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Brightness temperature simulations for the physical and synoptic interpretation of advanced microwave sounding unit moisture channels

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O rder N u m b e r 9 4 1 6 1 5 3
B rightness tem p eratu re sim ulations for the physical and
synoptic interpretation o f advanced m icrowave sounding unit
m oisture channels
Muller, Bradley Moore, Ph.D.
The Florida State University. 1993
DM I
300 N. Zeeh Rd.
Ann Arbor, MI 48106
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TH E FLORIDA STATE UNIVERSITY
C O LLEG E OF ARTS AND SCIENCES
BRIGHTNESS TEM PERATURE SIMULATIONS FOR TH E PHYSICAL
AND SYNOPTIC INTERPRETATION O F ADVANCED MICROWAVE
SOUNDING UNIT M OISTURE CHANNELS
By
Bradley M. Muller
A Dissertation submitted to the Department of Meteorology
in partial fulfillment of the requirements for the degree
of Doctor o f Philosophy
Degree Awarded:
Fall Semester, 1993
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The members of the Committee approve the dissertation of Bradley M.
Muller defended on November 2, 1993.
Henry EJJFuelberg
Professor Directing Dissertation
Georges L. Weatherly
^
Outside Committee Member
7? a
Noel E. LaSeur
Committee Member
Paul H. Ruscher
Committee Member
Eric A. Smith/
/
Committee Member
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ACKNOW LEDGEMENTS
I wish to express my deep gratitude to my major professor, Dr. Henry
Fuelberg, for his unwavering guidance, support, and flexibility throughout the
course of my research. I also would like to thank my committee members, Drs.
Eric Smith, Noel LaSeur, Paul Ruscher, and Georges Weatherly, for providing
guidance and support in the form of computer codes and scientific advice, and also
in the intangible form of helping direct and shape my natural curiosity through their
teaching and approaches to science.
Special thanks are due to Dr. Bill Lapenta of NASA/Marshall Space Flight
Center for providing the mesoscale model simulation for Phase 3 of my research,
and Mr. Rich Fulton of NASA/Goddard for providing the radar cross-section for
Phase 2. Dr. Xuwu Xiang is gratefully acknowledged for sharing his Sobolev
radiative transfer code, answering numerous questions about it, and engaging in
stimulating discussions on specific radiative modeling issues.
I also want to thank Drs. Pete Robertson and Gary Jedlovec of
NASA/Marshall for originally suggesting the topic of microwave water vapor
channels, providing assistance and support during my many trips to Marshall, and
numerous helpful discussions regarding both the LAMPS model and satellite issues.
iii
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Mr. Kevin Doty and Dr. Don Perkey were very helpful in answering numerous
questions about LAMPS. Ms. Jayanthe Srikishen, Mr. Anthony Guillory and Mr.
Rob Loring assisted with many computer problems.
Drs. Alberto Mugnai, Mike Yeh, Frank Marzano, George Diak and Mr.
Ralph Ferraro are acknowledged either for helpful discussions, or providing specific
information about AMSU. Mr. James Stricherz and Mr. A1 Davis assisted with
video production and are gratefully acknowledged. I also would like to thank Dr.
James O ?Brien for originally bringing me to FSU. Special thanks are due to Ms.
Anna Nelson Smith for making my academic life, and the lives of all graduate
meteorology students at FSU, a bit easier.
My everlasting love and appreciation go to Lois Nathan, to my parents
Stanley and Edith Muller, and to my brother and sister, Randy Muller and Carolyn
Muller.
This research has been supported by NASA/MSFC under the Graduate
Student Researchers Program Grant NGT-50524.
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TABLE O F CONTENTS
Page
LIST OF T A B L E S......................................................................................................viii
LIST OF F IG U R E S ......................................................................................................ix
A B S T R A C T ...........................................................................................................
xvii
Chapter
1.
Introduction ....................................................................................................
2.
Simulations of the Effects of Water Vapor, Cloud Liquid Water, and
Ice on AMSU Moisture Channel Brightness T em peratures.................... 5
2.1.
Introduction........................................................................................................ 5
2.2.
Radiative transfer considerations..................................................................
10
2.3.
M ethodology..................................................................................................
16
a. Radiative transfer m o d e ls ......................................................................
16
b. Atmospheric profile and cloud models ...............................................
18
2.4.
1
R e su lts............................................................................................................. 20
a. Clear atm ospheres.................................................................................. 20
b. Effects o f liquid c lo u d s ..........................................................................
31
1) Cloud liquid water versus cloudwater vapor ......................
31
v
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Chapter
Page
2) Effects of droplet mode radius and size
d istribution ....................................................................................... 34
3) Cloud liquid water content, altitude, and
thickness .........................................................................................
38
c. Effects o f ice c lo u d s .............................................................................
49
2.5.
Summary and conclusions
........................................................................
61
3.
An Alternative Representation of the IceCanopy for Calculating
Microwave Brightness Temperatures Over a Thunderstorm..................
66
3.1.
Introduction .................................................................................................
66
3.2.
Methodology for comparing simulated and observed TBs ....................
69
3.3.
R e su lts............................................................................................................ 74
3.4.
Conclusions .................................................................................................. 86
4.
A Simulation of Microwave Water Vapor Imagery and Upper Level
Features During ERICA IO P 4 ................................................................... 87
4.1.
Introduction .................................................................................................
87
4.2.
M ethodology.................................................................................................
89
4.3.
R e s u lts ........................................................................................................... 96
a. Water vapor image interpretation ....................................................... 96
4.4.
b. Synoptic summary and simulationverification..................................
106
c. 182 GHz Tb and Tropopause folding ...............................................
131
Summary and conclusions
.......................................................................
151
Appendix A ...........................................................................................................
156
VI
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Chapter
Page
A.I.
Multiple scattering radiative transfer model .........................................
156
A.2.
Single scattering model ............................................................................
169
A.3.
Microwave gaseous absorption ...............................................................
174
REFERENCES .....................................................................................................
176
BIOGRAPHICAL S K E T C H ...............................................................................
186
vii
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LIST OF TABLES
Table
Page
2.1.
Clear air brightness temperatures, surface
contributions, and CF peaks for eight soundings at
AMSU mositure channel frequencies............................................ 23
2.2.
Characteristics for soundings used to create Table
2.1
4.1.
4.2
4.3
4.4
24
Average precipitable water content above the 50%
and 90% cumulative TB contribution levels, and
average pressure of cumulative contribution levels,
s.d. is standard deviation. Data for all soundings and
for only clear soundings are given for three
time/dates........................................................................................
102
Vertically .averaged value of the frontogenetical
function (F2 in (4.3) x 10'11 g kg'1 m'1 s'1) for water
vapor and its terms, averaged over a box. CON is
confluence. SD is shearing deformation. TILT is
tilting. DIAB is gradients of water vapor sources and
sinks, i.e., moist diabatic processes.............................................
122
LAMPS parcel variables corresponding to trajectories
in Fig. 4.11, where p is pressure, q is specific
humidity, and 9 is potential temperature. Data are
given for starting and ending times of each
trajectory.........................................................................................
135
LAMPS parcel variables as in Table 4.3
corresponding to trajectories in Fig. 4.15..................................
143
vm
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LIST O F FIGURES
Figure
Page
2.1.
Contribution functions (km'1) for six AMSU moisture
channels for (a) uniform Tdd profile; (b) as in 2.1a
but with a single moist layer; (c) as in 2.1b but with
0.4 g m'3 liquid cloud water in the moist layer; and
(d) Skew-T In p plot of atmospheric temperature and
dewpoint (癈) profiles corresponding to 2.1a, b, and
c; dashed line indicates moist layer.
TBs and
fractional surface contributions for each channel are
given on the right portions of a-c................................................... 21
2.2.
TB (K) for a clear atmosphere as a function of the
height (km) of the top of a moist layer extending
from the surface to the given altitude for (a) surface
emissivity of 0.9; and (b) surface emissivity of 0.7..................... 29
2.3.
(a) Droplet number concentration as a function of
radius interval (number of droplets cm'3 pm'1) for
various theoretical cloud droplet SDFs. (b) TB as a
function of mode radius (pm) of each SDF in 2.3a.
(c) Extinction coefficient (xlO'7 m'1) as a function of
droplet radius (pm) for each SDF in 2.3a. The mode
radius (pm) of the corresponding SDF is given on the
right portion of each curve, (d) As in 2.3c but for
scattering coefficient........................................................................
2.4.
36
TB (K) as a function of liquid water path (kg m'2) for
altostratus clouds between (a) 6-7 km altitude; and (b)
2-3 km................................................................................................ 39
ix
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Figure
2.5.
2.6.
Page
Contribution functions (km'1) for six AMSU moisture
channels for altostratus clouds between (a) 6-7 km
(490-410 mb) with LWP of 0.062 kg m'2; (b) 6-7 km
(490-410 mb) with LWP of 0.625 kg m'2; (c) 2-3 km
(820-690 mb) with LWP of 0.062 kg m'2; and (d) 2-3
km (820-690 mb) with LWP of 0.625 kg m'2. TBs
and fractional surface contributions for each channel
are given on the right portion of each panel................................
41
T b (K) as a function of (a) cloud top height (km) for
a 0.5 km thick altostratus cloud; (b) as in 2.6a for a
3 km thick cloud; (c) moist layer top height (km) for
a 0.5 km thick clear but saturated layer, and (d) as in
2.6c but for a 3 km thick lay er.....................................................
44
2.7.
T b (K) as a function of surface emissivity for (a) a
clear but saturated moist layer between 4-5 km; (b)
an altostratus cloud between 4-5 km with LWP of
0.125 kg m'2; and (c) as in 2.7b but with LWP of
0.625 kg m'2...................................................................................... 47
2.8.
T b (K) as a function o f ice water path (kg m'2) for a
cirrus cloud between (a) 10-12 km; and (b) 6-8 km........................50
2.9.
As in Fig. 2.5 but for cirrus clouds between (a) 10-12
km (300-200 mb) with IWP of 0.113 kg m'2; (b) 1012 km (300-200 mb) with IWP of 0.562 kg m'2; (c)
6-8 km (490-360 mb) with IWP of 0.113 kg m'2; and
(d) 6-8 km (490-360 mb) with IWP of 0.562 kg
m'2
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53
Figure
Page
2.10.
T b (K) as a function of (a) cloud top height (km) for
a 1 km thick cirrus cloud; (b) as in 2.10a but for a 4
km thick cirrus cloud; note difference in temperature
scales; (c) moist layer top height (km) for a 1 km
thick clear but saturated layer; and (d) as in 2.10c for
a 4 km thick layer. ........................................................................ 55
2.11.
T b (K) as a function of surface emissivity for (a) a
clear but saturated layer between 8-10 km; (b) a
cirrus cloud between 8-10 km with IWP of 0.113 kg
m'2; and (c) as in 2.11b but with IWP of 0.563 kg
m .
60
10 cm radar reflectivity (dB) vertical cross-section
along the aircraft flight track. Flight direction was
from 0 to 70 km. North is to the left (after Fulton
and Heymsfield 1991).....................................................................
70
Calculated TBs (denoted by C?s) and aircraftmeasured TBs (denoted by A ?s) for the four AMMS
channels along the aircraft flight track. A "traditional"
M arshall-P alm er p article size distribution
representation for the ice water content was used.......................
76
Same as Fig. 3.2, but using an "alternative" approach
with 20% of the ice water content represented by
Marshall-Palmer spheres, and 80% represented by
modified gamma particle size distributions..................................
78
Same as Fig. 3.2, but with 100% of the ice content
represented by a modified gamma particle size
distribution........................................................................................
80
3.1.
3.2.
3.3.
3.4.
xi
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Figure
3.5.
3.6.
4.1.
4.2.
4.4.
4.5.
Page
Radar-derived columnar liquid water (dashed, kg m'2)
and ice "crystal" mass (solid, kg m'2) along the
aircraft flight track...........................................................................
83
T b contribution functions (km'1) based on the
alternative approach for the four AMMS channels in
(top) the mature convective core and (bottom) the
decaying convective core................................................................
84
(Top) Observed GOES/VAS 6.7 pm water vapor
image and (bottom) simulated LAMPS/AMSU 182
GHz water vapor image for (a)18Z/03 January1989,
(b) 06Z/04, and (c) 18Z/04................... ! ......................................
98
AMSU 182 GHz 50% cumulativecontribution level
(mb) over the LAMPS domain for (first panel)
18Z/03 January 1989, (second panel) 06Z/04, and
(third panel) 18Z/04.......................................................................
104
The 3-h storm track of the ERICA IOP4 cyclone
beginning at 00Z/04 January 1989 to 00Z/06 (after
Chang et al. 1993) with central pressures for selected
times estimated by Nieman and Shapiro (1993).........................
108
LAMPS sea level pressure (mb) for (first panel)
18Z/03 January 1989, (second panel) 06Z/04, and
(third panel) 18Z/04......................................................................
109
LAMPS 500 mb height field in decameters for (first
panel) 18Z/03 January 1989, (second panel) 06Z/04,
and (third panel) 18Z/04...............................................................
Ill
xii
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Figure
4.6.
4.7.
4.8.
4.9.
4.10.
Page
LAMPS 500 mb vertical velocities (pb s'1) for (first
panel) 18Z/03 January 1989, (second panel) 06Z/04,
and (third panel) 18Z/04. Negative values (upward)
are dashed. Contour interval is2 pb s'1.......................................
114
LAMPS 400 mb potential vorticity (x 10'6 K mb"1 s"1)
for (first panel) 18Z/03 January 1989, (second panel)
06Z/04, and (third panel) 18Z/04.................................................
116
LAMPS 300 mb wind speed (m s"1) for (first panel)
18Z/03 January 1989, (second panel) 06Z/Q4, and
(third panel) 18Z/04.......................................................................
120
Schematic illustration of geostrophic deformation
fields for a straight jet stream wind maximum for a
case of confluence with a component of cold
advection along the jet axis. Heavy full curves are
geopotential height contours; heavy broken curves are
isotachs; thin full lines are isentropes; arrows indicate
the sense of the ageostrophic circulation; plus or
minus signs give sense of the vertical motion (to)
(After Keyser and Shapiro 1986, and Carlson 1992)................
124
(Top) Cross section of observed data at 00Z/Q4
January 1989 of potential temperature (K, solid) and
section-normal wind speed (m s"1, dashed). The
heavy solid line is the 1 X 10"6 m2 s'1 K kg'1 isopletn
of potential vorticity denoting stratospheric values.
Note that this formulation of PV includes a factor of
1/g (gravity). Wind vector flags are 25 m s'1; full
barbs are 5 m s'1; half barbs are 2.5 m s'1. (After
Nieman
and Shapiro
1993).
(Bottom)
LAMPS/AMSU simulated 182 GHz TB (K) field at
00Z/04, and location of a LAMPS cross section
(shown in Fig. 4.11) coincident with Nieman and
xiii
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Page
Figure
4.11.
4.12.
4.13.
4.14.
Shapiro?s cross section..................................................................
129
LAMPS cross section (location shown in Fig. 4.10)
for 0OZ/04 with (panel 1) TBs (K) at 182 and 176
GHz along the section. Second panel: Vertical
velocity vectors (maximum vector length is 6.6 pb s'1)
and isopleths of wind speed (m s'1). Third panel:
Potential temperature (K) with stratospheric values of
10 and 20 x 10'6 K mb'1 s'1 superimposed. Fourth
panel: Specific humidity (g kg'1). Solid lines are
contour intervals of 0.5 g kg'1. Dashed lines are
contour intervals of 0.05 g kg'1 for values below 0.5
a kg'1.................................................................................................
130
LAMPS T3 at 18Z/03 January 1989 with numbered
air parcel trajectories ending at 500 mb at that time.
Position for cross section from Fig. 4.13 is indicated
by vertical bar. The location of maximum CCL50
(mb) is indicated by a "+"............................................................
133
Same as Fig. 4.11, but for 18Z/03. The cross section
location is shown in Fig. 4.12. Maximum vertical
velocity vector length is 10 pb s'1. Ending locations
of trajectories from Fig. 4.12 are indicated by
numbered circles............................................................................
134
Skew-T Log-p diagrams (left) of LAMPS gridresolved temperature and dewpoint at 18Z/03. Right:
corresponding LAMPS/AMSU contribution functions
and T bs (K) for 182 and 176 GHz. Top panels are
for the point of maximum TB. Bottom panels are for
the point of maximum CCL50. These locations are
shown in Fig. 4.12.........................................................................
137
xiv
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Figure
4.15.
LAMPS T b at 18Z/04 with numbered air parcel
trajectories ending at vertically distributed points at
locations (top) in the upper part of the tropopause
fold on the north side of the warm radiometric
signature and (bottom) near the lower tip of the
tropopause fold and at the location of the warmest TB
along the cross section. Vertical bar marked "A? is
the location of a cross section from Fig. 4.16, while
that marked "B" corresponds to the cross section in
Fig. 4.19. A circle marks the location of parcel 5 as
it passes through cross section B at OOZ/04................
4.16.
Same as Fig. 4.13 but for 18Z/04 January 1989; axis
corresponds to "A" in Fig. 4.15. Maximum vertical
velocity vector corresponds to 10 pb s'1. Ending
locations of trajectories from Fig. 4.15 are indicated
by numbered circles........................................................
4.17.
Danielsen?s (1968) schematic representation of
transverse ageostrophic circulations (solid stream
lines) associated with tropopause folding. Dashed
line indicates the tropopause (after Carlson 1992). . .
4.18.
Same as Fig. 4.14 but for 18Z/04 January 1989. Top
panels are for endpoint of trajectories 1-3 on the
north side of the TBmaximum. Bottom panels are for
endpoint o f trajectories 4-7 at the TB maximum along
the cross section. These locations can be seen in Fig.
4.15................................................................................ .
7
4.19.
Same as Fig. 4.11 but for 00Z/04 January 1989.
Maximum vertical velocity vector corresponds to 5.9
pb s'1. Numbered circle denotes the location of parcel
5 from Fig. 4.15. Cross section location corresponds
to "B? in Fig. 4.15..........................................................
xv
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Figure
A.I.
A.2.
Page
Upward and downward intensities in a layer with
optical depth increasing from ^ to T, for a plane
parallel atmosphere.........................................................................
157
Relation of scattering, zenith, and azimuthal angles
for incident beam A and scattered beam B (after Liou
1980)................................................................................................
158
xvi
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ABSTRACT
Radiative transfer simulations are performed to determine how water vapor
and cloud constituents affect brightness temperatures (TBs) of moisture sounding
channels on the Advanced Microwave Sounding Unit (AMSU) and AMSU-like
instruments. The purpose is to promote a general understanding of passive top-ofatmosphere (TOA) TBs for AMSU moisture channels. The research is performed
in three phases. Phase 1 employs idealized profiles of water vapor, cloud liquid
water, and cloud ice as input to the radiative transfer model to investigate how
AMSU frequencies at 23.8, 89, 157, 176, 180 and 182 GHz respond to clear and
cloudy non-precipitating atmospheres. Phase 2 represents an effort to verify the
microwave radiative transfer approach using observed data from an aircraft-mounted
prototype radiometer, the Advanced Microwave Moisture Sounder (AMMS).
Passive microwave TBs near 92 and 183 GHz from an aircraft thunderstorm
overflight are compared with values calculated from radar-derived hydrometeors and
a modified proximity sounding. Phase 3 of the research employs output from a
mesoscale model simulation of the ERICA IOP4 cyclone in an effort to gain insight
about the synoptic interpretation of microwave water vapor image signatures.
Model soundings are used in the radiative transfer code to generate synthetic 182
xvii
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GHz imagery, as if a satellite were viewing the model atmosphere.
In Phase 1, cloud effects are considered in terms of five basic properties:
droplet size distribution, phase, liquid or ice water content, altitude, and thickness.
Both liquid and ice clouds are found to impact the TBs, particularly at higher
frequencies.
Contribution functions show that clouds depress TBs of the higher
frequency channels by suppressing or obscuring TB contributions from below.
Liquid water attenuates the upwelling radiance by absorbing and re-emitting at a
colder temperature, while cirrus ice attenuates through scattering. Clouds affect
TOA TBmeasurements near 183 GHz due to both the presence of hydrometeors,
and the saturated layers of water vapor.
The water vapor alone comprises a
significant percentage of the total cloud attenuation at this frequency. TBs at 23.8
GKz and 89 GHz are more strongly affected by "altostratus" liquid clouds than by
"cirrus" clouds for equivalent water paths. On the other hand, channels near 157
and 183 GHz are more strongly affected by ice clouds. Higher clouds have a
greater impact on T3 than do lower clouds.
In Phase 2, two methods for modeling particles in the radar-derived
thunderstorm ice canopy are contrasted.
The first is a "traditional" approach
employing Marshall-Palmer ice spheres.
The second or "alternative" method
partitions 20% of the ice water content into a Marshall-Palmer component for
xviii
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graupel and hail, and 80% into a modified gamma spherical particle size distribution
function representing ice crystals. Results from the alternative approach are found
to be superior to those from the traditional method in the anvil and mature
convective core. In the decaying convective region, the traditional approach yields
better agreement with observed magnitudes. However, neither method matches the
geometry of the observed TB depression associated with the decaying convective
core. This is likely due to the presence of graupel which is not detected as a
special signature in radar reflectivity, but does diminish TBs through scattering. TBs
at the relatively high microwave frequencies considered here are shown to be very
sensitive to the ice particle size distribution.
Phase 3 results of using mesoscale model soundings in the radiative transfer
code show that on average, 50% of the radiance contribution at 182 GHz for clear
atmospheres emanates from the upper 0.35 mm of precipitable water, while 90%
comes from the top 1.5 mm. The average 50% cumulative contribution level for
the model domain is 380-400 mb.
That is, on average, 50% of the radiance
emanates from above this level, while 50% comes from below. The simulated
water vapor channel image signatures at 182 GHz appear similar to observed 6.7
pm imagery. A warm radiometric feature is related to the upper level dry intrusion
accompanying the ERICA IOP4 storm. The feature occurs near the lower end of
a tropopause fold. The warmest TBs are skewed equatorward of the driest air due
to the strong tropospheric temperature gradient. Dry upper and middle tropospheric
xix
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air over the extremely dry formerly stratospheric air brought down by the
tropopause fold allow the simulated 182 GHz channel to sense the strong vertical
moisture gradient at the bottom edge of the upper level frontal zone. Hence, where
it "sees" lowest, the channel receives 50% of its radiance contribution from below
700 mb.
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CHAPTER 1
INTRODUCTION
Atmospheric moisture is one of the fundamental meteorological variables. Its
vertical and horizontal distribution profoundly affects the radiation, energy balances,
and weather conditions within the atmosphere. A new generation of operational
polar orbiting satellites being launched in the 1990?s has improved capabilities for
sensing and tracking water in both vapor and condensed forms. Some satellites will
carry a new passive atmospheric sensor known as the Advanced Microwave
Sounding Unit (AMSU). Until recently, most operational imaging and sounding
from space has been provided by instruments sensitive in the infrared (IR) and low
frequency microwave (MW) portions of the electromagnetic spectrum.
Recent
advances in technology, however, have extended the range of available channels to
the higher frequency bands of the MW regime, including those at 89 GHz and 183
GHz to be flown on the AMSU sensor. Compared to the IR domain, the MW
region is attractive for examining weather systems from space because it is less
affected by cloudiness. Hence, in areas where cirrus or other cloud layers might
preclude or contaminate the gathering of lower level IR information, MW
instruments can penetrate to provide alternative data.
1
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Satellite-derived products from the IR spectrum have been used extensively in
operational meteorology. Window channels, such as the 11.2 pm band, provide
information about terrestrial and cloud top temperatures from which storm structure
can be deduced. The 6.7 pm band, known as the "water vapor channel", senses the
upper few millimeters of precipitable water in the atmosphere (Chesters et al.
1982), thus revealing flow patterns within the middle and upper troposphere. Such
channels have been flown aboard the NOAA (National Oceanic and Atmospheric
Administration), TTROS (Television InfraRed Operational Satellite), and GOES
(Geostationary Operational Environmental Satellite) platforms.
MW analogues to the 11.2 pm and 6.7 pm channels, such as the 89 GHz and
183 GHZ bands, are particularly appropriate for tracking atmospheric moisture. The
first falls within a window region, and over land detects radiation attenuation by
liquid and ice particles associated with the precipitation process.
Signatures of
liquid and ice particles at 89 GHz can reveai important characteristics of storm
structures, in some cases similar to what is observed by ground-based radars pointed
at the upper parts of the storms (e.g., Heymsfield and Fulton 1988; Adler et al.
1990). Their ability to penetrate portions of thunderstorm anvils to delineate the
essential structures of convective cores adds a new dimension beyond those of
traditional space-based IR measurements. The three 183 GHZ channels lie within
a water vapor absorption region, and therefore respond to absorption and emission
of radiation by water vapor, as well as attenuation by liquid and frozen particles.
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3
The imagery from this band is related to water vapor distributions in clear as well
as cloudy atmospheres, and provides valuable information about meteorological
processes.
This research focuses on the physical and synoptic interpretation of moisture
signatures in AMSU imagery. It employs a radiative transfer modeling approach
to determine how vertical distributions of atmospheric constituents and properties
contribute to upwelling brightness temperatures (TB) in the 23.8, 89.0, 157.0, and
three 183 GHz frequencies.
In this work we refer to channels at various
frequencies within the 183 GHz water vapor absorption line generically as "183
GHz channels." Similarly we refer to window frequencies from previous sensors
at 85.5, 89.0, 90, and 92 GHz generically as 89 GHz channels. Specific channels
will be referred to by channel numbers or their specific frequency. The research
was performed in three phases.
Phase 1 is described in Chapter 2 and also in
Muller et al. (1994). It uses idealized cloud, temperature, and water vapor profiles
as input to a radiative transfer model to produce TB simulations at the previously
mentioned frequencies, for clear and cloudy non-precipitating atmospheres. Both
liquid and ice clouds are examined.
The purpose is to promote a general
understanding about the effects of water vapor and liquid and ice clouds on
individual TB measurements from AMSU and AMSU-like moisture sounding
channels. Phase 2 is presented in Chapter 3 and Muller et al. (1993). It represents
results of an effort to verify the MW radiative transfer approach using observed
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data. Radar-derived liquid and ice contents in conjunction with modified proximity
soundings are employed as input to the radiative transfer code to simulate upwelling
TBs along an aircraft flight track over a thunderstorm during COHMEX
(Cooperative Huntsville Meteorological Experiment).
The simulated TBs are
compared with measurements from an aircraft-mounted prototype instrument at
selected frequencies near those of AMSU. The TBs are shown to be very sensitive
to ice particle size distributions. Finally, phase 3 of the research is presented in
Chapter 4. Mesoscale model output for a simulation of ERICA IOP4 (Experiment
on Rapidly Deepening Cyclones over the Atlantic Intensive Observing Period 4) is
used as input to the radiative transfer code to simulate MW water vapor image
signatures near 183 GHz.
The simulation is used to gain insight about how
midlatitude weather systems are perceived at 182.3 GHz, and also to relate very
warm radiometric signatures to the upper level frontal system/tropopause fold that
accompanied the ERICA IOP4 cyclone.
A derivation of the Sobolev radiative
transfer approach (Xiang 1989) and description of Mie scattering (Wiscombe 1980)
and MW gaseous absorption (Liebe 1985) algorithms are presented in Appendix A.
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CHAPTER 2
SIMULATIONS OF THE EFFECTS OF WATER VAPOR, CLOUD LIQUID
WATER AND ICE ON AMSU MOISTURE CHANNEL BRIGHTNESS
TEMPERATURES
2.1. Introduction
New generations of polar orbiting weather satellites to be launched in the
1990s will have improved capabilities for sensing moisture in both vapor and
condensed forms. With channels near 89, 157, and 183 GHz, these satellites will
achieve higher vertical and horizontal resolution than the current Microwave
Sounding Unit (MSU) and will be less sensitive to clouds than infrared (IR)
sensors.
The new Advanced Microwave Sounding Unit (AMSU) will provide
operational weather information from the NOAA-Next series of satellites and also
research data as an instrument for NASA?s Earth Observing System (EOS). AMSU
consists of two components: AMSU-A includes temperature sounding channels and
two moisture channels at 23.8 and 89 GHz with nadir resolution of 50 km. AMSUB contains moisture sounding channels at 89, 150, 183.31�Q, 183.31�0, and
183.31 �0 GHz with nadir resolution of 15 km. Additionally, the Defense
s
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Meteorological Satellite Program?s (DMSP) SSM/T-2. (Special Sensor Microwave
T-2) instrument, launched in November 1991, contains frequencies similar to
AMSU-B, as will the DMSP?s future SSMIS (Special Sensor Microwave
Imager/Sounder). There also are plans for microwave (MW) sounders to be carried
on future geostationary platforms.
While AMSU data will provide operational temperature and moisture
profiles for use in numerical weather prediction, some channels will yield imagery
similar to those of current IR window and water vapor channels. For example, 89
GHz is a window frequency that can be considered an MW analogue to the 11 pm
IR window channel. An important difference is that the MW channel can partially
penetrate clouds; thus, aircraft measurements at 92 GHz have correlated with radar
echoes from the upper portions of convective storms (Hakkarinen and Adler 1988;
Heymsfield and Fulton 1988). Mugnai et al. (1993) give a detailed discussion of
the microphysicai constituents and source layers directly sensed by multifrequency
passive MW observations. The 183 GHz channels are located in a strong water
vapor absorption line and are MW analogues to IR channels in the 6.3 pm water
vapor vibration-rotation band. Imagery from frequencies sensitive to middle and
upper tropospheric water vapor produce brightness temperature (TB) signatures
associated with kinematic, dynamic, and thermodynamic atmospheric processes
(e.g., Petersen et al. 1984; Uccellini et al. 1985; Muller and Fuelberg 1990; Weldon
and Holmes 1991).
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Meteorologists traditionally have viewed MW channels as relatively
transparent to non-precipitating cloud water. However, Mugnai and Smith (1984),
Mugnai and Smith (1988), Mugnai et al. (1990), and Adler et al. (1991) have shown
that cloud liquid water significantly affects MW TBs. At the so-called millimeter
wave frequencies of 89, 157 and 183 GHz, TB effects from cloud liquid water can
be substantial (Isaacs and Deblonde 1987; Muller et al. 1992; Huang and Diak
1992).
Additionally, a crucial question regarding these high frequency MW
channels is how their measurements respond to cirrus ice clouds (e.g., Eyre 1990;
Wilheit 1990).
Much of the previous research on MW moisture channels has focused on
water vapor profiling. Wang et al. (1989) noted that channels near the weak water
vapor line at 22.2 GHz provide only enough sensitivity to measure total column
(precipitable) water vapor, and cannot be used over land where the high emissivity
obscures the atmospheric contribution.
They do have the advantage of being
relatively insensitive to non-precipitating clouds. The 183 GHz channels first were
investigated using radiative transfer simulations for clear sky water vapor profiling
(Schaerer and Wilheit 1979; Rozenkranz et al. 1982; Kakar 1983; Kakar and
Lambrigtsen 1984; Wang et al. 1983). More recent simulations have begun to
include the effects of cloud liquid water on retrievals (Isaacs and Deblonde 1987;
Eyre 1990; Wilheit 1990; Wang et al. 1989; Wang and Chang 1990; Diak et al.
1992). For example, Wilheit pointed out that clouds themselves can provide water
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8
vapor information for retrievals.
However, these studies have not examined
scattering from large liquid cloud droplets or effects of cloud ice. The current
research addresses these issues, and attempts to separate the contributions of cloud
water and water vapor within cloud layers to upwelling TBs.
The literature contains few studies about the impact of non-precipitating
cloud ice on millimeter wavelength channels.
Aircraft observations of
thunderstorms indicate that the 92 and 183 GHz frequencies are significantly less
sensitive to anvil cirrus than are corresponding IR measurements (Hakkarinen and
Adler 1988; Heymsfield and Fulton 1988).
Thus, many previous modeling
experiments have concentrated on the effects of precipitation-sized liquid and ice
particles (e.g., Wilheit et al. 1982; Wu and Weinman 1984; Yeh et al. 1990).
Nevertheless, spherical cirrus ice particles with radii ranging from 50 to 1000 pm
reduced TBs through scattering in simulations of the 118 GHz oxygen channel
(Weinman 1988). More recently, Muiier et al. (1993) used spherical particles to
demonstrate the importance of accounting for cirrus-sized ice in TB simulations near
90 and 183 GHz over a thunderstorm. Smith et al. (1992) discussed spherical ice
crystal parameterization for calculating TBs at MW frequencies up to 128 GHz over
a precipitating model thunderstorm. The shape of ice particles also affects TBs
(Evans and Vivekanandan 1990). They found that hexagonal plate sizes from 60
to 2000 pm produced simulated 157 GHz TBs that deviated from the equivalent
spherical approximation by up to 15癈.
The goal of our research is to explore
I
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the use of AMSU imagery for interpreting dynamic, kinematic, and synoptic
properties of the atmosphere.
This requires a thorough understanding of the
physical processes that lead to upwelling T3s, as well as the typical ranges and
sensitivities of those TBs to atmospheric constituents. The purpose of this chapter
is to promote a general understanding about the effects of water vapor, and liquid
and ice clouds on TBs from AMSU and AMSU-like moisture sounding channels.
We employ a conceptually simple framework utilizing idealized cloud, temperature,
and water vapor profiles as input to a radiative transfer model to produce TB
simulations for non-precipitating atmospheres. The frequencies being examined are
23.8, 89, 157, 176.31, 180.31, and 182.31 GHz.
After our simulations were
completed, 150 instead of 157 GHz was established as the AMSU-B channel to be
employed on the first few launches. However, this minor difference in frequencies
does not substantially affect the basic concepts discussed in this chapter.
Precipitation signatures for TBs near 89 and 183 GHz have been addressed
elsewhere (e.g., Wilheit et al. 1982; Heymsfield and Fulton 1988; Fulton and
Heymsfield 1991; Hakkarinen and Adler 1988; Adler et al. 1990; Adler and
Hakkarinen 1991; Yeh et al. 1990a; Muller et al. 1993) and are considered in
Chapter 3.
This chapter is presented in five major sections. Theoretical considerations
pertaining to the physical interpretation of AMSU moisture channel TBs are
presented in Section 2.2. Methodology about the radiative transfer model, cloud
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10
models, and idealized atmospheric profiles is described in Section 2.3. Section 2.4
gives results of TB simulations for both clear and cloudy atmospheres. Conclusions
are presented in Section 2.5.
2.2. Radiative transfer considerations
Upwelling top-of-atmosphere (TOA) TBs result from a complex combination
of radiative interactions with atmospheric constituents and the earth?s surface.
Important atmospheric radiative processes in the MW spectrum include gaseous
absorption and emission, and absorption, emission, and scattering from both liquid
and frozen hydrometeors. Important surface radiative processes include absorption,
emission and reflection. Contribution functions (CFs) quantitatively describe these
processes, and thus are useful for analyzing the TOA TB. They represent the
proportion of radiation per vertical kilometer of atmosphere that each layer
contributes to the total TB, and the fraction contributed by the surface. The CF
formulation employed here follows from the radiative transfer equation.
It is
analogous to Smith and Mugnai?s (1989) and Mugnai et al.?s (1993) "generalized
weighting function", but is calculated in terms o f radiance (intensity) rather than
irradiance (flux).
The radiative transfer equation for a plane-parallel atmosphere is
i
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11
V .^= I-J,
iz
(2.1)
where I is the radiance, x is the cumulative optical depth increasing from the TOA
downward, u is the cosine of the zenith angle defined as a positive quantity
throughout this paper, and J is the source function incorporating emission and
scattering. With the assumption of azimuthal independence, and with I expressed
in terms of brightness temperature, J is given by
( 2 .2 )
+ (1 - co(t �(t ) ,
where co, P, and T are the single scatter albedo, the average scattering phase
function for an ensemble of particles, and the environmental temperature, all at I.
P(x;p,pO describes the average contribution from radiation incident on particles at
arbitrary zenith angle u' that is scattered into the observation zenith angle, p. Thus,
the first term of (2.2) quantifies the scattering source while the second term
describes the source due to atmospheric emission.
A solution to (2.1) for upwelling radiation incorporating the boundary
condition for a Lambertian surface is
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12
where I -I is the average downwelling radiance at the surface expressed in terms
of brightness temperature, Ts is the surface skin temperature, es is the surface
emissivity, and t s is the optical depth of the entire atmosphere.
Smith and Mugnai (1989) showed that the contribution to the upwelling
intensity, Q, from a thin layer of optical depth, St, at altitude z, to radiance at the
"top" of the atmosphere, z = Zj., is
5T
C/z,p) = ? /fc ii) exp[ z i � ]t
V-
(2.4)
where i(z) represents the optical depth between the source level z and
r(z) = f zJ pea( z ) d z / ,
where fSei. is the volume extinction coefficient.
(2.5)
(2.4) essentially represents the
integrand of (2.3) (Wu and Weinman 1984). Physically, it expresses the radiative
sources from an atmospheric layer at height z, attenuated by the transmittance,
exp(-T/u).
For a Lambertian surface, the surface contribution to the upwelling
intensity, Q , is given by the first term of (2.3):
L
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13
/
Cc = [ ( l - e s) / i + e sTj]exp
\
?xs
( 2 . 6)
The first term on the right represents surface reflection of downwelling radiation,
while the second term denotes surface emission. The transmittance factor exp(-xs/iu)
attenuates the surface emission and reflection through cumulative extinction by the
optical depth. The sum of the contributions from all thin layers of optical depth,
plus the surface contribution, is the TOA TB that would be measured by a satellite:
T.= 'EC fz,ti+ C s,
0-.1)
i- 1
where N is the number of layers in the discretized model atmosphere. To obtain
the contribution functions, we simply calculate the fractional contributions by
dividing the C;s for each layer by the TOA Ts, and then normalize by the vertical
thickness of the emitting layer to obtain units of km'1
<2J0
Similarly, the fractional surface contribution is
i
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14
CF(z=0,p) = ? .
Tb
(2.9)
Like Mugnai et al.?s (1993) generalized weighting function, the CF is normalized
such that integrating it with respect to height, and adding the fractional surface
contribution, yields a value of 1.0. In contrast to traditional clear air weighting or
contribution functions of well mixed gases such as C 0 2 and 0 2, the vertical
structure of our CFs is highly variable due to the concentrations and altitudes of
water vapor, precipitation, and cloud liquid and ice particles (i.e., those constituents
that comprise the optical depth). (2.4) and (2.6) along with (2.2) indicate that TOA
Tbs
are determined by the temperature and emissivity of the emitting medium, the
scattering source, and the attenuation of these contributions by the intervening
optical depth between the sensor and sources. Attenuation (extinction) can occur
tV>mn crh
?> H crvm tion
or
o*
The electromagnetic spectrum for the MW region (e.g., Ulaby et al. 1981)
determines the radiative and gaseous interactions for the AMSU moisture channels.
The main atmospheric absorbing gases are water vapor and oxygen. Since the 23.8
GHz AMSU channel is located on the wings of a weak water vapor absorption line,
radiation absorption by water vapor is relatively small.
The 89 GHz channel
exhibits slightly greater water vapor absorption due to the continuum, but in a clear
atmosphere, surface contributions dominate both channels. This is very important
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15
for interpreting TBs, because surface emissivity in the MW region is highly variable.
On the other hand, the proximity of AMSU?s three 183 GHz channels to the center
of the 183.31 GHz water vapor absorption line determines their response to the
vapor. Each AMSU channel in this portion of the spectrum exploits the relative
symmetry of the line by measuring in bands on both sides to improve its signal-tonoise ratio. In clear conditions, the 183.31�0 and 183.31�0 GHz frequencies
respond mostly to absorption and emission by lower and mid-tropospheric water
vapor where pressure broadening makes contributions from the wings relatively
strong. Conversely, the 183.31 �0 GHz frequency measures radiation near the line
core, and thus is sensitive to even the small amounts of water vapor in the middle
and upper troposphere.
These effects strongly differentiate TBs of the three
channels in clear air. We will refer to frequencies near 183 GHz as "water vapor"
channels, while those at 23.8 and 89 GHz will be termed "window" channels.
O
T.
J
O C U C i i l l C ? U C l 1 VC u
<4�
a
Ia v x ta tlv ^ ii
oi
Cl�.
f K a
I
A
wilw i v n
fl
Uaw*
�
a
tx
number of fundamental cloud properties: altitude, vertical depth, and microphysical
characteristics such as phase, liquid or ice content, and particle size, shape, and
density.
These microp?n ysical parameters determine the optical properties for
ensembles of cloud particles. In terms of spherical particles, the ratio of the radius
r to the radiation?s wavelength X, known as the size parameter x, is given by
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16
x=2n�.
I
(2-10)
If we adopt x=0.1 as the cutoff separating Rayleigh particles from those where Mie
scattering becomes important (e.g., Wallace and Hobbs 1977), the full Mie solution
is required for sizes greater than approximately 200 pm at 23.8 GHz, and above 60
pm at 89 GHz. The cutoff for 157.0 GHz is approximately 40 pm, while for the
three 183 GHz channels it is approximately 30 pm. For a radius of 40 pm, the
difference in x between 176.31 and 182.31 GHz is only about 3%. This means that
all three 183 GHz channels respond nearly equally to hydrometeors. However,
contrasting gaseous absorption tends to differentiate TBs of the three channels.
Section 2.4 utilizes radiative theory to explain how specific atmospheric profiles
result in TOA TBs.
2.3. Methodology
a. Radiative transfer models
Our radiative transfer model is based on Xiang?s (1989) multilayer Sobolev
solution to the radiative transfer equation. It is a plane-parallel two-stream multiple
scattering solution for TB that is comparable to an Eddington model (e.g., Wu and
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Weinman 1984).
It has shown good accuracy when compared to multistream
models. An unpolarized version having 76 vertical layers at a resolution of 0.25
km and viewing at nadir has been employed for Chapter 2. Optical parameters for
polydisperse size distributions of spherical liquid and frozen hydrometeors were
calculated for each layer using Wiscombe?s (1980) Mie algorithm.
Complex
refractive indices of water were calculated according to Ray (1972) while those of
ice used the algorithms of Warren (1984). For computational efficiency, look-up
tables of the optical parameters were constructed based on temperature and liquid
or ice water content (LWC or IWC).
Gaseous absorption for each layer was
calculated from idealized soundings using an updated version of Liebe?s (1985)
algorithm.
Several simplifications shaped our radiative transfer approach.
All
hydrometeors were assumed spherical, homogeneous, and either liquid or frozen.
The density of frozen particles was set at 0.917 g cm'3. Tne calculations were
performed monochromatically at nadir viewing angle for frequencies representing
each AMSU moisture channel. For computational efficiency, only one side of the
two-sided 183 GHz channels was calculated (e.g., Kakar 1983). The Rayleigh-Jeans
approximation to the Planck function was applied so that upwelling radiance was
calculated directly in terms of T3. Since the atmosphere was assumed plane-parallel
for each sounding, the calculated TBs represent conditions everywhere within a
satellite footprint. Thus, as with Isaacs and Deblonde (1987), these calculations
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may represent an upper bound for the impacts of stratified clouds.
The nadir
viewing and spherical particle framework eliminate the need to consider
polarization.
b. Atmospheric profile and cloud models.
Experiments were performed using both clear and cloudy atmospheric
profiles. All temperature profiles employed the U.S. Standard Atmospheric lapse
rate of 6.5癈 km '1. Surface temperature (and consequently all temperatures above)
were adjusted according to the needs of the particular experiment. Moisture profiles
generally were defined by a constant background tropospheric dewpoint depression
(Tdd), with specific moist layers superimposed in some cases.
The atmosphere
within a cloud layer was specified to be saturated, that is, Tdd was set to zero.
Above the tropopause, the dewpoint temperature (Td) decreased linearly to a
constant value of -80癈.
Droplet size distribution functions (SDFs) for water clouds were calculated
using the modified gamma function (Deirmendjian 1969; Tampieri and Tomasi
1976; Falcone et al. 1979; Welch et al. 1980; Smith et al. 1992; Muller et al. 1993).
The modified gamma function yields a generic family of curves whose parameters
can be fit to actual particle distributions. Integrating the particle SDF and volume
formula with respect to radius gives LWC or IWC. A given size distribution can
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19
be scaled to a desired LWC by multiplying the droplet number concentration in
each radius category by the ratio of the desired LWC to the original LWC. The
modified gamma parameters used here described altostratus clouds having a mode
radius (radius of maximum particle frequency) of 4.5 pm (Falcone et al. 1979;
Isaacs and Deblonde 1987).
Cirrus clouds were specified by Starr and Cox?s (1985) bimodal version of
the modified gamma function which represents a large particle mode superimposed
on a small particle mode, similar to observations by Heymsfield (1975). The Starr
and Cox formulation gives crystal lengths rather than spherical radii. Therefore,
despite shortcomings of the spherical approximation, we transformed their SDFs to
spherical radii of equivalent mass using their exponential formulas for particle mass
as a function of crystal length. We employed their parameters for cirrus with small
and large particle mode lengths of 10 and 500 pm, respectively, retained their
equipartition between bullet rosette and column crystal habits, and assumed an ice
density of 0.917 g cm'3. This yielded SDFs for equivalent spherical particles with
mode radii of approximately 2 pm and 110 pm for the small and large crystal
modes, respectively.
Since much of the ice mass is concentrated in the small
particle mode of the bimodal distribution, we expect TBs to be affected somewhat
less by the spherical assumption than the calculations by Evans and Vivekanandan
(1990).
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20
2.4. Results
The results section describes the influence of atmospheric temperature, water
vapor, liquid and ice clouds, and surface emissivity on AMSU moisture channel
Tbs.
The experiments on clouds examine TBs in terms of five basic cloud
properties: droplet size distribution, phase, liquid or ice content, altitude, and
vertical thickness.
a. Clear atmospheres
AMSU moisture channels detect water vapor over a range of altitudes in the
troposphere. As an example, Fig. 2.1a shows CFs, fractional surface contributions,
and TOA TBs for an atmosphere having a 1000 mb temperature of 25癈, a lapse
rate of 6.5癈 km'!, and the uniform Tdd of 15癈 (solid lines in Fig. 2.Id). We have
labeled channels 1 through 6 in order of increasing altitude of maximum sensitivity
and frequency, that is, 23.8, 89.0, 157.0, 176.31, 180.31, and 182.31 GHz,
respectively. Figure 2.1a shows that channels 1, 2, and 3 all have strong surface
contributions, while channel 4 peaks near 790 mb and channels 5 and 6 peak near
590 and 440 mb, respectively.
Other aspects of Fig. 2.1 will be discussed in
Section 2.4b.
It is informative to examine how variations in water vapor, temperature and
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21
SFC EMI S.
GH:
7B=
GH:
TB=
GH:
18=
GH:
TB=
GH!
TB=
GHz
TB=
1- 23.8
2- 89.0
3-157.0
4-176.31
5-180.31
6-182.31
^
400
-
500
1-SFC
2-SFC
3-SFC
4-SFC
5-SFC
6-SFC
CONT
CONT
CONT
CONT
CONT
CONT
=
=
=
=
=
=
I VP = 0 . 0 0 0
0.882.
0.848
0.532
0.053
0.000
0.000
CONTRIBUTION
.5
.7
.8
0
4-176. 3-1
6-132.31
L*J 3 0 0
3-Sru
c/J 4 0 0
4 - SFC
5 - S FC CON'
6 - S FC CON
600
700
800 3 3 4
900 H A
1000
.1
.2
CON
UVP = 0 . 5 0 0
.3
.4
CONTRIBUTION
-
23.8
39.0
I VP = 0 . 0 0 0
f-
(KM- 1I
5FC E MI S .
GH:
TB=
T3=
TB=
TB=
F3=
13=
SFC CONi
[----
1
.
500
Kg m - 2 .6
1
SFC EMI S. = 0 . 9 0
GH:
TB= 2 7 5 . 8 6
TB= 2 7 7 . 8 9
GH:
GH:
TB= 2 8 6 . 2 2
3-157.0
T3= 2 7 5 . 3 9
4 - 1 7 6 . 3 1 GH:
T3= 261 . 24
5 - 1 8 0 . 3 1 GH:
TS =250.57
GH:
182.3
0.872
1- S F C CONT
0.836
2 - S F C CONT
3 - S F C CONT
0.505
0.041
4 - S F C CONT
5 - S F C CONT
0.000
6 - S F C CONT
0.000
ui 4 0 0
1000
.4
1
100
=0.90
275.62
277.68
287.17
279.52
265.46
251 . 8 7
100.0
-
90.0
-
80.0
-
70.0
.5
l
Kg m-2 -
'
.6
.7
?
1
.8
(KM-1 )
-
60.0
-
50.0
-
40.0
=0.90
276.98
276.97
273.97
267.14
259.43
250 4
0.810
0.498
0.234
0.018
0.000
2.000
Kg m-2
?
.1
.2
.3
.4
CONTRIBUTION
[ KM- 1)
Fig. 2.1. Contribution functions (km'1) for six AMSU moisture channels for (a)
uniform Tdd profile; (b) as in 2.1a but with a single moist layer; (c) as in 2.1b but
with 0.4 g m'3 liquid cloud water in the moist layer, and (d) Skew-T log p plot of
atmospheric temperature and dewpoint (癈) profiles corresponding to 2.1a, b, and
c; dashed line indicates moist layer. TBs and fractional surface contributions for
each channel are given on the right portions o f a-c.
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22
surface emissivity affect TBs from the AMSU moisture channels. Simulated TBs for
8 different clear atmospheric soundings are provided in Table 2.1. The table also
includes percentages of surface TB contributions and the pressure levels of CF
peaks. Table 2.2 describes characteristics of the idealized soundings. All employ
the U.S. Standard atmospheric lapse rate of 6.5癈 km-1. TB effects due solely to
water vapor can be investigated by changing the dewpoint profile while holding the
temperature constant. Sounding 1 represents a very moist July sounding with a
1000 mb temperature of 30癈 and a tropospheric Tdd of 5癈, while sounding 2
contains the same temperature structure, but is much drier (a tropospheric Tdd of
20癈).
Both use a "land" surface emissivity value of 0.9.
Decreasing the
tropospheric water vapor content allows the water vapor channels to see the lower,
wanner portions of the atmosphere. For example, CF peaks for channels 4, 5, and
6 of sounding 1 are 610, 450 and 330 mb, respectively. However, they move to
790, 600, and 460 mb for the drier sounding 2. This finding agrees qualitatively
with results of Schaerer and Wilheit (1979) and Wang et al. (1983). The greater
contributions from the lower, warmer layers increase TBs for channels 4, 5, and 6
by approximately 15 K (to 285, 271, and 256 K, respectively).
Tbs for channels 1 and 2 experience the opposite trend, decreasing by 6 and
9 K (to 280 and 282 K) for the drier profile. This response is due to the changing
contrast between emission from the relatively warm lower troposphere, and the
radiometrically cool surface background emission given by the product of es (0.9)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.1. Clear air brightness temperatures, surface contributions, and CF peaks for eight soundings at AMSU moisture frequencies.
sounoing rjumoer
1
2
3
4
5
6
7
8
TB (K)
Sfc. Contribution (%)
CF Peak (mb)
286.27
72.6
sfc
280.06
88.5
sfc
260.68
69.9
sfc
236.48
86.3
sfc
281.96
84.4
sfc
248.34
96.7
sfc
243.50
81.9
sfc
198.72
95.8
sfc
TB(K)
Sfc. Contribution (%)
CF Peak (mb)
290.70
59.2
sfc
281.82
85.7
sfc
276.07
57.0
sfc
241.68
83.4
sfc
284.70
79.5
sfc
248.62
96.4
sfc
251.94
76.8
sfc
199.28
95.6
sfc
TB (K)
Sfc. Contribution (%)
CF Peak (mb)
287.89
13.5
860
291.67
55.5
sfc
287.55
13.4
860
279.34
53.5
sfc
292.57
41.6
sfc
252.36
89.3
sfc
286.91
40.4
sfc
212.03
87.3
sfc
TB (K)
Sfc. Contribution (%)
CF Peak (mb)
270.87
0.0
610
284.95
6.3
790
270.87
0.0
610
284.89
6.3
790
280.38
1.8
720
262.16
60.1
sfc
280.37
1.7
720
248.38
57.8
sfc
TB (K)
Sfc. Contribution (%)
CF Peak (mb)
255.91
0.0
450
270.66
0.0
600
255.91
0.0
450
270.66
0.0
600
265.70
0.0
540
261.34
22.7
900
265.70
0.0
540
260.27
22.4
900
TB (K)
S fc . Contribution (%)
CF Peak (mb)
239.62
0.0
330
255.57
0.0
460
239.62
0.0
330
255.57
0.0
460
250.17
0.0
410
251.88
5.7
730
250.17
0.0
410
251.82
5.7
730
Channel
to
u>
24
Table 2.2. Characteristics for soundings used to create Table 2.1.
Sounding lOOOmbTemp. Tropospheric Tdd
(deg C)
(deg C)
Surface Emissivity
Comments
1
30.0
5.0
0.9
July, very humid,
"land" surface.
2
30.0
20.0
0.9
July, low humidity,
"land" surface.
3
30.0
5.0
0.7
July, very humid,
"ocean" surface.
4
30.0
20.0
0.7
July, low humidity,
"ocean" surface.
5
30.0
15.0
O.S
July, moderate humidity,
"land" surface.
6
0.0
15.0
0.9
January, low humidity,
"land? surface.
7
30.0
15.0
0.7
July, moderate humidity
"ocean" surface.
8
0.0
15.0
0.7
January, low humidity,
"ocean" surface.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25
and Ts (303.15 K) as 272.8 K. That is, as the profile dries, emission from warm
atmospheric water vapor in the lower layers decreases, and the TOA TB cools
toward that of the surface emission.
For large values of surface emissivity, esTs
is the dominant term of (2.6). In summary, while MW water vapor channel TBs
(i.e., those near 183 GHz) generally are warmed because drying enables them to
"see" to lower, warmer atmospheric layers, TBs of the MW window channels (23.8
and 89 GHz) are cooled because drying exposes more o f the radiometrically cool
surface contribution.
In agreement with Kakar and Lambrigtsen (1984), decreasing the surface
emissivity from the land value enhances the influence o f water vapor on TBs in
some channels. Soundings 3 and 4 are the same as 1 and 2, but employ a surface
emissivity of 0.7 to simulate the ocean. It should be noted that oceanic emissivity
is variable across frequency and also depends strongly on the physical condition of
the surface. Nevertheless, the single value of 0.7 has been applied here to all the
channels for convenience.
The work of previous authors (e.g., Wilheit 1978)
suggests that sea surface emissivities could be as low as 0.4 for lower frequency
channels such as 23.8 GHz (channel 1). This substantially affects calculated TBs.
Qualitatively, however, the value of 0.7 serves to generically illustrate the effects
of reducing emissivity.
In the case of soundings 3 and 4, the surface emission
(� ^ = 2 1 2 .2 K) is radiometrically colder than emission from the lower atmosphere,
causing channels 1 and 2 to be more sensitive to water vapor changes in the lower
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
26
levels. For example, TBs for channel 2 decrease by 34 K from sounding 3 to 4,
compared with only a 9 K decrease from sounding 1 to 2. This again is due to the
radiometric temperature contrast between emission from the warm lower
troposphere and the surface contribution.
That is, the change in atmospheric
emission from the moist to the dry sounding becomes greater in proportion to the
surface signal when surface emissivity is low. This increased TB sensitivity to
water vapor over the ocean is consistent with Kakar and Lambrigtsen (1984), Isaacs
and Deblonde (1987), and Wilheit (1990) who found that lower tropospheric water
vapor profiles from MW sounders with both water vapor and window channels will
be significantly less accurate over land surfaces than the ocean.
Channel 3 at 157 GHz represents a transition between window and water
vapor channels. Thus, in a very humid atmosphere (soundings 1 and 3 of Table
2.1) it behaves more like a water vapor channel with its CF peaking at 860 mb for
iX)u1a "land" \~0 9) and. "oceanic" (=0.7) surf2.es crniss^v'tiss
^or the dner
profile (soundings 2 and 4), channel 3 responds more like the window channels
with its CF peaking at the surface and its surface contributions exceeding 50% for
both emissivities.
Channels 4-6 show little or no impact from these emissivity
changes.
Combining the effects on TBof temperature changes with those produced by
water vapor variations complicates TB interpretation.
Sounding 5 represents a
middle latitude July profile with a 1000 mb temperature of 30癈, a 15癈
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tropospheric T^, and a "land" surface with an emissivity of 0.9.
Sounding 6
denotes a January profile with a 1000 mb temperature of 0.0癈, a 15癈 tropospheric
Tdd, and surface emissivity of 0.9. Although these two profiles represent distinctly
different clear atmosphere cases, their TBs at 182.31 GHz (channel 6) differ by less
than 2 K. Conversely, there is a 40 K difference at 157.0 GHz (channel 3). The
decrease in water vapor from profile 5 to 6, by itself, would cause significant
warming in channel 6 by lowering the CF peak from 410 mb to 730 mb. However,
this effect is nearly compensated by the 30癈 cooling of the temperature profile.
Thus, channel 6 senses the temperature of water vapor in the upper troposphere of
sounding 5, but senses the temperature of the lower tropospheric water vapor in
sounding 6, and even receives 5.7% of its TB contribution from the surface. Wang
et al. (1992) recently exploited the relative transparency o f dry northern latitude
atmospheres to calculate precipitable water from aircraft measurements near 183
GHz. Channel 4 is sensitive to conditions nearer the surface, receiving only a 1.8%
surface contribution with sounding 5, but 60.1% from the surface for sounding 6.
Only CFs for channels 5 and 6 do not peak at the surface for cold, dry sounding 6.
Again, surface emissivity exerts a profound influence on T3s from the lower
frequency AMSU moisture channels. Soundings 7 and 8 are identical to soundings
5 and 6 (Table 2.2), but use an "oceanic" surface emissivity of 0.7. The TB spread
between soundings 7 and 8 (Table 2.1) for channels 1 through 5 is greater than that
from soundings 5 and 6 because the drier sounding aiiows much more of the
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surface contribution to come through. The TB spread for channel 6 is approximately
the same as before. This suggests that surface effects might be separated from
atmospheric effects by comparing the variability of TBs from surface sensitive
channels to those of water vapor sensitive channels, or even oxygen channels from
AMSU-A.
It is useful to know the heights at which moist layers begin to affect TBs of
the various AMSU moisture channels. Figure 2.2 shows TBs as a function of the
height of a moist layer extending from the surface up to that level. These heights
increase in increments of 1 km for surface emissivities of 0.9 (Fig. 2.2a) and 0.7
(Fig. 2.2b). The temperature at 1000 mb is set to 25癈 in both cases, while the Tdd
is 15癈 within the dry tropospheric background layer and 3癈 within the moist
layer. Above the tropopause, Td decreases linearly to -80癈, where it becomes
constant.
PrvnciH/arinor rhp l^n/i~ mcp
<j 0 9a chnu/Q that rnannpl f \ T\,q hpcrin rn
~ ~ fircf -hi-o*----??
---- --------- - ~
decrease as the top of the moist layer rises above 5 km, dropping 10 K over the 10
km range of heights. Channel 5 TBs start to decrease when the top of the moist
layer reaches 2 km, while channel 4 already is decreasing above 1 km.
Like
channel 6, channels 4 and 5 decrease by approximately 10 K over the entire range
of altitudes.
One should note that the curve for channel 4 begins to level off
between 9 to 10 km, that is, it shows little sensitivity to moisture above these
levels. Channels 2 and 3 are unaffected by water vapor added above 7 km, while
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29
300
SFC EMIS
_ 290
. 280
y 270
co
FI 260
m 240
230
1
3
5
7
HOIST LAYER TOP
9
11
(km)
300
SFC EMIS
_ 290
. 280
y 270
co
LU
^ 260
= 250
CD
?
?I
m 240
230
3
7
HOI ST LAYER TOP
9
11
(km)
Fig. 2.2. T b (K) for a clear atmosphere as a. function of the height (km) of the top
of a moist layer extending from the surface to the given altitude for (a) surface
emissivity of 0.9; and (b) surface emissivity of 0.7.
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
channel 1 appears insensitive to the addition of water vapor above 4 km.
Unlike the higher frequency channels, TBs for channels 1 and 2 increase
slightly as water vapor is added below approximately 4 km (Fig. 2.2a). For a moist
layer between 0-1 km, the surface contributions of channels 1, 2, and 3 are 84%,
75%, and 33%, respectively. Thus, they are affected more by changes in surface
emissivity and temperature than are water vapor channels 4, 5, and 6. When the
depth of the surface based moist layer increases to 3 km, surface contributions for
channels 1, 2, and 3 decrease to 79%, 67%, and 22%. Since this deeper layer still
is radiometrically warmer than the surface background EsTs of 268 K, it contributes
to warmer TBs for channels 1 and 2 (approximately 2 K). Conversely, channel 3
has a sufficiently small surface contribution so that the atmospheric contribution
dominates. Thus, adding moisture to cooler layers of the atmosphere produces
cooler T bs.
previously noted, effects nre more evident over ,Toce3.nMsurfaces with
an  of 0.7 (Fig. 2.2b). Channels 4, 5, and 6 are virtually unaffected by the surface
contribution, and thus the changed surface emissivity. However, channels 1 and 2
now show much greater sensitivity than before (Fig. 2.2a) to the low level v,rater
vapor changes. For example, TBs for channel 1 increase from 241 K for a 1 km
thick moist layer to 248 K for a 3 km thick layer. This increase again is due to the
contrast between the radiometrically warm moist layer and the radiometrically cool
surface background of 209 K. Thus, as described earlier, Fig. 2.2 confirms that
I
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31
channels 1 and 2 are much more sensitive to atmospheric water vapor for an
oceanic case.
b. Effects o f liquid, clouds
1) CLOUD LIQUID WATER VERSUS CLOUD WATER VAPOR
Section 2.4b examines how various properties of liquid water clouds affect
TOA T bs. We begin by separating TB effects due to cloud water from those strictly
due to the presence of the saturated layer within the cloud. Our procedure is to first
superimpose a saturated layer (Fig. 2. Id, dashed) and then altostratus cloud on the
original uniform dewpoint profile of Fig. 2. Id (solid). Figure 2.1b shows CFs when
the saturated layer (0癈 Tdd, but no cloud water) is added between 5 and 6 km (570490 mb). The CFs for all channels gain a primary' or secondary peak within the
moist layer. The greatest TBchange occurs in channel 5, from 265 K with no moist
layer to 261 K. Conversely, channel 6 shows little change because a substantial
portion of its radiance emanates from above the 5-6 km layer.
The saturated layer produces characteristically distinct TB changes at 23.8
GHz (channel 1, Figs. 2.1a and b) compared with those at higher frequencies.
Specifically, while the layer attenuates TBs near 157 and 183 GHz (channels 3-6)
by absorbing and re-emitting the radiation from below at cooler temperatures, TBs
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
for channel 1 increase slightly (from 275.62 K to 275.86 K). Since the temperature
of the humid layer ranges from approximately 268 K at its bottom to 260 K at the
top, emission alone cannot explain the warmer TB.
However, examining the
different components of TOA TBs described by the CF formulation (Section 2.2)
does provide an explanation, and reveals the balance of attenuating and emitting
processes that can lead to warmer or cooler TBs by adding a moist layer. Below
5 km, atmospheric contributions (given by (2.4)) are slightly smaller for the profile
containing the saturated layer than for the drier profile. While the radiative sources
for these layers do not change between the different profiles, the optical depth x
between them and the satellite does become slightly greater with the addition of the
absorbing medium (the moist layer), thereby decreasing the transmittance exp(-x/p).
Since the transmittance above 6 km is virtually the same for both profiles, the
greater optical depth 8x of the saturated layer between 5 and 6 km contributes more
up-welling radiance than does the uniform profile for the same layer. Above 6 km,
atmospheric contributions from corresponding layers are essentially equivalent.
Thus, in terms of upwelling atmospheric contributions, the moist layer adds
radiance, but also attenuates radiance emanating from below by an even greater
amount. By themselves, these processes would lead to cooler TBs in the presence
of a saturated layer.
Therefore, it is the surface boundary contribution (2.6) that leads to the
warmer TOA TBfor channel 1. Specifically, since surface emission esTs is constant
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
for the two profiles (Fig. 2.Id), only the surface reflection term can account for the
warmer TB. In fact, before attenuation, 6.13 K of radiance reflects from the surface
of the moister profile compared with 5.68 K from the uniform Tid profile. After
attenuation by the entire atmosphere, surface reflection contributes 5.36 K versus
5.03 K, respectively. Thus, it appears that the additional downwelling radiation
emitted from the saturated layer and then reflected back upward and transmitted to
the satellite, supplies just enough radiance to compensate for the increased
attenuation by that moist layer. The consequence for image interpretation is that
the addition of water vapor to a cool layer may slightly warm the TBs of channels
having a large surface contribution. However, this phenomenon would not be likely
in the higher frequency water vapor absorption channels.
Clouds exert a major influence on the CFs and TBs of the AMSU moisture
channels. Superimposing an altostratus cloud with LWC of 0.4 g i r r and mode
radius of 4.5 pm on the saturated layer between 5 and 6 km (Fig. 2.1c) depresses
Tbs in channels 2-6, but increases the TB in channel 1. As simulated in Isaacs and
Deblonde (1987), Muller et al. (1992), and Diak et al. (1992), the cloud water
further deforms the contribution (or weighting) functions from their clear air
counterparts (Fig. 2.1a). Analyzing atmospheric and surface contributions as done
above provides a similar explanation for the warming in channel 1. Scattering can
be neglected because in this case, volume absorption coefficients at 23.8 GHz are
six orders of magnitude larger than volume scattering coefficients, and four orders
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
larger at 182.31 GHz. Cloud water has a substantial impact on channels 3 and 4,
reducing TBs by 12 and 8 K, respectively from those of the saturated layer alone
(Figs. 2.1b and c). In going from a sounding with no moist layer to one having a
moist layer plus cloud, the TBs in channels 3 and 4 decrease by 13 K and 12 K,
respectively (Figs. 2.1a and c). Thus, in channel 3, the moist layer alone accounts
for only 7% of the total decrease, while cloud water contributes 93%. However,
for channel 4, located on the wings of the 183 GHz water vapor absorption line, the
moist layer yields 33% of the depression, while cloud water accounts for 67%.
Although the TB depression from water vapor and clouds is small in channel 6
because of overlying water vapor, the 1.3 K TB decrease from the saturated layer
comprises 89% of the total decrease (1.46 K) due to both water vapor and cloud
water. The important point is that clouds can have a substantial impact on AMSU
moisture channel TBs; however, a significant portion of that effect is due to the
vapor within the saturated. c*ouci laye7*
2) EFFECTS OF DROPLET MODE RADIUS AND SIZE DISTRIBUTION
We now address an issue that has received little previous attention, that is,
MW radiative scattering by droplets smaller than precipitation size. Microwave
modelers often have treated cloud water in terms of absorption/emission processes
based on liquid water content using the Rayleigh approximation (e.g., Ulaby et al.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
1981). Falcone et al. (1979) have shown that this is appropriate for small particle
sizes at microwave frequencies (e.g., drop size distributions with mode radii less
than 10 pm).
However, Fraser et al. (1975) showed that while the Rayleigh
approximation at 300 GHz is valid for fair weather cumulus, it is not adequate for
cumulus congestus at this frequency. Mugnai and Smith (1988) have indicated that
a large droplet mode can cause appreciable MW extinction due to Mie scattering,
and Wiscombe et al. (1984) asserted that very large cloud droplets may be more
common than previously thought
To further explore the issue of Mie scattering from large cloud droplets, we
have investigated radiative effects from a range of SDFs. SDFs having mode radii
increasing in multiples of 10 pm through 100 pm were prepared by adjusting values
of the original altostratus distribution used in Fig. 2.1c. Each SDF then was scaled
to yield a constant LWC of 0.41 g m'3, equivalent to the unsealed altostratus drop
distribution of* Fslccnc st 2I (1979)
Tlis rssu^tin.^
cnnQi with a
mode radius of 4.5 pm are shown in Fig. 2.3a. These clouds were placed in the
600-500 mb layer for the TB simulations.
The effect on TE of increasing the mode radius is seen in Fig. 2.3b.
Channels 3 and 4 are affected significantly at mode radii larger than about 20 pm.
Effects on channel 2 are important beyond 30-40 pm. Only absorption/emission is
significant for drop sizes in the Rayleigh regime, that is, attenuation is proportional
to LWC, which we hold constant. Therefore, the varying TBs indicate that Mie
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36
CLOUD DROP S IZ E D IS T .
TB V S .
MODE RADIUS
4-176.31
5-100.31
6-182.31
GHz
GHz
GHz
280.
'.1E-02
o
Z.1E-03
o
o
c: 240.
O.1E-05
230.
. I E - 0 1 . 1 E+0 0 , 1E*01 . 1E+02 .1 E� , 1 E * 0 4
RADIUS
0
20.
( mi c r o n )
EXTINCTION COEFF.
100
40.
MODE RADIUS
60.
80
(MICRON)
SCATTERING COEFF.
30
90
25
80
e
f-:
*
70
20
60
s
50
5
x
w r%
ou
30
x
L
d
Q
uU5
m
20
10
0
5
0
0
100.
200
300.
DROPLET RADIUS
400.
turn)
500
0
100
200.
300.
DROPLET RADIUS
400.
500
(urn)
Fig. 2.3. (a) Droplet number concentration as a function of radius interval (number
of droplets c m 3 pm '*) for various theoretical cloud droplet SDFs. (b) Tg as a
function of mode radius (pm) of each SDF in 2.3a. (c) Extinction coefficient (xlO-7
m'1) as a function of droplet radius (um) for each SDF in 2.3a. The mode radius
(pm) of the corresponding SDF is given on the right portion of each curve, (d) As
in 2.3c but for scattering coefficient.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37
scattering becomes important for these drop distributions. Changes in mode radius
have little impact on channels 5 and
6,
only because their effects are muted by
absorption/emission from intervening water vapor above cloud top. Channel 1 is
unaffected by the varying droplet distributions due to its lower frequency.
To fully understand these results, it is necessary to relate scattering and
extinction to the entire droplet spectrum for each SDF, and not simply to its mode
radius. Therefore, extinction and scattering coefficients for channel 3 (157 GHz)
were plotted as a function of droplet radius for each SDF in Fig. 2.3a (Figs. 2.3c
and d). These coefficients are based on a temperature of 268 K (that of supercooled
droplets near the middle of the cloud layer) and an LWC of 0.41 g m'3. From left
to right, each curve in both panels corresponds to SDFs with progressively larger
mode radii. Figures 2.3a and d reveal an important result: Though there are fewer
large droplets, the greatest scattering for each curve occurs at radii much larger than
the mode radius for that particular SDF. For example, the scattering coefficient
curve corresponding to a mode radius of 40 pm peaks near 90 pm, while the curve
corresponding to a mode radius of
100
pm peaks near
210
pm.
Greatest values of the extinction coefficients (Fig. 2.3c) are at least four
times larger than those of the scattering coefficient (Fig. 2.3d). Thus, absorption
is the dominant extinction process for all the SDFs, but scattering becomes
increasingly important for the larger particle sizes.
Extinction peaks occur at
somewhat smaller radii than for scattering, but still are associated with the large
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droplet tails.
For example, the peak extinction for a 60 pm mode radius SDF
occurs near 100 pm.
Summarizing these results, scattering becomes important
beyond a mode radius of 20 pm at 157 and 183 GHz, and beyond 30-40 um at 89
GHz, due mainly to droplets larger than the mode radius in the tail of the
distributions. Rauber (1992) presented a droplet spectrum for an orographic cloud
with mode radius of 30 pm, and Pruppacher (1981) quoted several studies showing
mode radii between 30-40 pm for tropical cumulus and orographic clouds. We
have not found examples in the literature of droplet spectra with mode radii larger
than 30-40 pm.
Nevertheless, for millimeter sounding channels and droplet
distributions in the 30-40 pm mode radius range, current results suggest that it may
be important to go beyond the Rayleigh approximation, including scattering in the
radiative calculations to deal with the large droplet portions of the SDFs. This may
be especially important for possible future MW instruments at frequencies even
lu g iic i
L
10 9
m a n
i o j
3) CLOUD LIQUID WATER CONTENT, ALTITUDE, AND THICKNESS
Cloud water content also is an important variable affecting TOA TBs in the
AMSU moisture channels. Figure 2.4 relates TBs to cloud water content expressed
in terms of liquid water path (LWP). These LWPs range from 0.0 to 0.625 kg m'2
for altostratus clouds that are l km thick. Figure 2.4a is for supercooled clouds
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39
290
c_ 270
co 260
co
� 240
6 - 7 km _
230
0.0
.1
3
.2
.4
L I Q U I D WATER PATH
290
I ? "T
? 3 - -3?
l
I
? ?0
~ 280
M
CL
7
(Kg m - 2 )
I
J,
?- 4 - - 3 ?3
4
*
?
-
X
6
5
4
270
- 5 - ?5-?5----9
s - 5 -5-
LlJ
� 260
CO
LlJ
jz :
-
250
6 ? -6- - 6
6
6
6 ? 6? 6
6
-6
CD
D 240
2-3 km.
230
0 .0
i
i
.1
.2
.3
i
i
.4
.5
__
.6
LIQUID WATER PATH (Kg m- 2]
Fig. 2.4. T b (K) as a function of liquid water path (kg m ) for altostratus clouds
between (a) 6-7 km altitude; and (b) 2-3 km.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
between 6-7 km altitude (490-410 mb), while results for similar clouds between 2-3
km (820-690 mb) are given in Fig. 2.4b. The LWPs correspond to LWCs ranging
from 0.0 g m'3 (i.e., a saturated layer, but no cloudwater) to 0.50 g m '3 in
increments of 0.05 g m?3. The clouds are superimposed on a sounding with a 1000
mb temperature of 25癈 and tropospheric background Tdd of 15癈 (except for the
cloudy layer).
TBs for all channels are greater for the warmer 2-3 km cloud (Fig. 2.4b) than
for the colder 6-7 km cloud (Fig. 2.4a). In addition, TBs for channels 3 through
6
of the 6-7 km case are affected more strongly by changes in LWP, generally
decreasing with increasing LWP. For example, the channel 4 TB for the 6-7 km
cloud with an LWP of 0.062 kg m'2 (0.05 g m'3) is 274 K. This value decreases to
263 K for an LWP of 0.625 kg m '2 (0.5 g m'3). For a 2-3 km cloud, the channel
4 Tb at 0.062 kg irf 2 is 276.5 K, but decreases only slightly to 275.5 K at 0.625 kg
m'2. Thus, Tb variabiiiiy due to variations in water content is enhanced by cloud
altitude.
CFs clarify why cloud water variations at higher altitudes have a greater
impact on channel 3 through
6
TBs than do variations at lower altitudes. Figure 2.5
shows CFs for clouds between 6-7 km (490-410 mb, Figs. 2.5a and b) and 2-3 km
(820-690 mb, Figs. 2.5c and d), with LWPs of 0.062 kg m'2 and 0.625 kg m '2. For
channels 4, 5, and especially
6,
much of the TB contribution emanates from water
vapor above the 2-3 km cloud (i.e., above 690 mb), and thus is affected little by the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
SFC E M I S .
GHz
T9 =
2- 89.0
TB=
3-157.0
TB=
176.31
T3 =
TB=
5-180.31
6-182.31
TB=
EMIS
=0.90
2 7 5 .84
277.99
284.15
274.15
259.77
248.95
1- 23.8
2- 89.0
3-157.
4-176.3
5-180.31
b-182.31
1- S F C CONT = 0 . 8 6 6
2 - S F C CONT = 0 . 7 8 6
3 - S F C CONT = 0 . 4 7 4
in 4 0 0
Ld
300
x
400
4- SFC CONT = 0 . 0 4 2
1 - S F C CONT
2 - S F C CON'
3 - S F C CON'
4-SFC
5 - S F C CONT = 0 . 0 0 0
6 - S F C CONT = 0 . 0 0 0
LVP = 0 . 0 6 2
CONT
CON i
Kg m- 4 -
0.625
1000
.2
.3
.4
CONTRIBUTION
.7
.6
.8
(KM-11
CONTRIBUTION
100 i
100
SFC E MI S .
GHz
TB=
GHz
TB=
GHz
TB=
157.0
TB=
4 - 1 7 6 . 3 1 GHz
GHz
TB=
180.3
73=
6 - 1 6 2 . 3 1 GHz
200
u
.5
1-SFC
2-SFC
3-SFC
4-SFC
5-SFC
6 -SFC
380
in
in 4 0 0
o- 5 0 0
900 ?
CONT
CONT
CONT
CONT
CONT
CuNT
=0.90
277.46
281.62
286.75
276.54
265.05 251.86
-23.8
-89.0
-157.0
4-176.31
2 00
0.841
0.7401
0.357
u j
0.014 J
0.000
|
300
in 4 0 0
[KM-i:
SFC E M I S . = 0 . 9 0
TB= 2 7 9 . 1 0
GHz
GHz
TB=285.98
T 3=282.94
GHz
78= 2 7 5 . 4 7
GHz
73= 2 6 5 . 0 0 T3= 251.86
1-SFC
2-SFC
3-SFC
4-SFC
5-SFC
0.000
CONT
CONT
CONT
CONT
CONT
=
=
=
=
=
0.799
0.445 "
0.131
0 . 0 0 5 _j
0.000 !
oao I
LWP = 0 . 0 6 2
.1
.2
.3
.4
CONTRIBUTION
IKM-1 )
CONTRIBUTION
(KM-1 !
Fig. 2.5. Contribution functions (km-1) for six AMSU moisture channels for
altostratus clouds between (a) 6-7 km (490-410 mb) with LWP of 0.062 kg r n ( b )
6-7 km (490-410 mb) with LWP of 0.625 kg m'2; (c) 2-3 km (820-690 mb) with
LWP of 0.062 kg m'2; and (d) 2-3 km (820-690 mb) with LWP of 0.625 kg m'2.
TBs and fractional surface contributions for each channel are given on the right
portion of each panel.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
cloud water content. With channel 6 , virtually all of the TBcontribution is from the
atmosphere above the 2-3 km cloud, that is, the cloud is virtually obscured by the
intervening water vapor. In addition, for channels 3 and 4, the higher, colder cloud
provides greater radiometric contrast with the low level water vapor contributions
and warm surface background. This results in greater TB changes from increasing
cloud LWP at high altitude. Recall that the contribution curves are normalized, that
is, the integrated area under the CF curves plus the fractional surface contribution
equals 1.0. It is clear from Figs. 2.5a and b that increasing the LWC of the higher
cloud suppresses TB contributions from below; that is, the cloud partially obscures
the lower atmosphere. For example, at 0.062 kg m '2 (Fig. 2.5a), the channel 4 CF
for the higher cloud contains two peaks: a value o f
0 .2
km"1 within the cloud, and
the value 0.17 km "1 at its "natural" peak near 800 mb, well below cloud height.
When LWP is increased to 0.625 kg m "2 (Fig. 2.5b), the channel 4 CF peak within
the cloud increases to a value of 0.7 km'1, while the 800 mb peak decreases to
approximately 0.07 km"1, with significantly less area under the lower part of the
curve than for the drier cloud.
T bs for channels 1 and 2 (23.8 and 89.0 GHz) respond differently to
increasing cloud water (Fig. 2.4) than do the higher frequency moisture channels.
Channel 1 TBs for both the low and high cloud cases increase less than 2 K with
the addition of more cloud liquid water. For a 2-3 km cloud (Fig. 2.4b) channel 2
Tbs increase from 282 K at 0.062 kg m "2 to 286 K at 0.625 kg m"2, while for the 6-
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
43
7 km cloud (Fig 2.5a) channel 2 TBs decrease by
6
K. Just as with water vapor in
a clear atmosphere, the addition of cloud liquid water to a relatively warm layer of
the atmosphere yields radiative emissions that contrast with those of the
radiometrically cooler surface background contribution. And as cloud liquid water
increases for the lower cloud, peak values of corresponding CFs for channel 2 (Figs.
2.5c and d), increase from 0.12 km '1 to 0.46 km'1 within the cloud layer, while the
surface contribution is suppressed from 74% to 45%.
We next examine further details about how changes in cloud altitude affect
T b s.
Figure 2.6 contains plots of TB variations as a function of the tops of
altostratus clouds with thicknesses of 0.5 km (Fig. 2.6a) and 3 km (Fig. 2.6b). Each
cloud contains 0.2 g m'3 of cloud water corresponding to an LWP of 0.150 kg m '2
for the 0.5 km thick cloud, and 0.650 kg m '2 for the 3 km thick cloud. It should
be noted that the LWPs may appear slightly larger than suggested by the LWC and
the nominal thickness of the cloud due to vertical averaging for layer quantities in
the numerical algorithms.
Moving the top of the 0.5 km cloud upward from 3 km to 7 km (Fig. 2.6a)
cools 7 Bs in all channels, but by relatively small amounts.
For example, the
channel 1 TB decreases only about 1 K, while those of channels 3 through 5
decrease by 4 to 5 K. In contrast, cloud top temperatures decrease 26 K over this
range of heights. Thus, variations in equivalent blackbody temperatures measured
by a co-located IR sensor should greatly exceed TB variations measured by AMSU.
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
44
290
-
280
a
270
-r
LlJ
290
2
280
獵O260
LU
?
250
0.5
Km AS
CLD
230
230
4
2
CLOUD TOP
2
6
HEI GHT
8
/
2
( Km)
3
4
CLOUD TOP
290
290
280
C 280
o. 2 7 0
c l
5
6
HEI GHT
8
/
( Km)
270
UJ
玦n 260
260
L lI
252
c
a
-
240
0.5
Km L s y e r
230
Km L d y e r
230
2
3
4
5
6
MOI ST LAYER TOP HEI GHT
7
2
(Km)
3
4
MOI S T LAYER
5
6
7
HEI GHT TOP
8
( Km)
Fig. 2.6. Tb (K) as a function of (a) cloud top height (km) for a 0.5 km thick
altostratus cloud; (b) as in 2.6a for a 3 km thick cloud; (c) moist layer top height
(km) for a 0.5 km thick clear but saturated iayer; and (a) as in 2.6c but for a 3 km
thick layer.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Compared to the 0.5 km cloud, TBs for the 3 km thick cloud (Fig. 2.6b) decrease
more steeply with increasing cloud height. For example, channel 1 decreases over
5 K while channels 2 and 3 cool nearly 15 K.
Channels 4 and 5 decrease
approximately 13 K and 9 K. TB variations in channel 6 , the most vapor sensitive
frequency, are muted by overlying water vapor for both cloud thicknesses.
In
comparing effects of 0.5 km and 3 km thick clouds, it is interesting that slopes of
the Tb curves for channels 1 and 2 of the thick clouds change mostly by warming
at the low end of the altitude curve. This response is different than that of IR
window measurements which would be more closely associated with the cloud top
temperature for both clouds. Slopes of the TB curves for channels 3 through
6
are
steepened mainly by cooling the TBs at the higher altitude cloud tops.
The effects of varying cloud altitudes (Figs. 2.6a and b) should be compared
with those due strictly to water vapor, that is, saturated layers with zero cloud water
(Figs. 2.6c and d). Moving the top of a 0.5 km saturated layer from 3 km to 7 km
(Fig. 2.6c) yields TB variations ranging from 0.25 K of warming in channel 4 to
approximately 3 K of cooling in channel 5. Cooling occurs in all channels for a 3
km thick moist layer (Fig. 2.6d).
In general, slopes corresponding to altitude
changes of the moist layers are smaller than those due to changes in cloud height.
The cloudy case T 3 curves for channels with strong surface contributions (1 and 2)
begin at warmer values than those for clear moist layers. However, in the more
absorptive channels (4 through
6 ),
the cloud case TBs nearly equal their clear
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
counterpans at the lower altitudes, but they then cool even more as the cloud is
raised. Thus, cloud water accounts for some, but not all of the height related T 3
variations. Height variations of saturated layers alone exert a substantial influence
on TBs, and these effects are more pronounced for thicker layers.
Surface emissivity varies much more at MW frequencies than for IR
channels. Figure 2.7 shows how changing surface emissivity affects T3s of the
AMSU moisture channels.
The three panels represent an atmosphere with a
saturated moist layer but zero cloud water (Fig. 2.7a), a cloud with LWC of 0.1 g
m'3 (LWP of 0.125 kg m"2, Fig. 2.7b), and a cloud with LWC o f 0.5 g m'3 (LWP
of 0.625 kg m?2, Fig. 2.7c). All clouds and moist layers are between 4 and 5 km
altitude (630 to 570 mb). Surface emissivity increases in increments of 0.1 from
0.5 to 0.9. Surface emissivities of 0.5 to 0.7 correspond to those found over the
ocean while 0.9 indicates land. Channels 1 and 2 are most strongly affected by
surface emissivity variations whereas, consistent with Kakar?s (1983) results for
clear air, the water vapor absorption channels (channels 4, 5, and 6 ) are virtually
unaffected. For example, TBs for channel 1 range from 196 K at es=0.5, to 276 K
at =0.9 for the single moist layer with no cloud water (Fig. 2.7a). Adding 0.125
kg m '2 of cloud water (Fig. 2.7b) slightly diminishes the effect o f surface emissivity
variations in channels 1, 2, and 3. Increasing the cloud water content to an LWP
of 0.625 kg m'2 (Fig. 2.7c) further diminishes the emissivity effect by obscuring the
surface contribution, particularly in channels 2 and 3.
r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
*
270
250
8
6
1 .0
SURFACE EMI S S I VI TY
*
270
250
21 0
190
4
6
8
SURFACE EMI S S I VI TY
T
*
I
270
�2 5 0
u
230
.4
.6
.8
1.0
SURFACE EMI S S I VI TY
Fig. 2.7. T 3 (K) as a function of surface emissivity for (a) a clear but saturated
moist layer between 4-5 km; (b) an altostratus cloud between 4-5 km with LWP of
0.125 kg m'2; and (c) as in 2.7b but with LWP of 0.625 kg m'2.
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
The effect of cloud water on surface TB contributions can be seen by
examining channels 1, 2, and 3 at an "oceanic? emissivity of 0.7 (not shown).
Surface contributions for a clear moist layer are 84%, 80%, and 47%, respectively.
With 0.125 kg m'2 of liquid water, surface contributions diminish to 83%, 70%, and
39%, while 0.625 kg m '2 of cloud water yields contributions of only 78%, 43%, and
17%. Clearly, the presence and liquid content of cloud water affects channels 2 and
3 more than channel 1. Thus, with a dense liquid cloud cover, variations in surface
emissivity will cause large variations in channel 1 TB, but TB variations in channels
2 and 3 will be moderated. With light (low cloud water contents) cloud cover,
surface emissivity variations still can cause large TB changes in channels 1 and 2.
At this point, it is worthwhile to summarize characteristics of AMSU
moisture channel TBs in comparison with IR channel imagery over altostratus liquid
clouds. At a relatively small LWP of 0.062 kg m'2, AMSU moisture channels show
considerable ability to penetrate clouds (Fig. 2.5a). This is seen, for example, in
significant TBcontributions from subcloud layers o f channels 4 and 5. As the LWP
increases, the channels? ability to "see" through the clouds diminishes, as indicated
by subcloud contributions in Fig. 2.5b. This sensitivity to LWP has allowed Huang
and Diak (1992) to develop AMSU cloud retrieval algorithms from various twochannel combinations. At the same time, the ability to "see" into clouds means that
the MW
T bs
respond less to variations in cloud altitude than do IR frequencies.
Typical altostratus clouds are optically thick (i.e., relatively opaque) in the IR
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
channels so that their equivalent blackbody temperatures correspond more closely
to cloud top temperatures than do the AMSU TBs. Based on the current research
and studies of millimeter wave signatures over precipitating storms, it appears that
AMSU moisture channel imagery will provide information that is intermediate
between, and complementary to IR frequencies and ground based weather radars.
As is widely recognized however, special care must be taken in interpreting imagery
from surface sensitive MW channels, because surface emissivity variations are much
greater at these frequencies than for IR channels.
c. Effects o f ice clouds
We now examine the effects of cirrus clouds on AMSU moisture channel
Tbs.
The methodology for these simulations employed the bimodal cirrus
representation described in Section 2.3b. The first issue is the variation of TBs with
cloud ice content. Figure 2.8 gives TBs as a function of ice water path (IWP) for
2 km thick cirrus between 10-12 km (300-200 mb, Fig. 2.8a) and
6 -8
km (490-360
mb, Fig. 2.8b). The 1000 mb temperature was 25癈, the tropospheric T ^ was 15癈
(except for 0癈 within the cloud layer), and Td decreased above the tropopause to
-80癈 where it became constant. The IWP was varied between 0.0 and 0.563 kg
mf2 corresponding to IWC increments of 0.05 g m?3 from 0.0 to 0.25 g m'3.
Channels 1 and 2 are affected little by variations in cirrus ice content at
I
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
50
2 90
10-12 km
280
. 270
t 1 260
zc 240
m 230
220
2
0. 0
3
4
6
ICE PATH (k g m- 2)
290
?
6-8 km
280
. 270
260
m 230
220
0.0
1
2
3
4
5
6
ICE PATH (k g m- 2 )
Fig. 2.8. Tb (K) as a function of ice water path (kg m 2) for a cirrus cloud between
(a) 1 0 - 1 2 km; and (b) 6 - 8 km.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
either altitude (Figs. 2.8a and b). At 10-12 km for example, channel 1 TBs are
virtually constant over the entire range of IWPs, while channel 2 TBs drop only
about 3 K. In contrast, cirrus ice content significantly affects channels 3 through
6,
particularly when that ice is at the high altitudes. TBs generally decrease with
increasing IWP, mainly because of scattering. For example, channel 4 TBs for a 12
km cloud top range from 279 K at 0.0 kg m?2 IWP, to 247 K at 0.563 kg m '2 IWP.
Increasing ice contents causes the TB curves for channels 4, 5, and
6
to
converge to cooler values, particularly for the lower cloud (Fig. 2.8). This results
from two effects mentioned in Section 2.2: The channels? differing responses to
water vapor versus their comparable responses to ice. Multiple scattering from
cirrus particles extracts similar amounts of radiation from channels 4, 5, and
However, since there is more water vapor above the
6 -8
6.
km cloud than the 10-12
km cloud, the scattering effects of cirrus are more strongly counteracted by water
vapor emission above the lower cioud. The result is most prominent in channel 6 ,
where TBs for the higher cirrus decrease 16 K as IWP increases from 0.0 kg m '2 to
0.563 kg m'2, but decrease only 1.8 K for the lower cloud.
variations with respect to IWP for a
6 -8
The curves of TB
km cirrus cloud (Fig. 2.8b) generally are
similar in appearance to those with respect to LWP for an altostratus liquid cloud
at 6-7 km (Fig. 2.4a). However, cloud ice appears to produce more attenuation than
cloud liquid for equivalent path lengths at frequencies near 157 and 183 GHz
(channels 3-6). On the other hand, cirrus ice is more transparent to radiation at
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
23.8 and 89 GHz (channels 1 and 2) than is liquid cloud water.
CFs again explain the response of the various AMSU moisture channels to
cirrus clouds. Figure 2.9 shows CFs for 10-12 km (300-200 mb) clouds at IWPs
of 0.113 kg m'2 (Fig. 2.9a) and 0.562 kg m'2 (Fig. 2.9b) and for
6 -8
km (490-360
mb) clouds at the same IWPs (Figs. 2.9c and d, respectively). TBs for channels 1
and
2
receive little contribution from the cloud layers, as observed earlier with their
small Tb variations (Fig. 2.8). CFs for channel
6
illustrate how the effects of cloud
ice and water vapor interact to produce TB variations. The channel
6
CF for a 12
km cloud top with 0.113 kg m '2 IWP (Fig. 2.9a) has a peak vaiue of 0.21 km '1 near
cloud top (around
200
mb), and also exhibits a lower, but broader peak of 0 .1 1 km '1
near 450 mb. Thus, there are substantial TBcontributions from both the cloud layer
and the water vapor below. A significant portion of the CF value within the cloud
layer is supplied by the water vapor in that layer. Specifically, the channel
6
CF
for a moist layer with zero cloud water (not shown) has a peak o f 0.19 km ' 1 within
the moist layer. For an IWP of 0.562 kg m '2 (Fig. 2.9b), more of the overall TB
contribution emanates from the cloud layer, with the channel
6
CF now peaking at
approximately 0.35 km'1. The mid-tropospheric CF peak decreases to about 0.08
km'1, in conjunction with the TBcooling seen in Fig. 2.8a. Attenuation by the cloud
of subcloud Tb contributions stems mainly from two processes: Absorption by the
saturated layer of water vapor, and scattering due to the ice particles. This contrasts
with altostratus clouds in which the dominant effect of liquid water is absorption
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
i
I
i
i
I
SFC E MI S . = e . 9 0
?- 2 3 . 8
GH;
T 8 = 2 7 5 . 6e
2 - 89 . 8
GH;
TB = 2 7 7 . 0 1
3-157.0
GH;
TB = 2 8 2 . 0 8
4 - 1 7 6 . 3 1 GH;
T3=271.9B
5-180.31
6-182.31
GH;
GH;
CONT
CONT
CONT
CONT
CONT
CONT
e . 88i
.3
.4
CONTRIBUTION
3-157
76.31
180.31
182.31
70 p
5-180.31
6-182.31
e.049
0.000
0.000
Kg m-2
.6
1-SFC
2-SFC
3-SFC
4-SFC
5-SFC
6 -SFC
60 0 E�
8 0 0 k-
.2
(KH- 1 1
.3
.4
ONTP.I 8 UTION
T3= 2 7 7
iS= 281
3= 2 6 9 . 5 2
0 . 8 ei
C0N7
CONT
CONT
CONT
CONT
CONT
0.829
0.423
0.036
0.000
0.000
.5
5-180.31
6-1 82. 31
.7
.6
.8
I KH-11
73 =
75=
15=
75 =
73 =
73 =
B9.0
246.23
0 . B7 2
75= 2 3 4 . 0 7 7
73= 2 2 7 . 8 1
I UP = 0 . 5 6 2
1 000
.7
14 4 0 0
=0 . 9 0
275.71
274.62
264.23
251.30
247.09
244.81
700 r.
14 4 0 0 15
0.489
0.04e
0 .0 0 0
0.000
1020
GH;
GH;
w 400
0.844
3.508
IWP = 0 . 1 1 3
1000
SFC E H I S . = 0 . 9 0
GH;
TB= 2 7 5 . 5 8
GH;
75= 2 7 4 . 4 0
GH;
73= 2 6 3 . 37
GH;
7 5 = 2 4 6 . 94
7 8 = 2 5 6 . 4e
TB = 2 4 0 . i e
14 4 0 0
1-SFC
2-SFC
3-SFC
4-SFC
5-SFC
6 -SFC
I Bs r
* g a;
r-
3-SFC
4-SFC
5-SFC
6 -SFC
6 0 0 IE 5 ^
700
800
903
.2
3N i R i a l )
CON'
CON
CON
CON'
.3
.4
CONTRIBUTION
:kk-:
Fig. 2.9. As in Fig. 2.5 but for cirrus clouds between (a) 10-12 km (300-200 mb)
with IWP of 0.113 kg m 2; (b) 10-12 km (300-200 mb) with PAT of 0.562 kg m'2;
(c) 6 - 8 km (490-360 mb) with IWP of 0.113 kg m?2; and (d) 6 - 8 km (490-360 mb)
with IWP of 0.562 kg m-2.
I
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
54
of radiation. Using a cloud-radiarion model, Smith et al. (1992) documented a case
of very low TBs over a thunderstorm where emission from ice particles actually
yielded a significant contribution to the TOA TB. This probably does not occur
here, however, where TBs are much warmer.
For lower cirrus clouds, water vapor constitutes an even greater proportion
of the cloud layer?s contribution to channel
layer between
6 -8
6
TBs. The channel
6
CF for a cloud
km (490-360 mb) and IWP=0.113 kg m'2 (Fig. 2.9c) peaks near
390 mb at 0.62 km'1, while for a moist layer with no cloud ice (not shown) it peaks
at 0.60 km'1. When cloud IWP is increased to 0.562 kg m '2 (Fig. 2.9d), the peak
CF value increases by only a few percent to 0.68 km'1. Since the cloud is placed
near the clear air CF peak for channel
6,
the secondary mid-tropospheric peak
observed for the higher cloud (Fig. 2.9a) does not occur. This, and the fact that a
significant contribution to channel
6
TB comes from above the cloud, leads to the
relatively small TB changes with IWP for clouds at the
6 -8
km level (Fig. 2.8b).
It is important to examine the effects of cimis altitude in further detail.
Figure 2.10 shows how TBs vary with cloud height for 1 km (Fig. 2.10a) and 4 km
thick cirrus (Fig. 2.10b). Abscissas refer to the altitude of the top of the cloudy
layers. The IWC of each cloud is 0.2 g m'3, corresponding to 0.25 kg m '2 and 0.85
kg m'2 for 1 km and 4 km thick clouds, respectively. Raising a 1 km thick cirrus
layer from
8
km to 12 km (Fig. 2.10a) decreases TBs for channels 5 and
approximately 3 K and
8
K, respectively.
6
Channels 1 through 4 are virtually
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
290
280
280
270
c! 270
c_ 260
2:
21
UJ
260
u05 252
jE 250
? 240
Id
230
1
230
220
13
CLOUD TOP HEIGHT
7
(km)
11
12
CLOUD TOP HEIGHT
(km)
S
9
13
290
- 280
270
c. 270
260
L
� 250
c 240
230
230
7
8
9
10
11
MOIST LAYER TOP HEIGHT
12
(Km)
12
7
o
9
10
MOIST LAYER TO? HEIGHT
2
-
(Km)
Fig. 2.10. Tb (K) as a function of (a) cloud top height (km) for a 1 km thick cirrus
cloud; (b) as in 2.10a but for a 4 km thick cirrus cloud; note difference in
temperature scales; (c) moist layer top height (km) for a 1 km thick clear but
saturated layer, and (d) as in 2.10c for a 4 km thick layer.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
unaffected by these altitude changes.
To understand these TBvariations (Figs. 2 .10a and b), one must compare the
cloud Tb curves with those produced by a moist layer with no cloud water. Graphs
of corresponding TB changes for 1 km and 4 km thick saturated moist layers with
zero cloud ice are given in Figs. 2.10c and d, respectively. First, note that TBs for
channels 3 through
6
generally are cooler with cloud ice (Fig. 2.10a) than with
moist air alone (Fig. 2.10c). In the case of channels 4 and 5, lifting the top of the
clear saturated layer from
8
km to 12 km actually warms the TBs slighdy (Fig.
2.10c). This occurs because the saturated layer between 7-8 km contains 1.12 mm
of precipitable water while the one at 11-12 km contains only 0.15 mm.
In
addition, as the moist layer rises, its cooling effect moves above the range of
influence for these channels, thereby allowing more of the warmer, lowertropospheric Tb contributions to reach the satellite. The channel 4 CF (not shown)
for the clear moist layer at 7-8 km has one peak o f 0.09 km'1, and a lower altitude
peak of 0.19 km'1. When the saturated layer is between 11-12 km, its channel 4 CF
peak diminishes to
0 .0 1
km'1, while the lower level peak increases to
0 .2 1
km'1.
Thus, with increasing cirrus height the presence o f ice (Fig. 2.10a) almost exactly
counterbalances the effects of saturated layer water vapor changes so that TBs are
nearly constant with increasing cirrus cloud height. In channel 5, the cloud ice
actually prevails so that TBs decrease from 253.1 K to 250.2 K over the 4 km range
o f cloud altitudes. Since ice particles are effective dielectrics, they do not absorb
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
or emit much radiation.
Therefore, this cooling is more a result of decreasing
emission from the shrinking column of water vapor above the rising cloud than it
is of cooling the ice. That is, the scattering signature of the ice becomes more
visible as the cloud is raised. In contrast, raising liquid clouds cools TBs in both
the MW and IR spectra by lowering the emitting temperature of the liquid water as
well.
Increasing the thickness of the cloudy (Fig. 2.10b) and moist layers (Fig.
2.10d) to 4 km accentuates the effects of cloud ice relative to the water vapor for
all channels except number 1 . Differences between channel 1 TBs for cloud ice
versus saturation alone are only 0.02 to 0.03 K. On the other hand, channel 2 TBs
are approximately 5 K cooler for the 4 km thick cirrus layer than the 4 km clear
moist layer. Nevertheless, raising the cloud top from
8
to 12 km elevation yields
only a 1.04 K decrease in channel 2 TB. Multiple scattering from cirrus particles
is the only mechanism which can explain the reduction of TBs by cloud ice when
little change is produced by moving the cloud upward. This result is consistent
with Muller et al. (1993) who demonstrated that scattering from cirrus-sized ice
particles was needed to account for TBs over a thunderstorm at microwave
frequencies near 90 and 183 GHz.
TBs for channels 5 and
scattering. Specifically, channel
6
6
(Fig. 2.10b) provide additional evidence of
TBs are warmer than those of channel 5 for cloud
tops of 10, 11, and 12 km. For the given atmospheric profile, this can only occur
I
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58
if there is scattering. The dominant effect of scattering is to extract energy out of
the radiation?s path to the satellite sensor. In channels 4, 5, and 6 , energy is added
back into the path by emission from water vapor. However, channel 5 is on the
wings of the water vapor absorption line. Thus, its TBs depend more on pressure
broadened line contributions, with less energy emitted back into the path above or
within the cloud layer at 180.3 GHz (channel 5) than at 182.3 GHz (channel 6 ).
This effect has been observed over thunderstorms (Heymsfield and Fulton 1988)
where high concentrations of ice particles cause TBs to be much colder than
thermometric temperatures of the atmospheric column. The fact that channel 4 TBs
still are warmer than those of either channels 5 or 6 demonstrates that the cirrus has
not totally obscured the atmosphere below. Thus, there is a significant TB
contribution from the lower to middle troposphere at 176.3 GHz.
It is important to note that unlike IR equivalent blackbody temperatures over
optically thick clouds, the calculated MW TBs often do not match cioud top
temperatures. For example, considering the 4 km thick cirrus at 12 km (Fig. 2.10b)
where above cloud water vapor is minimal, TBs range from 276 K in channel 1 to
225 K in channel 6 . By comparison, the cloud top temperature is 229 K. Although
not transparent, clouds are penetrable at the AMSU moisture channel frequencies,
and the channels "see" through the cloud top to warmer atmospheric layers. On the
other hand, scattering can yield TBs that are much colder than the cloud top
temperature. As a result of both these factors, cloud tops cannot be parameterized
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59
as emitting surfaces as often done in the IR spectrum.
Finally, we consider the effects of surface emissivity in the presence of
cirrus clouds. Figure 2.11 is similar to Fig. 2.7 for liquid clouds, but shows the
effects of surface emissivity variations for an atmosphere containing only a
saturated layer between 8-10 km (Fig. 2.11a), the same atmospheric profile
containing a 2 km thick cirrus cloud with 0.05 g m"' IWC (0.113 kg m '2 IWP, Fig.
2.11b), and one containing 0.25 g m '3 IWC (0.563 kg m '2 IWP, Fig. 2.11c).
Consistent with observations at 92 GHz by Hakarinnen and Adler (1988) and
Heymsfield and Fulton (1988), TBs for channels 1 and 2 are affected little by the
specified amounts of cloud ice (Fig. 2.10), and their TBs increase rapidly with
increasing surface emissivity.
Based on the large slopes of these curves, cloud
liquid water obscures surface emissivity variations (Fig. 2.7) in channels 2 and 3
more than does cloud ice (Fig. 2.11). On the other hand, ice significantly depresses
the Tes for channel 3 at all emissivities. As observed with liquid clouds, TBs of
channels 4, 5, and
6
are virtually unaffected by variations in surface emissivity,
although the cloud ice does uniformly reduce the TBs. Thus, channel 3?s responses
are characteristic of its spectral position between the water vapor absorption
channels near 183 GHz and the "window" frequency at 89 GHz. That is, like the
window channels, its TBs increase as surface emissivity increases; however, like the
higher frequency water vapor channels, its TBs are depressed by ice layers.
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60
290
^
270
cn
K 230
C
210
190
4
6
6
1 .0
SURFACE EMISSIVI TY
290
270
5
250
to
�
230
190
i
6
8
1 .0
SURFACE EMISSIVI TY
290
c
*
270
2
250
190
4
6
6
1 .0
SURFACE EMISSIVITY
Fig. 2.11. T b (K) as a function of surface emissivity for (a) a clear but saturated
layer between 8-10 km; (b) a cirrus cloud between 8-10 km with IWP of 0.113 kg
m'2; and (c) as in 2.1 lb but with IWP of 0.563 kg m'2.
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61
5. Summary and Conclusions
This chapter has sought a detailed understanding of atmospheric and surface
controls on passive top-of-atmosphere TBs at moisture sounding frequencies used
in the Advanced Microwave Sounding Unit and AMSU-like instruments.
Six
frequencies were investigated: 23.8, 89.0, 157.0, 176.31, 180.31, and 182.31 GHz.
We have performed radiative transfer simulations to determine how water vapor,
along with liquid water and ice particles within non-precipitating clouds affect the
frequency dependent TBs. Cloud effects were considered in terms of five basic
properties: droplet size distribution, phase, liquid water or ice content, altitude, and
thickness. Surface emissivity also has been addressed. TB contribution functions
have been presented as an aid to physically interpreting AMSU TBs.
TOA T bs for the AMSU moisture channels represent complex interactions
between radiation and the earth?s atmosphere and surface, including gaseous
absorption and emission, absorption, emission, and scattering by cloud and
precipitation particles, surface emission, and surface reflection of downwelling
radiation. In terms of TB image interpretation, the AMSU moisture channels can
be considered MW analogues to IR window and water vapor channels, but with a
number of important differences in their responses to surface characteristics and
clouds.
Results of simulations using clear atmospheric profiles provide insight into
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62
the effects of temperature and water vapor. Specifically, drying the atmosphere
while holding the temperature profile constant was found to move peaks of water
vapor channel contribution functions cioser to the surface, in agreement with
previous investigators.
This drying cools TBs at 23.8 and 89 GHz, but warms
values for channels near 183 GHz.
Adding the effects on T B of temperature
changes to those produced by water vapor variations complicates TB interpretation,
and various channels were observed to respond quite differently to varying sounding
conditions.
For example, changing from a moderately dry middle latitude July
sounding to a much cooler (and consequently drier) January sounding cooled TBs
at 157 GHz by 40 K, but only 2 K at 182.31 GHz. This small change at 182.31
GHz resulted from the temperature effect (cooling TB) balancing the drying effect
(warming TB).
Surface contributions to TB are highly dependent on the
atmosphere?s water vapor content, but generally are large at 23.8 and 89 GHz, and
small or non-existent near 183 GHz. As noted in previous studies, decreasing the
surface emissivity enhances TB sensitivity to water vapor at 23.8 and 89 GHz.
The addition of water vapor or clouds to a clear sounding sometimes yielded
results at 23.8 GHz distinct from their effects on the higher frequency channels.
For example, T Bs at 23.8 GHz increased slightly, even when the water vapor and
cloud were added to a layer whose thermometric temperature was cooler than the
radiometric temperature of the surface background.
This resulted from surface
reflection of the downward emission from the cloud and moist layer, which then
I
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63
affected upwelling TB because of additional transmission through the cloud.
The scattering of millimeter wavelength radiation by liquid droplets smaller
than precipitation size has received little previous attention in the literature.
Theoretical size distribution functions were examined for their effects on TOA TBs.
Current results indicate that the Rayleigh approximation is adequate for typical
cloud drop size distributions. However, Mie scattering effects become important
for SDFs with mode radii greater than 20 pm at 157 and 183 GHz, and greater than
30-40 pm at 89 GHz. The scattering results from the relatively small concentrations
of droplets much larger than the mode radius.
Orographic clouds and tropical
cumuli have been observed to contain droplet size distributions with mode radii in
the 30-40 pm range. Thus, as new instruments bridge the gap between MW and
IR to frequencies higher than those discussed here, radiative transfer modelers are
cautioned to explicitly address scattering characteristics of such clouds.
Both liquid and ice clouds were found to impact the TBs, particularly at
higher frequencies. Contribution functions show that clouds depress TBs of the
higher frequency channels by suppressing or obscuring TBcontributions from below.
Liquid water attenuates the upwelling radiance by absorbing and re-emitting at a
colder temperature, while cirrus ice attenuates through multiple scattering. Clouds
affect TOA TBs near 183 GHz due to both the hydrometeors and the saturated
layers o f water vapor. The water vapor alone comprises a significant percentage
of the total cloud attenuation.
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64
TBs at 23.8 GHz and 89 GHz are more strongly affected by "altostratus"
liquid clouds than by "cirrus" ice clouds. On the other hand, channels near 157 and
183 GHz are more strongly affected by the ice clouds. This occurs for two major
reasons. First, cirrus clouds are higher in the atmosphere, so there is less water
vapor above them to obscure the cloud effects. Second, multiple scattering from
the ice particles substantially attenuates TBs at the high frequencies.
Variations in the altitudes of liquid clouds were found to affect TBs through
changes in the cloud?s emitting temperature and differences in the water vapor path
above the cloud. The altitudes of ice clouds are important at frequencies of 157
and 183 GHz because of the complex balance between the emitting temperature of
the water vapor within the cloud, changes in the water vapor content due to lower
saturation vapor pressure at higher altitudes, changes in the amount of obscuring
water vapor above cloud level, and the scattering effects of the ice particles which
depend little on temperature. Thus, with regard to cirrus, the behavior of TBs at
these high frequencies must be explained mainly in terms of multiple scattering
from ensembles of ice particles, in conjunction with absorption and emission by
water vapor.
For "typical" mid-latitude atmospheres, surface emissivity was observed to
have a strong impact on TBs at 23.8 and 89 GHz, but virtually no effect near 183
GHz. Liquid water clouds tend to suppress the effect of surface emissivity on TBs,
particularly at 89 GHz, but non-precipitating ice clouds are relatively transparent
i
I
i~
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
below 89 GHz, and thus do not obscure variations in surface emissivity.
Cimrent results are important for physically interpreting TBs from new
sensors such as AMSU and the SSMIS as well as the recently launched SSM/T2
moisture sounder.
In addition, frequencies above 183 GHz show considerable
sensitivity to water vapor.
Thus, the results presented here have important
implications for possible future instruments that might extend to frequencies beyond
183 GHz, both in terms of water vapor effects, and scattering from ice and liquid
cloud particles. Work presented in Chapter 4 will employ a mesoscale atmospheric
model in conjunction with the radiative transfer model to show how spatial patterns
of AMSU water vapor channel imagery can be used to make inferences regarding
middle and upper tropospheric dynamics and kinematics.
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CHAPTER 3
AN ALTERNATIVE REPRESENTATION OF THE ICE CANOPY FOR
CALCULATING MICROWAVE BRIGHTNESS TEMPERATURES OVER A
THUNDERSTORM
3.1. Introduction
One of the most important factors influencing upwelling microwave (MW)
radiances over thunderstorms is how the radiation interacts with frozen
hydrometeors generated in the convective process.
Vivekanandan et al. (1991)
asserted that the ice phase may be the most inherently observable feature for
scattering based frequencies above 37 GHz. Therefore, accurate representations of
ice/radiation interactions in forward radiative transfer calculations are a key element
of physical remote data retrieval methods that use such frequencies. The spherical
ice representation by Marshall and Palmer (1948, hereafter denoted M-P) is a
"traditional" scheme used in the forward radiative transfer calculation for MW
frequencies (e.g., Savage 1978; Wilheit et al. 1982; Spencer et al. 1983; Huang and
Liou 1983). This chapter addresses an alternative methodology for calculations near
92 and 183 GHz. Specifically, we have incorporated a particle size distribution
66
I
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67
function (SDF) which accounts for ice crystals in addition to the M-P representation
for precipitation-sized particles such as graupel and hail.
Our purpose is to
demonstrate the sensitivity of simulated upwelling brightness temperature (TB) to
simple SDFs of spherical particles for characterizing the ice canopy.
Knowledge about the interactions between passive MW radiation and frozen
hydrometeors has increased steadily since the 1970s.
Using observations and
modeling, Wilheit et al. (1982) were the first to demonstrate that scattering from
precipitation-sized ice particles can account for extremely cold (140 K) TBs at 92
and 183 GHz. Spencer et al. (1983) modeled similar signatures over land at 37
GHz. Aircraft overflights show that the 92 and 183 GHz frequencies are much less
sensitive to anvil cirrus than are corresponding infrared measurements; however,
scattering associated with large ice particles in active convective cores can produce
T bs over land which are much colder than any thermometric temperatures in the
atmospheric column (Hakkarinen and Adier 1988; Adier et al. 1990; Heymsfield
and Fulton 1988; Fulton and Heymsfield 1991).
Ice canopies affect top-of-atmosphere TB through both their bulk and
microphysical properties.
For example, increasing the bulk ice concentration
diminishes TBs. On the other hand, particle density affects upwelling TB through
the complex index of refraction and particle size distribution (Smith and Mugnai
1989; Vivekanandan et al. 1990, Yeh et al. 1990a). These investigators showed that
increasing density leads to decreasing TB. Particle shape also has an effect,
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68
particularly as particle size and MW frequency increase. Modeling results indicate
that the use of equivalent volume ice spheres can lead to errors in simulated TBs;
however, calculations of this impact are very computer intensive (Evans and
Vivekanandan 1990).
Nevertheless, there still exists a need for fast radiative
transfer models in physical rainfall and other retrieval algorithms. This chapter
describes an attempt to incorporate a spherical treatment for ice crystals into such
models as an improvement over the M-P distribution.
Recent studies have begun to explore the important links between radar
observations and passive MW data. Modeling results indicate that the 85 and 183
GHz channels "see" only the upper 3-5 km of optically thick clouds containing ice
hydrometeors (Wu and Weinman 1984). Thus, aircraft measurements of TBs at 92
and 183 GHz are well correlated with radar echoes from the upper portions of
convective systems (Hakkarinen and Adler 1988; Heymsfield and Fulton 1988).
Consequently, Yeh et al. (1990a) could simulate MW TBs along an aircraft flight
track by using vertical profiles of hydrometeor data derived from radar reflectivity
as input to a radiative transfer model, thereby inferring information about particle
size distribution and phase. Multiparameter radar measurements also have been
used in both observational and modeling studies to characterize ice phase
microphysics and its relationship to above-cloud microwave TBs (Evans and
Vivekanandan 1990; Vivekanandan et al. 1990; Vivekanandan et al. 1991; Fulton
and Heymsfield 1991).
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69
3.2. Methodology for comparing simulated and observed TBs
We have employed the methodology of Yeh et al. (1990a) to compare AMMS
(Advanced Microwave Moisture Sounder) TBs from a
thunderstorm overflight
(Fulton and Heymsfield 1991) with calculations of passive microwave TB at
frequencies near 92 and 183 GHz. This flight occurred on 11 July 1986 during
COHMEX (Cooperative Huntsville Meteorological Experiment). TB values were
computed from a radar reflectivity cross-section (Fig. 3.1) and a modified proximity
sounding.
Two methods were used to specify particle size distribution: (1) a
"traditional" representation of radar-derived liquid and ice water content based on
the M-P distribution; and (2) an alternative approach partitioning 80% of the ice
content into a modified gamma distribution representing ice crystals (Welch et al.
1980), and 20% into M-P precipitation-sized particles such as graupei and hail. To
our knowledge, previous calculations in the literature of MW TBs from radar data
have not explicitly accounted for scattering from a separate category of cloud ice
crystals.
The AMMS (Wilheit et al. 1982) has frequencies in the window region at 92�GHz and in the strong water vapor absorption line at 183.3�GHz, 183.3�GHz,
and 183.3�GHz. For computational efficiency, we adopted the approach of Kakar
(1983) in modeling only one side of the two-sided AMMS channels at 90, 174.3,
178.3, and 181.3 GHz, and hereafter refer to the channels by these values. Fulton
I
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70
?2
1
5
5U
T
C
s o lN
20
40
30
2
0 3
0 4
0 5
06
0 7
0
X
(k
m
)
Fig. 3.1. 10 cm radar reflectivity (dB) vertical cross-section along the aircraft flight
track. Flight direction was from 0 to 70 km. North is to the left (after Fulton and
Heymsfield 1991).
1
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and Heymsfield (1991) provide a full description and analysis of the radar and
aircraft radiometric measurements used for this case.
The radiative transfer approach is based on a microwave version of Xiang?s
(1989) multilayer Sobolev solution to the radiative transfer equation. It is a planeparallel two-stream multiple scattering solution for TB that is comparable to an
Eddington model (e.g., Wu and Weinman 1984) and has shown good accuracy
when compared to multistream models. Yeh et al. (1990b) have demonstrated that
an Eddington model can result in discrepancies compared with TBcalculations from
a more sophisticated radiative treatment. The Sobolev model used here may suffer
from similar limitations which could account for some of the discrepancies between
observed and calculated TBs in Section 3.3. An unpolarized version having 100
vertical layers and "viewing" at nadir was used here. Surface emissivity was set at
0.9. Optical parameters for polydisperse size distributions of spherical liquid and
___
U O Z cil
?
i
3 ---------nyUiUUiCiCUAa WCIC tc u tu x a iC u
r?
i
v
i
c a ^ n la y v i u d iu g
^
i 3vuuil �
v o
/ioc> a\
uv
algorithm. For computational efficiency, look-up tables of these parameters were
constructed based on temperature and liquid/ice water content, (LWC/IWC).
Gaseous absorption for each layer was calculated from the modified sounding using
the algorithm of Liebe (1985).
The modified gamma SDF (Deirmendjian 1969) is given by Welch et al. (1980)
as
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72
n (r) = a r ? exp
/ Ay
a r
7 v~ "j
( 3 . 1:
where n(r) is the number concentration of droplets with radius r, and rc is the modal
radius (radius of maximum particle frequency). The modified gamma function
yields a generic family of curves whose parameters rc, a, a , and y can be fit to
actual particle distributions. Integrating the particle SDF and the volume formula
with respect to radius gives LWC or IWC. A given size distribution can be scaled
to a desired IWC by multiplying the particle number concentration in each radius
category by the ratio of the desired IWC to the raw IWC.
Thus, rc remains
constant, regardless of the final IWC. We used modified gamma parameters for
cirrus ice particles (Welch et al. 1980) with rc=175 um, a=4.0xl0'lj, a=5, and Y=1.0.
This cirrus model represents the large particle mode of the bimodal distribution
shown in Welch et al. (p. 44). They noted that typical ice crystal lengths in cirrus
might be 3-5 times those of equivalent spherical radii. Ice densities were set at
0.917 g cm'3, i.e., of pure ice. We contrast two types of TB calculations: those for
which all radar-derived liquid and ice water content is represented by the M-P SDF,
versus those in which 80% of the ice content is represented by the modified gamma
function for cirrus ice crystals, and 20% by the M-P SDF for hail and graupei.
The decision to partition ice mass into 80% "crystal" and 20% precipitatior.sized components was somewhat arbitrary. Nevertheless, it reflects the fact that
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
channels at 92 and 183 GHz are sensitive mainly to upper layers of the convective
system, where crystals rather than precipitation-sized particles are expected to
predominate. Applying formulas from Starr and Cox (1985), the assumed spherical
mode radius of 175 pm can be compared with crystal lengths for particles of
equivalent mass. Using our assumed ice density of 0.917 g cm"3 yields approximate
crystal mode lengths of 1120, 775, and 910 pm for column, bullet rosette, and plate
habits, respectively. These are in or near the range of mean particle sizes from 600
to 1000 pm reported by Heymsfield and Knollenberg (1972).
Vertical profiles of liquid and frozen water content were constructed from the
10 cm radar reflectivity cross-section (Fig. 3.1) following the methodology of Yeh
et al. (1990a). This employs Marshall and Gunn?s (1952) modification of the
classic Marshall and Palmer (1948) Z-R relation, with a correction for ice
reflectivity (Smith 1984). The ice correction yields greater equivalent LWC than
does the same reflectivity for liquid droplets. Given the radar reflectivity factor, Z
(mm 5 m"3), the formula for LWC (g m"3) is (Yeh et al. 1990a):
LWC = a Z \
(3.2)
where a=0.0039i and b=0.55. Tne corrected formula for ice water content is
IWC = 5.284 a Z b.
(3.3)
The factor 5.284 is equivalent to adding 7.2 dB to radar reflectivities expressed in
dB.
Smith and Mugnai (1989) and Yeh et al. (1990a) have emphasized the
importance of MW TB calculations including a "mixed phase layer" of supercooled
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74
liquid drops and ice particles above the freezing level. Therefore, the proportion
of ice to liquid water content has been assumed to increase linearly between 0.0 癈
and -30 癈. Sensitivity tests have indicated that this yields a positive impact at 90
GHz, but produces little or no change in the three 183 GHz frequencies.
Temperature and water vapor profiles within the thunderstorm depicted on the radar
cross-section were calculated from the proximity sounding released from
Booneville, MS at 1845 UTC. The aircraft flight time was approximately 2155 UTC
(1655 local daylight time). Saturated adiabatic ascent was assumed within the cloud
starting at cloud base, with a dewpoint depression of zero within the cloud. At
levels above the height at which radiosonde dewpoint information terminates, the
environmental dewpoint depression was specified to be 30 癈.
Heymsfield and Fulton (1988) and Yeh et al. (1990a) noted the potential for
aircraft position errors due to drift in the inertial navigation system. Therefore,
following Yeh et al. who used feature identification for matching radar crosssections with flight tracks, the aircraft measurements have been matched to the
calculated TBs by aligning very cold values in the convective core. This required
an adjustment of 5 km.
3.3. Results
Figure 3.1 is a vertical cross-section of radar reflectivities along aircraft flight
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
track 9 from Fulton and Heymsfield (1991). It was reconstructed from the volume
scan occurring from 2155 to 2159 UTC, approximately concurrent with the TB
measurements. The aircraft was heading southward toward 70 km. Facing from
70 to 0 km along the cross-section, the track is oriented approximately 15� to the
right of the downshear vector which we have estimated at approximately 325� from
two-dimensional AMMS images. The storm motion vector is 250� at 11 m s'1
(Fulton and Heymsfield 1991). Three distinct features of this convective storm are
relevant to our study: an anvil cirrus region from 7 to 30 km, a decaying convective
core at 44 km (denoted by "A") with maximum low level reflectivites over 40 dB,
and a mature convective core near 58 km (denoted by "B") with maximum
reflectivities exceeding 50 dB.
Figure 3.2 presents observed and calculated TBs for the four AMMS
channels.
The calculated TBs (denoted by "C") were based on the "traditional
approach", i.e., all hydrometeors were represented by the M-P SDF. The observed
AMMS T bs (denoted by "A") indicate anvil cirrus as a region of gently sloping
values from 5 to 30 km along the flight track. The local minimum of observed T b
at about 39 km is associated with the decaying convective core, but is
approximately 5 km downshear of the lowlevel reflectivity maximum. The coldest
AMMS TBs, ranging from 108 K at 174.3 GHz to 113 K at 178.3 GHz, are located
near 57 km in conjunction with the mature convective core. Fulton and Heymsfield
(1991) noted a hail signal in the multiparameter radar data for this region, indicating
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76
AIRCRAFT
VS.
C A L C.
T3
300
220
- 180
1 40
:h a n
60
0
10
20
30
20
30
70
260
220
- 180
CHAN
60
0
10
50
60
70
CHAN
0
300
6e
10
20
30
40
50
60
70
;------------- ;-------------:-------------:-------------:-------------:------------ :-------------;
----------------- :------------------:----------------- :----------------------------------- :-----------------i----------------- i
Z
-Z
22
32
DI STANCE
40
50
62
72
:kn:
Fig. 3.2. Calculated TBs (denoted by C ?s) and aircraft-measured TBs (denoted by
A ?s) for the four AMMS channels along the aircraft flight track. A "traditional"
Marshall-Palmer particle size distribution representation for the ice water content
was used.
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77
large ice particles that can cause sigificant scattering and, hence, very cold TBs.
Relatively warm TBs, ranging from approximately 260 K at 181 GHz to 290 K at
90 GHz, are found upshear of the thunderstorm from approximately 60 to 70 km.
Some low level clouds occur in this region.
Figure 3.3 repeats the observed AMMS TBs from Fig. 3.2, but contains
calculated values based on the 80/20% partitioning of ice content into the modified
gamma and M-P components. Except for the decaying convective region near 39
km and the results at 174/178 GHz in the mature core, the agreement between
aircraft and simulated values is superior to the traditional 100% M-P representation.
For example, TBs in the anvil region calculated using the traditional method (Fig.
3.2) range from 20 to 60 K colder than observed for all four channels. However,
corresponding TBs at 90 GHz calculated by the alternative method (Fig. 3.3) range
from nearly equaling the AMMS values to approximately 10 K colder. The
alternative TBs at 174, 178 and 181 GHz also give closer agreements in the anvii
region, but still average approximately 15 K too cold.
The main effect of applying the ice crystal SDF while retaining some
precipitation-sized ice hydrometeors (i.e., the alternative approach) is to increase the
number of small particles, while at the same time decreasing the proportion of
larger hydrometeors. The result is reduced scattering and warmer TBs. Despite the
Tb improvements, calculated values in the anvil still are too cold. There are several
possible explanations for this result. As noted earlier, decreasing ice density can
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78
AIRCr?Ar-
VS.
CALC
13
300
260
- 1 80
CHAN
1 00
60
10
0
30
50
30
50
70
300
260
CHAN
20
0
60
70
300
a
1 7 9 . 3 GHr
CHAN
60
0
10
20
30
70
30 0
260
220
h
CHAN
60
0
20
30
DISTANCE
50
t KM
70
1
Fig. 3.3. Same as Fig. 3.2, but using an "alternative" approach with 20% of the ice
water content represented by Marshall-Palmer spheres, and 80% represented by
modified gamma particle size distributions.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
increase TBs, and our value of 0.92 g cm '3 corresponds to that of pure ice, not the
air/ice mixture that characterizes graupel and ice crystals.
In addition, the
assumption of saturated adiabatic vertical profiles of temperature and dewpoint
within the radar echo region may overestimate water vapor content in the anvii
region. Performance at 90 GHz is best of the four channels in the area, perhaps
because it is in a window region of the spectrum and is only minimally affected by
water vapor absorption. Furthermore, even a 20% concentration of M-P ice spheres
may place too many large ice particles in the anvil region. Tests using a 100%
cirrus ice representation are shown for comparison in Fig. 3.4. Multichannel TB
agreements in the anvil from 5 to 20 km are better than those from the alternative
approach. However, this is not true in other storm regions. Thus, a 100% cirrus
crystal scheme appears inappropriate for these areas.
T bs calculated by the alternative method (Fig. 3.3) also are an improvement
over traditionally derived values (Fig. 3.2) in the mature convective core region
near 57 km.
For example, the traditional method gives T3s that range from
approximately 15 K too cold at 181 GHz to approximately 35 K too cold at 178
GHz. This method yields a mature core that is wider than observed at all
frequencies. The alternative method, on the other hand, produces values that are
nearly equal to those observed at 90 GHz, and are within 10 K at 181 GHz. It also
appears to better capture the width and basic geometry of the observed TB
depressions.
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80
AIRCRAFT
V S.
CA L C,
T3
308
26 8
228
-
180
140
CHAN
0
10
28
38
50
78
0
0
28
30
50
'0
300
260
26 8
j-
C2
W5
;han
z
z
20
30
50
60
70
30e
26 0
22 0
2
0
30
DI STANCE:
I KM !
Fig. 3.4. Same as Fig. 3.2, but with 100% of the ice content represented by a
modified gamma particle size distribution.
i
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81
Calculated TB values at 174 and 178 GHz still are approximately 35 K too cold
in the mature core, suggesting that errors remain in both the ice particle distribution
specification and the assumed water vapor profiles. The extremely cold TBs imply
that even the alternative approach overestimates scattering from ice particles at high
microwave frequencies.
However, in terms of its effect on TBs, concomitant
overestimation of water vapor profiles may compensate for errors in the ice
specification, especially at 181 GHz. Channels nearest the center of the 183 GHz
water vapor absorption line are most sensitive to upper level water vapor. Thus,
sensitivity studies (not shown) reveal that using a saturated adiabatic dewpoint
profile, as employed in this work, adds 26 K of TB at 181 GHz to that calculated
using the unmodified environmental dewpoint profile. This procedure adds only
8
K and 3 K respectively, at 178 and 174 GHz.
Although the alternative methodology improved TBs in the anvil and mature
core, that is not the case in the decaying convective core near 39 km. Specifically,
the traditionally derived TBs (Fig. 3.2) are closer to observed values than those from
the alternative procedure (Fig. 3.3). For example, traditionally calculated TBs range
from approximately 15 K warmer than the observed relative minimum at 90 GHz
to nearly 30 K too warm at 181 GHz. T3s from the alternative approach are as
much as 55 K too warm at 174 GHz. Neither method reproduces the geometry of
the observed depression in TBs. This may be attributable to large ice particles in the
form of graupel which are not indicated by the radar reflectivity signal.
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This
82
hypothesis is supported by Fulton and Heymsfield (1991). Specifically, they show
time series of AMMS TB for an earlier storm in which a relative minimum of TB
occurs at the same time that radar reflectivities increase monotonically.
This
minimum is associated with an enhanced Linear Depolarization Ratio signal from
the multiparameter radar, suggesting the presence of graupel or aggregates of
snowflakes.
We speculate that a similar mechanism is operating here.
current case it appears that the
10
In the
cm radar reflectivity signal simply cannot
distinguish between graupel particles to which the aircraft radiometer is highly
sensitive, and other forms of ice and liquid mass.
Radar-derived columnar liquid water and ice "crystal" masses along the
aircraft flight track (Fig. 3.5) and TBcontribution functions (Fig. 3.6) for the mature
and decaying convective regions help explain why the alternative method gives
superior results in the mature core while the traditional approach yields better
agreements in the decaying convective region. Values of precipitation-sized ice
particle mass have not been plotted. The peak liquid water path in the mature core
exceeds 14 kg m'2 (Fig. 3.5). The 7 kg m '2 of ice crystal mass is located at higher
levels of the storm. The sharp peaks of the contribution functions for the mature
core (Fig. 3.6, top) near 14 km (about 170 mb) at 176, 178 and 181 GHz, and 11
km (about 250 mb) at 90 GHz suggest that the MW radiometer is "seeing" only the
uppermost portions of the core. It seems likely that a proportion of precipitation�
sized ice particles greater than
20%
would be appropriate below the crystal layers,
I
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83
0
WATER/ ICE
PATH
(Kg/m2l
0
0
20
30
DISTANCE
40
60
70
(KM)
Fig. 3.5. Radar-derived columnar liquid water (dashed, kg m'2) and ice "crystal"
mass (solid, kg m'2) along the aircraft flight track.
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84
S FC EMI S .
.90 -
1
2 :1
o
1-
90.0
GHz
UJ
2-174.3
GHz
TB=
3-178.3
GHz
TB= 8 5 . 1 4 -
4-181.3
GHz
TB= 1 0 5 . 8 5 _
2
1
3
TB= 1 1 6 . 0 0 '
80.34 -
4
. 90 -
1
TB= 2 4 3 . 6 5
21 1
i?
o
bJ
1
2
CONTRI BUTI ON
I KM-T J
Fig. 3.6. T b contribution functions (km'1) based on the alternative approach for the
four AMMS channels in (top) the mature convective core and (bottom) the decaying
convective core.
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85
but their contribution is obscured from the satellite by the thick, mostly crystal
canopy above. Therefore, the alternative approach works well for this region. In
contrast, the ice crystal mass in the decaying core (Fig. 3.5) is less than 0.5 kg m '2
while the liquid water path for this region is 2 kg m'2. Contribution functions for
this area (Fig. 3.6, bottom) extend over a broad vertical portion of the storm. Thus,
in this case, the 90 and three 183 GHz channels penetrate to layers in which the MP representation appears more appropriate.
A final point concerns the close match between calculated and observed TBs at
181 and 178 GHz between 65 and 70 km, i.e., upsnear of the storm (Figs. 3.2 and
3.3). These channels are most sensitive to middle and upper level water vapor.
The relatively good agreement suggests that our arbitrary choice of a 30 K dewpoint
depression above the last level of dewpoint information is reasonable for this
region.
The slight observed dip at 90 and 174 GHz is not reproduced in the
calculated values.
It may be attributed to lower level clouds not seen in radar
reflectivities, but appearing in visible aircraft imagery (Fulton and Heymsfield
1991), or a surface emissivity fluctuation; it apparently is obscured by overlying
water vapor at 178 and 181 GHz. Muller et al. (1992) have shown that channels
near the center of the 183 GHz water vapor line receive little or no surface
contribution in a clear atmosphere, and that lower to middle clouds can be obscured
by water vapor between them and the sensor.
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86
3.4 Conclusions
In summary, inclusion of an 80% ice crystal representation and a 20% M-P
distribution gives overall results that are superior to the "traditional?' approach for
modeling aircraft measured TBs in the anvil and mature convective core regions.
In the decaying convective core region, however, the traditional approach, i.e.,
100% M-P distribution, gives better agreement. Neither method matches the
geometry of the dip in TBs in the decaying convective region. This is likely due
to the presence of graupel which is not detected as a special signature in radar
reflectivities, but does depress observed TBs through scattering. To a significant
degree, the 181 and 178 GHz channels are found to be sensitive to the upper level
water vapor profile.
Many previous authors have shown the importance of large ice particles for
passive MW radiometry. The current work demonstrates that TBs at relatively high
MW frequencies are very sensitive to the particle size distributions. It emphasizes
that particles smaller than given by the conventional M-P SDF strongly affect the
forward radiative transfer calculation, and therefore should be accounted for in
physical retrieval schemes.
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CHAPTER 4
A SIMULATION OF MICROWAVE WATER VAPOR IMAGERY AND UPPER
LEVEL FEATURES DURING ERICA IOP4
4.1. Introduction
This chapter describes a simulation and meteorological analysis of imagery
from the AMSU-B water vapor channel
6
at 182.3 GHz. Again we have modeled
only one side of the two-sided channel at 183.3�0 GHz. We refer to frequencies
within the water vapor absorption line centered at 183.31 GHz generically as "183
GHz channels." Specific channels are referred to by their specific frequency. The
simulation uses output soundings of temperature, water vapor, cloudwater, and
precipitation from the Limited Area Mesoscale Prediction System (LAMPS) model
as input to radiative transfer algorithms. The case examines the rapid development
phase of an extremely intense low pressure center that formed during the
Experiment on Rapidly Intensifying Cyclones in the Atlantic Intensive Observing
Period 4 (ERICA IOP4) on 3-5 January 1989.
Since satellite borne 183 GHz
radiometers did not exist at that time, the simulated imagery is compared with
existing GQES/VAS (Visible Infrared Spin-Scan Radiometer Atmospheric Sounder)
6.7 um images. The response of the AMSU-B 183 � 1.0 GHz channel to water
87
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88
vapor in clear atmospheres is similar to that of the 6.7 pm channels.
Since the original efforts of Mugnai and Smith (1984), the combining of
numerical meteorological models with radiative transfer codes has become an
established method for studying signatures in satellite imagery. At the cloud scale,
non-hydrostatic models have been sufficiently realistic to use in developing passive
microwave retrieval schemes for cloud and precipitation constituents (Mugnai and
Smith 1988; Smith and Mugnai 1989; Mugnai et al. 1990; Smith et al. 1992;
Mugnai et al. 1993; Yeh et al. 1990; Adler et al. 1991).
At the mesoscale,
hydrostatic models combined with radiative transfer codes have become a useful
tool for interpreting satellite imagery and testing retrieval schemes in both the IR
(Kalb et al. 1987; Benoit et al. 1989; Muller and Fuelberg 1990) and MW portions
of the spectrum (Diak et al. 1992; Pudykiewicz et al. 1992).
Our research focuses on a warm (dry) TB band in the simulated imagery that
accompanies a tropopause fold and upper level jet-front system located upstream
of the explosively deepening surface cyclone during ERICA IOP4. Understanding
warm (dry) features in water vapor imagery is important because warm 6.7 or 6.3
pm signatures have been associated with several significant weather phenomena.
These include the initiation of convection (Allison et al. 1972; Petersen et al. 1984;
Rogers et al. 1985; Smith and Gall 1989), surface cyclogenesis (Uccellini et al.
1985; Reed and Albright 1986; Young et al. 1987) tropopause folding (Uccellini et
al. 1985; Moore and Fuelberg 1988; Muller and Fuelberg 1990), and upper level jet
I
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89
streaks (Sechrist et al. 1986) and jet streams (Martin and Salomonson 1970;
Rodgers et al. 1976). Weldon and Holmes (1991) attached particular significance
to the boundaries between dry and moist air that are evident in water vapor
imagery. This chapter examines how warm (dry) signatures in water vapor imagery
near 183 GHz relate to kinematic and dynamic features in the middle and upper
troposphere before and during the period of rapid cyclogenesis during ERICA IOP4.
We interpret the signatures in light of current theories on upper level fronts and
tropopause folding.
4.2. Methodology
The data set for this study consisted of hourly history files of basic
meteorological variables from a LAMPS run provided by Dr. Bill Lapenta of
NASA/Marshall Space Flight Center.
LAMPS (Perkey 1976) is a hydrostatic,
primitive equation, mesoscale model.
It includes prognostic equations for grid
resolved cloud and rain water, a feature that is advantageous for the MW radiative
transfer simulations. Convection is parameterized using a sequential plume model
(Kreitzberg and Perkey 1976). The version employed here had 20 sigma-height
levels from the surface to 16 km, a horizontal grid spacing of approximately 70 km,
time dependent boundary conditions from linearly interpolated (in time) NMC
(National Meteorological Center) grids with a four gridpoint "sponge? layer on each
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90
boundary. Model initial conditions were prepared from the NMC 381 km mesh
global analysis interpolated to the LAMPS grid as a first guess field and then
modified with sounding data. The model domain was 15.0 - 62.5� N and 27.55 115.7� W. The model simulation was initialized at 1200 UTC 3 January 1989 and
run 36 hours at 1 minute time steps until 0000 UTC 5 January. This simulation
was nearly identical to that described by Doty and Perkey (1993) who provide a
more complete description of LAMPS and the initial analysis procedures.
The hourly history files were employed to calculate trajectories and MW T3s
at 176.31 and 182.31 GHz. Hereafter we refer to these simply as 176 and 182 GHz
respectively.
Doty and Perkey (1993) demonstrated that accurate trajectory
calculations for this case required hourly or higher frequency history data for
reasonable accuracy due to strong gradients of vertical velocity. Our trajectories
utilized hourly data and were computed kinematically from the three dimensional
model wind field using an iterative technique (Muller and Fuelberg 1990).
Additional diagnostic parameters were calculated at three hour intervals from
LAMPS output interpolated to constant pressure surfaces. Potential vorticity was
computed on pressure surfaces using the isobaric form given by Crum and Stevens
(1988).
The frontogenetical function (Miller 1948) can be applied to water vapor.
In this context it quantifies the kinematics of dry/moist boundary formation and
evolution.
It is given in isobaric coordinates by
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91
2
d |V ^
5t
ox
, , d q d q , 3d)
L(- ^ - 3 p ^
ok
oy
ay
_ 3 q i q (| v ^ 3u
ox o y Ox o y
, 3ct 3 q \ 3a)-,
C- 3 y - 3 p ; - 3 y J
, d q 3 , d q ) + d q d . d q ) l}
?3y-3y^aEn '
(4>1)
where
V2gj = t
( | | ) 2
+ ( | | ) 2] 4 /
( 4 *2:
and q is the specific humidity, u, v, and 0 ) are the 3-dimensional wind components,
and t is time. Equation (4.1), similar to the Anthes et al. (1982) version in sigma
coordinates, describes the changes in magnitude of horizontal gradients of q
following the 3 -dimensional movements of a parcel. Terms on the right-hand-side
of (4.1) represent contributions (from left to right) of (a) confluence, (b) shearing
deformation, (c) differential vertical motion (or tilting), and (d) the gradients of
sources and sinks of water vapor due to aiabatic moist processes. TBs at 182 GHz
represent radiance contributions from deep layers of the atmosphere. Contribution
functions indicate that moisture and temperature variability within the layer from
800 to 200 mb is largely responsible for the variability in radiance at 182 GHz.
Therefore F2 and its four components were averaged vertically according to
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,
92
(4.3)
where p = 2 0 0 mb and pb=800 mb.
The final term in (4.1) presents special problems for calculation.
Our
method was to expand the total derivative dq/dt, and calculate the local tendency
3q/3t using centered time differences. However, explicit model calculated values
of 0 q/8 t are not suitable for this purpose since they exhibit large discontinuities
when the convective moisture tendencies are incorporated into the grid resolved
computations. After extensive sensitivity tests of different time intervals using
special time series of q and dq/3t at every model time step
(1
minute), we decided
to use half hour centered differences of q (i.e., 2At=30 minutes) to approximate the
local derivative.
The radiative transfer formulations are described in Sections 2.3, 3.2, and
Appendix A. Modified gamma distributions representing altostratus clouds (Falcone
et al. 1979) were applied to LAMPS liquid cloud water while the Starr and Cox
(1985) bimodal crystal formulation was applied to LAMPS cloud ice contents. A
Marshall-Palmer (1948) distribution was assumed for LAMPS rainwater and
precipitating ice. Our version of LAMPS did not calculate separate categories of
liquid and frozen hydrometeors; therefore, a mixed layer of liquid and frozen
particles was assumed. Specifically, the proportion of liquid to ice contents for
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93
both clouds and rain decreased linearly with respect to temperature between 258 and
248 K.
The satellite zenith angle was allowed to vary during the image simulations.
Although AMSU will be placed on a polar orbiting satellite, the zenith angles
employed here were those of the GOES during ERICA IOP4 to facilitate
comparison with its 6.7 pm channel. Thus, the angles vary from a minimum of 18�,
to 82� in the northeast comer of the LAMPS domain. The AMSU scans across
track, varying from a nadir viewing angle to a maximum of ��. The 182 GHz
channel is unpolarized, while the 176 GHz channel receives a changing combination
of vertical and horizontal polarizations based on its scan angle. However, this
polarization has been neglected since we refer to 176 GHz TBs only peripherally
and since the radiance contributed by the surface at 176 GHz generally is less than
30% over most of the LAMPS domain. In addition to polarization, the zenith angle
also affects TOA TBs through its scaling of the vertical optical depth. For example,
182 GHz T bs for a clear southern mid-latitude LAMPS profile range from 248.4 K
at 0� zenith angle to 238.9 K at 60�.
Values for a clear northern ^mid-latitude
sounding vary from 241.9 K at 0� to 234.0 K at 60�. Thus, a portion of the overall
south to north TB gradients in this study can be ascribed to variations of the
modeled zenith angle.
AMSU-B will have a nadir instantaneous field-of-view (IFOV) of 15 km,
with a 52 km IFOV at the maximum scan angle of 49.5�. Our research does not
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94
address the nominal AMSU-B resolution or attempt to reconcile it with the LAMPS
grid spacing of 70 km.
Instead, it is assumed that each LAMPS sounding
represents conditions everywhere within a pixel and that the pixel resolution is
equal to the LAMPS grid spacing.
The proper incorporation of convective and grid-resolved atmospheric
profiles into the radiative transfer calculations presents difficult philosophical
challenges. We utilized specially modified LAMPS code to write the convective
profiles to the history files. Separate T 3 calculations were made for each convective
profile and grid resolved sounding.
The two were then combined based on a
volume weighted average of the convective cloud volume and the grid box volume
minus the convective volume. LAMPS never yielded a convective volume of more
than 15% of the total grid volume (approximately 70x70x16 km).
Thus, the
convective profiles never affected the TBs by more than a few degrees. These small
convective volumes lead us to question their representativeness for large areas of
convection, although they may be appropriate for the convective cores.
As a test, we computed a numerical average of AMMS (Advanced
Microwave Moisture Sounder, discussed in Chapter 3) 183�GHz TBs along the
thunderstorm overflight described in Section 3.2.
The 70 km flight track is
approximately equal to the LAMPS grid spacing. Clear air T3s outside the storm
were approximately 260 K while those in the convective core were as cold as 111
K. We can crudely estimate volume percentages if we assume, in analogy to the
I
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95
LAMPS model, that these TBs represent the grid resolved and convective profiles.
Since the numerical average of all the TBs along the transect was approximately 220
K, this implies a convective volume of about 25%. Of course it is imperative to
note that the satellite beam-filling problem is highly non-linear, and thus our
estimate is only a single illustrative example out of many possible physical
configurations. Nevertheless, it suggests that the LAMPS convective scheme may
not give percentages of convective areal coverage appropriate for combining
convective and grid resolved TB calculations.
Current efforts to incorporate
downdrafts in the LAMPS convective scheme may improve its suitability in this
regard.
An additional consideration is that a convective cloud sometimes can be
much shallower than a grid resolved cloud at the same location. This can lead to
convectively derived TBs being warmer than those from the grid resolved sounding.
This suggests that a gridpoint with convective cloud and rainwater also should
incorporate grid resolved cloud and rainwater into the convective TB calculation.
This was not done for our research. In the current simulation the coldest TBs occur
from grid resolved ice concentrations.
Again, because of the small convective
volumes, the impact of the convective profiles on the combined TBs is minimal.
Since this study concentrates on interpreting warm Ts signatures, the convective
results are not crucial to our analysis.
As a final note on methodology, it should be mentioned that the LAMPS
I
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96
model extends only to near 100 mb.
An extra 100 mb of atmosphere must be
prescribed in the radiative transfer model. Therefore, temperatures from the top of
LAMPS to 0.01 mb (approximately 75 km) were specified as isothermal, while
moisture content was assumed to decrease linearly. This assumption may not be
appropriate for such a thick atmospheric layer.
For example, in the northeast
portion of the LAMPS domain, where it is relatively moist near 100 mb, this
procedure may overestimate the stratospheric vapor content, and thereby bias some
CFs upward. Fortunately, however, most regions of the domain, including the main
area of interest, are drier near
100
mb, and the simulated radiometer receives
virtually no radiation from this topmost layer. Past estimates of stratospheric water
vapor have not always been reliable. High quality field measurements recently have
begun to address this concern (e.g., Rind et al. 1993; Kelly et al. 1993). Our future
research will incorporate these recent results to provide a more realistic upper
profile for those few regions of the LAMPS domain where it may be important.
4.3. Results
a. Water vapor image interpretation.
Simulated AMSU 182 GHz images and observed GOES 6.7 um images for
1800 UTC 3 January 1989, 0600 UTC 4 January 1989, and 1800 UTC 4 January
I
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97
1989 are given in Fig. 4.1. It should be noted that the simulated AMSU imagery
at 182 GHz has the horizontal resolution of LAMPS at 70 km while the GOES 6.7
urn channel has a horizontal resolution of
8
km. Hereafter we adopt the time/date
convention of Uccellini et al. (1985) wherein times are abbreviated to two digits
followed by "Z" for UTC, and two digits represent the date in January 1989 (e.g.,
18Z/03). These image times represent periods prior to, during, and near the end of
the rapid development phase of the ERICA IOP4 storm. For ease of comparison,
both the simulated and observed, images have been mapped onto a common
geostationary projection using MCIDAS (Man-Computer Interactive Display and
Analysis System). Dark shades in the images represent warm equivalent blackbody
temperatures (TBB) for 6.7 pm, or warm brightness temperatures TBin the simulated
182 GHz images, respectively. They generally correspond to relatively diy regions
in the upper and middle troposphere. Light shades correspond to cooler radiometric
temperatures, and usually reflect moist or cloudy regions (Petersen et al. 1984;
Muller and Fuelberg 1990; Weldon and Holmes 1991). The ERICA IOP4 storm
was accompanied by a pronounced band o f warm radiometric temperatures at 6.7
pm.
Tnis band is clearly evident at I8Z/03 (Fig. 4.1a) over the Ohio and
Mississippi River Valleys. LAMPS also generated a similar feature at 182 GHz.
It is over the East Coast at 06Z/04, and by 18Z/04 is well out over the Atlantic.
It has assumed a long cyclonically curving shape as the "dry slot? region associated
with the ERICA IOP4 comma cloud pattern. This band is the primary focus of this
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98
a
4.i. (Top) Observed GOES/VAS 6.7 urn water vapor image and (bottom.)
simulated LAMPS/AMSU 182 GHz water vapor image for (a) 18Z/03 January
1989, (b) 06Z/Q4, and (c) 18Z/04.
M g.
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Fig. 4.1--continued.
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100
Fi" 4.1--continued.
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101
section.
Radiance contributions in water vapor channels emanate from deep layers
of the atmosphere and can be quantified using the contribution function (CF, see
Section 2.2). A simple measure of the depth to which a satellite channel penetrates
the atmosphere is given by the 50% cumulative or median contribution level
(CCL50). That is, 50% of the radiance reaching the satellite emanates from above
this level, and 50% from below. Table 4.1 presents precipitable water content
(PWC) and pressure level statistics from LAMPS/AMSU TB calculations at 182
GHz for both 50% and 90% CCLs. The precipitable water is calculated from the
top of the LAMPS atmosphere down to the pressure level of the 50 or 90% CCL.
The 90% CCL (CCL90) is that level above which 90 % of the radiance contribution
emanates, while 10 % comes from below. The PWCs were calculated from the
vertical sounding but then scaled by 1/cos 0 to account for the slant path. Statistics
were calculated for all LAMPS soundings and for clear soundings only.
Table 4.1 indicates the variability of CFs over the range of tropical to
northern mid-latitudes portrayed by the LAMPS soundings. For clear soundings
only, the average CCL50 ranges from 383 mb with a standard deviation of 94 mb
at 18Z/03, to 399 and 76 mb at 182704. For CCL90 the values range from 555 mb
and standard deviation of 82 mb, to 567 and 82 mb.
The statistics reveal the
sensitivity of this channel to the upper level water vapor profile. For example, for
clear LAMPS soundings, 50% of the radiance contribution is produced by the top
I
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102
Table 4.1. Average precipitable water content (PWC) above the 50% (top two
sections) and 90% (bottom two sections) cumulative TB contribution levels, and
average pressure (p) of cumuladve contribution levels, s.d. is standard deviation.
Data for all soundings and for only clear soundings are give for three time/dates.
Time/date
18Z/03
06Z/04
18Z/04
CCL50
(All soundings)
Ave. PWC (mm)
s.d. PWC (mm)
Ave. p (mb)
s.d. p (mb)
0.29
0.13
332
125
0.29
0.12
341
124
0.29
0.12
353
118
(Clear soundings)
Ave. PWC (mm)
s.d. PWC (mm)
Ave. p (mb)
s.d. p (mb)
0.35
0.09
383
94
0.36
0.10
393
93
0.36
0.09
399
76
CCL90
(All soundings)
Ave. PWC (mm)
s.d. PWC (mm)
Ave. p (mb)
s.d. p (mb)
1.41
0.28
561
99
1.37
0.35
544
113
1.37
0.37
540
121
(Clear soundings)
Ave. PWC (mm)
s.d. PWC (mm)
Ave. p (mm)
s.d. p (mb)
1.53
0.22
555
82
1.56
0.24
566
82
1.57
0.22
567
82
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103
0.35-0.36 mm of precipitable water sensed by the 182 GHz channel as it views
downward into the atmosphere. On the other hand, 90% of the radiance is produced
by the top i.53-1.57 mm of vapor. Note that these are scaled values of the slant
path. These numbers are, of course, slighdy smaller for cloudy or rainy soundings
because average CCLs are higher in the atmosphere due to the presence of
hydrometeors.
Pressure contours of CCL50 (Fig. 4.2) are related to the LAMPS/AMSU
water vapor images (Fig. 4.1). Specifically, areas of warm TBs (dark) in the images
generally correspond to local maxima of CCL50 pressure, indicating that the
simulated radiometer "sees" down to relatively warm layers of the atmosphere. In
fact, the 182 GHz warm signature that propagates from the midwestem United
States at 18Z/03 to the western Atlantic at 18Z/04 accompanying the ERICA IOP4
storm occurs in a region of extreme upper and middle level dryness. Fully 50% of
the radiance at the maximum CCL50 comes from below 700 mb at 18Z/03, 734 mb
at 06Z/04, and 715 mb at 18Z/04. This suggests that the so-called 700 mb "dry
punch" used in severe storm forecasting (Fawbush et al. 1951; Miller 1959) can,
under some conditions, be detected at 182 GHz. Ucceilini et al. (1985) noted that
warm 6.7 pm signatures associated with the Presidents? Day cyclone coincided with
dry areas at 700 mb. It is interesting to note that the location of the CCL maximum
(e.g., southwest of the Great Lakes at 18Z/03) does not coincide with the warmest
LAMPS/AMSU TB (see Fig. 4.12 in Section 4.3c). This reflects the strong lower
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06 0 0 UTC 04 JAN 1989
Fig. 4.2. AMSU 182 GKz 50% cumulative contribution level (mb) over the LAMPS
domain for (first panel) 18Z/03 January 1989, (second panel) 06Z/04, and (third
panel) 18Z/04.
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105
LAMPS/AMSU 182 GHz 50% Cum . C on trib . L ev el (m b )
'3 .3 '
1 8 0 0 UTC 0 4 JAN 19 8 9
Fig. 4.2--continued.
I
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106
tropospheric temperature gradient in the region. In a clear atmosphere, cooling the
ambient temperature profile while holding the water vapor constant can decrease the
radiometric temperature without changing the height of the contribution function.
Thus, since the radiative transfer equation convolves the effects of moisture and
temperature, there is an inherent ambiguity as to whether the warmest TBs reflect
the driest upper and middle tropospheric profile.
In fact, in the presence of
horizontal temperature gradients they may not. Specific examples of this effect will
be examined more closely in Section 4.3c.
b. Synoptic Summary and Simulation Verification.
This section compares simulated 182 GHz image features with those of
observed GOES 6.7 pm water vapor imagery and LAMPS kinematic parameters,
along with an overview of their relation to the ERICA IOP4 surface low.
In
particular, we focus on the dry intrusion signature, that is, the warm T3 feature
accompanying the upper front/tropopause fold.
In a general sense LAMPS
generated a realistic simulation of the warm radiometric signature and synoptic
patterns. However, it did not achieve the magnitude of surface deepening actually
observed.
Synoptic aspects of this storm have been discussed previously by
Wakimoto et al. (1992), Nieman and Shapiro (1993), Nieman et al. (1993), and
Chang et al. (1993).
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107
Figure 4.3 (Chang et al. 1993) gives positions of the ERICA IOP4 cyclone
center from 0OZ/04 to 00Z/06 along with selected central pressures estimated by
Nieman and Shapiro (1993).
LAMPS-derived sea level pressure patterns
corresponding to the satellite image times (Fig. 4.1) are presented in Fig. 4.4. The
incipient ERICA IOP4 cyclone appears in the LAMPS initial conditions (see Doty
and Perkey 1993) as a surface low centered over Wisconsin at 12Z/03 (not shown).
The initial analysis produces a LAMPS sea level pressure of 1008.9 mb compared
with 1006.4 mb on the NMC surface analysis (not shown). Observed pressures are
falling rapidly to the southeast of the incipient cyclone.
By the first image time at 18Z/03 (Fig. 4.1a), the observed low (not shown)
had moved over Michigan while a secondary low pressure center of 1003 mb was
developing over the Kentucky-West Virginia border. Observed downward pressure
tendencies exceeding 5 mb/ 3 h already were occurring at many stations from Ohio
southeast to the Eastern Seaboard. The LAMPS simulation (Fig. 4.4) portrays a
similar scenario with a broad area of low pressure stretching from the Great Lakes
to the southeastern United States ahead of a diffluent shortwave trough at 500 mb
(Fig. 4.5).
In LAMPS, the southernmost low at 1004.5 mb appears to be the
dominant center, positioned somewhat south of the observed location. The separate
strong low south of Newfoundland is not addressed in this study.
By 06Z/04 the observed surface low has moved over the Atlantic east of
Virginia (near 70癢 37癗, Fig. 4.3) with a central pressure of 974 mb (Nieman and
I
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Fig. 4.3. The 3-h storm track of the ERICA IOP4 cyclone beginning at 00Z/04
January 1989 to 00Z/06 (after Chang et al. 1993) with central pressures for selected
times estimated by Nieman and Shapiro (1993).
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109
LAMPS SEA LEVEL PRESSURE (m b )? ERICA IOP 4
180 0 UTC 0 3 JAN 1989
LAMPS SEA LEVEL PRESSURE (m b )? ERICA IOP 4
0 6 0 0 UTC 0 4 JAN 1989
Fig. 4.4. LAMPS sea level pressure (mb) for (first panel) 18Z/03 January 1989,
(second panel) 06Z/04, and (third panel) 18Z/04.
i
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110
LAMPS SEA LEVEL PRESSURE ( m b ) ? ERICA IOP 4
o
?iw� i
1800 UTC 0 4 JAN 1989
Fig. 4.4?continued.
I
r
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Ill
-3 9 3 .1
180
CONTOUR FROM 498 TO 600 BY 6
fA
?582
j
>06
4 JAN 1.989'
CONTOUR FROM 496 TO 600 3Y 6
Fig. 4.5. LAMPS 500 mb height field in decameters for (first panel) 18Z/03 January
1989, (second panel) 06Z/04, and (third panel) 18Z/04.
r
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112
tfn'27 /?
rft
O?
'
i
.3 0
18 ?0
CONTOUR FROM 498 TO 600 BY 6
Fig. 4.5?continued.
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Shapiro 1993). The corresponding LAMPS surface low (Fig. 4.4) was located near
70癢 35癗 with a central pressure of 992 mb, still beneath the diffluent flow
downstream of the 500 mb trough axis (Fig. 4.5). The LAMPS simulation never
achieved the magnitude of deepening that actually was observed, probably due to
its 70 km resolution (Doty and Perkey 1993). The lowest central pressure reached
by LAMPS was 968 mb, compared with an estimated central pressure of 936 mb
(Nieman and Shapiro 1993). At 18Z/04, 30 hours into the simulation, the ERICA
IOP4 storm had deepened to a central pressure of 941 mb at about 62癢 38癗 (Fig.
4.3). Concurrently, LAMPS showed 973 mb at 64癢 36癗 (Fig. 4.4), with the 500
mb trough axis (Fig. 4.5) now located almost over the surface low.
The observed GOES 6.7 pm water vapor image for 18Z/03 (Fig. 4.1a)
exhibits a pronounced warm signature over the Ohio and Mississippi River Valleys,
while its simulated AMSU 182 GHz counterpart is centered south westward of this
location over northern Arkansas.
The LAMPS feature is near to, but slightly
lagging the 500 mb trough axis (Fig. 4.5) in a region of sinking motion (Fig. 4.6).
Its leading edge, that is, the strongest radiometric gradient, is over central Tennessee
in both the observed and simulated images, and is punching into an area of middle
tropospheric ascent.
The LAMPS T 3 maximum accompanies an upper level
disturbance marked by the maximum of local potential vorticity (PV) at 400 mb
(Fig. 4.7). The TB feature is located southwest of the PV center, and approximately
1000 km west of the surface low.
There also is a streak of relatively warm
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114
5-S0
j
''V e r
hv'?- /
A
? ?'
??'
Jv-T^uT;
'L Y v4y
V
r^)d;r o^ ar^ s^ > < ^ \
$
.? '
(" fx
/-\--V s \
? A
? !
� A
^ A
\
'^ F e A
'
?
V <?
A A V
- '?
'? ?
jX ../7 J b O j b C l P * ^ \ X S > t \
%'XrXSy|PSL?,?.
A
'
. ^ ,
S i .08 ^ V * 5 =^ v s p U ?^ 2 :i j .:;
>
/ ^
5v
V' V z \
y
J > ( <Us^/ ? ?/ ?; Tjy >
?
? /f e � .., r X X X y . y
f
i
/ i^ v > r y s yp--..
CONTOUR FROM - 3 0 TO 3 0 BY 2
:ONTOUR FROM
Fig. 4.6. LAMPS 500 mb vertical velocities (pb s'1) for (first panel) 182703 January
1989, (second panel) 06Z/04, and (third panel) 18Z/04. Negative values (upward)
are dashed. Contour interval is 2 ub s'1.
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115
CONTOUR FROM - 3 0 7 0 3 0 BY 2
Fig. 4.6?continued.
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116
LAMPS 4 0 0 m b PV (x 10x* - 6 K / m b / s )
$:\ h
1 8 0 0 UTC 0 3 JAN 1 9 8 9 C o n to u r bv
o
AMPS 4 0 0 m b PV (x 10 * * - 6 K / m b / s )
I.
C [
V 'V \
0 6 0 0 UTC 0 4 JAN 1 9 8 9 C o n t o u r b v
5
Fig. 4.7. LAMPS 400 mb potential vorticity (x 10 K mb s ) for (first panel)
18Z/03 January 1989, (second panel) 06Z/04, and (third panel) 18Z/04.
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117
LAMPS 4 0 0 m b PV (x 1 0 * * -6 K / m b / s )
1 8 0 0 UTC 0 4 JAN 1 9 8 9 C o n t o u r by
5
Fig. 4.7--continued.
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radiometric temperatures extending northward across Minnesota and into Canada
in both the 6.7 pm and 182 GHz images. This image feature coincides with a band
of maximum PV at 400 mb.
Intrusions o f dry, PV rich stratospheric air into the troposphere are
intimately related to warm TBBpatterns on 6.7 pm images (e.g., Moore and Fuelberg
1988; Appenzeller and Davies 1992). Our simulations suggest a corresponding
relation for 182 GHz imagery as indicated by the similarites between patterns of PV
at 400 mb (Fig. 4.7) and patterns of CCL50 (Fig. 4.2). This agreement occurs
because regions of stratospheric PV penetration into the troposphere also are very
dry, allowing the simulated radiometer to "see" down to lower layers. Thus in
many cases, fields of TB, PV, and CCL50 exhibit similar patterns although their
maxima may be displaced. For example, at 18Z/04 the warm TBfeature off the
United States East Coast, the accompanying stratospheric intrusion, and the contours
of CCL50 all show cyclonically curving patterns associated with the ERICA IOP4
cyclone.
It is difficult to assess the precise role of jet maxima in forming the warm
Tb maximum. However, as noted by Petersen et al. (1984), this process was aided
by examining animated hourly 182 GHz imagery on McIDA.S and three hourly 6.7
urn loops, as well as by studying standard NMC 300 and 200 mb charts. Relations
between 6.7 pm image patterns and upper level features during ERICA IOP4 bear
many similarities to those during the Presidents? Day cyclone of 18-19 February
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119
1979 (Uccellini et al. 1985). The LAMPS-derived jet structure for ERICA IOP4
at 300 mb (Fig. 4.8) is complex. At 18Z/03 a jet streak is present over the eastern
United States. Observed NMC 300 and 200 mb charts for several days prior (not
shown) reveal that this is a subtropical jet maximum that had propagated from the
southwest and was now merging into the polar jet stream farther north. In addition,
an upstream polar jet streak that had propagated from the northwest is merging into
the entrance region of this downstream subtropical streak.
Finally, another
subtropical jet streak is moving northeastward from Baja California.
The warm radiometric feature at this time (Fig. 4.1a) appears to represent
the merging and intensification of two separate image features seen earlier (not
shown), a configuration that typically occurs in conjunction with merging polar and
subtropical jets (Uccellini et al. 1985; Petersen et al. 1984).
One had been
associated with the polar jet disturbance signified by the 400 mb PV maximum
(Fig. 4.7), while the other was developing nearer the subtropical flow. As in the
Presidents? Day case, the intensification of the merging TB features occurs in the
confluent entrance region of the downstream subtropical jet streak, and in the right
front quadrant of the propagating polar jet streak. Meteorological factors leading
to moisture gradient formation can be quantified by averaging the terms of F2 for
water vapor over a subjectively chosen box encompassing the warm image feature
and the developing radiometric gradient downstream. Results (Table 4.2) indicate
that confluence (3.20 X 10'11 g kg'1 m '1 s'1) is the dominant component of the total
I
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CO N TOUR FROM 0 TO 2 0 0 BY 10
Fig. 4.8. LAMPS 300 mb wind speed (m s'1) for (first panel) 18Z/03 January 1989,
(second panel) 06Z/04, and (third panel) 18Z/04.
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121
3 2 - 2
x ^ y '^ l
;
;^ ;
si. as
"%
/
7
V n * \\& i
CONTOUR FROM 0 TO 2 0 0 BY 10
Fig. 4.8?continued.
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122
Table 4.2. Vertically averaged value of the frontogenetical function (F2 in (4.3)
x 10'11 g kg' 1 m '1 s'1) for water vapor and its terms, averaged over a box. CON is
confluence. SD is shearing deformation. TILT is tilting. DIAB is gradients of
water vapor sources and sinks, i.e., moist diabatic processes.
Time
18Z/03
06Z/04
18Z/04
CON
3.20
1.53
2.36
SD
1.45
2.07
5.13
TILT
0.38
13.31
11.78
DIAB
-1.18
-14.43
-24.66
F2
3.85
2.5
-5.39
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123
F 2 (3.85 X 10'u g kg'1 m '1 s'1) at 18Z/03. Shearing deformation also is important,
contributing 1.45 X 10"11 g kg'1 m '1 s'1, while moist diabatic processes with a value
of -1.18 X 10'11 g kg'1 m '1 s'1 act to diminish the strength of the water vapor
gradients. Tilting becomes important only later in the simulation period.
Jet characteristics during ERICA IOP4 are consistent with those of previous
studies. Keyser and Shapiro (1986, also given in Carlson 1992) have described an
advective jet model of confluent flow with an along-stream component of
temperature gradient (Fig. 4.9, after Keyser and Shapiro 1986).
Conditions
consistent with this model usually occur in regions of northwesterly flow. The polar
jet streak is upstream of the large scale trough axis and cold advection occurs along
the jet axis. Subsidence (co>0) occurs along the length of, and directly under the
jet streak, with rising cells in the right rear and left front jet quadrants.
The
schematic of vertical motion associated with this model (Figure 4.9) corresponds
well 'with conditions during ERICA IOP4, e.g., Fig. 4.6 showing 500 mb vertical
motions and Fig. 4.8 depicting the LAMPS 300 mb jet at 18Z/03. The LAMPSderived band of sinking motion occurs mostly beneath the 300 mb polar jet streak
southwest of the Great Lakes. A cell of rising motion is located in the right rear
quadrant over the Rocky Mountains.
A more intense cell of rising motion is
located in the left front quadrant south of the Great Lakes. In addition, NMC 300
mb charts for 12Z/03 and 00Z/04 (not shown) indicate that cold advection indeed
was occurring along the polar jet.
From a synoptic perspective, the warm TB
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124
C
O
L
D
WARM
Z
-F
A
Z
Z
+A
Z
Fig. 4.9. Schematic illustration of geostrophic deformation fields for a straight jet
stream wind maximum for a case of confluence with a component of cold advection
along the jet axis. Heavy full curves are geopotential height contours; heavy
broken curves are isotachs; thin full lines are isentropes; arrows indicate the sense
of the ageostrophic circulation; plus or minus signs give sense of the vertical
motion (co) (After Keyser and Shapiro 1986, and Carlson 1992).
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125
feature is most clearly associated with negative vorticity advection behind the 500
mb trough axis. In fact, the observed NMC 500 mb vorticity pattern at 12Z/03 (not
shown) reveals that the two merging radiometric features occur in conjunction with
a vorticity maximum and a vorticity lobe extending to its southwest. Muller and
Fuelberg (1990) showed that warm TBB features in 6.7 pm imagery were associated
with vorticity features and negative vorticity advection.
Conditions at 06Z/04 now will be examined. The GOES 6.7 pm warm
image feature (Fig. 4.1b) is centered near 76� W 33癗 off the South Carolina coast
with its leading edge pushing eastward to approximately 70癢. It is separated from
a broad region of warm TBBs to its south by a band of cooler TBBs reflecting water
vapor or cirrus clouds. The storm-related moisture pattern has begun to assume the
classical comma shape, with a large cold cloud head and a tail consisting of a line
of convection that had formed earlier within the leading edge of the warm feature.
By comparison, the LAMPS simulated warm feature (Fig. 4.1b) also is
centered off the South Carolina coast (approximately 76癢 and 33癗), but with its
leading edge not as far east as observed. It is not separated from the warm TB area
to the south, although its individual identity is evident in hourly image loops. Tne
maximum T 3 exceeds 260 K. Cold T3s associated with large ice content produced
by the deepening storm are evident ahead of the warm TB feature as an incipient
comma head. In contrast to the observed configuration, the center of the LAMPS
surface low (Fig. 4.4) is ahead and to the left of the warm TB feature, not beneath
I
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126
it.
The LAMPS warm image feature (Fig. 4.1b) again exists in a region of
mostly sinking vertical motion at 500 mb (Fig. 4.6), but overlaps into the area of
ascent ahead of the 500 mb trough axis. Maximum TBs now are located within the
right front quadrant of the merged 300 mb jet streak (Fig. 4.8). A band of warm TBs
extends upstream to the northwest. However, its axis is displaced southwestward
from the axis of the 300 mb polar jet; that is, looking downstream it is to the right
of the jet axis for its whole length.
F 2 for water vapor averaged over a region within and ahead of the warm TB
feature (Table 4.2) still is positive at 2.5 x 10'11 g k g 'W V .
The, tilting and
diabatic moist processes are much greater in magnitude than the other terms, nearly
balancing each other.
Spatial patterns (not shown) indicate that tilting and
"diabatic" contributions to moisture gradient formation are essentially collocated but
opposite in sign. This implies evaporation in regions of sinking motion adjacent
to condensation in areas of ascent. The balance between these two terms allows
shearing and confluence to combine with tilting for an overall strengthening of the
moisture gradients.
The PV maximum at 400 mb over the East Coast for 06Z/04 (Fig. 4.7) has
increased in magnitude indicating the continuing intrusion of stratospheric air into
the troposphere.
It is north of the maximum TB.
Causes for the specific
juxtapostions of the warm feature, PV, dry air, and CCL50 will be examined in
!
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127
Section 4.3c.
The cyclone and image feature continue to evolve rapidly during the next
twelve hours. At 18Z/04 (Fig. 4.1c) the observed GOES 6.7 pm warm feature has
propagated well over the Atlantic, curving cyclonically from eastern Tennessee to
near 57癢 42癗. It is wrapping into the comma cloud pattern subsequent to the
"T-bone" phase as warm core seclusion begins (Nieman and Shapiro 1993). The
warm feature has curved around the southern and eastern sides of the surface low.
The LAMPS simulation of the warm TB feature at 18Z/04 (Fig. 4.1c)
remains reasonably faithful to the observed version. It also has begun to wrap
around the southeast side of the surface low (Fig. 4.4). Consistent with LAMPS?
failure to sufficiently deepen the surface low, the warm TB feature does not appear
as "wrapped up" as the corresponding observed 6.7 pm feature. It extends eastward
to a location (60癢 37癗) southwest of the observed position, as was the surface
iow (Figs. 4.4 and 4.3). It stiii is generally confined to the poleward side of the
300 mb jet axis (Fig. 4.8), and still is mostly behind the 500 mb shortwave trough
(Fig. 4.5).
The sum of contributions to the water vapor gradient (Table 4.2) has become
frontolytic (-5.39 X 10'11 g kg"1 m '1 s"1) due to moist diabatic processes. Although
the shearing contribution has become steadily greater, and the confluence and tilting
terms remain positive, they cannot offset the destruction of the water vapor gradient
from condensation and evaporation of hydrometeors.
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128
Cross-sectional analyses of both observed and simulated data provide a final
verification of the LAMPS model run. Keyser et al. (1978) previously have used
a LAMPS simulation with a grid spacing of 120 km to examine upper level frontal
structure. Figure 4.10 (top; from Nieman and Shapiro 1993) shows a cross section
of observed wind, potential temperature, and PV across the upper frontal zone at
00Z/04 during ERICA IOP4. Figure 4.10 (bottom) depicts LAMPS/AMSU 182
GHz Tb patterns at the same time and the location of a model cross section
coincident with that of Nieman and Shapiro (1993). The LAMPS cross section
(Fig. 4.11) contains four panels: TBs at 182 and 176 GHz, total wind speed (m s'1)
with vectors of vertical velocity (pb s'1), potential temperature with stratospheric
contours of PV (i.e., 10 and 20 x 10'6 K mb'1 s'1, hereafter termed 10 or 20 PV units
in the text), and specific humidity (g kg'1). Northeast is to the left and southwest
is to the right. It is clear that LAMPS did a credible job of handling the upper
ievei features. Tne LAivlrS-derived jet structure and potential temperature fields
appear very similar to those observed (Fig. 4.10). The simulation captures the
sloping frontal zone and folding tropopause depicted by the PV contours. They
encompass a region of downward instantaneous vertical velocity with a maximum
value of 6.6 pb s'1. The LAMPS 10 unit PV contour extends 'lower than observed,
down to nearly 900 mb, and may encompass a region of local diabatic PV
production as well as stratospheric air. The moisture field indicates that drying
associated with the stratospheric air had extended to 800 mb.
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150
,50
200
?3 6 0
?3 4 0
340
250
320
300
300
5
330
400
?------ 30
5 00
320
290
700
?vO -
? 10
1000
FNT
WMW
OAY GSO
BNA
CKl
S it
2 5 0 km
LAMPS/AMSU 1 82 GHz TB (K);
X - S e c t i o n L o c a t io n
0 0 0 0 UTC 0 4 JAN 1S89
Fig. 4.10. (Top) Cross section of observed data at 00Z/04 January 1989 of potential
temperature (K, solid) and section-normal wind speed (m s 1, dashed). The heavy
solid line is the 1 X 10?6 m2 s'1 K kg'1 isopleth of potential vorticity denoting
stratospheric values. Note that this formulation of PV includes a factor of 1/g
(gravity). Wind vector flags are 25 m s'1; full barbs are 5 m s'1; half barbs are 2.5
ix x
o
(
A f t/w
cvi
V
i p m
p n
I 'i i v i i i u i i
p n o
^ n u ^ /* A v
1 Q Q 'X 'Y
s s
j *
^ T 3 r \ t - r / '- \ r r > \ 7
A
/
A A /iC 7 7
J / r k i n j v/
o n .n c A i.u .i.v O
1 Q 0
iO � ->
GHz T b (K) field at 002704, and location of a LAMPS cross section (shown in Fig.
4.11) coincident with Nieman and Shapiro?s cross section.
I
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130
LAMPS/AMSU 182 AND 176 GHZ TB (K)
176GHz
182 GHz
200 r
NE
VTS ( m / s ) / OMEGA
- LAMPS/ERICA I0 P 4
SW
_D 2 0 0
C 500 T '
'
700 -
THETA /P V (X l0 * * -6 ) - LAMPS/ERICA I0P 4
300
Q ( g /k g ) - LAMPS/ERICA IOP4
lea ttr 300 -
0 0 0 0 UTC 04 JAN 1 9 8 9
Fig. 4.11. LAMPS cross section (location shown in Fig. 4.10) for 0OZ/04 with
(panel 1) TBs (K) at 182 and 176 GHz along the section. (Second panel) Vertical
velocity vectors (maximum vector length is 6.6 ub s'1) and isopleths of wind speed
(m s'1). (Third panel) Potential temperature (K) with stratospheric values of 10 and
20 x 10'6 K mb'1 s'1 superimposed. (Fourth panel) Specific humidity (g kg'1). Solid
lines are contour intervals of 0.5 g kg'1. Dashed lines are contour intervals of 0.05
g kg'1 for values below 0.5 g kg'1.
L
i
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131
In summary, LAMPS produced realistic radiometric signatures and appeared
to simulate the observed upper level structures faithfully.
There were two
limitations. The simulated warm radiometric feature and surface low seemed to lag
the observed versions.
Furthermore, the simulated low never achieved the
deepening that was observed, and this probably affected LAMPS? version of the
comma cloud. Nevertheless, LAMPS reproduced the strong warm signals and even
some relatively subtle features of the observed imagery. Section 4.3c will use the
LAMPS model output to characterize and explain the warm radiometric signature
during ERICA IOP4, and how it is perceived at 182 GHz.
c. 182 GHz Tb and Tropopause Folding
"Tropopause folding" has been described in detail by numerous investigators.
It occurs in conjunction with the propagation of upper tropospheric jet streaks and
is associated with sloping upper level frontal zones beneath and on the poleward
side of the jet stream (Reed and Sanders 1953; Reed 1955; Danielsen 1968; Shapiro
1980; Uccellini et al. 1985).
In the tropopause folding process, ageostrophic
circulations accompanying the jet streak are responsible for extruding stratospheric
air downward as part of the sloping upper frontal zone (Shapiro 1981; Keyser and
Shapiro 1986).
PV, humidity, and ozone concentrations all have been used to
distinguish between stratospheric and tropospheric air near folds (Staley 1960;
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132
Danielsen 1968; Danielsen 1980; Shapiro 1980). In the absence of strong gradients
of diabatic temperature changes, PV greater than 10-20 units can be used to trace
stratospheric air (e.g., Uccellini et al. 1985). This section examines and explains
relationships between tropopause folding and the simulated warm radiometric
feature at 182 GHz during ERICA IOP4.
Figure 4.12 shows the location of a cross section (Fig. 4.13) across the
LAMPS/AMSU 182 GHz warm feature at 18Z/03. Also shown are seven back
trajectories, computed hourly for a six hour period, and ending at 500 mb along the
cross section, as well as the location of the maximum CCL50 (denoted by "+").
Parameters corresponding to the beginning and end of the trajectories are presented
in Table 4.3. The orientation of the trajectories (Fig. 4.12) confirms that the warm
feature forms in a zone of confluent airstreams with parcel
1
rising slightly from
513 to 500 mb while those farther north sink by varying amounts. Maximum time
integrated, subsidence occurs within and on the poleward side of the maximum TB.
For example, parcel 4 ends at the gridpoint of maximum 182 GHz TB south of the
10 unit PV contour denoting stratospheric air (Fig. 4.13).
It subsides 107 mb
during the six hour period ending at 18Z/03. Parcel 5 also ends within the warm
Tb feature, but north of the maximum T B. It terminates within the 10 unit PV
contour, and subsides 115 mb during the six hour period. The PV data (Fig. 4.13)
suggest that trajectory
6
ends within the core of the folded tropopause.
It has
subsided 106 mb in the previous six hours. One should note that parcels 5, 6 , and
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18 0 0 UTC 03 JAN 1989
Fig. 4.12. LAMPS TBat 18Z/03 January 1989 with numbered air parcel trajectories
ending at 500 mb at that time. Position for cross section from Fig. 4.13 is indicated
by vertical bar. The location of maximum CCL50 (mb) is indicated by a
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134
LAMPS/AMSU 182 AND 176 GHZ TB (K)
20C r
' 7 5 =?
150 4
;;.............
WS ( m / s , j / OMEGA
? LAMPS/ERICA IQP4
s
2C0r
VT* * V
TKETA /P V ( X 1 0 - - 6 ) - LAMPS/ERICA I0 P 4
Q (g /k g ) 180
LAMPS/ERICA IOP4
-----------------------------------------------------------------------------
-s 2CC -
1 8 0 0 UTC 03 JAN 1989
Fi�. 4.13. Sume 3.S F 1 2 . 4.11, but for I 8 Z/O0 . The cross section locution is shown
in Fig. 4.12. Maximum vertical velocity vector length is 10 pb s'1. Ending
locations of trajectories from Fig. 4.12 are indicated by numbered circles.
I
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135
Table 4.3. LAMPS parcel variables corresponding to trajectories in Fig. 4.1 1, where
p is pressure, q is specific humidity, and 0 is potential temperature. Data are given
for starting and ending times of each trajectory.
Time
P
(mb)
q
(g kg'1)
0
(K)
1
18Z/03
12Z/03
500
513
0.81
0.81
323.1
323.3
2
18Z/03
12Z/03
500
496
0.63
0.69
322.8
323.1
3
18Z/03
12Z/03
500
479
2.36
2.35
320.9
321.3
4
18Z/03
12Z/03
500
393
0.15
0.13
317.4
317.5
5
18Z/03
12Z/03
500
385
0.10
0.10
310.4
310.4
6
18Z/03
12Z/03
500
394
0.06
0.06
303.0
303.8
7
i o r-7? /a a
i
JW
427
f AA
A
AA A
Trajectory
12Z/03
AO
u.uo
0.08
J
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-T
/
294.7
7 with water vapor contents of 0.10, 0.06, and 0.08 g kg'1 are drier at 500 mb than
is parcel 4 (0.15 g kg'1) which ends at the location of the maximum TB. This low
humidity is consistent with the high PV values at the endpoints of trajectories 5-7,
and suggests that they originated in the stratosphere prior to the initial simulation
time. On the other hand, it appears that parcel 4 originated in the troposphere
(based on its higher humidity and lower PV), despite the fact that its integrated
subsidence during the previous six hours is roughly equivalent to that of the drier
parcels.
Comparing Fig. 4.2 with Fig. 4.12 reveals that the lowest level of CCL50
(i.e., the highest pressure, denoted by the "+" on Fig. 4.12) associated with the
warm TB feature occurs on the poleward side of the TB maximum.
Thus the
simulated radiometer "sees" deeper into the atmosphere northeast of the TB
maximum (at the location of the maximum CCL50) where the TB is 256 K than at
lu c
l O C a u u ii
v l
u ic
w o iu ic m
ig
x\
.).
u
i
o le
acuw uvc
i \j
c v v ^ ii
au iaix
changes in the water vapor content, this must be explained by the strong lower
tropospheric temperature gradient.
This gradient is evident in Fig. 4.14 which
presents soundings and CFs for (top) the griapoint of maximum 182 GKz T3 (i.e.,
the ending location of trajectory 4 in Figs. 4.12 and 4.13), and (bottom) the
gridpoint of maximum CCL50. The CF peak at the maximum 182 GHz (channel
6) TB occurs near 600 mb while dual peaks at the greatest CCL50 are found near
600 and 900 mb. These peaks occur because of the extremely dry layer of air of
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137
; msu
iec e -ce.c
-se.e
-*e
-oc c
2
contribution
function
-sc c
s -c
2C.C 3e e
2
CONTRIBUTION
;< h - i ;
AMSU CONTRIBUTION FUNCTION
-120.2
- ?5 0 . 2
-B2.0
-70.2
-00.0
-5e.0
-40.0
" !
r
SFC E HI S. = 0 . 9 0
ZENITH ANGLE= 44.
4 - 1 7 6 . 3 1 GHz TB* 2 7 2 . 7 2
6 - 1 8 2 . 3 1 GHz
TB* 2 5 6 . 4 2
4 - S r C CONT = 0 . 2 9 7 .
6 -SFC CONT = 0 . 0 0 2
to 4 0 0
500
7se pNg
?30.0
700
800
900
10 0 0
-
20.2
-
12.2
2.2
10.2
20.0
30
.
.0
.1
.2
.3
.4
CONTRIBUTION
.5
.6
.7
(Kh-1)
Fig. 4.14. Skew-T Log-p diagrams (left) of LAMPS grid-resoived temperature and
dewpoint at 18Z/03. Right: corresponding LAMPS/AMSU contribution functions
and T bs (K) for 182 and 176 GHz. Top panels are for the point of maximum TB.
Bottom panels are for the point of maximum CCL50. These locations are shown in
Fig. 4.12.
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138
stratospheric origin between 700 and 800 mb at the location of maximum CCL50.
This dry layer allows the radiometer to receive radiance contributions from moist
layers below 800 mb that are essentially obscured at the location of maximum TB.
This lower tropospheric dry layer does not exist beneath the warmest TB because
stratospheric air, as indicated by the 10 unit PV contour in Fig. 4.13, has not
penetrated this far south. Despite the contributions from lower layers at the greatest
CCL50, a comparison of the temperature profiles (Fig. 4.14) reveals that the lower
and middle troposphere are significantly cooler at this drier location. For example,
temperatures at 600 mb at the greatest CCL50 (bottom panels) are approximately
6 K cooler than those at the TB maximum (top panel). This offsets the radiometric
warming that results from penetrating lower into the atmosphere.
We now examine the 182 GHz warm feature in the context of tropopause
folding. As noted earlier, Fig. 4.13 is a cross section for 18Z/03 along the axis in
Fig. 4.12. Ending locations of the trajectories of Fig. 4.12 are indicated by the
numbered circles.
The cross section indicates that maximum instantaneous
subsidence (10 pb s 1) occurs within and poleward of the TBmaximum at 182 GHz.
The subsidence is beneath and north (left) of the 70 m s'1 jet core, within the
tropopause fold as indicated by the stratospheric PV. Even at this stage of the
ERICA IOP4 storm, the 10 unit PV contour reaches down to the 800 mb level.
Thus, as in the Presidents? Day storm (Uccellini et al. 1985), the tropopause folding
process appears to be well under way prior to the rapid deepening phase.
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A
139
downward depression of midtropospheric water vapor contours occurs in the region
of enhanced stability denoting the upper frontal zone that slopes downward and to
the south (right) in conjunction with stratospheric PV values. The warm TBfeature
is skewed slightly southward of the driest middle tropospheric moisture values
toward warmer temperatures due to the horizontal temperature gradient described
previously. This orientation is different from that shown by Muller and Fuelberg
(1990) for GOES 6.7 um imagery and from Ramond et al.?s (1981) analysis in
which warm TB3 maxima aligned with the upper parts of tropopause folds. These
differences may be related to the relative strengths of upper level features in the
respective cases. For example, Muller and Fuelberg showed a relatively weak case
of tropopause folding whereas the ERICA IOP4 storm contains intense upper level
features.
Proceeding to 18Z/04 when rapid deepening of the surface cyclone was well
under way, Fig. 4.15 (top and bottom) shows the location (labeled A) of a cross
section (Fig. 4.16) across the mature warm TBfeature over the Atlantic. Also shown
are the location (labeled B) of an additional cross section for 00Z/04 (to be
discussed later in this section and shown in Fig. 4.19), and numbered back
trajectories ending at points distributed vertically at two different locations.
Trajectories 1-3 end on the north side of the warm TB feature (Fig. 4.15), below and
within the upper part of the tropopause fold (Fig. 4.16). Trajectories 4-7 end in the
southern portion of the warm TB feature at the location of the warmest TB along
I
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140
LAMPS/AMSU 1 8 2 GHz TB (K); T r a j e c t o r ie s
1 8 0 0 UTC 0 4 JAN 1989
LAMPS/AMSU 1 8 2 GHz TE (K); T r a j e c t o r i e s
1 8 0 0 UTC 0 4 JAN 193S
Fig. 4.15. LAMPS TB at 18Z/04 with numbered air parcel trajectories ending at
vertically distributed points at locations (top) in the upper part of the tropopause
fold on the north side of the warm radiometric signature and (bottom) near the
lower tip of the tropopause fold and at the location of the warmest TB along the
cross section. Vertical bar marked "A? is the location of a cross section from Fig.
4.16, while that marked "B" corresponds to the cross section in Fig. 4.19. A circle
marks the location of parcel 5 as it passes through cross section B at 00Z/04.
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141
LAMPS/AMSU 182 AND 176 GHZ TE (K)
300
275
182 GHz
c,
200
WS ( m / s ) .
OMSC-A
- LAMPS/ERICA IOP4
2200-
籺tT
= 5C0 -
000 -
THETA /P V (X lO **?6) - LAMPS/ERICA I0 P 4
Q (g /k g ) -
LAMPS/ERICA I0 P 4
200
18 0 0 UTC 04 JAN 1989
Fig 4.16. Same as Fig. 4.13 but for 18Z/04 January 1989; axis corresponds to "A"
in Fig. 4.15. Maximum vertical velocity vector corresponds to 10 pb s'1. Ending
locations of trajectories from Fig. 4.15 are indicated by numbered circles.
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142
the cross section. Parameters corresponding to the trajectories appear in Table 4.4.
Stratospheric PV values (Fig. 4.16) associated with the fold/upper frontal zone
continue to reach as low as 800 mb. There also appears to be a second weaker fold
to the north, and some values greater than 10 units near the surface, probably
associated with diabatic production of PV due to model moist processes.
The warm 182 GHz TB feature (Fig. 4.16) now is directly over the
tropopause fold and is coincident with the region of middle tropospheric dryness,
where the 0.5 g kg"1 value of specific humidity is near 700 mb.
Maximum
instantaneous values of subsidence (7 pb s"1) again occur in the sloping frontal zone
comprising the tropopause fold.
The vertical motion field suggests transverse
circulations consistent with previous findings describing a confluent jet streak with
a component of cold temperature advection along its axis (Keyser and Shapiro
1986).
As noted in Section 4.3b, NMC 300 mb charts during this period (not
shown) indicate that cold advection was occurring along the jet.
The LAMPS
vertical motion field should be compared with Carlson?s Fig. 15.15 (from Danielsen
1968), reproduced here as Fig. 4.17. His schematic representation of tropopause
folding shows a thermally indirect circulation cell poleward of the upper frontai
zone and a direct cell above and to its warm side. The LAMPS vertical velocity
vectors (Fig. 4.16) also suggest a thermally indirect circulation, below and poleward
of the frontal zone, with a direct circulation on the equatorward side. The field of
subsiding instantaneous vertical velocities slopes downward to the south (right) and
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143
Table 4.4. LAMPS parcel variables as in Table 4.3 corresponding to trajectories in
Fig. 4.15.
Trajectory
Time
p
(mb)
q
(g k g 1)
0
(K)
1
18Z/04
12Z/03
700
975
1.65
3.51
293.3
281.4
2
18Z/04
17Z/03
500
309
0.02
0.04
309.7
310.2
3
18Z/04
22Z/03
400
267
0.05
0.03
320.4
321.7
18Z/04
12Z/03
950
813
4.81
1.85
289.1
283.0
18Z/04
14Z/03
700
365
0.18
0.10
301.4
306.3
18Z/04
16Z/03
500
330
0.03
0.14
318.2
318.0
18Z/04
16Z/03
400
320
0.08
0.12
321.9
321.7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
;
I
I
144
150
P ( mb)
N DI RECT
CELL
500
Distance
Fig. 4.17. Danielsen?s (1968) schematic representation of transverse ageostrophic
circulations (solid stream lines) associated with tropopause folding. Dashed line
indicates the tropopause (after Carlson 1992).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
145
is mainly confined within the upper level frontal zone/tropopause fold denoted by
stratospheric PV values.
LAMPS vertical profiles and CFs (Fig. 4.18) again are required to explain the
configuration o f TB features at 182 GHz. Sounding locations are at the endpoints
of the trajectories shown in Figs. 4.15 and 4.16. The first (top) is within the upper
part of the tropopause fold in Fig. 4.16. It is on the poleward (north) side of the
warm TB feature corresponding to the endpoints of trajectories 1-3. The second
(bottom) is further south, in the lower part of the fold at the gridpoint of the
warmest 182 GHz Tb. It corresponds to the endpoints of parcels 4-7. In both cases
the CFs for 182 GHz (channel 6) show weak peaks around 400 mb, and lower
sharper peaks associated with the strong vertical moisture gradient coincident with
the lower edge of the upper frontal zone/tropopause fold. This occurs near 550 mb
for the northern sounding and 700 mb to the south. In both cases the radiometer
senses down to layers of clouds and high humidity that form as trajectories of cool
air pick up moisture and destabilize over relatively warm water.
For example,
trajectory 4 (Table 4.4) ending below the tropopause fold at 950 mb has descended
from 813 mb, but its humidity has increased from 1.85 to 4.81 g kg'1 of water
vapor, and its potential temperature has warmed from 283 to 289 K.
Air within the tropopause fold also can be traced backward using
trajectories. For example, parcel 5 ending at 700 mb within the tip of the fold (Fig.
4.16) can be tracked upstream and related to a cross section (Fig. 4.19) to determine
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146
AMSU CONTRIBUTION FUNCTION
- 1 0 0 .0
-30.0
-<30
-
-60.0
-5 0 .0
-40
SFC ErtlS
ZENITH ANG!
4 - 1 7 6 . 3 1 GHz TB' 2 6 2 . 6 4
b - 1 8 2 . 3 1 GHz TB'
i
4- SFC CONT
400
c. 5 0 0
-30.0
-20.
20.0
.2
.3
.4
CONTRIBUTION
AMSU CONTRIBUTION FUNCTION
-100.0
-<30.0
-B0.0
-70.0
-60.0
-50.0
-40 .0
SFC EH I S . = 0 . 7 0
ZENITH ANGLE= 38.
4 - 1 7 6 . 3 1 GHz TB* 2 7 4 . 9 8
6 - 1 8 2 . 3 1 GHz TB* 2 5 6 . 6 6
Id 3 0 0
on 4 0 0 f
LU
\
,/P
4- SFC CONT = 0 . 0 7 2 J
&-SFC CONT s 0 . 0 0 0
Cd 5 0 0
700 r
?3e.0
-2 0 .0
-10.0
1000 fe
.1
.2
.3
.4
CONTRIBUTION
CKM-7 ]
Fig. 4.18. Same as Fig. 4.14 but for 18Z/04 January 1989. Top panels are for
endpoint of trajectories 1-3 on the north side of the TB maximum. Bottom panels
are for endpoint of trajectories 4-7 at the TB maximum along the cross section.
These locations can be seen in Fig. 4.15.
L
i
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147
LAMPS/AMSU 1 8 2 AND 176 GHZ TB (K)
380 c -
176 GHz
275 |
250 r
225
2e0 ?25 �
NE
�
200
182GHz
VJS ( m / 's ) / ' OMEGA
- LAMPS/ERICA 10P4
SW
-
Co 400 7
600 700 *
9001000
-
THETA / P V ( X 1 0 * '- 6 ) - LAMPS/ERICA I0 P 4
200
1000
Q (g /k g ) -
LAMPS/ERICA 10?
: 230 t 323 ?
U : 500-?
' 600
700
/me
,!!&
0 0 0 0 UTC 04 JAN 1989
Fig. 4.19. Same as Fig. 4.11 but for 00Z/04 January 1989. Maximum vertical
velocity vector corresponds to 5.9 ub s'1. Numbered circle denotes the location of
parcel 5 from Fig. 4.15. Cross section location corresponds to ?B" in Fig. 4.15.
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148
the environment of its origin. The parcel?s position at 002704 is denoted by a circle
on the cross section. The axis of the cross section is labled B on the trajectory plot
(Fig. 4.15, bottom), with a circle denoting the parcel?s postion.
At OOZ/04 the
parcel is located northwest of Lake Superior at 382 mb with a dry specific humidity
of 0.095 g kg'1 (not shown). It then descends 318 mb to the 700 mb level at 0.18
g kg'1 in 18 hours. (Note that the parcel parameters in Table 4.4 correspond to the
beginning and ending times of the trajectories and not to values at 00Z/04). On the
cross section at 00Z/04 (Fig. 4.19) it is located between the 10 and 20 unit PV
contours, that is, within stratospheric values in the vicinity of the relatively diffuse
upstream portion of the upper level front. By comparison, air parcel 6 ending
above the tropopause fold at the 500 mb level (Fig. 4.16) is at the 390 mb level at
00Z/04 (not shown) and sinks only 110 mb during the same time period. Parcel 7,
ending at 400 mb, sinks 66 mb in 18 hours. This vertical distribution of subsidence
represents vertical streicning.
This stretching could contribute to the spmup of
surface lows that has been described by Uccellini et al. (1985) as the upper front
and the surface system become phased.
Tracing these parcels back even further in the model simulation reveals
interesting relationships (Fig. 4.15). For example, parcel 5 ending in the fold at 700
mb (Fig. 4.16) crosses from the cyclonic side of the entrance region of the polar jet
streak at 18Z/03 (seen on the LAMPS 300 mb surface, Fig. 4.8) to the anticyclonic
side at 18Z/04. It appears to be of stratospheric origin. Comparing the parcel?s
R e p ro du ced with permission o f the copyright owner. Further reproduction prohibited without permission.
149
movement to Danielsen?s (1968) schematic of tropopause folding (Fig. 4.17)
suggests that it was part of the indirect transverse ageostrophic circulation on the
poleward side o f the fold. That is, it originated at a position above the tropopause
on the left side of the schematic and moved toward the right in the tropopause fold.
Parcel 6 ending at 500 mb and parcel 7 ending at 400 mb were on the anticyclonic
side of the jet at 18Z/03 and remain on that side through 18Z/04. Their origins, as
far back as LAMPS could trace them to 16Z/03 were at 330 and 320 mb
respectively, that is, at or just below tropopause level.
Again, comparing their
movements to Fig. 4.17 suggests that these parcels were in the direct transverse
circulation cell on the warm (equatorward) side of the tropospause fold. That is,
they move slightly leftward in the schematic as they descend from the upper
troposphere. As noted previously, parcels 6 and 7 subside substantially less than
parcel 5 within the frontal zone.
Nevertheless, by bringing down dry tropopause
level air, they play an important role in maintaining the dryness of the upper and
middle troposphere. Their aridity, combined with the extreme dryness of the air
within the fold, allows the simulated AMSU 182 GHz channel to sense the sharp
vertical moisture gradient below 700 mb at this location (Fig. 4.18, bottom),
resulting in the warm TB maximum.
It is enlightening to examine parcels 1-3 (Fig. 4.15, Table 4.4) ending
poleward of the TB maximum below or within the upper part of the tropopause fold
(Fig. 4.16). Parcel 1 ending at 700 mb is below the fold. It has risen from 975 mb
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150
at 12Z/03, and is relatively moist, decreasing from a specific humidity of 3.51 g
k g 1 to 1.65 g kg'1. In contrast, parcel 2 ending within the fold at 500 mb and 0.02
g kg'1 descends 186 mb from the 314 mb level with a specific humidity of 0.04 g
kg'1 at OOZ/04. Parcel 3 ending at 400 mb, also within the fold, descends 135 mb
from the 265 mb level during the same time period.
Again, it is this layer of
general subsidence that maintains the upper dryness through the deep layer
necessary for the radiometer to "see" down to the sharp vertical moisture gradient
(Fig. 4.18, top) just below the tropopause fold. In this case, it receives a strong
signal from the moisture between 500 and 700 mb. In contrast to the southern
sounding (Fig. 4.18, bottom), water vapor below 700 mb is mostly obscured so the
radiometer cannot receive radiation from the warmer lower tropospheric layers. In
addition, the northern sounding (top) is significantly colder than the profile at the
T b maximum. Thus, unlike the situation for soundings at 18Z/03 described earlier,
both the water vapor and the temperature profiles act together to yield a cooler TB
to the north (252 K) than to the south (258 K).
As a final note, some trajectories (not shown) ending near the eastern tip of the
dry feature have begun to rise after their long descent. Thus, in agreement with
Rodgers et al. (1976), Young et al. (1987), and Muller and Fuelberg (1990), warm
features in the water vapor imagery may reflect a long history of parcel subsidence,
but do not necessarily imply the presence of instantaneous sinking motion at their
location.
I
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151
4. Summary and Conclusions
A LAMPS mesoscale model simulation has been used to generate synthetic
satellite imagery for the AMSU-B water vapor channel at 182.3 GHz during ERICA
IOP4 (3-4 January 1989).
Model soundings were input to a radiative transfer
algorithm to simulate brightness temperatures (TB) patterns which then were verified
against observed GOES 6.7 pm channel water vapor imagery. The purpose was
twofold. The first was to investigate characteristics of this new type of microwave
satellite imagery and how it perceives mid-latitude weather systems. The second
was to analyze observed and simulated warm radiometric signatures and their
relation to upper level features during a period of rapid cyclogenesis. In particular,
the association between very warm TB and tropopause folding was examined.
Under clear conditions, upwelling radiance contributions at 182 GHz, like
those at 6.7 pm, emanate from deep layers of the atmosphere.
The 182 GHz
frequency is very sensitive to upper level water vapor. Statistics for three LAMPS
times during ERICA IOP4 indicated that the average level of 50% cumulative
contribution (CCL50) viewing downward (i.e., the level in the atmosphere above
which 50% of the radiation contribution emanates, while 50% comes from below)
ranged from 383 to 399 mb with standard deviations of 94 and 76 mb, respectively.
For CCL90 the values ranged from 555 to 567 mb with standard deviations of 82
mb for both. Clear LAMPS soundings indicated that 50% of the upwelling radiance
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
contribution was produced by the top 0.35-0.36 mm of precipitable water
encountered by the simulated 182 GHz channel as it viewed downward into the
model atmosphere. On the other hand, 90% of the radiance was produced by the
top 1.53-1.57 mm of vapor. In essence, the channel senses the temperature of this
vapor. Thus, in dry upper and middle tropospheric regions, the 182 GHz channel
"sees" lower into the atmosphere, sensing the temperature of moisture in the warmer
layers below. At the maximum value of CCL50, 50% of the radiance contribution
came from below 700 mb. This suggests that under conditions of a very dry middle
and upper troposphere, the so-called 700 mb "dry punch" used in severe storm and
tornado forecasting (Fawbush et al. 1951; Miller et al. 1959) can be detected at 182
GHz.
LAMPS generated a realistic simulation of the warm radiometric signature
and synoptic patterns during ERICA IOP4. Its main limitations were that it did not
acnieve ine magnitude of surface deepening actually observed, and that the
simulated warm radiometric feature and surface low seemed to lag the observed
versions.
Nevertheless, LAMPS reproduced the strong warm signals of the
observed imagery, and faithfully captured the jet structure, potential temperature
fields, and sloping upper level frontal zone and tropopause fold depicted by Nieman
and Shapiro (1993).
In many respects, the formation and evolution of the warm radiometric
features were very similar to those during the Presidents? Day cyclone (Uccellini
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153
et al. 1985).
Intensification of the warm signature occurred after two separate
features merged in the confluent entrance region of a subtropical jet streak, and in
the right front quadrant of a polar jet streak. The frontogenetical function for water
vapor showed confluent deformation as the dominant contribution to moisture
gradient formation between 800 to 200 mb within and ahead of the warm 182 GHz
T b feature at 1800 UTC 3 January 1989. Shearing deformation was second in
importance at this time. The warm TB signature occurred mostly in areas of 500
mb sinking motion in the region of negative vorticity advection behind the 500 mb
trough. In agreement with Muller and Fuelberg?s (1990) findings about 6.7 pm
warm features, however, its presence could not simply be equated to intantaneous
subsidence because its leading edge overlapped into an area of ascent.
Polar jet characteristics and vertical motion patterns for this case were
consistent with previous studies.
They appear similar to Keyser and Shapiro?s
(1986) schematic models of confluent fiow with a component of cold temperature
advection along the jet axis. The vertical motion field at 18Z/04 and air parcel
trajectories suggested the presence of indirect and direct transverse ageostrophic
circulations like those depicted in Danieisen?s (1968) schematic of tropopause
folding.
Contribution functions (CFs) and LAMPS soundings helped explain TB
configurations. They revealed that radiometric signatures near the upper jet/front
system were produced by the sharp vertical moisture gradient associated with the
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154
lower side of the upper level frontal zone or tropopause fold. In one example, the
warmest 182 GHz TBs were skewed southward of the fold and the driest middle and
lower tropospheric air, toward warmer ambient temperatures. This was due to the
strong horizontal temperature gradient associated with the developing cyclone. In
the other example, the warmest TBs were found over the lower tip of the tropopause
fold denoted by stratospheric values of potential vorticity (PV). This is different
than the case of Ramond et al. (1981) in which the warmest 6.7 pm signatures were
associated with the "tropopause break", that is, the upper part of a tropopause fold.
Maximum subsidence occurred within the tropopause fold, within or
poleward of the warm 182 GHz TB feature.
Trajectories ending at vertically
distributed points at the location of the warm TB maximum showed that a parcel
ending at 700 mb within the tip of the tropopause fold subsided substantially more
(318 mb in 18 hours) than one ending above the fold at 500 mb (118 mb in 18
hours). Nevertheless, by bringing down dry tropopause level air, trajectories ending
above the fold played an important role in maintaining the dryness of the upper and
middle troposphere.
Their aridity, combined with the extreme dryness of the
originally stratospheric air within the fold, is what allowed the simulated AMSU
182 GHz channel to sense the sharp vertical moisture gradient created by the
bottom edge of the tropopause fold/upper level frontal zone.
Atmospheric
water
vapor
is
significant
both
synoptically
and
climatologically. As new satellite-borne microwave moisture sounders with channels
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near 183 GHz are launched, it becomes increasingly important to understand their
characteristics. The current analysis provides guidance for interpreting imagery from
the microwave water vapor channels, and also elucidates meteorological conditions
associated with IR water vapor imagery.
In addition, it describes important
atmospheric structures and how they contribute to upwelling TBs.
Synoptic
analysis, and both physical and statistical retrieval strategies for water vapor and
other constituents, can benefit from a detailed understanding of atmospheric TB
properties. This research has sought to provide such knowledge as a means to
better utilize state-of-the-art satellite information.
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APPENDIX A
RADIATIVE
TRANSFER,
SINGLE
SCATTERING,
AND
GASEOUS
ABSORPTION MODELS
A .l Multiple scattering radiative transfer model
The current research employs the two-stream Sobolev (1975) multiple scattering
algorithm developed by Xiang (1989).
It has been adapted for the microwave
region (Xiang, personal communication). This version is derived here following
Xiang (1989), but incorporating the appropriate modifications.
Two stream approaches seek to simplify the source integral of the radiative
transfer equation through an expansion and truncation of the phase function to two
terms. The Sobolev treatment further simplifies the source integral by expanding
the radiance in terms of the cosine of the azimuth angle. These assumptions allow
for an approximate analytic solution to the RTE. Referring to Figs. A .l and A.2,
the transfer equation for a plane-parallel atmosphere with optical depth, x,
increasing downward and p > 0 for downwelling radiation is
jtfCqMO = _/(T;p4)) + / (t;Pi<5)) t
dx
156
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(A.l)
157
Fig. A .l. Upward and downward intensities in a layer with optical depth increasing
from x0 to Xj for a plane parallel atmosphere.
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158
Z e n ith
Fig. A.2. Relation of scattering, zenith, and azimuthal angles for incident beam A
and scattered beam B (after Liou 1980).
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159
where
I = diffuse radiant intensity or radiance,
u = cosQ is the cosine of the zenith angle,
(J) = azimuth angle,
J = source function,
kex[ = extinction coefficient,
p = density of medium, and
z = vertical distance.
The appropriate source function for the microwave region is
J J P
0 -1
where ]i' =
0' =
(
i
)dp! d.0' * (1 - co) B ( T ) ,
(A.2)
cosine of the zenith angle of a beam incident
on a scattering particle,
azimuth angle of the incident beam,
P = scattering phase function defining the amplitude of the scattered
intensity in the direction p,<j) from an incident beam in the direction
to =
ps / pe is the single scattering albedo defined by the ratio of the
volume scattering coefficient to the volume
extinction coefficient,
B(T) =monochromatic Planck Function, and
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160
T =
ambient temperature.
The first term on the right represents contributions
to theradiation beam in the
direction p, 0 from scattered incident radiation integrated over all incident directions
u', 0 ?.
The second term represents thermal emission from gasesand hydrometeors.
Within
theMW spectrum, we can approximate the Planck Function using the
Rayleigh-Jeans Law (Liou 1980, p. 276)
BV(T ) - (2Kvzlc 2)T ,
where v =
(A.3)
frequency,
K=
Boltzmann?s constant, and
c=
speed of light.
This leads to the definition of an equivalent brightness temperature, TB,
/v = (2Kv2/ c 2)TB(y) .
(A.4)
Substituting these expressions into (A.l), the factor of (2Kv2/c2) cancels out of all
the terms, and the radiant intensity is expressed as equivalent TB. Following the
conventional notation we will allow I to represent the brightness temperature, and
substitute T for B(T) in the thermal source term. The transfer equation becomes
iTt -1
j i i L = - / + J! L f ( V / d p W + O - ( 0 ) 1 .
dx
4 jt J J
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(A.5)
161
The phase function
can be written as P(cos0) where 0 is the
scattering angle, i.e., the angle between the incident and scattered beams (see Fig.
A.2). Typically in radiative transfer computations, the phase function is expanded
as a series of Legendre Polynomials:
Xt pt (cos�) ,
P(cos0)
(A-6)
i*)
where X, =
p, =
Legendre Coefficients, and
Legendre Polynomials.
Coefficients can be fitted to the actual phase function using the orthogonal property
of Legendre Polynomials. This property can be stated as
*i
f p, (cos�) p (cos�) <2cos� = 0
m* I
(A.7)
{
for m=0,l,2,... and 1=0,1,2,...
Therefore, the coefficients are given by
Xt -
?i
- Jp(cosQ)pl(cosQ)dcosQ .
(A-8)
In practice, the phase function is computed from Mie theory, and the integral in
(A.8) is determined using a numerical quadrature formula.
In the two stream approximation, only the first two terms of the Legendre
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162
Polynomial expansion are retained. These terms are
p0(cos�) = 1 ,
(A.9)
Pj (COS0) = COS0 ,
while the first two coefficients are
?i
(A. 10)
Xj = -ijV (co s0 ) cos0dcos0 = 3g ,
2-.i
where g is called the asymmetry factor. Thus, the phase function for the two
stream approximation can be written
P (c o s 0 ) � 1 + XjCosG .
(A . 11)
In terms of p, p', 6, and 6 ', co s0 can be obtained from spherical geometry (Liou
1980, p.365)
cos� = pp; + ^(1 ? P2)(l ~P2) cos(0 -tj)7) ,
(A.12)
and the phase function becomes
PQi.bjp'.b') = 1 + PP; + Xjt/(1 - p 2)(l - p 2) cos(b - b 7) ?
(A-13)
The Sobolev approach seeks analytic solutions to the radiative transfer equation
for a layer by expanding the radiance in terms of the cosine of the azimuth angle
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163
/(T,p,<i>) = /0(T,p) + / j (t ,u) cos4> .
(A-14)
We can substitute (A. 13) and (A. 14) into the source term of the transfer equation
(A.5) to obtain
{l + X1pp/ + x j ( \ - p 2)( l - p 2) cos(<f> -q/ )}tip/ ti<!)/ + (1 -co)T .
Then, noting that
2 re
Jcosq d& = 0
o
and
J'cos2^ d� = n ,
o
(A. 16)
c o s ( d - p ') = cosq cosb' + sinb sinq7,
(A. 17)
applying the trigonometric formula
the approximate relation
1 f / 0 (T, p/ ) p 2 d p
2 玕
� 1 /(T ),
3
(A?18)
and the fact that
j j l Q z p ' t f )?/1 - p7 2 sinq' dp' dq' = 0,
(A.19)
0 -1
v/e perform the integration within the source term to transform (A. 15) to obtain
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164
d l0{%]i ) +
c o s 0 = - / 0(x,p) -^ (x q O c o s q + 0 /(x )
dL(^
dr
4x
(A.20)
+ c o x i e r ) + ( o X j / l - p 2 G(x)cos<t) + (1 - 0 ) 7 ,
where
?i
/(X) = i . f/oCxy )dp.'
2 -i
(A2I)
is the mean diffuse radiation,
?i
H(x) = 1 f/oCxy )p'
2 -i
(A-22)
where 4 tiH(x) is the flux of diffuse radiance in the direction of increasing optical
depth, and
G(x) = _Lj / 1(x,p/ ) ^ l
VVC
^
C d il
lillC ^ ld lC
/? A
AA
y r \.j~ \J )
\ ---------------A
U V Cl y
1A U U 1
A
VJ
IV J
A ?
2 dp' ?
U IV U
,1 , f / A
O r \\
U iu iu ^ ij
vsi - i . . Z - w /
(A.23)
u
, .
u y
lC A
v v o y
r> ~ A
again integrate over � to obtain separate equations for !<, and Ij
[d/�(T,P) = - /0(x,p) + co/(x) + 0 X,p H(x) + (1 - 0 ) 7
ox
P
4x
= -/,(x,p/ ) + 0 /XIV/l - p 2 G(x) .
(A-24)
(A-25)
In his original model, Xiang (1989) found that better results were obtained when
the term containing G was neglected. This also is done for the MW model. To
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obtain equations for I and H, we first integrate (A.24) over u from -1 to +1, then
multiply (A.24) by u and again integrate over p, yielding, respectively
d /^ x) = ( 1 - ( o)[T -7 ( t )]
dx
� 1 ^ 1 = - ( 3 -to X j m
dx
(A-26)
(A-27)
A common method for treating the thermal emission term is to consider T as a
linear function of optical depth over a layer (e.g. Wiscombe 1976; Huang and Liou
1983; Evans and Stephens 1990)
r=
P6 + P1( t - t0) ,
(A.28)
where x0 is the optical depth at the top of the layer and x is the optical depth
anywhere within the layer such that at the top, x - x0 = 0 while at the bottom,
x - x0 = Ax. The constants for the layer, (30 and p1? can be found by considering
(A.28) for a single atmospheric layer between levels i-1 above and i below. At
levels i-1 and i,
Ti-\ = Po + P r 0 ?
(A.29)
therefore,
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To find solutions of (A.26) and (A.27) for I and H, we apply the linear
approximation for the source term, then differentiate with respect to z and substitute
to yield a coupled set of second order, linear, non-homogeneous, differential
equations
? H Q = k 2H (z) + (1 -co )^ ,
dx1
= k 2I - / : 2[p 0 +(31( T - x 0)] ,
d
(A.31)
(A.32)
dx 2
where k2 = (1 - 0))(3 - ooXj). (A.32) can be solved by finding a homogeneous
solution and adding a particular solution. The result is
T(z) = Cl e ^ + c, e * + [ p0
(z -zQ)] ,
(A.33)
We can substitute(A.33) into (A.27) to find a solution for H
H (z) = ___ ____ [c.e -*1- c.t *] + ----- -----(3 - coXj)
2
(3 -c o X .)
(A.34)
To findvalues for the coefficients, C] and c2, we can apply the boundary
conditions at the top and bottom of the atmosphere, and require that I and K for
one layer be equal to I and H from an adjacent layer at the interface. This yields
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167
a coupled set of linear equations from which the Cj?s and c2?s for each layer can be
found by Gaussian elimination.
The boundary condition at the top of the atmosphere is
7(0) = -2/7(0) + 2.7 ,
where 2.7 K is the cosmic background radiance.
(-A'35)
At the surface, the boundary
condition is
/(t,) = 2H(xz) * (1 - 8 ) [ / ( t j) - 2 H(zs)] * eT ,
(A.36)
where xs is optical depth at the surface, e is the surface emissivity, and Ts is the
surface skin temperature.
We now have what we need to compute upwelling radiances in terms of known
atmospheric properties.
Referring back to Fig. A .l, a solution to the radiative
transfer equation (A .l) is (Liou 1980; Chandrasekhar 1960)
(A.37)
Often in radiative transfer calculations, separate formulations for upward and
downward radiance are used so that u is always treated as a positive quantity.
Since p < 0 for upward radiation in the convention used here, we have substituted
-p for p to obtain (A.37).
From (A.20), the source term is
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168
7(x;jj,<5>) =
cd/ ( x )
- coXjp/ZCO + (1 -co)[(30 +
( x - t 0) ] ,
(A-38)
where the term containing G has been neglected and again we have replaced u by
-u. Substituting the solutions for I, (A.33), and H, (A.36), and collecting terms
with like powers of x, we obtain an expression of the form
J = C0 + D0(x -x0) + D ,e 't: + Z)2e fct ,
(A.39)
where
( A
,A A ,)
Do = ft ?
D, " oc,[l - |iX,
U.
2
k ?1 ,
(3 -COXj)
. . . .
k
2
1 (3 -,)
= 0 )C ,ll + p x ,
'4 0 )
J .
(A.42)
(A.43)
Note that C0, D0, D 1? and D2 are all constant with respect to x within a layer. Thus,
we substitute (A.39) into (A.37) and perform the simple integration of the source
term analytically. For a single layer, i, between levels i-1 above, and i below,
referring again to Fig. A .l, we note that x^ is equivalent to x0 in (A.37), and xs is
equivalent to x,. Thus, the expression for up welling TB for a layer is
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169
/(x ;_! ,p) = /(x.,p)e
(A.44)
?][e
�
-1]
ts-.-O
For a multilayer atmosphere, the upwelling radiation calculation begins with the
surface boundary condition, then steps upward through the layers, computing the
radiance from (A.44) at the top of each new layer, 1^, using the upward radiance
from the last layer, 1^ as the bottom boundary condition.
A.2 Single Scattering Modei
Output from the Mie scattering codes provides information on the optical
properties of the atmosphere as input to the Sobolev radiative transfer modei. The
algorithm (Wiscombe 1979, 1980) assumes a monochromatic plane wave incident
on a spherical, homogeneous particle.
The basic formulas of the Mie theory
(Wiscombe 1979) are as follows. The size parameter is
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170
2izr
(A.45)
x ~~ r
where r = droplet radius,
A.
= wavelength of incident radiation,
m = m,. - i m; is the complex refractive index of droplet
relative to surrounding medium,
i = (-1)1/2,
m, = real part corresponding to scattering, and
mt = imaginary part corresponding to absorption.
The extinction efficiency factor is given by
Q~ = ^ t v
A
(A.46)
n + \)Re[an+bn] ,
n籰
where 2^ and bn are Mie coefficients defined later in this section, and
N = required number of terms for sufficient accuracy.
The scattering efficiency factor is
Q玜 =
X - n-1
(2n + ^ [ M
+
?
(A.47)
The absorption efficiency is simply
Q
?s = -^exi
Q - Q si
*~qd
(A.48)
The asymmetry factor is given by
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171
(A.49)
where * indicates the complex conjugate which arises through the complex
refractive index.
The scattering amplitudes are
(A.50)
(A.51)
where 7tn(p) = Pa'(p) is the derivative of the Legendre Polynomial with respect to
P.
Tn(p) = p jtnOi) - (1 - p2) 7i? (u), and
p = cos� is the cosine of the scattering angle (not to be confused with the
cosine o f the zenith angle), and the ' denotes differentiation w/r u.
The Mie coefficients are given by
a,'n
(A.52)
where z = mx,
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172
[.mAn(z) + 1 ] \|tn(x) - ^ ( x )
bn = __________ i ________________________________(A.53)
[mAn(z) + .1 ]�(*) - ^_.(x)
\jrn(x) and Cn are Ricatti-Bessel functions:
\]/n(x) = xJn(x) ,
Xn(x) = - f (x) ,
(A.54)
L b ) = � ? ( * ) + lX j x) ,
and
An(z) = "(z) / (z) where the ' denotes differentiation with respect to z.
The scattered intensity for perpendicular and parallel components, respectively, is
(Liou 1980)
i, = i Sj |2
i2 = | S 2 |2 .
(A.55)
Thus, Q,.^, Q.^, g, Sl5 and S2 are expressed in terms o f known functions of the
complex refractive index, the size parameter, and the scattering angle.
Volume scattering and extinction cross sections are obtained from
<3-0
Jt r 2 ,
(A.56)
=Q ^r2,
where k is the number, not the function in (A.52) and (A.53). The absorption cross
section is simply
(A.57)
<3a - <3e
- o
s
or
aa = Q
.izr2 .
**abs
The volume scattering coefficient is obtained by integrating the scattering cross
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section over a drop size distribution (Liou 1980)
(A.58)
where n(r) = number of droplets per unit volume,
dn(r)/dr = number concentration for a given radius interval, and
rt and r2 are lower and upper drop radius limits.
Similar expressions exist for the extinction and absorption coefficients, j \ and pc.
The single scattering albedo is
to
(A.59)
The scattering phase function is computed by integrating the scattered intensity
components over the drop size distribution and normalizing by the scattering
coefficient
r.
(A.60)
inis phase function can be fitted by Legendre Polynomials whose coeffients are
found as described in Section A .l, equation (A.8).
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174
A.3 Microwave Gaseous Absorption
Gaseous absorption due to water vapor, molecular oxygen, and continuum
contributions is calculated using the algorithm of Liebe (1985).
This routine
includes many empirical findings of Liebe, and various investigators compiled by
Liebe, to represent the physics of moist air microwave absorption, accomodating the
research up through 1985 and some more recent findings. Input parameters are
frequency, temperature, pressure, and water vapor pressure for a homogeneous
layer, while the output is gaseous absorption coefficient, $a. The absorption spectra
are obtained from
nm
nh
N "< j) = 'E iS F " ). + N " * � ( S F " ), + N " ,
i-1
<A-61>
i-1
where f = frequency in GHz,
S = absorption line strength from empirical formulas,
F " = Van Vleck-Weisskopf function modified by Rosenkranz (1975) and
given below,
Np = continuum spectra for dry air,
Ne = continuum spectra for water vapor,
na = 48 oxygen lines, and
nb = 30 water vapor lines.
F " gives local absorption line profiles in the form
I
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where v0 = line center frequency,
y = line width from empirical formulas,
5 = line overlap correction from empirical formulas,
X = (v0 - f)2 + f , and
Y = (v0 + f)2 +
f.
The dry air continuum absorption is given by
JV" ( / ) = (2a0 {y0[ 1 + ( � ) 2 ] [ 1
To
60
+ a p d z5) f p d 2 ,
'
(A.63)
where a0 is an empirical constant,
ap is a function of frequency,
Yo is & function of p, e, and 0.
p = dry air pressure,
e = partial pressure of water vapor, and
9 = T/3QG is a function of temperature.
The continuum absorption for water vapor is
A'f
( / )/ = [ bfp
ew
Jc + b <e6 3] /e 8 15 ,
(A.64)
where bf is a constant, and
be is a constant.
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BIOGRAPHICAL SKETCH
Bradley M. Muller was born in Mill Valley, California on December 4,
1955. He graduated from Tamalpais High School in Mill Valley in 1974. He
attended College of Marin for two years, where he edited The Mariner, College of
Marin?s literary and artistic publication, during 1975-1976. Mr. Muller obtained his
bachelor of Science in Meteorology from San Jose State University, winning the
Albert Miller Award for the Best Senior Thesis. The thesis was the culmination of
research on heavy precipitation and flash flooding performed at NOAA?s
Atmospheric Physics and Chemistry Lab in Boulder, Colorado, while Mr. Muller
was a Cooperative Education Student there.
Mr. Muller worked as an Air Quality Scientist at AeroVironment, Inc. from
1980 to 1985.
He subsequently returned to graduate school at Florida State
University where he obtained his Master of Science in Meteorology in August,
1988. His work has been published in Monthly Weather Review, Journal o f Applied
Meteorology, and National Weather Digest.
186
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
0.10
0.10
310.4
310.4
6
18Z/03
12Z/03
500
394
0.06
0.06
303.0
303.8
7
i o r-7? /a a
i
JW
427
f AA
A
AA A
Trajectory
12Z/03
AO
u.uo
0.08
J
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-T
/
294.7
7 with water vapor contents of 0.10, 0.06, and 0.08 g kg'1 are drier at 500 mb than
is parcel 4 (0.15 g kg'1) which ends at the location of the maximum TB. This low
humidity is consistent with the high PV values at the endpoints of trajectories 5-7,
and suggests that they originated in the stratosphere prior to the initial simulation
time. On the other hand, it appears that parcel 4 originated in the troposphere
(based on its higher humidity and lower PV), despite the fact that its integrated
subsidence during the previous six hours is roughly equivalent to that of the drier
parcels.
Comparing Fig. 4.2 with Fig. 4.12 reveals that the lowest level of CCL50
(i.e., the highest pressure, denoted by the "+" on Fig. 4.12) associated with the
warm TB feature occurs on the poleward side of the TB maximum.
Thus the
simulated radiometer "sees" deeper into the atmosphere northeast of the TB
maximum (at the location of the maximum CCL50) where the TB is 256 K than at
lu c
l O C a u u ii
v l
u ic
w o iu ic m
ig
x\
.).
u
i
o le
acuw uvc
i \j
c v v ^ ii
au iaix
changes in the water vapor content, this must be explained by the strong lower
tropospheric temperature gradient.
This gradient is evident in Fig. 4.14 which
presents soundings and CFs for (top) the griapoint of maximum 182 GKz T3 (i.e.,
the ending location of trajectory 4 in Figs. 4.12 and 4.13), and (bottom) the
gridpoint of maximum CCL50. The CF peak at the maximum 182 GHz (channel
6) TB occurs near 600 mb while dual peaks at the greatest CCL50 are found near
600 and 900 mb. These peaks occur because of the extremely dry layer of air of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
137
; msu
iec e -ce.c
-se.e
-*e
-oc c
2
contribution
function
-sc c
s -c
2C.C 3e e
2
CONTRIBUTION
;< h - i ;
AMSU CONTRIBUTION FUNCTION
-120.2
- ?5 0 . 2
-B2.0
-70.2
-00.0
-5e.0
-40.0
" !
r
SFC E HI S. = 0 . 9 0
ZENITH ANGLE= 44.
4 - 1 7 6 . 3 1 GHz TB* 2 7 2 . 7 2
6 - 1 8 2 . 3 1 GHz
TB* 2 5 6 . 4 2
4 - S r C CONT = 0 . 2 9 7 .
6 -SFC CONT = 0 . 0 0 2
to 4 0 0
500
7se pNg
?30.0
700
800
900
10 0 0
-
20.2
-
12.2
2.2
10.2
20.0
30
.
.0
.1
.2
.3
.4
CONTRIBUTION
.5
.6
.7
(Kh-1)
Fig. 4.14. Skew-T Log-p diagrams (left) of LAMPS grid-resoived temperature and
dewpoint at 18Z/03. Right: corresponding LAMPS/AMSU contribution functions
and T bs (K) for 182 and 176 GHz. Top panels are for the point of maximum TB.
Bottom panels are for the point of maximum CCL50. These locations are shown in
Fig. 4.12.
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138
stratospheric origin between 700 and 800 mb at the location of maximum CCL50.
This dry layer allows the radiometer to receive radiance contributions from moist
layers below 800 mb that are essentially obscured at the location of maximum TB.
This lower tropospheric dry layer does not exist beneath the warmest TB because
stratospheric air, as indicated by the 10 unit PV contour in Fig. 4.13, has not
penetrated this far south. Despite the contributions from lower layers at the greatest
CCL50, a comparison of the temperature profiles (Fig. 4.14) reveals that the lower
and middle troposphere are significantly cooler at this drier location. For example,
temperatures at 600 mb at the greatest CCL50 (bottom panels) are approximately
6 K cooler than those at the TB maximum (top panel). This offsets the radiometric
warming that results from penetrating lower into the atmosphere.
We now examine the 182 GHz warm feature in the context of tropopause
folding. As noted earlier, Fig. 4.13 is a cross section for 18Z/03 along the axis in
Fig. 4.12. Ending locations of the trajectories of Fig. 4.12 are indicated by the
numbered circles.
The cross section indicates that maximum instantaneous
subsidence (10 pb s 1) occurs within and poleward of the TBmaximum at 182 GHz.
The subsidence is beneath and north (left) of the 70 m s'1 jet core, within the
tropopause fold as indicated by the stratospheric PV. Even at this stage of the
ERICA IOP4 storm, the 10 unit PV contour reaches down to the 800 mb level.
Thus, as in the Presidents? Day storm (Uccellini et al. 1985), the tropopause folding
process appears to be well under way prior to the rapid deepening phase.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A
139
downward depression of midtropospheric water vapor contours occurs in the region
of enhanced stability denoting the upper frontal zone that slopes downward and to
the south (right) in conjunction with stratospheric PV values. The warm TBfeature
is skewed slightly southward of the driest middle tropospheric moisture values
toward warmer temperatures due to the horizontal temperature gradient described
previously. This orientation is different from that shown by Muller and Fuelberg
(1990) for GOES 6.7 um imagery and from Ramond et al.?s (1981) analysis in
which warm TB3 maxima aligned with the upper parts of tropopause folds. These
differences may be related to the relative strengths of upper level features in the
respective cases. For example, Muller and Fuelberg showed a relatively weak case
of tropopause folding whereas the ERICA IOP4 storm contains intense upper level
features.
Proceeding to 18Z/04 when rapid deepening of the surface cyclone was well
under way, Fig. 4.15 (top and bottom) shows the location (labeled A) of a cross
section (Fig. 4.16) across the mature warm TBfeature over the Atlantic. Also shown
are the location (labeled B) of an additional cross section for 00Z/04 (to be
discussed later in this section and shown in Fig. 4.19), and numbered back
trajectories ending at points distributed vertically at two different locations.
Trajectories 1-3 end on the north side of the warm TB feature (Fig. 4.15), below and
within the upper part of the tropopause fold (Fig. 4.16). Trajectories 4-7 end in the
southern portion of the warm TB feature at the location of the warmest TB along
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
140
LAMPS/AMSU 1 8 2 GHz TB (K); T r a j e c t o r ie s
1 8 0 0 UTC 0 4 JAN 1989
LAMPS/AMSU 1 8 2 GHz TE (K); T r a j e c t o r i e s
1 8 0 0 UTC 0 4 JAN 193S
Fig. 4.15. LAMPS TB at 18Z/04 with numbered air parcel trajectories ending at
vertically distributed points at locations (top) in the upper part of the tropopause
fold on the north side of the warm radiometric signature and (bottom) near the
lower tip of the tropopause fold and at the location of the warmest TB along the
cross section. Vertical bar marked "A? is the location of a cross section from Fig.
4.16, while that marked "B" corresponds to the cross section in Fig. 4.19. A circle
marks the location of parcel 5 as it passes through cross section B at 00Z/04.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
141
LAMPS/AMSU 182 AND 176 GHZ TE (K)
300
275
182 GHz
c,
200
WS ( m / s ) .
OMSC-A
- LAMPS/ERICA IOP4
2200-
籺tT
= 5C0 -
000 -
THETA /P V (X lO **?6) - LAMPS/ERICA I0 P 4
Q (g /k g ) -
LAMPS/ERICA I0 P 4
200
18 0 0 UTC 04 JAN 1989
Fig 4.16. Same as Fig. 4.13 but for 18Z/04 January 1989; axis corresponds to "A"
in Fig. 4.15. Maximum vertical velocity vector corresponds to 10 pb s'1. Ending
locations of trajectories from Fig. 4.15 are indicated by numbered circles.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
142
the cross section. Parameters corresponding to the trajectories appear in Table 4.4.
Stratospheric PV values (Fig. 4.16) associated with the fold/upper frontal zone
continue to reach as low as 800 mb. There also appears to be a second weaker fold
to the north, and some values greater than 10 units near the surface, probably
associated with diabatic production of PV due to model moist processes.
The warm 182 GHz TB feature (Fig. 4.16) now is directly over the
tropopause fold and is coincident with the region of middle tropospheric dryness,
where the 0.5 g kg"1 value of specific humidity is near 700 mb.
Maximum
instantaneous values of subsidence (7 pb s"1) again occur in the sloping frontal zone
comprising the tropopause fold.
The vertical motion field suggests transverse
circulations consistent with previous findings describing a confluent jet streak with
a component of cold temperature advection along its axis (Keyser and Shapiro
1986).
As noted in Section 4.3b, NMC 300 mb charts during this period (not
shown) indicate that cold advection was occurring along the jet.
The LAMPS
vertical motion field should be compared with Carlson?s Fig. 15.15 (from Danielsen
1968), reproduced here as Fig. 4.17. His schematic representation of tropopause
folding shows a thermally indirect circulation cell poleward of the upper frontai
zone and a direct cell above and to its warm side. The LAMPS vertical velocity
vectors (Fig. 4.16) also suggest a thermally indirect circulation, below and poleward
of the frontal zone, with a direct circulation on the equatorward side. The field of
subsiding instantaneous vertical velocities slopes downward to the south (right) and
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143
Table 4.4. LAMPS parcel variables as in Table 4.3 corresponding to trajectories in
Fig. 4.15.
Trajectory
Time
p
(mb)
q
(g k g 1)
0
(K)
1
18Z/04
12Z/03
700
975
1.65
3.51
293.3
281.4
2
18Z/04
17Z/03
500
309
0.02
0.04
309.7
310.2
3
18Z/04
22Z/03
400
267
0.05
0.03
320.4
321.7
18Z/04
12Z/03
950
813
4.81
1.85
289.1
283.0
18Z/04
14Z/03
700
365
0.18
0.10
301.4
306.3
18Z/04
16Z/03
500
330
0.03
0.14
318.2
318.0
18Z/04
16Z/03
400
320
0.08
0.12
321.9
321.7
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;
I
I
144
150
P ( mb)
N DI RECT
CELL
500
Distance
Fig. 4.17. Danielsen?s (1968) schematic representation of transverse ageostrophic
circulations (solid stream lines) associated with tropopause folding. Dashed line
indicates the tropopause (after Carlson 1992).
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145
is mainly confined within the upper level frontal zone/tropopause fold denoted by
stratospheric PV values.
LAMPS vertical profiles and CFs (Fig. 4.18) again are required to explain the
configuration o f TB features at 182 GHz. Sounding locations are at the endpoints
of the trajectories shown in Figs. 4.15 and 4.16. The first (top) is within the upper
part of the tropopause fold in Fig. 4.16. It is on the poleward (north) side of the
warm TB feature corresponding to the endpoints of trajectories 1-3. The second
(bottom) is further south, in the lower part of the fold at the gridpoint of the
warmest 182 GHz Tb. It corresponds to the endpoints of parcels 4-7. In both cases
the CFs for 182 GHz (channel 6) show weak peaks around 400 mb, and lower
sharper peaks associated with the strong vertical moisture gradient coincident with
the lower edge of the upper frontal zone/tropopause fold. This occurs near 550 mb
for the northern sounding and 700 mb to the south. In both cases the radiometer
senses down to layers of clouds and high humidity that form as trajectories of cool
air pick up moisture and destabilize over relatively warm water.
For example,
trajectory 4 (Table 4.4) ending below the tropopause fold at 950 mb has descended
from 813 mb, but its humidity has increased from 1.85 to 4.81 g kg'1 of water
vapor, and its potential temperature has warmed from 283 to 289 K.
Air within the tropopause fold also can be traced backward using
trajectories. For example, parcel 5 ending at 700 mb within the tip of the fold (Fig.
4.16) can be tracked upstream and related to a cross section (Fig. 4.19) to determine
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146
AMSU CONTRIBUTION FUNCTION
- 1 0 0 .0
-30.0
-<30
-
-60.0
-5 0 .0
-40
SFC ErtlS
ZENITH ANG!
4 - 1 7 6 . 3 1 GHz TB' 2 6 2 . 6 4
b - 1 8 2 . 3 1 GHz TB'
i
4- SFC CONT
400
c. 5 0 0
-30.0
-20.
20.0
.2
.3
.4
CONTRIBUTION
AMSU CONTRIBUTION FUNCTION
-100.0
-<30.0
-B0.0
-70.0
-60.0
-50.0
-40 .0
SFC EH I S . = 0 . 7 0
ZENITH ANGLE= 38.
4 - 1 7 6 . 3 1 GHz TB* 2 7 4 . 9 8
6 - 1 8 2 . 3 1 GHz TB* 2 5 6 . 6 6
Id 3 0 0
on 4 0 0 f
LU
\
,/P
4- SFC CONT = 0 . 0 7 2 J
&-SFC CONT s 0 . 0 0 0
Cd 5 0 0
700 r
?3e.0
-2 0 .0
-10.0
1000 fe
.1
.2
.3
.4
CONTRIBUTION
CKM-7 ]
Fig. 4.18. Same as Fig. 4.14 but for 18Z/04 January 1989. Top panels are for
endpoint of trajectories 1-3 on the north side of the TB maximum. Bottom panels
are for endpoint of trajectories 4-7 at the TB maximum along the cross section.
These locations can be seen in Fig. 4.15.
L
i
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147
LAMPS/AMSU 1 8 2 AND 176 GHZ TB (K)
380 c -
176 GHz
275 |
250 r
225
2e0 ?25 �
NE
�
200
182GHz
VJS ( m / 's ) / ' OMEGA
- LAMPS/ERICA 10P4
SW
-
Co 400 7
600 700 *
9001000
-
THETA / P V ( X 1 0 * '- 6 ) - LAMPS/ERICA I0 P 4
200
1000
Q (g /k g ) -
LAMPS/ERICA 10?
: 230 t 323 ?
U : 500-?
' 600
700
/me
,!!&
0 0 0 0 UTC 04 JAN 1989
Fig. 4.19. Same as Fig. 4.11 but for 00Z/04 January 1989. Maximum vertical
velocity vector corresponds to 5.9 ub s'1. Numbered circle denotes the location of
parcel 5 from Fig. 4.15. Cross section location corresponds to ?B" in Fig. 4.15.
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148
the environment of its origin. The parcel?s position at 002704 is denoted by a circle
on the cross section. The axis of the cross section is labled B on the trajectory plot
(Fig. 4.15, bottom), with a circle denoting the parcel?s postion.
At OOZ/04 the
parcel is located northwest of Lake Superior at 382 mb with a dry specific humidity
of 0.095 g kg'1 (not shown). It then descends 318 mb to the 700 mb level at 0.18
g kg'1 in 18 hours. (Note that the parcel parameters in Table 4.4 correspond to the
beginning and ending times of the trajectories and not to values at 00Z/04). On the
cross section at 00Z/04 (Fig. 4.19) it is located between the 10 and 20 unit PV
contours, that is, within stratospheric values in the vicinity of the relatively diffuse
upstream portion of the upper level front. By comparison, air parcel 6 ending
above the tropopause fold at the 500 mb level (Fig. 4.16) is at the 390 mb level at
00Z/04 (not shown) and sinks only 110 mb during the same time period. Parcel 7,
ending at 400 mb, sinks 66 mb in 18 hours. This vertical distribution of subsidence
represents vertical streicning.
This stretching could contribute to the spmup of
surface lows that has been described by Uccellini et al. (1985) as the upper front
and the surface system become phased.
Tracing these parcels back even further in the model simulation reveals
interesting relationships (Fig. 4.15). For example, parcel 5 ending in the fold at 700
mb (Fig. 4.16) crosses from the cyclonic side of the entrance region of the polar jet
streak at 18Z/03 (seen on the LAMPS 300 mb surface, Fig. 4.8) to the anticyclonic
side at 18Z/04. It appears to be of stratospheric origin. Comparing the parcel?s
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149
movement to Danielsen?s (1968) schematic of tropopause folding (Fig. 4.17)
suggests that it was part of the indirect transverse ageostrophic circulation on the
poleward side o f the fold. That is, it originated at a position above the tropopause
on the left side of the schematic and moved toward the right in the tropopause fold.
Parcel 6 ending at 500 mb and parcel 7 ending at 400 mb were on the anticyclonic
side of the jet at 18Z/03 and remain on that side through 18Z/04. Their origins, as
far back as LAMPS could trace them to 16Z/03 were at 330 and 320 mb
respectively, that is, at or just below tropopause level.
Again, comparing their
movements to Fig. 4.17 suggests that these parcels were in the direct transverse
circulation cell on the warm (equatorward) side of the tropospause fold. That is,
they move slightly leftward in the schematic as they descend from the upper
troposphere. As noted previously, parcels 6 and 7 subside substantially less than
parcel 5 within the frontal zone.
Nevertheless, by bringing down dry tropopause
level air, they play an important role in maintaining the dryness of the upper and
middle troposphere. Their aridity, combined with the extreme dryness of the air
within the fold, allows the simulated AMSU 182 GHz channel to sense the sharp
vertical moisture gradient below 700 mb at this location (Fig. 4.18, bottom),
resulting in the warm TB maximum.
It is enlightening to examine parcels 1-3 (Fig. 4.15, Table 4.4) ending
poleward of the TB maximum below or within the upper part of the tropopause fold
(Fig. 4.16). Parcel 1 ending at 700 mb is below the fold. It has risen from 975 mb
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150
at 12Z/03, and is relatively moist, decreasing from a specific humidity of 3.51 g
k g 1 to 1.65 g kg'1. In contrast, parcel 2 ending within the fold at 500 mb and 0.02
g kg'1 descends 186 mb from the 314 mb level with a specific humidity of 0.04 g
kg'1 at OOZ/04. Parcel 3 ending at 400 mb, also within the fold, descends 135 mb
from the 265 mb level during the same time period.
Again, it is this layer of
general subsidence that maintains the upper dryness through the deep layer
necessary for the radiometer to "see" down to the sharp vertical moisture gradient
(Fig. 4.18, top) just below the tropopause fold. In this case, it receives a strong
signal from the moisture between 500 and 700 mb. In contrast to the southern
sounding (Fig. 4.18, bottom), water vapor below 700 mb is mostly obscured so the
radiometer cannot receive radiation from the warmer lower tropospheric layers. In
addition, the northern sounding (top) is significantly colder than the profile at the
T b maximum. Thus, unlike the situation for soundings at 18Z/03 described earlier,
both the water vapor and the temperature profiles act together to yield a cooler TB
to the north (252 K) than to the south (258 K).
As a final note, some trajectories (not shown) ending near the eastern tip of the
dry feature have begun to rise after their long descent. Thus, in agreement with
Rodgers et al. (1976), Young et al. (1987), and Muller and Fuelberg (1990), warm
features in the water vapor imagery may reflect a long history of parcel subsidence,
but do not necessarily imply the presence of instantaneous sinking motion at their
location.
I
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151
4. Summary and Conclusions
A LAMPS mesoscale model simulation has been used to generate synthetic
satellite imagery for the AMSU-B water vapor channel at 182.3 GHz during ERICA
IOP4 (3-4 January 1989).
Model soundings were input to a radiative transfer
algorithm to simulate brightness temperatures (TB) patterns which then were verified
against observed GOES 6.7 pm channel water vapor imagery. The purpose was
twofold. The first was to investigate characteristics of this new type of microwave
satellite imagery and how it perceives mid-latitude weather systems. The second
was to analyze observed and simulated warm radiometric signatures and their
relation to upper level features during a period of rapid cyclogenesis. In particular,
the association between very warm TB and tropopause folding was examined.
Under clear conditions, upwelling radiance contributions at 182 GHz, like
those at 6.7 pm, emanate from deep layers of the atmosphere.
The 182 GHz
frequency is very sensitive to upper level water vapor. Statistics for three LAMPS
times during ERICA IOP4 indicated that the average level of 50% cumulative
contribution (CCL50) viewing downward (i.e., the level in the atmosphere above
which 50% of the radiation contribution emanates, while 50% comes from below)
ranged from 383 to 399 mb with standard deviations of 94 and 76 mb, respectively.
For CCL90 the values ranged from 555 to 567 mb with standard deviations of 82
mb for both. Clear LAMPS soundings indicated that 50% of the upwelling radiance
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contribution was produced by the top 0.35-0.36 mm of precipitable water
encountered by the simulated 182 GHz channel as it viewed downward into the
model atmosphere. On the other hand, 90% of the radiance was produced by the
top 1.53-1.57 mm of vapor. In essence, the channel senses the temperature of this
vapor. Thus, in dry upper and middle tropospheric regions, the 182 GHz channel
"sees" lower into the atmosphere, sensing the temperature of moisture in the warmer
layers below. At the maximum value of CCL50, 50% of the radiance contribution
came from below 700 mb. This suggests that under conditions of a very dry middle
and upper troposphere, the so-called 700 mb "dry punch" used in severe storm and
tornado forecasting (Fawbush et al. 1951; Miller et al. 1959) can be detected at 182
GHz.
LAMPS generated a realistic simulation of the warm radiometric signature
and synoptic patterns during ERICA IOP4. Its main limitations were that it did not
acnieve ine magnitude of surface deepening actually observed, and that the
simulated warm radiometric feature and surface low seemed to lag the observed
versions.
Nevertheless, LAMPS reproduced the strong warm signals of the
observed imagery, and faithfully captured the jet structure, potential temperature
fields, and sloping upper level frontal zone and tropopause fold depicted by Nieman
and Shapiro (1993).
In many respects, the formation and evolution of the warm radiometric
features were very similar to those during the Presidents? Day cyclone (Uccellini
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153
et al. 1985).
Intensification of the warm signature occurred after two separate
features merged in the confluent entrance region of a subtropical jet streak, and in
the right front quadrant of a polar jet streak. The frontogenetical function for water
vapor showed confluent deformation as the dominant contribution to moisture
gradient formation between 800 to 200 mb within and ahead of the warm 182 GHz
T b feature at 1800 UTC 3 January 1989. Shearing deformation was second in
importance at this time. The warm TB signature occurred mostly in areas of 500
mb sinking motion in the region of negative vorticity advection behind the 500 mb
trough. In agreement with Muller and Fuelberg?s (1990) findings about 6.7 pm
warm features, however, its presence could not simply be equated to intantaneous
subsidence because its leading edge overlapped into an area of ascent.
Polar jet characteristics and vertical motion patterns for this case were
consistent with previous studies.
They appear similar to Keyser and Shapiro?s
(1986) schematic models of confluent fiow with a component of cold temperature
advection along the jet axis. The vertical motion field at 18Z/04 and air parcel
trajectories suggested the presence of indirect and direct transverse ageostrophic
circulations like those depicted in Danieisen?s (1968) schematic of tropopause
folding.
Contribution functions (CFs) and LAMPS soundings helped explain TB
configurations. They revealed that radiometric signatures near the upper jet/front
system were produced by the sharp vertical moisture gradient associated with the
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154
lower side of the upper level frontal zone or tropopause fold. In one example, the
warmest 182 GHz TBs were skewed southward of the fold and the driest middle and
lower tropospheric air, toward warmer ambient temperatures. This was due to the
strong horizontal temperature gradient associated with the developing cyclone. In
the other example, the warmest TBs were found over the lower tip of the tropopause
fold denoted by stratospheric values of potential vorticity (PV). This is different
than the case of Ramond et al. (1981) in which the warmest 6.7 pm signatures were
associated with the "tropopause break", that is, the upper part of a tropopause fold.
Maximum subsidence occurred within the tropopause fold, within or
poleward of the warm 182 GHz TB feature.
Trajectories ending at vertically
distributed points at the location of the warm TB maximum showed that a parcel
ending at 700 mb within the tip of the tropopause fold subsided substantially more
(318 mb in 18 hours) than one ending above the fold at 500 mb (118 mb in 18
hours). Nevertheless, by bringing down dry tropopause level air, trajectories ending
above the fold played an important role in maintaining the dryness of the upper and
middle troposphere.
Their aridity, combined with the extreme dryness of the
originally stratospheric air within the fold, is what allowed the simulated AMSU
182 GHz channel to sense the sharp vertical moisture gradient created by the
bottom edge of the tropopause fold/upper level frontal zone.
Atmospheric
water
vapor
is
significant
both
synoptically
and
climatologically. As new satellite-borne microwave moisture sounders with channels
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near 183 GHz are launched, it becomes increasingly important to understand their
characteristics. The current analysis provides guidance for interpreting imagery from
the microwave water vapor channels, and also elucidates meteorological conditions
associated with IR water vapor imagery.
In addition, it describes important
atmospheric structures and how they contribute to upwelling TBs.
Synoptic
analysis, and both physical and statistical retrieval strategies for water vapor and
other constituents, can benefit from a detailed understanding of atmospheric TB
properties. This research has sought to provide such knowledge as a means to
better utilize state-of-the-art satellite information.
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APPENDIX A
RADIATIVE
TRANSFER,
SINGLE
SCATTERING,
AND
GASEOUS
ABSORPTION MODELS
A .l Multiple scattering radiative transfer model
The current research employs the two-stream Sobolev (1975) multiple scattering
algorithm developed by Xiang (1989).
It has been adapted for the microwave
region (Xiang, personal communication). This version is derived here following
Xiang (1989), but incorporating the appropriate modifications.
Two stream approaches seek to simplify the source integral of the radiative
transfer equation through an expansion and truncation of the phase function to two
terms. The Sobolev treatment further simplifies the source integral by expanding
the radiance in terms of the cosine of the azimuth angle. These assumptions allow
for an approximate analytic solution to the RTE. Referring to Figs. A .l and A.2,
the transfer equation for a plane-parallel atmosphere with optical depth, x,
increasing downward and p > 0 for downwelling radiation is
jtfCqMO = _/(T;p4)) + / (t;Pi<5)) t
dx
156
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(A.l)
157
Fig. A .l. Upward and downward intensities in a layer with optical depth increasing
from x0 to Xj for a plane parallel atmosphere.
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158
Z e n ith
Fig. A.2. Relation of scattering, zenith, and azimuthal angles for incident beam A
and scattered beam B (after Liou 1980).
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159
where
I = diffuse radiant intensity or radiance,
u = cosQ is the cosine of the zenith angle,
(J) = azimuth angle,
J = source function,
kex[ = extinction coefficient,
p = density of medium, and
z = vertical distance.
The appropriate source function for the microwave region is
J J P
0 -1
where ]i' =
0' =
(
i
)dp! d.0' * (1 - co) B ( T ) ,
(A.2)
cosine of the zenith angle of a beam incident
on a scattering particle,
azimuth angle of the incident beam,
P = scattering phase function defining the amplitude of the scattered
intensity in the direction p,<j) from an incident beam in the direction
to =
ps / pe is the single scattering albedo defined by the ratio of the
volume scattering coefficient to the volume
extinction coefficient,
B(T) =monochromatic Planck Function, and
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160
T =
ambient temperature.
The first term on the right represents contributions
to theradiation beam in the
direction p, 0 from scattered incident radiation integrated over all incident directions
u', 0 ?.
The second term represents thermal emission from gasesand hydrometeors.
Within
theMW spectrum, we can approximate the Planck Function using the
Rayleigh-Jeans Law (Liou 1980, p. 276)
BV(T ) - (2Kvzlc 2)T ,
where v =
(A.3)
frequency,
K=
Boltzmann?s constant, and
c=
speed of light.
This leads to the definition of an equivalent brightness temperature, TB,
/v = (2Kv2/ c 2)TB(y) .
(A.4)
Substituting these expressions into (A.l), the factor of (2Kv2/c2) cancels out of all
the terms, and the radiant intensity is expressed as equivalent TB. Following the
conventional notation we will allow I to represent the brightness temperature, and
substitute T for B(T) in the thermal source term. The transfer equation becomes
iTt -1
j i i L = - / + J! L f ( V / d p W + O - ( 0 ) 1 .
dx
4 jt J J
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(A.5)
161
The phase function
can be written as P(cos0) where 0 is the
scattering angle, i.e., the angle between the incident and scattered beams (see Fig.
A.2). Typically in radiative transfer computations, the phase function is expanded
as a series of Legendre Polynomials:
Xt pt (cos�) ,
P(cos0)
(A-6)
i*)
where X, =
p, =
Legendre Coefficients, and
Legendre Polynomials.
Coefficients can be fitted to the actual phase function using the orthogonal property
of Legendre Polynomials. This property can be stated as
*i
f p, (cos�) p (cos�) <2cos� = 0
m* I
(A.7)
{
for m=0,l,2,... and 1=0,1,2,...
Therefore, the coefficients are given by
Xt -
?i
- Jp(cosQ)pl(cosQ)dcosQ .
(A-8)
In practice, the phase function is computed from Mie theory, and the integral in
(A.8) is determined using a numerical quadrature formula.
In the two stream approximation, only the first two terms of the Legendre
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162
Polynomial expansion are retained. These terms are
p0(cos�) = 1 ,
(A.9)
Pj (COS0) = COS0 ,
while the first two coefficients are
?i
(A. 10)
Xj = -ijV (co s0 ) cos0dcos0 = 3g ,
2-.i
where g is called the asymmetry factor. Thus, the phase function for the two
stream approximation can be written
P (c o s 0 ) � 1 + XjCosG .
(A . 11)
In terms of p, p', 6, and 6 ', co s0 can be obtained from spherical geometry (Liou
1980, p.365)
cos� = pp; + ^(1 ? P2)(l ~P2) cos(0 -tj)7) ,
(A.12)
and the phase function becomes
PQi.bjp'.b') = 1 + PP; + Xjt/(1 - p 2)(l - p 2) cos(b - b 7) ?
(A-13)
The Sobolev approach seeks analytic solutions to the radiative transfer equation
for a layer by expanding the radiance in terms of the cosine of the azimuth angle
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163
/(T,p,<i>) = /0(T,p) + / j (t ,u) cos4> .
(A-14)
We can substitute (A. 13) and (A. 14) into the source term of the transfer equation
(A.5) to obtain
{l + X1pp/ + x j ( \ - p 2)( l - p 2) cos(<f> -q/ )}tip/ ti<!)/ + (1 -co)T .
Then, noting that
2 re
Jcosq d& = 0
o
and
J'cos2^ d� = n ,
o
(A. 16)
c o s ( d - p ') = cosq cosb' + sinb sinq7,
(A. 17)
applying the trigonometric formula
the approximate relation
1 f / 0 (T, p/ ) p 2 d p
2 玕
� 1 /(T ),
3
(A?18)
and the fact that
j j l Q z p ' t f )?/1 - p7 2 sinq' dp' dq' = 0,
(A.19)
0 -1
v/e perform the integration within the source term to transform (A. 15) to obtain
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164
d l0{%]i ) +
c o s 0 = - / 0(x,p) -^ (x q O c o s q + 0 /(x )
dL(^
dr
4x
(A.20)
+ c o x i e r ) + ( o X j / l - p 2 G(x)cos<t) + (1 - 0 ) 7 ,
where
?i
/(X) = i . f/oCxy )dp.'
2 -i
(A2I)
is the mean diffuse radiation,
?i
H(x) = 1 f/oCxy )p'
2 -i
(A-22)
where 4 tiH(x) is the flux of diffuse radiance in the direction of increasing optical
depth, and
G(x) = _Lj / 1(x,p/ ) ^ l
VVC
^
C d il
lillC ^ ld lC
/? A
AA
y r \.j~ \J )
\ ---------------A
U V Cl y
1A U U 1
A
VJ
IV J
A ?
2 dp' ?
U IV U
,1 , f / A
O r \\
U iu iu ^ ij
vsi - i . . Z - w /
(A.23)
u
, .
u y
lC A
v v o y
r> ~ A
again integrate over � to obtain separate equations for !<, and Ij
[d/�(T,P) = - /0(x,p) + co/(x) + 0 X,p H(x) + (1 - 0 ) 7
ox
P
4x
= -/,(x,p/ ) + 0 /XIV/l - p 2 G(x) .
(A-24)
(A-25)
In his original model, Xiang (1989) found that better results were obtained when
the term containing G was neglected. This also is done for the MW model. To
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obtain equations for I and H, we first integrate (A.24) over u from -1 to +1, then
multiply (A.24) by u and again integrate over p, yielding, respectively
d /^ x) = ( 1 - ( o)[T -7 ( t )]
dx
� 1 ^ 1 = - ( 3 -to X j m
dx
(A-26)
(A-27)
A common method for treating the thermal emission term is to consider T as a
linear function of optical depth over a layer (e.g. Wiscombe 1976; Huang and Liou
1983; Evans and Stephens 1990)
r=
P6 + P1( t - t0) ,
(A.28)
where x0 is the optical depth at the top of the layer and x is the optical depth
anywhere within the layer such that at the top, x - x0 = 0 while at the bottom,
x - x0 = Ax. The constants for the layer, (30 and p1? can be found by considering
(A.28) for a single atmospheric layer between levels i-1 above and i below. At
levels i-1 and i,
Ti-\ = Po + P r 0 ?
(A.29)
therefore,
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To find solutions of (A.26) and (A.27) for I and H, we apply the linear
approximation for the source term, then differentiate with respect to z and substitute
to yield a coupled set of second order, linear, non-homogeneous, differential
equations
? H Q = k 2H (z) + (1 -co )^ ,
dx1
= k 2I - / : 2[p 0 +(31( T - x 0)] ,
d
(A.31)
(A.32)
dx 2
where k2 = (1 - 0))(3 - ooXj). (A.32) can be solved by finding a homogeneous
solution and adding a particular solution. The result is
T(z) = Cl e ^ + c, e * + [ p0
(z -zQ)] ,
(A.33)
We can substitute(A.33) into (A.27) to find a solution for H
H (z) = ___ ____ [c.e -*1- c.t *] + ----- -----(3 - coXj)
2
(3 -c o X .)
(A.34)
To findvalues for the coefficients, C] and c2, we can apply the boundary
conditions at the top and bottom of the atmosphere, and require that I and K for
one layer be equal to I and H from an adjacent layer at the interface. This yields
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167
a coupled set of linear equations from which the Cj?s and c2?s for each layer can be
found by Gaussian elimination.
The boundary condition at the top of the atmosphere is
7(0) = -2/7(0) + 2.7 ,
where 2.7 K is the cosmic background radiance.
(-A'35)
At the surface, the boundary
condition is
/(t,) = 2H(xz) * (1 - 8 ) [ / ( t j) - 2 H(zs)] * eT ,
(A.36)
where xs is optical depth at the surface, e is the surface emissivity, and Ts is the
surface skin temperature.
We now have what we need to compute upwelling radiances in terms of known
atmospheric properties.
Referring back to Fig. A .l, a solution to the radiative
transfer equation (A .l) is (Liou 1980; Chandrasekhar 1960)
(A.37)
Often in radiative transfer calculations, separate formulations for upward and
downward radiance are used so that u is always treated as a positive quantity.
Since p < 0 for upward radiation in the convention used here, we have substituted
-p for p to obtain (A.37).
From (A.20), the source term is
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168
7(x;jj,<5>) =
cd/ ( x )
- coXjp/ZCO + (1 -co)[(30 +
( x - t 0) ] ,
(A-38)
where the term containing G has been neglected and again we have replaced u by
-u. Substituting the solutions for I, (A.33), and H, (A.36), and collecting terms
with like powers of x, we obtain an expression of the form
J = C0 + D0(x -x0) + D ,e 't: + Z)2e fct ,
(A.39)
where
( A
,A A ,)
Do = ft ?
D, " oc,[l - |iX,
U.
2
k ?1 ,
(3 -COXj)
. . . .
k
2
1 (3 -,)
= 0 )C ,ll + p x ,
'4 0 )
J .
(A.42)
(A.43)
Note that C0, D0, D 1? and D2 are all constant with respect to x within a layer. Thus,
we substitute (A.39) into (A.37) and perform the simple integration of the source
term analytically. For a single layer, i, between levels i-1 above, and i below,
referring again to Fig. A .l, we note that x^ is equivalent to x0 in (A.37), and xs is
equivalent to x,. Thus, the expression for up welling TB for a layer is
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169
/(x ;_! ,p) = /(x.,p)e
(A.44)
?][e
�
-1]
ts-.-O
For a multilayer atmosphere, the upwelling radiation calculation begins with the
surface boundary condition, then steps upward through the layers, computing the
radiance from (A.44) at the top of each new layer, 1^, using the upward radiance
from the last layer, 1^ as the bottom boundary condition.
A.2 Single Scattering Modei
Output from the Mie scattering codes provides information on the optical
properties of the atmosphere as input to the Sobolev radiative transfer modei. The
algorithm (Wiscombe 1979, 1980) assumes a monochromatic plane wave incident
on a spherical, homogeneous particle.
The basic formulas of the Mie theory
(Wiscombe 1979) are as follows. The size parameter is
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170
2izr
(A.45)
x ~~ r
where r = droplet radius,
A.
= wavelength of incident radiation,
m = m,. - i m; is the complex refractive index of droplet
relative to surrounding medium,
i = (-1)1/2,
m, = real part corresponding to scattering, and
mt = imaginary part corresponding to absorption.
The extinction efficiency factor is given by
Q~ = ^ t v
A
(A.46)
n + \)Re[an+bn] ,
n籰
where 2^ and bn are Mie coefficients defined later in this section, and
N = required number of terms for sufficient accuracy.
The scattering efficiency factor is
Q玜 =
X - n-1
(2n + ^ [ M
+
?
(A.47)
The absorption efficiency is simply
Q
?s = -^exi
Q - Q si
*~qd
(A.48)
The asymmetry factor is given by
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171
(A.49)
where * indicates the complex conjugate which arises through the complex
refractive index.
The scattering amplitudes are
(A.50)
(A.51)
where 7tn(p) = Pa'(p) is the derivative of the Legendre Polynomial with respect to
P.
Tn(p) = p jtnOi) - (1 - p2) 7i? (u), and
p = cos� is the cosine of the scattering angle (not to be confused with the
cosine o f the zenith angle), and the ' denotes differentiation w/r u.
The Mie coefficients are given by
a,'n
(A.52)
where z = mx,
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172
[.mAn(z) + 1 ] \|tn(x) - ^ ( x )
bn = __________ i ________________________________(A.53)
[mAn(z) + .1 ]�(*) - ^_.(x)
\jrn(x) and Cn are Ricatti-Bessel functions:
\]/n(x) = xJn(x) ,
Xn(x) = - f (x) ,
(A.54)
L b ) = � ? ( * ) + lX j x) ,
and
An(z) = "(z) / (z) where the ' denotes differentiation with respect to z.
The scattered intensity for perpendicular and parallel components, respectively, is
(Liou 1980)
i, = i Sj |2
i2 = | S 2 |2 .
(A.55)
Thus, Q,.^, Q.^, g, Sl5 and S2 are expressed in terms o f known functions of the
complex refractive index, the size parameter, and the scattering angle.
Volume scattering and extinction cross sections are obtained from
<3-0
Jt r 2 ,
(A.56)
=Q ^r2,
where k is the number, not the function in (A.52) and (A.53). The absorption cross
section is simply
(A.57)
<3a - <3e
- o
s
or
aa = Q
.izr2 .
**abs
The volume scattering coefficient is obtained by integrating the scattering cross
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section over a drop size distribution (Liou 1980)
(A.58)
where n(r) = number of droplets per unit volume,
dn(r)/dr = number concentration for a given radius interval, and
rt and r2 are lower and upper drop radius limits.
Similar expressions exist for the extinction and absorption coefficients, j \ and pc.
The single scattering albedo is
to
(A.59)
The scattering phase function is computed by integrating the scattered intensity
components over the drop size distribution and normalizing by the scattering
coefficient
r.
(A.60)
inis phase function can be fitted by Legendre Polynomials whose coeffients are
found as described in Section A .l, equation (A.8).
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174
A.3 Microwave Gaseous Absorption
Gaseous absorption due to water vapor, molecular oxygen, and continuum
contributions is calculated using the algorithm of Liebe (1985).
This routine
includes many empirical findings of Liebe, and various investigators compiled by
Liebe, to represent the physics of moist air microwave absorption, accomodating the
research up through 1985 and some more recent findings. Input parameters are
frequency, temperature, pressure, and water vapor pressure for a homogeneous
layer, while the output is gaseous absorption coefficient, $a. The absorption spectra
are obtained from
nm
nh
N "< j) = 'E iS F " ). + N " * � ( S F " ), + N " ,
i-1
<A-61>
i-1
where f = frequency in GHz,
S = absorption line strength from empirical formulas,
F " = Van Vleck-Weisskopf function modified by Rosenkranz (1975) and
given below,
Np = continuum spectra for dry air,
Ne = continuum spectra for water vapor,
na = 48 oxygen lines, and
nb = 30 water vapor lines.
F " gives local absorption line profiles in the form
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where v0 = line center frequency,
y = line width from empirical formulas,
5 = line overlap correction from empirical formulas,
X = (v0 - f)2 + f , and
Y = (v0 + f)2 +
f.
The dry air continuum absorption is given by
JV" ( / ) = (2a0 {y0[ 1 + ( � ) 2 ] [ 1
To
60
+ a p d z5) f p d 2 ,
'
(A.63)
where a0 is an empirical constant,
ap is a function of frequency,
Yo is & function of p, e, and 0.
p = dry air pressure,
e = partial pressure of water vapor, and
9 = T/3QG is a function of temperature.
The continuum absorption for water vapor is
A'f
( / )/ = [ bfp
ew
Jc + b <e6 3] /e 8 15 ,
(A.64)
where bf is a constant, and
be is a constant.
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