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An improved microwave radiative transfer model for tropical oceans

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AN IMPROVED MICROWAVE RADIATIVE TRANSFER
MODEL FOR TROPICAL OCEANS
A Dissertation
by
JEFFREY RANSDELL TESMER
Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
December 1995
Major Subject: Meteorology
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AN IMPROVED MICROWAVE RADIATIVE TRANSFER
MODEL FOR TROPICAL OCEANS
A Dissertation
by
JEFFREY RANSDELL TESMER
Submitted to Texas A&M University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Approved as to style and content by:
Thomas T. Wilheit
(Chair of Committee)
Gerald R. North
(Member)
Co*
Richard E. Orville
(Member)
Cam V
v ti Nguyen
(Member)
yuan B. Valdes
' (Member)
(Head of Department)
December 1995
Major Subject: Meteorology
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ABSTRACT
An Improved Microwave Radiative Transfer Model
for Tropical Oceans. (December 1995)
Jeffrey Ransdell Tesmer, B.S., Texas Tech University;
M.S., Texas Tech University
Chair of Advisory Committee: Dr. Thomas T. Wilheit
In preparation for the launch of TRMM, new algorithms must be created that take
advantage of the combined data from radar and microwave radiometers that will be on board
the satellite. A microwave radiative transfer algorithm with a one-dimensional cloud model
is created that incorporates data from radar and radiometers using data obtained from TCM90 and TOGA-COARE flown over the western Pacific in 1990 and 1993, respectively.
First, a convective cloud model (CCM) was created that contained a CLW
distribution and vertical rain rate structure that were common in previous studies. The
brightness temperature - rain rate (T-R) relationships generated by the CCM are shown to
produce warmer brightness temperatures at low rain rates and lower brightness temperatures
at high rain rates than the W ilheit et al. (1977) model (WILM) and TOGA-COARE
observations.
Next, a hybrid cloud model (HCM) was developed using observations from TOGACOARE, TCM-90, and other field projects. Observations changed the cloud model in four
ways. First, stratiform clouds with low rain rates were shown to have a low CLW content
(< 0 .1 g n r 3). Second, radar data showed a linear decrease in the logarithm of the
backscatter of ice particles above the freezing level. Third, tropical clouds contained more
small drops and fewer large drops than predicted by the Marshall - Palm er drop-size
distribution (DSD). Last, the reflectivity of ocean surface appears to be specular.
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The T-R relationships generated by the HCM are different from the CCM. The
HCM predicts colder brightness temperatures at low rain rates than in the CCM because of a
low CLW content in the cloud at rain rates < 5 mm h*1. At higher rain rates, the vertical
precipitation structure and DSD above the freezing level in the HCM make the cloud
transparent to microwave radiation resulting in warmer upwelling brightness temperatures at
each frequency.
The brightness temperatures generated by the HCM closely agree with observations
from TOGA-COARE. This study shows that a plane-parallel microwave radiative transfer
algorithm coupled with a cloud model based on microphysical observations can accurately
simulate rainfall observed in the tropics.
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V
ACKNOW LEDGM ENTS
First, I would like to thank my advisor Dr. W ilheit for his expertise, guidance, and
funding he has provided while I attended Texas A&M University. A lot of thanks goes to
Drs. Orville and Zipser for their suggestions and comments about cloud microphysics. I
also want to acknowledge my other committee members, Drs. North, Valdes, Nguyen, and
W agner for taking their time to be on my committee.
I would like to thank the founding members of the Microwave Remote Sensing
Group, Ye Hong and Alex Wang for their scientific help and insights about the language
and culture of China. To also wish to thank the other "old-timers", Don Conlee and
Abdulrahman Al-Khalaf for making the microwave group a great environment to work in. I
also w ant to thank fellow W ilheitians, Stepheni M oore, Will M anning, and Clay
Blankenship for keeping life interesting in the group.
Finally, I wish to thank my parents as well as my brother and his wife for all their
encouragement over the past few years.
This work was supported by NASA Grants NAG-5-1423 and NAG-5-1568.
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TABLE OF CONTENTS
CHAPTER
Page
I
INTRODUCTION................................................................................................
1
II
PREVIOUS W ORK.............................................................................................
4
1. Rainfall estimation from s p a c e ...................................................
2. Characteristics of western Pacific c lo u d s.................................
3. Dissertation objectives based on previous work........................
4
10
15
III
D A T A ...................................................................................................................
18
IV
A FOUNDATION FOR RADIATIVE TRANSFER.....................................
20
V
A CONVECTIVE CLOUD M O D E L ..............................................................
25
VI
MODEL COMPARISON....................................................................................
29
VD
THE CCM VS. O B SER V A TIO N S................................................................
35
1. 2200 - 2225 UTC 10 February 1993..........................................
2. 2145:14 - 2149:30 UTC 20 February 1993................................
35
37
AN IMPROVED MODEL USING OBSERVATIONAL D A T A ................
41
Vm
1.
2.
3.
4.
5.
6.
7.
IX
Changes to the amount and vertical distribution of CLW
Changes to the vertical precipitation structure.........................
Changes to the DSD......................................................................
Changes to the reflectivity of the ocean su rfa c e .......................
The HCM vs. the CCM.................................................................
The HCM vs. the W ILM ..............................................................
The HCM vs. observations.........................................................
42
43
44
46
48
53
56
CONCLUSION.....................................................................................................
64
R E FE R E N C E S .......................................................................................................................
68
APPENDIX
A
CLOUD MODEL EQ U A T IO N S......................................................................
73
B
THE RADIATIVE TRANSFER M O D E L ......................................................
78
C
HCM SENSITIVITY............................................................................................
83
V IT A .........................................................................................................................................
87
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LIST OF TABLES
TABLE
1
Page
Description of the radiometer and radar that will be on board
TRMM (from Simpson et al. 1988)......................................................................
2
2
List of computed Z-R relationships for tropical oceanic clouds........................
16
3
The moist tropical sounding used to initialize the CCM ....................................
26
4
Brightness temperatures calculated at the initial condition by the
CCM and WILM using a 4 and 5 km freezing le v e l........................................
32
Initial brightness temperatures for 13.8, 18.7, 21.3, and 37 GHz from
the HCM, CCM, WILM, and average brightness temperatures
observed during 1 1 - 1 2 January 1993.................................................................
51
Changes in brightness temperature as a result of altering the surface
temperature, RH profile, CLW content, DSD, and surface
reflectivity at each frequency...............................................................................
84
5
6
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LIST OF FIGURES
FIGURE
Page
1
Schematic of the Wilheit et al. (1977) radiative transfer model
(from W ilheit et al. 1991)........................................................................................ 21
2
Calculated brightness temperatures for 19 GHz at nadir for various
freezing levels (from W ilheit et al. 1977)..............................................................
23
T-R relationships generated by the CCM and the WILM using a 4 and 5 km
freezing level at (a) 13.8 GHz; (b) 18.7 GHz; (c) 21.3 GHz; (d) 37 GHz . . . .
30
3
4
Nadir backscatter observed by ARMAR and corresponding nadir radiometric
brightness temperatures observed by ARMAR and AMMR at 13.8, 18.7,
21.3, and 37 GHz for 2200 - 2225 UTC 10 February 1993 during
T O G A -C O A R E ..........................................................................................................
36
5
As in Fig. 4, except from 2145:14 - 2149:30 UTC 20 February 1993 ...............
38
6
Nadir backscatter observed by radar during TCM-90 in super typhoon Flo
for 0932:43 - 0954 UTC 18 September 1990........................................................ 47
7
T-R relationships generated by the HCM and the CCM at (a) 13.8 GHz;
(b) 18.7 GHz; (c) 21.3 GHz; (d) 37 GHz..............................................................
49
T-R relationships generated by the HCM and the WILM at (a) 13.8 GHz;
(b) 18.7 GHz; (c) 21.3 GHz; (d) 37 GHz..............................................................
54
9
As in Fig. 4, except from 2324 - 2328:24 UTC 22 February 1993 ...................
60
10
As in Fig. 4, except from 2131:30 - 2136 UTC 22 February 1993 ...................
62
11
Transmittance as a function of frequency (from Liou 1980)................................
81
8
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1
CHAPTER I
INTRO DUCTIO N
The ocean dominates the hydrological cycle, occupying nearly three-fourths of the
earth's surface.
Over the rem aining one-quarter o f the earth's surface, observational
netw orks and research programs have been concentrated on the continents to study
meteorological processes such as rainfall. Tropical oceanic phenomena such as El Nino
have shown the importance of the tropics in dictating rainfall over continents and oceans
(Browning 1990). Measurements of rainfall in the tropics are particularly scarce since there
is only a small ratio of land to water. Satellites offer a reasonable measurement approach
with suitable temporal and spatial coverage to monitor oceanic rainfall.
The Tropical Rainfall Measuring Mission (TRMM) satellite, which will be launched
in 1997, will provide improved observations of rainfall over the oceans relative to previous
satellites. The TRMM objectives are directed toward our understanding of the hydrological
cycle over the tropical oceans. TRMM will have a low altitude of 350 km for better
instrumental resolution and a low inclination of 35 degrees (the maximum latitude of the
satellite's orbit) for increased temporal coverage. The TRMM satellite will use a radar at
14 GH z in conjunction with microwave radiometers at 10, 19, 21, 37, and 85.5 GHz
(Simpson et al. 1988). A brief summary of the relevant sensors on board TRMM is listed in
Table 1. The unique overlapping coverage of the radar and radiometers will allow a deeper
understanding of rainfall over the oceans. It is seen from Table 1 that the radar's swath
width is only one third of the microwave sensor swath. TRMM algorithm development
must take advantage of the information gained from the radar data such as the height of the
freezing level and apply it over the remaining two-thirds of the TRMM swath.
The citations follow the style of the Journal o f Atmospheric and Oceanic Technology.
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2
Table 1. Description of the radiometer and radar that will be on board
TRMM (from Simpson et al. 1988).
TRMM Microwave Imager
TMI
10.65 GHz V,H
19.35 GHz V,H
21.3 GHz V
37 GHz V,H
85.5 GHz V,H
Radar
13.8 GHz
4 km footprint
250 m range resolution
220 km swath width
760 km swath width
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3
In preparation for the data received from the TRMM satellite, two airborne
experiments were flown over the western Pacific in 1990 and 1993. The Tropical Cyclone
Motion - 90 (TCM-90) experiment and the Tropical Ocean Global Atmosphere - Coupled
Ocean Atm osphere Response Experiment (TOGA-COARE) created an opportunity to
integrate airborne radar data with collocated microwave radiometers as the aircraft flew over
highly organized systems such as typhoons and through less organized smaller scale tropical
cloud systems. The experiments contained radars and microwave sensors at frequencies
very similar to the TRMM instruments. Rainfall algorithm development using the collocated
radar and radiometer data should give a better estimate of rainfall than just radiometer data
alone. The main objective of this paper is to develop a better microwave radiative transfer
algorithm using radar and radiometer data taken from the TCM-90 and TOGA-COARE
experiments. Improved microphysical observations of tropical oceanic clouds is at the core
of the improved model. The radiative transfer theory is based on well understood physical
principles.
The development of an improved radiative transfer model will involve two steps.
First, a radiative transfer model will be created that incorporates the known physics of the
atmosphere. A more sophisticated one-dimensional cloud model will be added to the
radiative transfer algorithm that contains microphysics similar to what was used in previous
studies. This model will be compared to the W ilheit et al. (1977) model and TOGACOARE observations. Second, this paper will explore what microphysical changes are
forced by the observations. With microphysical changes added to the cloud model, the
improved radiative transfer algorithm should be able to reproduce brightness temperatures
observed by TOGA-COARE microwave sensors.
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4
CHAPTER II
PREVIOUS WORK
1. Rainfall estimation from space
a. Rainfall estimation using visible and infrared frequencies
The use of satellites for determining rainfall over the oceans is not new. Some of the
first studies completed by Barrett (1970) and Martin and Suomi (1972) used visible satellite
data to identify rain cells over the ocean. Barrett (1970) used visible frequencies from
m eteorological satellites to m ap rainfall over the oceans into monthly rainfall averages.
M artin and Suomi (1972) used the visible satellite pictures in combination with groundbased radar. Although the visible satellite data indicated that the heaviest rainfall occurred
under the brightest clouds, radar revealed a rainfall pattern that was more variable than what
was suggested by satellite pictures.
Satellites carrying infrared sensors became important for rainfall studies over the
oceans because infrared wavelengths offered a marked improvement over visible satellite
pictures. Unlike visible, infrared can be used both day and night thus increasing temporal
coverage. Martin and Scherer (1973) reviewed visible and infrared satellite techniques for
studying rainfall. They determined that the best rainfall estimation came from combining
visible, infrared, and m icrow ave techniques.
The authors concluded that infrared
frequencies had limitations caused by cirrus contamination and shear within the clouds.
Since infrared radiation could only penetrate the very tops of convective clouds, the shear
caused the brightest and coldest cloud tops to be displaced from the location of the heaviest
rainfall.
Griffith et al. (1978) used visible and infrared geosynchronous satellite data with
ground radar over south Florida. They studied cloud evolution and its rainfall signature as
viewed from radar and satellite images. Radar indicated that the m aximum echo size
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5
occurred well before the cloud shield became large. This result produced low correlation
between the infrared and radar rainfall patterns. They further concluded that the differences
between infrared and visible radiation were also due to cirrus anvil outflow. Arkin (1979)
used an infrared and radar technique over the GARP Atlantic Tropical Experiment (GATE)
network. He found that GATE rainfall was explained by a linear function of the fractional
infrared cloud coverage above 10 km. However, this successful technique was only valid
for the tropical oceans during summer and needed to be modified for different latitudes and
seasons.
b. Rainfall estimation from passive microwave satellites
The use of passive microwave observations for determining rainfall over the oceans
began in earnest with the launch of the Nimbus 5 Electrically Scanned M icrowave
Radiometer (ESMR). Wilheit et al. (1976) was the first study to look into rainfall estimation
using this satellite. M icrowave radiation has key advantages over infrared and visible
radiation. W hile visible and infrared can only penetrate the highest layers of a cloud,
microwave radiation can penetrate into the clouds and to the ocean surface. Non-raining
clouds that have little liquid water content are relatively transparent at microwave frequencies
while clouds with rain influence microwave radiation by their relatively high liquid water
content and absorption properties mainly due to the precipitation itself. The ocean appears
very cold and highly polarized at large incidence angles since the ocean has low emissivity
(or high reflectivity) (Nordberg et al. 1971). This cold background is easily distinguished
from clouds that contain precipitation. W ilheit et al. (1977) was the first study to create a
model relating microwave radiance to rainfall over the oceans.
The range of m icrowave frequencies dealt with in this study is < 37 GHz.
Frequencies < 60 GHz are dominated by emission from liquid hydrometeors (Huang and
Liou 1983; W ilheit 1986). However, these frequencies are not immune to the effects of
scattering of radiation by ice particularly when the ice layer thickness is large. With minimal
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6
scattering effects, frequencies below 60 GHz can be used to retrieve information about the
atmosphere below the freezing level (Spencer et al. 1989). Therefore, these frequencies are
dominated by the absorption and emission due to precipitation particles, cloud liquid water,
water vapor, and to a lesser extent, by scattering by frozen and liquid hydrometeors.
Emission-based approaches integrate a radiative transfer equation to predict a brightness
temperature for a given rainfall rate.
Algorithms that use high frequencies to determine surface rain rate are referred to as
scattering-based models (Adler et al. 1991; Grody 1991). Microwave frequencies above
60 GHz are sensitive to precipitation-sized particles located above the freezing level (Wilheit
et al. 1982). Higher frequencies are sensitive to cloud droplets so that deep convective
clouds attenuate the radiation more rapidly than at lower frequencies. Frequencies above
60 GHz are also sensitive to clouds that contain large amounts of ice (Wu and Weinman
1984; W ilheit 1986). Since scattering-based algorithms use frequencies that contain
information only from the upper parts of a cloud, additional ground-based observations are
needed to fill in the data void below the freezing level. Therefore, a majority of scatteringbased approaches use a statistical relationship between satellite observed brightness
temperature and ground-based data either from radar, lower frequency microwave channels,
or rain gauges. There are algorithms that use a combination of emission and scatteringbased approaches (i.e. Spencer et al. 1989; Kummerow and Giglio 1994a,b). The model
used in this study includes emission and scattering to predict a microwave brightness
temperature associated with a given rainfall rate.
Most models (including the one that will be used in this study) assume a planeparallel atmosphere with axisymmetric scattering. Naturally, rainfall is highly variable even
within a single satellite footprint and plane-parallel models do not account for this pattern
(Kummerow and Weinman 1988). Finite cloud models such as the one developed by
Kummerow and Weinman (1988) take into account the horizontal variability of clouds
within a field of view. Theoretically, finite models would seem to be a major improvement
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7
over plane-parallel models. However, studies such as Kummerow and Weinman (1988)
and Spencer et al. (1989) show that finite cloud m odels underestim ate brightness
temperatures as seen by satellite or aircraft. Finite cloud models are also computationally
intensive in comparison to plane-parallel models. Considering all the trade-offs involved, it
is still unknown whether finite models are better than models that assume a plane-parallel
atmosphere. However, results from plane-parallel models seem to agree with actual data so
it appears that these algorithms do a good job of modeling the atmosphere.
Weinman and Guetter (1977) created a plane-parallel model using 37-GHz data from
the Nimbus 6 ESMR. They found that since clouds depolarized upwelling radiation, they
were distinguishable from the highly polarized ocean surface. W ilheit et al. (1977) used
Nimbus 5 ESMR data at 19 GHz. They found that 19 GHz was affected by scattering from
large rain drops created in rainfall greater than 20 mm h 'l . W ilheit et al. (1982) modified
the model used in Wilheit et al. (1977) to include an ice layer above the freezing level. They
concluded that 19 GHz was not particularly sensitive to ice but 92 and 183 GHz were highly
susceptible to ice scattering. Huang and Liou (1983) found that clouds over the oceans
depolarized the upwelling radiation from the surface. This conclusion was sim ilar to
Weinman and Guetter (1977) and showed that deep convective clouds remained unpolarized
and easily distinguishable from the polarized ocean surface. Wu and Weinman (1984) used
m ultiple frequencies ranging from 19 to 183 GHz.
They found that intense storms
produced ice scattering signatures at frequencies as low as 37 GHz. Asymmetrical rain
drops made little difference in their model but asymmetrical ice particles affected model
brightness temperatures. Olsen (1987) used a plane-parallel model based on averaged
soundings of tropical storms to study tropical cyclone microwave signatures from Scanning
Multichannel Microwave Radiometer (SMMR) data.
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8
c. Multi-dimensional cloud models
The recent trend in modeling has been to use the output of more sophisticated cloud
m odels as input for the radiative transfer algorithms. The radiative transfer models
described above such as the model discussed in W ilheit et al. (1977) only used a single
atmospheric profile for a range of rain rates. The idea that one-dimensional cloud models
were apparently too simple to model the real atmosphere led to the appearance of more
sophisticated multi-dimensional cloud models.
Two and three-dimensional cloud models have been developed to simulate realistic
microphysics and precipitation-sized particles for use in convective-scale radiative transfer
modeling. Mugnai and Smith (1988) and Smith and Mugnai (1988) used a sophisticated
two dimensional cloud model that evolved over time to study frequencies ranging from 19 to
231 GHz within their plane-parallel radiative transfer model. The cloud model produced
large amounts of cloud liquid water (CLW) that was found to mask the rain layer below the
freezing level. The large am ount of CLW in tall non-precipitating clouds produced
erroneous rainfall amounts in the model. They also found that the evolution of the cloud
played an important part in their results. Changes in the CLW and drop-size distribution
(DSD) over the lifetime of the cloud produced large differences in the brightness temperature
- rain rate (T-R) relationships.
Adler et al. (1991) used a three-dimensional cloud model to study the effect o f cloud
evolution on microwave T-R relationships at 10, 19, 37, and 86 GHz. The case study
involved a mesoscale convective system (MCS) which evolved over tim e to produce areas
of convective and stratiform precipitation. The 1.5 km horizontal resolution allowed the
authors to examine the role the changing CLW and ice distributions had on the T-R
relationship. Their results showed that a three-dimensional model was needed to resolve the
CLW and ice distributions within the convective and stratiform regions in the system. They
found that CLW and ice played a significant role in the T-R relationships. Areas in the
system that contained little rainfall but had high amounts of CLW showed much higher
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9
brightness temperatures than the regions that contained little or no CLW. The fluctuations
of ice in the system caused large deviations in the upwelling brightness temperatures at the
higher frequency channels. The ice effect was even more complicated by the fact that CLW
masked the scattering signature when it was distributed near the tops of the clouds. Since
the amount and distribution of ice changes for both convective and stratiform structure, the
life cycle of the system played an important part in the results.
Smith et al. (1992) and M ugnai et al. (1993) used a hybrid statistical-physical
precipitation algorithm containing a three-dimensional cloud model. The authors concluded
that a high-resolution three-dimensional cloud model was necessary in order to understand
the m icrophysics of clouds.
Use of the three-dimensional cloud model showed that
frequencies > 19 GHz could not sense the low-level rainfall due to emission and attenuation
process above the freezing level. The T-R relationships were affected by the CLW, ice
particles, and supercooled water in the upper levels of the cloud. They also found that the
vertical distribution of particles within the cloud had a large impact on upwelling brightness
temperatures.
One of the biggest problems with multi-dimensional cloud models is that they are too
computationally intensive. Recent papers by Bauer and Schluessel (1993) and Kummerow
and Giglio (1994a,b) have tried to speed up the process by selecting a finite number of
cloud models based on stratiform or convective structure. The algorithms select a particular
cloud model that fits the geophysical situation. Bauer and Schluessel (1993) pointed out
that their use of multiple cloud models oversimplified the atmosphere. However, their
results showed that the vertical liquid water profile and vertical rain rate distribution could be
simplified without significant error.
The algorithm used by Kummerow and Giglio (1994a,b) selected various types of
stratiform and convective cloud structures based on the climatic freezing level. The
determination of which cloud structure to use was left up to the algorithm. This technique
worked well when high resolution data from aircraft was used. However, as resolution
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10
degraded, the algorithm had trouble with rainfall patterns below the resolution of the
radiometer footprint. The authors concluded that this problem was contained in either the
cloud structure selection process itself or was due to the three-dimensionality of the radiative
transfer problem.
2. Characteristics of western Pacific clouds
This section reviews work on the microphysics and precipitation associated with
western Pacific clouds. Three important aspects of clouds will be dealt with because of their
importance to upwelling microwave brightness temperatures. First, CLW will be examined
since its amount and vertical distribution within a cloud is important, especially at 37 GHz.
Second, the vertical precipitation structure will be looked at since it affects all the
frequencies examined in this study at high rain rates. Third, the DSD will be examined
since it determines the amount of absorption and scattering produced by precipitation-sized
particles in the model atmosphere. The vertical precipitation structure and DSD are related
and have an effect on all of the microwave frequencies examined in this study. A brief
summary of Z-R relationships for oceanic convection is also mentioned in the DSD section.
The Z-R relationship is derived from the DSD and is a fundamental way of monitoring the
vertical reflectivity structure of the cloud.
a. Cloud liquid water
Studies of CLW over the oceans has been confined to aircraft observations.
Numerous studies have shown that oceanic cells have weaker updraft velocities than
continental clouds (Zipser and LeMone 1980; Szoke et al. 1986; Lucas et al. 1994;
Jorgensen and LeMone 1989). Zipser and LeMone (1980) studied convective cells during
(GATE). The weak updraft velocities in the cells led them to conclude that little liquid water
could exist above 5 km (-5 to -10 °C) since most of the water would fall out as precipitation
or be converted to ice. Szoke et al. (1986) confirmed these observations from a later study
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11
using GATE data. Black and Hallett (1986) studied CLW in hurricanes. They also found
little CLW above the freezing level. They concluded that the abundance of small ice
particles above the freezing level were the result of CLW being converted into ice.
Jorgensen and LeM one (1989) used data obtained in the Taiwan Area M esoscale
E xperim ent (TAMEX). They found that CLW decreased rapidly above the freezing level
due to the conversion of liquid water into ice and graupel. Gamache (1990) studied
convection near Australia during the Summer MONsoon E xperim ent (SMONEX). He
showed that CLW did not exist at temperatures below -10 to -22 °C. The CLW content
never exceeded 0.2 g n r 3 above the freezing level, even in convection. The CLW content
above the freezing level in convection during SMONEX in many cases was below
0.1 g n r 3. The CLW reduction was due to the large concentrations (approx. 800 L_1) of
ice particles just below 0 °C. Gamache (1990) found that most of the ice particles in
stratiform regions came from the convective updrafts. Houze et al. (1992) studied the
source regions for stratiform precipitation in hurricane Norbert which formed over the
eastern Pacific in 1984. They concluded that most of the ice particles found in the
stratiform regions came from convective cores.
Since CLW disappears within a few kilometers of the freezing level in convection
and convective updrafts are the source regions for stratiform precipitation, it is reasonable to
assume that little or no CLW exists in stratiform regions. Adler et al. (1991) found that the
three-dimensional mesoscale model used in their study produced regions of stratiform
precipitation where there was almost no CLW. McGaughey et al. (1995) studied stratiform
regions of two systems in TOGA-COARE using the Advanced M icrowave Precipitation
Radiometer (AMPR). Their stratiform cloud model contained a CLW content of 0.1 g n r 3
for specified layers in the model atmosphere. They remarked that this CLW value was
probably too high. Therefore, the model used in this paper needs to take into account the
amount and vertical distribution of CLW. The cloud model will follow the observations by
not allowing a significant amount of CLW above the freezing level, even in convection.
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12
b. Vertical reflectivity structure
Data from GATE showed researchers that the vertical reflectivity structure of tropical
oceanic systems was significantly different from mid-latitude continental storms above the
freezing level (Szoke et al. 1986; Zipser and Lutz 1994). Hurricanes and tropical storms
also contained a similar vertical reflectivity structure as GATE cells (Black and Hallett
1986). A similar structure was observed in mesoscale systems during TAMEX (Jorgensen
and LeM one 1989). Most studies have concluded that oceanic clouds contain a relatively
constant reflectivity structure below the freezing level and a rapid decrease with height
immediately above the freezing level to the top of the cloud. Continental systems share a
similar structure below the freezing level but have a more gradual reflectivity decrease with
height above the 0 °C level.
GATE studies provided an explanation for the vertical reflectivity structure of
oceanic clouds. The vertical profiles were caused by low updraft velocities promoting
collision and coalescence, large raindrops > 1 mm in diameter falling out before the freezing
level was reached, and the absence of CLW below a temperature of -20 °C (Szoke et al.
1986). The first factor would result in high rain rates from shallow convection. The second
two of these three factors would cause the logarithm of the backscatter to drop off quickly
above the freezing level since there were no large particles there. Also, the particles above
the freezing level were mostly ice that have an order of magnitude lower reflectivity than
liquid drops of the same size (Jorgensen and LeMone 1989). The rain rates were weaker
below the freezing level in stratiform clouds but similar to convection above the freezing
level because convection had weak updrafts. The backscatter structure above the freezing
level in stratiform clouds was due to falling and growing snow due to deposition, riming
and aggregation near the freezing level (Szoke et al. 1986).
D ata from the warm pool showed that these clouds have a similar backscatter
structure with height as GATE clouds (W illiams et al. 1992; Zipser and Lutz 1994).
Vertical reflectivity profiles o f convective cells over Darwin, Australia had maximum
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13
reflectivities below the freezing level and decreased rapidly above the freezing level (Zipser
and Lutz 1994). Zipser and Lutz (1994) showed the lapse rate for the logarithm of the
backscatter of ice was 6.5 dBZ km-1 in the TOGA-COARE region with 6.0 dBZ km-1 in
GATE —both a factor of 2 to 3 more than continental systems. It appears that most of the
clouds observed during TOGA-COARE have the identical vertical reflectivity structure as
those described by Zipser and Lutz (1994).
McGaughey and Zipser (1995) studied two TOGA-COARE systems that occurred
during February 1993. The amount of ice present above the freezing level determined the
vertical reflectivity structure in the systems. The younger system on 22 February contained
either more or larger ice particles in the upper levels of the cloud so that the backscatter fell
less with height than in the older 20 February system. Both stratiform areas showed a
nearly linear decrease in the logarithm of the backscatter of ice particles with height above
the freezing level. McGaughey et al. (1995) noted that the 85-GHz brightness temperatures
during TOGA-COARE were consistently warmer than 85-GHz scattering signatures over
land. The scattering signature was a result of the weak vertical updrafts not being able to lift
large particles high into the atmosphere. This allowed for absorption in the lower parts of
the atmosphere to warm the upwelling brightness temperatures. McGaughey et al. (1995)
found that even the strongest convection was unable to produce noticeable ice scattering at
19.35 GHz. Since the vertical distribution of precipitation affects upwelling brightness
temperatures, the cloud model used in this paper m ust simulate the vertical reflectivity
structure found in oceanic convection.
c. Drop-size distribution
M easured DSDs vary widely, depending on the experiments created to measure
them. The most commonly used DSD is the M arshall-Palmer (M-P) DSD (Marshall and
Palm er 1948). DSDs can vary between stratiform and convective clouds due to the
differences in the strength of the updraft. The radiative transfer model used in this paper
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14
uses an exponential fit for its DSD; although, many studies use a gamma distribution. There
has been a considerable amount of theoretical work done on DSDs (List and McFarquhar
1990; Brown 1988; Brown 1990). These studies suggested that DSDs were not exponential
such as the M-P DSD but contained three peaks. The cause of the peaks was due to filament
and sheet breakups (List and McFarquhar 1990). Filament breakups produced a peak in
small drops while sheet breakups caused a peak in medium-sized drops. Disk breakups
were found to be unimportant in their study. Brown (1988,1990) found that the effects of
filament, sheet, and disk breakup caused the DSD to reach an equilibrium state (i.e., the
slope did not change as rain rate increased). The breakup of drops produced more small
drops and fewer large drops than the M-P DSD. The M -P DSD was measured from
continental clouds and was supposed to account for spontaneous drop breakup. However,
spontaneous breakup was later found not to make a difference in the development of a DSD
(List and McFarquhar 1990). The peaks produce a greater concentration of smaller drops
than predicted by the M-P DSD (Valdez and Young 1985).
From observations taken during TOGA-COARE, Tokay and Short (1994) found
from data taken on Kapingamarangi Atoll that from 1 - 1 0 mm h '1, convection had a large
number of small to medium size drops < 2 mm in diameter while stratiform rain had more
large drops. They pointed out that a M-P DSD did not fit the observed rainfall well.
Jorgensen and Willis (1982) found that the Z-R relationship derived from the M-P DSD
underestimated heavy rainfall in hurricanes. Willis and Tattelman (1989) also looked at
tropical storms and hurricanes, but with rain rates > 25 mm h_1. They found no drops
> 5 mm in diameter. The maximum drop sizes stabilized or even decreased at high rain
rates. A smaller amount of large drops (> 4 mm diameter) was found than predicted by the
M-P DSD. They used a gamma distribution to fit the DSDs for high rain rates.
The fact that TOGA-COARE cells have small buoyancies (weak vertical velocities)
means that there is more time for the warm rain process to act. Once the particles grow too
large for the updraft to sustain, they fall out of the cloud. Jorgensen and LeMone (1989)
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15
and Black and Hallett (1986) both found that low updraft speeds in oceanic clouds observed
in TAMEX and hurricanes, respectively, did not produce rain drops > 3 mm in diameter in
convection. Gamache (1990) looked at ice distributions above the freezing level in clouds
during SMONEX. He found that concentrations of ice particles were greater in convective
clouds than in stratiform clouds. Data suggested that the N0 intercept for ice particles was
greater than 108 n r 4. The DSD used in this paper will be an inverse-exponential DSD that
contains a greater num ber of small precipitation particles and a fewer num ber of larger
precipitation particles than the M-P DSD. As an example, the model uses a DSD intercept
(N 0) of around 107 n r 4 that is five times greater than the M-P DSD. A more detailed
explanation of this DSD is left for a later discussion.
A Z-R relationship is derived from the DSD.
This relationship will change
depending on the DSD used and can be different for rain and snow and for convective and
stratiform areas. The most recent studies indicated that there should be two separate Z-R
relationships for convective and stratiform rain (Thiele et al. 1994; Tokay and Short 1994).
A Z-R relationship is unreliable since it depends on the sixth moment of the drop diameter.
This introduces a large dependence on the largest drops that happen to be the least well
known size. If a M -P DSD is used, the corresponding Z-R relationship is Z = 296 R 1-47.
A commonly used Z-R relationship is Z = 200 R *-6. Table 2 lists the Z-R relationships for
tropical oceans including the TOGA-COARE region. The DSD used in this paper produces
a Z-R relationship of Z = 103 R 1-61. Subsequent references to a rain rate derived from the
logarithm of the backscatter will be made using this relationship.
3.
Dissertation objectives based on previous work
The cloud model developed in this dissertation represents a middle ground between
the Wilheit et al. (1977) model and the multi-dimensional cloud models used in Adler et al.
(1991), M ugnai and Sm ith (1988), and Kummerow and W einm an (1988).
O ne­
dimensional cloud models such as the one used by Wilheit et al. (1977) are too simple in
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16
Table 2. List of computed Z-R relationships for tropical oceanic clouds.
Z-R RELATIONSHIP
Z = 230 R
Z = 300 R 1-35
Z = 276.7 R 129
Z = 4 0 0 R 13
STUDY
AREA
Hudlow (1979)
GATE
Jorgensen and Willis (1982)
hurricanes
Willis (1984)
hurricanes
Williams et al. (1992)
Darwin, Australia
Z = 170 7?147 strat.
Z = 3 0 0 /? 150 conv.
Thiele et al. (1994)
TOGA-COARE
Z = 139 R >-43 strat.
Z = 367 /? 130 conv.
Tokay and Short (1994)
TOGA-COARE
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17
handling the microphysical and vertical structure of the cloud. The radiative transfer models
that use m ulti-dim ensional cloud models are very com plicated and probably too
sophisticated to allow any meaningful interpretation of important variables involved in
microwave radiative transfer. The cloud model developed in this paper is one-dimensional,
integrated along the vertical axis. A one dimensional cloud model allows the variables to be
fully understood so that knowledge is gained about what is happening to the upwelling
brightness temperatures.
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18
CHAPTER III
DATA
The TCM-90 and the TOGA-COARE data used in this study were obtained from the
western Pacific in 1990 and 1993, respectively. The TCM-90 experiment contained
collocated radar and radiometers on board the NASA DC-8 aircraft. The radar operated at
10 and 34.4 GHz but only the lower frequency was used in this study. The 10 GHz radar
was fixed at nadir with a beam width of 5.2°. The sensitivity of the radar was < 3 dBZ.
The TOGA-COARE data used in this study were collected from two sensors on
board the NASA DC-8 aircraft during January - February 1993. Radar data were collected
from the Airborne Rain MApping Radar (ARMAR). The ARMAR measured brightness
temperatures and backscatter at a frequency of 13.8 GHz. The antenna had an aperture
diam eter of 0.4 m with a 3 dB beamwidth of 3.8°. ARMAR also used a small fraction of
the time between pulses to function as a 13.8 GHz radiometer. The radiometer had a Noise
Equivalent AT (NEAT) of 1 K. The instrument scanned ± 20° crosstrack from nadir
producing a 9 km swath at a 12 km altitude. The minimum detectable backscatter at 10 km
was 10 dBZ (approximately 0.2 mm h r1). Only the nadir brightness temperatures and
backscatter from ARMAR were studied here. The second sensor utilized was the Airborne
Multichannel Microwave Radiometer (AMMR). AMMR operated at 18.7, 21, and 37 GHz
for this experiment. The antenna had a 3 dB beamwidth of 6° at each frequency. The
accuracy of brightness temperatures in rain was ± 3 K. The instrumental position was fixed
at nadir.
Vertical backscatter and AMMR data were received from archives at the Goddard
Space Flight Center. The ARMAR radiometer data were extracted from an 8 mm tape
received from the Jet Propulsion Laboratory. The data set consisted of thirteen missions
flown within a two month period during TOGA-COARE. AMMR data were sampled every
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19
second while the ARMAR data at nadir were sampled approximately every two seconds.
The difference in sampling was due to the ARMAR scanning capability that only allowed a
nadir observation every other second as the instrument scanned ± 20° crosstrack. The
ARMAR data were linearly interpolated to match the AMMR data set. The two data sets
were combined with housekeeping data from the Data Acquisition and Distribution System
(DADS) to eliminate aircraft pitch and roll > ± 5° and land surfaces. Backscatter from
ARMAR was calculated at nadir at heights above 1 km over the ocean surface to eliminate
range sidelobe contamination near the surface. The retrieved backscatter was then used to
calculate a radar estimated rain rate from a Z-R relationship.
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20
CHAPTER IV
A FOUNDATION FOR RADIATIVE TRANSFER
The model described in W ilheit et al. (1977) is used as a physical foundation for
microwave radiative transfer. The model represents the current knowledge about the
interaction of microwave radiation with CLW, precipitation, and m olecular atmospheric
constituents. The physics in the model is discussed in more detail in W ilheit et al. (1977).
Even though the algorithm handled the radiative transfer correctly, the model atmosphere
was unrealistic. Figure 1 shows a schematic of the Wilheit et al. (1977) model.
The W ilheit et al. (1977) model used a M -P DSD for rain drops and ice. The rain
rate was assumed to be constant from the surface to the freezing level. The freezing level
was a selectable parameter of the model. The vertical relative humidity profile increased
linearly from 80% at the surface to 100% at the freezing level and remained at 100% up to
11 km. The temperature lapse rate was a constant 6.5 K km-1 to resemble a U.S. Standard
Atmosphere. A CLW content of 0.5 g n r 3 was confined to a 0.5 km layer immediately
below the freezing level.
The cloud model was one-dimensional with the microphysics and thermodynamics
explicitly specified. The algorithm configuration was based on fundamental physics of
radiative transfer in the atmosphere to generate upwelling brightness temperatures from
selected rain rates. Even though the model atmosphere was simplistic, it emphasized the
important features that influence upwelling brightness temperatures such as the rain layer
thickness while the model de-emphasized the contribution from CLW.
At frequencies < 37 GHz, the upwelling brightness temperatures are mainly affected
by absorption from CLW and precipitation and are not greatly influenced by scattering from
ice particles. The W ilheit et al. (1977) model was designed without an ice layer above the
freezing level. However, when the ice layer thickness becomes large, scattering by ice
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21
FREEZING LEVEL
NON-PRECIPITATING
CLOUD 0 .5 g /m 3
MARSHALL PALMER
RAIN DROPS
ADJUSTED FOR DENSITY
1 /2 km
1 0 0 % RELATIVE
HUMIDITY
LAPSE RATE
6 .5 °C /k m
8 0 % RELATIVE
HUMIDITY
OCEAN SURFACE
Figure 1. Schematic of the Wilheit et al. (1977) radiative transfer model
(from Wilheit et al. 1991).
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22
becomes more important. Wilheit et al. (1982) added an ice layer above the freezing level to
account for the scattering by ice. However, the main source of scattering at frequencies
< 37 GHz comes from the scattering by large rain drops at heavy rain rates.
Since
upwelling brightness temperatures are only weakly affected by ice, the ice shape becomes
irrelevant so that assuming spherical ice particles causes little error. In nature, there are an
infinite variety of ice shapes that are completely unknown; therefore, ice modeling will
always remain an approximation. There are other reasons why the ice layer is unimportant
in tropical oceanic clouds but this will be discussed in more detail later.
The M-P DSD was chosen since it represented a widely-used inverse-exponential
DSD. Wilheit et al. (1977) showed that the DSD had a minor effect on the T-R relationship
at 19 GHz. Therefore, altering the DSD in the model did not produce a significant change in
the upwelling brightness temperatures. Figure 1 shows that the model atmosphere only
contained a 0.5 km cloud. The limited amount of CLW led the authors to conclude that the
CLW only contributed a couple of degrees to the upwelling brightness temperature at
19 GHz. CLW is made up of droplets < 100 |im in radius. At this size, absorption is
proportional to the mass of the droplets. At low rain rates, the increase in brightness
temperatures were the result of the absorption by precipitation-sized particles (>100 pm
radius) in the model atmosphere. Wilheit (1986) remarked that the Wilheit et al. (1977)
model could be in great error if the CLW assumption was incorrect.
Based on the height of the freezing level, a series of T-R relationships generated by
the W ilheit et al. (1977) model is shown in Fig. 2. For each freezing level, the brightness
temperature increases as rain rate increases until a saturation point is reached and then the
brightness temperature falls as the rain rate increases further. Since the thermodynamic
profile and CLW content in the model remain constant, the upwelling brightness
temperatures increase at low rain rates as the result of the absorption by rain drops. At high
rain rates, the brightness temperatures fall due to scattering by large rain drops produced by
the M-P DSD. It is seen from Fig. 2 that rain drops influence the brightness temperatures
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23
* 2S0
200
5 km
4 km
150
0.1
1
10
100
1000
RAINFALL RATE (mm/hr)
Figure 2. Calculated brightness temperatures for 19 GHz at nadir for
various freezing levels (from Wilheit et al. 1977).
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24
measurably at rain rates > 1 mm h '1. The change in brightness temperatures as the freezing
level increases indicated the importance of the rain layer thickness on the upwelling
brightness temperatures.
Over the years, aircraft and satellite observations have shown that the W ilheit et al.
(1977) model produces an acceptable T-R relationship at 19 GHz. Despite the simplistic
atmospheric model, the similarity between observations and theory shows that an algorithm
based on first principles can reliably simulate upwelling brightness temperatures.
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25
CHAPTER V
A CONVECTIVE CLOUD MODEL
Figure 1 shows that the W ilheit et al. (1977) model does not have a realistic
atmosphere. If realistic microphysics were added to a radiative transfer model, would the
fundam ental concepts behind the W ilheit et al. (1977) model still hold? W ill the T-R
relationships still be valid? To answer these questions, a new radiative transfer model was
developed with realistic convection. The new model and the Wilheit et al. (1977) model will
be referred to hereafter as the convective cloud model (CCM) and WILM, respectively. A
more detailed discussion of the thermodynamic and microphysical equations used in the
CCM is located in Appendix A. Appendix B contains the relevant equations for microwave
radiative transfer. The CCM integrates the vertical velocity of a parcel along the vertical axis
every 100 m. Based on observations of clouds over the western Pacific, the cloud base is
set at 0.6 km. The parcel follows a pseudo-adiabatic lapse rate until its vertical velocity
reaches zero. The parcel's ascent is hindered by entrainment and liquid water loading. The
CCM is run using the sounding listed in Table 3. The sounding is representative of average
atmospheric conditions over the tropical oceans. Later, it is discussed that changes in the
temperature and RH profiles do not significantly influence modeled upwelling brightness
temperatures. The environmental freezing level is located at 4.4 km and the integrated water
vapor content (IWVC) is 4.80 g cm’2.
The CCM assumes a constant cloud radius with height. The cloud model also has
the capability to produce clouds with anvils. From Appendix A, it is shown that as the
cloud radius increases the entrainment decreases which suggests that large clouds have less
entrainm ent in their cores. Therefore, larger clouds can rise higher into the atmosphere
since they have lower saturated lapse rates than smaller clouds. As the cloud forms, it
modifies the atmosphere by changing the temperature and moisture profiles.
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26
Table 3. The moist tropical sounding used to initialize the CCM.
pressure
(mb)
height
(km)
1013
1000
950
900
850
700
500
300
100
0.0
0.1
0.5
1.0
1.5
3.0
5.6
9.1
16.5
temperature
(K)
301.0
299.7
295.7
290.0
288.0
281.0
266.0
240.0
191.0
RH
(%)
80
85
90
90
80
75
70
50
8
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27
In Chapter II, it was discussed that oceanic clouds have low vertical velocities. It
should be noted that the equations used for determining the vertical velocity of the cloud
described in Appendix A produce vertical velocities that are unrealistically high (>10 m s '1)
for the majority of oceanic convection. However, the main purpose of the vertical velocity
in the CCM is to determine the cloud top. A damping factor is introduced into the buoyancy
equation in Appendix A to assure that the vertical velocities are always less than 6 m s * 1.
This adjustment has no affect on the thermodynamics and produces little change in the
height of the cloud. For tall clouds that extend well above the freezing level, a change in
cloud top height of 1 km will not produce any significant change in the upwelling brightness
temperatures generated by the CCM.
The amount and vertical distribution of CLW are handled separately from the
thermodynamics. The CLW amount can vary as the rain rate changes and the vertical
distribution of CLW can assume any profile. The amount and vertical distribution of CLW
influence the upwelling brightness temperatures the most at low rain rates. For the purposes
of comparing the CCM to the WILM, the CLW content at low rain rates will be set at a
maximum value of 0.5 g n r 3 at the freezing level. For moderate and high rain rates, the
CLW content will increase to a maximum value of 1.2 g n r 3 at the freezing level. For all
rain rates, the vertical distribution of CLW will increase from cloud base to a maximum
value at the freezing level and then linearly decrease to zero at the top of the cloud. This
CLW profile is similar to the profile described in Bauer and Schluessel (1993). The initial
condition (0 mm h_1) of the CCM contains a 0.5 km thick cloud located immediately below
the freezing level. However, unlike the WILM, the CCM does not saturate the atmosphere
above the freezing level.
The precipitation-sized particles within the cloud are dependent on the rain rate. The
particles fall at their calculated fall speeds, independent of the updraft velocity. There are
three classes of hydrometeors: rain drops, supercooled water, and ice. There is no mixedlayer containing both liquid and ice particles. Even though mixed layers exist in nature, the
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28
thickness o f these layers as well as their location above the freezing level is unimportant for
frequencies < 37 GHz. For comparison with the W ILM, a M -P DSD is assum ed for
precipitation above and below the freezing level. All precipitation-sized particles are
considered to be spherical.
Supercooled water is more im portant to the upw elling
brightness temperatures than ice because liquid water contributes to the rain total rain water
thickness. The total rain water thickness is defined as the vertical distance in the atmosphere
that contains liquid water drops. The rain profile in the CCM is constructed so that it
conserves mass (i.e., adjusted for density) between the surface and freezing level. The rain
rate linearly decreases to zero between the freezing level and the top of the cloud. The
precipitation profile above the freezing level is similar to profiles discussed in B auer and
Schluessel (1993) and Kummerow et al. (1989).
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29
CHAPTER VI
MODEL COMPARISON
Figure 3 shows four T-R relationships generated by the CCM and the WILM using a
4 and 5 km freezing level for 13.8, 18.7, 21.3, and 37 GHz at 4.5° from nadir. At this
angle, the vertical and horizontal polarizations are approximately the same. For comparison,
both models assume a Lambertian (rough) ocean surface and a sea surface temperature of
301 K. In the CCM, the freezing level rises as the rain rate increases because the cloud
parcels become less entrained. In contrast, the freezing level in the WILM was independent
of the rain rate. This is important because the initial (non-raining) condition of the CCM has
an environmental freezing level at 4.4 km and should be compared to the WILM using a
4 km freezing level.
A t the initial condition, both models contain a 0.5 km non­
precipitating cloud located immediately below the freezing level. Table 4 shows that at the
initial condition the WILM using a 4 km freezing level and the CCM are nearly identical.
This result is not surprising since the only difference between the two models at this point is
in the RH profiles. Table 4 indicates that the CCM and the WILM have similar model
atmospheres.
When rain is introduced into the model atmosphere, the freezing level in the CCM is
within 300 m of 5 km from 0.25 - 150 mm h '1. Therefore, the brightness temperatures
generated by the CCM from rain should correspond to the WILM using a 5 km freezing
level without appreciable error. Therefore, both models are compared to each other using a
5 km freezing level.
Figure 3 shows that large differences exist between the T-R
relationships generated by the CCM and the WILM. At low rain rates, the CCM is 10 40 K higher than the WILM. The opposite is true at moderate and high rain rates where the
brightness temperatures generated from the WILM become much warmer than the CCM
brightness temperatures. At low rain rates, the combination of large quantities of CLW and
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30
275 (a) 13.8 GHz
WILM 4 km
WILM 5 km
CCM
225
£ 175
150
0.1
1
10
100
Rain rate (mm/hr)
275 -(b) 18.7 GHz
WILM 4 km
WILM 5 km
X 250
CCM
S 225
3 200
«
175
150
100
Rain Rate (mm/hr)
Figure 3. T-R relationships generated by the CCM and the WILM using a 4 and
5 km freezing level at (a) 13.8 GHz; (b) 18.7 GHz; (c) 21.3 GHz;
(d) 37 GHz.
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31
275
_(c) 21.3 GHz
WILM 4 km
WILM 5 km
CCM
«» 250
os
225
200
0.1
1
10
100
Rain rate (mm/hr)
275 -(d) 37 GHz
WILM 4 km
WILM 5 km
CCM
9 250
£ 225
Q£
•C 200
175
0.1
1
10
100
Rain rate (mm/hr)
Figure 3. Continued.
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32
Table 4. Brightness temperatures calculated at the initial condition by
the CCM and WILM using a 4 and 5 km freezing level.
Frequency
(GHz)
CCM
(K)
13.8
18.7
21.3
37
134.9
164.4
205.5
189.3
4 km WILM
(K)
135.4
167.8
206.4
192.7
5 km WILM
(K)
140.7
184.2
231.9
202.5
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33
precipitation above the freezing level in the CCM increases the opacity of the model
atmosphere and produces a dramatic increase in the upwelling brightness temperatures at
each frequency, especially at 37 GHz. At moderate and high rain rates, the increased
opacity from rain drops above the freezing level causes saturation to be achieved earlier in
the CCM resulting in lower upwelling brightness temperatures. The CCM also contains a
large ice layer thickness above the freezing level because the cloud extends to a height of
> 10 km. Ordinarily, ice is not a concern at frequencies < 37 GHz. In the CCM, the M-P
DSD combined with the linearly decreasing rain rate above the freezing level produces a
considerable number of large ice particles above the freezing level especially at moderate and
high rain rates. The increased scattering by ice suppresses the brightness temperatures at
these rain rates. However, ice scattering is still not a factor in the CCM when considering
the relevant dynamic ranges of the frequencies. The relevant dynamic range of the T-R
relationship is located where brightness temperatures measurably change with increasing
rain rate. From the CCM, the high rain rate cut-off in the dynamic range at 13.8, 18.7,
21.3, and 37 GHz is approximately 25, 15, 10, 3 mm h '1, respectively, which contrasts the
results from the WILM where the upper limit at each frequency is more than a factor of 1.5
larger than for the CCM.
The reason for the decrease in the high rain rate cut-off in the dynamic range at each
frequency is due to the amount of CLW and precipitation in the CCM. The CLW and
precipitation not only suppress the theoretical brightness temperatures at high rain rates but
they also reduce the dynamic range by introducing more absorption earlier at low rain rates
(see Fig. 3). The CCM begins the first rain rate calculation with a 10 km tall cloud in the
model atmosphere containing a large amount of ICLW. The CCM altered the amount and
vertical distribution of CLW at each rain rate. In contrast, the W ILM assumed a constant
amount and vertical distribution of CLW at each rain rate. For all rain rates, the CCM has a
ICLW content o f > 0.25 g cm '2 while the WILM has a ICLW content of 0.03 g c m '2.
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34
Since ice plays a minor role at low rain rates, the CCM with 6 km of ice above the freezing
level and the WILM have the same vertical precipitation structure.
The effects of CLW and precipitation at low rain rates are best illustrated by
comparing the T-R relationships produced by the WILM and the CCM at 37 GHz. The 37GH z channel is the most sensitive to CLW and small precipitation-sized particles.
Therefore, at 37 GHz the vertical CLW and rain rate distributions should produce the
biggest difference between the CCM and the WILM. This is verified by comparing the
37 GHz curves in Fig. 3d. The greater amount of ICLW and precipitation above the
freezing level have increased the brightness temperatures at 0.25 mm h '1 by > 40 K. For
frequencies < 37 GHz, the effect of CLW is not as great so the differences between the
CCM and the WILM are not as large at low rain rates.
In summary, the net effects of adding a realistic cloud to the CCM are to decrease the
dynamic range for each of the frequencies, increase the brightness temperatures at low rain
rates due to absorption of CLW and rain drops, and lower the brightness temperatures at
higher rain rates due to scattering by precipitation-sized particles above the freezing level.
Com bined, these elem ents produce large differences between the T-R relationships
generated by the CCM and the WILM.
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35
CHAPTER VII
THE CCM VS. OBSERVATIONS
Does the CCM generate brightness temperatures that were observed during TOGACOARE? Several case studies are selected to compare the CCM with the observations. The
first case study involves a segment observed from 2220 - 2225 UTC 10 February 1993.
This interval contained a stratiform precipitation event containing light rain typically
observed over the TOGA-COARE region. This case study will test the CCM at low rain
rates. The second case study involves a convective region containing heavy rain and a
stratiform region that was observed from 2145:14 - 2149:30 UTC 20 February 1993. This
event was selected to test the CCM at moderate and high rain rates. The CCM is not
expected to match the observations precisely but the model should be within 5 K of the
observed brightness temperatures.
1. 2200 - 2225 UTC 10 February 1993
Figure 4 shows the vertical backscatter structure from ARM AR and the
corresponding radiometer data for 2200 - 2225 UTC 10 February 1993 during TOGACOARE. The radar cross-section clearly shows the surface (indicated by the broad white
horizontal line) and the freezing level. Data was cutoff at the top of the radar image but at
least 4 to 5 km of ice was present above the freezing level in this system. The brightness
temperatures from the radiometers were nearly constant for three-quarters of the time
segment but began to rise at 2224 UTC. The time segment of interest (2220 - 2224 UTC)
was an area where the radar was barely detecting rainfall at the surface . For most of this
region, the radar indicated a backscatter between 10 and 20 dBZ which equated to rain rates
< l m m h ' 1. In several sections, the backscatter had fallen below the minimum detectable
rain rate near the ocean surface (< 0.2 mm h_1). The uniformity of the observed brightness
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
30
40
50 dBZ
Nadir Radar Backscatter
N adir Radiometric Brightness Temperatures
250
00
•c
100--------
22 :20:00
22 :21:00
22 :22:00
22:23:00
22:24:00
22:25:00
Tim e (UTC)
Figure 4. Nadir backscatter observed by ARMAR and corresponding nadir radiometric
brightness temperatures observed by ARM AR and AM M R at 13.8, 18.7, 21.3,
and 37 GHz for 2200 - 2225 UTC 10 February 1993 during TOGA-COARE.
The orange, red, blue, and black colors correspond to 13.8, 18.7, 21.3, and 37
GHz, respectively.
u>
On
37
temperatures at 37 GHz indicated that there was not much variation in the rainfall or CLW
content.
Com paring the T-R relationships generated by the CCM in Fig. 3 with the
observations shows large discrepancies between the two. If the rain rate was approximately
0.25 mm h '1, the CCM overestimates the brightness temperatures for all the frequencies by
more than 30 K at low rain rates. The rain rate estimation from radar backscatter can easily
be in error by a factor of 2, but Fig. 4 shows that there was measurable surface rainfall. At
each frequency, the CCM indicates that it was raining «
0.25 mm l r 1 in this region.
Heavier stratiform rain began after 2224 UTC where the near surface backscatter rose to
approximately 28 dBZ (3 mm hr1). The brightness temperatures increased by only 20 K at
each frequency. The CCM still predicts a rain rate < 0.25 mm h_1. The 37-GHz brightness
tem peratures produced by the CCM appear to have a substantially different rainfall
m easurement than the radar at low rain rates. The radar and CCM estimated rain rates
should be within a factor of 2 of each other, not a factor of 20. This case study indicates
that the CCM is not valid at low rain rates.
2.
2145:14 - 2149:30 UTC 20 February 1993
Figure 5 shows radar and radiometer measurements of a convective line - trailing
stratiform region observed from 2145:14 - 2149:30 UTC 20 February 1993 during TOGACOARE. The radar became partially attenuated as it passed over the convection. The
attenuation occurred because the precipitation particles near the freezing level produced a
large enough backscatter that radiation emitted by the radar was unable to penetrate a
substantial distance below the freezing level. The attenuation was indicated by lower
backscatter near the surface from 2146 - 2147 UTC. As a result, an average backscatter of
45 dBZ (35 mm h_1) in this region was an underestimate. The convection appeared to be
confined to below the freezing level around 2146 UTC indicating that the warm rain process
was probably prevalent there. However, by 2146:30 UTC ice appeared above the
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Nadir Radar Backscatter
11.0-1
*
Nadir Radiometric Brightness Temperatures
280
3 180
.op
M 130
21:46:00
T im e (UTC)
Figure 5. As in Fig. 4, except from 2145:14 - 2149:30 UTC 20 February 1993.
oo
39
freezing level, indicating that a cold rain process had developed. The system became more
stratiform at 2147:30 UTC. The stratiform region contained areas of very light to moderate
rainfall with an extensive layer of ice above the freezing level.
The observed brightness tem peratures at 13.8, 18.7, and 21 GHz were
approximately 270 K in the convective line while the 37 GHz varied between 230 - 260 K.
Curiously, brightness temperatures in excess of 270 K at 13.8 GHz indicated a surface rain
rate > 30 mm h '1 but 18.7 and 21.3 GHz remained well above 260 K. The CCM is within
reasonable proximity to the observed brightness temperatures in magnitude but does not
predict brightness temperatures > 268 K at 13.8, 18.7, or 21 GHz. The T-R relationships
generated by the CCM show that rain rates > 30 mm h '1 in the convective line should have
suppressed 18.7 and 21 GHz to < 260 K, indicating that this is another large discrepancy
between the CCM and the observations.
One possible explanation for the differences between the model and observations in
heavy rain is that the precipitation in the convective line was restricted to below the freezing
level preceding 2146 UTC. The CCM has a considerably deeper vertical precipitation
structure. However, as precipitation appeared above the freezing level later in time (after
2146 UTC), there was still no meaningful change in the brightness temperatures at 13.8,
18.7, or 21 GHz. Therefore, the vertical precipitation structure above the freezing level is
not the cause of the discrepancy. The observations show that the CCM cannot model the
warm upwelling brightness temperatures in the convective region. The 37-GHz channel
brightness temperatures showed a minimum of 230 K at 2147:15 UTC as a significant
number of ice particles appeared above the freezing level. At 2147:15 UTC, the 37-GHz
brightness temperatures generated by the CCM matched the observations but for the
majority of the convective line the 37-GHz brightness temperatures remained around 250 K
—20 K higher than predicted by the CCM.
After 2147:30 UTC, the rainfall decreased and becam e more stratiform .
At
2148 UTC, the backscatter of 24 dBZ (1.7 mm h '1) was slightly higher than at 2224 -
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40
2225 UTC 10 February (Fig. 4). As a result, the observed brightness tem peratures at
2148 UTC 20 February were nearly the same and slightly higher than 2224 - 2225 UTC
10 February. Once again, the CCM is overpredicting the brightness temperatures and
considerably underestimating the rain rate in this region just as it did in the previous case
study. As the rainfall increased in the stratiform region at 2149 UTC, the brightness
temperatures increased 10 - 50 K. Radar indicated a surface rain rate of around 8 mm h '1
(34 dBZ) in this region. At 8 mm h"1, the CCM predicts brightness temperatures that are
around 10 to 30 K higher than the observations. The CCM would interpret the observations
in this region as having a rain rate of approximately 2 mm f r 1.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
CHAPTER VIII
AN IM PROVED MODEL USING OBSERVATIONAL DATA
In Chapter VII, the CCM failed to reproduce observed brightness temperatures from
TOGA-COARE. The CCM rain rate estimations differed from the radar by more than a
factor of 2. These results indicate that either the microphysics or the thermodynamics is not
being handled correctly by the CCM. Another potential source o f error in the CCM is the
handling of the surface reflectivity. A change from a Lambertian to a specular (smooth)
ocean surface will have a large impact on upwelling brightness temperatures at low and
moderate rain rates, especially at 13.8 GHz.
The thermodynamics in the CCM cannot be a large source of error since the cloud
modified RH and temperature profiles do not significantly alter the initial model sounding at
low levels. The largest changes in the RH and temperature profiles, which are a result of
convection, occur well above the ocean surface.
As the atm ospheric pressure and
tem perature decrease, the effect of water vapor on upwelling brightness temperatures
becomes smaller. Appendix C shows that the environmental RH profile does not greatly
affect upwelling brightness temperatures when clouds are present in the tropics. Similarly,
the change in the temperature profile is most noticeable at the mid-levels of the atmosphere.
Tropical oceanic cloud buoyancies are usually no m ore than 3 K w arm er than the
environmental sounding (see Chapter II). The effect of the altered temperature profile on the
upwelling brightness temperatures is much less than the accuracy of the radiometers used in
TOGA-COARE. Therefore, microphysics is left as large source of error in the CCM. The
three relevant microphysical factors that need a close examination for frequencies < 37 GHz
are CLW, vertical precipitation structure, and DSD. The new model that contains the
microphysical modifications is referred to as the hybrid cloud model (HCM).
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42
The HCM assumes that low rain rates (< 10 mm h '1) come from stratiform clouds.
This is not a bad assumption since the majority of low rain rate observations comes from
stratiform clouds. Therefore, the dynamic range at each frequency can be thought of as a
cloud evolution. This concept alters how the microphysics is defined at each rain rate in the
HCM. At low rain rates, the microphysics will reflect conditions observed in stratiform
clouds whereas high rain rates will have microphysics characteristic of convective clouds.
In contrast, the W ILM and the CCM assumed that all rain rates were a result of convection.
The transition between convective and stratiform precipitation is usually defined around
10 mm hr1 (see Chapter II). However, observations from TOGA-COARE have made this
distinction less clear.
In the HCM, the CLW changes rapidly around a rain rate of
10 mm h_1. The DSD and vertical precipitation structure are not affected by the transition
to convective rainfall at 10 mm h’ 1. The HCM applies a different TOGA-COARE cloud
structure to each rain rate. This assumption can result in potential errors produced by
significant departures in the CLW content, vertical precipitation structure above the freezing
level (e.g., warm rain), or DSD.
1.
C h an ges to th e am ou n t an d vertical d istribu tion o f C L W
A t low rain rates, CLW is the most important factor influencing the upwelling
radiation because the absorption from the relatively few precipitation-sized particles is not
significant. The HCM assumes that low rain rates are produced by stratiform clouds which
have low CLW contents. Convective clouds have higher amounts of CLW but the effect of
CLW is negligible at rain rates > 5 mm h"1, even at 37 GHz (see Appendix C). Therefore, it
is crucial that the CLW is correctly determined at rain rates < 5 mm h '1. Previous work
from observational and modeling studies have shown that oceanic stratiform clouds contain
low amounts of CLW (see Chapter H). These findings effectively constrain the amount of
CLW that clouds in the HCM can contain at low rain rates.
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43
The CLW in the HCM is dependent on the rain rate. The CCM and the WILM have
a constant maximum CLW content of 0.5 g n r 3 for rain rates < 5 mm h '1. Using results
from observations, the CLW in the HCM is set at a maximum value of 0.1 g n r 3 for rain
rates < 5 mm h '1. The CLW in the HCM increases slowly as rain rate increases until around
10 mm h_1 where a transition is made to convective rainfall. From this point, the CLW
quickly rises to a maximum value of 1.2 g n r 3 at 150 mm h '1.
The vertical distribution of CLW is important to upwelling brightness temperatures
at low rain rates. In the WILM, the CLW was constrained to a 0.5-km layer below the
freezing level producing a ICLW content of 0.03 g cm-2. The CCM altered the vertical
distribution of CLW by extending the CLW from the cloud base to the cloud top. The CCM
has a ICLW content of 0.3 g cm '2 which is a factor of 10 greater than in the WILM. The
HCM modifies the vertical CLW distribution to match observations made of CLW over the
tropical oceans (see Chapter II). The vertical CLW distribution is constructed so that it
decreases linearly from a maximum CLW content at the cloud base to zero several
kilometers above the freezing level. The height that the CLW reaches is dependent on the
rain rate. Therefore, clouds with higher rain rates have a greater CLW depth. At low rain
rates, the clouds in the HCM do not have any significant ICLW. At rain rates < 5 mm h_1,
the ICLW is only 0.03 g cm '2 which is identical to the WILM. It was shown in Chapter II,
that CLW does not extend very far above the freezing level, even in convection. The
absence of large amounts of CLW above the freezing level in convection produces a ICLW
content of < 0.4 g cm-2. This number is significantly lower than the ICLW contents
described in previous studies (e.g., Smith and Mugnai 1988) but a factor of 16 greater than
in the WILM at high rain rates.
2. C h an ges to the vertical p recip itation stru ctu re
The HCM modifies the precipitation structure above the freezing level. The model
still assumes a constant rain rate below the freezing level as in the CCM and the WILM.
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44
Observations showed that when CLW decreased above the freezing level so did the amount
of liquid precipitation (see Chapter II). The rapid conversion of liquid w ater into ice
suggests that the total thickness of the supercooled water layer reaches no more than 1 to
2 km above the freezing level, even in strong convection.
In response to this, the
supercooled water layer in the HCM ranges from zero in stratiform clouds up to 1 km at
150 m m h '1. The supercooled water layer is unchanged from the CCM.
Previous
microphysical studies found that the rapid conversion of CLW and liquid water into ice
above the freezing level was accompanied by a significant amount of small ice crystal
production (see Chapter II). The lack of any significant amount of large ice particles
combined with the weak updrafts in oceanic clouds resulted in large gradients for the
logarithm of the backscatter above the freezing level. From Chapter II, a lapse rate for the
logarithm of the backscatter of 6 dBZ k m '1 was found to be common for convective and
stratiform clouds above the freezing level.
The HCM assumes a 6 - 8 dBZ km-1 lapse rate above the freezing level. A linear
decrease in the logarithm of the backscatter of ice is the same as an inverse exponential
decrease in the snowfall. Therefore, an exponential function is applied to the ice particles to
maintain a linear lapse rate for the logarithm of the backscatter above the freezing level. The
exponential ice decrease above the freezing level is considerably different than the linear ice
profile used by the CCM. Since the snowfall at a particular level in the model atmosphere is
influenced by the number of precipitation-sized particles located there, a linear lapse rate for
the logarithm of the backscatter of ice above the freezing level makes the ice layer much
m ore transparent to microwave frequencies by decreasing the amount and size of
precipitation-sized particles.
3.
C h an ges to th e D SD
The DSD developed for this model is an inverse-exponential DSD similar to the M-P DSD.
The distribution in terms of radius, (p, is
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45
N{<p) = N0e -Al»
(8.1)
where
N q = 0.8 cm -4
*
120
l
A = ^ 0* Cm
The variable X is a rain param eter used to vary the true rain rate (Equation (a. 10) in
Appendix A). The rain parameter generated for this distribution is within 30% of the true
rain rate for all rain rates calculated in the model. For comparison, the rain parameter for a
M-P DSD is within 20% of the true rain rate.
The new DSD was developed from TOGA-COARE observations (see Section 7a)
and data from other field projects. The DSD fits the observations of small ice particles
above the freezing level and warm scattering signatures from MCSs during TOGA-COARE
(see Chapter II). The N q value shown above is a factor of 5 greater than the N0 used in the
M -P DSD. This, combined with a greater slope, produces a greater num ber of small drops
and fewer large drops than the M-P DSD. The combination of the new DSD and vertical
precipitation structure above the freezing level results in an ice layer that is more transparent
to microwave frequencies. The DSD can easily be converted to a Z-R relationship. The
resulting equation is Z = 103 R 161. This Z-R relationship is considerably different than the
relationships listed in Table 2. Even though the new DSD is a significant departure from the
M-P DSD, the changes in the derived rain rates are small for backscatter < 35 dBZ.
W ilheit et al. (1977) showed that the T-R relationship at 19 GHz was relatively
insensitive to the DSD. From Appendix C, it is shown that the DSD does not significantly
affect the T-R relationships at 18.7 and 21.3 GHz but the DSD has a larger effect at 13.8
and 37 GHz. The DSD used in the HCM is based on observations and seems to be more
appropriate than the M -P DSD. The new DSD causes a lag in the response of the HCM at
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46
low rain rates and increases the dynamic range of each frequency at the high rain rate cut­
off. Each frequency is sensitive to the DSD at different rain rates. For example, at
13.8 GHz the DSD affects the brightness temperatures around 10 mm h '1 since this part of
the T-R relationship is highly sensitive to absorption from precipitation-sized particles. A
M-P DSD causes the brightness temperatures to rise much more rapidly at low and moderate
rain rates because it contains larger drops than the new DSD.
4.
C h an ges to th e reflectivity o f th e ocean su rface
Figure 6 shows convective and stratiform precipitation during TCM-90 in super
typhoon Flo from 0932:43 - 0954 UTC 18 September 1990. The ocean surface is shown as
a broad black horizontal line. False precipitation below the ocean surface was a result of
multiple reflections from precipitation-sized particles between the surface and freezing level.
For instance, the false bright band that appeared below the ocean surface in Fig. 6 was a
result of the radiation from the radar that was reflected off the ocean surface which returned
to the bright band where the radiation was reflected by rain drops there and returned to the
ocean surface and reflected back to the radar on board the aircraft. The result is a mirror
image that appears below the real ocean surface.
If the ocean surface were Lambertian then there would be no clear pattern of false
precipitation below the ocean surface. There is a possibility that a mirror image of the bright
band would also appear if the ocean surface is rough but the result would be a diffuse false
bright band that is not the same distance from the ocean surface as the real bright band. A
Lam bertian ocean surface assumes that upwelling radiation leaving the ocean is a
contribution from radiation approaching the ocean from many angles. The result is a
maximum contribution from incoming radiation at approximately 45° from nadir. Since the
majority of multiple reflections that would occur would be received a different angles, the
false bright band would appear farther from the ocean surface and diffuse. Figure 6 shows
that the false bright band was approximately the same distance from the ocean surface as the
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Nadir Radar Backscatter
1*
'5
33
09:54:00
09:32:43
Time (UTC)
B
s
10
is
20
25
30
35
40
45
50
55 dBZ
Figure 6. Nadir backscatter observed by radar during TCM -90 in super typhoon Flo for
0932:43 - 0954 UTC 18 September 1990.
48
real bright band. The mirror images of the precipitation were distinct even outside of
stratiform regions. Radar data from TOGA-COARE (not shown) also indicated that a
specular ocean surface assumption was more valid than the Lambertian assumption used by
the WILM and the CCM. The specular assumption assumes that the ocean surface acts like
a m irror and only the incoming radiation that contributes to the upwelling brightness
temperatures is from one incidence angle. Table 6 in Appendix C shows that the change in
the ocean reflectivity results in brightness temperature differences of < 5 K.
5.
T h e H C M vs. th e C C M
Four T-R relationships produced by the HCM and CCM at 13.8, 18.7, 21.3, and
37 GHz are shown in Fig. 7. The temperature and RH profiles o f both models are
identical. Cloud tops range from 10.4 km at 0.25 mm h '1 to 13.3 km at 150 mm hr1. The
brightness temperatures are calculated by the HCM at similar sea surface temperature and
view angle as in the CCM and the WILM. From radar data, the only modification made to
the radiative transfer portion of the HCM is a conversion to a specular ocean surface. The
change in the surface reflectivity affects the brightness temperatures at low rain rates before
the absorption from CLW and precipitation dominate the model atm osphere even at
incidence angles near nadir (see Appendix C). Table 5 lists the brightness temperatures for
the initial atmosphere generated by the HCM, CCM, and WILM, and average clear sky
brightness temperatures taken during the 11 -1 2 January 1993 TOGA-COARE flight.
The warmer brightness temperatures generated by the CCM and the WILM at 13.8,
18.7, 21.3, and 37 GHz in Table 5 are due to the CLW inserted at the initial condition. This
is not significant besides the fact that the HCM and the WILM are two different approaches
leading up to a rain rate of 0.25 mm hr1. The W ILM was designed so that the initial
condition was the minimum brightness temperature above which rain was detected. Too
many uncertainties exist in either model to retrieve rain rates < 0.25 mm h_1. From Table 5,
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49
275 (a) 13.8 GHz
CCM
HCM
£ 250
225
150
0.1
1
10
Rain Rate (mm/hr)
100
275 -(b ) 18.7 GHz
CCM
HCM
* 250
5 225
200
«
175
150
0.1
100
Rain Rate (mm/hr)
Figure 7. T-R relationships generated by the HCM and the CCM at (a) 13.8 GHz;
(b) 18.7 GHz; (c) 21.3 GHz; (d) 37 GHz.
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50
CCM
275
Brightness Temperature (K)
HCM
250
225
200
100
Rain Rate (mm/hr)
275 -(d) 37 GHz
CCM
Brightness Temperature (K)
HCM
250
225
200
175
0.1
10
100
Rain Rate (mm/hr)
Figure 7. Continued.
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51
Table 5. Initial brightness temperatures for 13.8,18.7,21.3, and 37 GHz
from the HCM, CCM, WILM, and average brightness temperatures
observed during 1 1 -1 2 January 1993.
Frequency
(GHz)
13.8
18.7
21.3
37
HCM
(K)
CCM
(K)
4 km WILM
(K)
observed
(K)
128.6
152.7
191.4
166.7
134.9
164.4
205.5
189.3
135.4
167.8
206.4
192.7
133.1
159.8
185.2
173.1
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52
the clear sky observations from 1 1 -1 2 January 1993 fall between the HCM and the other
two models.
Figure 7 shows that low rain rate brightness temperature values are significantly
different between the CCM and the HCM with the largest changes occurring as the
frequency increases. The differences are the result of the changes in the amount and vertical
distribution of CLW, DSD, vertical precipitation structure, and surface reflectivity. At low
rain rates, the changes in the CLW and surface reflectivity are the reasons for lower
brightness temperatures at each frequency in the HCM. The CCM contains a factor o f 10
more ICLW at low rain rates (0.25 g cm*2 vs. 0.03 g cm-2) and a factor of 2 more ICLW at
high rain rates (0.8 g cm '2 vs. 0.4 g cm-2). The specular ocean surface contributes to a
brightness temperature decrease of approximately 5 K at each frequency.
The differences in the T-R relationships generated by the HCM and the CCM at
moderate and high rain rates are a result of the changes to the DSD and vertical precipitation
structure. At high rain rates, the CLW amount becomes identical in the two models but the
ICLW in the CCM is still greater by a factor of 2. In the HCM, the precipitation-sized
particles start to influence the upwelling radiation at low rain rates and becom e the
dominating factor at rain rates > 5 mm h '1 (see Appendix C). At 37 GHz, the reason the
CCM has colder brightness temperatures at high rain rates is due to larger precipitation-sized
particles and higher rain rates generated by both the M-P DSD and linearly decreasing rain
rate structure above the freezing level, respectively. At frequencies < 37 GHz, the effect of
scattering by ice above the freezing level is not as great; therefore, the differences between
the HCM and the CCM are a result of the increase in scattering by large precipitation-sized
particles below the freezing level.
It is interesting to note from Fig. 7 that 13.8 GHz has approximately the same
sensitivity to low rain rates as 18.7 GHz and to a lesser extent, 21.3 GHz. This is the result
of the changes made to the CLW, vertical precipitation structure, and DSD at low rain rates.
This conclusion is not identified in previous literature because most studies add a moderate
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53
amount of CLW at low rain rates that results in a rapid change in the brightness temperatures
as the frequency increases (compare the curves generated by the HCM and CCM in Fig. 7ad). However, in the HCM there is almost no CLW at low rain rates. This results in an
increase in brightness tem peratures based solely on changes in the precipitation-sized
particles. Observations will prove valuable to test this theory.
Figure 7 shows that the dynamic range is much larger at each frequency than in the
CCM. This result is a combination of lower CLW and specular ocean surface at low rain
rates and a more transparent precipitation structure above the freezing level at moderate and
high rain rates. The changes in CLW, vertical precipitation structure, DSD, and surface
reflectivity require a higher rain rate to saturate each frequency. The 13.8, 18.7, and 21.3GHz channels easily reach 275 K (10 K higher than in the CCM) even though the clouds in
the HCM contain 7 km ice layers.
Observations are useful to test the assumptions of CLW at low rain rates, the DSD at
moderate rain rates, and the vertical precipitation structure at moderate and high rain rates in
the HCM.
6.
T he H C M vs. the W IL M
The T-R relationships generated by the HCM are more similar to the W ILM than to
the CCM. Figure 8 shows that the HCM produces colder brightness temperatures at low
rain rates, the same brightness tem peratures at saturation, and warm er brightness
temperatures after saturation than the WILM at each frequency. The change in the vertical
CLW distribution and vertical precipitation structure above the freezing level have brought
the HCM closer to the WILM. If the observations of the microphysical structure above the
freezing level had been different, then the HCM and the W ILM would not be similar.
However, it has been shown that the precipitation and microphysics are not factors above
the freezing level in tropical clouds over the dynamic range of each frequency at low rain
rates. The ICLW contents of both models are identical at low rain rates (0.03 g cm-2).
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54
275 (a) 13.8 GHz
WILMS km
HCM
£250
225
£
200
150
0.1
1
10
100
Rain Rate (mm/hr)
275 -(b) 18.7 G Hz
WILM 5 km
HCM
& 250
8 225
8 200
«
175
150
0.1
100
Rain Rate (mm/hr)
Figure 8. T-R relationships generated by the HCM and the WILM at (a)13.8 GHz;
(b) 18.7 GHz; (c) 21.3 GHz; (d) 37 GHz.
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55
275
_(c) 2 1 3 GHz
WILM 5 km
Brightness Temperature (K)
HCM
250
225
200
0.1
100
Rain rate (mm/hr)
275 -(d) 37 GHz
WILM 5 km
Brightness Temperature (K)
HCM
250
225
200
175
100
Rain Rate (mm/hr)
Figure 8. Continued.
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56
Therefore, the differences between the two models are only a result of the changes in the
DSD and reflectivity of the ocean surface. From Appendix C, it is shown that a change
from a specular to a Lambertian ocean surface only amounts to differences of < 5 K in the
brightness temperatures generated by the HCM. Therefore, TOGA-COARE observations at
low rain rates are useful to determine whether the new DSD is correct.
The combination larger drop sizes and Lambertian ocean surface in the WILM at low
rain rates produces a net increase in brightness temperatures of 5 - 20 K above the HCM
depending on the frequency.
At saturation, both models produce sim ilar brightness
tem peratures at each frequency.
The greater dynamic range and higher brightness
temperatures generated by the HCM at moderate and high rain rates are a result of changes
in the DSD, since CLW does not influence the upwelling brightness temperatures at rain
rates > 5 mm h_l. The reflectivity of the ocean surface is also not a factor at moderate and
high rain rates since the opacity of the atmosphere dominates the changes made at the
surface.
7. T h e H C M vs. ob servation s
a. 2220 - 2225 UTC 10 February 1993
Earlier, Fig. 4 was described as an area containing a region of very light rain
< 1 mm h '1 from 2220 - 2224 UTC. The HCM predicts values of 139, 168, 213, and
198 K at 13.8, 18.7, 21.3, and 37 GHz, respectively, for a path average rain rate of
0.25 mm I r 1. The observations show that 37-GHz brightness tem peratures averaged
200 K from 2220 - 2224 UTC. The similarity between the brightness tem peratures
generated by the HCM and observations indicates that the model handles CLW correctly at
low rain rates. The observations show an average of 140, 170, and 205 K at 13.8, 18.7,
and 21.3 GHz, respectively, from 2220 - 2224 UTC. The HCM agrees closely with the
observed brightness temperatures at each frequency for a rain rate of approxim ately
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57
0.25 mm h_1. The estimated path average rain rate between the surface and freezing level
from the HCM agrees well with the radar.
Cold brightness temperatures at low rain rates in TOGA-COARE were one of the
reasons a new DSD was created in the HCM. The effect of the new DSD is seen by
comparing the observations to the HCM and the W ILM. The HCM and W ILM have the
same ICLW content (0.03 g cm-2) at low rain rates. The microphysics in the HCM at low
rain rates makes it identical to the WILM above the freezing level. The combination of the
new DSD and the vertical precipitation structure in the HCM makes the cloud above the
freezing level almost transparent to microwave frequencies < 37 GHz. From the previous
section, the differences between the HCM and the W ILM at low rain rates are only a result
of changes in the reflectivity of the ocean surface and the DSD. Since the differences in the
upwelling brightness temperatures as a result of changes in the reflectivity of the ocean
surface are < 5 K, any large differences between the HCM and the WILM are a result of the
differences between the M -P DSD and the new DSD. At 37 GHz, the HCM and the WILM
differ by 20 K at rain rates < 1 mm h_1 (Fig. 8d). The brightness temperatures generated by
the WILM are the result of the increased opacity in the model atmosphere created by the
absorption of large drops produced by the M -P DSD. The W ILM overestim ates the
observed brightness temperatures by at least 15 K in this region if the ocean reflectivity is
taken into account. The new DSD brings the HCM closer to the observations.
b. 2145:14 - 2149:30 UTC 20 February 1993
Earlier, Fig. 5 was described as an MCS containing large areas of convective and
stratiform rain. The warm brightness temperatures of 275 K in the convective region from
2145:14 - 2149:30 UTC are easily reproduced by the HCM. The region of observed
brightness temperatures > 270 K at 13.8 GHz is indicated by the HCM as having a path
average rain rate between the surface and freezing level of > 35 mm h '1. Radar indicated a
similar rain rate with a slightly attenuated backscatter around 45 dBZ (35 mm h '1). The
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58
HCM indicates that 18.7 and 21.3 GHz should remain near 270 K, even at 35 mm I r 1.
This is verified by the observations. The 37-GHz channel became saturated as it passed
over the convective line. The HCM predicts a brightness temperature of around 250 K for a
35 mm h '1 rain rate. The brightness temperature predicted by the HCM is close to the
majority of observed 37-GHz brightness temperatures in this region. The 37-GHz channel
is not important for path averaged rain rate measurements in the convective line; however, it
does indicate whether the HCM handles the precipitation structure above the freezing level
correctly.
The observations provided important information about the effect of ice on the
upwelling brightness temperatures. In the HCM, the ice layer contains a high concentration
of small ice particles that decreases rapidly with height which makes the ice layer transparent
at frequencies < 37 GHz, even if it has a thickness of 7 km. An inspection of the observed
37-GHz brightness temperatures throughout Fig. 5 shows that this frequency only varied by
20 K over the entire tim e segment. This variation is remarkable considering that the
observations indicated heavy precipitation with no precipitation above the freezing level,
heavy rain with a significant amount of ice above the freezing level (at 2147:15 UTC), and
stratiform rain. The HCM predicts a range of 20 K at 37 GHz for rain rates of 5 50 mm h '1. At 13.8, 21.3, and 18.7 GHz, the effect of ice is even less noticeable. For
instance, within the convective line the observed brightness temperatures remained constant
even though the precipitation structure above the freezing level went from no ice to 5 km of
ice.
A stratiform precipitation region was seen after 2147:30 UTC. This area was
characterized by light to moderate rain. At 2148 UTC, the radar indicated a rain rate of
approxim ately 1.7 mm h’ 1 (24 dBZ). The HCM closely agrees with the radiom eter
brightness temperatures for the same rain rate. Radar observations indicated that rainfall
increased at 2149 UTC to around 8 mm h '1 (34 dBZ). Again, the brightness temperatures
generated by the HCM agree with the observations and are all within a factor of 2 of the
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59
radar estimated rain rate. A comparison between observed 13.8, 18.7, and 21.3-GHz
brightness temperatures in this area showed that the 13.8 GHz had the same sensitivity to
low rain rates as the two higher frequencies. This result was predicted by the HCM.
c. 2324 - 2328:24 UTC 22 February 1993
Figure 9 depicts a stratiform region with moderate rainfall observed from 2324 2328:24 UTC 22 February 1993. The stratiform region contained a well developed bright
band and 5 to 6 km of ice above the freezing level. Radar indicated an average near-surface
backscatter of approximately 36 dBZ (10 mm h '1). At this rain rate, the CLW in the HCM
increases rapidly as the model makes a transition from stratiform to convective rainfall.
However, Appendix C indicates that CLW does not influence the upwelling brightness
temperatures as much as the DSD at these rain rates.
In Fig. 9, the 21.3 and 37-GHz brightness temperatures remained nearly constant
from 2324 - 2328:24 UTC because both of these frequencies had low sensitivity at
10 mm h_1. The brightness temperatures at 13.8 and 18.7 GHz showed more variation
since they were the most sensitive at this rain rate. The observed brightness temperatures at
18.7 GHz ranged from 240 - 270 K with an average of 260 K. In the HCM, this range
equates to path averaged rain rates of 7.5 - 16 mm h '1 with an average of 12 mm h"1. The
13.8-GHz channel is the
most sensitive frequency to a rain rate of approximately
10 mm h"1. The observed brightness temperatures at 13.8 GHz varied from 180 - 240 K
which translate to a path averaged rain rate of 6 - 16 mm h '1 in the HCM. The HCM
predicted rain rates for 13.8 and 18.7 GHz are within a factor of 2 of the radar estimated
rain rate. The variability in the brightness temperatures at 13.8 GHz and the errors
associated with the radar estimated rain rate made it difficult to test the DSD in the HCM in
this region. If a M-P DSD is assumed, the brightness temperatures generated by the HCM
are approximately 10 K warmer at 13.8 GHz. The HCM using a M-P DSD would shift
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10
20
30
N adir Radar Backscatter
14.0-1
E
£
eo
'8
H
7.0«
N adir Radiometric Brightness Temperatures
300
ga 250
o>
cu
£ 200
m 150
23:24:00
23:25:00
23:26:00
Tim e (UTC)
23:27:00
Figure 9. As in Fig. 4, except from 2324 - 2328:24 UTC 22 February 1993.
23:28:00
40
50 dBZ
61
the path average rain rate to 4 - 13 mm h_1. Changing the DSD has led to a slightly lower
model estimated rain rate that is still within a factor of 2 of the radar.
d. 2131:30-2136 UTC 22 February 1993
Figure 10 shows an MCS observed from 2131:30 - 2136 UTC 22 February 1993.
The radar data revealed a classical MCS containing a leading convective line (2135 UTC)
and a trailing stratiform region (2132 - 2134:30 UTC). The radar became attenuated at
2135 UTC because of a large amount of precipitation-sized particles (probably containing
graupel) located near the freezing level. The convective line tilted from east to west (west is
located on the left hand side of the image).
Shear carried precipitation through the
convective line and into the stratiform region to the west.
The HCM assumption that the majority of low rain rate observations comes from
stratiform clouds is examined in this MCS. In Fig. 10, the num ber of low rain rate
stratiform observations exceeded the number of observations in growing convective cells
with the same rain rate by a ratio of > 100:1. The only region that contained growing
convective cells with light precipitation could only have occurred around 2135 UTC while
stratiform precipitation was prevalent from 2132-2134 UTC.
Since 37 GHz was saturated for most of the system, any quantitative measurement
of the rain rate was lost. However, it is worth mentioning that 37 GHz decreased to a
minimum of 220 K between 2134-2135 UTC when a considerable amount of precipitation
appeared above the freezing level.
The brightness tem peratures at 13.8, 18.7, and
21.3 GHz indicated that the rain rate was lower than in the convective line further east. The
high shear in the system displaced the greatest amount of precipitation above the freezing
level away from the heaviest surface rainfall. Microwave algorithms that base their rain rate
retrievals on the scattering of precipitation-sized particles above the freezing level would
misinterpret the surface rain rate in this system.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
10
20
30
40
SO dBZ
N adir Radar Backscatter
11.0-1
N adir Radiom etric Brightness Temperatures
300
<i>
250c3
<L>
ex
6<L> 2 0 0 H
cn
c<nU
C 150■M
•§>
•c
CQ 100 "
_
21:32:00
21:33:00
21:34:00
Tim e (UTC)
21:35:00
Figure 10. As in Fig. 4, except from 2131:30 - 2136 UTC 22 February 1993.
21:36:00
63
The stratiform region observed between 2132 - 2134:30 UTC was unusual because
it produced rain rates that were normally considered convective. Radar indicated an average
near-surface backscatter of 38 dBZ (13 mm h '1). However, Fig. 10 shows an obvious
bright band in this region. The 18.7 and 21.3-GHz frequencies were saturated in this
region, making them insensitive to changes in the rain rate below the freezing level. The
HCM interprets the brightness temperatures at 18.7 and 21.3 GHz as having a rain rate
betw een 15 - 20 mm h_1. Between 2133 - 2134:30 UTC, the 13.8-GHz brightness
temperatures ranged from 230 - 260 K which is interpreted by the HCM as a rain rate o f 12
- 23 mm h*1. The brightness temperatures at 13.8 GHz were stable enough between 2133 2133:50 UTC to test of the DSD used by the HCM. Unfortunately, the rain rate in this
region reduced the sensitivity to the DSD at 13.8 GHz to near the accuracy of the
radiometers (see Appendix C). The HCM using a M-P DSD still estimates a rain rate that is
slightly lower than the HCM using a new DSD but is still within a factor of 2 of the radar.
Radar attenuation in the convective region (around 2135 UTC) made it impossible to
estim ate surface rain rate. However, it was possible to estimate a path average rain rate
from the radiometers. The 13.8-GHz brightness temperatures rose to > 270 K while
brightness temperatures at 18.7 and 21.3 GHz decreased, probably due to scattering from
large precipitation-sized particles near the freezing level. Assuming 13.8 GHz was not
saturated, the HCM suggests a rain rate > 40 mm h '1 in this region. At this rain rate, 18.7
and 21.3 GHz would remain above 265 K in the HCM (Fig. 8). The observations show
that these two frequencies do not fall below 260 K. Assuming the HCM handles the
precipitation structure above the freezing level correctly, lower brightness temperatures at
18.7 and 21.3 GHz in the convective line were not a result of scattering by ice above the
freezing level but a result of the scattering by large rain drops below the freezing level.
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64
CHAPTER IX
CONCLUSION
An improved microwave radiative transfer model was developed to sim ulate
observed brightness temperatures from tropical oceanic clouds with rain. The HCM uses a
one-dimensional cloud model integrated along the vertical axis. The simplicity of the cloud
model in the HCM allowed the alteration of relevant thermodynamic and microphysical
profiles according to observations. It was shown that a plane-parallel radiative transfer
model based on fundamental physics coupled with a one-dimensional cloud model can
produce brightness tem peratures that correspond closely to the observations if the
microphysics and reflectivity of the ocean surface are accurately described.
Initially, the CCM was developed using microphysical profiles described in previous
studies. The T-R relationships produced by the CCM were considerably different than the
WILM. The CLW and vertical precipitation structure in the CCM resulted in anomalously
high upwelling brightness temperatures at low rain rates when compared to the W ILM and
observations from TOGA-COARE. The DSD and vertical precipitation structure in the
CCM contributed to upwelling brightness temperatures that were too low at moderate and
high rain rates. Even though the CCM contained a CLW and vertical precipitation structure
that was consistent with previous studies, the model did not produce brightness
temperatures that were close to the observations.
O bservations from previous field studies had shown that CLW and vertical
backscatter decreased rapidly above the freezing level for all rain rates The amount of CLW
was found to be near zero in stratiform areas from modeling and observational studies. The
rapid conversion of liquid water into ice and the production of numerous small ice crystals
led to steep backscatter lapse rates above the freezing level. Studies found that a linear lapse
rate for the logarithm of the backscatter of ice was common for tropical oceanic convection.
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65
A linear decrease in the logarithm of the backscatter of ice is the same as an inverse
exponential decrease in the snowfall above the freezing level. Observational and theoretical
work has shown that the M -P DSD does not describe the DSD in tropical clouds. The M-P
DSD continually overestimates the number of large drops and underestimates the number of
small drops. A new DSD was created to increase the number of small drops and decrease
the number of large drops.
Radar data from TCM -90 and TOGA-COARE show that the ocean surface is
specular. If a specular surface is assumed, the resulting brightness temperatures would be
approximately 5 K lower at low and moderate rain rates even at incidence angles near nadir.
A Lambertian ocean used by the CCM and the WILM assumes that the upwelling brightness
temperatures are a result of a contribution from downwelling radiation from many angles. A
specular ocean acts like a flat mirror so only downwelling radiation at one angle contributes
to the upwelling radiation; therefore, the upwelling brightness temperatures are colder than
those generated by a Lambertian ocean surface. The HCM was created to incorporate the
changes to the CLW, vertical precipitation structure, DSD, and reflectivity of the ocean
surface.
The HCM assumes that low rain rates are produced by stratiform clouds. If the
HCM assumes that the microphysics present in the cloud at low rain rates is associated with
stratiform clouds and that high rain rates originate by convective clouds, then the model
represents a cloud evolution over the dynamic range of each frequency.
The T-R
relationships generated by the HCM were much closer to the W ILM than the CCM.
However, there were some noticeable differences between all three models. The main factor
that contributes to the differences between the HCM and the CCM is the characteristics of
the cloud above the freezing level. The changes to the CLW, vertical precipitation structure,
and DSD in the HCM made the ice layer much more transparent at each frequency than in
the CCM. This brought the HCM closer to the WILM in this respect. However, the
additional CLW in the WILM at low rain rates resulted in warmer brightness temperatures
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66
than in the HCM. The CCM had much warmer upwelling brightness temperatures than the
HCM at low rain rates because the CCM contained a factor of 10 more ICLW than the
HCM. At moderate and high rain rates, the M-P DSD and linear rain rate structure above
the freezing level in the CCM caused saturation and scattering occur much earlier than in the
HCM .
Next, the HCM was compared to observations from TOGA-COARE. The similarity
between the HCM and the observations for all rain rates showed that the microphysics
above the freezing level had no effect at 13.8, 18.7, and 21.3 GHz. The microphysics
affected 37 GHz at high rain rates but well beyond the dynamic range of the frequency.
The brightness tem peratures generated by the HCM at 37 GHz were close to the
observations at low rain rates. This indicates that the model handles the CLW correctly in
stratiform regions. The warm brightness temperatures observed in convection at moderate
and high rain rates was also accurately simulated by the HCM. The warm upwelling
brightness tem peratures generated by the HCM at 13.8, 18.7, 21.3, and 37 GHz were a
result of the changes to the DSD and vertical precipitation structure above the freezing level.
The new DSD in the HCM was verified by the observations at low rain rates.
The
brightness temperature differences of 15 K between the HCM and the WILM at low rain
rates were mainly a result of the changes in the DSD. Since the HCM was similar to the
observations, the new DSD appears to be a better approximation than the M-P DSD.
The HCM consistently produced rain rates that were within a factor of 2 of the radar
estimated rain rate. However, backscatter from radar is unreliable because it relies on the
sixth moment of the drop radius as well as having as having calibration difficulties. This
uncertainty is carried over to the Z-R relationship that estimates a surface rainfall from radar
backscatter. Therefore, radar cannot be considered a reliable method for determining the
rain rate "ground truth." The primary reason that the radar and radiometer data correspond
closely with each other was due to the way the Z-R relationship was determ ined.
Observational and theoretical work combined to produce a Z-R relationship that originated
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67
from a new DSD. Perhaps the DSD has acted as a correction factor applied to the radar.
New m ethods for determining rainfall, such as the development of a new DSD from
microwave and microphysical observations, may be necessary to produce "ground truth" for
TRMM.
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68
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, A. T. C. Chang, M. S. V. Rao, E. B. Rodgers, and J. S. Theon, 1977: A satellite
technique for quantitatively mapping rainfall rates over the ocean. J. Appl. Meteor.,
16, 551-560.
, ____ , J. L. King, and E. B. Rodgers, R. A. Nieman, B. M. Krupp, A. S. Milman,
J. S. Stratigos, and H. Siddalingaiah, 1982: Microwave radiometric observations
near 19.35, 92 and 183 GHz of precipitation in tropical storm Cora. J. Appl.
M eteor., 21, 1137-1145.
, 1986: Some comments on passive microwave measurements of rain. Bull. Amer.
Meteor. Soc., 67, 1226-1232.
, A. T. C. Chang, and L. S. Chiu, 1991: Retrieval of monthly rainfall indices from
microwave radiometric measurements using probability distribution functions. J.
Atmos. Oceanic Technol., 8, 118-136.
W illiams, E. R., S. A. Rutledge, S. G. Geotis, N. Renno, E. Rasmussen, and T.
Rickenbach, 1992: Radar and electrical study of tropical "hot towers". J. Atmos.
Sci., 49, 1386-1395.
Willis, P. T., 1984: Functional fits to some observed drop size distributions and
parameterization of rain. J. Atmos. Sci., 41, 1648-1661.
, and P. Tattelman, 1989: Drop-size distributions associated with intense rainfall. J.
Appl. M eteor., 28, 3-15.
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72
Wu, R., and J. A. Weinman, 1984: Microwave radiances from precipitating clouds
containing aspherical ice, combined phase, and liquid hydrometeors. J. Geophys.
Res., 89, 7170-7178.
Zipser, E. J., and M. A. LeMone, 1980: Cumulonimbus vertical velocity events in
GATE. Part II: Synthesis and model core structure. J. Atmos. Sci., 37,
2458-2469.
, and K. R. Lutz, 1994: The vertical profile of radar reflectivity of convective
cells: A strong indicator of storm intensity and lightning probability? Mon. Wea.
R e v .,122, 1751-1759.
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73
APPENDIX A
CLOUD MODEL EQUATIONS
The following section contains the primary thermodynamic and microphysical
equations used in the CCM.
The equation for a saturated adiabatic process with entrainment given in terms of
entropy, S, is
s = (mdcPj + m,cw) l n^
l nPd + ^ j r + y - ( 7’- T')m d + j { r w- r)md + const (a. 1)
where
m j. mass of dry air, kg;
m v: mass of water vapor, kg;
mt: total mass of water vapor and condensed water, kg;
cw: specific heat capacity of condensed water, J kg_1K**;
Cpj. specific heat capacity of dry air, J kg^K r1;
Pd'- pressure, kg n r 1 s'2;
rw: mixing ratio of the cloud, kg k g '1;
r: mixing ratio of the environment, kg k g '1;
lv: latent heat or vaporization, J k g '1;
T: temperature of cloud, K;
T': temperature of environment, K;
Rd'. gas constant for dry air, J k g ^ K '1;
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74
Equation (a .l) is sim ilar in form to Equation (80) in Chapter 7 of Iribame and Godson
(1981) except that the forth and fifth terms on the right hand side have been added for the
effect of entrainment. It can be shown that Equation (a .l) yields
-fiU T -T 'l + i q r . - r ]
C_j
pd
1
(a. 2)
where
cpv: specific heat capacity of water vapor, J kg^K "1;
e: vapor pressure, kg n r 1 s-2;
ew: saturation vapor pressure, kg n r 1 s’2;
g: gravity, m s*2;
E: entrainment, (p_1;
Equation (a.2) is sim ilar in form to Equation (26) in Chapter 9 of Iribame and Godson
(1981). Equation (a.2) is the saturated lapse rate of a parcel affected by entrainment.
Equation (a.2) is similar to a pseudo-adiabatic lapse rate since the terms related to condensed
water have been removed. When a layer in the model is assumed to be totally made up of
ice, the appropriate variable substitutions are made to the vapor pressures and mixing ratios.
The entrainment, E, (Wallace and Hobbs 1977) is given by
where m is the mass, z is the height, and (p is the radius of the cloud. The 0.3 value
in the numerator is a typical value used for entrainment.
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75
The saturation mixing ratio is defined as
rw = ~ ^ ~
(a. 4)
P~ew
where £ = R ^ R V = 0.622 and R v is the gas constant for moist air.
Therefore, the change in the saturated mixing ratio and the change in the saturation
mixing ratio with height are
drw =
p -e w
dew -
£e” dp
( p ~ e w)
(a. 5)
and
drw _^elvrw + r2J v dT
dz
RdT 2
rw
dz
dp
p - e w dz
The mixing ratio of the condensate, rt, is the amount of liquid water per kilogram of
air in kg/kg. The mixing ratio of the condensate is zero at cloud base. The change in the
liquid mixing ratio with height inside the cloud is given by
Equation (a.7) is similar in form to Equation 4.23 in Rogers and Yau (1989).
Buoyancy is calculated by
B=C
T -T
.
(a. 8)
Equation (a.8) is similar in form to Equation 4.15 in Rogers and Yau (1989). A damping
factor, C, has been added to account for the lower updraft velocities in oceanic convection.
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76
The change in vertical velocity, w, with height is given by
*L = g *+iLi _ £w
dz
w
(«.9)
w
This equation is similar in form to Equation 4.22 in Rogers and Yau (1989).
The rain rate is computed by
An
R = — \N((p)(p3V((p)d(p
(a. 10)
5 Jo
where R is the true rain rate in mm h '1, V((p) is the fall velocity as a function of radius, and
N(q>) is the drop-size distribution as a function of radius. The vertical rain rate structure can
be specified at any level in the model.
The fall velocity, v, of precipitation-sized particles is calculated using
0.4
1.147
Po
V(<p) = 943 \ - exp\ _
1 0.177J
(a. 11)
which is a modified equation from Foote and duToit (1969) where p 0 and p are the sea level
and layer air densities, respectively, and the radius, <j0, is in centimeters.
The inverse-exponential M-P DSD used in the CCM is given by
N((p) = N0e-Av
(a. 12)
where
N0 = 0.16cm-4
*
a
81
=y °^
1
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77
The variable X is a rain parameter used to generate a true rain rate, R, in Equation (a. 10).
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78
APPENDIX B
THE RADIATIVE TRANSFER MODEL
W ilheit et al. (1977) gives the equation of radiative transfer for a plane-parallel
atmosphere with axisymmetric scattering using the Rayleigh-Jeans approximation as
d^
dz
y
eJ B(0 ) = yJOI, \ T B( e j P ( d , e j s i n d M + y ^ J z )
Jo
(b. i)
where
Yscat: scattering coefficient, km-1;
Yobs', absorption coefficient, km-1;
Yext- Tabs + TscaU k m '1;
T g. brightness temperature, K;
Tiayer\ thermodynamic temperature, K;
z: distance along path, km;
P (6 ,6 S): scattering phase function normalized to unity over the solid angle
Equation (b. 1) can rewritten as
^
= (Tlayet ~ T b( 0 ) \ 1 ~ e - ' “) + (Tscal - TB(d))(l - e-'*)
(b. 2)
where
u = --------cos( 6)
Tsca, = \ T B(e)P(G,es)dQ
Jo
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79
The first term on the right hand side of (b.2) is the contribution of radiation from absorption
to the brightness temperature in the z direction. The second term on the right hand side of
{b.2) is the contribution to the brightness temperature in the z direction from scattering.
Tscat is the source function that represents the amount of radiation scattered into the field of
view. Tscat and Tiayer both represent sources of energy directed into the z direction while
each is offset by the loss term, Tg, that represents energy lost by absorption or scattering.
If only absorption is present in the atmosphere then Equation (b.2) can be directly
integrated.
com plicated.
How ever, when scattering is introduced, the problem becom es more
From Equation (b.2), Tscat requires knowledge about the radiation
approaching from all angles. The effect of scattering is solved by iterating (b.2) using the
scattered radiation from the previous iteration. The convergence of brightness temperatures
at the top of the atmosphere relies heavily on the accuracy of the first guess. Therefore,
radiative transfer calculations at low rain rates require fewer iterations than at high rain rates
because the effect of scattering is less prominent at low rain rates where the first guess is
closer to convergence. The model atmosphere is divided into 200 layers at 100 m intervals.
Integration of the equation of radiative transfer begins at the top of the atmosphere starting
with the cosmic background (2.7 K) and works its way down to and off the surface and
then returns. The program iterates until the brightness temperatures at the top of the
atmosphere converge to < 0.001 K.
The ocean surface has a low emissivity compared to land. However, the dielectric
constant, used to calculate the horizontal and vertical reflectivity of the ocean surface, varies
as the wavelength, temperature, viewing angle, and salinity change. The ocean surface can
be assumed to be Lambertian, specular, or a combination of both. W ind speed is not
considered a factor in the model. The index of refraction for each layer in the model
atmosphere and the ocean surface is found using data given in Lane and Saxton (1952).
The Fresnel relations are used to find the horizontal and vertical polarizations of radiation
leaving the ocean surface. They are defined by Blue (1980) as
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80
(n2 - sin2(0 j)'/2 - n 2 cos( 9)
K(6) =
(n - s i n (6))
+ n cos(d)
(b. 3)
{n2 - sin2( Q)^n - cos(0)
Rh O ) =
(n2 - sin2( d))'/2 + cos( 9)
where
n: the complex index of refraction
The absorption of microwave radiation is dominated by oxygen, water vapor, and
CLW. Figure 11 shows the atmospheric transmittance as a function of frequency. It is seen
that an oxygen absorption band is centered at 60 GHz. The frequencies dealt with in this
study are still affected by oxygen absorption. Oxygen contributes only a minor amount
(< 10 K) to the total brightness temperature (Wilheit et al. 1977). Oxygen is computed
using an updated version of the Rosenkranz model similar to the one discussed in
Rosenkranz (1975).
The water vapor spectrum contains an absorption line at 22.2 GHz (Fig. 11).
Although relatively weak compared to the 183 GHz water vapor line, the 22.2 GHz band
affects all of the frequencies discussed in this paper. The 18.7 and 21.3-GHz channels are
affected the most by this line. The program calculates water vapor absorption from a model
described by Liebe (1985).
CLW absorption is calculated using Rayleigh theory. From Gunn and East (1954),
the absorption coefficient can be written as
Yabs = Ycxi = 0- 063 • CLW -v-Im
7 1 -1
n2 + 2
(b. 4)
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81
0.9
T o ta l
TRANSMITTANCE
0.8
H2 0
0.7
0.6
0.5
0.4
0.3
0.2
20
40
F R E Q U E N C Y ( GHz)
Figure 11. Transmittance as a function of frequency (from Liou 1980).
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82
where v is the frequency in GHz. The absorption cross section is proportional to the
volume of the droplet. Equation (b.4) results in 37 GHz being a factor of 4 more sensitive
to CLW than 18.7 GHz. The frequency factor in Equation (b.4) and frequency dependence
on the dielectric constant combine to make the CLW effect proportional to the square of the
frequency.
Gunn and East (1954) also specify the extinction and scattering cross section of
liquid water drops or ice spheres (radii > 100 |im ) as
(b. 5)
where an and bn are the magnetic and electric 2n pole coefficients. M ie theory is more
mathematically involved since the magnetic dipole, an, and higher mutlipole moments cannot
be neglected as is the case in Rayleigh theory. The model calculates the water and ice
extinction and scattering cross-sections for each layer containing precipitation-sized
particles. The amount of scattering or absorption in a model layer depends on the DSD.
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83
APPENDIX C
HCM SENSITIVITY
The simplicity of the HCM allows the sensitivity of the model to be tested by altering
the thermodynamics and microphysics. Five sensitivity tests were performed on the surface
temperature, RH profile, CLW content, DSD, and surface reflectivity at 4.5° from nadir.
Changes in the above quantities do not affect the vertical precipitation profile above the
freezing level. Table 6 lists the amount of sensitivity (in absolute AT) in the HCM for each
frequency.
Due to the inaccuracies of the radiom eters used in TOGA-COARE, any
brightness temperature differences < 3 K are not meaningful.
The surface temperature and RH profile were altered to test the sensitivity of the
model. Table 6 indicates that changing the surface temperature has little effect on the HCM.
The emissivity of the ocean varies inversely with its surface temperature. This results in a
brightness tem perature em itted from the surface that is nearly independent of the
thermodynamic temperature at 19 GHz. The changes in RH profile produce measurable
effects at frequencies > 13.8 GHz for clear sky conditions. However, as soon as any
appreciable cloud containing rain is added to the model, the RH profile becomes irrelevant.
The formation of clouds assures that the atmosphere is near saturation, regardless of the
original RH profile. Below cloud base, the altered RH profile produces a small change in
the upwelling brightness temperatures. Changing the temperature profile (not shown) does
not affect the brightness temperatures as much as modifying the RH profile. Overall, the
HCM is not sensitive to the thermodynamics of the atmosphere.
Two microphysical quantities were tested in the HCM. Appendix B shows that the
effect of CLW is proportional to the square of the frequency; therefore, 37 GHz is
approximately a factor of 4 more sensitive to CLW than 18.7 GHz. The CLW was lowered
by 0.1 g n r 3 at each rain rate. At 13.8, 18.7, and 21.3 GHz, the biggest changes occur at
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84
Table 6. Changes in brightness temperature as a result of altering the surface
temperature, RH profile, CLW content, DSD, and surface reflectivity
at each frequency. Numbers represent the absolute change in brightness
temperature.
Rain Rate (mm hr1)
3
5
7.5
0.25
1
1 K sfcdecr: 0.4
0.4
0.3
0.3
0.3
20% RH deer: 2.0
0.0
0.1
0.2
0.1 g n r 3 deer: 0.0
3.0
2.9
DSD change: 0.0
0.5
reflect, change: 1.3
18.7 GHz
13.8 GHz
10
15
20
25
50
0.3
0.2
0.2
0.1
0.1
0.0
0.1
1.1
1.2
0.5
1.1
0.9
0.1
2.6
2.4
1.9
1.5
0.9
0.5
0.3
0.0
0.1
3.2
6.4
8.8
9.4
8.0
5.4
2.8
2.2
2.2
2.7
3.9
4.8
5.3
5.4
4.9
3.5
2.5
0.4
0.25
1
Rain Rate (mm hr1)
3
5
7.5
10
15
20
25
50
1 K sfc deer: 0.3
0.3
0.3
0.3
0.2
0.2
0.1
0.1
0.1
0.0
0.0
20% RH deer: 7.0
0.3
0.5
0.5
0.6
1.2
1.1
0.5
0.3
0.1
0.1
0.1 g n r 3 deer: 0.0
4.1
3.9
3.1
2.3
1.5
0.9
0.3
0.1
0.0
0.0
DSD change: 0.0
0.6
0.1
2.7
4.0
3.3
1.7
1.3
3.2
4.0
4.6
reflect, change: 3.5
4.5
4.8
5.4
5.2
4.4
3.3
1.7
0.9
0.5
0.2
0.25
1
Rain Rate (mm h*1)
3
5
7.5
10
15
20
25
50
0.2
0.2
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
20% RH deer: 13.2 0.4
0.8
0.8
0.8
0.8
0.6
0.5
0.1
0.0
0.2
21.3 GHz
0
0
0
1 K sfc deer: 0.2
0.1 g m -3 deer: 0.0
3.0
2.7
2.0
1.3
0.8
0.4
0.1
0.0
0.0
0.1
DSD change: 0.0
0.4
0.0
1.1
1.1
0.2
0.6
3.5
4.4
4.6
5.1
reflect, change: 5.2
5.4
5.2
4.6
3.6
2.6
1.6
0.6
0.3
0.2
0.3
0.25
1
Rain Rate (mm hr1)
3
5
7.5
10
15
20
25
50
1 K sfc deer: 0.0
0.0
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
20% RH deer: 5.1
0.2
0.2
0.3
0.3
0.0
0.1
0.3
0.2
0.2
0.7
0.1 g n r 3 deer: 0.0
11.6
8.1
2.8
0.9
0.4
0.3
0.2
0.2
0.2
0.2
DSD change: 0.0
1.6
2.4
4.3
5.4
6.0
5.9
5.8
5.9
6.0
7.3
reflect, change: 3.3
4.8
4.7
2.5
0.9
0.4
0.3
0.3
0.5
0.7
0.8
37 GHz
0
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85
rain rates < 5 mm h_1. The change in the brightness temperatures due to CLW is equivalent
to the radiometer calibration uncertainty (3 K) at these frequencies. At 37 GHz, the change
in CLW is more noticeable at rain rates < 3 mm h*1. The CLW effect virtually disappears by
5 mm h '1 at each frequency. However, CLW in the HCM is constrained to near zero
because of the stratiform-based assumption at low rain rates. Since observations indicate
that stratiform clouds always contain small amounts of CLW, then CLW is nearly constant
at low rain rates. Observations have made the HCM insensitive to CLW for all rain rates.
The second microphysical parameter considered was the DSD. The changes in
brightness temperatures are a result of the differences between the new DSD used in the
HCM and the M-P DSD. At 18.7 and 21.3 GHz, the sensitivity of the HCM to the DSD is
small at low rain rates but the differences increase as the rain rate increases. W ilheit et at.
(1977) found that the brightness temperatures and rain rate had similar moments to the DSD.
This indicated that the brightness temperature and rain rate moments were both dependent on
the DSD but neither were greatly dependent on the characteristics of the DSD. At 18.7 and
21.3 GHz, the brightness temperature and rain rate have similar dependence on the DSD so
they are relatively insensitive to the changes in the DSD. At moderate and high rain rates,
the DSD influences the upwelling brightness temperatures as a result of scattering by large
precipitation particles above and below the freezing level.
At 13.8 GHz, the brightness temperature and rain rate moments of the DSD are not
as similar as at 19 GHz. Therefore, 13.8 GHz is affected the most by the changes in the
DSD below the freezing level. On the other hand, 37 GHz is affected by changes in the
DSD above the freezing level. Since the backscatter lapse rate remains the same above the
freezing level, the differences in the brightness temperatures are a result of changes in
scattering above the freezing level. Larger precipitation-sized particles generated by the M-P
DSD above the freezing level produce lower brightness temperatures in moderate and heavy
rain at 37 GHz.
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86
Changing the reflectivity of the ocean from a Lambertian to a specular surface results
in brightness temperature differences that are generally < 5 K at each frequency. The
surface reflectivity has the greatest effect at low and moderate rain rates where the opacity of
the atmosphere is low. Therefore, the reflectivity of the ocean surface influences the lower
frequencies over a greater range of rain rates than at the higher frequencies. A specular
ocean surface produces lower brightness temperatures than a Lambertian surface because
downwelling radiation from only one incidence angle contributes to the upwelling radiation.
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87
V ITA
Jeffrey Ransdell Tesmer was bom in Seattle, Washington on August 30,1965. He
graduated from Los Alamos High School in Los Alamos, New M exico in 1984. He
enrolled at Texas Tech University in September 1984 and received his Bachelor of Science
degree in Geophysics in May 1988. He graduated with a M aster of Science degree in
Atmospheric Science at Texas Tech University in December 1990. His thesis dealt with the
evolution of a Mesoscale Convective System that was observed over Kansas and Oklahoma
in June 1985. He entered the doctoral program in Meteorology at Texas A&M University in
September 1990. He became part of the Microwave Remote Sensing Group and centered
his interest on microwave radiative transfer in the atmosphere.
Correspondence during transitional periods may be directed to: Mr. & Mrs. Joseph
R. Tesmer, 408 Rover Blvd., Los Alamos, NM 87544.
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