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Satellite and ground passive microwave remote sensing studies of ice and snow on and near Lake Superior

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SATELLITE AND GROUND PASSIVE MICROWAVE REMOTE SENSING
STUDIES OF ICE AND SNOW ON AND NEAR LAKE SUPERIOR
By
ANDREW NESS PILANT
A DISSERTATION
Submitted in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
(Geology)
MICHIGAN TECHNOLOGICAL UNIVERSITY
1996
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This dissertation, “Satellite and Ground Passive Microwave Remote Sensing o f Ice and
Snow On and Near Lake Superior", is hereby approved in partial fulfillment of the
requirements for the degree of DOCTOR OF PHILOSOPHY in the field of Geology.
Department of Geological Engineering
and Sciences
Signatures:
Dissertation Advisor
Department Head
__________ I ^
l ) <?<-
William I. Rose
William I. Rose
(
e7 1?
Date
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Abstract
The subject of Lake Superior snow and ice passive microwave remote sensing is
addressed in a series of satellite image analyses and in situ ground truth studies. The moti­
vation is cryospheric monitoring in the North American Great Lakes region for climatological and navigational-industrial applications. The satellite passive microwave studies of
Great Lakes ice are believed to be the first reported.
The utility of SSM/I (Special Sensor Microwave/Imager) as a Great Lakes ice moni­
toring tool is investigated. Lake Superior ice conditions on February 1 and 4, 1996 are
examined using SSM/I, AVHRR (Advanced Very High Resolution Radiometer) and
National Ice Center ice chart data. Results indicate that lake ice brightness temperature
(Tb) and emissivity are similar to those of new and young sea ice, and that for the 37 GHz
horizontal polarization channel they appear to increase with increasing ice thickness.
The seasonal evolution of Lake Superior and Great Lakes ice cover was investigated
using time series of SSM/I brightness temperature images, and air temperature and snow
accumulation data for the Michigan Technological University weather station. Computer
animated SSM/I image time series of the Great Lakes at daily time steps reveal patterns of
ice growth from shore to mid-lake, and patterns of ice decay with accumulation of floes in
the downwind south and east shores.
Topographic transects were surveyed across four commonly occurring nearshore ice
facies at 0.2 cm vertical and 5.0 cm horizontal resolutions to study ice roughness as a con­
trolling factor in ice backscatter and emission. The four facies rank in roughness as fol­
lows (RMS roughness (cm) / correlation length (cm) in parentheses): single large pressure
ridge (30/125), series of small pressure ridges (16/110), consolidated shuga zone (8/70)
and young congelation ice cakes (5/145). Snow cover (0-24 cm) was widespread.
The effect of topographically controlled solar insolation on snow properties and 37
GHz TB was investigated in the field. Snow grain size and TB were measured on the north
and south facing slopes of a 10 m wide east-west trending gully. Differential timing of
melting during the diurnal cycle was observed, producing a time lag in brightness temper­
ature between north and south facing slopes. The two slopes were not distinguishable on
the basis of grain size distribution. Approximately 49% of the sieved snow grains were
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larger in diameter than the 37 GHz free space wavelength (8.1 mm), suggesting that vol­
ume scattering was an important process in this relatively typical snow pack.
An appendix summarizes in situ snow apparent brightness temperature measure­
ments and computer programs used in these and related studies.
ii
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Acknowledgments
I thank my committee for helping me navigate to the distant shore: William I.
Rose, Charles T. Young, Ann L. Maclean and Alex Kostinski. I thank Bill Rose for sug­
gesting ‘just go for it’ as a working philosophy, and for demonstrating the link between
science and fun. Chuck Young helped me to conceptualize one of nature’s most elegant
phenomena, electromagnetic waves, and provided many helpful reviews. I thank MTU as
an entity for being an environment where one can go wherever the imagination leads. Bert
Davis (U.S. Army Cold Regions Research and Engineering Laboratory) has been a fine
volunteer mentor in cryospheric remote sensing. Tony England and John Galantowicz
(University of Michigan Radiation Laboratory) have been very generous with their radi­
ometer and guidance.
I gratefully acknowledge financial support from the following sources: NASA Fel­
lowship for Global Change Research #1956 GC92-0312, the MTU Graduate School and
Department of Geological Engineering and Sciences, Michigan Space Grant Consortium
Seed Grant 79827 and NASA NAGW-4989 The Keweenaw Research Center provided
cold room access and meteorological data. The weather station sampling site fence and
electricity were provided by the Office of the Provost and the Physical Plant. Satellite data
were provided by the NASA Marshall Space Flight Center Hydrologic DAAC, the NOAA
Satellite Active Archive, the National Snow and Ice Data Center and the National Ice Cen­
ter (ice charts).
I have enjoyed tremendous logistical support: departmental (Bonnie Gagnon, Bob
McCarthy), Research Services (Lisa Jukkala, Anita Quinn, Connie Tuohimaa, Sharlene
Kanniainen), Graduate School (Mina Grudnowski, Sung Lee), Photo Services (Chris
Webb, Susan Hershberg). Special thanks go to Bonnie Gagnon for her unsolicited initia­
tive, and to Bob McCarthy for troubleshooting my construction projects. Jim Carstens is
much appreciated for establishing and operating the MTU weather station. Bob Landsparger and Dave Hale helped with computing.
I thank my undergraduate and masters degree mentors for initializing my momen­
tum: Norm Anderson, Ai Eggers, Stuart Lowther, Z. F. Danes (University of Puget
Sound), J. C. Griffiths and Duff Gold (The Pennsylvania State University). In addition, I
iii
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applaud the generally unrecognized dedication of my public school teachers such as Mr.
Lloyd, Mr. Havel, Mr. Calloway and Mr. Eastley. They tried to teach, and they got through
to some of us.
Central to a good dissertation are good humored, helpfull colleagues: Dave
Schneider, Ashok Agarwai, Darrel Sofield, Mike Dolan, Heather Shocker, Paul Kimberly,
Amy Snyder, Dave Delene, J.P. Suchoski, Renshou Dai, Chris Williams, Emily Constan­
tine, Tianxu Yu. Special thanks go to Dave Schneider for his generosity, insights and wit.
Mike Dolan made UNIX a very comfortable environment for this research. I thank review­
ers Deb Shueller, Gregg Bluth and Jon Graf. Jim Weinman, Dorothy Hall, Jim Foster and
Ted Engman (Goddard Space Flight Center) and Henry Santeford (MTU) provided guid­
ance regarding cryospheric subjects.
I acknowledge the support and comradery of kindred spirits: Tim White, Dave
Diodato, Stefan Richardson, the members of Cry On Cue, Steve Thome, Peter Boies, Patti
Pawlicki, Jim Vallance, John Gierke, Charlie Phelps, John and Mary Anderson, Gail
Green, Mike Jones, Doug Olson, Zhenya Koplunyenko, Don and Jan Anderson, Brandy,
Kona and Tupi. Special thanks go to Bemie Larson for all his help, and for bringing music
to Houghton.
My focus on Lake Superior was a direct outgrowth of my participation in the Superior-Baikal Connect international environmental stewardship project. I thank the sponsors
(MTU, Lake Superior Center, Adventure Club-Moscow) and my teammates for steering
me in this direction.
I can only attempt to acknowledge the vast contributions of my family. Unlimited
thanks go to my parents Marjie and George for instilling in me the love of learning, and to
George and Laura for their ongoing support.
Some contributions are so significant as to simply defy adequate acknowledgment:
Bono Sen and Jackie Huntoon.
iv
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Dedication
This dissertation is dedicated to my parents and to Banalata Sen.
V
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No summer is long enough to take away the winter.
Barry Lopez, Arctic Dreams
Its the mathematics of ice, and how it fits into the landscape of the mind.
Peter Hoeg, Smilla's Sense o f Snow
vi
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Table of Contents
Section
page
i
Abstract
Acknowledgments
iii
Glossary
xiii
Acronyms, Symbols and Abbreviations
xix
Chapter 1: Overview
I
Outline
1
Environmental Context
2
Motivation
2
Mechanisms
3
A Conceptual Remote Sensing Model
4
Sources of snow and ice data
7
Bibliography
9
Chapter 2: Lake Superior ice cover viewed using SSM/I
passive microwave imagery
10
Abstract
10
Introduction
11
Motivation
11
Remote sensing context
12
Outline
14
Data: SSM/I, AVHRR, NIC ice charts
15
Dates
15
SSM/I passive microwave brightness temperature imagery
15
AVHRR thermal infrared and visible imagery
19
NIC ice charts
19
Digital coregistration of imagery and ice charts.
20
Comparison of raw and registered Tg profiles
21
Image analysis
23
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Imagery
23
Microwave TB, emission and ice stage of development
30
Results
42
Discussion
45
Conclusions:
48
Acknowledgments
49
Bibliography
49
Chapter 3: SSM/I Time Series Observations of Great Lakes Ice and Snow
52
Abstract
52
Introduction
52
Data and processing
53
Discussion
55
LandTB
58
Lake TB
59
Snow accumulation
59
85 and 37 GHz image time series
60
Comparison of AVHRR and SSM/I images
60
Conclusions
61
Acknowledgments
63
Bibliography
63
Chapter 4: Nearshore Ice Surface Roughness Surveys on Lake Superior
64
Abstract
64
Introduction
64
Field Observations
65
Results and Conclusion
71
Acknowledgments
71
References
71
viii
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Chapter 5: Meter range 37 GHz Passive Microwave Observations
of Snow on North and South Facing Slopes
74
Abstract
74
Introduction
74
Field Observations
Study area
75
Snow apparent brightness temperature measurement
75
Snow characterization
76
Brightness temperature
77
Grain size
79
Discussion
Conclusions
81
Acknowledgments
81
Bibliography
81
Chapter 6: Conclusions and Recommendations
83
Conclusions
83
Recommendations
84
Ice surface roughness
84
Melt state
85
Lake Superior environmental geographic information system
85
Bibliography
88
Appendix A: Field measurements of snow 37 GHz brightness temperature
Field Measurements
89
89
Equipment
Snow sampling supplies
89
Instruments
89
Measurement Procedures
90
Calibration and data acquisition
90
Snow TB measurements
93
ix
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Sky TB measurements
93
Data format
93
Measuring e’
93
Equipment Descriptions
94
Radiometer Tower
94
Radiometer System
95
Site Descriptions
96
MTU weather station site
96
Gully Site
96
Airport site
97
Discussion: the downwelling sky brightness problem
Snow emission model
99
99
Field Data
100
Field procedures
100
Specular Scattering
103
Fresnel Reflection Coefficients
104
Lambertian Scattering
105
Example: calculation of the total downwelling brightness
originating in the hemisphere of sky
106
Calculation of the proportion of total reflected sky brightness
intercepted by the beam of a radiometer with a beamwidth of 3°. 107
Examples of sky corrections
107
Bibliography
110
Snow Brightness Temperature Graphs
111
Appendix B: Computer Programs
129
Program: get_ssmi_low_frequency_channel.pro
129
Program: get_ssmi_high_frequency_channel.pro
130
Program: ice_penetration_depth.pro
132
Program: mixing_model_dry.pro
133
Progam: mixing_model_wet.pro
134
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Program: fresnel_snow.pro
135
Program: pIot_fresnel_wet_dry.pro
136
Program: compare_specuIar_lambertian.pro
138
Program: mm_to_phi.pro
139
Program: magnitude_sky_contribution.pro
139
Program: fractal_topography.pro
141
Program: aschbacher__snow_depth.pro
145
Program: chang_foster_hall_90_snow_depth.pro
146
Program: nagler_snow_depth.pro
147
xi
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List of Figures
Figure number
page
Chapter 2
2.1
Example of coastline fit for registered SSM/I image
2.2
Locations of east-west TB profiles on raw, Lambert azimuthal projection
21
and UTM projection images
22
2.3
Comparison of raw and registered brightness temperature profiles
23
2.4
AVHRR image of Great Lakes, February 4, 1996
32
2.5
SSM/I T b image of Great Lakes, February 4, 1996
33
2.6
Lake Superior TB: all SSM/I frequency-polarization combinations
and Tb profile plots, February 4, 1996
34
2.7
Early ice growth phase in ice chart time series
35
2.8
February 1 ice conditions
36
2.9
February 4 ice conditions
37
2.10
Ice microwave apparent emissivity, February 4
38
2.11
February 1 ice polygons and 37 GHz hpol mean TB
39
2.12
February 4 ice polygons and 37 GHz hpol mean TB
40
2.13
February 4 ice polygons and 37 GHz hpol mean emissivity
41
2.14
Image combination: SSM/I 85 GHz Hpol TB (red), ice chart (green),
2.15
AVHRR band 4 (blue)
42
Statistics for February 4, 1996 ice and ice free regions
44
Chapter 3
3.1
Comparison of a raw and seven day mean SSM/I images
54
3.2
Winter 1993-94 time series comparison of raw and averaged TB
55
3.3
Winter 1993-1994 time series of air temperature, 85 GHz hpol
brightness temperature and snow accumulation
56
3.4
Image time series of 85 GHz hpol TB spanning winter 1993-94
57
3.5
Image time series of 37 GHz hpol TB spanning winter 1993-94
58
3.6
AVHRR and SSM/I images of Lake Superior on 9 March 1994
62
xii
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Chapter 4
4.1
Locations of ice topographic transects
65
4.2
Location of ice transects 1, 3 and 4
66
4.3
Location of ice transect 2
67
4.4
Autoleveling survey in the small pressure ridge facies (Facies 2)
68
4.5
Small pressure ridge (Facies 2)
69
4.5
Topographic profiles of surveyed ice facies
70
Chapter 5
5.1
Topographic cross-section of gully
75
5.2
Example of snow conditions 31 March 94, 17:00
76
5.3
TAP profiles
78
5.4
Grain size distribution histograms
80
Appendix A
A .l
Voltage to brightness temperature conversion
A.2
Contributions to T ^ in idealized specular and Lambertian
91
surface scattering endmembers
102
A.3
TApSnow (*) ^
TBsky(triangIe) in a typical data run
103
A.4
Measured (solid line) and fitted (squares and triangles) sky brightness
103
A.5
Calculated Fresnel reflection coefficients: wet and dry snow cases
105
A.6
Comparison of specular vs. Lambertian and wet vs. dry snow
T Bsky corrections
A .l
Enlarged comparison of specular vs. Lambertian and wet vs. dry snow
TBsky corrections
A.8
109
110
Comparison of specular and Lambertian sky corrections for dry snow case:
e=(1.7e’+ O.Ole” ) (enlargement of Figure A-6)
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111
List of Tables
Table number
page
Glossary
G. 1
Electromagnetic quantities in the microwave and optical regions
xvi
Chapter 1
1.1
Spectral regions, electromagnetic effects and important physical properties
6
1.2
Electromagnetic Quantities
7
Chapter 2
2.1
SSM/I (and AMSR) frequencies and footprints
16
2.2
Penetration depths of freshwater ice at SSM/I frequencies
18
2.3
WMO Stage of Development
18
2.4
Timing of input to February 5 ice chart
20
2.5
February 1 and 4 ice covered region TB statistics
45
2.6
February 1 and 4 ice free region TB statistics
45
Chapter 4
4.1
Field measured ice roughness and snow thickness parameters
71
Appendix A
A. 1
Radiometer system characteristics
96
A.2
Physical parameters measured in the field
101
xiv
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Glossary
Definition
Term
absorptivity
Ratio of absorbed to incident energy
active sen­
sor
A remote sensing system that transmits a signal of known characteristics
and receives a return signal reflected (backscattered) from a target (e.g.,
lidar, or radar systems such as ERS-1/2, JERS and RADARS AT).
albedo
Ratio of reflected to incoming radiation
AMSR
Advanced Microwave Scanning Radiometer.
antenna
temperature
Apparent brightness temperature received at an antenna, uncorrected for
emission and extinction in the medium between the target and antenna
apparent
brightness
tempera­
ture,
Brightness temperature received at a sensor and uncorrected for atmo­
spheric (and cosmic) brightness contributions.
AVHRR
Advanced Very High Resolution Radiometer (visible and infrared)
backscatter
Radiation reflected back toward the sensor. In radar remote sensing, it
refers to the reflection of the transmitted wave toward the receiving
antenna.
blackbody
Idealized, perfectly opaque material that absorbs all the incident radia­
tion at all frequencies, reflecting none (Ulaby et al., 1981). A blackbody
is a perfect emitter. An ideal emitter that radiates energy at the maximum
rate per unit area at each wavelength for a given temperature (Siegal and
Gillespie, p. 687)
brightness
Radiated power (W) per unit solid angle (sr-1 m-2) (Ulaby et al., 1981)
brightness
tempera­
ture (Tb)
TB=Emissivity*physical temperature; the physical temperature of a
blackbody emitting the same amount of energy at a particular wave­
length as the body under consideration
complex
dielectric
constant, e
£=£' + j£ ”
cryosphere
That portion of the earth covered perennially or seasonally by ice or
snow or significantly affected by ice or snow cover. The major subdivi­
sions are glaciers and ice sheets, sea ice, lake and river ice, seasonal
snow cover and permafrost.
XV
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Glossary
Term
Definition
dielectric
constant
Ratio of complex permittivity of a medium to that of free space ratio of
the electric field strength in a vacuum to the electric field strength within
the material, for the same distribution of charge (SIPRE, 1951). It is
commonly measured by observations of the capacitance: e=C/Co
egg code
Numeric code used to describe World Meteorological Classification of
sea ice in terms of total concentration, partial concentrations of major ice
types, stage of development (thickness) and form of ice (see Chapter 2).
electromag­
netic spec­
trum
The entire frequency (wavelength) range of electromagnetic radiation.
EOSDIS
Earth Observing System Data and Information System
ERS-1,
ERS-2
European Remote-Sensing Satellites 1 and 2 (C-band radar).
flaw
A narrow separation zone between pack ice and fast ic e ;... it forms when
pack ice shears under the effect of a strong wind or current along the fast
ice boundary (WMO, 1970).
frazil
Fine spicules or plates of ice suspended in water.
granule
The smallest aggregation of data which is independently managed (i,e„
described, inventoried, retrievable). Granules may be managed as logical
granules and/or physical granules. Source: NASA EOSDIS glossary.
grey body
A body that emits less than a blackbody and does not necessarily absorb
all the energy incident upon it (Ulaby, et al., 1981, p. 200)
DDL
Interactive Display Language (data visualization software from
Research Systems International)
imaginary
part of
dielectric
constant, e’
The imaginary part of the complex dielectric constant, e” . This factor
controls attenuation of a wave in a dielectric medium.
ir
Infrared (radiation) (near ir ~ 0.72-1.30 pm) (mid ir -1.30-3.00 pm)
(thermal infrared (dr) ~ 7.0-15.0 pm)
JERS-1
Japanese Earth Resources Satellite-1 (L band radar).
lake ice
Freshwater ice formed on the surface of a lake.
lead
Any fracture or passage-way through sea ice which is navigable by sur­
face vessels (WMO, 1970).
xvi
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Glossary
Definition
Term
longwave
Thermal infrared
microwave
Refers to the portion of the electromagnetic spectrum between - 1 mm 1 m (300 - 0.3 GHz)
MIMR
Multifrequency Imaging Microwave Radiometer. Spatial resolution:
4.86 km (90 GHz), 11.62 km (36.5 GHz), 22.3 km (23.8 GHz), 22.3 km
(18.7 GHz), 38.6 km (10.65 GHz), 60.3 km (6.8 GHz) (Source: EOS
Handbook web document, 1996.) 3-day global coverage of the Earth.
nir
Near infrared (0.72-1.30 Jim)
passive
microwave
Referring to remote sensing utilizing thermal (blackbody) emission in
the 0.3-30 cm wavelength portion of the electromagnetic spectrum.
passive sen­
sor
A remote sensing system that receives naturally upwelling reflected and
emitted radiation from a scene (e.g., visible and infrared sensors
AVHRR and Landsat, or passive microwave sensor SSM/I).
phenology
a branch of science dealing with the relations between climate and peri­
odic biological phenomena. In an ice climatology context it refers to the
timing of annual ice freeze-up and break-up, generally studied over
many years.
polynya
Any non-linear shaped opening enclosed in ice. Polynyas may contain
brash ice, new ice, etc.
radiance
Radiant flux per unit solid angle leaving an extended source in a given
direction per unit projected source area in that direction (W m-2 sr-1)
(Suits, G. H., “The Nature of Electromagnetic Radiation” in Colwell,
1983)
real part
dielectric
constant
s ’. This part controls the velocity and wavelength of an electromagnetic
wave in a medium.
radiative
transfer
Theory dealing with the propagation of electromagnetic radiation
through a medium (NASA, 1994).
radiometer
An instrument that quantitatively measures electromagnetic radiation
(NASA, 1994).
reflectivity
Ratio of reflected to incident energy.
remote
sensing
The technology of acquiring data and information about an
object or phenomenon by a device that is not in physical contact with it
(NASA, 1994).
xvii
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Glossary
Term
Definition
snow
As snow on the ground, a mixture of ice crystals and grains, air pores
and possibly liquid water. Also, the atmospheric precipitate formed of
ice crystals.
SSM/I
Special Sensor Microwave / Imager (passive microwave sensor with
channels at 19, 22, 37 and 85 GHz).
stereology
The branch of science concerned with inferring the three-dimensional
properties of objects based on two-dimensional views (e.g., analysis of
snow plane (thin-) sections).
TeraScan
Image processing software from SeaSpace Corporation.
transmissiv­
ity
Ratio of transmitted to incident energy.
vis
Visible light (-0.38-0.72 |im).
Bibliography
Colwell, R. E., (Ed), Manual o f Remote Sensing, 2nd ed, Vol 1, pp 475-515., American
Society of Photogrammetry, Sheridan Press, 1983.
NASA, Looking at Earth From Space: Glossary of Terms. NASA, Office of Mission to
Planet Earth, Educational Reference EP302, August 1994.
Siegal, B. S. and A. R. Gillespie (eds.), Remote Sensing in Geology, John Wiley and Sons,
New York, 702 pp., 1980.
SIPRE, Review o f the Properties o f Snow and Ice, Snow, Ice and Permafrost Research
Establishment, U.S. Army Corps of Engineers, SIPRE Report 4, 156 pp., 1951.
Ulaby, E T., Moore, R. K., and A. K. Fung,, Microwave Remote Sensing-- Active and Pas­
sive. Artech House, Norwood, MA, 3 vol., 2162, 1981.
WMO (World Meteorological Organization), WMO Sea Ice Nomenclature, WMO Report
259, Secretariat of the World Meteorological Organization, Geneva, Switzerland, 159 pp.
1970.
xviii
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Table 1: Electromagnetic quantities in the microwave and optical regions (modified
after Ulaby, et al., 1981)a
Microwave
Optical
Defining
equation
Abbreviation
Unit
energy
radiant energy
joule
J
energy density
radiant density
joule m '3
Jm '3
power
radiant flux
P=dE/dt
joule sec'1
=watt
W
power/flux
density
radiant flux
S=dP/dA
W m'2
radiation inten­
sity
radiant inten­
sity
F=dP/dO
W sr'1
brightness
radiance
B=d2P/dQdA
W sr^m '2
emissivity
emissivity
e=B/Bjj[ac|C(j(Xjy
reflectivity
reflectance
y=?SPf
y
absorptivity
absorptance
a= Pa/Pi
a
transmittance
transmissivity
T=Pt/Pi
T
a. This table is an extension o f the glossary included to clarify terminology which tends to vary
depending upon the spectral region under consideration. For the most part, the nomenclature
used in this dissertation is that o f microwave remote sensing.
b. r=reflected, i=incident, a=absorbed, t=transmitted.
xix
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Acronyms, Symbols and Abbreviations
AVHRR
Advanced Very High Resolution Radiometer
E
complex dielectric constant
£’
real part of the dielectric constant
e”
imaginary part of the dielectric constant
0
angle of incidence
x
transmissivity
tj
intrinsic impedence
T
reflectivity
T
transmissivity
p
density (e.g., snow, g/cm3)
C
Celsius, centigrade (degrees)
emf
electromagnetic field
Ex, Ey
x and y components of the electric field vector
GOES
Geostationary Operational Environmental Satellite
hpol
horizontal polarization
HTML
hypertext markup language.
ir
infrared (all infrared, or commonly all infrared other than thermal infrared
(tir)
K
Kelvin (degrees)
MSFC
Marshall Space Flight Center
NIC
National Ice Center
nir
near infrared
SSM/I
Special Sensor Microwave/Imager
Tant
antenna temperature
TAP
apparent brightness temperature
Tb
brightness temperature
^Bsnow
snow brightness temperature
Tssky
sky brightness temperature
XX
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^Bsky_corrected
snow brightness temperature corrected for atmospheric contribution
tir
thermal infrared
tk
physical temperature
tdr
time domain reflectometer
URL
Universal Resource Locator (World Wide Web document address)
vis
visible (light)
vpol
vertical polarization
xxi
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1
Chapter 1: Overview
The subject of this dissertation is passive microwave satellite remote sensing of ice
and snow on and near Lake Superior. Four individual investigations are presented: two sat­
ellite image studies and two field studies, all interrelated by a theme of microwave remote
sensing o f snow and ice. The scientific context is cryospheric remote sensing and hydro­
logic monitoring. The motivation is to improve ice and snow remote sensing capabilities
for application to climate change detection, measuring energy and mass fluxes at the earthatmosphere interface, hydrology, meteorology, limnology, navigation and resource man­
agement.
1.1 Outline
Chapter I outlines the context of these studies and introduces some of the fundamen­
tal physical and electromagnetic concepts underlying this work.
Chapter 2 is a first look at Lake Superior ice cover using SSM/I passive microwave
brightness temperature imagery. The motivation is to exploit the SSM/I all-weather daynight imaging capability to improve the temporal resolution of existing methods to one to
six images per day. In addition, thermal emission of microwave radiation from ice conveys
information on the physical properties of the ice (e.g, thickness, concentration, surface
melt state). Digitally coregistered SSM/I, AVHRR and National Ice Center ice chart
images are used to investigate the utility of SSM/I as a tool for daily Great Lakes ice mon­
itoring. Ice covered and ice free regions are discussed in terms of their microwave and
thermal infrared signatures.
Chapter 3 (Pilant, 1996a) is a passive microwave time series analysis of Great Lakes
ice cover for the winter of 1993-94. Time series of SSM/I TB are compared with air tem­
perature and snow accumulation data, illuminating relationships between ice cover and
climate. Image time series of 37 and 85 GHz TB spanning the 1993-94 season display spa­
tial patterns of ice growth and decay.
Chapter 4 (Pilant, 1996b) presents ice surface roughness surveys on four nearshore
ice facies on the coast of the Keweenaw Peninsula, MI. Surface roughness is a controlling
factor in radar backscatter and microwave emission, and commonly is genetically related
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2
to ice type.
Chapter 5 (Pilant, 1994a) is a field study of the effect of topographic aspect on snow
Tb . Brightness temperature varies as a function of snow wetness, grain size and physical
temperature (among other factors), factors affected by solar insolation, which is in turn
controlled locally by topographic aspect. Snow 37 GHz TB and grain size measurements
were made in the north and south facing slopes of a gully through a number of diurnal
cycles.
Appendix A (Pilant, 1994a,b) contains a description of field experiments to measure
snow pack and sky brightness temperature (37 GHz vertical and horizontal polarization)
using a tower-mounted radiometer. The field studies were motivated by the need for field
verification of satellite passive microwave remote sensing and computer modeling of snow
radiative transfer processes. Graphs are presented showing snow and atmosphere TB ver­
sus observation incidence angle.
Appendix B contains examples of computer programs used in these analyses.
A glossary and list of abbreviations are provided to help the reader manage poten­
tially unfamiliar, acronym-rich nomenclature.
1.2 Environmental Context
The term cryosphere refers to that portion of the earth perennially or seasonally cov­
ered by snow or ice or in some significant measure affected by water in the solid state.
This definition comprises the environments of perennial continental ice sheets (Antarctica
and Greenland), alpine glaciers and snowfields, Arctic and Antarctic sea ice, seasonal
snow cover, seasonally frozen lakes and rivers and permafrost areas. Here it refers specifi­
cally to seasonal ice and snow cover on Lake Superior and snow cover on the Keweenaw
Peninsula. Cryospheric remote sensing has in the last two decades emerged as a remote
sensing field o f expertise, with some degree of specialization in the above environments.
1.3 Motivation
The cryosphere is inherendy sensitive to climate condidons. Signals of potendal glo­
bal climate change, if any, may be expected to appear earlier in the cryosphere than in
other environments (e.g., Thomas, 1991; Gurney et al., 1993). Ice sheets, glaciers, sea ice
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3
and seasonal snow are all satellite monitored toward detection of potential climate change
signals. In this context, lake ice phenology (annual timing and dynamics of lake ice evolu­
tion) may also be monitored as a possible indicator of climate trends (Wynne and Lillesand, 1993; Liston and Hall, 1995 a,b). On the other side of the equation, it is important to
predict what impacts climate change may have on the Great Lakes (Hartman, 1990; Assel,
1991; Smith 1991). For example, General Circulation Model results indicate that at 2x
current CO2 levels, mean annual temperatures in the Great Lakes basin would rise by 2-4
°C (Canada and U.S. EPA, 1995). The consequent increases in evaporation and evapotranspiration could cause drops in lake levels of 0.5 to 2 m with consequent impacts on the
shipping and hydroelectric industries, to shoreline infrastructure, and upon wetlands and
nearshore habitats.
Additional motivations for using remote sensing techniques to monitor snow and ice
include water supply management, changes in lake and river levels, flood control, naviga­
tion, changing shoreline processes (erosion, transport, deposition, ice damage), military
target recognition, avalanche safety and recreation.
1.4 Mechanisms
Seasonal snow cover has a major impact on the global environment, as well as in the
Great Lakes region. The magnitude of the impact stems from the radical degree to which it
alters the energy balance between earth and atmosphere. The dominant mechanisms and
physical properties are:
•
high (-0.8-0.98) visible albedo;
•
high thermal insulation value;
•
water storage capacity;
•
ability to transfer heat to the atmosphere during evaporation (e.g., lake effect
snow);
•
vast areal extent; and
•
ephemeral nature.
Ice is present on the Great Lakes for two to four months a year, and, like snow, radi­
cally alters the lake-atmosphere energy balance. The principal mechanisms by which lake
ice influences the surrounding environment are as follows:
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4
•
thermal insulator to limit heat transfer from lake to atmosphere;
• physical barrier to mass transfer from lake to atmosphere;
• physical barrier to kinetic energy transfer from wind to lake;
• electromagnetic barrier to solar insolation and outgoing longwave radiation; and
• control of thermal gradients influencing lake circulation.
1.5 A Conceptual Remote Sensing Model
A target (snow, ice) radiates electromagnetic energy via a combination of reflection
(surface and volume scattering), emission and transmission. The amplitude, polarization
and phase of the outgoing wave is dependent upon the physical and electromagnetic prop­
erties of the target medium. A satellite, aircraft or ground sensor measures the intensity,
and possibly polarization and phase, of the incoming electromagnetic field and stores this
information digitally. These data are then digitally processed and (visually) enhanced to
extract information about some geophysical parameter of interest. The fundamentals of
snow and ice remote sensing are discussed in Hall and Martinec (1985), Thomas (1991),
Carsey (1992), Colwell (1983), Ulaby, et al. (1981), Mellor (1964), SIPRE (1951) and
Elachi (1987).
Snow and ice are compositionally simple, being composed of hydrogen, oxygen and
air. However, they are surprisingly complex electromagnetically, due principally to the
large dielectric contrast between liquid and solid water (-80 versus 3 at the microwave fre­
quencies of interest). Solid and liquid water may very well coexist in the sensor field of
view, and may fluctuate from a frozen to thawed state in a complex manner both diumally
and seasonally. The radiative transfer issue is further complicated by geometric or struc­
tural properties such as grain size and layering, and spatial and temporal variability.
In this dissertation, snow generally refers to snow deposited on the ground, vegeta­
tion or ice, as opposed to the form of atmospheric precipitate. Snow may be operationally
defined as a layered mixture of ice grains and crystals, air, impurities and (possibly) liquid
water. The term ‘ice’ generally refers to the lake ice cover on Lake Superior. In discussion
of electromagnetic topics such as the dielectric constant, ‘ice’ may refer more specifically
to solid water, as in ice crystals and snow grains.
Table 1 summarizes the fundamental snow and ice remote sensing relationships rele­
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5
vant to the chapters that follow. The principal physical properties controlling microwave
emission from snow are (in roughly descending order of priority):
•
wetness (the effect of dielectric contrasts between solid and liquid water);
•
snow pack thickness;
•
grain size;
•
layering; and
•
temperature.
The principal factors controlling microwave emission from lake ice are (in roughly
descending order of priority):
•
wetness;
•
thickness;
•
surface roughness;
•
snow cover;
•
internal features (e.g., air bubbles, layering, fractures); and
•
temperature.
Mie scatter dominates the snow grain - microwave interaction. The snow pack may
be internally layered, the stratigraphic record of the pack’s (primarily) thermal metamorphic history. Such layers, as well as the snow-soil, snow-air, ice-water and ice-air inter­
faces, reflect and refract radiation. Boundary surface roughness at the various interfaces is
a factor in emission and backscatter. Microwave emission and scattering are both sensitive
to volume and surface conditions, while in contrast, visible and infrared emission and
scattering are primarily surface phenomena (shorter wavelengths = shallower skin depths).
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6
Table 1.1: Spectral regions, electromagnetic effects and important physical
properties
Spectral
region
Electromag­
netic effects
Physical properties affecting signal
Typical sensors
SNOW
gamma ray
transmis­
sion, attenu­
ation
snow thickness
aircraft (National
Operational Hydro­
logic Remote Sens­
ing Center)
visible
reflection
grain size, density, wetness, age
AVHRR, GOES,
Landsat, SPOT,
MODIS
near
infrared
reflection
grain size, temperature
AVHRR, Landsat,
SPOT, aircraft
MODIS
thermal
infrared
emission
grain size, temperature
AVHRR, GOES,
Landsat, aircraft,
MODIS
passive
microwave
emission
dielectric constant, wetness, grain
size, thickness, surface roughness
SSM/T, aircraft,
AMSR, MIMR,
active
microwave
reflection/
transmis­
sion
surface roughness, dielectric con­
stant, wetness, thickness
RADARSAT,
ERS1-2, JERS-1,
Shuttle Imaging
Radar; aircraft
visible
reflection
wetness, roughness, age, thickness
(see SNOW sensors
above)
near
infrared
reflection
grain size
thermal
infrared
emission
temperature, roughness, thickness
passive
microwave
emission,
transmis­
sion
dielectric constant, thickness,
structure, wetness, surface rough­
ness, snow cover
active
microwave
surface and
volume
scattering
surface roughness, wetness, thick­
ness, structure, inhomogeneities,
impurities
ICE
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Table 1.2: Electromagnetic Quantities9
Microwave terminology
Optical terminology
Defining
equation
Abbreviation
energy
radiant energy
joule
J
energy density
radiant density
joule/m3
Jm '3
power
radiant flux
P=dE/dt
W
power/flux density
radiant flux
S=dP/dA
Wm'2
radiation intensity (or
radiation pattern
radiant intensity
F=dP/dQ
W sr'1
brightness
radiance
B=d2P/
dQdA
W s r 'V 2
emissivity
emissivity
e=B/Bbb
reflectivity
reflectance
T=Pr/Pia
absorptivity
absorptance
a=Pa/Pi
transmittance
transmissivity
t=Pt/Pi
a. From Ulaby, et al., 1981; Table 4.1
1.6 Sources of snow and ice data
There are a number of agencies and sources dealing with snow and ice information,
most of which are available online through the World Wide Web. The NOHRC (National
Operational Hydrologic Remote Sensing Center) provides weekly snow charts for the U.S.
The National Ice Center (NIC, formerly the Joint Ice Center) produces ice concentration
charts for civilian and military use. The Canadian Ice Service is the NIC’s Canadian coun­
terpart. The U.S. National Weather Service provides climate and meteorological informa­
tion. Satellite data are available from a number of sources, most notably in this document
from the NOAA Satellite Active Archive and the Marshall Space Flight Center (both of
these are NASA DAAC (Distributed Active Archive Centers)).
1.7 Bibliography
Assel, R. A., Implications of C 0 2 global warming on Great Lakes ice cover. Climatic
Change, 18, pp 377-395, Kluwer Academic Publishers, 1991.
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8
Canada and US EPA, The Great Lakes- An Environmental Atlas and Resource Book (3rd
ed.): Government of Canada and U.S. Environmental Protection Agency, Canada Centre
for Inland Waters, Burlington, ONT, 46 pp., 1995.
Carsey, F. D. (ed.), Microwave Remote Sensing o f Sea Ice: American Geophysical Union
Monograph 68, Washington, D.C., 440 pp., 1992.
Colwell, R. E., (Ed), Manual o f Remote Sensing, 2nd ed, Vol 1, pp 475-515., American
Society of Photogrammetry, Sheridan Press, 1983.
Elachi, C., Introduction to the Physics and Techniques o f Remote Sensing, 1st ed, John
Wiley & Sons, New York, 1987.
Gurney, R. J., Foster, J. L. and C. L. Parkinson (eds.), Atlas o f satellite observations
related to global change: Cambridge University Press, 470 pp., 1993.
Hall, D. K. and J. Martinec, Remote sensing o f ice and snow. Chapman and Hall, New
York, 189 pp. 1985.
Pilant, D., Measuring snow and soil moisture conditions using time domain
reflectometry and ground penetrating radar, presented at 50th Anniversery Meeting
Eastern Snow Conf- Joint Meeting with the Western Snow Conf, Quebec City, Canada,
June 8-10, 1993.
Pilant, D.„ Meter-range 37 GHz passive microwave time series measurements of
terrestrial snow cover (abstract): 1994 Fall Meeting Amer. Geophys. Union, EOS
supplement Nov. I, 238. 1994a
Pilant, D., Close-range 37 GHz microwave observations of snow on north and south
facing slopes, IGARSS94 Proc. Int. Geosci. Remote Sensing Symp., Pasadena, August 812, 1994b.
Pilant, D.,. SSM/I time series observations of Great Lakes Ice and Snow: Proc. 52nd
Eastern Snow Conf, June 8-9, 1995, Toronto, pp. 21-28, 1996a
Pilant, D., Ice surface roughness surveys on Lake Superior: IGARSS96 Proc. Int. Geosci.
Remote Sensing Symp., May 27-31, 1996b.
Pilant, D., Lake Superior ice concentration using SSM/I, presented at IGARSS96 Int.
Geosci. Remote Sensing Symp., May 27-31, 1996c.
SIPRE, Review of the Properties of Snow and Ice, Snow, Ice and Permafrost Research
Establishment, U.S. Army Corps of Engineers, SIPRE Report 4, 156 pp., 1951.
Smith, J.B., The Potential impacts of climate change on the Great Lakes. J Bull. Am. Mete­
R e p ro du ced with permission o f the copyright owner. Further reproduction prohibited without permission.
9
orological Soc, 72, pp21-28, American Meteorological Society, 1991.
Thomas, R. H., Polar Research from Satellites. Joint Oceanographic Institutions, Wash­
ington, D. C., 58 pp. 1991.
Ulaby, F. T., Moore, R. K., and A. K. Fung,, Microwave Remote Sensing— Active and Pas­
sive. Artech House, Norwood, MA, 3 vol., 2162, 1981.
Wynne, R. H. and T. M. Lillesand, Satellite observation o f lake ice as a climate indicator.
initial results from statewide monitoring in Wisconsin, Photogrammetric Engineering and
Remote Sensing, 59, 1023-1031, 1993.
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10
Chapter 2: Lake Superior ice cover viewed using SSM/I passive
microwave imagery
key words: lake ice, microwave brightness temperature, Great Lakes, SSM/I, satellite
monitoring, cryosphere
Abstract
Ice cover is significant in the Laurentian Great Lakes annual hydrologic cycle, as an
indicator o f climate trends, and in influencing or controlling a variety of natural and indus­
trial processes. Limitations to current satellite monitoring capabilities include illumination
and cloud conditions (visible and infrared), and cost and temporal resolution (radar). Pas­
sive microwave imagery from SSM/I (Special Sensor Microwave/ Imager) offers comple­
mentary information to augment existing remote sensing capabilities. Three sun
synchronous SSM/I sensors provide up to six illumination and weather-independent
images per day, four of which are routinely available on the Internet within hours of acqui­
sition. The seven SSM/I microwave channels are inherently sensitive to ice conditions
(dielectric properties, thickness, surface roughness, temperature). The purpose of this
study was to investigate the potential utility of SSM/I as a tool in monitoring Great Lakes
ice.
Ice conditions on Lake Superior for February 1 and 4, 1996 were examined using
combinations of SSM/I imagery, AVHRR (Advanced Very High Resolution Radiometer)
imagery and National Ice Center ice charts. The 37 and 85 GHz SSM/I channels were
selected for detailed examination because o f their relatively higher spatial resolution and
penetration depths commensurate with ice thicknesses characteristic of the Great Lakes.
Horizontal polarization was selected to exploit the large emissivity contrast between water
and ice. Lake ice (egg code categories 1,4 and 5 (0-30 cm)) 37 GHz hpol T b ranges from
approximately 160-220 K, with a mean of 201 K (19 K s.d.) for the two dates. Similarly,
the regions mapped as ice free range from approximately 137-160 K, with a mean of 145
(10 K s.d.). These values are comparable to T b documented for young sea ice. Regions
mapped as ice free display downwind-increasing T b gradients which may indicate the
downwind accumulation of new ice undetectable by other means. The spatial distribution
of T b is consistent with downwind ice accumulation. Ice apparent emissivities were calcu­
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11
lated and range from 0.7-0.88 (37 GHz hpol) and 0.7-0.9 (85 GHz hpol). Western basin ice
exhibits higher T b and emissivity, consistent with an accumulation of older, more
deformed ice, reflecting the overall ice development chronology, with the east basin last to
freeze up. Digitally coregistered SSM/I images and ice charts indicate an increase of T b
(and emissivity) with increasing stage of development (or thickness) (subject to provisos
o f registration accuracy).
Despite the low spatial resolution (13-69 km pixels), SSM/I may provide timely and
pertinent information, particularly in documenting the daily chronology of ice extent (and
possibly type), freeze-up, break-up, and spring surface melt events. Spatial resolution and
consequent monitoring capabilities will be greatly improved with the launch of the next
generation of passive microwave imagers.
2.1 Introduction
2.1.1 Motivation
Ice cover is an integral component of the North American Great Lakes annual hydro­
logic cycle, influencing a host of lake and atmospheric processes. Inclement conditions
and large areal extents (Lake Superior: -81,200 km2) make direct observations of Great
Lakes ice difficult, motivating the use of satellite remote sensing as the foundation of lake
ice monitoring. Current methods are based primarily on analysis of visible (vis) and ther­
mal infrared (tir) and secondarily radar imagery, and are limited by cloud cover (vis, tir),
solar illumination (m ), acquisition scheduling (radar) and cost (radar). Rapidly evolving
and ephemeral ice phenomena (e.g., freeze-up, break-up, growth, ice motion) may be
infrequently imaged as a result. This paper is an investigation of the utility of SSM/I (Spe­
cial Sensor Microwave / Imager) passive microwave imagery in observing Lake Superior
ice cover. Though the 13-69 km footprint dimensions are at the limit (spatially) of utility
for the Great Lakes, the enhanced temporal resolution (up to 6 weather and illumination
independent images per day) and inherent sensitivity to ice thickness merit investigation.
Great Lakes ice research has a number of operational and climatological motivations
(Bolsenga, 1992). Navigation is prominent; duration and thickness of ice cover control the
shipping season (Great Lakes-St. Lawrence Seaway Winter Navigation Board, 1975). Ice
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12
cover influences lake levels, affecting hydroelectric power generation, shipping channel
navigability and shoreline processes such as sedimentation, erosion and sediment trans­
port (Marsh et al., 1975; Barnes et al., 1994). Ice jams may produce flooding and struc­
tural damage; frazil ice may clog municipal and industrial water intakes. In the biological
realm, phytoplankton photosynthesis is limited by reduced solar insolation reaching the
water column and shorefast ice provides important fish habitats.
The climatological dimension of ice cover centers on regulation of mass and energy
fluxes at the lakes’ surfaces. Ice is an electromagnetic barrier that reduces incoming solar
flux and outgoing longwave emission, and a physical barrier that restricts sensible and
latent heat loss, water vapor loss and kinetic energy transfer from wind to lake. The lakes
supply heat and water vapor to the atmosphere for months after land surfaces have cooled
below freezing, and thereby modify mesoscale weather systems. Ice cover restricts evapo­
ration and, consequently, lake-effect snow production, a significant meteorologic and eco­
nomic feature of the Great Lakes snow belt. Evaporation, largely ice cover controlled, is a
major term in the hydrologic budget and may account for approximately half of Lake
Superior’s annual outflow at the St. Mary’s River (Bennet, 1978). Lake circulation is influ­
enced by ice cover by reducing wind coupling with the lake surface and by altering ther­
mal gradients in time and space as ice moves around.
The cryosphere is inherently sensitive to climate, and for this reason may be moni­
tored remotely for climate change signals. While satellite sea ice monitoring is a fairly
mature discipline, lake ice monitoring by satellite is relatively underdeveloped. A number
of authors have looked at freshwater ice trends as climate indicators (Wynne and Lillesand, 1994; Liston and Hall, 1995 a,b; Assel, et al., 1994; Hall et al., 1994). The phenological variables studied are primarily timing of freeze-up, break-up and overall ice season
duration. Because of the unusual size of the Great Lakes, additional measurable parame­
ters of total areal extent at a given time and ice location may yield potentially useful infor­
mation.
2.1.2 Remote sensing context
2.1.2.1 Visible and infrared
Remote sensing of Great Lakes ice cover to date has emphasized visible and thermal
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13
infrared imagery from AVHRR (Advanced Very High Resolution Radiometer) (McMillan,
1975; Quinn et al., 1978; Wiesnet, 1979; Bell, 1982; Schwab et al., 1992; Leshkavich,
1995), and to a lesser degree Landsat (Leshkevich, 1985). These wavelengths discriminate
ice (except thin ice) and water very well as a result of strong contrasts in albedo and phys­
ical temperature. The temporal resolution is potentially very high, with up to four AVHRR
images per day, and GOES (Geostationary Operational Environmental Satellite) imagery
every thirty minutes. The problem is the dependency upon clear skies and solar illumina­
tion for visible imagery, and upon relatively clear skies for infrared. Cloud cover may
obscure a lake or portions thereof for days at a time. There is a high probability that clouds
will be present in most scenes; open water areas are particularly obscured as they are
sources of intense evaporation and lake-effect cloud formation.
2.1.2.2 Active microwave
Active microwave remote sensing of Great Lakes ice cover has been applied inter­
mittently, originally in the form of airborne side-looking radar (SLAR) (Hagman, 1976;
Bryan and Larson, 1975; Bolsenga, 1978). Satellite SAR (synthetic aperture radar) imag­
ery has been available since the 1991 launch of ERS-1 (European Remote-sensing Satel­
lite), followed by ERS-2, JER S-1 (Japanese Earth Resources Satellite) and most recently,
RADARSAT. SAR is an extremely powerful tool in ice studies: imagery is virtually
weather-independent and is completely day-night independent; the return signal conveys
information regarding ice surface and volume scattering characteristics (which relate to
ice type); and the high dielectric contrast of water and ice leads to a high degree of dis­
crimination between water and many ice types. The limitations of SAR imagery are essen­
tially as follows. It is less frequently acquired (greater than three day repeat cycle), the
sensor requires advance scheduling for image acquisition, SAR imagery is relatively
expensive, it tends to require more complex digital processing than vis-tir and correlations
between backscatter and ice types are not completely developed.
2.1.2.3 Passive microwave
Passive microwave remote sensing complements existing methods in two ways:
increased temporal resolution (up to six weather and solar-illumination independent
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14
images per day between the SSM/I sensors on platforms F8, F10 and F13) and sensitivity
to ice thickness (emitted energy is roughly proportional to ice thickness). Coarse spatial
resolution (tens o f km) is the primary limitation, due to the large footprints necessary to
sense the relatively low intensity microwave radiation emitted by earth targets.
Microwave radiometery has received little attention in freshwater ice studies; nearly
all have been aerial surveys of smaller lakes. Swift et al. (1980) report on aerial surveys
over Lake Erie using a 4.5-7.2 GHz radiometer that show brightness temperature propor­
tional to ice thickness. Hall et al. (1981) used airborne radiometry to measure ice thickness
on Walden Reservoir in Colorado. They report a strong correlation between Tb and ice
thickness at 6.0 cm wavelength, and weaker correlations at 1.67, 1.35 cm and 0.81 cm. A
nadir look angle yielded the best results, inclined look angles being complicated by sens­
ing greater thicknesses of ice. Schmugge et al. (1973) describe overflights of Bear Lake,
Utah with similar results.
Even fewer reports of satellite passive microwave observations of lakes exist. Walker
and Davey (1994) used the SSM/I 85 GHz channel to monitor freeze-up and break-up on
Great Slave Lake. Pilant (1995) presented a time-series of 85 and 37 GHz SSM/I images,
air temperature and snow accumulation to encapsulate the 1993-94 Great Lakes ice sea­
son. Ice growth, decay and drift patterns were highly evident in computer animations of
daily brightness temperature images.
2.1.3 Outline
Because so little has been published on freshwater ice cover microwave radiometry,
this preliminary, empirical investigation focuses on two basic issues: what are the general
microwave brightness temperature (Tb) characteristics of Lake Superior ice cover, and is
there a correlation between Tb and ice stage of development (essentially, ice thickness)?
The approach is largely visually oriented, using a series of interpreted SSM/I and AVHRR
satellite images. National Ice Center ice charts are used as ground truth. Digitally merged
SSM/I images and ice charts are used to assess the correlation between ice Tb (and emis­
sivity) and stage of development.
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15
2.2.0 Data: SSM/I, AVHRR, NIC ice charts
2.2.1 Dates
The 1996 winter produced an extensive ice cover on Lake Superior. February 1 and
4,1996 were selected for analysis based on the large areal extent of ice cover, the presence
of ice free regions for signature contrast and a relatively clear atmosphere. February 4 was
particularly cloud free, allowing computation of ice microwave apparent emissivity for
that date.
2.2.2 SSM/I passive microwave brightness temperature imagery
2.2.2.1 Data Description
The Department of Defense (DOD) operates a constellation of polar orbiting sunsynchronous satellites under the DMSP (Defense Mapping Satellite Program). The mis­
sion objective is to support DOD operational needs in meteorology, oceanography and
solar-geophysics. Satellites F10, F l l and F13 carry the SSM/I sensor, a four frequency,
dual polarization imaging radiometer (Hollinger et al., 1990) (Table 2.1) (attributes of
AMSR, a future EOS radiometer, are included for comparison). SSM/I is used extensively
in sea ice (Carsey, 1992; Haykin et al., 1994) and snow cover monitoring. NASA’s Mar­
shall Space Flight Center (MSFC) Hydrologic Cycle Distributed Active Archive Center
maintains an online, near real-time archive of F10 and F13 data, and was the source of
SSM/I data for this investigation. SSM/I data used here are referred to as “full resolution
(or ‘swath’) brightness temperature data”. The antenna beam intersects the earth surface
normal at a nominal incidence angle of 53.1 degrees.
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16
Table 2.1: SSM/I (and AMSRa) frequencies and footprints
Frequency (GHz); wavelength
(mm) (polarization)11
(AMSR frequency in {})
Approximate Footprint
Size
Along-track x Along-scan
(km)
(AMSR dimensions in {})
Pixel size of MSFC
full resolution
brightness
temperature data
(km)
19.35 G H z; 15.5 mm (v,h) (18.7 GHz)
69 x 43
(22x13}
25x25
22.235 ; 13.5 (v only) (23.8 GHzJ
60 x 40
(25x15)
25x25
3 7 .0 ;8 .1 (v,h)
{36.5 GHz}
37 x 28
(12x7}
25x25
85.5 ; 3.5 (v,h)
(89.0 GHz}
15 x 13
(5x3}
12.5x12.5
a. AM SR: Advanced Microwave Scanning Radiometer, scheduled for launch on the EOS PM-1
platform .
b. v, h = vertical or horizontal polarization.
Brightness temperature is the fundamental unit of microwave radiometry. It may be
defined as the product of an object’s emissivity (e) and its physical (thermometric) temper­
ature (Tp) and is expressed in units of degrees Kelvin (K):
TB=e*TP.
Emissivity is the ratio of the amount of energy emitted by an object to the amount of
energy radiated by a perfect emitter (blackbody) at the same physical (kinetic) tempera­
ture; it varies between 0 and 1.0. Thus, a target will always have a brightness temperature
less than or equal to its physical temperature.
The T b reported here are corrected (by MSFC) for antenna pattern and along-scan
bias, but are not corrected for atmospheric or cosmic background contributions. This is
considered reasonable here given the relatively dry, clear atmosphere over Lake Superior
in February. Field observations of 37 GHz atmospheric brightness temperature were mea­
sured intermittently by the author at MTU over the 1993-94 winter (Appendix A). Sky
apparent brightness temperatures at an incidence angle of 55 degrees (near the SSM/I
beam incidence angle of 53.1 degrees) averaged over the season and under a variety of
atmospheric conditions were as follows: horizontal polarization, mean=32.2 K, standard
deviation=32.1, n=4; vertical polarization, mean=24.3, standard deviation=15.7, n=23.
These observations were made under conditions ranging from clear sky to precipitating
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17
snow clouds. These values give an indication of the magnitude of contributed sky bright­
ness.
The values reported are more accurately termed apparent brightness temperature and
apparent emissivity, but are hereafter referred to as Tb and emissivity for convenience.
Band ratioing techniques such as those employed in sea ice algorithms would partially
negate atmospheric contributions to Tb, but due to the preliminary nature of this investiga­
tion, the data are of necessity evaluated in their simplest forms, Tb and emissivity.
Raw (unprocessed) data preserve maximum radiometric fidelity. Registered data
may lose radiometric fidelity, but registration permis digital fusion with ice charts and
AVHRR images, and the image geometry may be easier to interpret. SSM/I data are pre­
sented here primarily in raw, unregistered ‘swath’ form, directly from the original HDF
files from MSFC DAAC. Processing is limited to contrast enhancement. The intent is to
preserve maximum spectral fidelity. Coregistration of SSM/I, AVHRR and ice charts
images to a common map projection facilitates integrated analysis. Registered versions of
SSM/I images are confined to Section 3.2. SSM/I images used here were selected more on
the basis of scene geometry (closest to satellite subtrack, minimizing off-nadir geometric
distortions) than on more exact temporal matching with the AVHRR imagery. These SSM/
I brightness temperatures have a radiometric resolution of 0.1 K.
2.22.2 Microwave Penetration Depths and Ice Code Thicknesses
Penetration depth is defined as the depth in a medium (e.g., ice) at which an electro­
magnetic wave decreases in amplitude to 1/e of its original value. It indicates the maxi­
mum depth of a medium that contributes to brightness temperature. Hallikainen and
Winebrenner (1992) provide the following expression for penetration depth:
dp = sqrt(e’) / (k * e” )
where e ’= dielectric constant (or real part of the relative permittivity), k is the wave num­
ber (2kIX) and e” is the dielectric loss factor (or imaginary part of the relative permittiv­
ity). The dielectric constant has an essentially invariant value between 10 MHz - 1000
GHz (Cummings, 1962; Matzler and Wegmuller, 1987):
e’=3.17
The dielectric loss factor, e ” , for freshwater ice maybe calculated as follows (Matzler and
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18
Wegmuller, 1987):
e ” = A/f + Bf*~
where f is frequency (in GHz) and A, B and C are empirically derived constants.Table 2.2
summarizes ice penetration depths at SSM/I frequencies computed using the above equa­
tion.
Table 2.2: Penetration depths of freshwater ice at SSM/I frequencies
ice
temperature
22.35 GHz
19.35 GHz
37.0 GHz
85.5 GHz
- 5 “C
139 cm
108 cm
43 cm
9 cm
- 15 UC
184 cm
140 cm
51 cm
10 cm
The World Meteorological Organization (WMO, 1970) prescribes the following
code (known as the ‘egg code’) to describe freshwater ice ‘stage of development’, with
associated ice thicknesses (Table 2.3).
Table 2.3: WMO Stage of Development
code
stage of development
thickness (cm)
1
new
0-5
4
thin
5-15
5
medium
15-30
7
thick
30-70
very thick
70-120
1.
Tables 2.2 and 2.3 together indicate the ice thic! ness each SSM/I channel is sensing.
The 19 and 22 GHz channels sense greater thicknesses and are minimally affected by the
atmosphere, but have impractically coarse spatial resolution.
The 85 GHz channels have the highest spatial resolution (12.5 km pixels), but 85
Ghz radiation may experience significant atmospheric contributions (attenuation, extinc­
tion), particularly from precipitating rain clouds. This generally precludes unsupervised
quantitative interpretation of T b . This channel is perhaps best suited for applications such
as nominal ice detection (presence- absence, perhaps including thin ice), melt onset and
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19
snow cover analysis.
The 37 GHz channels experience minimal atmospheric contributions, and have pen­
etration depths commensurate with Lake Superior ice thicknesses. Horizontal polarization
was selected to exploit the high emissivity contrast between water (low) and ice. The spa­
tial resolution (25 km pixels, based on a 37x28 km footprint) is near the limit (spatially) of
utility, but will be shown to be sufficient for a number of applications, including daily
monitoring of ice presence and ice edge location.
2.2.3 AVHRR thermal infrared and visible imagery
AVHRR Level 1 b local area coverage (LAC) images were acquired from the NOAA
Satellite Active Archive (SAA). Two channels were used in this analysis: band 1 (visible,
0.58-0.68 p.m) and band 4 (thermal infrared, 10.3-11.3 |im). The spatial resolution is nom­
inally 1.1 km at nadir. Image to map registration was based on satellite ephemeris infor­
mation contained in the level 1 b image header.
2.2.4 NIC ice charts
The U. S. National Ice Center (NIC) and Canadian Ice Service perform ice cover
analyses in support of winter operations on the Great Lakes. The NIC distributes these
analyses in the form of Great Lakes ice charts, three per week, available by fax or ftp. Ice
charts are used as ground truth in this study to help interpret microwave imagery, and to
test for sensitivity of T b to ice thickness. An ice chart consists of a simple outline of the
Great Lakes, with inscribed polygons drawn to represent regions of ice unified into mappable units by genetic characteristics. Polygons range in size from approximately 10010,000 km2. Each ice polygon is described by a sequence of code numbers inside an
ellipse (the World Meteorological Organization egg code (WMO, 1970)). Variables
mapped are /) total concentration, 2) partial concentrations of the three most extensive
ice types, 3) stage o f development (~ thickness) of the ice type(s), and 4) form of ice (flow,
brash, pancake, etc.) (form is typically either fast ice (code 8) or is omitted on the Lake
Superior charts). Examples of ice charts appear in Section 3.
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20
NIC ice charts are based on a combination of satellite image interpretation, freezing
degree day models, aerial reconnaissance and ship and shore reports (S. Young (NIC), per­
sonal communication). AVHRR imagery is the foundation of the analysis, providing syn­
optic coverage, normally a few times per week, depending on cloud conditions. Aerial
reconnaissance reports are largely a by-product of intermittent Coast Guard search and
rescue flights. Trained ice observers visually interpret ice conditions based on a combina­
tion of color, roughness, location and antecedent conditions. Ship observations are rou­
tinely reported to the NIC. A network of shore stations provides nearshore observations of
ice thickness. To a significant degree, ice thickness is estimated using freezing degree-day
(FDD) models (e.g., Assel et al., 1983). A FDD is defined as the average of the daily max­
imum and minimum temperature. A running total of FDDs serves as an index of winter
severity. Midlake thickness estimates rely particularly on these models due to the unavail­
ability of in situ measurements.
Note that an ice chart generally indicates ice conditions on the day preceeding the
chart’s analysis dates. February I and 4 satellite images are associated with February 2
and 5 ice charts, respectively. Table 2.4 summarizes the February 5 ice chart legend.
Table 2.4: Timing of input to February 5 ice chart
Date
Data Source
Reconnaissance Flight
02 Feb 96
Ship
04 Feb 96
Shore
04 Feb 96
Visible/Infrared
04 Feb 96
2.2.5 Digital coregistration of imagery and ice charts.
Images and ice charts were digitally coregistered to integrate ice charts and
Tb
in
Section 3.2. Registration software was used to ingest and register the SSM/I and AVHRR
imagery to a common map projection. SSM/I images were registered using latitude and
longitude of pixel centers provided with the data. AVHRR images were registered using
ephemeris information in the image header. Supervised image rectification (in addition to
the unsupervised mathematical transform) was performed overlaying a digital Lake Supe­
rior coastline and interactively repositioning the image to a visual best fit with the coast­
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21
line. No such supervised rectification was required for the AVHRR imagery, but SSM/I
imagery generally requires it. (This may related to limitation of the map registration algo­
rithms (A. Maclean, personal communication)). Registered SSM/I images were spatially
resampled to a pixel size of 1.1 km on a side. The map registration process consisted of
two steps due to software limitations. The images were first registered to a Lambert azi­
muthal projection in Terascan, and subsequently transformed to a UTM projection for pro­
cessing using ENVI. Ice charts were registered to the AVHRR images using ground
control points. Figure 2.1 displays an example of SSM/I image registration accuracy.
Figure 2.1. Example of coastline fit for registered SSM/I image. 37 GHz hpol, 25 km pix­
els, February 1.
Image brightness is proportional to Tb* The image was interactively rectified in addition to
the unsupervised registration based on pixel earth coordinates. This is an ‘optimal’ regis­
tration.
2.2.6 Comparison of raw and registered T b profiles
Geometric resampling during the map registration process necessarily involves spec­
tral resampling. Radiometric fidelity of a map registered image may be an issue in certain
applications. Here, the original pixels are geometrically redistributed to a new coordinate
system (UTM and Lambert azimuthal), and resized from 12.5 or 25 km to 1.1 km. New,
smaller pixels are generated and their values are typically assigned by either a nearest
neighbor or bilinear interpolation approach; nearest neighbor was used here. This section
compares raw and registered T b profiles to understand how resampling may introduce
spectral artifacts (i.e., artificial interpolated Tb values).
Trans-lake Tb profiles were extracted from the raw and registered images (37 GHz
hpol) (Figure 2.2) . A horizontal east-west profile was extracted from the Lambert azi-
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22
'ill J»3l
Figure 2.2. Locations of east-west T b profiles on raw, Lambert azimuthal projection and
UTM projection images.
37 GHz hpol; 25 km pixels. All three images were smoothed in processing for display.
muthal image; approximately the same profile was extracted from the UTM image. The
spatial correspondence is approximate due to slight geometric differences between these
two map projections.
The same profile was identified and extracted from the raw SSM/I data, made diffi­
cult due to the unrotated, swath-view perspective of the data; there may be mislocation
error at this step. There were 58 pixels in the raw profile, versus 600 in the Lambert and
614 in the UTM profiles. The raw profile was expanded by a factor of 10 to 580 pixels for
graphing with the registered profiles.
Figure 2.3 is a comparison of the three profiles. Overall, it appears that the difference
in T b varies from 0 to 4 K between raw and registered data (feature I). The two registered
profiles are nearly identical. The raw data graph has a stair-step appearance reflecting the
coarse pixel size and large Tb changes between land, ice and water. The largest source of
potential misinformation stems from the smoothing of the registered data between original
data points (feature 2). This is important in that the registered data make T b transitions
appear to be more gradual than they actually are in the original data, and in that they intro­
duce artifacts (T b of intermediate value) between ice and water pixels that do not exist in
the original data. The horizontal offsets o f the three graphs are produced by the different
pixel length o f each profile. The offset effect is magnified (artificially) toward the east end
of the graph (due to the differing lengths of the profiles). The artifacts revealed by this
graph do not significantly affect this analysis.
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23
24-0
230
Raw-
220
21 O
Lambert
UTM
200
19 0
18 0
1 70
16 0
15 0
1 4-0
1 30
O
west
200
4-00
. . . . .
_.
pixel position along profile
600
east
Figure 2.3. Comparison of raw and registered brightness temperature profiles.
Horizontal offset of the profiles results from differing lengths of profiles and from error
of visually estimating the position of each profile. Two radiometric resampling effects are
demonstrated. 1) Raw versus registered Tb values differ by approximately 0-4 K. 2) The
registered values are interpolated and smoothed between raw data values.
2.3.0 Image analysis
Section 2.3.1 describes Lake Superior ice conditions using a series of SSM/I,
AVHRR and ice chart images. The series is introduced with AVHRR and SSM/I images of
the Great Lakes on February 4. Next, the seven SSM/I frequency-polarization combina­
tions are displayed together for Lake Superior, elucidating typical brightness temperature
patterns o f ice, water and land. Following that, conditions on the two dates are examined
in greater detail using images of 37 and 85 GHz hpol Tb- Finally, February 4 ice emissiv­
ity is computed by dividing the SSM/I Tb image by the AVHRR Tp image. Section 3.2
discusses relationships between Tb and ice stage of development indicated on ice charts.
Mean Tb and emissivity of ice chart ice polygons are calculated.
2.3.1 Imagery
2.3.1.1 AVHRR thermal infrared temperature Great Lakes image, February 4
Figure 2.4 is an AVHRR band 4 (10.3-11.3 (im) thermal infrared image of the Great
Lakes at 08:11 on February 4; it is intended to set the stage for the SSM/I images that fol­
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24
low and to provide a sense for the regional context. Band 4 brightness temperature was
converted to physical temperature by multiplying by an ice emissivity of 0.98 (Warren,
1982). This single emissivity was used for the entire image, regardless of landscape classi­
fication; thus, Tp is accurate only for the ice cover, and not necessarily for the water sur­
face, land and clouds. Tp is more accurate north of the translucent clouds spanning the
southern lakes (and outside of obvious lake-effect clouds). Snow cover is almost certainly
widespread on the ice, but its exact distribution is unknown and no snow cover assump­
tions or corrections are made in these estimations.
Three different display techniques were used to examine temperature distribution,
yielding a three or four component thermal structure on the ice cover. The temperature
scale for the main image (A) is a linear stretch between -40 and 0 °C, displaying the ice
temperature distribution as a continuum (linear contrast stretches are used throughout to
simplify visual estimation of T b ). The Lake Superior subimage (B) density slices the ice
into five ten-degree classes. Color combinations of thermal infrared bands 4 and 5 (not
shown) suggest a somewhat tripartite thermal structure: cold, old ice; warm, new ice; ice
free, cold clouds. Ice pixels range in temperature from approximately -0.1 to -35 to -40 °C.
The following enumerated comments apply specifically to Lake Superior, but extend
in general to the other Great Lakes in Figure 2.4. Interpretations are based on a combina­
tion of visual analysis, cross-lake temperature profiles, images and ice charts viewed in
time series, trends observed in historical data (e.g., Assel et al., 1983) and field observa­
tions of ice forming processes. As a working framework, it is useful to consider the overall
thermal regime of this scene to comprise six principal thermal feature classes: four lake
classes, clouds and land.
1. Wanner, new, thin ice. An early February freezing event (February 1-4) produced vast
expanses (on the order of 25,000 km2) of new ice in the midlake areas. The February 5 ice
chart (Section 3.2) indicates that, on Lake Superior, most of this ice is mixtures of stage of
development codes 5, 4 and 1, with thickness ranging from 0-30 cm. Thinner ice is
warmer due to greater heat flux from underlying warm water. It is assumed to be relatively
little deformed, having had less opportunity for deformation due to its younger age.
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25
2. Colder, older medium to thick ice. A second class is older, colder ice, thickened by a
combination of longer periods of in situ growth, and by mechanical thickening through
accretion and imbrication. Ice accumulates early in the season in bays and coastal zones,
and, as the season progresses, tends to accrete episodically from coast to midlake (see ice
chart series below). Bay ice examples include Saginaw Bay on Lake Huron and Green Bay
on Lake Michigan. The NW coast of the Keweenaw Peninsula on Lake Superior is an
example of a windward shore developing ice in a series of accretionary belts. Bay ice and
coast ice may be shorefast for extended periods. In restricted places such as between Isle
Royale and the north shore o f Lake Superior, the coastline geometry traps drifting ice,
causing deformation and thickening. This class is more discernible in the full image than
the subimage.
3. Leads /fractures /cracks. The bright, warm fracture-like patterns in the ice cover indi­
cate, by temperature and form, flaws, leads and fractures. The linear segmentation resem­
bles extensional fractures in rigid plates (e.g., earth’s crust), probably resulting from wind
shear along zones of weakness, commonly in shore parallel zones (flaws). The upstream
ends of certain isolated lake-effect clouds appear to emanate from these features.
4. Open water / ice free regions / lake effect clouds. This class consists of the regions
mapped as ‘ice free’ on ice charts and are identified in this image by the abundant lake
effect clouds. They tend to be intimately associated with and obscured by the lake-effect
clouds they produce. Rather than being entirely ice free, these regions most likely contain
mixtures of water and ice, and are important centers of new ice growth through much of
the winter.
A polynya is a “nonlinearly shaped opening enclosed in ice” (Carsey, 1992). The
east basin ice free region is such a feature, remaining open for much of the ice season.
Polynyas are important features in the polar sea ice environment, being centers of high
heat flow, evaporation and strong density/salinity gradients. The east basin polynya per­
sists for much of the winter (unpublished image analysis, and Assel et al., 1983) and
behave like a poly polynya (except for salinity-related phenomena).
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26
5. Clouds. Clouds have two principal forms in this image. First and thermally most signif­
icant are the above mentioned lake-effect clouds produced by evaporation over leads and
ice free areas. The high temperature and vapor pressure gradients at the water-air interface
generate intense evaporation. Turbulent boundary layer convection cells (boundary layer
rolls) spiral in long (1-100 km), linear, wind-parallel cloud bands across the lake, carrying
high snow loads. The second cloud form is the translucent haze over the southern lakes.
Coastline and drainage patterns are distinctly visible beneath the cloud, giving a qualita­
tive indication of its optical depth. Notable but unexplained, this translucent cloud-covered
region is distinctly bright in the 85 GHz vpol image that follows (Figure 2.5).
6. Land. Land is the coldest class in the image, mostly below -25 °C, and generally readily
distinguishable from ice in the thermal infrared.
At 1.1 km pixel resolution, the ice appears to be a continuous layer on each of the
lakes, but ice charts indicate that midlake ice concentrations (percentage of lake surface
area covered by ice) range from 90-100%.
2.3.1.2 SSM/Ipassive microwave Great Lakes image, February 4
Figure 2.5 is an 85 GHz vpol image of the Great Lakes at 22:45 UTC on February 4.
Image brightness is proportional to brightness temperature; a linear contrast stretch was
applied to enhance ice-water features. The only data transformation applied was a rotation
to force the top of the image to be north. All the lakes are visible except Lake Ontario.
Land is largely masked out, being radiometrically darker than 230 K. The lakes show
ice free regions as black and dark grey, and ice covered regions as grey to white. The ice
free regions (as corroborated by ice charts) display a Tb gradation from 230 to about 240
K. The
Tb
range suggests some combination of either wind-induced water surface rough­
ening or presence of ice.
2.3.1.3 SSM/I seven channel Lake Superior image, February 4
Figure 2.6 summarizes the frequency-polarization behavior of the Lake Superior
scene in a simultaneous display of all seven SSM/I frequency-polarization combinations.
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27
The associated graphs of T b along a west-to-east transect display characteristic vertical
and horizontal polarization T b values versus pixel position for water, ice and land in each
subimage.
The decrease in spatial resolution with frequency is pronounced, leading to consider­
able blurriness at 19 GHz. The changes in relative brightness between ice and land are due
primarily to the dependence of emissivity on frequency and polarization. The relative
brightness differences between ice, water and land provide a sense for the degree to which
mixed pixels are an issue, and the direction (i.e., positive or negative) in which ice Tb may
be modified. For example, coastline ice mixed pixel Tb will be reduced by land contribu­
tions at 37 GHz hpoi, and increased at 37 GHz vpol.
2.3.1.4 NIC Lake Superior Ice Charts, January 1 - February 2
Figure 2.7 displays early season ice development in a time series of NIC ice charts
spanning January 1 to February 2, 1996. The lack of midlake ice is notable for most of
January; ice is confined to bays and shore belts. Note that the total ice coverage is not
monotonically increasing; for example, the total ice covered area is greater on January 24
than 31. The ‘missing’ ice may be fairly accounted for by wind-driven imbrication and lat­
eral accretion to existing nearshore facies. A regional cold spell drove a rapid growth epi­
sode between the January 31 and February 2 charts, and again before the February 5 chart
(see Section 2.3.2). Figure 2.7 provides a sense for the episodic, accretionary nature of ice
cover development.
2.3.1.5 February 1: SSM/I, AVHRR and ice chart
Figure 2.8 depicts February 1 ice conditions with an ice chart, AVHRR visible band
1, SSM/I 85 GHz hpol and SSM/I 37 GHz hpol T b images. The images are displayed
together to facilitate comparison. The SSM/I data are unregistered, and each is displayed
in three different linear contrast enhancements: one for the entire lake (C, F), and two
highlighting the ice free region (D, E, G, H).
The February 1 ice chart (A) shows midlake areas to be ice free, with ice confined to
circumscribing shore belts (for greater detail, see enlarged ice charts in Section 2.3.2). The
northern ice belts and the northern edge of the ice free region are visible in the AVHRR
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28
image (B). The AVHRR image displays fairly typical cloud conditions for this time of
year, obscuring much of the lake. A number of narrow lake effect clouds appear to ema­
nate from a presumed flaw or shore lead along the northwest shore.
SSM/I images C and F (85 and 37 GHz) show essentially two radiometric regimes:
dark, midlake ice free regions, and intermediate to bright shore belt ice regions. Both
regimes display ranges of T b within their boundaries (as opposed to being radiometrically
homogenous). Ice T b (37 GHz hpol) ranges from approximately 180-210 K near shore to
180-160 K at the edge of the ice free region. Ice concentrations in the belt zones are on the
order of 90-100%. Ice stages of development present comprise ice codes I, 4 and 5 (0-5,
5-15, 15-30 cm).
Images D, E, G and H focus on the ice free regions. The contrast enhancement
stretches T b over a smaller range than in C and F, spanning only the radiometrically cold­
est pixels, thus highlighting the ice free region. In these images, the ice free region appears
to be segregated into two zones rather than the one large zone indicated on the ice chart.
The east and west zones are separated by a brighter
Tb
region, suggesting that ice is
present NW of the Keweenaw Peninsula (cf. ice chart). The east basin ice free region dis­
plays considerable variability not visible in the broader
Tb
stretch used in whole-lake
images C and F. They appear to brighten to the SE. The question arises: what is the source
of the variability of T b in this region?
Tb
for a given pixel can be elevated through increasing any combination of the fol­
lowing: ice concentration; ice thickness; ice surface roughness; water surface roughness;
atmospheric emission. It is impossible to separate these effects using a single band, but to
speculate, perhaps the most likely scenario is that it is some combination of wind effects
and presence of ice. Wind direction is indicated by the linear cloud bands, and is nearly
ubiquitious over Lake Superior in winter. It is likely that, given the air temperatures (-30
°C) and environment (polynya), new ice of unspecified types is present in the ice free
region. Likely types would include frazil ice, shuga, grease ice and nilas. It can be argued
that because the pixels within the ice free region brighten toward the south east, it is more
likely to an effect of ice rather than wind. Wind effects would be expected to be more uni­
form over the region because the ice north of the ice edge has essentially no wind-break
effect on the water surface.
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29
Examination of a 37 GHz hpol T b profile across the lake (Figure 2.8 J) indicates a
large drop in T b near 160 K in the transition zone between ice and water. Thus, it may be
convenient to operationally define the 37 GHz hpol ice-water transition or ice edge at the
160 K brightness temperature contour. Ulaby et al. (1986) state that above about 10 GHz,
salinity is a minor factor in water emissivity for the range of 0 to 37 ppm (normal sea
water). This provides a partial rationale for using sea surface roughness effects on T b to
estimate the wind contribution to lake T b .
2.3.1.6 February 4: SSM/I, AVHRR and ice chart
Figure 2.9 displays February 4 ice conditions in the same manner as Figure 2.8, sub­
stituting thermal infrared for visible in the AVHRR image. The SSM/I images use the
same T b ranges for the contrast enhancements on the two dates, making Figure 2.8 and 2.9
directly comparable.
A number of features may be noted. First, the ice free region in the east basin
appears to have become ice covered, indicated by the T b increase in both channels. In fact,
it had become one o f the brightest areas of the 85 GHz image. This region along the wind­
ward high-energy coast of the Keweenaw Peninsula tends to accumulate ice in ephemeral
belts. The opportunity for deformation is relatively high. Thus, the elevated
Tb
may be
due to increased thickness and roughness associated with deformation. (There may also be
increased snow accumulation enhanced by greater surface roughness.)
The east basin ice free region has been reduced by some 25 to 50 km on a side (esti­
mated by comparing the size of the two ice free regions in Figures 2.8 (G,H) and 2.9
(G,H). (Note that the two images have different viewing geometries, so direct comparison
of sums of pixels is not possible.) In both Figures 2.8 and 2.9, the minimum T b pixels
occupy less than a third of the ice free region (G,H), and are concentrated in the northern
and western reaches. The images brighten to the southeast, consistent with accumulations
of wind drifted ice.
2.3.1.7 February 4: microwave emissivity
Figure 2.10 shows microwave emissivity at each of the SSM/I frequency-polariza­
tion combinations, calculated using the unusually clear-sky AVHRR image acquired on
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30
February 4. Band 4 radiance was converted to physical temperature by multiplying the
scene by an ice emissivity of 0.98 (Warren, 1982):
T p=(Tb band 4 )*0.98.
The emissivity image was calculated using this expression:
eimage=TB_image / T pjm age
where T b =SSM/I brightness temperature image; Tp=AVHRR physical temperature
image)
Ice emissivities are theoretically accurate (ignoring atmospheric effects), but the ice free
region (and land) emissivities are not necessarily accurate because they were calculated
using physical temperatures based on an ice emissivity, rather than land and water emis­
sivities. Other images from February 4 (not shown) indicate that ice surface physical tem­
peratures was relatively stable throughout the day, mitigating potential error due to the
time gap between AVHRR and SSM/I image acquisitions.
Calm water should, theoretically, display an emissivity (37 Ghz hpol) of about 0.35,
calculated from the Fresnel relations. An empirical emissivity may be calculated using a
mean ice free region T b of 145 K (from Table 2.5), and assuming Tp of 253 and 273 K,
yields emissivities of 0.53 and 0.57, respectively. The empirical values are considerably
higher than the theoretical value, lending support to the hypothesis that some combination
of ice and wind roughened water) is present in the ice free region. It may also provide an
indication of the magnitude of atmospheric contribution to T b .
2.3.2 Microwave T b, emission and ice stage of development
This section address the issue of correlation between T b , and emissivity, and ice
stage of development. Ice stage of development is equivalent to ice thickness. Ice charts
and SSM/I images from February 1 and 4 were coregistered and the boundaries of ice
chart polygons greater than 625 km2 (i.e., one 37 GHz pixel) were digitized. The means
and standard deviations of 37 GHz hpol T b were calculated and graphed in Figures 2.11
and 2.12. The same was performed in Figure 2.13 for 37 GHz hpol emissivity on February
4.
2.3.2.1 February I: 37 GHz hpol Tb and ice chart stage o f development
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31
Figure 2.11 shows the February 1 data. Not unexpectedly, the graph shows Tb
increasing from ice free region to old bay ice. Standard deviations diminish with increas­
ing
Tb.
This may reflect contamination by land pixels in the case of polygons 2, 3 and 4,
and ice contamination in the case of polygon 1 (recall the east-west division of the ice free
region in Figure 2.8). Also, the mean T b for the ice free region is about 180 K, versus 145
K (estimated in Table 2.5). The higher mean reflects the unintentional incorporation of ice
in this calculation that was avoided in the manually selected ice free region calculation for
Table 2.5. There is no strong correlation of Tb with polygon size (B), though the two
brightest polygons are small and certainly nearing the limit of spatial resolution. They
would be the most likely candidates for contamination by radiometrically brighter land
pixels.
2.3.2.2 February 4: 37 GHz hpol Tb and ice chart stage o f development
February 4 data in Figure 2.12 display the same trends as on February 1 (Figure
2.1 1); T b increases from ice free region to shore belts to bay ice. Again, the brightest three
polygons (8,9,10) are in smaller bays, and have the greatest potential for contamination by
surrounding land pixels, so may be eliminated consideration.
The shore belt polygons (3,4,5,6,7) T b ranges from approximately 193 to 209 K.
2.3.2.3 February 4: correlation o f 37 GHz hpol emission and ice chart stage o f develop­
ment
Figure 2.13 recapitulates Figure 2.12, substituting emissivity for T b - The trend is
parallel to that of Figure 2.12 (T b ), with emissivity increasing with ice stage of develop­
ment, as expected.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
04
NJ
m e d i u m - t h i c k ice ( 1 5 - 7 0 c m )
D e n s ity slice im age
Kj j c t ,r c c i n t e r v a l s
t hi n ice ( 5 - 1 5 c m )
-20-10 0 ' !
.
:
leeward leads/cracks
:\
■
. " T v
.V
i ce f r ee r e g i o n
C
V
Luke Superior \ , ’ ^
t h i c k - v e r y t h i c k ice ( 7 0 - 1 2 0 c m )
lake-effect clouds
c r a c k s / leads
<
-a
X
•
■S
.
■
image # : n 14.96035.0811 ^
08:11 L'TC
igure 2.4. A. AVHRR image o f
Great Lakes, February 4, 1996.
B. Density slice version o f A.
AVHRR band 4 (thermal infrared).
Image brightess is proportional to
physical temperature; dark is cold,
bright is warm. Ice cover is wide­
spread; open water is confined prima-1
rily to the areas under clouds. IR= Isle |
Royale; KP=Keweenaw Peninsula;
MP=M ichipicoten Island.
Saginaw Bay
Luke Ontario
Luke Huron
p h y s ic a l tem perature ( l>Cj
Lake Erie
Lake Michigan
33
85 G H / v p o l
L ake Michigan
f 13_Tb_96035_26A
Feb. 4 2 2 : 3 2 U T C
............. ..
Figure 2.5. SSM/I T b image of Great Lakes, February 4, 1996.
Pixel size=12.5 km. Image brightness is proportional to brightness temperature. Older,
thicker ice is radiometrically bright; younger, thinner ice is radiometrically dark. Water is
black. The dashed line divides the landscape into cold (dark) northwest and warm (light)
southeast regions. The radiometrically warmer southeast regions appears as a translucent
cloud in AVHRR thermal infrared imagery (dark southeastern area in Figure 2.4).
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34
p o rtio n along * « a t-« a « t tronM ot
o d e fixation: y rtfcol fthin). horizontal (thick)
Figure 2.6. Lake Superior T b : all SSM/I frequency-polarization combinations and T b pro­
file plots, February 4, 1996.
Images: image brightness is proportional to T b ; frequency and polarization are indicated.
Graphs: west-east T b profile taken on indicated transect. Pixel size: 85 GHz, 12.5 km; all
others, rebinned to 12.5 km from initial 25 km. These images have been smoothed for dis-
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35
Figure 2.7. Early ice growth phase in ice chart time series.
Lines=ice polygon boundaries. Symbols are explained in enlarged form in Figure 2.11.
Five of the 12 January ice charts are presented. Ice is confined to bays early in the
sequence. Floes form and dissipate with time. Growth is episodic, displaying an overall
accretionary pattern with a progression from older, thicker ice along shore to younger,
thinner ice midlake.
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36
h a n d 1 visibl e
ice polygons
I ,
\
n!4. 96Q32. 1W A f r i t u '- '' ’• •18:54 U I’C
* y ' ' im a g e #: .
wl960202
'
-V
xvAv■v'"
/
,ye
—
.V
m
220 K
137
160 K
1
f
220 r
1A land
1
z
*
Isle Royale
la n d /- :
A\
ke r* I A
•
1
/
P
'Cr
r
1
water
190
Pi
ice profile
P i’
pixel
P2
pixel
>P2>
ice free profile
Figure 2.8. February 1 ice conditions.
A: NIC ice chart. B: AVHRR band 1 visible. C,D,E: SSM/I 85 GHz hpol T b - F, G, H: SSM/I 37 GHz hpol
T b . I: T b profile P l - P l ’ across ice (location indicated in F). J: T b profile P2-P2’ across the ice free region
(location indicated in F). The 85 and 37 GHz images are each displayed in three enhancem ents (grey scale
stretches), for the entire lake (C,F) and for the ice free region (D,E and G,H). Ellipses in A and C delimit a
region where the ice chart indicates ice free and SSM/I indicates ice present. Keys to the gray scales are pro­
vided; T b in units o f degrees K. Note scale change on vertical axes o f I and J.
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37
^ . S
W1960205
^
image #:
n 14.96035.0811
19:44 UTC
band 4
145 K
220 K
160 K
Figure 2.9. February 4 ice conditions.
A: Ice chart. B: AVHRR band 4 thermal infrared. C,D,E: SSM/I 85 GHz hpol T b . F,G,H:
SSM/I 37 GHz hpol T b . The 85 and 37 GHz images are each displayed in three enhance­
ments, for the entire lake (C,F) and for the ice free region (D,E and G,H).Grey bars indi­
cate T b in K, and grey scale ranges are identical between Figures 2.8 and 2.9. (D and E in
Figure 2.9 have a minimum of 173 K, as opposed to 170 K in 2.8, but the difference is not
significant to visual interpretation of T b .)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
Figure 2.10. Ice microwave apparent emissivity, February 4.
Grey bars and values indicate emissivity range used in linear contrast stretch. Emissivity
contour interval = 0.1. Clouds were not masked out in the emissivity calculation, so ice
free region emissivity values are actually lower than indicated.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
230
id
"o
a.
si
220
o
r-~
m
80
210
200
j s
90
X
a
H
c
C3
O
s
70
60
50
40
30
O
B
2
4
1O
8
6
February 1 ice polygon
rank
ice polygon
1 ice free region
2 South shore
3 Ontonagon
4 Northeast shore
5 North central
6 W est shore
7 Isle Royale
8 Duluth
9 W hitefish Bay
km2
44798
9265
3659
3678
10754
6584
2550
1619
928
# of 25x25 km pixels
72
15
5.9
5.9
17.2
10.5
4.1
2.6
___ -•
1.5
D
To
Total concentration
Partial concentrations
Stages o f development
Forms o f ice
:hart #: wl960202
£
y
-3
I
i_5
Figure 2.11. February 1 ice polygons and 37 GHz hpol mean T b A: Graph plots polygon mean Tb and plus/minus one standard deviation. B: Rank, area and equivalent num ­
ber o f 25x25 km pixels contained in each polygon. C: Ice chart showing location and rank o f each polygon.
D: W M O ice code. The associated ice polygon is 10 tenths covered, subdivided into 6 tenths code 5 ice, 2
tenths code 4 ice, and 2 tenths code 1 ice. The form o f ice is not indicated in this example. Ice chart code is
explained in Table 2.3.
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40
230
220
o
Q.
.C
SI
X
o
cn
CQ
H
c
au
<
210
200
190
180
1 70
160
150
1 4-0
130
4
-
6
8
10
12
February 4 ice polygon
g
rank polygon
1 ice free region
2 ice free region rim
3 East shore
4 mid-lake
5 East Keweenaw
6 West shore
7 Isle Royale
8 Whitefish Point
9 Duluth
10 Whitefish Bay
km2
9379
755
9984
18192
2223
2813
1676
747
651
1400
# o f 25x25 km pixels
15
6.0
16
29.1
3.6
36.5
2.7
1.2
1.0
2.2
chart #: w!960205
Figure 2.12. February 4 ice polygons and 37 GHz hpol mean T b .
A: Graph plots polygon mean Tb and plus/minus one standard deviation. B: Rank, area
and equivalent number of 25x25 km pixels contained in each polygon. C: Ice chart show­
ing location and rank of each polygon.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
o
Q.
JZ
N
1 .o o
X
0.90
cn
0.80
>
a!
U3
0.70
c
u
c
0.60
O
r~
35
<U
0.50
1
2
3
4
5
6
7
8
9
10
February 4 ice polygon
B
rank ice polygon
1
ice free region
2
ice free region rim
3
East shore
mid-lake
4
East Keweenaw
5
6
W est shore
Isle Royale
7
W hitefish Point
8
Duluth
9
10 W hitefish Bay
km J
9379
3755
9984
18192
# o f 25x25 km pixels
222
22813
1676
747
651
1400
fib
chart #: wl960205
! 46 N
FREE
Figure 2.13. February 4 ice polygons and 37 GHz hpol mean emissivity.
A: Graph plots polygon mean emissivity and plus/minus one standard deviation. B: Rank,
area and equivalent number o f 25x25 km pixels contained in each polygon. C: Ice chart
showing location and rank of each polygon.
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42
Figure 2.14 is a color combination o f SSM/I, ice chart and AVHRR band 4 for Feb­
ruary 4. It gives a sense for how well registered SSM/I data agrees with ice chart delinea­
tions.
Figure 2.14. Image combination: SSM/I 85 GHz hpol T b (red), ice chart (green), AVHRR
band 4 (blue).
The red zone shows the correspondence between SSM/I and ice chart for delineating the
ice free region, and indicates the degree of SSM/I registration accuracy. The dark lines are
ice chart polygons. The large SSM/I pixels are evident around the edges of the ice free
region. Fusion of SSM/I and AVHRR in the red-green-blue color space does not necessar­
ily yield an easily interpreted image. It may require more sophisticated techniques, such as
the hue-saturation-intensity (HSI) transform.
2.4.0 Results
The results of this investigation may be summarized as follows.
Ice-water Detection
•
Ice and water can be discriminated using each of the seven SSM/I frequency-polar­
ization combinations (Figure 2.6).
•
37 GHz (hpol) and 85 GHz (hpol and vpol) are the channels best suited for opera-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
tionally detecting ice and water based on the criteria o f having the highest spatial reso­
lution and the existence strong emissivity contrasts between ice, water and land
(Figures 2.8-9).
•
Brightness temperature variations were detected using 37 and 85 GHz hpol T b in
the ice free regions on February 1 and 4 which plausibly indicate the presence of thin
ice undetectable by other means (Figures 2.8, 2.9 D, E, G, H). The pattern of occur­
rence
(T b
increasing to southeast) is consistent with a hypothesized downwind con­
centration of ice resulting from wind drift under the region’s dominant northerly and
westerly winds.
•
The ice-water transition appears gradational in the imagery due to the averaging
effect of the large pixels. At 37 GHz hpol the transition occurs in the range of 150 to
180 K.
Brightness Temperature:
•
37 GHz
Tb
values appear to be comparable to those of new and young sea ice
(Eppler et al., 1992; Table 4.1. Grenfell et al., 1992, Figure 14-6).
•
Figures 2.11 and 2.12 indicate a correlation between ice stage of development
(thickness) and
T b,
as would be expected. This suggests that passive microwave radi-
ometry may be useful in mapping ice thickness after higher resolution satellite radiom­
eters become available.
•
Interpolation artifacts introduced by spectral resampling during registration to a
map projection were found to be on the order of 0-4 K for a 37 GHz hpol transect
across Lake Superior (Figure 2.2, 2.3).
Emissivity:
•
Ice apparent microwave emissivity ranges from approximately 0.6-0.95 (over all
SSM/I channels) (Figure 2.10).
•
Figure 2.13 indicates a correlation between ice thickness and emissivity.
•
Lake ice emissivity appears to be comparable to that of new and young sea ice
(e.g., Eppler et al., 1992, Table 4.1: Grenfell et al., 1992, Figure 14-5).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
Registration:
•
Shorelines and the ice free regions boundaries appear to match reasonably well
between coregistered SSM/I, AVHRR and ice chart images (Figure 2.14). Note that
best results require additional interactive pixel relocation in addition to the automated
registration based on predicted pixel centers. This is a limitation on automated image
analysis.
Tables 2.5 and 2.6 summarize brightness temperature statistics for ice covered and
ice free regions on February 1 and 4. These are displayed graphically in Figure 2.15.
February 1: ic e c q y e re jjre g h ^ ^
February 4: ice covered region
max.
std. dev.
mean
td. dev.
....
22°
o 190
- min.
I9v
19h
22v 37v
37h
19v 19h
85v 85h
230
230
200
200
100
180
g 160
160
140
140
120
120
19v
19h
22v 37v
37h
85v 85h
37h
85v 85h
February 4: ice free region
February j : ice free region
B
22v 37v
19v 19h
22v 37v
37h
85v 85h
Figure 2.15. Statistics for February 4, 1996 ice and ice free regions.
A: Aggregate statistics for all ice covered regions. B: Aggregate statistics for all ice free regions. (A and B
graph means, m inim a, maxima and plus/minus one standard deviation around mean.). T b thresholds
between ice covered and ice free regions are described in Tables 2.5 and 2.6.
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45
Table 2.5: February 1 and 4 ice covered region T b statistics"b
std. dev.
Feb. 1 Feb. 4
maximum
Feb. 1 Feb. 4
frequency /
polarization
mean
Feb. 1 Feb. 4
19 v
218.2
213.4
16.6
11.7
183.9
182.2
246.9
242.0
19 h
189.0
182.4
30.2
22.6
119.9
111.3
237.8
231.9
22 v
219.1
216.2
15.0
10.1
187.8
187.5
244.6
241.8
37 v
226.6
227.0
7.4
5.7
204.60
204.5
239.6
237.2
37 h
201.6
199.0
21.6
16.8
145.9
140.0
235.6
229.2
85 v
239.9
245.0
5.4
6.5
229.0
230.3
251.7
255.4
85 h
218.6
221.5
13.8
12.6
174.1
179.9
237.2
237.3
minimum
Feb. 1 Feb. 4
a. The ice region was selected by digitizing the pixels highlighted using this threshold: 233 <
85 GHz vpol T b < 255 K. Im ages were raw, not registered.
b. February 1: n=573 pixels. February 4: n=516 pixels. In each case, pixel size = 12.5 km.
Table 2.6: February 1 and 4 ice free region T b statistics"bc
frequency /
polarization
mean
Feb. 1
Feb. 4
std. dev.
Feb. 1 Feb. 4
minimum
Feb. 1
Feb. 4
maximum
Feb. 1 Feb. 4
19 v
185.8
186.9
8.6
6.9
177.0
179.9
219.7
209.9
19 h
121.9
121.2
16.2
14.0
105.4
105.4
185.5
164.0
22 v
188.5
191.1
7.5
6.2
181.0
184.7
221.2
210.6
37 v
205.1
206.8
4.7
4.5
200.6
202.8
226.2
219.5
37 h
145.9
145.2
10.4
10.3
136.9
137.1
200.8
177.3
85 v
228.8
231.0
1.1
0.7
225.4
229.5
231.9
232.5
85 h
175.8
176.9
3.7
2.7
169.2
173.1
190.1
185.0
a. Ice free region was selected by digitizing the pixels highlighted using this threshold: 85 GHz
vpol T b < 233 K. Images were raw, not registered.
b. February 1: n=155 pixels. February 4: n=59 pixels. In each case, pixelsize = 12.5 km.
c. Only the east basin ice free region for February 1 is reported.
2.5.0 Discussion
Implications fo r Daily Monitoring o f Great Lakes Ice Cover
Advantages of SSM/I are multiple images per day (up to six), online availability
within hours of overpass, the all-weather, day-night imaging capability, and inherent sen-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
sitivity to ice physical properties, including thickness and surface roughness. The disad­
vantage is the large footprint. With these features in mind, perhaps the greatest potential
use for SSM/I in Great Lakes ice monitoring would be in mapping the chronology of ice
development on the Great Lakes on a daily to multi-hour basis. An achievable geophysical
product would be a daily estimate of the total area covered by ice, the location of the ice
edge and the general spatial distribution of ice on the lakes. Also, with the assumption that
the ice free regions are significant to lake processes in ways similar to polynyas in polar
seas (e.g., new ice growth, heat exchange, thermal gradients), the ice free regions can be
better monitored through their typically cloud-covered conditions.
Ice Detection
The potential for simple detection of presence or absence of ice in a given pixel is
good at both 37 and 85 GHz. Because the 37 GHz channel is relatively unaffected by
weather, 37 GHz channel data interrogation can be largely automated. The 85 GHz chan­
nel is more affected by weather, limiting certain applications. The potential for automated
interrogation at 85 GHz may be improved by incorporating precipitation flags (e.g., Bauer
and Grody, 1995) to identify pixels with a high probability of containing a precipitation
signal. Note that rain is more problematic than precipitating snow (which is more charac­
teristic of Lake Superior winter conditions). The relative abundance of weather stations
and online weather data for the Great Lakes region improves the opportunities for incorpo­
ration of atmospheric corrections to T b .
Ice Thickness
Section 3.2 demonstrates a correlation between 37 GHz hpol
Tb
and ice thickness.
SSM/I spatial resolution is perhaps too coarse for this application; mixed pixels, primarily
in the form of land contamination, are a significant issue. After higher resolution passive
microwave imagery becomes available (e.g., AMSR, MIMR), ice thickness may be a more
viable target. However, the effects of snow cover and surface roughness may overwhelm
the thickness-derived signal.
SSM/I Registration
It is possible to visually interpret and analytically manipulate Great Lakes SSM/I
imagery in swath form without registering the data to a map projection. However, registra­
tion facilitates analysis in two ways: it permits direct digital integration with other data
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47
types, and it removes viewing geometry distortions inherent in the 1400 km wide swath.
Brightness temperature images from MSFC are accompanied by geolocation grids that
permit automated registration. Registration accuracy is application dependent. Additional
interactive image navigation was required in this analysis to permit merging of the
AVHRR and ice chart data.
Automated Processing
SSM/I image files are archived in Hierarchical Data Format (HDF), a NASA EOSDIS standard. Currently, individual swaths are archived online for approximately 10 days
after acquisition. Long-term archives use data granules comprising one day, with each
granule containing all 28 o f the day’s passes (i.e., the entire earth, twice). The user will
find it advantageous to gather these data in quasi-real time from the temporary online
archive. The Great Lakes subscene can be automatically subsetted from the swath based
on the latitude-longitude grid file. Because the pixels are so large, Great Lakes browse
images require relatively little disk space, making it convenient to view data using com­
puter animations of image time series.
Note that at present, NASA MSFC offers T b data from only the F10 and FI 1 plat­
forms, limiting the normal data stream to the user to four images per day (as opposed to
six if platform F8 were included). Two of the day’s four total passes have greater off-nadir
geometric distortions, and so may require registration whereas scenes acquired closer to
nadir may not require registration, depending on the application.
Algorithm Development
It is likely that algorithms can be developed to extract various geophysical parame­
ters with minimal operator intervention. A necessary step is to examine SSM/I Tb time
series to further develop ice
Tb
signatures as they evolve through the season. National
Snow and Ice Data Center SSM/I brightness temperature grids on CDROM would be a
logical place to begin to understand the seasonal variation of brightness temperature. The
images are registered to a polar stereographic projection, greatly facilitating compilation
of
Tb
time series. Note, however, that at least some of these data products suffer from
missing data at this latitude, due to tape recorder failures onboard the FI 1 satellite (Figure
3.1). Seven day averaging was used by Pilant (1996a) (Chapter 3) to produce visually
acceptable images, but the alteration of the radiometric characteristics of the scene have
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48
not yet been fully addressed.
Daily ice detection at the level of presence-absence is certainly possible using the 37
and 85 GHz channels (Figures 2.5,6,8,9,11-13). Moreover, the penetration depths at 37
and 85 Ghz are commensurate with characteristic Great Lakes ice thicknesses (< 50 cm).
The pixel sizes of the lower frequencies are essentially too coarse. Thicker ice does occur,
particularly in deformed ice (ridges, hummocks) and ice foot, but the sensor spatial resolu­
tion will have to improve significantly before the 22 and 19 GHz channels are practical.
In theory, ice concentration may be estimated by adapting the multispectral algo­
rithms used in sea ice remote sensing. A potential limiting factor here is the use of the 19
GHz channels. Their low spatial resolution is more appropriate for the areally more exten­
sive ice o f the polar regions than for Great Lakes ice. Land contamination is significant in
the Great Lakes for 19 GHz SSM/I footprints.
2.6.0 Conclusions
The purpose of this study was to investigate the utility of SSM/I as an ice monitoring
tool for the Great Lakes. The temporal resolution (up to 6 images per day) is an enhance­
ment of existing imaging capabilities that rely on visible, infrared and radar sensors. SSM/
I can be used for daily mapping of ice conditions (location of ice and ice edge, and possi­
bly ice stage of development) and in detecting freeze-up, break-up and spring surface melt
events. The seven combinations of frequency and polarization together permit a relatively
high degree of discrimination between ice, water and land. Multispectral feature extraction
presumably has even greater potential. Single band
Tb
(and emissivity) (37 and 85 GHz
hpol) was shown to be sensitive to ice stage of development and capable of locating the ice
edge. The SSM/I map registration process was described, and the magnitude of radiomet­
ric artifacts was found to be in the range of approximately 0-4 K. Lake ice Tb and emissiv­
ities were observed to be comparable to those of new and young sea ice, indicating that
developments in sea ice radiometry may be studied for application to lake ice. Future
microwave sensors such as MIMR and AMSR will improve available satellite bome pas­
sive microwave spatial resolution by a factor of at least two, permitting ice detection at the
5 km scale.
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49
2.7.0 Acknowledgments
This research was funded in part by NASA Global Change Fellowship # 1956GC92-0312 and Michigan Space Grant Consortium Seed Grant # 79827. Data were pro­
vided by the NOAA Satellite Active Archive, Marshall Space Flight Center Hydrologic
DAAC and National Ice Center. The author thanks Chuck Young, Bill Rose, Ann
Maclean, Alex Kostinski and Dave Schneider for helpful comments and Mike Dolan for
computer support.
2.8.0 Bibliography
Assel. R. A., Quinn, F. H., Leshkevich, G. A., and S. J. Bolsenga, Great Lakes Ice Atlas,
Great Lakes Environmental Research Laboratory, Ann Arbor, MI, 115 pp. 1983.
Assel, R. A., Croley II, T. E. and K. Schneider, Computer visualization of long-term aver­
age Great lakes temperature and ice cover: J. Great Lakes Res., 20,4, 771-782, 1994.
Barnes, P. W„ Kempema, E. W., Reimnitz, E. and M. McCormick, Influence of ice on
southern Lake Michigan coastal erosion: J. Great Lakes Res., 20, 1, 179-15, 1994.
Bauer, P. and Grody, N.C., The potential of combining SSM/I and SSM/T2 measurements
to improve the identification of snowcover and precipitation, IEEE Trans. Geosci. Remote
Sensing, 33, 2, 252-261, 1995.
Bell, A. L., Satellite observations of Great Lakes ice, 1980-81, NOAA, National Earth Sat­
ellite Service report 119, 1982.
Bennet, E. B., Water budgets for Lake Superior and Whitefish Bay, J. Great Lakes Res., 4,
331-342, 1978.
Bolenga, S. J., On the use of multispectral radar to define certain characteristics of Great
Lakes ice, NOAA Technical Memorandum ERL GLERL-17, 11 pp., 1978.
Bolsenga, S. J., A review of Great Lakes ice research: J. Great Lakes Res., 18, 169-189,
1992.
Bryan, M.L. and R. W. Larson, The study of fresh-water lake ice using multiplexed imag­
ing radar, J. Glaciology, 14, 72,445-458, 1975.
Carsey, F. D. (Ed.), Microwave Remote Sensing o f Sea Ice, American Geophysical Union
Monograph 68, Washington, D.C., 440 pp., 1992.
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50
Grenfell, T. C., Cavalieri, D. J., Comiso, J. C., Drinkwater, M. R., Onstott, R. G., Rubenstein, I., Steffen, K. and D. R Winebrenner, Considerations for microwave remote sensing
fo thin sea ice, in Microwave Remote Sensing o f Sea Ice, edited by F. D. Carsey, pp. 292301, American Geophysical Union Monograph 68, Washington, D.C., 440 pp., 1992.
Great Lakes-St. Lawrence Seaway Winter Navigation Board, Annual Report- Great
Lakes-St. Lawrence Seaway Winter Navigation Board: 53 pp.Great Lakes- St. Lawrence
Seaway Navigation Board,
Hagman, B. B., On the use of microwave radiation for Great Lakes ice surveillance,
NOAA Technical Memorandum ERL GLERL-13, 11 pp., 1976.
Hall, D. K., Foster, J. L., Chang, A. T. C. and A. Rango, Freshwater ice thickness observa­
tions using passive microwave sensors, IEEE Trans. Geosci. Remote Sensing, 19, 189-193,
1981.
Hall, D. K., Fagre, D. B., Klasner, F., Linebaugh, G. and Liston, G.E., Analysis of ERS 1
synthetic aperture radar data of frozen lakes in northern Montana and implications for cli­
mate studies. J. Geophys. Res., 99, C l l , 473-482, 1994.
Hollinger, J., Pierce, J. L. and G. A. Poe, SSM/I instrument evaluation, IEEE Trans.
Geosci. Remote Sensing, 28, 5, 781-790, 1990.
Haykin, S., Lewis, E. O., Raney, K. R. and Rossiter, J. R., Remote Sensing o f Sea Ice and
Icebergs: John Wiley and Sons, New York, 689 pp, 1994.
Leshkevich, G. A., Machine classification of freshwater ice types from Landsat-l digital
data using ice albedos as training sets: Remote Sensing Environment, 17,3,251-263, 1985.
Leshkevich, G. A., Satellite mapping of Great Lakes ice cover, in Proceedings o f the First
Moderate Resolution Imaging Spectroradiometer (MODIS) Workshop on Snow and Ice,
NASA Conference Publication 3318, D. K. Hall (ed.), pp. 87-91, 1995.
Liston, G. E., and Hall, K. D., An energy-balance model of lake-ice evolution: J. Glaciol­
ogy, 41, 373-382, 1995a.
Liston, G. E., and Hall, K. D., Sensitivity of lake freeze-up and break-up to climate
change: a physically based modeling study, Annals Glaciology, 21, 387-393, 1995b.
McMillan, M. C. and Forsyth, D., Satellite images of Lake Erie ice: January - March 1975
(technical report), NOAA National Environmental Satellite Service, 1975.
Marsh, W. M., Marsh, B. D. and Dozier, J., 1973. Formation, structure and geomorphic
influence of Lake Superior icefoots: Am. J. Science, 273,48-64, 1973.
Quinn, F.H., Assel, R.A., Boyce, D.E., Leshkevich, G.A., Snider, C.R. and D. Wienet,
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51
Summary of Great Lakes weather and ice conditions, winter 1976-77, NOAA Technical
Memorandum ERL GLERL-20, 141 pp., 1978.
Schwab, D. J., Leshkevich, G. A. and Muhr, G. C., Satellite measurement of surface water
temperature in the Great Lakes: Great Lakes Coastwatch. J. Great Lakes Res., 18, 2, 247258, 1992.
Swift, C. T., Jones, W. L. Jr., Harrington, R. F., Fedors, J. C ., Couch, R. H. and B. L. Jack­
son, Microwave radar and radiometric remote sensing measurements of lake ice: Geophys.
Res. Letters, 1 ,4, 243-246, 1980.
Ulaby, F. T., Moore, R. K., and A. K. Fung,, Microwave Remote Sensing- Active and Pas­
sive, Volume 1, Microwave Remote Sensing, Fundamentals and Radiometry, Artech
House, Norwood, MA, 456 pp., 1981.
Ulaby, F. T„ Moore, R. K., and A. K. Fung,, Microwave Remote Sensing- Active and Pas­
sive, Volume 3, From Theory to Applications, Artech House, Norwood, MA, 2162 pp.,
1986.
Warren, S. G., Optical properties of snow, Rev. Geophys. Space Phys., 20, 1, 67-89, 1982.
Wiesnet, D.R., Satellite studies of fresh-water ice movement on Lake Erie, J. Glaciology,
24,90,415-426, 1979.
WMO (World Meteorological Organization), WMO Sea Ice Nomenclature, WMO Report
259, Secretariat of the World Meteorological Organization, Geneva, Switzerland, 159 pp.
1970.
Wynne, R. H. and Lillesand, T.M., Satellite observation of lake ice as a climate indicator:
initial results from statewide monitoring in Wisconsin, Photogram. Eng. Remote Sensing,
59, 1023-1031, 1993.
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52
Chapter 3: SSM/I Time Series Observations of Great Lakes Ice and
Snow
Abstract
Special Sensor Microwave Imager (SSM/I) time series data are presented to qualita­
tively examine regional scale snow and ice phenomena for the Great Lakes winter of
1993-94. Microwave brightness temperature, air temperature and snow accumulation time
series for the Keweenaw region of Lake Superior are graphed together and compared.
Image time series are presented showing the winter evolution of Great Lakes ice cover.
Daily time step computer animations (mpeg) of SSM/I imagery in are included in the
appendix. Same-day SSM/I and Advanced Very High Resolution Radiometer (AVHRR)
images of Lake Superior are compared, showing the potential of SSM/I as a regional-scale
ice-detection tool.
Key words: ice, snow, Great Lakes, passive microwave, remote sensing.
3.1.0 Introduction
The Great Lakes hydrologic system is integral to midcontinent weather and climate.
Lake ice and snow are important to climate change studies and to the daily lives of the
approximately 42 million people living in the Great Lakes-St. Lawrence basin. Lake ice
modulates heat and longwave radiation fluxes between lake and atmosphere, controls pen­
etration of shortwave radiation used in photosynthesis, affects shoreline processes and
determines the shipping season. Snow modulates shortwave and longwave radiation and
heat fluxes between land/ice and atmosphere, as well as being a dominant factor in ground
and surface water recharge.
Remote sensing in the microwave portion of the spectrum has been useful in provid­
ing information about snow and ice and has led to a number of application in hydrology
and climatology (Barry, et al., 1993; Grody, 1991; Foster, et al., 1984). Microwaves are
relatively unaffected by atmospheric conditions, permitting imagery to be acquired day or
night in all seasons. This is a distinct advantage over daylight and weather sensitive visible
and infrared imagery. The principal disadvantage of microwaves is the coarse spatial reso­
lution (12.5 and 25 km pixels for SSM/I). The intensity of earth microwave emission is
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53
relatively low, requiring larger field of views to obtain an adequate signal to noise ratio.
This chapter presents primarily qualitative observations of Great Lakes ice and snow
for the winter of 1993-94. The time period was selected based on data availability, and
related field work (Appendix A). The objective is to gain basic insight regarding the pas­
sive microwave expression of the Great Lakes surfaces and surrounding landscape chang­
ing through a winter season.
The passive microwave data are described. The problem of missing data is treated by
averaging over time-sequential images. Graphs of air temperature, snow accumulation and
microwave brightness temperature are used to display interrelationships among these vari­
ables. Time series of 37 and 85 GHz microwave imagery display the geophysical evolu­
tion of the landscape through the winter at the 10-1000 km scale.
3.2.0 Data and processing
The Special Sensor Microwave Imager is a meteorological instrument aboard the
Department of Defense DMSP satellites (Hollinger, et al. 1987). There are four frequen­
cies (GHz) and two polarizations (seven channels in total): 19h, 19v, 22v, 37h, 37v, 85h,
85v (h/v = horizontal/vertical polarization). The sensor measures the intensity of
upwelling radiation emitted by land, water and atmosphere in the instrument field of view,
typically reported in units of brightness temperature (TB, in degrees Kelvin). Brightness
temperature is defined as (Fung and Ulaby, 1983, eq. 4-45):
TB=e*T
where e=object emissivity and T=object physical temperature.
The SSM/I data used here are from the DMSP F-l 1 Brightness Temperature Grids
(CD-ROM) series produced by the National Snow and Ice Data Center (in Boulder, Colo­
rado). Raw data on CD are brightness temperatures on a polar stereographic projection
binned to 12.5 km (85 GHz) and 25 km (19,22 and 37 GHz) pixels with a 0.1 K radiomet­
ric resolution. The daily ascending and descending satellite passes are averaged at NSEDC,
thereby assigning a single daily TB value to each grid position for each channel. The entire
winter of 1993-94 is available on one CD, in all seven frequency-polarization combina­
tions. Horizontal polarization (hpol) TB is used in this analysis because of the stronger
contrast between water and non-water.
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54
Missing data are pervasive at this latitude due to tape recorder failures onboard the
FI 1 satellite, leading to degradation of this data set (Figure 3.1). To generate a more con­
sistent image time series, each pixel on each date was averaged over the three preceding
and subsequent dates, thus filling in missing pixels with seven day mean. Averaging
reduces the radiometric fidelity of the TB data, but provides a much cleaner data set for
visual interpretation. Visual inspection of images indicated that a seven-day mean pro­
vides a relatively complete image with an acceptable number of missing pixels for a given
day in the time series. Comparison of raw pixels and seven day means (Figure 3.2) shows
RMS errors of ~ 3% for land TB and ~ 11% for lake TB (37 GHz); the correlation is ade­
quate for this qualitative study of regional-scale phenomena. The larger RMS error of
averaged lake TB is probably due to more rapidly changing conditions on the lake (e.g.,
drifting ice and changes in water surface roughness).
raw
averaged over seven days
Figure 3.1. Comparison of a raw and seven day mean SSM/I images.
Great Lakes (3 January 1994, 37 GHz hpol). The black land pixels and swaths are miss­
ing data. All channels and most dates are similarly degraded. White ellipse indicates the
Keweenaw Peninsula region (sampling region for data in Figures 3.2 and 3.3).
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55
3.3.0 Discussion
Julian Day
244
263
283
303
323
343
363
18
38
58
78
98
118
138
300
273 k
Imd pi xel
O
250
.o o
o
o
^
'o
<s>
o
o
200
a
H
150
Al
ake p ixel
10 0
»
cep 1
I
L i
sep 20
l l L
oct
i
10
I
t-I
.
7
I
I
I
oct 2 0 nov 19
»
I
■
dec 9
1
•
dec 29
I -1-1-1
jo n
18
L .l_ l _ l - I . J
fed 7
— I— — I - 1 - L- I— I—
fed 27 m ar 19
L
1 - 1 — L _ J— I— I— U _
opr 8
a p r 28 may
18
Time
Figure 3.2. Winter 1993-94 time series comparison of raw and averaged TB.
Tg (37 GHz hpol) for one land and one lake pixel is shown through the 1993-94 winter.
Key: Time tick marks=5 days. Lines = seven day mean TB. Diamonds = raw land TB. Tri­
angles = raw lake TB. RMS error land = 9.9 K. RMS error lake = 14.7 K. Missing pixels
were omitted from computation. The convex-up feature in the lake pixel graph (-Febru­
ary 7-April 8) is interpreted as the ice season signature, increasing to values of 200-200
K.
Interrelationships among time series of air temperature, snow accumulation and
brightness temperature are apparent in Figure 3.3. Graphs of daily air temperature and
snow depth/daily accumulation are from the Michigan Technological University (MTU)
on-campus weather station. Brightness temperature (85 GHz) histories of three land and
three lake pixels are graphed. Each pixel was selected to be relatively proximal to the
MTU weather station but far enough (>12.5 km) from the narrow peninsula to be either
completely land or completely water (i.e., not mixed pixels). Interpretations of Figure 3.3
were aided by visual inspection of computer animations of microwave image time series
included on floppy disk in the Appendix.
Figures 3.4 and 3.5 are time series of 85 and 37 GHz images spaced at 20 day inter­
vals (corresponding to the vertical grid lines in Figure 3.3). The relatively high spatial res-
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56
Julian Day
244
263
283
303
34 3
323
363
18
38
surfa:eair
58
78
III
98
116
III 1
rature
Tb (K)
snow
b.
snow iccu mulatto
LAL-I
sep 1 sep 20 o ct 10 oct 30 nov 19
d ec 9
d ec 29 jan 18
feb 7
feb 27 m ar 19 ap r 8
ap r 28
TIME
Figure 3.3. Winter 1993-1994 time series of air temperature, 85 GHz hpol brightness tem­
perature and snow accumulation.
Horizontal axis = time in days. Each tick mark = 5 days. The vertical axis plots daily mean
surface air temperature (K) (1.5 m above ground), snow depth/daily accumulation (cm)
and brightness temperature (K) (85 GHz, hpol. The land and lake graphs are seven day
means of three land (thin lines) and three lake (thick lines) pixels (approximate pixel loca­
tions in the Keweenaw Peninsula region are indicated in Figure 3.1). Snow accumulation
and air temperature data are from the MTU weather station (courtesy of Jim Carstens).
olution (12.5 km) of the 85 GHz data enhances interpretability. The 37 GHz data (25 km
pixels) are presented as well. This frequency is used because it is minimally affected by
the atmosphere, is intermediate in resolution between 85 and 19 GHz, has a penetration
depth commensurate with typical Lake Superior ice thicknesses (Table 2.6) and is the fre­
quency most sensitive to snow grain size.
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57
Figure 3.4. Image time series of 85 GHz hpol TB spanning winter 1993-94.
Image brightness is proportional to TB. Time step = 20 days.
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58
Figure 3.5. Image time series of 37 GHz hpol TB spanning winter 1993-94. Image bright­
ness is proportional to TB. Time step = 20 days.
3.3.1 Land TB
The land TB graph (85 GHz hpol) in Figure 3.3 parallels air temperature relatively
closely as might be expected, despite averaging. It decreases in a subtle manner with air
temperature as winter progresses, dropping only -5-10 K while air temperature drops 30
K between September 1 and February 7. Local TB minima and maxima follow air temper­
atures, reflecting the direct linear dependence of TB on physical temperature. The three
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59
land pixel graphs maintain their relative brightness relationships, perhaps indicative of ini­
tial differences in emissivity.
3.3.2 Lake TB
The lake TB graph (85 GHz hpol) in Figure 3.3 represents the season’s history of ice
development and decay. The open water period spans -September 1-January 10. Lake TB
is low, in the range of -190-210 K. Lake TB drops -5-10 K with air temperature, but does
not parallel local air temperature minima and maxima to the degree that land TB does.
Ice begins forming in early January, indicated by the increase in lake TB from —180200 K to 230-250 K. Ice emissivity is higher than that of water at 85 GHz (this is true at all
SSM/I frequencies), and thus is radiometrically brighter. The convex up feature spanning
-January 13-April 3 corresponds approximately to the period of ice development and
decay visible for the entire lake in the complete image time series (computer animations).
The sharp drop on February 17 is probably a mixed water-ice signal resulting from windinduced opening in the ice pack north and east of the Keweenaw Peninsula, with ice
returning in subsequent days, producing an increase in TB.
There is a general decrease in lake TB from -February 27-April 8. The ice surface
evolves throughout the season, with ephemeral melts being a feature of late winter-spring.
Melt-related phenomena (surface water, recrystallization, slush ice formation) tend to have
a large effect on TB and are probably embedded in the TB signature for this time period.
The two small humps between -A pril 8 and 28 may be periods of increased ice concentra­
tion.
3.3.3 Snow accumulation
The daily snow accumulation graph is characteristic of the lake effect snow history
in this region. The onset of snow accumulation coincides with the mean daily air tempera­
ture decreasing below 0° C. Daily snow accumulation is inversely related to lake TB. As
ice cover increases (indicated by increasing lake TB), open water available for evaporation
decreases, limiting water vapor available for lake effect snow. Daily snow accumulation
decreases to a few cm/day around January 13, coinciding with the increase in lake TB
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60
marking the onset of local ice development. There are only a few sporadic snow events
between January 28 and March 17, coinciding with the period of maximum areal extent of
ice cover. Three 5-20 cm snow events occur in late March as lake Tg returns to its back­
ground water value (circa April 3, -200 K), signalling a movement toward dominantly
unfrozen conditions. Snow accumulation effectively ceases near the peak in the lake Tg
graph around February 1, coinciding with the period of maximum areal extent of lake ice
as indicated by the image time series.
3.3.4 85 and 37 GHz image time series
The 85 and 37 GHz image time series (Figures 3.4 and 3.5) are similar in overall
character. The following remarks apply to both image sequences.
Pre-snow conditions in October are indicated by radiometrically warm land and cold
water. By November 19, snow has begun to accumulate in the northern regions, lowering
land TB (darkening the image). Ice begins forming in western and eastern Lake Superior
by January 18 (brightening the image). Lakes Superior, Huron and Erie are extensively ice
covered on February 7 and 27. Land T B is darkest in this interval, suggesting lowest tem­
peratures and maximum snow pack thickness (see also Figure 3.3). March 19 and April 8
images show the effect of northwest winds concentrating ice in southeast portions of
Lakes Superior, Huron and Erie during ice breakup. Lakes Michigan and Ontario maintain
lesser ice coverage.
3.3.5 Comparison of AVHRR and SSM/I images
Figure 3.6 is a thermal infrared AVHRR image acquired at approximately 10 a.m.
local time on March 12, and an 85 GHz SSM/I image from the same date (the average of
the day’s ascending and descending passes). Two principal points emerge. The spatial res­
olution of the AVHRR image (1.1 km) is superior to SSM/I (12.5 km) for ice identifica­
tion/concentration studies. However, note the general agreement in patterns of image tone,
indicating that the SSM/I image can roughly delimit presence and absence of ice in a given
region of the lake, and provide an estimate of total ice cover over the lake. Two or more
SSM/I images are available each day. AVHRR data are acquired twice daily, but clouds
obscure the lake more than not. The NOAA Satellite Active Archive (SAA, 1995) was
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61
searched for a set of AVHRR images for March 1994. Only five images were obtained that
contained less then -30% cloud cover over Lake Superior. This highlights the ice-detection utility of an all weather, day-night microwave sensor such as SSM/I or a radar (e.g.,
ERS-1/2, RADARS AT).
3.4.0 Conclusions
This paper presents some speculations on broad-scale interrelationships among
microwave brightness temperature, air physical temperature and snow accumulation for
the Keweenaw region of Lake Superior. The timing of Lake Superior ice development and
decay is tracked by following Tg time series for land and lake pixels. The suppression of
lake effect snow development by ice cover growth is demonstrated. The seasonal changes
of land and lake brightness temperature are displayed in time series of 85 and 37 GHz
imagery. SSM/I data have the potential to enhance Great Lake ice monitoring programs,
particularly in combination with AVHRR data. Synthetic aperture radar data provides
superior spatial and textural information, but is acquired less frequently (-3 days for
RADARS AT), and has greater acquisition and processing costs.
The NSIDC SSM/I brightness temperature grids on CD-ROM provide straightfor­
ward access to passive microwave data for Great Lakes snow and ice studies. These data
are well suited to image time series analysis, observing lake freeze-up and break-up,
detecting presence and absence of ice, and possibly to estimating concentration. Limita­
tions of this particular data product are missing data (at this latitude) and a single daily TB
value. Other NSIDC data products are increasingly available that provide separate ascend­
ing and descending pass Tg values. Missing pixels were replaced in this study by seven
day time averaging, with a consequent decrease in radiometric resolution to within
approximately 3% (land) and 11% (lake) of the original Tg. A single daily Tg value is lim­
iting in studies requiring higher temporal resolution (e.g., monitoring spring ice surface
melt). Computer animation of Tg image time series was found to provide a powerful tool
for visualization of time-dependent regional-scale snow and ice conditions. Mpeg anima­
tions are included in Appendix A.
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62
AVHRR band 4 (10.3-llr3 \u
Figure 3.6. AVHRR and SSM/I images of Lake Superior on 9 March 1994.
Water is black, ice is medium grey tones, land is grey-white tones. Note the difference in
spatial resolutions (AVHRR: l .l km; SSM/I: 12.5 km) and degree of ice detectability
using SSM/I.
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63
3.5.0 Acknowledgments
The author thanks Jim Carstens for MTU weather station data, NSIDC for SSM/I
data, Mike Dolan, Bob Landsparger, Matt Wacholz and John Gierke for computer support
and Bono Sen, Gregg Bluth, David Delene and anonymous reviewers for helpful com­
ments. This research was funded by NASA Graduate Student Fellowship for Global
Change Research #1956-GC9203I2.
3.6.0 References
Barry, R.G., Armstrong, R.L., and A. N. Krenke, An approach to assessing changes in
snow cover- an example from the former Soviet Union, in 50th Anniversary Proc. Eastern
Snow Conf., June 8-10, 1993, Quebec City, Quebec, 25-33, 1993.
Foster, J.L, Hall, D.K., and A.T.C. Chang., An overview of passive microwave snow
research and results: Rev. Geophys. Space Phys., 22, 2, 195-208, 1984.
Fung, A.K. and Ulaby, F.T., Matter-energy interaction in the microwave region, in Manual
o f Remote Sensing, 2nd ed., Am. Soc. Photogrammetry, I, 115-164, 1983.
Grody, N.C., Classification o f Snow Cover and Precipitation Using the Special Sensor
Microwave Imager: J. Geophys. Res., 96, D 4 ,7423-7435, 1991.
Hollinger, J., Lo, R, Poe, G., Savage, R. and J. Pierce, Special Sensor Microwave/Imager
User’s Guide, Naval Research Laboratory, Washington, DC, 120, 1987.
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64
Chapter 4: Nearshore Ice Surface Roughness Surveys on Lake Superior
Abstract
Nearshore ice surface roughness and snow thickness were surveyed with an
autolevel on Lake Superior for application to multisensor, particularly microwave, satellite
remote sensing o f Great Lakes ice cover. Topographic transects across four commonly
occurring ice facies were measured with 0.2 cm vertical and 5.0 cm horizontal resolutions.
The four ice facies rank in roughness as follows (RMS roughness (cm) / correlation length
(cm) in parentheses): single large pressure ridge (30/125), series o f small pressure ridges
(16/110), consolidated shuga zone (8/70) and young ice cakes (5/145). Snow cover was
widespread on the nearshore facies.
4.1 Introduction
Ice cover is a major component of the Great Lakes annual hydrometeorological
cycle, governing winter and spring mass and energy fluxes at the lakes surfaces, weather,
shipping season duration and shoreline processes. Current ice monitoring programs
(National Ice Center (U.S.), Canadian Ice Service (Canada)) employ combinations of
shore, ship, aircraft and multisensor satellite observations to produce ice cover informa­
tion products. Radar sensors (RADARS AT, ERS-1, ERS-2) are used increasingly to pro­
vide day/night, weather independent, high spatial resolution ( 1 0 -1 0 0 m) ice cover
information.
Microwave backscatter and emission from freshwater ice are controlled in large part
by surface roughness. This is the motivation for this in situ surface roughness study. The
physical-electromagnetic properties of Great Lakes ice have received considerably less
attention than polar sea ice. Previous studies of Great Lakes ice properties include Marsh
et al. (1975), Marshall (1977), Bolsenga (1988) and Assel et al. (1983), and specific
microwave studies include Bryan and Larson (1975) and Hagman (1976).
This chapter is primarily descriptive in nature, part of an ongoing process to develop
on-ice ground truth for multisensor remote sensing of Great Lakes ice cover. Ice rough­
ness profiles and statistics presented here may be useful to readers interested in Great
Lakes and, comparatively, sea ice roughness characteristics. Alternative surface roughness
R e p ro du ced with permission o f the copyright owner. Further reproduction prohibited without permission.
65
measurement methods are discussed in Chapter 6 .
4.2 Field Observations
Four study transects were surveyed with an autolevel in late February 1996 at two
sites on Michigan’s Keweenaw Peninsula (Figure 4.1) with the objective of measuring ice
surface roughness and snow thickness. Ice heights are collected by sighting through an
autolevel to a stadia positioned at regular intervals along the transect (Figure 4.5). Supraice snow thickness was measured concurrently.
:e;efl|ctcl^u'
o
100 km
Figure 4.1. Locations of ice topographic transects.
Facies (F) 1-4 on Michigan’s Keweenaw Peninsula (KP) on Lake Superior. Thermal
infrared image (band 4 AVHRR) 8:11 UTC February 4, 1996. Old, deformed ice (F 13) appears in brighter grey-white tones (~ -24 to -18 C) and young ice (F 4) in medium
grey tones ( - -17 to -2 C). The lake is extensively ice covered with young ice; open
water is confined primarily to the polynya beneaththe lake effect snow clouds in the
east basin.
Autoleveling is advantageous in that it is relatively inexpensive, requires no sophisti­
cated electronic equipment and permits surveying of long (10-100 m scale) transects. The
disadvantage here is the limit on horizontal sampling resolution (operationally imposed by
the width of the stadia base, -4.0 cm).
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66
nsect 1
Transect 4
^
vTranseCi 3
Figure 4.2. Location of ice transects 1, 3 and 4.
Location: McLain State Park, NW side of Keweenaw Peninsula. Ice accretion began with
the icefoot in December, 1995 and proceeded episodically through February, 1996. Fast
ice extended Iakeward from the outer edge of the icefoot. Leads and open water appeared
lakeward of the large pressure ridge intermittently throughout the ice season, particularly
during March and April.
This is a ‘macro-roughness’ study, in contrast with sub-cm resolution micro-roughness surveys which require more specialized equipment (e.g., Johnson et al. (1993) and
Simila et al. (1992)). A laser profiling system is state of the art, but such instruments are
relatively rare and expensive at the time of writing.
Four common and morphologically distinct ice facies were surveyed: 1) a portion of
a single large pressure ridge (Figure 4.2), 2) a rafted accretionary sequence of several
small pressure ridges (Figure 4.3,4.5), 3) a consolidated shuga zone and 4) young ice
cakes. Results are presented in Figure 4.6 and Table 4.1.
The four ice facies appear by visual inspection and field experience to be representa-
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67
fimnovolcanoes
Keweenaw Bay
Transect 2
|
SMALL IMBRICATED PRESSURE RIDGES
YOUNG CONGELATION ICE
Figure 4.3 Location of ice transect 2.
Location: west shore Keweenaw Bay. The 4-6 cm thick plates of Facies 2 accreted to
the ice foot in a series o f compressional events spanning several days in February, 1996.
Further compression and deformation was minimal after Keweenaw Bay filled with fast
ice. Subsequent snows and several spring melt-freeze cycles smoothed the imbricated
plates to a skiiable crust o f hummocks.
tive of major ice types in the region. They fall into two thermal signature categories evi­
dent in Figure 4.1: facies 1-3 occur in colder, thicker, older, deformed shore fast ice; facies
4 represents warmer, thinner young ice that probably formed in a Great Lakes -wide freez­
ing event around February 2, 1996. Transects 1-3 were oriented perpendicular to shore;
transect 4 was oriented to cross two ice cakes.
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Figure 4.4 Autoleveling survey in the small pressure ridge facies (Facies 2).
The stadia operator positions the stadia at 5.0 cm intervals along the transect reference line
(a measuring tape suspended between tripods). The autolevel operator reads the relative
elevation in the telescope’s crosshairs. A third person records the ice elevation and snow
thickness data.
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69
Figure 4.5 Small pressure ridge (Facies 2).
A: Keweenaw Bay, looking bayward (SE). Facies 2 at arrow. Icefoot edge on right. Ice
axe is 65 cm tall. B: Close up of small pressure ridge consisting o f imbricated slabs of
congelation ice. This ridge is approximately one to two weeks old.
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0
100
200
300
400 500
600
700
F a c ie s 2: s e r i e s o f s m a l l p r e s s u r e
500
1000
1500
2000
2500
800
900
1000
r id g e s
3000
3500
4000
H
X
g
5
F a c i e s 3: consolidated shuga
s ie8
58
200
400
600
1000
F a c ie s 4: y o u n g
50
0
800
200
400
600
800
1000
1200
1400
1600
1800
ice
1200
1400
1600
1800
2000
POSITION ALONG TRANSECT (cm)
Figure 4.6 Topographic profiles of surveyed ice facies.
Thick line=ice height above local base level; thin line=snow thickness above ice. Profiles
1-3 extend lakeward from 0 position (Figures 4.2,4.3). Profile four was not systematically
oriented with respect to the shoreline; rather, it was placed to cross two ice cakes and inter­
stitial brash ice. See Table 4.1 for roughness statistics.
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71
Table 4.1: Field measured ice roughness and snow thickness parameters
ice slab
thickness
(cm)
min-max
snow
thickness
(cm)
mean/
std. dev.
snow
thickness
(cm)
transect
length
(m)
horizontal
sam pling
interval
(cm)
72
30-40
0-14
3.2 / 3.8
10
5.0
110
63
4-6
1-38
13.9/6.8
32
5.0
20
21
10-40
0-24
7.9 / 5.3
18
20.0C
negligi­
ble snow
n.a.
20
5.0
RMS
rough­
ness
(cm)
correlat
ion
length
(cm)a
mean
height
b
1. la rg e p re s ­
su re rid g e:
rafted clear
thick congela­
tion ice
30.2
125
2. sm all p re s ­
su re ridges:
accretionary
sequence o f
rafted clear
thin congelation
ice
15.7
3. consoli­
d a te d sh u g a:
ice balls and
slush ice
conglom erate
7.8
4. young ice:
2 clear ice
cakes and inter­
stitial brash ice
4.8
facies
(cm)
(ball
diameter)
145
30
20-30
a. Correlation length: distance at which normalized autocorrelation function=l/e.
b. M ean height above transect base level.
c. 20 cm for first 16 m o f transect; 5 cm for final 2 m.
4.3 Results and Conclusion
The ice surface roughness and snow depth data collected form ground truth for satel­
lite data analysis and computer modeling. Two major morphogenetic regimes were sam­
pled; old, moderately deformed shore fast ice, and clear, young congelation ice. These two
regimes are readily discriminated by temperature in AVHRR thermal infrared imagery,
and can probably be discriminated in satellite synthetic aperture radar imagery. Snow
cover was nearly ubiquitous on the shore fast facies, with consequent implications for ice
cover and electromagnetic signature evolution.
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72
4.4 Acknowledgments
The author thanks a host of undergraduate and graduate student colleagues for their
enthusiastic field assistance: Matt Wachholz, Ashok Agarwal, Kindra Wicklund, Dan
Brugeman, Dan Wrona, Heather Shocker, Jon French, Seth Lemke, Bill Schulz and
Michelle Mars. Dave Schneider provided helpful commentary. The AVHRR satellite
image was obtained from the NOAA Satellite Active Archive. This research was funded
in part by NASA Global Change Fellowship # 1956-GC92-0312 and Michigan Space
Grant Consortium Seed Grant # 79827.
4.5 Bibliography
Assel, R. A., Quinn, F. H., Leshkevich, G. A., and S. J. Bolsenga, Great Lakes Ice Atlas,
NOAA Great Lakes Environmental Research Laboratory, 1983.
Bolsenga, S. J., Nearshore Great Lakes ice cover, Cold Regions Sci. Tech., 15, 99-105,
1988
Bryan, M. L. and R. W. Larson, The study of freshwater ice using multiplexed imaging
radar, J. Glaciology, 14,72,445-458, 1975.
Hagman, B. B., On the use of microwave radiation for Great lakes ice surveillance, NOAA
Tech. Mem. ERL-GLERL-13, 1976
Johnson, F., Brisco, B. and R. J. Brown, Evaluation of limits to the performance of the sur­
face roughness meter, Can. J. Remote Sensing, 19, 2, 140-145, 1993.
Marsh, W. M., Marsh, B. D. and J. D. Dozier, Formation, structure, and geomorphic influ­
ence of Lake Superior icefoots. Am. J. Sci., 273,48-64, 1975.
Marshall, E. W., The geology of the Great Lakes ice cover. Ph.D. thesis, Geology, Univ. of
Michigan, 614 pp., 1977
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
Simila, M., Lepparanta, H. B., Granberg, H. B. and J. E. Lewis, The relation between SAR
imagery and regional sea ice ridging characteristics from BEPERS-8 8 , Int. J. Remote
Sensing, 13, 13, 2415-243, 1992.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
Chapter 5: Meter range 37 GHz passive microwave
observations of snow on north and south facing slopes
Abstract
Sun position and topographic aspect geometrically control solar insolation, thereby
influencing snow pack thermal metamorphism and consequent physical state and micro­
wave emission characteristics. A time series of 37 GHz vertical polarization radiometer
observations was made in an east-west trending gully to investigate the possibility that
north- and south-facing slopes may display distinct emission characteristics resulting from
differential solar influx. A time lag in brightness temperature between north- and southfacing slopes due to differential timing of melting during the diurnal cycle was observed.
Vertical core samples were sieved; the two slopes were not distinguishable on the basis of
grain size distribution. Approximately 49% of the sieved snow grains were larger in diam­
eter than the 37 GHz free space wavelength (8.1 mm), suggesting that volume scattering
was an important process in this snow pack.
5.1 Introduction
Microwave emission from seasonal snow cover is controlled in large part by snow
pack wetness, temperature, thickness, grain size, stratigraphy and surface roughness (Edgerton et al., 1971; Hofer and Schanda, 1978; Ulaby et al., 1981; Foster et al., 1984). The
development of these properties by late winter-spring is dominantly controlled by thermal
metamorphism in the snow pack, driven by temperature gradients. Solar insolation plays a
significant role in this process through differential heating of the surface layers of the pack
as a function of topographic aspect (azimuth of slope surface normal vector).
This chapter reports the results of a field experiment performed to look for differ­
ences in microwave brightness temperature between a north-facing slope (NSF) and a
south-facing slope (SFS). Significant differences in snow properties and consequent
brightness temperature as a function of topographic aspect may require attention in inter­
pretation of airborne and satellite microwave brightness temperature data.
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75
5.2 Field Observations
5.2.1 Study area
The study area is located in an east-west trending gully 50 m NW of a weather sta­
tion on the Michigan Technological University (MTU) campus, situated on a low-relief
glaciated upland. Figure 5.1 is an autolevel surveyed topographic cross-section of the
gully.
4
0 8 :0 0
solar elevation
3
radiometer
2
1
SO U TH
NORTH
0
1
meters
Figure 5.1. Topographic cross-section of gully.
5
1o
15
Solid line = snow surface. Dashed line = soil surface. Rays from antenna symbol indi­
cate radiometer incidence angles at 15 0 increments. A-E = locations of sieve samples.
(Note: vertical exaggeration distorts angular appearance of rays. Target locations on the
snow surface as a function of 9 are not distorted.) Solar elevation arrows indicate vectors
of sun beams at the indicated local times.
5.2.2 Snow apparent brightness temperature measurement
The sensing system consists of a 37.4 GHz (500 MHz bandwidth) double-sideband
unbalanced Dicke-type radiometer (3° EFOV, 3 dB half beamwidth) and a lock-in ampli­
fier. The radiometer was mounted on a horizontal axle approximately 1.6 m above the
snow surface at nadir, allowing target viewing at any incidence angle (0 ) in a vertical
north-south plane. Twenty-two data runs were made under various ambient conditions
from 31 March to 11 April 1994. A data run consisted of three brightness temperature
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76
measurements at each 5 degree increment from 0 = 0 (vertical) to 0 = 90 (horizontal) to
the north (viewing the SFS) and to the south (viewing the NFS). Calibration was per­
formed in the field by measuring emission from warm and cold absorbers (ambient tem­
perature and 79 K (liquid nitrogen-soaked)). Snow emission is converted to
assuming
a linear sensor response between the warm and cold calibration targets. The data are pre­
sented here as apparent brightness temperature CIap); they have not been corrected for
scene geometry or scattered sky contribution.
5.2.3 Snow characterization
The physical state of the snow was assessed at various times during the experiment
by visual examination in snow pits (Figure 5.2), grain size analysis from sieved samples
and time domain reflectometry to measure snow dielectric constant (e’snow)- Solid samples
of undisturbed snow were collected and processed in preparation for stereological analysis
to statistically characterize the scattering structure of grains and pores (see Perla, 1982;
Shi et al., 1993).
i Thickness TpJ
( Density
Hardness
j (cm)
|
j (g cm ' 3)
(penetrability)
1
1
(C°)
i £’
1
Air
new
crust
old
Snow
Air | *
New | 12
Snowj
1“
Old | 30
Snowj
1
1 *
1 0.35
1.7
1
0.1
*
I finger
1
1
0.1
1
1
0.45
1
*
knife blade
Soil !"*
* *
. 2.1
1
J
Soil
| 1.0
1
_|
,
1
1
*
1*
*
Figure 5.2. Example of snow conditions 31 March 94, 17:00.
The snow pack underwent a number of melt-freeze cycles during the study. The pack
appeared vertically homogeneous to visual inspection; there were no obvious indicators of
persistent grain size variation or ice lenses in the snow pits examined. A buried surface
crust (probably a melt-freeze crust) occurred at approximately 30 cm beneath new snow.
The snow surface was wind rippled with wavelengths of approximately 10 to 20 cm and
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77
amplitudes o f 0 to 1.5 cm. Five vertical core samples of the entire snow pack were col­
lected for sieve analysis on 9 April along the NS radiometer profile (see Figure 1). These
were shaken for approximately 30-90 seconds in each of seven sieves ranging from 25.4
mm to 0.7 mm grid size.
A time domain reflectometer (TDR) was used to measure
e ’sn0w
in both vertical and
horizontal profiles intermittently during the study period. The TDR unit is a commercially
available soil moisture probe with internal calibrations for converting from apparent
dielectric constant to volumetric soil moisture. Conversion factors for converting from
e’snow to volumetric snow water content have not been established, so only e ’snow is
reported in Figure 5.2.
5.3 Discussion
5.3.1 Brightness temperature
A subset of the brightness temperature data is presented in Figure 5.3. The complete
Tap time series data show subtle differences between the NFS and SFS, but the exact
causes of these differences cannot be stated precisely in the present analysis. The domi­
nant brightness temperature patterns observed are attributed to melting and freezing in the
diumal cycle.
Certain melt-freeze patterns associated with the diumal cycle recur throughout the
study period. Before sunrise and in early morning, both slopes are radiometrically cold,
with TAP in the 150-200 K range (Figure 3-A). The snow has a frozen surface crust; there
is commonly liquid water present in a variably thick zone below the surface crust extend­
ing upward from the base of the pack.
Figure 3-A also shows a pattern present in many of the data runs; a general decrease
in T ^ from 0 = 0 to 9 = -40 degrees. It is probably not a function of changing angle of
incidence: due to the gully geometry, actual angles of incidence are within approximately
15° of the surface normal at each target. A possible explanation is the presence of small
amounts of liquid water continuously supplied to the pack through diffusion of water
vapor originating in the sub-snow stream. The result would be higher TAP in the snow
proximal to the water source.
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78
3 00
‘ 9 4 0 4 0 4 0 8 :0 0
250
200
150
0
20
40
60
80
3 00
11:00
-9 4 0 4 0 4
250
wet
200
150
0
20
40
60
300
80
wet
250
- 940404
1 5 :0 0
200
150
0
40
60
20
incidence angle (0)
80
Figure 5.3. TAp profiles
Tap for three successive runs. * = SFS.
Q
nfs.
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79
The increase of NFS
at about 60 degrees is an effect of the radiometer sensing
radiometrically warmer ground through the thinner snow pack near sample site D.
The elliptical feature showing separation between the NSF and SFS between 40 and 60
degrees is present in most of the runs made under frozen conditions. Because the angles of
incidence and the thicknesses are approximately the same, it is probable that this feature is
due to subtle, localized differences in grain size or layering not recognized in the field.
Figure 3-B shows typical midmoming conditions. Solar radiation warms the SFS,
melting the surface layer (perhaps melting throughout), producing a radiometrically
warm, near-blackbody emitter, with T ^ generally within a few degrees of 273 K. The
NFS is still frozen, retaining its low night time TAP (-160-240 K) (the time lag effect).
Figure 3-C shows a full melt condition in midaftemoon. Both slopes have TAP in the
255-271 K range, approaching blackbody conditions. Targets with lower TAP (-260K)
may indicate scattering loss due to locally increased surface roughness.
5.3.2 Grain size
Figure 4 shows histograms of grain size distributions for the five vertical core sam­
ples sieved.The actual sieve sizes were 25.4, 13.3, 9.4, 4.0, 2.0, 1.0, and 0.7 mm. The
sieves used do not fall on evenly spaced intervals in either mm or phi space, so for plotting
purposes they were rebinned to regular intervals of one phi size. The percentages for the
new bins were estimated using a graphical technique.
The mean histogram (mean of samples A-E) indicates that approximately 49% of the
grains sampled are larger than 8 mm (-3 phi), in the Mie scattering region for 37 GHz (8 . 1
mm) radiation. Note that the mean grain size of monocrystalline snow grains in this snow
pack is approximately 0.5 to 2.0 mm (based on visual inspection with a calibrated magni­
fying lense). The grain-size fractions greater than approximately 2 mm consist of poly­
crystalline aggregates.
There do not appear to be distinct differences in grain size distributions between the
NFS and SFS. In other words, the two slopes cannot be distinguished on the basis of grain
size alone.
The samples taken from lower in the gully (B, C and D), as opposed to higher on the
gully flanks (A and E) are considerably coarser-grained. One could expect volume scatter-
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80
■■■■I,
- 4 - 3 - 2 - 1 0
1 2
3
phi size
Figure 5.4. Grain size distribution histograms. Actual sieve sizes: 25.4, 13.3, 9.4,4.0, 2.0,
1.0,0.7 mm.
Sample locations A-E indicated in Figure 5.1.
.5
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81
ing to be more significant in these locations. Hydrology may explain the predominance of
larger grains at the bottom of the gully. The subsnow stream provides water vapor which
diffuses through the gully-bottom snow, contributing to the development of large, poly­
crystalline grain aggregates.
5.4 Conclusions
North-facing and a south-facing slope were observed intermittently through several
diumal cycles with a 37 GHz radiometer to investigate to what degree solar aspect influ­
enced brightness temperature through control of snow pack physical properties. The time
series TAp data show a distinct time lag in the NFS TAp due to preferential melting of the
SFS. Five vertical core samples of the snow pack were sieved; the grain size distributions
indicate that volume scattering was a significant process in this snow pack. The two slopes
were not discriminable on the basis of grain size.
5.5 Acknowledgments
The author thanks John Galantowicz and Anthony England (University of Michigan
Radiation Lab) for use of the radiometer system. Bert Davis (U.S. Army Cold Regions
Research and Engineering Lab) provided guidance in preparation o f stereological sam­
ples. Don Hopper provided assistance with sieving and computer graphics. Pat McEnaney
assisted with auto leveling and Mary Larson with data entry. Deb Schueler, Jim Vallance,
John Graf and Bill Rose provided helpful reviews. This research was funded by NASA
Graduate Student Fellowship for Global Change Research #1956-GC92-0312.
5.6 Bibliography
Edgerton, A.T., Ruskey, F., Williams, D., Stogryn, A., Poe, D., Meeks, D., and O. Russell,
Microwave emission characteristics of natural materials and the environment (a summary
of six years research), Final Technical Report 9016R-8, Aerojet-General Corporation, El
Monte, CA, February 1971.
Foster, J.L., Hall, D.K., and A.T.C, Chang, An overview of passive microwave snow
research and results, Rev. .Geophys. Space Phys., 22, 2,195-208, 1984.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
82
Hofer, R., and E. Schanda, Signatures of snow in the 5 to 94 GHz range, Radio Science,
13, 2, 365-369, 1978.
Perla, R., Preparation of section planes in snow specimens, J. Glaciology, 28,98, 199-204,
1982.
Shi, J., Davis, R.E., and J. Dozier, Stereological determination of dry-snow parameters for
discrete-scatterer microwave modeling, Annals Glaciology, 17, 295-299, 1993.
Ulaby, F.T., Moore, R.K., and A.K. Fung, Microwave Remote Sensing— Active and Pas­
sive. Norwood, MA: Artech House, 1981.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
83
Chapter 6: Conclusions and Recommendations
This dissertation comprises a set of studies on the theme of passive microwave
remote sensing of Great Lakes ice and snow. Principal results are summarized below, and
recommendations for future studies are made.
6.1 Conclusions
The objective of Chapter Two was to use SSM/I to remotely sense Lake Superior ice
conditions and to explore the utility of the instrument as a tool in Great Lakes ice monitor­
ing. The principal advantages of SSM/I are its enhanced temporal resolution (up to six
images per day) and inherent sensitivity to ice conditions. Ice covered and ice free regions
located using SSM/I agreed well with AVHRR imagery and NIC ice charts. A correlation
between 37 GHz hpol TB (and emissivity) and ice stage of development was demonstrated
using coregistered images and ice charts. Lake ice TB and emissivity appear to be compa­
rable to those of new and young sea ice. Great Lakes ice monitoring opportunities will
expand after the launch of higher spatial resolution passive microwave radiometers such as
AMSR and MIMR.
Chapter Three uses SSM/I to explore the seasonal evolution of Great Lakes ice cover
for the 1993-94 winter. Spatial patterns of ice growth and decay on the Great Lakes were
highly evident in animated sequences of daily SSM/I images (included on diskette in the
Appendix). Graphs of TB display the radiometric evolution of individual lake and land
pixels through the ice season. Missing pixels were replaced by the mean TB of the three
preceding and three following days for which TB values were present, providing images
suitable for visual interpretation and certain quantitative applications.
Chapter Four is a surface roughness study of four nearshore ice facies. The motiva­
tion was to quantify surface roughness for radar backscatter and microwave emission
ground truth and computer modeling. The facies rank as follows (decreasing root mean
square surface roughness): large pressure ridge, small pressure ridges, consolidated shuga
and young congelation ice. The first three form a group of older, colder, thicker moder­
ately deformed ice, discriminated in AVHRR thermal imagery from the younger, warmer,
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84
thinner congelation ice.
Chapter Five investigates the effects of solar angle on 37 GHz snow brightness temperature
and grain size. Snow brightness temperatures were measured on north and south facing slopes in a
15 m wide gully. The slopes warmed and melted differentially during the diumal cycle due to dif­
ferences in solar angle, and exhibited consequent differences in TB history. Five vertical snow
pack samples were sieved to determine the grain size distribution; no solar insolation derived dif­
ferences in grain size were found. Approximately half of the primarily polycrystalline grains were
larger in diameter than 8 .1 mm, the free space wavelength of the radiometer. This grain size distri­
bution appears to be relatively representative of Keweenaw snow pack (unpublished observa­
tions), suggesting Mie scattering as an important process in this geographic region.
6.2 Recommendations
As with many research projects, these studies generated more questions than they answered.
The remarks below address some of the issues that emerged in the course of these studies.
6.2.1 Ice surface roughness
In situ ice surface roughness measurements are important for computer modeling of micro­
wave backscatter and emission, and in recognition of characteristic ice types in the field. Surface
roughness is a function of antecedent conditions including deformation history, ice thickness and
snow cover. A primary goal of satellite SAR ice mapping is to identify ice types present in a
scene. Different ice types generally have different roughness characteristics (e.g., smooth new ice
versus moderately deformed older ice).
There are a number of approaches to measuring ice roughness. The method used in Chapter
4 consists of surveying a transect using an autolevel telescope and stadia rod. Perhaps the simplest
method is to photograph an ice profile in front of a dark backdrop displaying a superimposed grid
(e.g., a yellow centimeter grid imprinted on a black sheet of metal). Ice roughness is later quanti­
fied by digitizing the profile of the ice in the photograph with the centimeter grid for scale. Cur­
rently, the highest resolution roughness profiles are measured using a laser profileometer.
Unfortunately, such instruments are expensive and not readily available. Beaudoin et al. (1990)
report using an electro-mechanical profiler with good results. The apparatus consists of moveable
metal rods suspended vertically in a frame. The rods are adjusted to follow the elevation profile of
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85
the ice surface of interest. The movement of the rods is detected electromechanically using
potentiometers, converted to voltage, quantized and downloaded to computer.
The above methods each generate a one dimensional elevation profile. It is theoreti­
cally possible to produce a two dimensional surface elevation model using close range ste­
reo photography and generation o f a three dimensional stereo model. The procedure is to
take two overlapping vertical photographs from an elevation of perhaps 0.5 to 5 m. Photos
taken at night can be artificially illuminated from the side (simulating shadow-enhancing
low sun angles) using either flash or continuous light sources. A stereo model can be gen­
erated manually using the resultant stereo pair and a stereoscope. Alternatively, the stereo
photos can be scanned into a computer and processed using software designed for generat­
ing stereo models (at present, such software is relatively expensive). This photogrammetric technique has two principal potential problems. First, it may be difficult to create
sufficient shadowing in smooth as opposed to jagged surfaces of low relief. Second, it may
be difficult to achieve sufficient contrast to clearly identify corresponding features in the
two photos.
6.2.2 Melt state
The dielectric properties of snow and ice are controlled principally by whether the
snow or ice target is dry (fully frozen) or wet (partially melted). It is recommended that
measurements and image acquisition (e.g, SAR) be scheduled for times when ice and
snow are likely to be frozen to avoid complications introduced by the presence of liquid
water of unknown concentration (unless melt conditions are the subject of the study). Such
times would be approximately mid-December through March, and at night before and
after this period. Note that liquid water commonly exists within the spring snow pack after
melt episodes even when the surface is frozen.
6.2.3 Lake Superior environmental geographic information system
One of the principal issues that emerged from these studies was the need to analyze
ice satellite imagery in the context of environmental conditions surrounding the date under
consideration, and a need for a means of combining satellite data from different sensors
with a minimum of processing steps. A geographic information system (GIS) approach
provides a means to address this. A conceptual model for a prototype GIS is outlined
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86
below; the prototype is being designed and developed at the time of writing.
The purpose of the GIS is to gather environmental data from the Internet in quasireal time
during the ice season, as opposed to retrospectively, and to automatically organize it in a form
accessible through hypertext documents (e.g., HTML World Wide Web pages). The main motiva­
tions are
•
to provide an organizational structure to facilitate image browsing;
•
to capture ephemeral satellite and weather from the Internet before it is archived in long­
term form (e.g., SSM/I) or destroyed (e.g, GOES imagery); and
•
to facilitate study of ice conditions as the season progresses to help plan field studies.
The design emphasizes 1) collating data freely available on the Internet, and 2) use of simple
UNIX scripts and programs to automatically gather data via ftp (file transfer protocol), and to
automatically generate web documents accessing the database. The design philosophy parallels
that of the UNIX operating system: flexibility and simplicity based on combinations of simple
tools and data structures. The data can be reorganized or ingested into a GIS package (e.g.,
GRASS) or image processing package as necessary. The disadvantages of more powerful special­
ized image processing software and geographic information systems tend to be overhead in terms
of cost, specialized file modification and learning curves for high level languages. These are
avoided to some degree by relying on highly portable UNIX scripts, and existing UNIX software
toolkits such as xv, pbmtools and IPW (Image Processing Workbench) (all are either free or inex­
pensive for educational applications).
There are four main structural elements in the system:
•
a browse image archive with a hypertext document user interface;
•
a raw data archive with a hypertext document user interface;
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87
•
metadata files documenting the lineage (processing steps) of each image and data
file; and
•
UNIX scripts for manipulating the data.
The emphasis is on minimizing complexity by using basic UNIX commands, scripts
and data structures as much as possible for creating and maintaining the data archive and
web document browse facility. This greatly facilitates batch processing and documentation
of data lineage.
Web documents will be generated automatically from standard templates to provide
a simple interface to the browse image and raw data archives. The user will query the
browse and metadata archives by opening an HTML document associated with a given
date. Options for creating image time series animations can be included. Simple data
structures (binary and hierarchical data format, HDF) and standard image formats (GIF,
JPEG, etc.) will be used. Templates will be used in both web documents (the user inter­
face) and data directory structures (the data archive) to maintain standard forms that facil­
itate operations based on scripts.
A variety of Great Lakes environmental data is available on the Internet or World
Wide Web. The primary data layers anticipated in the prototype version of the system are
as follows:
• SSM/I brightness temperature (lake surface conditions);
• SSM/T (atmospheric sounder for measuring atmospheric conditions);
• GOES (used to identify clear sky images, or for situations requiring high temporal
resolution (30 minutes) (e.g., preceding SAR image acquisition));
• AVHRR (collected opportunistically, depending on conditions and application);
•
RADARSAT (collected only when an image acquisition is requested);
•
synoptic weather maps;
•
buoy / lighthouse data (point data, 15 minute temporal resolution);
• NEXRAD (National Weather Service weather radar for detecting precipitation
events); and
•
wind data.
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88
6.3 Bibliography
Beaudoin, A., Gwyn, Q. H. J., Bordeleau, G. and P. Cliche, An economical electronic roughness
sampler for radar land studies, Proc. IGARSS90, pp. 1181-1184, 1990.
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89
Appendix A: Field measurements of snow 37 GHz brightness
temperature
Abstract
Radiometer observations were made at and near Michigan Technological University
(MTU) to measure snow 37 GHz brightness temperature. Snow properties were measured
intermittently during the series o f observations. The motivation was to improve under­
standing of snow emission of 37 GHz radiation for application to satellite remote sensing
and computer modeling o f the radiative transfer process. Three sites were visited intermit­
tently between December 1993 and April 1994: MTU weather station, a gully near the
weather station, and the Keweenaw Research Center. A 37 GHz passive microwave radi­
ometer measured snow microwave emission under various ambient snow conditions, at
multiple incidence angles (0-90°, 5° increments) and in vertical and horizontal polariza­
tion. Sky brightness was measured at lesser angular resolution. Snow thickness, tempera­
ture profile, density, dielectric constant (real part) and layering were measured
intermittently. Several snow samples were sieved to measure grain size distributions. Eight
solid samples were collected and processed for future stereological analysis. Results to
date have been presented in Pilant (1994 a) and published in Pilant (1994 b, Chapter 5 of
this dissertation).
A .l Field Measurements
The following snow measurements were standard for the field experiments:
•
brightness temperature (TB)
•
depth
•
physical temperature (Tp).
These measurements were made intermittently during the winter:
•
real part of the snow dielectric constant (e’)
•
density (p)
•
grain size (gs)
•
grain shape
•
stratigraphy
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90
•
snow sieving
•
snow pack and snow grain photography
•
snow stereological samples.
A.2 Equipment
A.2.1 Snow sampling supplies
The snow sampling tool kit comprised the following:
•
plastic tool box
•
snow tube and scale (for measuring density in core samples)
•
spatula
•
saw blade
•
comparator ( lOx magnifying lense with calibrated particle size graticule)
•
duct tape
•
sample bags and containers
•
waterproof labelers
•
tweezers
•
paint brush ( I cm wide)
•
8
•
dimethyl pthalate (for preparing stereological samples)
and 10 mm wrenches (for radiometer system adjustments)
A.2.2 Instruments
The radiometer tower consisted o f two 3 m tripod-supported uprights, one 1.5 m pvc
axle, one 1 m metal pipe axle handle, two 1 m metal horizontal braces and one 5 m cable
and pulley for lifting the radiometer.
Electronic equipment used in this study comprised:
•
radiometer system
•
time domain reflectometer
•
thermocouples/thermometers
Radiometer System:
•
radiometer with insulating box
•
lock-in amplifier with insulated box and electric heating pad
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91
•
AC-DC converters for radiometer, fan and heater
•
2
•
power strip
•
extension cords
•
inclinometer
•
Echosorb foam absorbers
•
liquid nitrogen
•
duct tape and bungee cords
coaxial cables for radiometer to lock-in amplifier
Time Domain Reflectometer
•
Trase System I time domain reflectometer (soil moisture sensing instrument)
•
waveguide head
•
coaxial connector cable
•
15 and 45 cm waveguides
•
AC power transformer (optional)
Temperature Sensors
•
3 digital thermometers
•
thermocouple sensor, thermocouples
•
pvc tube for mounting thermocouples for insertion at fixed spacings
A.3 Measurement Procedures
A.3.1 Calibration and data acquisition
This is a description of the radiometer calibration procedure. The radiometer out­
put is the intensity of the linearly polarized electric field component of the incoming 37
GHz signal; the units are microvolts. Three data are taken at each angle of incidence. They
are subsequently converted to TAP; an average of the three TAP is taken to represent the
brightness temperature of the target at that incidence angle.
Calibration is the process of measuring the voltage produced by two Echosorb
foam targets which are assumed to be blackbodies (Echosorb foam is high emissivity foam
used as wall covering in antennae testing chambers). The ‘hot’ target radiates at ambient
temperature (measured in situ with a thermocouple). The ‘cold’ target is a foam absorber
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92
soaked in liquid nitrogen (LN2) (79 K). For each target there is a data couplet: physical
temperature and voltage. Because each is a blackbody, the physical temperature is identi­
cal to the brightness temperature. The hot and cold target define two points in voltage-temperature space; a linear function connects them (Figure A.l). Raw field data are converted
from voltage to TAP by plotting the voltage on the linear curve.
hot calibration target
snow target
u
a00
o>
cold calibration target
0
79
300
physical temperature (K)
Figure A. 1 Voltage to brightness temperature conversion.
The brightness temperature is found by plotting the voltage of a snow target on the
function defined by two calibration targets. The radiometer is pointed at two black­
body calibration targets (pieces of Echosorb foam) and the resulting voltages recorded.
The physical temperatures of the two targets are also recorded. For a blackbody,
T b =Tjx The endpoints of the linear calibration function are thus defined.
Liquid nitrogen calibration is the preferred method (LN2 is not always available in
field circumstances). In addition to calibration, there is potential for error with instrument
drift, and with the actual physical temperature of the absorber. The physical temperature
of the cold absorber is not measured; at approximately 79 K, it is beyond the range of the
thermocouple. The temperature of the LN 2 soaked source is assumed to be 79 K. It is crit­
ical that the measurement be made within a few seconds of removing the foam from the
LN2 bath; otherwise, ‘hot’ air at ambient temperature will rapidly warm the foam, causing
it to radiate at an unknown temperature above 79 K, thereby corrupting the calibration
curve. This problem was observed in some of the earlier experiments.
The couplet of calibration data and voltage data filename are entered into an IDL
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93
program, calibrate.pro. Calibrate.pro retrieves the raw data file (voltages), and calculates
Tap data using the linear regression equation defined by the calibration curve.
The radiometer is subject to instrument drift, therefore a single regression equation
will not suffice for all conversions from raw voltages to TAP Each data run may be slightly
different in its absolute calibration.
The operator turns on the amplifier and radiometer at least one hour prior to taking
measurements to allow the components to warm and stabilize. The heater built in to the
radiometer maintains an internal temperature of approximately 33 C. An electric hot pad
is inserted below the amplifier in the lock-in amplifier box when temperatures are below
approximately -4 C. The radiometer built-in heaters function effectively, permitting data
acquisition in virtually any conditions. The equipment is covered with tarps in case of
snow or rain.
The operator directs the antenna beam at a specific incidence angle by turning the
axle handle and locking it into position using a bolt through the appropriate hole in a tem­
plate mounted on the tower. The angle is verified using a dial inclinometer mounted on the
radiometer box. In the event of disagreement between template and inclinometer, the incli­
nometer takes precedence. Small adjustments (e.g., one to three degrees) can be made by
applying pressure to the handle. Readings are taken once the values have stabilized to
within 0.2 microvolts about a central value; this normally takes 5 to 10 seconds. Three
readings are taken at each observation angle and later averaged to compute a single TB
value. Wind may vibrate the tower, causing minute movements of the antenna beam. In
this case, the operator mentally estimates an average value of the displayed voltages. This
procedure is repeated at each 5° increment of incidence angle between 0 and 90°. Such a
data run takes from five to fifteen minutes, depending on wind and temperature conditions.
Automatic data logging is possible, but these data were all collected manually on data
forms and subsequently entered into ASCII files for processing. The procedure is most
efficient when one person operates the radiometer and reads the amplifier voltage display,
while the other operator records voltages and weather observations
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94
A.1.1 Snow T b measurements
In general, TBsnow measurements are made each 5° from 0 = 0 to 90°, in both verti­
cal (vpol) and horizontal (hpol) polarization. If time or conditions restrict measurements to
one polarization, vpol is generally selected. At the weather station, snow targets are mea­
sured in the east direction only (radiometer looking east). At the gully site, the radiometer
looks both north and south. At the airport, the radiometer looks north and south, then the
tower is pivoted to view the snow east and west.
A.1.2 Sky T b measurements
Measurements of TBsky are made at least once during each multiple hour series of
observations. They are made in 5, 10, 15 or 30 degree increments, depending upon sky
conditions (cloudy or clear) and weather conditions. TBsky values tend to be relatively low,
ranging from approximately 10 to 40 in the incidence angle range of 0 (nadir) to 70
degrees. The reflected sky contribution to Ta n j is of correspondingly low magnitude.
Data that have been corrected for atmospheric contributions are referred to using labels of
this form. TBsky correcte£j.
A. 1.3 Data format
Raw field data are entered into ASCII data files with filenames that indicate the date,
time, polarization, target and direction. For example, the file 940319_1350_hskyW is
interpreted as 19 March 1994, 1:50 p.m., horizontal polarization, TBsky looking west.
Snow voltage data files consist of four columns and 19 rows: column 1 = incidence angle;
columns 2-4 are the three microvoltages recorded for averaging and computation of a sin­
gle Tb . Each row is a separate incidence angle from 0 to 90 degrees.
A. 1.4 Measuring e’
The real part of the dielectric constant of the snow or soil is measured with a time
domain reflectometer (TDR) soil moisture probe from SoilMoisture Corp., Santa Barbara,
CA. The measurement concept is this. The velocity of an electromagnetic wave in a
medium is inversely proportional to the dielectric constant of the medium. The TDR oper-
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95
ates by measuring the two-way travel time of an electromagnetic pulse down a pair of
metal rods (waveguides). As liquid water content, and, hence, £’, increases, the velocity of
the wave decreases and travel time increases.
In general, vertical snow profiles are measured in snow pit walls. Snow liquid water
content is highly variable with position in the snow pack. For this reason, three TDR mea­
surements are made for averaging at each horizon sampled. The snow is generally sampled
in a vertical profile at 5 or 10 cm intervals, with additional measurements taken at horizons
of interest. Vertical or oblique top-to-bottom measurements were taken also to measure the
bulk e’ of the snow pack. The 15 cm waveguides were used early in the season. The 45 cm
waveguides were adopted in February and used thereafter. Use of the 45 cm waveguides is
thought to increase the accuracy of the readings (R. Dai, personal communication). In
principle, the 45 cm waveguides should increase the accuracy of the reading because the
reflection time can be measured with a greater number of samples. The 15 cm waveguides
were used in all soil sampling because the region of radiometric interest is the top several
cm (i.e., the microwave penetration depth) (and it is difficult to insert longer waveguides
into soil without bending them).
A.2 Equipment Descriptions
A.2.1 Radiometer Tower
A 3 m tower was constructed from lengths of wooden “two-by-four” inch common
lumber (44.5 x 88.9 mm) to provide a stable platform for mounting the radiometer. A tri­
pod was used initially but the tower provides greater stability and accuracy in reoccupation
of repeat-visit sites. Another advantage is unrestricted viewing at any angle in a vertical
plane (with the exception of a cross-bar support at zenith, and, if attached, a cross-bar at 0
= ~20°). The tower is relatively stable, even in high winds (a not infrequent condition at
the experiment sites). This permits the operator to leave the radiometer in position and
running throughout a series of measurements.
The radiometer box is bolted to a horizontal pvc axle (-12 cm diameter) resting in
holes in the uprights. Several pairs of holes are available, providing nadir heights of 0.9 to
2.6 m. A plywood template is bolted to one of the uprights.Holes were drilled in two con-
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96
centric circles at 5° increments. The operator may then point the radiometer at any target
in a 360° vertical plane, and lock the axle in place by blocking it with a bolt in a template
hole. The template is a useful element of the tower in that it increases stability and repeat­
ability, and permits a single operator to collect data.
A.2.2 Radiometer System
The radiometer system comprises a Dicke-type radiometer, a lock-in amplifier and
AC-DC power converters. The radiometer was designed and built by Dr. John Galantowicz with Professor Anthony England at the University of Michigan Radiation Laboratory.
Discussions of radiometer fundamentals can be found in Ulaby et al. (1981; chapter 5),
Colwell (1983, Chapter 11) and Siegal and Gillespie (1980, Chapter 11).
The radiometer antenna is sensitive to the electric field component of an incoming
electromagnetic field at a frequency o f 37.5 GHz. A local oscillator tuned to the antenna
frequency responds to the incoming electromagnetic field. The low intensity signals are
amplifed in the receiver. The radiometer output is displayed as a voltage (units of micro­
volts) on the lock-in amplifier. Strip heaters on the radiometer chassis maintain the internal
temperature at approximately 33 C°, even when the air temperature is as low as -20 °C. A
box (styrofoam and wood) provides thermal insulation and mechanical protection. Table
A. 1 presents radiometer system characteristics.
Table A .l: Radiometer System Characteristics
center frequency
37.5 GHz
band width
500 MHz
beamwidth
3 degrees (half width, full power)
power consumption
15 VDC
A.3 Site Descriptions
The measurements reported in this dissertation were made at three sites on upper
peninsular Michigan’s Keweenaw Peninsula: weather station, gully and airport. The
Keweenaw Peninsula is a narrow spine of Precambrian basalt and sandstone extending
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97
northeast approximately 50 km toward the center of Lake Superior. Uplands are domi­
nantly northern mixed deciduous trees; low areas and plains contain types ranging from
deciduous, mixed deciduous-conifer and wetlands (marshes, ponds). Boundary layer
meteorology is dynamic; weather changes are commonly rapid, frequent and may be of
relatively large magnitude. Winds are dominantly from the N-NW; dry winds from Can­
ada (to the northwest) collect moisture over Lake Superior and annually deposit 3-5 m of
snow on the peninsula.
A.3.1 MTU weather station site
The MTU weather station is located at an elevation of 245 m on a forested upland
near the campus sports complex. This was the primary TB measurement site for the 199394 winter. The weather station is operated by Jim Carstens o f the MTU School of Technol­
ogy; measurements of temperature (current, minimum and maximum) and precipitation
amount are taken in standard U.S. Weather Service format between 16:00 and 17:00 daily.
The site is a grassy field adjacent to a parking lot, a strip of forest, a small drainage chan­
nel and a soccer field. Due to the open nature and highland position of this site, wind is a
significant factor in weather and snow pack evolution. A 15x 15 m cyclone fence surrounds
the electrified weather station site.
The tower is positioned against the west fence line; TBsn0W measurements are taken
looking east. TBs|cy is measured looking east and west. The soil surface slopes down
approximately 3-4° toward the east; it is assumed that the snow surface paralleled the soil
surface. The radiometer lens to ground distance was 1.6 m at nadir.
A.3.2 Gully Site
The gully site is a small stream channel trending N 100 E located 30 m north of the
weather station (see Chapter 5). The tower was placed at the bottom of the drainage, strad­
dling an ice bridge, oriented so that the radiometer looked north and south. The lense to
ground distance is 1.6 m at nadir.
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98
A.3.3 A irport site
The Houghton County Airport is located on a Pleistocene lake bed on a highland at
an elevation o f 334 m 13 km northeast of the MTU campus. The Keweenaw Research
Center (KRC) operates an autologging weather station next to the runway. The radiometer
tower was located 20 m west of the weather station tower. Measurement runs were made
looking northeast and southwest, and after pivoting the tower, southeast and northwest.
Winds are very strong at this site, leading to wind slab development in the snow pack
which also tends to be thinner at this site than at the MTU weather station due to wind
ablation. Strong winds and blowing snow commonly interfere with data collection.
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99
A.4 Discussion: the downwelling sky brightness problem
The remainder of Appendix A discusses issues relating to contributions of atmo­
spheric emission to TBsn0W. The principal objective of the field radiometer experiments
was to measure the radiobrightness of the snow pack under various environmental condi­
tions, and to correlate changes in the brightness signature with measured physical proper­
ties of the snow pack. A downward looking radiometer receives a signal consisting of
contributions from the snow, and also from reflected and reemitted downwelling sky
brightness (Figure A.2). Downwelling sky brightness is energy emitted by matter in the
atmosphere. The contribution of the downwelling sky brightness must be removed to solve
for true snow brightness temperature. Equation A. 1 expresses this relationship.
TAP(Q,q) = TBsnoJQ,q) + R(Q,q)*TBsky(Q,q) (A.I)
where
TAP(Q,q) = the apparent brightness temperature measured by the radiometer
TBsnow(Q,q) = snow brightness temperature, the quantity of interest
R(Q,q) = Fresnel reflection coefficient at the air-snow interface.
TBsky(Q,q) = sky brightness temperature
0
= angle of incidence measured from the normal to the snow surface (0 snow=O is looking
straight down; 0 5 ^ = 0 is looking straight up. 0=90 is horizontal in both cases.)
q = polarization (vertical or horizontal).
The objective is to calculate TBsnow(Q,q) using (1.1) based on direct field measure­
ments of TAP(Q,q) and TBskv(Q,q). The reflection coefficients R(Q,q) are computed using
field measured snow permittivity data.
Definition: brightness temperature. Brightness temperature (TB) is a measure of
the energy radiated by an object relative to the energy radiated by a blackbody at the same
physical (kinetic) temperature. It is defined as (rearranging Ulaby, et al., 1981, eqn. 4.47):
TB(Q$)=B(Q$)X2/(2k df)
(A.2)
where
5(0,4>) = brightness (W m-2 sr-1)
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100
X = wavelength
k = Boltzman’s constant
df= differential frequency range.
Emissivity (e) is defined as (ibid., eqn. 4.48)
e=B(Q,ty)/Bblackbody = Tb(Q$)/T°
(7° is physical temperature) (A.3)
In practice it is convenient to express brightness temperature by rearranging (A.3):
^ Bobject =
emissivityobject *7°object
(A-4)
Tb of a target (snow) is determined by comparing the voltage of the 37 GHz electric field
emitted by the object with a linear function defined by the 37 GHz intensity emitted by
two blackbody targets of known physical temperature (i.e., a hot target at ambient temper­
ature (-273 K), and a cold target at 79 K) (Figure A.l).
A.4.1 Snow emission model
Microwave energy is not solely reflected at the air-snow boundary, as is visible
light from a mirror. Rather, some of the energy is transmitted through the boundary,
absorbed by the snow, volume scattered within the snow pack and reemitted to the atmo­
sphere. This process of absorption, scattering and emission, referred to here as snow emis­
sion, is complicated, beyond the descriptive capabilities of most (if not all) computer
radiative transfer models. While snow is very simple chemically, it is complex electromagnetically. Snow is a dense medium electromagnetically (the scatterers (snow grains) are
spaced close together, on the order of a few wavelengths), as opposed to a sparse medium
(e.g., a water cloud where the scatterers are relatively far apart). In a dense medium, the
field interactions between closely packed scatterers are significant and should not be
ignored; this is the impediment for existing emission models. A further complicating fac­
tor are the large and rapid changes in snow dielectric constant resulting from melting and
freezing.
There is no simple approach to correcting for reflected downwelling sky bright­
ness. Professor Tony England (University of Michigan Radiation Laboratory) suggested
(personal communication) estimating the magnitude of the downwelling sky contribution
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101
by (temporarily) ignoring volume scattering and emission, and computing two bounding
cases of surface scattering: specular and Lambertian. The specular case is a straightfor­
ward pairing o f the down-looking radiometer measurement at a certain incidence angle 9
with its corresponding sky brightness measurement at the same angle 0. This approach
was used in Pilant (1994). The Lambertian case is conceptually complicated and computa­
tionally involved.
A.4.2 Field Data
The parameters measured in the field are apparent brightness temperature
(TAP(Q,q)) when the radiometer points at the snow, and sky brightness temperature
(TBsky(Q,q)) when the radiometer points at the sky. The objective is to solve equation 1.1
for TBsnow. Snow dielectric constant is measured in situ using the time-domain reflectometer soil moisture probe and is used in computation of reflection coefficients. Table 1 lists
other parameters measured in the field.
Table A.2. Physical parameters measured in the field.
radiometer pointed at snow
l AP
radiometer
pointed at sky
Tfiskv
vertical profile
snow thermal temperature
vertical profile
snow density
real part; vertical profile; horizontal profile
snow dielectric constant
hand specimen; some photos; solid stereological
snow grain size
samples
snow stratification
(rarely strongly developed)
snow surface roughness
snow thickness
soil moisture/dielectric constant
soil temperature
surface to 15 cm
top several cm
air temperature
sky conditions
wind velocity
~ 1 m above snow
percent cloudy; types of clouds
direction accurate; speed only estimated
A.4.3 Field procedures
The field procedure was to measure TAP at five degree increments from 0 (vertical,
down-looking) to 90 degrees (horizontal) (19 measurements in total). At the weather sta­
tion site, the radiometer was pointed at targets in a single direction from nadir extending to
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102
the east. At the gully site, the radiometer was pointed in two directions, north and south at
the north and south slopes. At the Keweenaw Research Center (KRC) airstrip site, the
radiometer was pointed in two directions, northwest and southeast, and in some cases the
tower was pivoted in place by 90° to acquire more data in the northeast and southwest
directions. In the early experiments, TBsky was measured at five degree incidence angle
increments, but it became apparent that this angular resolution was not necessary due to
the slow rate of change of TBsky with incidence angle. In the later experiments, TBsky was
measured at 15 degree increments (except near the horizons where trees or other objects
are radiometrically much brighter). Near horizon measurements were made each five
degrees. If several snow data runs were made on a particular day, TBskv was not measured
for each data run because typically it does not vary rapidly with time. If atmospheric con­
ditions changed significantly, additional sky brightness temperature measurements would
be made accordingly.
The magnitude of TBskv is typically an order of magnitude less than that of TAP
(Figure A.4). Dry snow TAP generally falls in the 150-250 K range, more commonly in the
200-250 K range. Wet snow TAP is normally -273 K, exhibiting strong blackbody behav­
ior. TBsky generally ranges from - 5 to 30 K for 0 between 0 and 70 degrees. The treeeffect on the horizon is variable, but TBtree tends to range between 0 and 70-80 K (Figures
A.4-5). Clear sky is radiometrically colder than cloudy sky which has a greater atmo­
spheric path length and correspondingly higher brightness.
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103
AP.
Bskv
radiometer
AIR
v
7 —
SNOW
* ^ B sn o w
SPECULAR CASE
radiometer
AIR
SNOW
"
y
" 7 — ---------- --/ rr
1 Bsnow
LAMBERTIAN CASE
Figure A.2 Contributions to
in idealized specular and Lambertian surface scattering
endmembers.
In the specular case, sky brightness enters the antenna beam from only the direction
orthogonal to the antenna incidence angle. In the Lambertian case, energy is scattered into
the antenna beam from all directions, including those in the dimension out of the plane of
the page.
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104
APsnow
2 00
£
OQ
E-
1
oo
pure sky
trees and
Bsky
o
2©
eo
1
oo
Incidence Angle (0, degrees)
Figure A.3. Taps, ^ (*) and Tgsi^triangle) in a typical data run.
Note steep increase in TBslcy when radiometer points at trees. Also, snow is - 200 K
brighter than pure sky.
80
trees and sky
TBtrees= (2589)0 2
O
a
-(6554)0 + 4173
60 -
3
c3
u .
Cl
£ 4-0
£in
TBs b = ( 10-5)0 2- ( 2 -2)0 + 12.7
t/i
o
a=0.65 K
c
J3
.2P 2 0 fCQ
o
o.
0.5
pure sky
1 .O
Incidence Angle (0, radians)
1.5
70°
Figure A.4. Measured (solid line) and fitted (squares and triangles) sky brightness.
A.4.4 Specular Scattering
When a surface is smooth relative to wavelength, specular scattering dominates;
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105
essentially all o f the incident energy is reflected in the forward direction. The angle of
reflection equals the angle of incidence. In the simplified case, antenna beam side lobe
contributions are ignored. The specular scattering case is that of ‘mirror-like’ reflection.
The only signal that reaches the radiometer is that which is incident and reflected at the
radiometer angle o f observation, 0 , and within the vertical plane defined by the radiometer
and incident/reflected beams. For example, if the radiometer is down-looking to the south
at 0=45°, the downwelling sky contribution is considered to originate only at 0=45° in the
southern sky.
A.4.5 Fresnel Reflection Coefficients
Fresnel reflection coefficients describe the amount of energy reflected when an
electromagnetic wave encounters a boundary between two media of different permittivi­
ties. The coefficients depend on the polarization, complex dielectric constant and the angle
of incidence as follows:
' ftla ifios& + VuumfiOsB)
R Q'H= ftairCOrt
% V= (T]sno^osQ -WKWO) 1
+ T\ai£OSB)
(A.5)
(A.6 )
where
R0,p = complex Fresnel reflection coefficient at incidence angle 0 and polarization p (v or
h)
r) = complex intrinsic impedance of the medium.
The complex intrinsic impedance is defined as
r| = (jj7e) 1/2
(A.7)
where
p. = permeability (471*1 O' 7 Henry/m)
i = complex dielectric constant (£=£’ (real part) + £“ (imaginary part)).
The real part of the snow dielectric constant (e‘snow) is measured directly in the
field using a time domain reflectometer (TDR). This instrument does not directly measure
the imaginary part (£“snow) which controls attenuation of the wave in the snow (it may
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106
possibly be calculated from the amplitude versus time trace recorded by the TDR). The
calculations here use published values of e“snow from Ulaby, et al., 1981 (Volume 3).
Ulaby et al. (1981 p. 900) discuss the absorption and scattering coefficients, Ka and k5. ica
is influenced primarily by the imaginary part of the dielectric constant, and Ks is influ­
enced primarily by the real part.
Figure A.5 is a plot o f calculated Fresnel reflection coefficients. This plot illumi­
nates the contribution of downwelling sky radiance to TAP. For example, if the radiometer
is pointed at the snow at 0=55° (SSM/I incidence angle is -53.1°) in vertical polarization,
the corresponding Fresnel reflection coefficient for wet snow is -0.57 and for dry snow it
is - 0.35. From Figure A.3, we have Tfij.^(55°)~=20 K. Thus, the wet case specularly
reflected downwelling sky brightness contribution would be (0.57)(20)=11.4 K, and for
the dry case, (0.35)*(20)=7.0 K.
-i - O
Vpol
c
.a
o
£u
o
u
c
.O
O -S
wet snow (i =(5.0,0.5)
O - G
Hpoi
:
O - -4-
ou
e
_dry snow (e =(1.7,0.01)
o .o
O
S O
-4-0
S O
S O
1 O <
Incidence Angle (0, degrees)
Figure A.5. Calculated Fresnel reflection coefficients: wet and dry snow cases.
Wet snow has a higher reflectivity than dry snow.
A.5 Lambertian Scattering
When the surface is rough relative to wavelength, Lambertian, or diffuse/isotropic,
scattering occurs; energy is scattered more or less equally in all directions. The intensity of
scattering from a Lambertian surface varies with the cosine of 0 (Boyd, 1983, eqn. 2.19):
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107
1(6) = IJ6)*cos(6)
(A.8 )
where IJ6 ) is T g ^ at a given incidence angle.
The approach to the Lambertian case is as follows.
1. Calculate the total downwelling brightness originating in the hemisphere of sky
above the snow.
2. Compute Fresnel reflection coefficients as in the specular case above. (They are
identical.)
3. Calculate the proportion o f total reflected sky brightness intercepted by the
beam of the radiometer with a known beamwidth of 3°.
Combining 1,2 and 3 yields an approximation of the amount of brightness contributed by
the sky assuming that the snow scatters in a Lambertian manner.
A.5.1 Example: calculation of the total downwelling brightness originating in the
hemisphere of sky
Recall that the radiometer may be pointed upward as well as downward to measure
sky brightness directly. A quadratic function was fit to the data used in Figure A.3 to
obtain an expression that can be integrated analytically to solve for the total radiation orig­
inating in the sky hemisphere. This resulted in the following expressions:
Tgs/cy = (10.5)62 -(2.2)6 + 12.7 (forpure sky, 0<= 0 <= 1.3 radians (70°)
T gtrees = (2589)Q2 -(6554)6 + 4 1 7 3
(A .9)
(for tree and sky m ixture on horizon, > 1.3 radians)
(A. 10)
(Two expressions are required: one for pure sky (A.9), and one for the mixture of trees and
sky on the horizon (A. 10).)
Expressions (A.9) and (A. 10) sum to equal la in (A.8 ).
This is the integral representing the total downwelling sky brightness:
(A. 11)
The inner integral (0) computes the brightness that the radiometer measures by rotating in
the vertical plane from horizon to horizon (180°, or n radians). The outer integral (<}>) sums
the contributions as that vertical plane is rotated through the I n of the hemisphere.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
108
Equation A. 11 can be rewritten explicitly using coefficients from (A.9) and (A. 10),
and broken into two separate integrals representing pure sky and sky-tree mixture:
r2K ( fl-3
y
A
Jq M
[1O.5(0 z ) - 2.2(0) + 12.7] (0) cos (0)</0jr/<j>
puresky
tr«s“ l!ar
horizon
f
t f
(2589(82 ) - 5664(6) + 4 I73](0)coSf 0 ) < ie U
0 I
1.3
J
(A.12)
(A.13)
Each inner integral computes dQ for half the hemisphere, hence the factor of 2 above.
MAPLE software was used to compute the integrations. Integrating dQ in (4.5)
yields 15.25; two times this is 30.5. Multiplying by 2k yields a total pure sky brightness of
191.5 K originating in the pure sky portion of the hemisphere. Similarly, the total hemi­
spheric sky-tree mixture brightness is 27t*2*47.9 = 301.0. Thus, the total brightness tem­
perature radiated toward the snow from the sky is 191.5+301.0 = 492.5 K.
A.5.2 Calculation of the proportion of total reflected sky brightness intercepted by
the beam of the radiometer with a known beamwidth of 3°.
The radiometer beamwidth is 3° and the hemisphere is 180° across. Thus, the radi­
ometer intercepts /?(0,p)*(3/18O*27t) = R(Q,p)*(0.00265) of the total downwelling bright­
ness.
Example: 0=55°. For dry snow, the reflected sky contribution would be:
(reflection coef.)(fraction scattered into beam)(total sky brightness)
=(0.35)(0.0167)(493K)= 2.88 K.
A.5.3 Examples of Sky Corrections
Figures A.6 -8 are plots showing TAP and sky-corrected TB using specular and
Lambertian assumptions in calculating the reflected downwelling sky brightness. Also
shown are plots for two assumptions of snow dielectric constant. The dry snow case uses
Edry snow=( l-7e’+ O.Ole” ); the wet snow case uses £^vet_snow=(5.0e,+ 0.5e” ). The real part
(e’) is a measured field value. The imaginary part (e” ) is estimated from Ulaby et al.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
109
(1981, Vol. 3).
These plots indicate the size of the sky contribution. In general it ranges from ~ 2
to 10 K. That is, TBsnow is approximately ~ 2-10 K less than TAP> or about 1-4%. Specular
contributions are larger than Lambertian for all angles.
280
Bsnow _L ambertianjiry
260
Bsnow_spec tlar_dry
Bsnow _Lamberti an_we(
Bsnow_spec, ilar_wet
240
03
E-
220
200
180
0
20
40
60
80
Incidence Angle (0, degrees)
Figure A.6 . Comparison of specular vs. Lambertian and wet vs. dry TBsky corrections.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
110
280
275
AP
270
'_Lambertian_dry_
265
Bsnoy <_Lambenian_weL
Bsnow_spe cular_dry
260
t- 255
250
245
240
235
20
40
60
80
100
Incidence Angle (0, degrees)
Figure A .I. Enlarged comparison of specular vs. Lambertian and wet vs. dry snow TBsky
corrections.
Wet vs. dry differs by the snow dielectric constant values assumed in the calculation of
reflection coefficients (dry: i=(1.7e’+ O.Ole” ); wet: i=(5.0e + 0.5e” ))-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I ll
285
2 8 0
2 7 0
&
'Bsjww_UjmberticA
2 5 5
2 5 0
O
2 0
4 0
6 0
SO
1 OO
Incidence Angle (0, degrees)
Figure A .8 Comparison of specular and Lambertian sky corrections for dry snow case:
I=(1.7e’+ O.Ole” ) (enlargement of Figure A- 6 ).
A.9 Bibliography
Boyd, R. W., Radiometry and the Detection o f Optical Radiation: John Wiley and Sons,
254 pp., 1983.
Colwell, R. E., (Ed.), Manual of Remote Sensing, 2nd Ed., American Society of Photogrammetry, Sheridan Press, 2 vol, 1983.
Pilant, D., Meter-range 37 GHz passive microwave time series measurements of
terrestrial snow cover (abstract): 1994 Fall Meeting of the Amer. Geophys. Union, EOS
supplement Nov. 1, 238. 1994a
Pilant, D., Close-range 37 GHz observations of snow on north and south facing slopes,
Proc. Int. Geoscience Remote Sensing Symp., August 8-12, 1994, Pasadena, CA. 1994b.
Siegal, B. S. and A. R. Gillespie (Eds.), Remote Sensing in Geology, John Wiley and Sons,
New York, 702 pp., 1980.
Ulaby, F.T., Moore, R.K., and A.K. Fung. Microwave Remote Sensing- Active and Passive,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
Artech House, 3 vol., 1981.
A.10 Snow Brightness Temperature Graphs
The following are graphs of snow apparent brightness temperature versus incidence
angle (0 degrees is nadir looking down, 90 degrees is horizontal). Most of these are techni­
cally “apparent” brightness temperatures because they have not been corrected for
reflected atmospheric contributions. Those corrected have ‘corrected’ appended to the
title. They are arranged chronologically from December 16, 1993 to April 1, 1994. The
horizontal and vertical axes are identical throughout. Data were recorded at incidence
angle increments of 5 degrees. Each graph is labeled at the top with the name of the source
file which incorporates the date, time, polarization, target (snow in this case) and possibly
a code indicating the elevation of the radiometer above the ground. For example, the first
in the series is labeled “931216_1030_tap_vsnow”. This is interpreted as follows: Decem­
ber 16, 1993, 10:30 a.m., apparent brightness temperature, vertical polarization, radiome­
ter pointed at snow.
Summary information pertaining to the graphs is presented below. Typical snow con­
ditions in March and April, 1994 at the study sites were:
snow temperatures
+1 to -10 C
snow density:
-0.3-0.4 g/cm 3
grain size:
0.5-1.5 m single grains
< 10 mm polycrystalline grains
snow depth:
50 cm early season, diminishing to 0 cm in May.
snoT
grainS
airT
site
date
time
snoD
931216
2 0 :0 0
14
- 1.1
999
-0.3
met
931218
17:20
23
-0.5
1.0
-0 .6
met
940302
16:45
50
- 1.0
999
2.7
met
940303
08:34
54
-1.5
1.25
2.5
met
940310
09:30
8
-2.5
999
-2.5
kb
940311
10:30
50
-0.4
1.0
1.1
krc
940312
09:50
50
-0.4
1.0
1.4
krc
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
940315
13:25
48
-.7
1.0
-4.0
krc
940316
1 0 :0 0
48
-4.0
1.0
-10.3
krc
940319
13:10
50
- 1.0
1.0
4.0
met
940330
10:45
44
-0.5
999
1.6
met
940331
23:30
40
1.0
999
-0.5
gul
940404
1 2 :0 0
32
1.1
999
2.1
gul_south_side
940404
1 2 :0 0
60
1.2
999
2.1
gul_north_side
940405
08:10 999
<0 .0
999
-3.8
gul
940406
15:25 999
999
999
3.4
gul
940408
11:15 999
999
999
5.3
gul
rain
940409
18:00
35
999
999
4.3
gul
wind
940411
07:00 25?
999
999
2 .6
met
no._cold_calibration_point?
940411
11:55 25?
999
999
13.6
met
940417
07:20
12 ?
0.5
999
3.5
met
date
time snoD
snoT
grainS
airT
site
Notes:
date
Date of observations (yymmdd).
time
Generally time of the first of a pair of radiometer observational runs.
snoD
Snow depth (cm). Snow depth of a) the snow pit examined or
b) the average of a number of samples.
snoT
Mean snow pack temperature (C). This mean is a mentally
estimated average of available data (vertical profiles or individual data).
grainS
Estimate of mean grain size of the snow pack (mm).
airT
Air temperature (C).
site
met=MTU meteorological station. kb=Keweenaw Bay.
krc=Keweenaw Research Center. gul=gully. met2=site 10 m nw of
metstation site.
Gully site data are discussed in greater detail in Chapter 5.
999
Code indicating data were not measured on this date.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
114
Indicates value is questionable.
Snow brightness temperature graphs follow.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
115
SNOW TB Graphs
9 3 1 2 1 8_1 7 0 0 _ ta p _ h sn o w _ tr
300
931 2 1 6 _ 1 0 3 0 _ ta p _ v sn o w _ tr
300
250
250
-+++
□a 200
03
200
150
150
100
100
0
20
40
60
80
0
100
20
40
60
80
100
incidence angle
incidence angle
93 1 2 1 6_1 24 5_ta p _ h sn o w _ tr
9 3 1 2 1 8_1 7 0 0 _ ta p _ v sn o w _ tr
300
300
25 0
250
+H -
CD
CD
200
150
100
0
GO
40
60
80
0
100
20
40
60
80
incidence angle
incidence angle
100
931 2 1 6 _ 2 0 3 0 _ ta p _ v sn o w _ tr
9 4 0 3 0 2 —1 1 0 O —t a p —V S n o w —f v
3 00
300
2 50
250
200
03
i—
20 0
150
150
100
100
0
CD
20
20
40
60
80
0
100
20
40
60
80
100
incidence angle
incidence angle
9 3 1 2 1 6 _ 2 1 40_tap _h sn ow _tr
9 4 0 3 0 2 -1 2 1 0_tap _h sn ow Jv
300
300
2 50
250
200 ^ V
k
V
f
. . .
CD
i—
150
100
100
40
60
80
incidence angle
100
:
200
150
20
-4 -4 + + + 4 ^ -H -H -| k .
20
40
60
80
incidence angle
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
116
9 4 0 3 0 2 —1 5 4 0 - t a p - h s n o w J v
9 4 0 3 1 0 - 0 9 1 5 _ ta p _ h s o ils n o W —
300
3 00
250
2 50
200
200
150
150
100
100
CD
0
20
40
60
80
0
100
20
40
60
80
100
incidence angle
incidence angle
9 4 0 3 0 2 —1 61 5 _ t a p —v s n o w _ h z
9 4 0 3 1 0 _ 1 0 4 5 _ ta p _ v s o ils n o w —I
300
300
250
250
200
200
150
150
100
100
-H - H - l-H H -H I I l -Kf.
0
20
40
60
80
0
100
20
40
60
80
100
incidence angle
incidence angle
9 4 0 3 0 2 —1 7 4 0 —t a p —v s n o w -h ^
9 4 0 3 1 0_1 41 5 _ t a p —v s o ils n o w —I
30 0
300
25 0
250
H \ H - | I I I I I l-H I |+ +
200
200
03
150
150
100
100
0
20
40
60
80
0
100
20
40
60
80
100
incidence angle
incidence angle
9 4 0 3 1 1 _1 81 5 _ ta p _ v s n o w S E —t
9 4 0 3 0 2 - 2 2 1 5 _ tap _ v sn o v V -h ^
300
300
250
250
200
03
200
I—
CD
150
150
100
100
20
40
60
80
incidence angle
100
0
20
40
60
80
100
incidence angle
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
9 4 0 3 1 1_1840_tap_vsnowNW_f
300
30 0
250
25 0
/■>
CD
200
w 200
m
t—
150
150
100
j
:
100
0
20
4-0 60
80
in cid en ce angle
100
94031 1_1 900_tap_vsnowSW-^
0
20
40
60
80
incidence angle
100
94031 2_1223_tap_hsnowSW_l
300
3 00
2 50
250
/ “N.
cn
200
~ 200
m
t—
150
150
100
i , i
100
0
20
40
60
80
Incidence angle
100
9 4 0 3 1 2_0950_tap_vsnowSW-f
0
100
9 4 0 3 1 2_1305_tap_hsnowSE_f
300
30 0
250
25 0
200
03 200
150
150
100
20
40
60
80
in cidence angle
100
0
20
40
60
80
incid en ce angle
100
9 4 0 3 1 2_1000_tap_vsnowNE_l'
0
100
9 4 0 3 1 2_1 322_tap_hsnowNW_l
300
300
250
25 0
200
200
150
150
100
20
40
60
80
incidence angle
100
0
20
40
60
80
in cidence angle
100
0
20
40
60
80
incidence angle
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
118
94-0312_1405_tap_vsnowNW_t
CO
9 4 0 3 1 5_0952_2tap_vsnowNW-
300
300
250
250
'+ ,+ * ~ W
200
CD
I—
150
100
100
20
40
60
SO
in cid en ce angle
0
100
9 4 0 3 1 2 —1420_tap_vsnowSE_t
300 f
250
250
CD
150
100
100
20
40
60
80
in cid en ce angle
100
'
r~
• ■■ ' ' '
200
150
0
20
40
60
80
incidence angle
9 4 0 3 1 5_0952_tap_vsnowNW—f
300
200
.
200
150
0
hh
0
100
20
40
60
80
incidence angle
100
9 4 0 3 2 9 - 1 9 1 0_tap_vsnow_profile
3 00
300
250
250
4 -H 4 + 1 -H + H + H 4 -H + :
/*—
N
200
w 200
CD
1—
150
150
100
100
0
20
40
60
80
in cid en ce angle
0
100
94031 5—091 3_tap_vsnowSE-t
300
250
250
□a
200
150
150
100
100
0
20
40
60
80
incidence angle
100
100
9 4 0 3 3 0 —1055_tap—vsnow-profile
300
200
20
40
60
80
incidence angle
20
40
60
80
incidence angle
100
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
119
tap_940331 _ 1 8 3 0 —n v s n o w _ h
940330_1530_tap_vsnow_profilf
300
300
I I I I l-H-l I l*H
250
-H250
200
CD 200
CD
150
150
100
100
0
20
40
60
SO
0
100
40
60
80
100
incidence an g le
Incidence angle
tap_940331 _1825_svsnow_corre
ta p _ 9 4 0 3 3 1_2330_svsnow_corre
300
300
250
250
CD
CD
0
20
40
60
80
0
100
60
80
100
300
300
■++++++1l-H-l I I 1+H+
&-
250
200
200
CD
150
150
100
100
0
20
40
60
SO
0
100
20
40
60
80
100
incidence an g le
incidence ongle
tap—940331 _1 830_nvsnow_corre
ta p _ 9 4 0 3 3 1_2340_nvsnow_corre
300
300
250
40
tap_9 4 0 3 3 1 —2 3 3 0 —svsno\V —h
ta p _ 9 4 0 3 3 1_1825_svsnow_h
250
20
incidence angle
incidence angle
co
20
S++-h|4iH I I I l I
250
200
200
CD
cd
150
150
100
100
20
40
60
SO
incidence angle
100
20
40
60
80
incidence an g le
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
120
tap_940331 _2340_nvsnow_h
tap _94040l_1035_nvsnow _ h
300
300
=£fc±,
250
250
m 200
200
aa
»—
150
150
100
100
0
20
40
60
80
in c id e n c e angle
100
ta p _ 9 4 0 4 0 1_1 030_svsnow_corre
cn
0
100
tap_9 40401 _1540_svsnow_corre
300
300
250
250
200
20
40
60
80
incidence angle
m
i—
150
200
150
100
100
0
20
40
60
80
in cid en ce ang le
100
0
20
40
60
80
incidence angle
100
tap_940401_1 030_svsnovv_h
300
300
;l l-H -F f+ 4 -H -l | H + H f
1 1 H H a-M I I | I11 1 |»1~F .
250
ca
250
200
200
CD
i—
150
150
100
100
0
20
40
60
80
in cid en ce ang le
100
ta p _ 9 4 0 4 0 1_1035_nvsnow_corre
300
'
'
'
0
100
ta p _ 9 4 0 4 0 1_1 550_nvsnow_corre
'
300
250
m
20
40
60
80
incidence angle
250
200
CD
150
200
150
100
100
20
40
60
80
in cid en ce angle
100
20
40
60
80
incidence angle
100
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
tap_940401 _ 2 1 10_nvsnow_h
to p _ 9 4 0 4 0 1_1 550_n vsnow_h
300
300
250
2 DO
200
03
2 0 0
CD
►
—
150
1DO
100
100
0
20
40
60
80
in cid en ce angle
0
100
ta p _ 9 4 0 4 0 1_ 2 100_svsnow_corre
300
'I I I .
250 r 1
2DQ
200
CD
l—
:
I DU
100
100
20
40
60
80
in cid en ce angle
0
100
300
300
250
250
200
200
.. j
20
40
60
80
incidence angle
l
;
s
CD
cd
►
—
100
tap_940402_0950_svsnow _h
top_940401 _ 2 100_svsnow_h
150
150
100
100
0
20
40
60
80
in cid en ce angle
30Q
,
,
,
0
100
tap_940401_21 10_nvsnow_corre
,
20
40
60
80
incidence angle
100
tap_940402_1005_nvsnow _corre
300
'
'
'
'
250
250
CD
20 0 x
150
0
100
tap_940402_0950_svsnow _corre
300
CD
20
40
60
80
incidence angle
200
CD
200
150
150
100
100
0
20
40
60
80
incid en ce angle
100
0
20
40
60
80
incidence angle
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
122
tap_940402_1005_nvsnow _h
tap_940402_1 705_nvsnow_h
3 00 r
300
2 50
230
200
200
;
i
k
m
i—
CD
150
130
100
100
20
40
60
80
0
100
^
20
tap_940402_1 655_svsnow_corre
300
200
200
150
150
100
100
40
60
80
100
300
2 50
20
60
tap_940402_2040_svsnow _corre
250
0
40
\ :
incidence angle
in cid en ce angle
CD
w
80
0
100
20
40
60
80
100
incidence angle
in cid en ce angle
tap_940402_2040_svsnow _h
tap _940402_1 655_svsnow_h
300
300
250
250
200
03
i—
200
150
150
100
100
0
20
40
60
80
0
100
20
ta p _ 9 4 0 4 0 2 _ l 705_nvsnow_corre
,
300
,
i
r m> m
— |
.
i
40
60
80
100
incidence angle
in cid en ce angle
tap_940402_2045_nvsnow_corre
* -* i t
300
230
250
m 200
+
CD
2UU y
1—
150
130
100
100
0
20
40
60
80
in cid en ce angle
100
0
v
, ,
• " • H * l’W-KH + h ). :
20
40
60
80
100
incidence angle
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
123
t a p —9 4 0 4 0 3 —0 8 2 5 _ n v s n o w _ h
t a p —9 4 0 4 0 2 —2 0 4 5 —n v s n o w _ h
300
300 r
250
250
co 200
^++4'++'++’
m 200
150
150
100
100
20
40
60
80
S++++++
20
100
tap _940403_0820_svsn ow _corre
300
250
250
200
200
150
150
100
100
20
40
60
80
0
100
100
20
40
60
80
100
t a p —9 4 0 4 0 3 —1 7 0 0 _ s v s n o w —h
t a p —9 4 0 4 0 3 —0 8 2 0 —s v s n o w —h
300
300
250
250
200
200
CD
t—
150
150
100
100
0
20
40
60
80
0
100
20
40
60
80
100
incidence angle
incidence angle
tap _940403_0825_n vsn ow _corre
300
1
r~ ~ ~ '
'
t a p _ 9 4 0 4 0 3 —1 7 1 5 _ n v s n o w _ c o r r e
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CD
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aa
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t a p _ 9 4 0 4 0 3 —1 7 0 0 _ s v s n o w _ c o r r e
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incidence angle
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03
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tap_940404_1 130_nvsnow_h
tap_940403_1 71 5_nvsnow_h
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tap_940404_1 115_svsnow_corre
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tap_94Q404_1 455_svsnow_h
tap_940404_1 1 15_svsnow_h
CD
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tap_940404_1455_svsnow _corre
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$
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ta p _ 9 4 0 4 0 4 _ 1 1 30_nvsnow_corre
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tap_940404_1 505_nvsnow_corre
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/* N
✓—-s
w 200
0D
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i£
CD
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tap_940405_0820_nvsnow _h
tap_940404_1505_nvsnow _h
(XI
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tap_940405_0810_svsnow _corre
aa
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ta p _ 9 4 0 4 0 5 _ 1 140_svsnow_corre
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aa
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tap_940405_1 140_svsnow_h
tap_940405_0810_svsnow _h
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co
m
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tap_940405_0820_nvsnow _corre
CD
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03
h-
i
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ta p _ 9 4 0 4 0 5 _ 1 150_nvsnow _corre
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V^lr
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incidence angle
444si J-+4 4
f t
,
:
200 S * * J
130
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100
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tap_940405_1 150_nvsnow_h
tap_940405_2025_nvsnow_h
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300 r
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m 200
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o
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aa
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in cidence angle
tap _940405_201 5_svsnow_corre
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cn 200
200
co
t—
150
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100
0
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0
100
to p _ 9 4 0 4 0 5 _ 2 0 15_svsnow_h
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co
t—
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0
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top_940405_2025_nvsnow_corre
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100
to p _ 9 4 0 4 0 6 _ l 020_nvsnow_corre
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0
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incidence angle
tap_940406_1 005_svsnow_h
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0
ca
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top_940406_1005_svsnow _corre
300
ICD
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incidence angle
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incidence angle
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tap—9 4 0 4 0 6 —1 540_nvsnow_h
top_940406_1020_nvsnow _h
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y
cd
v
A
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CD
V
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tap_940406_1525_svsnow _corre
w
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100
ta p _940408—1 11 5_svsnow_corre
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30 0
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200
CD
CD
I—
I—
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0
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100
tap_9 4 0 4 0 8 —1 1 15_svsnow_h
tap—9 4 0 4 0 6 —1 525_svsnow_h
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250
+++++++*
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CD
CD
I—
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tap—9 4 0 4 0 6 —1540—nvsnow_corre
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tap _ 9 4 0 4 0 8 —11 20_nvsnow_corre
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ca
h-
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tap_940409_l 805_nvsnow_h
tap_940408_1 120_nvsnow_h
3 00
300
l+t^_
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CD 200
CD
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0
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0
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CD
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0
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100
tap_94041 1_Q750_hsnow_hI
tap_940409_1800_svsnow _h
CD
200
I—
I—
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150
100
100
0
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incidence angle
0
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incid en ce angle
100
tap_94041 1_1 1 55_hsnow_h^
tap_940409_1805_nvsnow _corre
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250
'X /
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CD
100
tap_94041 1_0730_vsnow_h>
tap_940409_1800_svsnow _corre
CD
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incid en ce angle
i; /H -
^+ + 4 - H m l
250
/ —N
*
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CD
CD
t—
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0
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TB (K)
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tap—94041 7_0 7 5 5 —vsnow—hj
tap_94041 7_1 230_vsnow_hc
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CD
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TB (K)
0
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100
tap_94041 8_ 0 7 2 0 —vsnow—
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ta p _ 9 4 0 4 17 _ 0 9 10_hsnow—hJ
tap—94041 8_0 7 5 0 —hsnow—h ‘
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300
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250
~
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200
CD
f-
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100
0
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tap—94041 7 _ 1 1 4 5 _ h s n o W - iK
TB (K)
0
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tap _940417_0 8 4 5 —vsnow—hj
0
TB (K)
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100
old_tap—940401 _1 540_svsnow_cor
3 00
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w 200
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Appendix B: Computer Programs
This appendix compiles a number of IDL (Interactive Display Language software
from Research Systems International, Boulder, CO) programs written by the author for a
variety of purposes related to this dissertation. They are provided here as examples to help
the reader implement their own algorithms. Some will run in the form presented here; oth­
ers require data files as input. The name of each program is listed on the first line. The pro­
gram name is indicative of its function. Generally there is a comment under “Objective” or
“Purpose” to indicate more specifically the function of the program. Several algorithms
are based on equations found in Ulaby et al. (1981) (abbreviated ‘UMF’ below):
Ulaby, F. T., Moore, R. K., and Fung, A. K, Microwave Remote Sensing—Active and Pas­
sive. Artech House, Norwood, MA, 3 vol., 2162, 1981.
B .l Program: get_ssmi_low_frequency_channel.pro
pro get_ssmi_low_frequency_channel,image,sds_id
;USER NOTE: modify these variables: dataset, channel, filename
dataset= 6
;USER: modify ‘dataset’ value to select either 85vpol or 85 hpol
; 2=19V 3=19H 4=22V 5=37V 6=37H
channel=’37h’
;USER: modify channel value to correspond to channel selected (e.g.,
channel=’2 2 v’ if dataset=4)
filename=’fl0_Tb_96035_04A.hdf’
;USER: modify ‘filename’ to select the HDF SSM/I brightness temperature file of
interest.
;PURPOSE: extract a high resolution brightness temperature array from a MSFC SSM/I
Tb HDF file.
;author: Drew Pilant April 4, 1996
;This file was written to subset an F10 Ascending path. The subsetting values
;may not always return the area of interest. If so, remove the subset array
;indices, display the entire swath, and subset using whatever new coordinates
;are appropriate. The IDL ‘profiles’ command is useful in determining the
;rows of interest. It is generally most convenient to select the entire
;swath (128 columns for high resolution data, 64 columns for the low resolution
;data.
;HOW TO USE:
; 1. Select the Tb array of interest by changing the value of ‘filename’ above
;at the idl command line prompt, type
;IDL> .run getssmi
;IDL> getssmi,h85,sds_id
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132
;The Tb grid will be returned in the array ‘data’. The sds_id is there to
;permit additional queries (e.g., check the header, dimensions, etc).
sd_id=hdf_sd_start(filename,/read);start the hdf interface, get the scientific data id (sd_id)
sds_id=hdf_sd_select(sd_id,dataset) ;get the Scientific Data Set ID # (sds_id)
;(this is how the individual arrays in the HDF file are referenced)
hdf_sd_getdata,sds_id,image;get the actual data from the sds, place it in array ‘image’
image=image(* ,575:624)
;subset the great lakes
;USER: modify the row index as necessary
;(row index varies with F 10 and F I3, and with
ascending or descending mode)
image=image/100.0
;rescale the Tb data to degrees Kelvin
image=rebin(image,2*64,2*50) ;enlarge the array by 4x for display
window,6,xs=2*64,ys=2*50
;make a display window
tvscl, image
outfile=filename+’.’+channel+’.bin’
openw,l,outfile & writeu,l,image & close, 1
hdf_sd_endaccess,sds_id;terminate access to scientific data set
hdf_sd_end,sd_id;terminate interface with hdf file
end
;retum to IDL prompt
B.2 Program: get_ssmi_high_frequency_channel.pro
pro get_ssmi_high_frequency_channel,image,sds_id
dataset= 8
;USER: modify ‘dataset’ value to select either 85vpol or 85 hpol
; 7=85V 8=85H
channel=’85h’ ;USER: modify channel value to correspond to channel selected (e.g.,
channel=’85h’ if dataset=8 )
filename=’fl0_Tb_96035_04A.hdf’ ;USER: modify ‘filename’ to select the HDF SSM/I
brightness temperature file of interest.
;PURPOSE: extract a high resolution brightness temperature array from a MSFC SSM/I
Tb HDF file.
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133
;author: Drew Pilant April 4, 1996
;This file was written to subset an F10 Ascending path. The subsetting values
;may not always return the area of interest. If so, remove the subset array
;indices, display the entire swath, and subset using whatever new coordinates
;are appropriate. The IDL ‘profiles’ command is useful in determining the
;rows o f interest. It is generally most convenient to select the entire
;swath (128 columns for high resolution data, 64 columns for the low resolution
;data.
;HOW TO USE:
; 1. Select the Tb array of interest by changing the value of ‘filename’ above
;at the idl command line prompt, type
;IDL> .run getssmi
;IDL> getssmi,image,sds_id
;The Tb grid will be returned in the array ‘data’. The sds_id is there to
;permit additional queries (e.g., check the header, dimensions, etc).
sd_id=hdf_sd_start(filename,/read)
(sd jd )
;start the hdf interface, get the scientific data id
sds_id=hdf_sd_select(sd_id,dataset) ;get the Scientific Data Set ID # (sds_id)
;(this is how the individual arrays in the HDF file are referenced)
hdf_sd_getdata,sds_id,image
;get the actual data from the sds
image=image(*, 1150:1249)
;subset the great lakes
;USER: modify the row index as nec­
essary
;(row index varies with F10 and F I3,
and with ascending or descending mode)
image=image/100.0
;rescale the Tb data to degrees Kelvin
;image=rebin(image,4* 128,4* 100) ;enlarge the array by 4x for display
window,7,xs=128,ys=l00
;make a display window
tvscl,image
outfiIe=filename+’.’+channel+’.bin’
;outfile=filename+’.image.bin’
openw,l,outfile & writeu,l,image & close, 1
hdf_sd_endaccess,sds_id
;terminate access to scientific data set
hdf_sd_end,sd_id
;terminate interface with hdf file
end
;retum to IDL prompt
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134
B.3 Program: ice_penetration_depth.pro
pro ice_penetration_depth,penetration_depth
;Purpose: compute freshwater ice penetration depths fo r SSM/I frequencies
;Based on formulas in Hallikainen and Winebrenner in
;Carsey, F. D. (Ed.), Microwave Remote Sensing of Sea Ice, American Geophysical
.Union Monograph 6 8 , Washington, D.C., 440 pp., 1992.
;Author: Drew Pilant
;Date: Sep 27, 1996
;variables:
f=[19.35, 22.35, 37.0, 85.5]
;SSM/I frequencies in GHz
lambda=[0.0l55,0.0135,0.0081,0.0035];SSM/I wavelengths in m
pi=3.14159
;pi
epsilon_real=3.17
;e’ = dielectric constant;
;well-established value; Cummings,
1952
;Matzler and Wegmuller, 1987;
epsilon_imaginary=fltarr(4)
k=fltarr(4)
;wave number
penetration_depth=fltarr(4)
;epsilon_imaginary=A/f + BfAC
;
;
;formula for e” ;Matzler and Wegmuller, 1987.
SELECT A TEMPERATURE (-5 or -15 C):
;A=0.0026
;B=0.00023
;C=0.87
;for temperature= - 5.0 C
A=0.0013
B=0.00012
C=1.0
;for temperature= - 15.0 C
Compute dielectic loss factor (e” ) (epsilon_imaginary)
for i=0,3 do begin
epsilon_imaginary(i)=A/f(i) + B*f(i)AC
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135
k(i)=2 *pi/lambda(i)
;wave number
endfor
;reIative_permittivity=epsilon_real-(j)*(epsilon_imaginary);
;compute penetration depth vector (results are in m)
for i=0,3 do begin
penetration_depth(i)=sqrt(epsilon_real)/[k(i)*epsilon_imaginary(i)]
endfor
return
end
;RESULTS:
; 1.38894
; 1.83837
1.07798
1.39607
0.425672 0.0896776 (-5 C)
0.512896 0.0965223 (-15 C)
;REFERENCES:
;Matzler and Wegmuller, 1987. Dielectric properties of freshwater
;ice at microwave frequencies, Journal of Physics D,.-Applied Physics, 20,
;pp. 1623-1630.
B.4 Program: mixing_model_dry.pro
pro mixing_model_dry ;permittivity mixing model for dry snow
;VARIABLES
epsreal=1.5;measured; no mixing model needed because it was measured insitu
epsimag=0.05
;UMF Table E.3 (estimated for ice at -10 C, 37 GHz)
;(UMF=Ulaby et al., 1981)
vi=0.5
;voIume concentration of ice in snow; measured
;UMF E.8 8 Hallikainen (1986) dry snow permittivity mixing model
epsimag_ds= (0.34*vi*epsimag)/((l-(0.417*vi))A2)
;PRINT RESULTS
print,’epsreal=’,epsreal & print,’epsimag=’,epsimag
print,’vi=’,vi & print,’epsimag_ds=’,epsimag_ds
return
end
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136
B.5 Progam: mixmg_model_wet.pro
pro mixing_model_wet;permittivity mixing model for wet snow
;VARIABLES
epsreal_wet=4.0;
measured insitu
epsimag=0.3
vi=0.4
ice in snow)
f=37 ;radiometer frequency
rho_snow=0.4
measured;no mixing model needed because it was
from UMF fig. E.39; -7% liquid water (Mv)
;measured snow density (volume concentration of
;UMF E.96a permittivity mixing model; rearranged to compute Mv given epsreal
;NOTE: must estimate Mv for computation of A (it is a relatively minor term)
M vl=4
;question: Mv=4 (%), or Mv=0.04?
Al=0.78+0.03*f-0.58*(0.001)*fA2
;UMF E.99A
A2=0.97-0.39*f*(0.01)+0.39*(0.001)*fA2;UM FE.99B
B 1=0.3 l-0.05*f+0.87*(0.00 l)*fA2
;UMF E.99C
A= 1.0+1.83 *rho_snow+0.02*A 1*(Mv 1A1.015)+B 1 ;UMF E.97a
B =0.073* A 1
;UMFE.97b
C=0.073*A2
;UMF E.97c
x=1.3l
;UMF E.97d
fo=9.07e09
;UMF E.97e
Mv=(epsreal_wet-A)*( l+(f/fo)A2)/B;UMF E.96a
;PRINT
print,’epsreal_wet=’,epsreal_wet & print,’epsimag=’,epsimag & print,’vi=’,vi
print,’Mv=’,Mv & print,’A 1=’,A 1 & print,’A2=’,A2 & print,’B l= ’,Bl
print,’A=’,A & print,’B=’,B & print,’C=’,C & print,’x=’,x
print,’fo=’,fo & print,’f=’,f
return
end
B.6 Program: fresneI_snow.pro
pro fresnel_snow
;Purpose: compute Fresnel reflection coefficients fo r the air-snow
;boundary; in vpol and hpol.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
;USER: variables to change: eps2 (dielectric constant of snow (complex))
;Reflection coefficients are printed to the IDL window and plotted in a graph.
•.VARIABLE INITIALIZATION
speed=2.998e+08 & print,’speed=’,speed;speed of light
freq=double(37e+09) & print,’frequency=\freq
eps 1=1 .O&print,’eps 1= ’,eps 1
eps2=complex(5.0,0.5) ;wet
;NOTE: 0.4*eps2 is an ice-to-snow conversion; probably not valid. Yikes.
;eps2=complex(3.15,0.5);& eps2=0.4*eps2 & print,’eps2=’,eps2
mu= 1.0 & print,’mu=\mu ;permeability
mu2=4*(!pi)*10A(-7);test permeability
nl=sqrt(mu/epsl);complex intrinsic impedance (eta) (air)
n2 =sqrt(mu/eps 2 );complex intrinsic impedance (eta) (snow)
print,’n l,n 2 = ’,nl,n 2
lam bdal=0.0081
;wavelength of 37.5 GHz wave in air
print,’lambda 1= ’.lambda 1
lambda2=speed/(freq*sqrt(mu*3.15*0.4*0.9))
print,’lambda2 =’,lambda2
kl=(2*!pi)/(Iambdal);compute kl (k_air)
k2=(2*!pi)/(Iambda2);compute k l (k_air)
print,’k 1 ,k2 = ’,k 1,k2
;INCIDENCE ANGLES
thetal=[0,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90] &
print,’theta 1_orig=’.thetal
theta_deg=thetal
thetal=thetal/57.2958;convert deg. to radians
print,’theta l_rad=’,theta 1
;COMPUTE ANGLE OF TRANSMISSION VIA SNELL’S LAW
theta2 =asin(k 1*sin(theta 1)/k2 )
print,’theta2 _rad=’,theta2
print,’theta l_deg=’,theta 1*57.2958
print,’theta2 _deg=’,theta2 *!radeg
;COMPUTE FRESNEL REFLECTION COEFFICIENTS
rh=complexarr(19) & rv=complexarr( 19)
for i=0,18 do begin
rh(i)=(n 1*cos(theta 1(i))-n2 *cos(theta2 (i)))/ $
(nl*cos(thetal(i))+n2*cos(theta2(i))); rh=F.reflection coef., Hpol
rh=abs(rh)
rv(i)=(n 2 *cos(theta 1(i))-n 1*cos(theta2 (i)))/ $
(n2*cos(thetal(i))+nl*cos(theta2(i))); rv=F.reflection coef., Hpol
rv=abs(rv)
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138
endfor
plot,theta_deg,rh,psym=-4,xticklen=0.5,yticklen=0.5
oplot,theta_deg,rv,psym=-3
print,’rh=’,rh
print,’rv=’,rv
return
end
B.7 Program: plot_fresnel_wet_dry.pro
pro pIot_fresnel_wet_dry,rvdry,rhdry,rh,rv,thetaI ,eps2 _wet,eps2 _dry
;Purpose: compute Fresnel reflection coefficients fo r the air-snow
;boundary, in vpol and hpol, fo r wet and dry cases.
;USER: variables to change: eps2 _wet and eps2_dry (dielectric constant of wet and dry
snow (complex variable))
eps2_wet=complex(5.0,0.5)
eps2_dry=complex( 1.7,0.01)
;USER: modify as necessary
;esp2 _wet=wet snow complex dielectric constant
;USER: modify as necessary
;esp2 _dry=dry snow complex dielectric constant
;VARIABLE INITIALIZATION
e p sl= 1.0
speed=2.998e+08
freq=double(37e+09)
mu= 1.0
nl=sqrt(mu/epsl)
;complex intrinsic impedance (eta) (air)
n2 =sqrt(mu/eps2 _wet)
'.complex intrinsic impedance (eta) (snow)
lambda1=0.0081
;wavelength of 37.5 GHz wave in air
lambda2 =speed/(freq*sqrt(mu*float(eps2 _wet)))
kl=( 2 *!pi)/(lambdal) ;computekl (k_air)
k2 =(2 *!pi)/(lambda2 ) ;compute k2 (k_snow)
!p.charsize=1.5
;INCIDENCE ANGLES
theta l=fltarr( 19)
for i=0,18 do begin
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theta l(i)=i*5
endfor
thetal=thetal/57.2958 ;convert deg. to radians
;COMPUTE ANGLE OF TRANSMISSION VIA SNELL’S LAW
theta2 =asin(k 1*sin(theta 1)/k2 )
;COMPUTE FRESNEL REFLECTION COEFFICIENTS
rh=complexarr(19) & rv=complexarr( 19)
for i=0,18 do begin
rh(i)=(nl*cos(thetal(i))-n 2 *cos(theta2 (i)))/ $
(nl*cos(thetal(i))+n2*cos(theta2(i))) ; rh=F.reflection coef., Hpol
rh=abs(rh)
rv(i)=(n2 *cos(theta 1 (i))-n 1*cos(theta2 (i)))/ $
(n2*cos(thetal(i))+nl*cos(theta2(i))) ; rh=F.reflection coef., Hpol
rv=abs(rv)
endfor
•VARIABLE INITIALIZATION
e p s l= 1.0
speed=2.998e+08
freq=double(37e+09)
m u= 1.0
n 1=sqrt(mu/eps 1)
;complex intrinsic impedance (eta) (air)
n 2 =sqrt(mu/eps2 _dry)
;complex intrinsic impedance (eta) (snow)
lambda1=0.0081
;wavelength of 37.5 GHz wave in air
lambda2 =speed/(freq*sqrt(mu*float(eps2 _dry)))
k l= ( 2 *!pi)/(lambdal) ;computekl (k_air)
k2 =(2 *!pi)/(lambda2 ) ;compute k2 (k_snow)
;INCIDENCE ANGLES
theta l=fltarr( 19)
for i=0,18 do begin
theta l(i)=i*5
endfor
thetal=theta 1/57.2958 ;convert deg. to radians
;COMPUTE ANGLE OF TRANSMISSION VIA SNELL’S LAW
theta2 =asin(k 1*sin(theta 1)/k2 )
;COMPUTE FRESNEL REFLECTION COEFFICIENTS
rhdry=complexarr(I9) & rvdry=compIexarr(I9)
for i=0,18 do begin
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rhdry(i)=(nl *cos(thetal(i))-n 2 *cos(theta2 (i)))/ $
(nl*cos(thetal(i))+n2*cos(theta2(i))) ; rhdry=F.reflection coef., Hpol
rhdry=abs(rhdry)
rvdry(i)=(n2 *cos(theta 1(i))-n 1*cos(theta2 (i)))/ $
(n2*cos(thetal(i))+nl*cos(theta2(i))) ; rvdry=F.reflection coef., Vpol
rvdry=abs(rvdry)
endfor
;PLOTTING
plot,thetal*57.2958,rv,psym=-2,yticklen=0.5,xticklen=0.5;,$
;xtitle=’incidence angle’,ytitle=’Fresnel reflection coefficient’
oplot,thetal *57.2958,rh,psym=-4
oplot.thetal *57.2958,rvdry,psym=-2
oplot,thetal *57.2958,rhdry,psym=-4
;xyouts, 10,0.83,’eps=5.0,0.5’ & xyouts,l0,0.63,’*=vpol, diamond=hpol’
retail
end
B.8 Program: compare_specular_lambertian.pro
pro compare_specular_lambertian,rvdry,tap,tbsky,tbsnow_specular,tbsnow_lambertian
;PURPOSE: compare specular and lambertian scattering from snow surface
;USER: this program requires preexisting 19 element reflection coefficient files
;Use program fresnel_snow.pro to generate reflection coefficients.
;USER: specify filenames following the ‘openr’ statements (e.g., ‘rh_l.7_0.01’)
;to open and read the appropriate reflection coefficient files.
rhdry=fltarr(19) & rvdry=fltarr(19) & rvwet=fltarr(19) & rhwet=fltarr(19)
openr,l,’rh_1.7_0.01’ & readf,l,rhdry & close, 1
openr,l,’rv_1.7_0.01’ & readf,l,rvdry & close,1
openr,l,’rh_5.0_0.5’ & readf,l,rhwet & close, 1
openr,l,’rv_5.0_0.5’ & readf,l,rvwet & close, 1
;INCIDENCE ANGLES
theta l=fltarr( 19) & for i=0,18 do begin & theta l(i)=i*5 & endfor
;get tb_sky for specular case
;USER: modify ‘skyfile’ and ‘snowfile’ to get sky and snow apparent brightness tempera­
tures
skyfile=’tap_sky’ & snowfile=’tap_snow’
tbsky=fltarr( 19)&openr, 1,skyfile&readf, 1,tbsky&close, 1
tap=fltarr( 19)&openr, 1,snowfile&readf, 1,tap&close, 1
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tbsnow_specular=fltarr( 19)& tbsnow_Iambertian=fltarr( 19)
;perform tbsnow=tap-r*tbsky
for i=0,18 do begin
tbsnow_specular(i)=double(tap(i)-rvwet(i)*tbsky(i))
tbsnow_Iambertian(i)=double(tap(i)-rvwet(i)*493*(3.0/180.0))
endfor
plot, theta 1,tap, psym=-4,yrange=[ 190,280] ,xticklen=0.5,yticklen=0.5
oplot, theta 1,tbsnow_specular,psy m=-5
oplot,theta 1,tbsnow_lambertian,psym = -6
return
end
B.9 Program: mm_to_phi.pro
pro mm_to_phi,fl,result,out
;Purpose: convert size data in mm to phi scale
;Author: Drew Pilant, April, 1994
fl=dblarr( 2 ,8 )
f2=dblarr(3,8)
filename=’940405_avg.data’
openr, 1,filename & readf,l,fl & close, 1
;USER: modify filename
result=dblarr(2 ,8 ) & result=f 1
M=3.321928095
for j=0,7 do begin
result(0,j)=double(-1 *M*alog 10(f 1(0,j)))
endfor
out=dblarr(3,8)
out(0 ,*)=result(0 ,*)
out(l,*)=fl( 0 ,*)
out(2 ,*)=fl(l,*)
return
end
B.10 Program: magnitude_sky_contribution.pro
pro magnitude_sky_contribution,fl,f2 ,h_corrected_sky_tap,v_corrected_sky_tap,rh,rv
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;Purpose: plots magnitude of sky contribution to snow apparent brightness temperature for
specular and lambertion cases
;USER: variables to modify
filel=’tap_940406_1530_svsky_h3’ & file2=’tap_940406_1530_nvsky_h3’
fl=fltarr(l,19) & f2=fltarr(l,19)
openr, 1,file 1 & readf,l,fl & close, 1
openr,2 ,file2 & readf,2 ,f 2 & close ,2
;VARIABLE INITIALIZATION
eps 1= 1.0
eps2=complex( 1.5,0.1)
eps2_real= 1.50
;real part of eps2 for calc, of Iambda2,k2
speed=2.998e+08
freq=double(37e+09)
mu= 1.0
n 1=sqrt(mu/eps 1)
;complex intrinsic impedance (eta) (air)
n2 =sqrt(mu/eps2 )
;complex intrinsic impedance (eta) (snow)
lambda1=0.0081
;wavelength of 37.5 GHz wave in air
Iambda2 =speed/(freq*sqrt(mu*eps2 _real))
kl= ( 2 *!pi)/(Iambdal) ;com putekl (k_air)
k2 =(2 *!pi)/(lambda2 ) ;compute k2 (k_snow)
;INCIDENCE ANGLES
theta l=fltarr( 19)
for i=0,18 do begin
theta l(i)=i*5
endfor
thetal=thetal/57.2958 ;convert deg. to radians
;COMPUTE ANGLE OF TRANSMISSION VIA SNELL’S LAW
theta2 =asin(k 1*sin( theta 1 )/k2 )
;COMPUTE FRESNEL REFLECTION COEFFICIENTS
rh=complexarr(19) & rv=complexarr( 19)
for i=0,18 do begin
rh(i)=(nl*cos(thetal(i))-n 2 *cos(theta2 (i)))/ $
(nl*cos(thetal(i))+n2*cos(theta2(i))) ; rh=F.reflection coef., Hpol
rh=abs(rh)
rv(i)=(n2 *cos(theta 1(i))-n 1*cos(theta2 (i)))/ $
(n2*cos(thetal(i))+nl*cos(theta2(i))) ; rh=F.reflection coef., Hpol
rv=abs(rv)
endfor
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h_corrected_sky_tap=rh*f2 & v_corrected_sky_tap=rv*f2
print,’h_corrected_sky_tap=’,h_corrected_sky_tap
print,’v_corrected_sky_tap=’,v_coiTected_sky_tap
;PLOTTING
plot,v_corrected_sky_tap,psym = -2
oplot,h_corrected_sky_tap,psym = -6
oplot, 10 *rh,psym=-2 ,linestyle= 2 & oplot, 10 *rv,psym=-6 ,linestyle= 2
return
end
B .ll Program: fractal_topography.pro
pro fractal_topography,bw 2 pow,cycles_per_m,dem, bw, ni, ag, up,fbw,fni,fag,fup
; Purpose: compute fractal parameters fo r topography using digital elevation model
(dem)
; open and ingest dem data
!order=l
openr, 1 ,’midwest_dem.bin’ & dem=intarr( 1200,600) & readu,l,dem & close, 1
;USER: place this file in working directory.
;USER: to modify for use with other data sets, modify these variables:
;input file
;dem dimensions
; convert 16 bit to 8 bit; select 100 x 100 sets
dem=bytscl(dem)
; convert digital numbers to feet, then meters, then to 8 bit
; dem=(9.05894*(dem))-9.9l677 old values; based on 4 point regression
dem=(9.l3464)*(dem)-28.5891
dem=dem/3.280833
window,30,xsize=1200,ysize=600,title=’30 DEM (1 km pixels)’
tvscl,bytscl(dem)
;USER: modify row-column subsetting region as necessary
;USER: modify region variable names as necessary
;
boundary waters canoe area, ont
bw=dem(0:99,200:299) & bw2=dem(0:199,150:349)
nipigon.ont
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ni=dem(485:584,0:99) & ni2=dem(435:634,0:199)
;
ag area, ont
ag=dem(1020:1119,250:349) & ag2=dem(970:1169,200:399)
;
eastern u.p.
up=dem(850:949,400:499) & up2=dem(300:999,350:549)
;
set up windows for display
window, l,xsize=300,ysize=300,title=’ 1 bw’
window,2,xsize=300,ysize=300,title=’2 nipigon’
window,3,xsize=300,ysize=300,title=’3 ag’
window,4,xsize=300,ysize=300,title=’4 eastern u.p.’
;
display surface plots
wset,l & shade_surf, (bw),zrange=[170,710] & tvscl, bytscl(bw)
wset,2 & shade_surf,(ni),zrange=[ 170,710] & tvscl, bytscl(ni)
wset,3 & shade_surf,(ag),zrange=[ 170,710] & tvscl,bytscl(ag)
wset,4 & shade_surf, up,zrange=[ 170,710] & tvscl, bytscl(up)
;
convert x-axis from Fourier # to frequency
horiz=indgen( 100 , 1) & horiz=horiz + 1 ; array for x-axis (harmonic #)
cycles_per_m=horiz/( 1 0 0 .0 * 1000 .0 )
; convert from fourier #
; to cycles/m
SURFACE (2-D CASE) COMPUTATIONS
;
Compute FFT of sets; display power spectra
;
FFT of BOUNDARY WATERS
window,5, xsize=300,ysize=300,title=’5 BW power spectrum’
fbw=fft( bw,-l) & bw 2 pow=(abs(fbw ))A2
tvscl, rebin(shift(alogl0(bw2pow),256,256),300,300)
;
FFT of NIPIGON
window,6,xsize=300,ysize=300,title=’6 NIPIGON power spectrum’
fni=fft( ni,-l) & ni2 pow=(abs(fni))A2
tvscl,rebin(shift(alogl0(ni2pow),256,256),300,300)
;
FFT of AGAWA
window,7, xsize=300,ysize=300,title=’7 AGAWA power spectrum’
fag=fft( ag,-l) & ag 2 pow=(abs(fag) ) A2
tvscl,rebin(shift(alogl0(ag2pow),256,256),300,300)
;
FFT of UP
window,8 , xsize=300,ysize=300,title=’8 Eastern UP power spectrum’
fup=fft( up,-l) & up 2 pow=(abs(fup) ) A2
tvscl,rebin(shift(alog!0(up2pow),256,256),300,300)
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;
plot log*log of 2 -d power spectra
; THINK THINK about the bw2pow array
window,9, xsize=300,ysize=300,title=’9 BW Iog*Iog of 2-D power spectrum’
plot_oo,cycles_per_m( 1:49),bw2pow( 1:49,1:49),psym=4
window, 10, xsize=300,ysize=300,title=’ 10 NIPIGON log*log of 2-D power spectrum’
plot_oo,cycles_per_m( 1:49),ni2pow( 1:49,1:49),psym=4
window, 11, xsize=300,ysize=300,tide=’ 11 AGAWA log*log of 2-D power spectrum’
plot_oo,cycles_per_m(0:49),ag2pow(0:49,0:49),psym=4
window, 12, xsize=300,ysize=300,title=’ 12 Eastern UP log*log of 2-D power spectrum’
plot_oo,cycles_per_m(0:49),up2pow(0:49,0:49),psym=4
PROFILE (1-d) COMPUTATIONS
;
extract 1-dimensional profiles; p=profile,w=west,n=north, etc
pwbw=bw(*,50) & pnbw=bw(50,*) & pwni=ni(*,50) & pnni=ni(50,*)
pwag=ag(*,50) & pnag=ag(50,*) & pwup=up(*,50) & pnup=up(50,*)
;
perform fft for profiles; f=fft, etc
fpwbw=fft(pwbw,-l) & fpnbw=fft(pnbw,-l) & fpwni=fft(pwni,-l) &fpnni=fft(pnni,-l)
fpwag=fft(pwag,-l) & fpnag=fft(pnag,-l) & fpwup=fft(pwup,-l) &fpnup=fft(pnup,-l)
;
make power spectrum arrays for profiles; pow=power
bwwpow=(abs(fpwbw ))A2 & bwnpow=(abs(fpnbw ))A2
niwpow=(abs(fpwni))A2 & ninpow=(abs(fpnni))A2
agwpow=(abs(fpwag))A2 & agnpow=(abs(fpnag ))A2
upwpow=(abs(fpwup))A2 & upnpow=(abs(fpnup ))A2
;
plot power spectra of profiles; fit lines using poly_fit
;
(lfpwbw= “line fft profile west boundary water”)
window,!3,xsize=300,ysize=300,title=’ 13 Boundary Waters log 10 fft of WE profiles’
plot_oo,cycles_per_m(25:49),bwwpow(25:49),psym=l
lfpwbw=poly_fit(cycles_per_m(25:49),bwwpow(25:49),2)
oplot,lfpwbw,linestyle= 0
window,23,xsize=300,ysize=300,title=’23 Boundary Waters NS profile power spectrum’
pIot_oo,cycles_per_m(15:39),bwnpow(15:39),psym=5,title=’23 Boundary Waters NS
profile power spectrum’
lfpnbw=poly_fit(horiz( 15:39),bwnpow( 15:39), 1) & oplot,lfpnbw,linestyle=0
window,!4,xsize=300,ysize=300,title=’ 14 Nipigon log 10 fft of profiles (WE & NS)’
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146
plot_oo,niwpow(0:49),horiz,psym=l & oplot,ninpow(0:49),psym=5
lfpwni=poly_fit(horiz(0:49),niwpow(0:49), 1) & oplot,lfpwni,linestyle= 1
lfpnni=poly_fit(horiz(0:49),ninpow(0:49), 1) & oplot,lfpnni,linestyle=2
window, 15,xsize=300,ysize=300,title=’ 15 Agawa log 10 fft of profiles (WE & NS)’
plot_oo,agwpow(0:49),horiz,psym=2 & oplot,agnpow(0:49),psym=5
Ifpwag=poly_fit(horiz(0:49),agwpow(0:49), 1) & oplot,lfpwag,linestyle= 1
lfpnag=poly_fit(horiz(0:49),agnpow(0:49), 1) & oplot,lfpnag,linestyle=2
window, 16,xsize=300,ysize=300,title=’ 16 UP log 10 fft of profiles (WE & NS)’
plot_oo,upwpow(0:49),horiz,psym=l & oplot,upnpow(0:49),psym=5
lfpwup=poly_fit(horiz(0:49),upwpow(0:49), 1) & oplot,lfpwup,linestyle= 1
lfpnup=poly_fit(horiz(0:49),upnpow(0:49), 1) & oplot,lfpnup,linestyle=2
;
enter profiles into arrays for display as images;
warray=intarr(100,16) & narray=intarr(16,100)
for i=0,3 do begin
warray(*,i)=pwbw & warray(*,i+4)=pwni
warray(*,i+ 8 )=pwag & warray(*,i+ 12 )=pwup
narray(i,*)=pnbw & narray(i+4,*)=pnni
narray(i+ 8 ,*)=pnag & narray(i+ 12 ,*)=pnup
endfor
plot topographic profiles for comparison, plus display as images
window,20,xsize=900,ysize=300,title=’20 PLOTS of W-E topographic profiles’
!p.region=[0 .0 ,0 . 1, 1 .0 , 1 .0 ] ; make space for
plot,horiz,pwbw,yrange=[60,230] ,xtitle=’West-East dimension’,$
ytitle=’elevation (in DN)’,xrange=[0,l 10]
xyouts,105,165,’BW’ & xyouts, 105,115,’NI’
xyouts,105,180,’AG’& xyouts, 105,90,’UP’
xyouts,-30,30,’BW,NI,AG,UP’
oplot,pwni,linestyle= 1
oplot,pwag,linestyle=2 & oplot,pwup,linestyle=3
tvscl,congrid(warray,300,32)
window,2 l,xsize=300,ysize=300,title=’21 PLOTS of N-S topographic profiles’
plot,horiz,pnbw,yrange=[60,230],xtitle=’North-South dimension’, $
ytitle=’elevation (in DN)’,xrange=[0,110]
xyouts, 105,175,’BW’ & xyouts, 105,100,’NI’
xyouts, 105,160,’AG’& xyouts, 105,70,’UP’
xyouts,-30,30,’BW,NI,AG,UP’
oplot, pnni,linestyle= 1
oplot,pnag,linestyle=2 & oplot,pnup,linestyle=3
tvscl,rotate(congrid(narray,32,300),4)
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147
;
compute STATISTICS for the sets
zmean=fltarr(4) & zmax=intarr(4) & zmin=intarr(4) & zmedian=fltarr(4) & zsd=fltarr(4)
;mean(0)=avg( bw) & mean(l)=avg( ni) & mean(2)=avg
combo=intarr( 100,100,4)
combo(*,*,0)= bw & combo(*,*,l)= ni & combo(*,*,2)= ag
combo(*,*,3)= up
for i=0,3 do begin
zmean(i)=avg(combo(*,*,i)) & zmax(i)=max(combo(*,*,i))
zmin(i)=min(combo(*,*,i)) & zmedian(i)=median(combo(*,*,i)) & $
zsd(i)=stdev(combo(*,*,i))
endfor
openw,l,’stats.out’
printf, 1,zmean,zmax,zmin,zmedian,zsd
print,’
bw
nipigon
ag
east-u.p.’
print, zmean,zmax,zmin,zmedian,zsd
close, 1
return
end
B.12 Program: aschbacher_snow_depth.pro
pro aschbacher_snow_depth,input_19v,input_37v,big_input_19v,big_input_37v,depth,
big_depth
;PURPOSE: estimate snow thickness using the Aschbacher algorithm and SSM/I data
;USER: modify infile_19v and infile_37v as necessary (they are two-dimensional SSM/I
brightness temperature images in binary format).
;USER: pass the variables to the IDL environment then display (e.g., IDL> tvscl,
big_depth)
;NOTE: the input SSM/I data are three-dimensional arrays (an image for each day
between the dates indicated in the filename)
;Algorithm source:
;from Nagler, Thomas and Rott, Helmut, 1991. Intercomparison of snow mapping
;algorithms over Europe using SSM/I data: Interim report to the SSM/I Products
;Working Team, January 1991, 14 p.
infile_19v=’~/research/ssmi/Fl 1_VOL10/DATA/19H/94030 l_940531_19vgl_ave.bin’
infile_37v=’~/research/ssmi/F 1l_VOL 10/DATA/37H/940301_94053 l_37vgl_ave.bin’
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
148
input_19v=intarr(50,70,91) & input_37v=intarr(50,70,92)
depth=intarr(50,70,91);depth in cm
openr,l,infile_19v & readu,l,input_19v & close, 1
openr,2,infile_37v & readu,2,input_37v & close,2
;if (19v-37v) gt 2k, then snow
depth=0.68*(input_19v-input_37v)-0.67
big_input_19v=rebin(input_19v,200,280,91/sample)
big_input_37v=rebin(input_37v,200,280,91/sam ple)
big_depth=rebin(depth,200,280,91/sample)
return
end
B.13 Program: chang_foster_hall_90_snow_depth.pro
pro
chang_foster_hall_90_snow_depth,input_19h,input_37h,big_input_19h,big_input_37h,de
pth, big_depth
;PURPOSE: estimate snow thickness using the Chang-Foster-Hall algorithm and SSM/I
data
;USER: modify infile_19v and infile_37v as necessary (they are two-dimensional S
SM/I brightness temperature images in binary format).
;USER: pass the variables to the IDL environment then display (e.g., IDL> tvscl,
big_depth)
;NOTE: the input SSM/I data are three-dimensional arrays (an image for each day
between the dates indicated in the filename)
;Algorithm source:
;from Chang,Foster,Hall, 1990. Satellite sensor estimates of northern
;hemisphere snow volume; Int. Journal of Remote Sensing, 1990,
;v. 11, no. 1, 167-171
infiIe_19h=’~/research/ssmi/Fl 1_VOL10/DATA/19H/940301_94053 l_19hgl_ave.bin’
infile_37h=’~/research/ssmi/F 1l_VOL 10/DATA/37H/940301_94053 l_37hgl_ave.bin’
input_19h=intarr(50,70,92) & input_37h=intarr(50,70,92)
depth=intarr(50,70,92);depth in cm
openr,l,infile_19h & readu,l,input_19h & close, 1
openr,2,infile_37h & readu,2,input_37h & close,2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
149
depth=1.59*(input_19h-input_37h)
big_input_ 19h=rebin(input_ 19h,200,280,92/sample)
big_input_37h=rebin(input_37h,200,280,92/sample)
big_depth=rebin(depth,200,280,92/sample)
return
end
B.14 Program: nagIer_snow_depth.pro
pro nagler. snow .depth,input, 19v,input. 37v,big .input _19v,big_Jnput _37v,depth,
big_depth
;from Nagler, Thomas and Rott, Helmut, 1991. Intercomparison of snow mapping
;algorithms over Europe using SSM/I data: Interim report totheSSM/I Products
;Working Team, January 1991, 14 p.
;NOTE: the input SSM/I data are three-dimensional arrays (an image for each day
between the dates indicated in the filename)
infile_ 19v=’~/research/ssmi/Fl l_VOL 10/DATA/l 9H/940301_940531_ 19vgl_ave.bin’
infile_37v=’~/research/ssmi/Fl l_VOL10/DATA/37H/94030l_94053 l_37vgl_ave.bin’
input_l9v=intarr(50,70,91) & input_37v=intarr(50,70,92)
depth=intarr(50,70,91);depth in cm
openr,l,infile_l9v & readu,l,input_19v & close,1
openr,2,infile_37v & readu,2,input_37v & close,2
;NAGLER ALGORITHM
;if [(I9v-37v) GE 4 or ((37v-85v) ge 3 and 19H le 259)]
depth=1.4*(input_19v-input_37v)-0.1*(37v-85v)-l.l 1
;if (depth LE 5) then: thin snow cover with no further discrim, of depth.
big_input_ 19v=rebin(input_ 19 v,200,280,91 /sample)
big_input_37v=rebin(input_37v,200,280,91/sample)
big_depth=rebin(depth,200,280,91 ,/sample)
return
end
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