report fo r the First RadioBalance Experiment (R E B E X -J), October 1992-April 1993,
Dakota, Univ. of Michigan, Radiation Lab Technical Report
1995.
[59] Hollinger, J., D M SP Special Sensor M icrowave/Imager Calibration/Validation
Final Report Volume I, Naval Research Laboratory, Washington, DC 203755000, 1989.
[60] User Guide to Special Sensor Microwave/Imager (S S M /I) Data (N ESD IS Level
lb Format), Marshall Space Flight Center, Distributed Active Archive Center,
Huntsville, Alabama, 1994.
[61] Colbeck, S. C,, “Vapor-pressure dependence on tem perature in models of snow
m etam orphism ,11 J. Glaciol,, Vol. 36, No. 124, pp. 351-353, 1990.
[62] Arya, S. P., Introduction to Micrometeorology, Academic Press, San Diego, 1988.
221
[63] Farouki, 0 . T., Evaluation o f methods fo r calculating soil thermal conducing
ity, CRREL Report 82-8, U. S. Army Cold Regions Research and Engineering
Laboratory, Hanover, NH, 1982.
[64] Stogryn, A., “Estim ates of brightness tem peratures from scanning radiom eter
data,” IE E E Trans. Antennas and Propagation, Vol. AP-26, No. 5, pp. 720-726.
1978.
[65] Poe, G. A., “Optim um interpolation of imaging microwave radiom eter data."
IE E E Trans. Geosci. Rem. Sens., Vol. 28, No. 5, pp. 800-810, 1990.
[66] Backus, G., and G ilbert, F., “Uniqueness in the inversion of inaccurate gross
earth d ata,” Phil. Trans. Roy. Soc, London, Vol. A226, pp. 123-192, 1970.
[67] J. Hollingcr, personal communication. Space Sensing Branch, Naval Research
Laboratory, W ashington, DC 20375-5000, 1992.
[68] R E A D M E file fo r N O A A /N A S A Pathfinder Program S S M /I Level S Brightness
Temperatures Equal-Area S S M /I Earth Grid (EASE-G rid) CD, National Snow
& Ice Data Center, Boulder, CO, 1995.
Документ
Категория
Без категории
Просмотров
0
Размер файла
8 366 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа