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Use of TRMM precipitation radar for calibrating overland passive microwave rain retrieval

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Use o f TRMM Precipitation Radar for Calibrating Overland Passive
Microwave Rain Retrieval
Tufa Dinku, Ph. D.
U niversity o f Connecticut, 2005
The precipitation radar (PR) on board the TRM M satellite provides definitive
m easurem ents o f the 3D structure o f precipitation. However, its narrow sw ath (215km )
lim its the use o f this dataset. On the other hand, TM I and SSM/I provide w ider swath
coverage (760 km for TM I and 1400 km SSM/I) and higher sam pling frequency. Thus,
com bining the higher accuracy o f PR w ith the better spatial coverage and sam pling
frequency o f TM I and SSM /I w ould b e o f great value in a num ber o f applications in
m eteorology, hydrology, and w ater resources. One approach to do this is using PR to
calibrate the passive m icrowaves (PM ) data. Relationship betw een PR and PM m ay vary
from one rainfall regim e to another and from one season to another w ithin the same
regim e.
The goal o f this research is to develop a PR-calibrated TM I (PR-TM I) overland
rain retrieval algorithm , investigate its regional and seasonal differences, and explore
possibilities o f extending the PR-TM I algorithm to SSM /I calibration. A pplication o f the
PR-TM I algorithm to SSM/I is particularly im portant because SSM /I has long historical
data going back to 1987 and better sampling due to the m ore frequent overpasses and
w ider swath.
The PR-TM I algorithm developed here consists o f rain screening,
convective/stratiform rain classification, and non-linear (linear) regressions for stratiform
(convective) rain retrievals.
Four geographic regions from Central A frica (AFC),
A m azon (AM Z), continental US (USA), and South A sia (SAS) are selected for these
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Tufa Dinku- U niversity o f Connecticut, 2005
investigations.
The algorithm developed here outperform ed the TRM M -2A 12 V6
product w ith significant decrease in bo th random and systematic errors.
Regional
calibration perform s slightly better than the global calibration. However, the differences
are not significant particularly for AFC, AM Z and USA regions.
Com parisons o f
individual season calibrations w ith the annual calibration did not show significant
differences either. However, it w as observed that the perform ance o f the PM algorithm
varies am ong the different seasons. Com parison o f the current SSM /I rain estim ates w ith
that o f GPROF has shown that the current algorithm perform s better w ith very significant
reduction in bias and random errors.
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Use o f TRMM Precipitation Radar for Calibrating Overland Passive
Microwave Rain Retrieval
T ufa Dinku
B.Sc., Addis A baba University, 1986
M .Sc., U niversity o f Connecticut, 2001
A Dissertation
Subm itted in Partial fulfillm ent o f the
Requirements for the D egree o f
D octor o f Philosophy
at the
U niversity o f Connecticut
2005
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UMI Number: 3187723
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APROVAL PAGE
D octor o f Philosophy Dissertation
Use of TRMM Precipitation Radar for Calibrating Overland Passive
Microwave Rain Retrieval
Presented by
Tufa Dinku, B.Sc., M.Sc.
M ajor A dvisor
Immanouil N. Anagnostou
A ssociate A dvisor
Guiling W ang
Associate A dvisor
Robert F. Adler
U niversity o f Connecticut
2005
ii
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A CKN O W LED G EM EN T
First I w ould like to thank m y m ajor advisor, and dear friend, Dr. E. N. A nagnostou. His
support and guidance m ade everything possible. I cam e to U conn because o f his
extraordinary efforts. His support at every step o f m y academic life m ade things m uch
easier. A nd he m ade m y Ph.D. research very enjoyable b y giving m e valuable guidance
and great freedom to explore things. I thank Dr. R. F. A dler from N ational A eronautic
and Space A dm inistration (NASA) at Goddard Space Flight Center for consenting to b e
on m y com m ittee despite his busy schedule, and for traveling all the w ay from Greenbelt
(M D) to U conn for m y general exam and defense. I also thank Dr. G. W ang for being on
m y com m ittee and her valuable contributions. I am grateful to N ASA’s G lobal Water and
Energy Cycle program (N A G 5-11527) for supporting this research. Special thanks go to
Dr. Jeffrey M cC ollum o f N ational Oceanic and Atmospheric A dm inistration-N ational
Satellite, Data, and Inform ation Service who provided m e w ith the latest version o f
TRM M precipitation fields before the data was officially available.
I am also grateful to
N A SA /D A A C and N ASA /G HRC for providing m e w ith TRM M and SSM /I data.
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DEDICATION PAGE
To
Helina
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TABLE OF CONTENTS
I. Introduction.................................................................................................................................. 1
Overland Passive Microwave Rain Retrieval..............................................................................1
Using TRMM-PR for calibrating PM rain retrieval...................................................................4
Problem Statement........................................................................................................................7
Objectives.......................................................................................................................................8
Dissertation outline........................................................................................................................9
II. Regional differences in PR-TM I calibration for overland rainfall re trie v a l.............11
A bstract........................................................................................................................................11
Introduction................................................................................................................................. 12
Study regions and d a ta ............................................................................................................... 17
Rain retrieval methodology........................................................................................................18
Results and discussion................................................................................................................ 23
Conclusions and future studies.................................................................................................. 29
References................................
32
III. Seasonal Differences in PR-TM I calibration for Overland Rain R etriev al........... 59
A bstract........................................................................................................................................59
Introduction................................................................................................................................. 60
Study regions and d ata............................................................................................................... 63
Algorithm description................................................................................................................. 64
Seasonal calibration.................................................................................................................... 65
D iscussion................................................................................................................................... 70
Conclusions................................................................................................................................. 73
References................................................................................................................................... 75
IV. TRM M Calibration o f SSM /I A lgorithm for Overland Rainfall E stim ation.......... 90
A bstract........................................................................................................................................90
Introduction................................................................................................................................. 91
Study regions and d ata............................................................................................................... 93
Algorithm Description................................................................................................................ 95
Results and discussion................................................................................................................ 98
Summary and Conclusions....................................................................................................... 103
References................................................................................................................................. 105
V. Summary, conclusions and future research directions.................................................123
Summary....................................................................................................................................123
Conclusions............................................................................................................................... 125
Further research areas............................................................................................................... 127
VI. B ib lio g rap h y ........................................................................................................................128
V
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List o f figures
Figure 2.1:
The study region.
Figure 2.2:
Rain contours as a function o f 37 and 85 GHz brightness tem peratures
(T37 and T85) for the USA region.
Figure 2.3:
A FC region brightness tem perature (T37 and T85) versus rain rate values
o f com m on exceedance probabilities (quantiles) overlaid b y a fitted
regression line. The upper panel corresponds to 2A23 C/S classifications,
w hile the m iddle and low er panels correspond to the algorithm C/S
classification. The left and right panels are for stratiform and convective
rain type, respectively.
Figure 2.4:
A M Z region brightness tem perature (T37) versus rain rate values o f
com m on
exceedance probabilities
(quantiles)
overlaid
by
a
fitted
regression line. The convective/stratiform classification is based on our
algorithm.
Figure 2.5:
Same as in Fig.2. 4, but for the U SA region.
Figure 2.6:
Sam e as in Fig.2. 3, b u t for the SAS region.
Figure 2.7:
(a) C ontour plots o f HSS as function o f rain threshold, for the A FC region.
Top panels are for ALG1 (regional calibration) and A LG 2 (global
calibration), while the low er panels are for TM I-2A12 V.5 and V.6;
(b) Plot o f HSS values along the diagonal as function o f rain threshold;
(c) Relative frequency [%] o f the different TM I rain rate retrievals and PR
rain rates.
Figure 2.8:
Sam e as in Fig.2.7, b u t for AMZ.
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Figure 2.9:
Same as in Fig.2.7, but for USA.
Figure 2.10:
Same as in Fig.2.7, but for SAS.
Figure 2.11:
Sample cases o f coincident instantaneous rain rate m aps o f ALG1 (left
panel), PR (m iddle panel), and 2A12 V6 (right panel). The red lines show
the PR sw ath on the TM I rain rate maps.
Figure 3.1:
The study region.
Figure 3.2:
Brightness tem perature (T37) versus rain rate values o f com m on
exceedance probabilities (quantiles) overlaid b y a fitted regression line.
Top, m iddle and bottom panels are for AFC, SAS and A M Z regions,
respectively. Left panels are for stratiform rain and right panels for
convective rain type
Figure 3.3:
2D-HSS plots com paring seasonal and all-season calibrations for the A FC
region. The left panels are for individual season calibration, w hile right
panels are for the all-season calibration.
Figure 3.4:
1D-HSS plots for the AFC region. Panels (a), (b), and (c) com pare
seasonal vs. all-season calibration. Panel (d) compares using the sum m er
season’s ow n calibration vs. using calibration param eters from the other
two for sum m er season data.
Figure 3.5:
Sam e as Fig.3.2, but for SAS region.
Figure 3.6:
Same as Fig.3.3, b u t for SAS region.
Figure 3.7:
Sam e as Fig.3.2, but for AM Z region.
Figure 3.8:
Same as Fig.3.3, b u t for AM Z region
Figure 4.1:
The study region.
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Figure 4.2:
C om parison o f original TM I, rem apped TMI (Rem ap) and actual SSM I
brightness tem peratures at 85 GHz and 19 GHz channels. The histogram s
are com puted based on m atched Rem apped and SSM/I pixels.
Figure 4.3:
Brightness tem perature (T37) versus rain rate
values
o f com m on
exceedance probabilities (quantiles) overlaid b y a fitted regression
line.
The left and right panels are for stratiform and convective rain type,
respectively.
Figure 4.4:
HSS plots as function o f rain threshold. The bottom right panel shows
HSS values along the diagonal as function o f rain threshold.
Figure 4.5:
Cumulative density function o f rain rates estim ated from PR, TM I and
SSM/I.
Figure 4.6:
Sam ple cases o f coincident instantaneous rain rate m aps o f PR, TM I (PRTM I algorithm) and SSM/I (ALG10 and GPROF6 algorithm s) estimates.
Lines show the PR swath.
Figure 4.7:
Spatial error correlation o f A LG 10 and GPROF6 SSM /I estimates. Error
is defined as the difference o f SSM/I versus PR estimates.
Figure 4.8:
Same as Fig.44, for AM Z region
Figure 4.9:
Same as Fig.45, for AM Z region
Figure 4.10:
HSS and CDF plots as function o f rain threshold for the SAS region. The
bottom left panel shows HSS values along the diagonal, and bottom left
panel is the CDF.
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List o f Tables
Table 2.1: C alibration and validation data statistics for the four regions. The total data
used (N-total), percent o f pixels w ith rain (% Rain) and the proportion o f
convective rainfall (% Conv.) are shown.
Table 2.2: Correlation coefficients among the three predictors: 37G Hz (T37), 85GHz
(T85) and their product (T37*T85) determ ined w ith data from the A FC region.
Results are shown for C/S classifications perform ed using the herein described
algorithm and the C/S products from PR-2A23
Table 2.3: Linear correlation coefficients betw een PR rain rate and brightness
tem peratures at 37GHz (T37), 85GHz(T85) and their product (T37*T85)
determ ined w ith data from the A FC region. The m ulti-param eter correlation
coefficient betw een rain rate and the three predictors is also shown.
Table 2.4: As in Table 2, but for the SAS region.
Table 2.5: As in Table 3, but for the SAS region
T able 2.6a: C alibration param eter values o f Equations (1) and (2) for the four regions and
globally
Table 2.6b: Regression param eters o f the m ulti-linear equations for rain area delineation
(RD) and convective/stratiform (C/S) rain type classification, global calibration
case. First colum n is the constant, and the rest are coefficients
Table 2.7: V alidation statistics for the four regions: ALG1, A LG 2 and ALG3 are regional
calibration, global calibration, and regional calibration w ith 2A23
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convective/stratiform classification, respectively. V5 and V6 correspond to 2A12
version 5 and 6 algorithms
Table 2.8: C om parison o f E ff values for the different algorithms evaluated over the SAS
Table 3.1a: V alidation statistics for the AFC study region com paring calibrations for each
season vs. using all-season calibration param eters for each season, “szn”
represents seasonal calibration, while “all” stands for all-season calibration
Table 3.1b: V alidation statistics for the AFC study region com paring sum m er season’s
calibration vs. using calibration param eters from the other two seasons; ‘son’ and
‘m am ’ stand for SON and M A M calibrations
Table 3.2a: A s in Table 3 .1 a , b u t for the SAS region
Table 3.2b: A s in Table 3. lb , b u t for the SAS region
Table 3.3a: As in Table 3.1a, b u t for the AM Z region
Table 3.3b: As in Table 3.1b, but for the AM Z study region
Table 4.1: Contingency table used for com puting the Heidke skill score(H SS) PM , PR
and R thre are passive m icrow ave rain estimate, PR rain and the rain threshold,
respectively.
Table 4.2: V alidation statistics HSS, Correlation (Cor), Efficiency (Eff), and Bias as
defined in Section 4, for the AFC region. GPROF6 is the SSM /I surface rain rates
derived from the N ASA /G SFC Goddard profiling algorithm. A LG 25 and A LG 10
stand for regressions param eters derived at 25-km and 10-km grid resolutions,
respectively. TM I is TM I estimates from DA05 algorithm averaged to 25-km
Table 4.3: V alidation statistics for the AM Z region.
Table 4.4: V alidation statistics for the SAS region.
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I.
Introduction
Overland Passive Microwave Rain Retrieval
Passive microwave (PM) observations from radiometers onboard low earth
orbiting platforms have a better physical connection to precipitation processes as
compared to the Visible/Infrared (VIS/IR) sensors that can offer quasi-continuous
coverage from space. The measurement by PM radiometers is also less sensitive to
the presence o f cirrus clouds, which is one o f the major problems in IR-based rainfall
estimation algorithms.
The hydrometeors in the clouds and rain layers have
microwave absorption, emission, and scattering properties that can be used to derive
information about precipitation. The major shortcoming o f PM rainfall estimation is
its low temporal resolution and lack o f unique relationships to surface rainfall.
However, the increasing number o f satellite platforms carrying PM instruments makes
those observations attractive to applications that depend on large regional rainfall data
such as the study o f regional water and energy cycle, monitoring the soil moisture
variability and advancing flood forecasting and water management systems. Current
PM sensors used in rainfall studies are the Special Sensor Microwave Imager (SSM/I)
onboard the Defense Meteorological Satellite Program (DMSP) platforms, the TRMM
Microwave Imager (TMI) onboard the Tropical Rainfall Measuring Mission (TRMM)
satellite, and the recently launched Advanced Microwave Sounding Radiometer-Earth
Observing System (AMSR-E) onboard the AQUA satellite.
As part o f the
International Global Precipitation Measurement initiative, the current fleet o f PM
satellites is expected to reach a total number o f nine earth-orbiting satellites, which is
expected to increase the temporal resolution to an average o f three hours (Shepherd et
al. 2002).
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Research on the retrieval o f precipitation from passive PM observation goes
back almost three decades (e.g. Weinman and Guetter, 1977; Spencer et al., 1983;
Spencer, 1986). These were mainly based on data from the earlier PM platforms such
as Electronically Scanned Microwave Radiometer (ESMR) on Nimbus 5 and 6, and
the Scanning Multichannel Microwave Radiometer (SMMR) on Nimbus 7. However,
the 1987 launch o f SSM/I took PM rain retrieval research to a new level.
SSM/I
employs higher frequency channel (85 GHz) and has better spatial resolution than the
previous PM sensors. The fist SSM/I overland algorithm was that o f Spencer et al.
(1989).
Since then a number o f algorithms have been proposed, and Petty (1995)
presents a summary o f these algorithms. The widely known SSM/I overland rain
retrieval algorithms are those o f NOAA/NESDIS (National Oceanic and Atmospheric
Administration-National Satellite, Data, and Information Service) algorithm (Grody
1991; Ferraro and Marks 1995; and Ferraro 1997) and the Goddard scattering
algorithm (GSCAT) developed at Goddard Space Flight Center (GSFC) o f the
National Aeronautic and Space Administration (NASA) by Adler et al. (1994). The
most recent version o f the operational overland rainfall algorithms is that o f
McCollum and Ferraro (2003). The launch o f TMI in 1997, which has more spectral
channels and better spatial resolution than SSM/I, has resulted in more proposed PM
algorithms.
The current retrieval algorithms may be classified into two categories. The
first category is the physically based retrieval techniques, such as those by Olson
(1989), Smith et al. (1994), Evans et al. (1995), Kummerow et al. (1996), Pierdicca et
al. (1996), and Kummerow et al. (2001).
These algorithms use radiative transfer
computations on the basis o f cloud model simulations to generate large databases o f
simulated satellite observations and coincident precipitation profiles. The inverse
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solution is based on a Bayesian framework that identifies the database profile (or set
o f profiles) with simulated brightness temperatures closest to the satellite
observations.
This physically based approach is mainly used for over ocean
precipitation retrievals where the uniformly cold ocean background allows the use o f
lower frequency observation (10, 19, and 22 GHz for TRMM) that makes the inverse
solution more likely unique. Over land these low frequency channels cannot be used
because o f the relatively warm and non-homogeneous land background. Thus, the
physical approach would not have a unique solution over land. The second category
is that o f statistical precipitation retrieval algorithms such as those o f Ferraro and
Marks (1995), Conner and Petty (1998) and Grecu and Anagnostou (2001). These
algorithms can be applied both over land and ocean, but are mainly useful for
overland rain retrieval. The primary input to the overland retrieval is the brightness
temperature depression at 85-GHz, which occurs due to scattering by ice above the
freezing level. Overland PM rain retrievals have a host o f uncertainty sources. The
most important ones include the spatio-temporal variability in the background land
surface; the warm rain process that could give significant amounts o f rain but may not
produce enough ice aloft to be detected at 85 GHz; surface snow cover that could
have similar signature as ice aloft, consequently, confused with precipitation; the
beam filling problem, that is particularly important in cases o f small scale convective
systems; and the complex and highly variable relationship between the ice aloft and
the rainfall rate at the surface.
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Using TRMM-PR for calibrating PM rain retrieval
The statistical PM algorithms presented in the literature use different reference
rainfall sources for the calibration/validation o f the retrievals.
In situ rain gauge
rainfall measurements and rain gauge-adjusted radar rain retrievals have been used by
a number o f investigators (Ferraro and Marks 1995, and references therein).
The
main problem with using rain gauges is that point measurements are not well
representative o f the spatially averaged rainfall o f a satellite field o f view. Ground
radar (GR) observations are a better alternative; however, global coverage from wellcalibrated GR systems is limited, and practically non-existent for the major
convective regions o f the Earth. Besides, the observation geometry o f GR and PM
sensor observations is different; GR observes the cloud from below, while the PM
observes from above with an inclined view.
The TRMM satellite carries the first precipitation radar (PR) providing rain
estimates that are superior to any overland PM technique. The primary aspects o f PR
retrieval are the precipitation classification, which is facilitated by the high vertical
resolution (250 meters) reflectivity profile measurements, an inversion algorithm
controlled by a surface reference technique for path integrated attenuation (Meneghini
et al. 2000), and a reflectivity-to-rainfall relationship with parameters differentiated
for convective and stratiform rain regimes (Iguchi et al., 2000). Ground validation
studies using PR have shown high correlation (>0.9) and low (<7%) systematic
differences against rain gauge-calibrated GR rainfall estimates (Liao et al. 2001;
Anagnostou and Morales 2002). Consequently, PR offers an alternative to GR for
calibrating and validating a TMI rain algorithm over the Globe (e.g. Prabhakara et al.
2000; Grecu and Anagnostou 2001; McCollumn and Ferraro 2003). The use o f PR
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rain estimates has the added advantage that it offers a close coincidence with TMI
observations and balanced coverage o f the major convective regions on earth.
Passive microwave calibration may vary from one rainfall regime to another.
These variations are manifested as radiation/scattering signals and their relation to ice
and precipitation microphysics. These microphysical differences are compounded by
the fact that radar (in our case PR) and PM respond differently to differences in drop
size distributions (DSD). For example, a major algorithm parameter deviation would
be between convective systems with maritime (large raindrop sizes, little lightning
and suppressed ice phase) versus continental (numerous smaller raindrops; frequent
lightning; robust ice phase) characteristics (Petersen et al. 2002). Ferraro and Marks
(1995) investigated a radar-calibrated SSM/I rain algorithm over USA, Japan and UK,
where they employed a different regression for each region. A more recent study by
McCollumn and Ferraro (2003) has shown regional dependence on the TMI overland
rain retrieval error (particularly, a significant negative bias over the continental Indian
monsoon). The authors attribute this underestimation to the more maritime air mass
that produces less ice, and consequently less scattering. Studies have also identified
storm microphysical variations within smaller scale areas o f the same convective
region triggered by changes in the low-level wind direction, and/or modulations
originated by tropical easterly waves (Petersen et al. 2002; Petersen et al. 2003). PM
calibration may also vary from one season to the other within the same regime.
Seasonal variation could play a significant role in that cloud characteristics may vary
from one season to the other within the same region. For instance, Petersen and
Rutledge (2001) show that Amazon and southern India switch between continental
(maritime) characteristics during their respective spring (summer) seasons. The main
questions would be: what is the effect o f these variations on overland PM rain
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retrieval? Do we need a separate calibration for each climatic regime and each
season? Chapter 2 investigates the issue o f seasonal variation, while Chapter 3 deals
with the question o f seasonal variations.
PR may also be used to calibrate other PM sensors, such as SSM/I and
AMSR-E.
Calibration o f SSM/I using PR is particularly important for two main
reasons: (i) SSM/I has a historical data record going back to 1987; and (ii) better
sampling due to the more frequent overpasses (nominally two or three satellites in
orbit) and wider swath (1400 km versus the 760 km o f TMI). Chapter 4 investigates
the possibility o f using TRMM-PR for calibrating SSM/I for overland rain retrieval.
Problem Statement
The TRMM-PR provides definitive measurements o f the 3D structure o f
precipitation.
However, the narrow swath (215km) o f PR limits the use o f this
dataset. On the other hand, TMI and SSM/I provide wider swath coverage (760 km
for TMI and 1400 km SSM/I) and higher sampling frequency. Thus, combining the
higher accuracy o f PR with the better spatial coverage and sampling frequency o f
TMI and SSM/I would be o f great value in a number o f applications in meteorology,
hydrology, and water resources.
Attempts have already been made to combine PR and TMI by using PR to
calibrating TMI (e.g. Prabhakara et al. 2000; Grecu and Anagnostou 2001;
McCollumn and Ferraro 2003). Regional and seasonal differences may be expected
in PR-TMI calibrations owing to different cloud microphysics over different parts o f
the world during different seasons.
For instance, the Congo basin in Africa and
continental USA are known for intense convective activities (Mohr and Zipser, 1996;
Mohr et al., 1999; Nesbitt and Zipser, 2003).
On the other hand, Petersen and
Rutledge (2001) show that Amazon and southern India exhibit characteristics similar
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to those o f tropical oceans during their respective summer seasons and more
continental characteristics during the spring seasons.
According to Petersen and
Rutledge (2001), the largest systematic variability between regional wet-season
vertical precipitation structures is found above the freezing level.
It is noted that
every overland PM rain retrieval algorithm is based on observations o f ice scattering
originating above the freezing level. Thus, the regional/seasonal viabilities may lead
to different Tb-RR relationships for different regions/seasons. For instance, the 85Ghz channel is the widely used frequency for overland rain retrieval algorithms. But
would it equally work fo r regions o f intense convection and those o f shallow
convection?
Current operational overland PM rain retrieval algorithms, such as
TRMM-2A12 and Goddard Profiling (GPROF), use the same approach for all regions
and throughout the year. Would global calibration parameters equally apply to the
different convective regimes? Are the relationships between brightness temperature
and rain rate the same over the different seasons? And, are these relations the same
fo r convective versus stratiform rain profdes? Answers to such questions will help,
among other things, to fine-tune calibrations to specific regions/seasons, and
consequently improve the accuracy o f PM retrievals. It would also offer feedbacks
for improving current operational rain retrieval schemes. Nevertheless, studies that
address these issues in detail are not yet available.
One o f TRMM’s objectives has been to calibrate/validate other sensors; i.e.,
serve as a “flying rain gauge” (Simpson et al., 1988). In this respect, using TRMMPR for calibration SSM/I would be particularly attractive. The two main reasons are:
(i) SSM/I has a long data record (1987-2004), which would be useful in deriving
global precipitation climatology, (ii) better sampling due to the more frequent
overpasses (nominally two or three satellites in orbit) and wider swath (1400 km
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versus the 760 km o f TMI). Yet, there has not been much effort in this subject. The
main issue is in identifying closely matched (in space and time) observations by the
two sensors (PR and SSM/I). The two satellites have different pass times, observation
geometry, and spatial coverage.
This makes the collocation o f their observations
difficult and infrequent. The later poses an issue in terms o f the adequacy o f samples
available for use in calibration/validation.
Objectives
The major objectives o f this dissertation research are the following:
1.
Develop a PM algorithm for TRMM, which can consistently be
applied over different regions and seasons;
2.
Investigate the regional differences in PR-TMI calibration;
3.
Investigate seasonal differences in PR-TMI calibration; and
4.
Investigate transferring PR-TMI calibration to SSM/I.
Dissertation outline
The rest o f this dissertation includes three Chapters corresponding to the
issues o f regional calibration, seasonal calibration, and PR-SSM/I calibration. The
three Chapters are briefly described.
Chapter 2:
Regional differences in PR-TMI calibration for overland rainfall
retrieval
This chapter consists o f two main parts.
The first part presents the
development o f the PR-TMI algorithm. The choice o f the appropriate PM channel for
each region, the PM information used for rain area delineation and C/S classification,
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and the nature o f the brightness temperature-rain rate relationship for convective and
stratiform rain types are described. In the second part four geographically separated
convective regimes are used to study regional differences. The selected regions are
from central Africa, the Amazon basin in South America, the US southern planes, and
South Asia. These regions range from the major continental convective regime o f
Africa to the more maritime type climate o f South Asia. Two calibration strategies
are used. In the first case each region is calibrated separately, while in the second
case 25% o f the data from each region are combined to derive a “global” parameter
set. In addition to comparing regional calibration differences, Chapter 2 also assesses
the performance o f the PR-TMI algorithm with respect to the latest (V6) available
TMI-2A12 surface rainfall product.
For completeness, Chapter 2 also offers a
comparison between the older versions o f 2A12 (V5) with the latest product (V6).
Chapter 3:
Seasonal differences in PR-TMI calibration for overland rainfall
retrieval
The algorithm developed in Chapter 2 is used to investigate possible seasonal
variations in overland passive microwave calibrations. Three regions from central
Africa, the Amazon, and South Asia are selected for this study. Three relatively wet
seasons are selected for each region.
These are September-October-November
(SON), December-January-February (DJF), and March-April-May (MAM) for Africa
and Amazon. For the South Asia region, the seasons investigated are MAM, JuneJuly-August (JJA) and SON. For each region two sets o f calibration parameters are
derived. The first set o f parameters is derived from data coming from each specific
season. The second set o f parameters is derived from the combined data o f all the
months.
Both parameter sets are applied to validation data from each season to
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retrieve PM rain rates. Then the estimates are compared with PR rain estimates
(TRMM nomenclature 2A25). In addition, one season’s parameters are applied to
another to investigate the representativeness o f parameters calibrated in one season to
another.
Chapter 4:
Investigating the use of TRMM-PR for calibrating an overland
SSM/I rain retrieval algorithm
The PR-TMI algorithm developed in Chapter 2 is used to investigate TRMMbased calibration o f SSM/I rain retrieval.
algorithm has certain challenges.
PR-based calibration o f SSM/I rain
The major problem is the temporal and spatial
collocation o f data from PR and SSM/I sensors. The two sensors, being onboard
different satellites, have varying observation geometries, spatial coverage and
overpass times. As a result, to achieve adequate samples for calibration/validation
purposes requires compiling several years o f coincident TRMM and SSM/I data. To
overcome this problem, two indirect approaches are investigated. The first involves
remapping the TMI channels to the spatial resolutions o f the corresponding SSM/I
channels, and consequently using PR rainfall estimates to calibrate the parameters o f
the retrieval applied on the remapped data.
Rain retrieval is performed at 0.25°
resolution, which is representative o f the SSM/I lower resolution sensor observations.
The second approach involves calibrating the PR-TMI algorithm at coarser grid
resolution (i.e., 0.25°). Parameters obtained from the two approaches are applied to
actual SSM/I data to produce rain rates at 0.25° resolution.
These approaches
eliminate the need for directly matching data from the two satellite platforms.
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II.
Regional differences in PR-TMI calibration for overland
rainfall retrieval
Abstract
The Tropical Rainfall Measuring Mission (TRMM) satellite carries a combination o f
active (Precipitation Radar, PR) and multi-channel passive microwave (the TRMM
Microwave Imager, TMI) sensors. These sensors advance our ability to estimate
rainfall over land. Rain retrieval from PR is associated with an unprecedented
accuracy and resolution, but is limited in terms o f sampling due to the narrow PR
swath width (215 km). TMI provides wider coverage (760 km), but its observations
are associated with a more complex relationship to precipitation compared to PR
(especially over land). PR rain estimates are used here for calibrating an overland
TMI rain algorithm. The algorithm consists o f (1) multi-channel based rain screening
and convective/stratiform (C/S) classification schemes, and (2) non-linear (linear)
regressions for rain rate retrieval o f stratiform (convective) rain regimes. This study
examines regional differences in algorithm performance.
Four geographic regions
from central Africa (AFC), Amazon (AMZ), continental US (USA), and South Asia
(SAS) are selected. Data from three summer months o f 2000 and 2001 are used for
calibration; validation is done on summer 2002 data. The current algorithm is also
compared against the latest (Version 6) TRMM 2A12 product in terms o f rain
detection, and rain rate retrieval error statistics on the basis o f PR reference rainfall.
The performance o f the algorithm is different for the different regions. For instance,
the reduction in random error (relative to 2A12 V6) is about 24%, 36%, 57% and
165% for USA, AFC, AMZ and SAS, respectively. However, significant difference
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between global (the four regions combined) and regional calibration is observed only
for the SAS region.
Introduction
Passive microwave (PM) observations from radiometers onboard low earth
orbiting platforms have a better physical connection to precipitation processes as
compared to the Visible/Infrared (VIS/IR) sensors that can offer quasi-continuous
coverage from space. The measurement by PM radiometers is also less sensitive to
the presence o f cirrus clouds, which is one o f the major problems in IR-based rainfall
estimation algorithms.
The hydrometeors in the clouds and rain layers have
microwave absorption, emission, and scattering properties that can be used to derive
information about precipitation. The major shortcoming o f PM rainfall estimation is
its low temporal resolution. However, the increasing number o f satellite platforms
carrying PM instruments makes those observations attractive to applications that
depend on large regional rainfall data such as the study o f regional water and energy
cycle, monitoring the soil moisture variability and advancing flood forecasting and
water management systems. The current major PM sensors are the Special Sensor
Microwave Imager (SSM/I) onboard the Defense Meteorological Satellite Program
(DMSP) platforms, the TRMM Microwave Imager (TMI) onboard the Tropical
Rainfall Measuring Mission (TRMM) satellite, and the recently launched Advanced
Microwave Sounding Radiometer-Earth Observing System (AMSR-E) onboard the
AQUA satellite.
As part o f the International Global Precipitation Measurement
initiative the current fleet o f PM satellites is expected to reach a total number o f nine
earth-orbiting satellites, which is expected to increase the temporal resolution to an
average o f three hours (Shepherd et al. 2002).
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Research on precipitation retrieval from PM sensors has grown significantly
over the years. The current retrieval algorithms may be classified into two categories.
The first category is the physically based retrieval techniques, such as those by Olson
(1989), Smith et al. (1994), Evans et al. (1995), Kummerow et al. (1996), Pierdicca et
al. (1996), and Kummerow et al. (2001).
These algorithms use radiative transfer
computations on the basis o f cloud model simulations to generate large databases o f
simulated satellite observations and coincident precipitation profiles. The inverse
solution is based on a Bayesian framework that identifies the database profile (or set
o f profiles) with simulated brightness temperatures closest to the satellite
observations.
This physically based approach is mainly used for over ocean
precipitation retrievals where the uniformly cold ocean background allows the use o f
lower frequency observation (10, 19, and 22 GHz for TRMM) that makes the inverse
solution more likely unique. Over land these low frequency channels cannot be used
because o f the relatively warm and non-homogeneous land background. Thus, the
physical approach would not have a unique solution over land. The second category
is that o f statistical precipitation retrieval algorithms such as those o f Ferraro and
Marks (1995), Conner and Petty (1998) and Grecu and Anagnostou (2001). These
algorithms can be applied both over land and ocean, but are mainly useful for
overland rain retrieval. The primary input to the overland retrieval is the brightness
temperature depression at 85-GHz, which occurs due to scattering by ice above the
freezing level. Overland PM rain retrievals have a host o f uncertainty sources. The
most important o f those include the spatio-temporal variability in the background land
surface; the warm rain process that could give significant amounts o f rain but may not
produce enough ice aloft to be detected at 85 GHz; surface snow cover that could
have similar signature as ice aloft, consequently, confused with precipitation; the
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beam filling problem, that is particularly important in cases o f small scale convective
systems; and the complex and highly variable relationship between the ice aloft to the
rainfall rate at the surface.
The statistical PM algorithms presented in the literature have used different
reference rainfall sources for the calibration/validation o f the PM rain retrievals. In
situ rain gauge rainfall measurements and rain gauge-adjusted radar rain retrievals
have been used by a number o f investigators (Ferraro and Marks 1995, and references
therein). The main problem with using rain gauges is that point measurements are not
well representative o f the spatially averaged rainfall o f a satellite field o f view area.
Ground radar (GR) observations are a better alternative; however, the global coverage
o f well-calibrated GR systems is limited, and practically non-existent for the major
convective regions o f the Earth. Besides, the observation geometry o f GR and PM
sensor observations is different; GR observes the cloud from below, while the PM
observes from above in an inclined view.
The TRMM satellite carries the first precipitation radar (PR) providing rain
estimates that are superior to any overland PM technique. The primary aspects o f PR
retrieval are the precipitation classification, which is facilitated by the high vertical
resolution (250 meters) reflectivity profile measurements, an inversion algorithm
controlled by a surface reference technique for path integrated attenuation (Meneghini
et al. 2000), and a reflectivity-to-rainfall relationship with parameters differentiated
for convective and stratiform rain regimes (Iguchi et al., 2000). Ground validation
studies using PR have shown high correlation (>0.9) and low (<7%) systematic
differences against rain gauge-calibrated GR rainfall estimates (Anagnostou and
Morales 2002; Liao et al. 2001). Consequently, PR offers an alternative to GR for
calibrating and validating a TMI rain algorithm over the Globe (e.g. Prabhakara et al.
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2000; Grecu and Anagnostou 2001; McCollumn and Ferraro 2003). The use o f PR
rain estimates has the added advantage that it offers a close coincidence with TMI
observations and balanced coverage o f the major convective regions on earth.
This study builds upon Grecu and Anagnostou (2001) overland rain estimation
algorithm
introducing
new
parameterizations
for
rain
discriminations,
convective/stratiform classification and rain rate retrieval. A major objective is to
investigate the regional variability in terms o f the algorithm parameters and its
significance on the accuracy o f rain retrieval. Variations over different convective
regimes (Southern US, African, Amazonian, South Asia) are expected in terms o f
radiation/scattering signal and its relation to ice and precipitation microphysics.
These microphysical differences are compounded by the fact that radar (in our case
PR) and PM respond differently to differences in drop size distributions (DSD).
Radar backscatter is proportional to the sixth moment o f the DSD, while radiometer
has a third order dependence (e.g., Prabhakara et al. 2000, and references therein).
Thus, the relationship between PR and TMI may vary from one rainfall regime to
another (or even within the same regime). For example, a major algorithm parameter
deviation would be between convective systems with maritime (large raindrop sizes,
little lightning and suppressed ice phase) versus continental (numerous smaller
raindrops; frequent lightning; robust ice phase) characteristics (Petersen et al. 2002).
Ferraro and Marks (1995) investigated a radar-calibrated SSM/I rain algorithm over
USA, Japan and UK, where they employed a different regression for each region. A
more recent study by McCollumn and Ferraro (2003) has shown regional dependence
on the TMI overland rain retrieval error (particularly, a significant negative bias over
the continental Indian monsoon). The authors attributed this underestimation to the
more maritime air mass that produces less ice, and consequently less scattering.
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Studies have also identified storm microphysical variations within smaller scale areas
o f the same convective region triggered by changes in the low-level wind direction,
and/or modulations originated by tropical easterly waves (Petersen et al. 2002;
Petersen et al. 2003).
Four geographically separated convective regions are investigated in this
study. Those are in Africa (AFC), Amazon (AMZ), the US southern planes (USA),
and South Asia (SAS). Small-scale variations due to storm meteorological changes
and seasonal variations are not considered here, but the inclusion o f those aspects
would only strengthen the outcome o f the study. The PM rainfall algorithm follows
the basic structure o f Grecu and Anagnostou (2001) (hereafter named GA01), but
with modifications described in a subsequent section.
In addition to comparing
regional calibration differences for our algorithm, this study also assesses the
performance o f this algorithm with respect to the latest available TMI-2A12 surface
rainfall product. The current officially available TMI product is version 5, but we will
also use the upcoming version 61 (McCollum and Ferraro, 2003), which was made
available to us by Dr. Jeffrey McCollum. For completeness, we also offer a
comparison between the older version o f 2A12 (V5) and the latest product (V6).
Study regions and data
The four regions selected for this study are the following: (i) AFC, 15°S to
5°N and 10°E to 40°E; (ii) AMZ, 15°S to 5°N, and 70°W to 40°W; (iii) SAS, 22°N to
34°N, and 74°E to 99°E and (iv) USA, 22°N to 40°N, and 120°W to 75°W. Figure2.1
shows the location o f the four regions. Water surface and coastal pixels falling in
1This is not the official 2A12 version 6. It is a pre-delivery version from Dr. Jeff McCollum.
Consequently, there may be some differences from the final version that was delivered to the TRMM
data system.
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these areas were identified on the basis o f TMI-2A12 surface type and excluded from
the analysis.
The TRMM PR-2A25 (3D-rain rates) and PR-2A23 (rain type) products were
used to calibrate the PM algorithm applied to the TMI multi-channel brightness
temperature observations (1B11). The surface rain rates derived from the TRMM
2A12 algorithm (Version 5, and Version 6) were also used for comparison with the
developed retrieval. Each dataset was remapped to a common O.l-degreexO.l-degree
resolution grid. The PR rain rate for a pixel is derived from the vertical averaging
between 1 and 3 km height. Data from the respective summer season months o f each
region (January to March for AFC and AMZ, and June to August for SAS and USA)
are used. Calibration data came from the years 2000 and 2001, while validation data
were from 2002 (see Table 2.1 for details).
Rain retrieval methodology
The objective o f the current algorithm is to estimate precipitation from TMI
brightness temperature observations. The approach implemented here is a modified
version o f the GA01 algorithm. The GA01 algorithm consists o f the following three
major components: (i) Delineation o f rain area; (ii) classification o f rain into
convective and stratiform (C/S) rain types; and (iii) a multi-linear regression that
relates brightness temperatures to rain rate.
Rain area delineation and C/S rain
classification are based on a neural network (NN) scheme that uses features derived
from TMI data. The rain delineation scheme uses nine different features while the
C/S scheme employs six features.
The regression model o f GA01 uses three
predictors, namely, the 37 GHz and 85 GHz brightness temperatures and the product
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o f the two temperatures.
GA01 used PR-2A25 (PR-2A23) rain rate (rain type)
products as their reference dataset for algorithm calibration and validation.
The current algorithm follows the basic structure o f GA01 with some
modifications. The main goal o f these modifications is to simplify the retrieval
without compromising the accuracy o f the final product.
The simplifications are
needed to make the technique more efficient for adaptive and regional calibration.
The modifications are the following: (i) the NN schemes for rain area delineation and
C/S classification are replaced by multi-linear regressions; (ii) instead o f simply
classifying pixels into convective and stratiform, here we use relative coverage o f
stratiform (or convective) rain to classify rain into the two categories; (iii) the number
o f classifiers for rain area delineation is reduced to two without compromising the
discrimination accuracy, while one classifier is added for C/S; and (iv) the MW
channel used in rain rate retrieval is now part o f the regional calibration— for
example, the 37 GHz channel is used for USA, AFC, and AMZ, while the 85 GHz is
used in SAS.
For rain delineation we use the standard deviation o f an 85 GHz brightness
temperature array surrounding a TMI pixel, and the 85 GHz Polarization Corrected
Temperature (PCT— Spencer et al. 1989) o f that pixel.
These classifiers were
regressed against binary PR rain/no-rain calibration data and found to perform well—
even slightly better than the 9-feature NN scheme used by GA02. For example, in the
USA region the Heidke skill score (HSS— Bamstone 1992) increased from 0.66 for
the NN scheme to 0.72 for the two-parameter regression case. Here HSS is used as a
measure o f the degree o f consistency between the algorithm’s rain identification and
that o f PR (2A25).
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The model for C/S is also a multi-linear regression. All the parameters in
GA01 plus an additional parameter, namely, the 85 GHz polarization difference
(Olson et al. 2001) are used as predictors. The reference data used for calibration
come from the 2A23 rain type product.
For each 0.1-degree pixel the relative
coverage o f stratiform rain (or convective rain) is derived from 2A23. Then a
threshold value is used to group data into the two main categories (C/S). In the case
o f classifying pixels as stratiform or convective, one needs to address the issue o f
mixed rain types in the 0.1-degree grid box. Using relative coverage helps to avoid
this problem. Yet, all the seven predictors combined explain only about 26% o f the
total variance in the 2A23 stratiform coverage values (similar to what has been
reported by McCollum and Ferraro, 2003). The C/S classification scheme is still an
important component o f the overall algorithm. Later it will be shown that changes in
C/S classification accuracy significantly affect the overall performance o f the
algorithm.
The multi-parameter regression o f GA01 uses three predictors. However, as
shown in Table 2.2 these three predictors are highly correlated. The correlations are
particularly high in the convective rain types; which is true for both our C/S
classification and that o f 2A23. We include 2A23 classification to show that these
correlations are not a result o f potential C/S misclassifications by our technique. The
correlations shown in Table 2.2 are for the AFC region, but the values from the AMZ
and USA regions are quite similar. The exception is with the SAS region, which will
be addressed later in this section. Table 2.3 shows the linear correlation coefficients
for each o f the predictors and combination o f the predictors with respect to PR rain
rate. Again results shown here are for both using our C/S classification and that o f
2A23. The increase in correlation for the multi-predictor versus the single-parameter
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retrieval is insignificant. Thus, one predictor seems to be sufficient. Based on the
linear correlation coefficients, it seems that the 37-GHz brightness temperature (T37)
is the best choice. But this is true only if the relationship between the brightness
temperatures and rain rate is assumed to be linear. Later we will show that this may
not be always the case. Figure 2.2 shows two-dimensional contour plots o f mean
rainfall presented as function o f T37 and T85 for the convective and stratiform rain
regimes (C/S classification is based on 2A23 product). It is noted that T37 is more
sensitive to variations in rain rate than T85. The difference is more prominent for the
case o f stratiform rain type.
The sensitivity o f T85 increases towards higher
temperature values (low rain rates) in the convective case. The fact that T85 is more
sensitive at lower rain rates indicates the effect o f saturation at higher rainfall
intensities (major convective systems). This is mainly because the higher frequency
channel is more sensitive to smaller scattering particles than the lower frequency
channel. T85 also exhibits more scatter towards both lower and higher temperature
values. Thus, the lower sensitivity o f T85 to rain rate observed in Figure 2.2 is a
combined effect o f the higher scatter and saturation at high rain rates. Thus, despite
its better spatial resolution and higher dynamic range, T85 does not seem to be the
best estimator for rain retrieval in regions o f intense convective activity. Later it will
be shown that AFC, USA, and AMZ are regions having such intense convection.
Thus, in those situations T37 vertical polarization will be used for rain retrieval.
The SAS region has distinctively different characteristics as compared to the
other three regions. The main difference is that the convection over this region has
less ice scattering than the other regions (see section 4). The fact that part o f this
region is mountainous also plays a significant role.
Tables 2.4 and 2.5 show the
correlation coefficients corresponding to this region. The correlation values between
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T37 and the other two predictors shown in Table 2.4 are much lower than those
presented in Table 2.2. From Table 2.5 we note that the correlation between rain rate
and the predicators is higher for T85, which is in contrast to what is shown for the
other regions. The differences are more pronounced for the stratiform cases. Overall,
rain estimates from T37 exhibit higher random error and significant bias as compared
to those from T85. Thus, for SAS T85 vertical polarization is used.
The probability matching technique is used to select brightness temperature
(Tb)-rain rate (RR) pairs. This method is chosen to overcome the wide scatter o f TbRR relationships and the skewness o f RR distribution.
Probability matching is
implemented after rain area delineation and C/S classifications. Only data between
the 1st and 99th percentile are used. Then regression lines are fit to the paired data,
which is shown in Figures 2.3 through 2.6. As noted from the figures the stratiform
case is non-linear, while a linear fit seems reasonable for the convective case. We
attempted fitting non-linear relations for the convective case, but it did not improve
the results. Thus, for the stratiform rain regime we use an exponential model o f the
following form:
(2.1),
RR = a0E X P (-(T b -a l )2 /2 a 22)
where ao, ai and a2 are coefficients. For the convective case we use a linear regression
o f the form:
(2.2).
RR = b0 + b]Tb
Figures 2.3 through 2.6 show the corresponding fitted regression lines (gray line).
Both T37-RR and T85-RR plots are shown for AFC and SAS regions, while only
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T37-RR plots are shown for the other two regions. Also the case o f using 2A23 C/S
classification is shown only for AFC and SAS. The T85-RR fitted relations o f AMZ,
USA and AFC are similar. As shown in Fig.2.6, the T37-RR relation for the SAS
region is quite different from those shown for the other regions owing to difference in
ice microphysics. The convective cases are less affected by our C/S classification.
The main reason for this is that the convective rain regime might include low rainfall
values, thus misclassification o f a stratiform satellite pixel as convective would not
affect the convective relationship. On the other hand, as stratiform rain regime is
associated with low rain rates ( < 1 0 mm/h), convective rain rates misclassified as
stratiform would have an apparent effect on the relationship. This effect is exhibited
by the differences in the Tb-RR curves, particularly for the stratiform cases (Fig.2.3
and Fig.2.6). Nevertheless, even this level o f classification accuracy helps to improve
the overall algorithm performance.
The merit o f C/S classification has also been
shown in past studies (see for example Prabhakara et al. 2000, Grecu and Anagnostou
2001; and McCollum and Ferraro, 2003).
Finally, to examine the significance o f regional calibration two calibration
strategies were used. In the first case each region was calibrated separately, while in
the second case 25% o f the data from each region were combined to derive a “global”
parameter set.
T37 is used in global calibration.
The values o f the algorithm
parameters derived from the above calibration strategies are shown in Table 2.6a.
The coefficients used in the multi-linear regressions for rain area delineation and C/S
classification are given in Table 2.6b for the global calibration case. The performance
o f the algorithm based on the regionally determined parameter sets is compared over
each region to the performance o f the algorithm using the globally determined
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parameter set.
These results are further compared against the 2A12 V5 and V6
retrievals. This is presented and discussed in the next section.
Results and discussion
This assesses the significance o f regional calibration and compares algorithm
results against TRMM 2A12 (V5, V6) rain products. The validation data set comes
from the respective three summer months o f 2002. For each region the algorithm
produces rain rates based on two parameter sets: one obtained from regional
calibration, and a second single parameter set representative to all four regions (Table
2.6a shows the parameter sets o f each region and the global set). Results obtained
using the 2A23 convective/stratiform (C/S) classification, as opposed to our own
classification scheme, will also be presented.
This is intended to emphasize the
importance o f C/S classification accuracy on rain estimation.
For comparing the
different results we use the following statistics: linear correlation coefficient,
efficiency score, Heidke Skill Score (HSS), and bias.
HSS is a measure o f
correspondence between the estimate and the reference (see for example Bamstone,
1992, and Conner and Petty, 1998).
HSS combines the effects o f probability o f
detection, false alarm rate and occurrences by chance. Thus, it is a better measure as
compared to using just probability o f detection and false alarm rate. Here HSS is used
in two ways. First, scalar values o f HSS are used for assessing the rainfall detection
ability o f the algorithms. Second, one-dimensional (ID) and two-dimensional (2D)
plots o f HSS values at different thresholds o f estimate and reference rain rates, as
described in Conner and Petty (1998), are presented. The Efficiency (Eff) and Bias
statistics are defined as:
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Eff _ 1 VAR(Error)
VAR(PR)
(2.3)
SUM (PM )
Bias = --------------SUM(PR)
(2.4)
where, PR is the PR-2A25 rain rates, PM is the passive microwave estimate from the
various algorithms, and Error=PM-PR. Below we present results for each region
followed by a summary discussion.
a) AFC
Results for the AFC region are presented in Table 2.7, as well as Figures 2.7
and 2.11.
The error statistics do not show significant differences between the
algorithm runs performed using regionally (ALG1) versus globally determined
parameters (ALG2), except for a higher positive bias in ALG2. The 2D HSS plots in
Fig.2.7a for ALG1 and ALG2 are also very similar. Fig.2.7b presents the HSS values
along the diagonals o f the 2D HSS plots in Fig.2.7a. Similarly, ALG1 and ALG2 are
very close to each other.
The histogram shown in Fig.2.7c indicate that the two
algorithms give similar marginal rain rate distributions; with ALG2 being closer to PR
histogram in some rainfall ranges.
As shown in Table 2.7 the algorithm results
(ALG1 or ALG2) outperform V6 in terms o f all presented error statistics. The most
significant difference is the increase in efficiency (Eff) o f about 36% with respect to
V6.
The 2D HSS plots in Fig.2.7a show that V6 exhibits higher scatter than the
algorithm, while Fig.2.7b shows that the algorithm has higher HSS values than V6 for
the whole dynamic range o f rainfall rate thresholds.
The algorithm rain rate
histograms are closer to PR compared to V6 rain rate histogram (Fig.2.7c). Finally,
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we note that V6 significantly outperforms V5.
The Y6 has six times higher Eff
statistic than V5 and exhibits less bias and higher HSS values.
b) AMZ
Similarly with AFC, in this region ALG1 and ALG2 have very comparable
validation statistics. This is evident from the bulk statistics presented in Table 2.7 and
from the HSS and histogram plots in Fig.2.8. The algorithm exhibits significantly
better statistics than V6. The relative increase in Eff over V6 is 57%. In the 2D HSS
plots o f Fig.2.8a, it is shown that V6 exhibits both higher bias and variance compared
to both ALG1 and ALG2. The V6 estimates HSS values are lower than the algorithm
(Fig.2.8b). The algorithm rain rate histograms are closer to the PR histogram than V6.
Finally, V6 outperforms V5 in all statistical measures considered here.
c) USA
The only appreciable difference between ALG1 and ALG2 (Table 2.7) for this
region is on Eff, which is slightly higher for ALG1.
There are no significant
differences between the HSS and histogram plots for the two algorithm parameter sets
(Fig.2.9). Both ALG1 and ALG2 have better correlation, higher E ff and HSS values
than V6. Appreciable difference is observed between the histograms o f V6 with PR,
while the algorithm agrees fairly well with PR (Fig.2.9). Again here V6 offers an
improvement over V5 in terms o f all validation statistics and the HSS plots.
d) SAS
Among the four regions, SAS is the one exhibiting some difference between
the performances o f regional and global parameters. ALG1 has higher (by 37%)
25
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efficiency as compared to ALG2 (Table 2.7).
However, there are no significant
differences in terms the qualitative comparisons o f Fig.2.10. There is very significant
difference between our algorithm and that o f TMI-2A12 V6 for this region. All the
validation statistics in Table 2.7 as well as the plots in Fig.2.10 show that ALG1 gives
much better results than V6. Finally, V6 shows a slight improvement over V5, but
both exhibit very poor performances for this region.
e) Summary
The following overall conclusions are made from the above analysis.
The
regional calibration exhibited notable improvements only over the region where the
algorithm had a relatively poor performance (SAS). The largest difference between
our algorithm and V6 is also over the SAS region where V 6’s performance is poor.
The least difference between the two algorithms is over the USA region. It has also
been shown that V6 is an improvement over V5 for all regions.
Samples o f
instantaneous TMI (ALG1 and V6) and corresponding PR rainfall rate fields from the
four study regions o f the validation period are shown in Figure 2.11. The patterns in
each set o f precipitation fields look alike.
However, there are areas in the
precipitating regions that exhibiting differences in the magnitude o f rainfall between
the different retrievals. A common observation for the two TMI retrievals is that they
tend to overestimate the stratiform rainfall and underestimate the magnitude o f rain
rates in the convective centers. This effect is more apparent in V6 rain maps. Finally,
ALG1 rain fields seem to have higher spatial structure than V6, which is consistent to
the spatial variability observed in the PR rain rates.
Table 2.7 shows validation statistics for the case (ALG3) where rain regime
classification was based on 2A23 C/S classification product. The main difference
26
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between ALG3 and the other two (ALG1 and ALG2) that use our own C/S estimates
is the increase in Eff statistic; i.e., decrease in random error.
There is also a
significant increase in linear correlation coefficient. The improvement is greatest over
SAS exhibiting a 76% increase in Eff. The increase o f Eff in AFC, AMZ and USA is
29%, 32% and 31%, respectively. This again shows that a significant proportion o f
the random error comes from misclassification o f convective and stratiform rain
types. The difference between ALG3 and the other algorithms is more pronounced in
stratiform rain rates as compared to convective rain rates. Table 2.8 compares the Eff
values evaluated in SAS region separately for stratiform and convective rain types.
Except for ALG3 all other algorithms suffer from a high random error in the
stratiform rain regime. This difference is a result o f misclassification, indicating that
such an effect can have more severe consequences on stratiform rain rates. This result
also justifies the use o f a non-linear relation between brightness temperature and rain
rate for the stratiform case. Another important note is that the differences between
SAS and other regions decrease dramatically when the algorithm uses the improved
C/S classification from PR (ALG3). This indicates that it is possible to overcome
limitations in ice-scattering signatures and have reasonable estimates over regions like
SAS by improving C/S classification and selecting appropriate Tb-RR relationships.
Our future efforts will concentrate on that direction.
An important observation is that regions with better performance, both for our
algorithm and that o f 2A12, are those with the highest convective activity (e.g. AFC).
Mohr and Zipser (1996) and Mohr et al. (1999) used the SSM/I 85-GHz ice-scattering
signature to describe the size, intensity and geographic distribution o f mesoscale
convective systems (MCSs). They showed that tropical Africa and the North America
are regions o f intense convective activity. Peterson and Rutledge (2001) asserted that
27
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conyection over the Congo basin (part o f AFC region) is more vertically developed
than over Amazon. Nesbitt and Zipser (2003) also stated that tropical Africa and
United Sates-Mexico-Gulf o f Mexico regions contain some o f the most intense ice
scattering signatures from MCSs. Although convection over tropical Africa is more
intense than that over Amazon, the convection over Amazon is more frequent and has
wider spatial coverage (Mohr et al., 1999, Peterson and Rutledge, 2001). Peterson
and Rutledge (2001) stated that AMZ and SAS regions exhibit characteristics similar
to those observed for isolated regions o f tropical oceans. Mohr et al. (1999) actually
classified Amazon as “oceanic” region, while Congo and India/Southeast Asia (which
includes the SAS region) have been classified as continental regions.
Table 2.1 shows that SAS has higher proportion o f convective rain as
compared to the other regions. However, the convention over the SAS area is less
intense and has less ice formation compared to the other regions considered in the
current study (Mohr and Zipser, 1996; Mohr et al., 1999; Peterson and Rutledge,
2001; Nesbitt and Zipser, 2003).
Climatological studies o f this region show
widespread mass ascent, which is not favorable to intense convective. For example,
Ramage (1971) states that “[...] synoptic scale convergence in the friction layer
enhances total rainfall through massive ascent but, by increasing the depth o f moist air
and diminishing the laps rate, hinders thunderstorm development”. Raja et al. (1999)
also asserted that mass assent leads to synoptic-scale layered stratiform clouds with
embedded convective activity.
According to Peterson and Rutledge (2001), the
largest systematic variability observed between regional wet-season vertical
precipitation structures is found above the freezing level. And both our algorithm and
that o f 2A12 PM overland rain estimates are based primarily on ice scattering above
the freezing level.
Thus, the above variability could explain part o f the regional
28
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differences, and particularly why both our algorithm and that o f 2A12 rain retrieval
performance are different over the SAS region.
Conclusions and future studies
The objective o f this study has been to evaluate the significance o f using
regionally dependent calibrations. Four geographic regions, namely Africa (AFC),
Amazon (AMZ), USA and Southeast Asia (SAS) were selected for the study. The
retrieval algorithm used here is a modification o f Grecu and Anagnostou (2001). It
uses multi-channel rain screening and convective/stratiform (C/S) classification
schemes. For rain rate estimation the 37 GHz channel is used for AFC, AMZ and
USA regions and the 85 GHz channel for SAS. The relationship between brightness
temperature and rain rate was found non-linear (linear) for stratiform (convective)
rain regimes. Two calibration strategies were used: calibration for each region, and
‘global’ calibration (where 25% o f the data from each region were combined). In
addition to evaluating the significance o f regional calibration, this study also assessed
the performance o f the current algorithm with respect to TRMM 2A12 Versions 5 and
6
overland
rain retrievals.
The
study also
stressed
the
importance
of
convective/stratiform rain type classification in the accuracy o f PM retrievals.
The difference in algorithm performance run with regionally versus globally
calibrated parameters was shown to be insignificant for the AFC, AMZ and USA
regions.
For all practical purposes, the global calibration can be used over these
regions.
In SAS, where T85 was used instead o f T37, there was some difference
between the global and regional calibrations with 27% increase in random error.
This was ascribed to unique convective characteristics and topography o f this region.
The current algorithm (both using regional and global parameters) outperformed the
29
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2A12 V6, and consequently V5.
The major improvement was shown to be the
decrease in random error. The E ffvalues were shown to increase by 24%, 36%, 57%
and 165% for USA, AFC, AMZ, and SAS, respectively. It was also shown that TMI2A12 V6 is superior to the corresponding V5 in terms o f all the validation criteria
used here. The largest difference between V5 and V6 is over the AFC region and the
least improvement is over SAS.
Validation statistics are also performed for the case (ALG3) where PR-2A23
rain type classification was used in place o f our algorithm’s C/S classification
scheme. This resulted in improvements in terms o f rain estimation. The decrease in
random error was 29%, 31%, 32% and 76% for AFC, USA, AMZ and SAS,
respectively.
The greatest improvement was shown to be over regions where the
algorithm performance was relatively poor, and in particular in stratiform rain
regimes. This leads us to believe that (i) significant proportion o f the estimation error
comes form misclassification o f rain type; (ii) the use o f non-linear regression for the
stratiform case is justifiable; and (iii) improving C/S classification is the way to
improve PM rain retrieval accuracy, especially over regions where the ice-scattering
signature is relatively low.
The conclusions o f this study are based only on four geographic regions. An
issue is that these regions dot not represent all possible climatic regimes on earth.
Consequently, the ‘global’ algorithm may not be truly global. Another issue is the
fact that the selected regions may not be homogenous in terms o f the characteristics o f
the convection ice microphysics.
Comparing these regions to convective regimes
classified on the basis o f convective vertical structure (Boccippio et. al, 2004) shows
that the regions are relatively homogenous with the exception o f coastal areas. The
coastal areas remain to be the main source o f in-homogeneity in passive microwave
30
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retrievals. Furthermore, these regions could further be classified according to the
flow regime and storm meteorology (maritime vs. continental systems).
Another
shortcoming o f this study is that it is limited to three summer months. Thus, it does
not address the issue o f seasonal variability. We are working on several extension o f
this algorithm.
The most important works include (1) examining the regional
calibration using more objectively determined regions such as the regimes determined
on the basis o f convective vertical structure derived from (e.g., Boccippio et al. 2004),
flow regime and storm meteorology (Petersen and Rutledge 2001); (2) improving C/S
classification from combination o f PM and other sensor observations (e.g., model
predictions, coincident lightning data); and (3) applying the developed algorithm to
other passive microwave sensors (SSM/I, AMSR).
Acknowledgements: This study was supported by NASA’s Global Water and Energy
Cycle program (NAG5-11527). Dr. Jeffrey McCollumn o f NOAA/NESDIS provided
the V6 TRMM 2A-12 precipitation fields. TRMM data were provided by NASA
DAAC.
References
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spectrum: 1.Archetypical vertical structures. J. Clim., in press.
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Meneghini, R., T. Iguchi, T. Kozu, L. Liao, K. Okamoto, J. A.Jones, and J.
Kwiatkowski, 2000: Use o f surface reference technique for path attenuation
estimates from the TRMM precipitation radar. J. Appl. Meteor, 39, 2053-2070.
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Mohr, K. I. and J. S. Famiglietti and E. J. Zipser, 1999: The contribution to tropical
rainfall with respect to convective system type, size, and intensity estimated from
the 85-GHz ice-scattering signature. J. Appl. Meteor, 38,596-606.
Nesbitt, S. W. and E. J. Zipser, 2003: The diurnal cycle o f rainfall and convective
intensity according to three years o f TRMM measurements. J. Clim., 16, 14561475.
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Petersen, W.A., and S.A. Rutledge, 2001: Regional variability in tropical convection:
observations from TRMM. J. Clim., 14,3566-3586.
Petersen, W.A., S.W. Nesbitt, R. J. Blakeslee, R. Cifelli, P. Hein, and S.A. Rutledge,
2002: TRMM Observations o f Intraseasonal Variability in Convective Regimes
over the Amazon. J. Clim. 15, 1278-1294.
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Petersen, W.A., R. Cifelli, D.J. Boccippio, S. A. Rutledge, and C. Fairall. 2003:
Convection and Easterly Wave Structures Observed in the Eastern Pacific Warm
Pool during EPIC-2001. J. Atmos. Sciences, 60, 1754-1773
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Precipitation retrieval from spacebome microwave radiometers based on
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microwave radiometer rain rate estimation method with convective stratiform
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Raja, M. K., G.C. Asnani, P.S. Salvekar, A.R. Jain, D.N. Rao, S.V. Rao, P. Kishore
and M. Hareesh, 1999: Layered clouds in the Indian monsoon region. Proc. Indian
Acad. Sci. (Earth Planet. Sci.), 108(4), 287-295.
Ramage, C.S.,1971: Monsoon Meteorology. Academic Press, 107pp.
Smith, E.A., X. Xiang, A. Mugnai, and G. J. Tripoli, 1994: Design o f an inversionbased precipitation profile retrieval algorithm using an explicit cloud model for
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to 3-hourly precipitation estimates. GPM Report Series No. 7, NASA/Goddard
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and Ocean with the SSM/I: Identification and Characteristics o f the Scattering
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List o f Tables
Table 2.1: Calibration and validation data statistics for the four regions. The total data
used (N-total), percent o f pixels with rain (% Rain) and the proportion o f
convective rainfall (% Conv.) are shown.
Table 2.2: Correlation coefficients among the three predictors: 37GHz (T37), 85GHz
(T85) and their product (T37*T85) determined with data from the AFC region.
Results are shown for C/S classifications performed using the herein described
algorithm and the C/S products from PR-2A23
Table 2.3: Linear correlation coefficients between PR rain rate and
brightness
temperatures at 37GHz (T37), 85GHz(T85) and their product (T37*T85)
determined with data from the AFC region. The multi-parameter correlation
coefficient between rain rate and the three predictors is also shown.
Table 2.4: As in Table 2, but for the SAS region.
Table 2.5: As in Table 3, but for the SAS region.
Table 2.6a: Calibration parameter values o f Equations (2.1) and (2.2).
Table 2.6b: Regression parameters o f the equations for rain area delineation (RD) and
convective/stratiform (C/S) rain type classification, global calibration case.
First column is the constant, and the rest are coefficients
Table 2.7: Validation statistics
for the four regions:
ALG1, ALG2 and ALG3 are
regional calibration, global calibration, and regional calibration with 2A23
convective/stratiform classification, respectively. V5 and V6 correspond to
2A12 version 5 and 6 algorithms
Table 2.8: Comparison o f Zs/fvalues for the different algorithms evaluated over the
SAS region.
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Table 2.1: Calibration and validation data statistics for the four regions. The total data
used (N-total), percent o f pixels with rain (% Rain) and the proportion o f convective
rainfall (% Conv.) are shown.
Region
Calibration data
Validation data
N-total
% Rain
% Conv.
N-total
% Rain
% Conv.
AFC
495798
13
26
207685
11
25
AMZ
1637607
20
22
595840
18
24
SAS
466619
18
28
305084
14
28
USA
1111372
08
27
467443
07
22
36
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Table 2.2: Correlation coefficients among the three predictors: 37GHz (T37), 85GHz
(T85) and their product (T37*T85) determined with data from the AFC region.
Results are shown for C/S classifications performed using the herein described
algorithm and the C/S products from PR-2A23.
Stratiform
Convective
Algorithm classification
T85
T37*T85
T85
T37*T85
T37
0.84
0.91
0.86
0.92
T85
1.00
0.99
1.00
0.99
T37
0.85
0.91
0.89
0.94
T85
1.00
0.99
1.00
0.99
2A23 Classification
37
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Table 2.3: Linear correlation coefficients between PR rain rate and brightness
temperatures at 37GHz (T37), 85GHz(T85) and their product (T37*T85) determined
with data from the AFC region. The multi-parameter correlation coefficient between
rain rate and the three predictors is also shown.
T37
T85
T37*T85
Multiple
Algorithm
Stratiform
-0.603
-0.484
-0.531
0.608
classification
Convective
-0.575
-0.476
-0.512
0.585
2A23
Stratiform
-0.703
-0.597
-0.638
0.721
classification
Convective
-0.624
-0.563
-0.588
0.636
38
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Table 2.4: As in Table 2, but for the SAS region.
Stratiform
Convective
Algorithm Classification
T85
T37*T85
T85
T37*T85
T37
0.50
0.63
0.64
0.70
T85
1.00
0.99
1.00
0.99
T37
0.47
0.61
0.61
0.69
T85
1.00
0.98
1.00
0.99
2A23Classification
39
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Table 2.5: As in Table 3, but for the SAS region.
T37
T85
T37*T85
Multiple
Algorithm
Stratiform
-0.278
-0.429
-0.437
0.453
classification
Convective
-0.465
-0.440
-0.456
0.505
2A23
Stratiform
-0.347
-0.622
-0.619
0.636
classification
Convective
-0.471
-0.575
-0.582
0.606
40
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Table 2.6a: Calibration parameter values o f Equations (1) and (2)
aO
al
a2
bO
bl
AFC
75.0996
231.772
13.9420
195.591
-0.7018
AMZ
49.3084
232.892
15.2117
212.640
-0.7621
USA
113.470
221.212
17.4416
181.381
-0.6461
SAS
87.3240
119.163
49.5871
59.0828
-0.2140
Global
101.290
223.000
17.5269
199.766
-0.7113
41
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Table 2.6b: Regression parameters o f the equations for rain area delineation (RD) and
convective/stratiform (C/S) rain type classification, global calibration case. First
column is the constant, and the rest are coefficients.
C/S
2.2295
-0.0172
-0.0511
RD
2.8798
0.0218
-0.0095
-0.0212
-0.0046
0.0037
-0.2011
42
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0.03031
Table 2.7: Validation statistics for the four regions: ALG1, ALG2 and ALG3 are
regional calibration, global calibration, and regional calibration with 2A23
convective/stratiform classification, respectively. V5 and V6 correspond to 2A12
version 5 and 6 algorithms.
AFC
AMZ
USA
SAS
ALG1
ALG2
ALG3
V5
V6
HSS
0.76
0.76
0.76
0.68
0.74
Cor
0.72
0.74
0.79
0.62
0.68
Eff
0.45
0.41
0.58
0.05
0.33
Bias
0.96
1.21
0.97
1.20
1.13
HSS
0.68
0.66
0.66
0.56
0.61
Cor
0.71
0.72
0.78
0.60
0.66
Eff
0.44
0.44
0.58
-0.09
0.28
Bias
0.90
1.01
0.90
1.09
1.02
HSS
0.71
0.71
0.70
0.63
0.69
Cor
0.71
0.70
0.77
0.60
0.67
Eff
0.42
0.35
0.55
0.19
0.34
Bias
0.98
1.11
0.94
0.96
0.99
HSS
0.71
0.68
0.71
0.26
0.31
Cor
0.63
0.62
0.73
0.23
0.24
Eff
0.26
0.19
0.46
-0.51
-0.40
Bias
1.02
0.99
1.00
0.68
0.66
43
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Table 2.8: Comparison o f E ff values for the different algorithms evaluated over the
SAS region.
ALG1
ALG2
ALG3
V5
V6
stratiform
-1.56
-5.08
0.38
-5.52
-4.80
Convective
0.05
-0.07
0.08
-0.68
-0.59
44
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List o f figures
Figure 2.1:
The study region.
Figure 2.2:
Rain contours as a function o f 37 and 85 GHz brightness temperatures
(T37 and T85) for the USA region.
Figure 2.3:
AFC region brightness temperature (T37 and T85) versus rain rate
values o f common exceedance probabilities (quantiles) overlaid by a
fitted regression line. The upper panel corresponds to 2A23 C/S
classifications, while the middle and lower panels correspond to the
algorithm C/S classification.
The left and right panels are for
stratiform and convective rain type, respectively.
Figure 2.4:
AMZ region brightness temperature (T37) versus rain rate values o f
common exceedance probabilities (quantiles) overlaid by a fitted
regression line. The convective/stratiform classification is based on our
algorithm.
Figure 2.5:
Same as in Fig.2. 4, but for the USA region.
Figure 2.6:
Same as in Fig.2. 3, but for the SAS region.
Figure 2.7:
(a) Contour plots o f HSS as function o f rain threshold, for the AFC
region. Top panels are for ALG1 (regional calibration) and ALG2
(global calibration), while the lower panels are for TMI-2A12 V.5 and
V.6;
(b) Plot o f HSS values along the diagonal as function o f rain threshold;
(c) Relative frequency [%] o f the different TMI rain rate retrievals and
PR rain rates.
Figure 2.8:
Same as in Fig.2.7, but for AMZ.
Figure 2.9:
Same as in Fig.2.7, but for USA.
45
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Figure 2.10:
Same as in Fig.2.7, but for SAS.
Figure 2.11:
Sample cases o f coincident instantaneous rain rate maps o f ALG1 (left
panel), PR (middle panel), and 2A12 V6 (right panel). The red lines
show the PR swath on the TMI rain rate maps.
46
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AMZ
47
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Convective
S tratiform
SELL
48
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Stratiform
Convective
PR rain[mm/hr]
20
30
10
250
260
270
290
200
220
2+0
T37[k]
T37[k]
S tra tifo rm
C onvective
PR nain[mm/hr]
20
10
250
260
'0
200
290
2+0
260
280
T37[k]
T37[k]
S tra tifo rm
C onvective
PR rain[mm/hr]
50
1C'
260
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2ao
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2CO
T85[k]
Figure 2.3
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Convective
Stratiform
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PR ram I’m m /
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Figure 2.4
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S tra tifo rm
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Figure 2.5
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500
Stratiform
zo
Convective
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a.
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T37[k]
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Figure 2.6
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290
PR ram [m rn/hr]
PR rain[m m /hr]
0.8
8
PR
. 2A 12 V 5
_ ..
2A 12 V 6
2A 12V 6
ALG1
_ ALG1
8
HSS
.. ALG2
- - ALG2
+
u
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\A
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Rain [ m m /h r ]
o
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Figure 2.7
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PR nam[mm/hr]
PR rain[m m /hr]
0 .8
2 A 12 V 5
2A 12 V6
ALG1
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_
PR
..
2A 12V6
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, . ALG2
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ALG2
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IQ
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0
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Figure 2.8
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15
PR ram [m m /hr]
PR rain [m m /h r]
8
0.8
_ _
_
PR
2A 12 V5
..
2A12V6
2 A 1 2 V6
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$
ALG1
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K
fr
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s
|£
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IQ
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Rain [m m /h r]
50
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Rain [m m /h r]
Figure 2.9
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2A12 V6
— i
PR ram [m m /hr]
PR ram [m m /hr]
........ i............ 1........... ............
t
0,6
2A12 V5
__ 2A12 ve
___ALG1
ALG2
b
A
&
PR
ZA12 V6
ALG1
_
ALG2
a
0,+
s
■\
•\
■\
\
0,2 -
2
■>
■"'o __
0,0
\ v1V
^. \
............ i .
ia
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A-7.-r.r,f
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Rain [m m /h r]
o
0
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Rain [m m /h r]
Figure 2.10
56
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RR [m frt/hr]
AMZ
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III.
Seasonal Differences in PR-TMI calibration for Overland
Rain Retrieval
Abstract
Seasonal differences in the calibration o f overland passive microwave (PM) rain
retrieval are investigated. The objective is to explore the significance from calibrating
PM sensor retrieval separately by season versus using a single calibration parameter
set. A procedure that devises joint TRMM Precipitation Radar (PR) and Microwave
Imager (TMI) data to calibrate a TMI algorithm for overland rain estimation is used to
facilitate the study. Three geographic regions from central Africa, South Asia, and
the Amazon basin are selected due to their distinct convective characteristics. Three
seasons are selected for each region: the respective summer season and the seasons
preceding and following the summer season. Two scenarios o f algorithm calibration
are considered. In the first scenario, parameters sets are derived by calibrating the
TMI algorithm in each season. In the second scenario, common parameter sets are
derived from the combined dataset o f all seasons.
The parameter sets from both
scenarios are then applied to the validation datasets o f each season.
Results are
compared to determine the effect o f seasonal calibration. Furthermore, calibration
parameters from one season are cross-validated based on the validation dataset o f the
other season, and results are compared against those derived using the season’s own
parameters. No significant difference is observed between using individual seasonal
calibration and the all-season calibration. However, using one season’s parameter set
to retrieve rainfall at another season is associated with increased uncertainty—while
this effect is shown to vary by region.
It is shown that the performance o f TMI
58
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retrieval varies by season.
In central Africa, the best agreement between TMI
estimates and PR rainfall is observed during the season proceeding summer season
exhibiting a 42% decrease in random error. The pre-monsoon season performs best in
the South Asian region with a 14% decrease in random error.
Similar results are
observed in the Amazon region where the decrease in random error is shown to be
19%.
Introduction
This paper investigates the significance o f seasonal calibration in overland
passive microwave (PM) rain retrieval.
It compares effects o f using different
calibration parameters sets for each season versus using a single set o f parameters
representative o f all seasons. The PM retrieval devised for this investigation is the
overland rain estimation algorithm o f Dinku and Anagnostou (2005), hereafter named
DA05.
The algorithm has three main components: (i) selection o f the most
appropriate TMI channel for rain rate estimation over a given geographic region; (ii)
delineation o f the raining areas and classification o f rain into convective and
stratiform (C/S) types on the basis o f multiple channel observations; and (iii)
developing optimal brightness temperature-rain rate relationships for each rain type.
Estimation o f the optimal parameters controlling the different algorithm components
is based on joint data from the Tropical Rainfall Measuring Mission (TRMM)
Precipitation Radar (PR) rainfall estimates and Microwave Imager (TMI) multi­
channel brightness temperature measurements.
Dinku and Anagnostou (2005) have assessed the significance o f regional
variation in the PR-based calibration o f DA05 algorithm. The selected regions were
from central Africa, the Amazon basin, continental US, and in South Asia. It was
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found that the best single TMI channel for overland rain retrieval in the tropics is the
37 GHz.
Regional calibration was found to be important over South Asia, while
global calibration (i.e., use o f a constant parameter set) sufficed for the other three
continental regions. The performance o f DA05 relative to PR rainfall was compared
against the latest (Version 6) TRMM-2A12 surface rain estimates. It was shown to
perform better than TRMM-2A12 in the geographic regions and seasons the algorithm
was calibrated. The major demonstrated improvement was the decrease in random
error (and corresponding increase in correlation), being about 24%, 36%, 57% and
165% for the continental US, Africa, Amazon, and South Asia region, respectively.
This paper is concerned with the seasonal variations in the DA05 algorithm
parameters and assesses the significance o f regional calibration in terms o f rain
estimation accuracy.
This investigation could contribute valuable information to
other algorithms such as the Goddard PROFiling (GPROF) algorithm used in various
PM sensor observations (TMI, Special Sensor Microwave Imager, SSM/I, and the
Advanced Microwave Sounding Radiometer-Earth Observing System, AMSR-E).
Calibration o f GPROF parameters is limited to data from selected regions over the
globe and few representative months from each region (McCollum and Ferraro,
2003). As DA05 has shown a single global set o f parameters may be adequate for use
over different regions, as long the calibration data come from a representative sample.
Here we study the seasonal analogue o f algorithm calibration.
Three regions from central Africa, the Amazon basin, and South Asia are
selected.
These regions represent different convection regimes with varying
frequencies o f mesoscale convective systems (MCSs) and thunderstorm activities.
Three relatively wet seasons are selected for investigation for each o f the region.
These are September-October-November (SON), December-January-February (DJF),
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and March-April-May (MAM). For the Indian region MAM, JJA and SON will also
be referred to as pre-monsoon, monsoon, and post-monsoon seasons, respectively.
For each region two sets o f calibration parameters are derived.
parameters is derived from data coming from each season.
The first set o f
The second set o f
parameters is derived by combining data from all months. Parameter sets from both
calibration scenarios are applied to the TMI dataset o f each season to retrieve PM rain
rates. The TMI estimates are then compared against corresponding PR rain estimates
(TRMM nomenclature 2A25) to derive error statistics. A third investigation scenario
is to apply parameters estimated from one season to another within the same region.
This investigation explores the data sample representativeness issue in the calibration.
The three-month definition o f seasons used herein might not be the best way
for investigating seasonal variations in PM calibration, as precipitation characteristics
o f one season could overlap with another. Thus, one might consider calibration on a
monthly basis.
But even this may not work for regions like Amazon where the
characteristics o f the rain producing systems could reverse in a matter o f weeks (e.g.
Williams et al., 2002, Carvalho et al., 2002, Petersen et al., 2002).
This requires
incorporating flow regime information, which is left for further research. Here, as a
first step, we use the conventional season definition. The above constraints should be
kept in mind while assessing the results o f seasonal calibration differences. The paper
is structured as follows. The next section presents the study region and data.
section 3 we will summarize the DA05 algorithm architecture.
In
In section 4 we
present and discuss our results. Conclusions are offered in section 5.
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Study regions and data
Three regions are selected for this study; these are: Central Africa (AFC)
ranging from 15°S to 5°S and 15°E to 30°E; Amazon (AMZ) from 15°S to 5°N, and
65°W to 40°W; and South Asia (SAS) from 15°N to 25°N, and 75°E to 100°E. Figure
3.1 shows the location o f these regions.
These regions range from the major
continental convective regime o f AFC to the more maritime type regime o f SAS (e.g.
Mohr and Zipser (1996); Manohar et al., 1999; Toracinta and Zipser, 2001; Petersen
and Rutledge, 2001). The AFC region is convectively active with exceptionally high
lightning activity. On the other hand, the SAS region has more maritime type
convection, particularly during the monsoon season, and is characterized by less
frequent lightning and less vigorous convection. The Amazon region lies in between
the two regions. It may behave one way or the other based on the season, and shows
different characteristics even within the same season depending on flow regime
conditions (e.g. Williams et al., 2002; Carvalho et al., 2002; Petersen et al., 2002).
There are differences in the convective activity from one season to the other within
the same region. For instance, all three regions have enhanced convective activity
during the respective pre-monsoon season and suppressed convection during the
respective post-monsoon season (e.g. Mohr and Zipser, 1996; Manohar et al., 1999;
Toracinta and Zipser, 2001; Petersen and Rutledge, 2001).
The TRMM-PR rain rate and rain type products (2A25 and 2A23 TRMM
product nomenclatures) were used to calibrate the PM algorithm applied to the TMI
channel brightness temperature observations (TRMM product nomenclature 1B11).
Water surfaces and coastal pixels were identified on the basis o f surface types
identified by the TRMM product 2A12 and were excluded from the analysis. Each
dataset was remapped to a common 0.1° x 0.1° resolution grid. The PR rain rate for a
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given pixel is derived from the vertical averaging between 1 and 3 km height. For
AFC and AMZ calibration data come from the years 2000 and 2001, while validation
data are from 2002. For the SAS region the calibration data is from 2000, 2001 and
2002, while validation data come from 2003 and 2004. This was necessary to acquire
adequate data sample over SAS, which is associated with less land surface
background than the other two regions.
Algorithm description
The algorithmic structure for PR-based calibration procedure proposed by
DA05 for estimating rainfall from TMI brightness temperatures is used here without
changes.
In this section we just summarize the main components o f DA05: (i)
selection o f the most appropriate passive microwave channel over a given region; (ii)
delineation o f rain areas and classification o f precipitation into Convective and
Stratiform (C/S) rain types; and (iii) use o f the probability matching method to match
PR rain rate and TMI PM data; and (iv) selection o f the optimal brightness
temperature-rain rate relationship for each rain type. Calibration and rain retrieval is
performed at the nominal grid resolution o f 0.1 x 0.1 deg.
DA05 reported that 37-GHz is the channel with the least uncertainty in passive
microwave-rain rate relationship for the tropical convective systems.
Thus, this
channel is used in the current investigation. The standard deviation o f an 85-GHz
brightness temperature array surrounding a TMI pixel, and the 85-GHz Polarization
Corrected Temperature (PCT— Spencer et al. 1989) o f that pixel are used as
predictors for rain area delineation. These predictors are regressed against binary PRderived rain/no-rain classification data. The model for C/S classification is a modified
version o f Grecu and Anagnostou (2001). It is a multi-linear regression involving
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seven parameters extracted from the different PM channels. The reference data used
for C/S calibration come from the PR-2A23 rain type product.
The probability
matching technique is used to derive brightness temperature-rain rate (Tb-RR)
relationships. Probability matching is applied separately for convective and stratiform
rain types.
On the basis o f probability matching the Tb-RR relationship for the
stratiform rain regime is defined an exponential model o f the following form:
RR = a0EXP(-(Tb - a xf / 2 a 22).
(3.1)
while, for the convective case linear regression is applied:
RR —bo + biTb
(3.2)
Parameters ao, ai, a2 bo and bi are the regression coefficients determined through
calibration. Figure 2 shows plots o f the matched brightness temperature and rain rates
for the three study regions overlaid with the fitted regression lines. The stratiform case
is clearly non-linear, while a linear fit seems to be reasonable for the convective case.
Seasonal calibration
This section investigates algorithm performance associated with seasonal
calibration versus the all-season calibration parameters.
Three seasons, each
consisting o f three calendar months, are defined for each region. For AFC and AMZ
these are September-October-November (SON), December-January-February (DJF),
and March-April-May (MAM). And for the SAS region these are MAM, JJA and
SON.
Two calibration strategies are defined to examine the significance o f seasonal
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calibration. In the first scenario, the algorithm is calibrated separately in each season.
In the second scenario all available data for that region are used to derive a common
(all-season) parameter set. The two parameter sets are then used to derive rain rates in
the validation dataset for each season and region. Results are compared against PR
rain rates to study the significance o f seasonal calibration for the three different
regions.
Algorithm evaluation is based on the following statistics: linear correlation
coefficient, efficiency score {Eff), Heidke Skill Score (HSS), and Bias.
HSS is a
measure o f correspondence between the estimate and the reference (see for example
Bamstone, 1992, and Conner and Petty, 1998).
The Efficiency {Eff) and Bias
statistics are defined as:
Eff = X - VAR(Error)
VAR(PR)
(3.3)
SUM {PM)
Bias = --------------SUM{PR)
(3.4)
where, PR is the PR-2A25 rain rates, while PM is the corresponding passive
microwave estimate from the various algorithms, and Error is the PM-PR difference.
Heidke Skill Score, HSS (Heidke, 1926), is computed based on the
contingency Table 2. elements from the following expression:
H S S = ------------ 2 -(A -D - B - C ) -----------(A + C) • (C + D) + (A + B) •(B + D)
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Contingency Table is a two-dimensional matrix where each element counts the
number o f occurrences in which the PR and corresponding PM estimates exceeded or
failed to reach a certain rain rate threshold. The Table, elements are defined as: APM and PR estimates exceeded the threshold; B-PM exceeded the threshold but PR
not; C-PM did not reach the threshold but PR exceeded it; and D-PM and PR did not
reach the threshold. HSS combines the effects o f probability o f detection, false alarm
rate and occurrences by chance. Thus, it is a better measure as compared to using just
probability o f detection and false alarm rate. Here HSS is used in two ways. First,
scalar values o f HSS are used for assessing the algorithm’s rainfall detection ability.
Second, one-dimensional (ID ) and two-dimensional (2D) plots o f HSS values at
different rain rate thresholds, as described in Conner and Petty (1998), are presented.
Below we present results by region.
a) AFC
In AFC we compare results for three seasons: SON, DJF and MAM. Figures
3.3 and 3.4 present results in terms o f ID- and 2D-HSS plots. The 2D-HSS plots in
Figure 3.3 do not show any significant difference between the seasonal (left panels)
and the all-season calibration (right panels). This is more apparent by the 1D-HSS
plots o f Figure 3.4, which shows close agreement in the HSS performance o f seasonal
and all-season calibrations.
Table 3.1a summarizes all statistical comparisons. In
this Table “szn” represents calibration based on the specific season’s data while “all”
stands for the all-season calibration. As noted there are no significant differences
between the statistics for the seasonal and all-season calibrations.
We also investigate the effect o f using parameters set from one season to
another.
Figure 4d and Table 3.1b compare the effect o f using SON and MAM
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calibration parameters on the validation data set from DJF. Figure 3.4d shows notable
differences in rain rates above 10 mm/hr, estimates with SON and MAM parameters
have lower HSS values as compared to using DJF parameters. Table 3.1b also shows
that the E ff statistics is reduced by 24% and 7% as a result o f using SON and MAM
parameter sets, respectively. There is also a drop in the correlation coefficients for
SON and MAM relative to DJF. MAM also exhibits slightly higher bias.
Although there are not significant differences in terms o f seasonal calibration,
Figures 3.3 & 3.4 and Table 3.1a show that there are significant differences in terms
o f the PM algorithm performance among the different seasons. The best performance
is observed during SON. Note that in the 1D-HSS plot o f Figure 3.4 the minimum
HSS value for SON is above 0.4, while it falls below 0.2 for the other seasons. The
E ff statistics for SON exceeds those o f DJF and MAM by 7% and 42%, respectively.
b) SAS
The results for the SAS region are similar to what we have observed for the
AFC region. Figures 3.5 & 3.6 present the 2D- and 1D-HSS plots for this region,
while error statistics are summarized in Table 3.2a. There are no significant
differences in the algorithm performance from using seasonal versus annual
calibration parameters. The only observed difference is a 13% decrease in Eff score
for the MAM season as a result o f using an all-season calibration. Figure 3.6d and
Table 3.2b compare the effect o f using pre- and post-monsoon parameters on the
validation dataset o f the monsoon season. Using the post-monsoon season calibration
parameters on the monsoon season does not seem to bring about any significant
change. However, the pre-monsoon season calibration shows decrease in HSS for
rain rates above
7 mm/hr (Fig.3.6d).
Table
3.2b
also
shows
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significant
underestimation for the pre-monsoon calibration where bias doubles.
This
underestimation is a result o f using parameters derived from a convectively active
season, where there are more direct relations between ice aloft and surface rain rates,
to the monsoon season where there is reduced ice aloft but increased surface rain
rates.
Differences are also presented in terms o f the algorithm performance among
the different seasons. However, the differences in this region are not as pronounced
as what was observed for the AFC region. Relatively better correspondence between
PR and PM algorithm estimates are observed during the pre-monsoon and post­
monsoon seasons than during the monsoons season.
c) AMZ
Figures 3.7 & 3.8 show the 2D-HSS and 1D-HSS plots for AMZ, while error
statistics are summarized in Table 3.3a. Similarly to the other two regions, we note
insignificant algorithm performance differences between using seasonal and annual
calibration parameters. The use o f SON and MAM parameters on the summer season
data shows that MAM calibration is as good as the summer calibration itself, except
for the slightly higher bias (see Fig.3.8d and Table 3.3b). On the other hand, SON
calibration parameters do not work as well in the summer season, particularly in rain
rates above 10 mm/hr. However, the differences are still small in this region.
Again we show differences in the performance o f the algorithm across the
different seasons. The best correspondence between PM estimates and PR rain is
observed during SON. It has relatively higher HSS values, particularly for rain rates
above 10 mm/hr. This could be observed from the 1D-HSS plot (Fig.3.7), where HSS
values for SON fall below 0.4 for rain rates over 20 mm/hr, while this threshold is
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about 10 mm/hr for DJF. The ^ s t a t i s t i c for DJF is slightly higher than the others.
However, the HSS plots show that SON performs better. MAM exhibits the worst
performance with lower values o f the CC, Eff, and HSS statistics. Note also that the
2D-HSS plot for MAM has six gray shades, while those o f SON and DJF have seven
shades.
Discussion
Results presented in the previous section show that algorithm calibration for
individual seasons might not be necessary.
It seems that one set o f parameters,
derived from a data sample representative o f all the seasons, would be sufficient.
Different factors may have contributed to this result. First, the three-month seasons
are defined based on calendar months. They may not be well defined in terms o f
meteorological factors— i.e., there could be overlaps between successive seasons.
Thus, one three-month season may share some characteristics with the preceding or
following season. Another factor is that the selected boxes may not be homogenous
for a given season. For instance, the AMZ box behaves differently during different
parts o f the summer seasons (Williams et al., 2002; Carvalho et al., 2002; Petersen et
al., 2002). The SAS box is made larger in order to have enough data sample. But
according to Manohar et al., (1999), the occurrence o f thunderstorms during 12
months is bimodal over the southern part o f the box (over India), while it is more
unimodal over the northern part o f the box. Another factor could be that a three-moth
season might not be appropriate for such analysis.
We may need to consider
calibration on a monthly basis. But even this might not work for regions like AMZ
where the characteristics o f the rain producing system reverse in a matter o f weeks.
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In such cases one would need to incorporate flow regime information into the
retrieval.
Although there are no significant differences in the algorithm performance
between seasonal and annual calibration, the application o f parameter sets determined
from one season to another may not be appropriate. This is particularly true for the
AFC and SAS regions (see Fig.3.4d, Fig.3.6d, Table 3.1b, and Table 3.2b). These
effects are results o f differences in the convective system characteristics associated
with different seasons o f a same regioa We will discuss these differences briefly
later in this section.
The AMZ box behaves differently than the other two regions in
that the SON and AMA calibrations perform similarly with the DJF calibration in DJF
validation data (Fig.3.8 and Table 3.3b). Actually, the SON calibration was found to
perform slightly better than the DJF calibration in the rain rate range o f 8 to 12 mm/hr
(Fig.3.8d).
An interesting observation is that the performance o f the PM rain retrieval
algorithm varies across the different seasons. This shows that, despite the overlaps
and heterogeneities discussed above, the conventional seasons used here have their
own specific characteristics. The significance o f these differences varies from region
to region. The most significant interseasonal difference is observed over the AFC
box, while the least difference is over the SAS box. The AMZ box is somewhat inbetween the two. For AFC, the best performance is observed during SON, and the
worst performance is during MAM. The extreme performances o f the two seasons
correspond to significant differences in frequencies o f mesoscale convective systems
(MCSs) and accompanying lightning activities.
Toracinta and Zipser (2001) have
shown that for the AFC box there is significantly higher lightning activity during
SON than MAM.
The lightning activity during SON is even more than that during
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the summer season (Toracinta and Zipser, 2001; Petersen and Rutledge, 2001). The
lightning activity during DJF is slightly more than the activity during MAM.
The
frequency o f MCSs is also much higher during October as compared to April and
January, and that o f January is slightly more frequent than April (Mohr and Zipser,
1996).
For the SAS box there is more lightning activity dining the pre-monsoon
season (MAM) as compared to both monsoon and post-monsoon seasons (Manohar et
al., 1999; Toracinta and Zipser, 2001). The lightning frequency during summer is
higher than dining the post-monsoon season (Manohar et al., 1999; Toracinta and
Zipser, 2001; Petersen and Rutledge, 2001). The MCSs also show a similar pattern
(Mohr and Zipser, 1996). The seasonal differences in lightning activity and MCSs
frequency are not as pronounced as those observed for the AFC box. Consistently,
the differences in the performance o f the different seasons for the SAS box are found
to be not as significant as those for the AFC box. The performance o f the different
seasons over the AMZ box is somewhere between that o f AFC and SAS. Similar to
AFC, the best performance is observed during SON, and the least performance during
MAM. Again the differences in algorithm performance correspond to differences in
convective intensity as measured by the frequency o f MCSs and lightning activity.
The SON season has more frequent MCSs and more lightning counts than the other
two seasons (Mohr and Zipser 1996; Toracinta and Zipser, 2001; Petersen and
Rutledge, 2001).
Finally, we also observe differences in the performance o f the algorithm
among the three different regions. Overall comparison shows best performance for
the AFC box, followed by AMZ and SAS, which corresponds to differences in the
convective activities o f the three regions.
This confirms the understanding that
scattering based overland PM rain retrieval algorithms perform better over regions o f
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intense convection dominated by ice formation and lightning, where there is stronger
correspondence between ice aloft and surface rain rate.
Conclusions
The objective o f this research has been to investigate the benefits o f using
calibration parameters specific to a given season versus using one set o f parameters
for the whole year. A previously developed algorithm (Dinku and Anagnostou, 2005)
has been used for this study. This algorithm uses PR to calibrate DA05 algorithm that
uses TMI multi-channel observations for overland rain retrieval. Three regions in the
tropics, with different convective characteristics, were selected to facilitate our
investigation. These regions come from central Africa, South Asia, and the Amazon
basin.
For each region three relatively wet seasons are selected.
These are the
respective summer seasons o f each region and the two seasons preceding and
following the respective summer season.
Two types o f comparisons were undertaken.
In the first case calibration
parameters derived for each season and all-seasons combined were used to estimate
rainfall rates in the validation dataset. Difference statistics were evaluated for each
season by comparing the retrieved rain rates to PR rain estimates.
In the second
comparison, parameter sets from MAM and SON were applied to the validation
dataset from the summer season and compared to the calibration parameter o f the
summer season. Comparisons o f individual season calibrations with the all-season
calibration did not show any significant differences. This has partly been attributed to
the inhomogeneity o f the conventional three-month seasons and some o f the selected
regions. The application o f one season’s parameters sets to another has been found to
reduce the accuracy o f the retrieval, but the degree o f reduction in accuracy varies by
72
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region.
In AFC the random error increased by 24% as a result o f using SON
calibration parameters on the summer data. In SAS, bias doubles when pre-monsoon
season calibration parameters are applied to the validation dataset over the monsoon
season. No significant effect was observed over Amazon.
The performance o f the PM algorithm with respect to PR has been found to
vary among the different seasons for all regions. In AFC, the best agreement between
PM estimates and PR rain rates are observed during SON, while the least performance
is during MAM. The pre-monsoon season performs better in SAS region. In Amazon
region the MAM calibration performs the worst. However, the difference between
SON and DJF is not significant.
Calibration on the basis o f conventional three-month seasons did not show
significant differences in comparison with annual calibration. This is a useful finding.
However, this does not rule out seasonal calibration differences.
More detailed
investigation, on monthly basis, could reveal some differences. This would be one o f
the follow ups to this research. It has been mentioned that even monthly calibration
might not bring about a big differences for areas like Amazon where different rain
characteristics are observed within a matter o f weeks. In such cases flow information
may be used in order to determine the convective regimes. Another future direction
o f the current investigation would be to go outside the tropics, where more significant
seasonal differences are expected.
Acknowledgements'. This study was supported by NASA’s Global Water and Energy
Cycle program (NAG5-11527). Dr. Jeffrey McCollum o f NOAA/NESDIS provided
the V6 TRMM 2A-12 precipitation fields. TRMM data were provided by NASA
DAAC.
73
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References
Bamstone, A. G., 1992: Correspondence among the correlation, RMSE, and Heidke
forecast verification measures; refinement o f the Heidke score. Weather and
forecasting, 7, 699-709.
Carvalho L.M.V., C. Jones and M. A. F. Silva Dias (2002): Intraseasonal large-scale
circulations and mesoscale convective activity in tropical South America during
TRMM-LBA
campaign.
.
J.
Geoephys.
Res.,
107(D20),
doi: 10.1029/2001JD000745.
Conner, M. D., and G. R. Petty, 1998: Validation and intercomparison o f SSM/I rainrates retrieval methods over the continental Unites States. J. Appl.
Meteor.,37,
679-700.
Dinku T., and E.N. Anagnostou, 2005: Regional Differences in Overland Rainfall
Estimation from PR-Calibrated TMI Algorithm. J. Appl. Meteo., 44(2), 189-205.
Grecu M. and E. N. Anagnostou, 2001: Overland Precipitation Estimation from
Passive Microwave O bservations.. J. Appl. Meteor., 40, 1367-1380.
Manohar G. K., S. S. Kandalgaonkar, and I. R. Tinmaker (1999): Thunderstorm
activity over India and the Indian southwest monsoon. J. Geoephys. Res., 104(D4),
4169-4188
McCollum, J. R. and R. R. Ferraro, 2003: Next generation o f NOAA/NESDIS TMI,
SSM/I, and AMSR-E microwave land rainfall algorithms. J. Geoephys. Res.,
108(D8),doi:10.1029/2001JD001512.
Mohr, K. I. and E. J. Zipser, 1996: Mesoscale convective systems defined by their 85GHz ice scattering signature: size and intensity comparisons over tropical oceans
and continents. Mon. Weather Rev., 124, 2417-2437.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Petersen, W.A., and S.A. Rutledge, 2001: Regional variability in tropical convection:
observations from TRMM. J. Clim., 14, 3566-3586.
Petersen, W.A., S.W. Nesbitt, R. J. Blakeslee, R. Cifelli, P. Hein, and S.A. Rutledge,
2002: TRMM Observations o f Intraseasonal Variability in Convective Regimes
over the Amazon. J. Clim. 15,1278-1294
Toracinta, E. H. and J. Zipser, 2001: Lightening and SSM/I-Ice-scattering mesoscale
convective systems in the global tropics. J. Appl. Meteo., 40, 983-1002.
Williams E. et al., (2002): Contrasting convective regimes over Amazon: Implication
for
cloud
electrification.
J.
Geoephys.
Res.,
doi: 10.1029/2001JD0003 80.
75
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107(D20),
List o f Tables
Table 3.1a: Validation statistics for the AFC study region comparing calibrations for
each season vs. using all-season calibration parameters for each season, “szn”
represents seasonal calibration, while “all” stands for all-season calibration
Table 3.1b: Validation statistics for the AFC study region comparing summer
season’s calibration vs. using calibration parameters lfom the other two
seasons; ‘son’ and ‘mam’ stand for SON and MAM calibrations
Table 3.2a: As in Table 3. la, but for the SAS region
Table 3.2b: As in Table 3. lb , but for the SAS region
Table 3.3a: As in Table 3.1a, but for the AMZ region
Table 3.3b: As inT able 3.1b, but for the AMZ study region
76
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Table 3.1a: Validation statistics for the AFC study region comparing calibrations for
each season vs. using all-season calibration parameters for each season, “szn”
represents seasonal calibration, while “all” stands for all-season calibration.
SON-szn
SON-all
DJF-szn
DJF-all
MAM-szn
MAM-all
HSS
0.75
0.77
0.77
0.77
0.71
0.71
cc
0.71
0.70
0.70
0.68
0.66
0.66
Eff
0.44
0.42
0.41
0.40
0.31
0.32
Bias
0.98
1.05
1.07
1.04
1.05
1.05
Table 3.1b: Validation statistics for the AFC study region comparing summer
season’s calibration vs. using calibration parameters from the other two seasons; ‘son’
and ‘mam’ stand for SON and MAM calibrations.
DJF-szn
DJF-son
DJF-mam
HSS
0.77
0.77
0.76
CC
0.70
0.64
0.67
Eff
0.41
0.31
0.38
Bias
1.07
0.99
1.06
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Table 3.2a: As in Table 3. la, but for the SAS region
MAM-szn
MAM-all
JJA-szn
JJA-all
SON-szn
SON-all
HSS
0.70
0.70
0.69
0.69
0.70
0.70
CC
0.69
0.69
0.64
0.64
0.65
0.65
Eff
0.40
0.35
0.35
0.37
0.37
0.35
Bias
1.00
1.05
0.94
0.96
1.07
1.03
Table 3.2b: As in Table 3. lb, but for the SAS region
JJA-szn
JJA-mam
JJA-son
HSS
0.69
0.67
0.68
CC
0.64
0.65
0.64
Eff
0.35
0.40
0.33
Bias
0.94
0.88
1.06
78
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Table 3.3a: As in Table 3.1a, but for the AMZ region
SON-szn
SON-all
DJF-szn
DJF-all
MAM-szn
MAM-all
HSS
0.74
0.73
0.72
0.71
0.66
0.66
CC
0.71
0.73
0.74
0.73
0.69
0.68
Eff
0.41
0.45
0.49
0.47
0.38
0.40
Bias
1.01
0.98
1.04
1.07
1.03
0.98
Table 3.3b: As in Table 3.1b, but for the AMZ study region
DJF-szn
DJF-son
DJF-mam
HSS
0.72
0.71
| 0.71
CC
0.74
0.71
0.73
Eff
0.49
0.42
0.47
Bias
1.04
1.02
1.11
79
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List o f figures
Figure 3.1:
The study region.
Figure 3.2:
Brightness temperature (T37) versus rain rate values o f common
exceedance probabilities (quantiles) overlaid by a fitted regression line.
Top, middle and bottom panels are for AFC, SAS and AMZ regions,
respectively. Left panels are for stratiform rain and right panels for
convective rain type
Figure 3.3:
2D-HSS plots comparing seasonal and all-season calibrations for the
AFC region. The left panels are for individual season calibration, while
right panels are for the all-season calibration.
Figure 3.4:
1D-HSS plots for the AFC region. Panels (a), (b), and (c) compare
seasonal vs. all-season calibration. Panel (d) compares using the
summer season’s own calibration vs. using calibration parameters from
the other two for summer season data.
Figure 3.5:
Same as Fig.3.2, but for SAS region.
Figure 3.6:
Same as Fig.3.3, but for SAS region.
Figure 3.7:
Same as Fig.3.2, but for AMZ region.
Figure 3.8:
Same as Fig.3.3, but for AMZ region
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20
m
3CPV0 —6 0 —5 0 —fO —3 0 —20 —10 0
20
30
Fig.3.1
81
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S tra tifo rm
PR rain[m m/hr]
C c-nvective
20
10
250
270
230
240
260
15
10
20
E
c
E
a.
□.
10
0
250
270
220
240
260
230
300
15
30
10
E
E
20
c
K
a.
250
270
290
220
T37[K]
260
T37[k]
Fig.3.2
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300
SON calib ra tio n
PM Rain [ m m / h r ]
a ll-s e a s o n calib ra tio n
20
30
10
20
30
PR rain[mm/hr]
PR rain[mm/hr]
DJF calib ra tio n
a ll- s e a s o n calibration
40
PM Rafn[nnm /hr]
10
20
30
10
20
30
PR rain[mm/hr]
PR rain[mm/hr]
MAW calib ra tio n
a ll- s e a s o n calibration
PM R a fn[m m /h r]
10
10
20
10
30
PR rain[mm/hr]
20
30
PR rain[mm/hr]
F ig .3 .3
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0.8
0.8
DJF calibration
□II—season calibration
all—season calibration
HSS
SON calibration
0
20
10
0
30
20
10
MAM calibration
DJF calibration
all—season calibration
SDN calibration
30
HSS
MAM calibration
o.+
0
0
30
10
20
10
R a i n [m m /h r ]
Rain [m m /h r ]
Fig. 3.4
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30
MAW calib ra tio n
10
10
10
20
a ll-s e a s o n calib ra tio n
10
30
20
30
PR rain[mm/hr]
PR ram[mm/hr]
JJA calib ra tio n
a ll- s e a s o n calib ra tio n
20
10
30
20
30
PR rain[rnrn/hr]
PR rain[mm/hr]
SON calibration
a ll-s e a s o n ca lib ra tio n
20
10
30
20
30
PR ram[mm/hr]
PR rain[mm/hr]
Fig.3.5
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MAM calibration
JJA calibration
all—season calibration
all—season calibration
co
in
i
tn
I
0
20
10
0
30
20
10
0.8
SON calibration
JJA calibration
all—season calibration
MAM calibration
SON calibration
0.2
0
20
10
o
30
Rain [mm/hr]
20
10
Rain [mm/hr]
Fig. 3.6
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30
SO N c a l i b r a t i o n
PM Rain
a ll-s e a s o n calib ra tio n
10
20
10
30
20
30
PR rarn[mm/hr]
DJF calib ra tio n
a ll- s e a s o n calibration
PM R a in fm m /hr]
PR rain[mm/hr]
10
20
30
10
20
30
PR rain[mm/hr]
MAM calib ra tio n
a ll- s e a s o n calibration
40
PM R a in [m fn /h r]
PR nain[mm/hr]
10
20
PR
30
10
20
30
PR ram[rnm/hr]
ram [m F T i/hr]
F ig .3 .7
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SON colibration
DJF calibration
all—season calibration
all—season calibration
w
iin
m
ifi
X
0
20
10
0.1
30
0
30
10
o.s
MAM calibration
DJF calibration
all—season calibration
SDN calibration
MAM calibration
eft
ni
in
x
0
20
10
0
30
Rain [m m /h r ]
20
10
Rain [m m /h r ]
Fig.3.8
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30
IV.
TRMM Calibration of SSM/I Algorithm for Overland
Rainfall Estimation
Abstract
This paper extends the PR-TMI overland rain retrieval algorithm from Chapter 2 for
use with Special Sensor Microwave Imager (SSM/I) observations.
In Chapter 2,
Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) rainfall
estimates were used to calibrate Microwave Imager (TMI) retrieval.
Regional
differences in PR-based TMI calibration were investigated by testing the algorithm
over four geographic regions consisting o f Africa, Northern South America
(containing the Amazon basin), continental US, and South Asia. In this chapter we
demonstrate the performance o f PR-TMI technique applied on SSM/I data over three
o f the regions (Africa, Amazon and South Asia). Two approaches are investigated for
using PR rainfall products to calibrate the algorithm parameters. In the first approach,
TMI channels are remapped to the spatial resolutions o f the corresponding SSM/I
channels; then PR is used to calibrate the rain retrieval on the remapped TMI data. In
the second approach, the PR-based TMI algorithm calibration is performed at coarser
(0.25 deg) resolution. To asses the quality o f algorithm estimates with respect to PR,
rainfall fields derived from PR-TMI applied to SSM/I observations (using parameters
determined from both approaches) are compared against matched (within ±15-min o f
satellites’ overpass time difference) PR surface rain rates. Calibration data come from
the wet seasons (January to March) o f 2000 and 2001, while validation data cover a 5month period (December-April) o f 2002, 2003 and 2004. In comparison with the
latest version o f the Goddard Profiling (GPROF) algorithm rain estimates, the current
algorithm shows significant improvements in terms o f both bias and random error
89
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reduction. The paper also shows that rain estimation based on TMI observations is
associated with lower error statistics compared to the corresponding SSM/I retrievals.
Introduction
Since the early SSM/I retrievals o f Spencer et al. (1989) and Olson (1989), a
number o f algorithms have been developed, few o f which have been for overland rain
estimation. The widely known SSM/I overland rain retrieval algorithms are those o f
NOAA/NESDIS
(National Oceanic
and
Atmospheric
Administration-National
Satellite, Data, and Information Service) algorithm (Grody 1991; Ferraro and Marks
1995; and Ferraro 1997) and the Goddard scattering algorithm (GSCAT) developed at
Goddard Space Flight Center (GSFC) o f the National Aeronautic and Space
Administration (NASA) by Adler et al. (1994). Conner and Petty (1995) described
additional techniques and made validation comparisons with the NOAA/NESDIS and
GSCAT algorithms.
The most recent version o f the operational overland rainfall
algorithms is that o f McCollum and Ferraro (2003). This algorithm is calibrated using
TRMM-PR and is used to produce the latest versions o f global TRMM, SSM/I, and
Advanced Microwave Sounding Radiometer-Earth Observing System (AMSR-E) rain
products.
In this chapter we present an SSM/I overland rain retrieval that is a follow up
to the PR-TMI algorithm.
The PR-TMI algorithm uses passive microwave (PM)
observations from TRMM Microwave Imager (TMI) channels, and TRMM
Precipitation Radar (PR) rainfall estimates as reference to calibrate the algorithm
parameters. The algorithm components include: (i) selection o f the most appropriate
TMI channel for rain rate estimation over a given geographic region; (ii) delineation
o f the raining areas and classification o f rain into convective and stratiform (C/S)
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types on the basis o f multiple channel observations; and (iii) developing brightness
temperature-rain rate relationships for each rain type.
The rain estimates are
generated at a nominal 0.1-deg grid resolution.
The significance o f regional variation for the PR-based TMI algorithm
calibration was investigated for the PR-TMI algorithm over four different geographic
regions; i.e., central Africa (15°S to 5°N and 10°E to 40°E), Amazon basin (15°S to
5°N, and 70°W to 40°W), USA (22°N to 40°N, and 120°W to 75°W), and South Asia
(22°N to 34°N, and 74°E to 99°E). It was found that the best single TMI channel for
overland rain retrieval is 37 GHz for the first three regions and 85 GHz for South
Asia. Regional calibration was found to be important for this region, while global
calibration (i.e., constant parameters) sufficed for the other three continental regions.
The performance o f the PR-calibrated TMI algorithm was assessed with respect to the
latest (Version 6) TRMM-2A12 surface rain estimates.
It was shown to perform
better than TRMM-2A12 with the major improvement being the decrease in random
error (and corresponding increase in correlation), which was about 24%, 36%, 57%
and 165% for USA, Africa, Amazon, and South Asia, respectively.
In this study, the PR-TMI algorithm is extended to develop a PR-based SSM/I
algorithm calibration at a coarser (0.25-deg) resolution. This is particularly important
for two main reasons: (i) SSM/I has a historical data record going back to 1987; and
(ii) better sampling due to the more frequent overpasses (nominally two or three
satellites in orbit) and wider swath (1400 km versus the 760 km o f TMI). The use o f
TRMM data to calibrate rain algorithms applied on SSM/I observations is one o f
TRMM
science objectives,
i.e.,
serve as
a “flying rain
calibration/validation o f other sensors (Simpson et al., 1988).
gauge”
for the
Our approach is
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analogous to that o f McCollum and Ferraro (2003). For assessment, our algorithm
performance is compared to the McCollum and Ferraro (2003) algorithm.
PR-based calibration o f SSM/I rain algorithm has certain challenges.
The
major problem is the temporal and spatial collocation o f data from PR and SSM/I
sensors. The two sensors, being onboard different satellites, have varying observation
geometries, spatial coverage and overpass times. As a result, to achieve adequate
samples for calibration/validation purposes requires compiling several years o f
coincident TRMM and SSM/I data.
To overcome this problem, two indirect
approaches are investigated. The first involves remapping the TMI channels to the
spatial resolutions o f the corresponding SSM/I channels, and consequently use PR
rainfall estimates to calibrate the parameters o f the retrieval applied on the remapped
data.
Rain retrieval is performed at 0.25° resolution, which is representative o f
SSM/I low resolution observations. The second approach involves just calibrating the
algorithm at coarser grid resolution o f 0.25°.
Parameters obtained from the two
approaches are applied to actual SSM/I data to produce rain rates at 0.25° resolution.
These approaches eliminate the need for directly matching data from the two satellite
platforms.
In the following section, the study region and data used in this research are
presented. In section 3 we discus the algorithm architecture, and in section 4 we
present algorithm assessment and comparison with GPROF-based SSM/I rainfall
products. Summary and conclusions are discussed in section 5.
Study regions and data
Three study boxes are selected from central Africa (AFC), 15°S to 5°N and
10°E to 40°E; Amazon basin (AMZ), 15°S to 5°N, and 65°W to 40°W; and South Asia
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(SAS), 10°N to 26°N, and 75°E to 110°E, are selected for this study. Figure 4.1 shows
the location o f the selected regions. These regions range from the major continental
convective regime o f AFC to the more maritime type regime o f SAS (e.g. Mohr and
Zipser (1996); Manohar et al., 1999; Toracinta and Zipser, 2001; Petersen and
Rutledge, 2001).
Water surfaces and coastal pixels falling in the region were
excluded from the analysis using surface classification from TRMM product 2A12.
The TMI passive microwave data and coincident rain rates (PR-2A25) and
rain type (PR-2A23) products are used to drive calibration parameters. The TRMMcalibrated algorithm is then applied to the SSM/I brightness temperatures for rain
retrieval.
The SSM/I surface rain rates derived from the NASA/GSFC Goddard
profiling algorithm Version 6 (GPROF6) are used for comparison with the current
algorithm. Each dataset was remapped to a common 0.25°x0.25° resolution grid. The
PR rain rate for a pixel in the grid is derived from a vertical averaging between 1 and
3 km height. TRMM data from January to March for the years 2000 and 2001 are
used for calibration. For validation, we use matched datasets o f TRMM-PR rainfall
products and SSM/I sensor retrievals at the algorithm grid resolution (0.25°).
Matching is performed when a TRMM orbit is crosses the study region within +15
minutes o f an SSM/I overpass. Matched TRMM-SSM/I orbits found within the 30minute window are 191, 263, and 239, for AFC, AMZ and SAS, respectively. To
achieve adequate sample size for determining error statistics we compiled data from a
long (15-month) period comprising months o f December through April from 2002,
2003, and 2004.
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Algorithm Description
The objective o f the current algorithm formulation is to extend the PR-TMI
PR-calibrated TMI rain retrieval to SSM/I observations. In this section we summarize
the architecture o f PR-TMI algorithm, and describe the modifications made to adopt
SSM/I observations. The algorithm consists o f the following major components: (i)
selection o f the most appropriate passive microwave channel over a given region; (ii)
delineation o f rain areas and classification o f precipitation into Convective and
Stratiform (C/S) rain types; and (iii) selection o f the optimal brightness temperaturerain rate relationship for each rain type.
As found by PR-TMI, in the African region the 37-GHz is the channel with
the least uncertainty in passive microwave-rain rate relationship.
The standard
deviation o f an 85-GHz brightness temperature array surrounding a TMI pixel, and
the 85-GHz Polarization Corrected Temperature (PCT— Spencer et al. 1989) o f that
pixel are used as predictors for rain area delineation. These predictors are regressed
against binary PR-derived rain/no-rain classification data. The model for C/S
classification is also a multi-linear regression type involving seven parameters
extracted from the different passive microwave channels. The reference data used for
C/S calibration come from the PR TRMM-2A23 rain type product. The probability
matching technique is used to derive brightness temperature-rain rate (Tb-RR)
relationships. As in PR-TMI, probability matching is applied separately in convective
and stratiform rain types. The Tb-RR relation for the stratiform rain regime is defined
as an exponential model o f the following form:
(4.1)
RR = a0E X P ( - ( T b - ai)2 / 2 a 22).
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For the convective case linear regression is applied:
RR = b0 + b{Tb
(4.2)
Parameters ao, ai, a2 bo and bi are the regression coefficients determined through
calibration. Figure 4.2 shows plots o f brightness temperature versus rain rate and the
fitted regression lines for AFC. The stratiform case is non-linear, while a linear fit
seems to be reasonable for the convective case. For further details on the various PRTMI algorithm components the reader is referred to Dinku and Anagnostou (2005).
The major challenge in applying the PR-based calibration procedure o f PRTMI on SSM/I observations is the difficulty in matching (both in space and time)
observations from the two sensors (PR and SSM/I). To circumvent this problem, two
calibration scenarios that use only TRMM data are explored. The first approach is to
map the various TMI-channel brightness temperatures to the spatial resolutions o f the
corresponding SSM/I channels.
Remapping is done so that PR can be used to
calibrate the remapped TMI data instead o f trying to match PR and SSM/I data. The
remapping procedure involves a simple distance-weighted averaging.
It produces
“SSM/I-like” brightness temperatures. Then PR is used to calibrate the “SSM/I-like”
TMI data at 0.25° grid resolution.
The computed calibration parameters are then
applied to actual SSM/I data for rain retrieval. The rationale behind this approach is
that the TMI and SSM/I frequencies are identical except for the 21.3 GHz TMI
channel that differs by ~1 GHz from the corresponding 22.23 GHz channel o f SSM/I.
After remapping, PR is used to calibrate the “SSM/I-like” TMI data at 0.25° grid
resolution. The computed calibration parameters are then applied to actual SSM/I
data.
The remapping procedure produces reasonable “SSM/I-like” brightness
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temperatures.
Figure 3 shows comparison o f the actual TMI, remapped TMI
(“ SSM/I-like”), and actual SSM/I brightness temperatures at 19 and 85 GHz for the
AFC box. The time difference between TMI and SSM/I orbits used in this figure is
about two minutes. The two images and the corresponding histograms and scatter
plots show good agreement between the remapped TMI, and actual SSM/I brightness
temperatures. The agreement is better for the higher frequency, though the scatter
plots appear to favor the lower frequency channel.
The second (and simpler) TRMM-based calibration approach involves
calibration o f the DA05 retrieval algorithm at 0.25° grid resolution (instead o f the
original 0.1° used in DA05). Here the actual PR and TMI data are used to drive the
calibration parameters at 0.25° grid resolution; there is no remapping involved. The
computed calibration parameters are then used to estimate rainfall from actual SSM/I
data at 0.25° grid resolution.
Comparison o f results from the two approaches (not presented here) has
shown that the second approach performs better than the first. The main factors for
the disappointing performance o f the remapping approach could include the low
spatial resolution o f the remapped data, and the simple averaging method used. The
remapping approach is included here just to show what does not work, and it will not
be used in further analysis.
As will be shown in Section 4, the second approach
performs better when the rain delineation and C/S classification parameters evaluated
at 0.25° are used along with the Tb-RR relationship (Eqs 4.1 & 4.2) parameters
evaluated at 0.1-deg resolution.
The present analysis indicates that calibration at
higher resolution gives better results even though the parameters are applied to lower
resolution data. The above observation is not applicable in the evaluation o f rain area
and C/S classification parameters.
This is because in the case o f regression, the
96
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transition from 0.1 to 0.25-deg grids involves consistent averaging o f both regression
parameters (i.e., brightness temperature and rain rate), while this is not the case for
rain area delineation and C/S classification. In conclusion, the rain delineation and
C/S classification parameters are computed at 0.25 deg, while the Tb-RR regression
parameters are determined from PR-calibration o f TMI at 0.1-deg resolution.
Results and discussion
This section presents validation statistics comparing SSM/I rainfall estimates
to PR surface rainfall (TRMM-2A25 V6 product). We also compare our results with
the SSM/I rainfall estimates from GPROF6 algorithm. The following statistics are
used to asses the quality o f the PM estimates with respect to PR: linear correlation
coefficient, efficiency score, bias and Heidke Skill Score (HSS). The Efficiency (Eff)
and Bias statistics are defined as:
Eff = l _VmError)
VAR(PR)
B,as = SUM (f M >
SUM (PR)
(4.4)
PR is the PR-2A25 rain rates, PM is the passive microwave (SSM/I) estimates, and
Error=PM-PR.
HSS (Heidke, 1926), is computed based on the contingency table
elements from the following expression:
HSS = -------------2 ' (A ' D B C ) -----------(A + C) • (C + D) + (A + B) ■(B + D)
97
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Contingency table is a two-dimensional matrix where each element counts the number
o f occurrences in which the PR and corresponding PM estimates exceeded or failed to
reach a certain rain rate threshold. The table elements are defined as in Table 4. 1.
HSS is a measure o f correspondence between the estimate and the reference (e.g.
Bamstone, 1992, and Conner and Petty, 1998). Here HSS is used in two ways. First,
scalar values o f HSS are used for assessing the rainfall detection ability o f the
algorithms. Second, one-dimensional (ID ) and two-dimensional (2D) plots o f HSS
values at different thresholds o f estimate and reference rain rates, as described in
Conner and Petty (1998), are presented. The results are presented for each calibration
area below.
a) AFC
Table 4.2 compares validation statistics for three PM retrievals with respect to
PR surface rainfall. ALG25 is the PR-calibrated PR-TMI algorithm with parameters
determined on the basis o f TMI data at 0.25° (~25km).
ALG10 is the same as
ALG25, but the regression parameters come directly from calibration at 0.1° (~10km)
resolution. GPROF6 is the SSM/I surface rain rates derived from the NASA/GSFC
Goddard profiling algorithm. All validation statistics show that ALG10
is
significantly better than ALG25. This shows the significance o f evaluating Tb-RR
relationship parameters at higher resolution. It is also observed that both ALG25 and
ALG10 outperform GPROF6 in all validation statistics, except HSS.
As will be
shown later, the better HSS is true only at very low rainfall (< 1 mm/hr) thresholds.
The major improvement o f ALG10 with respect to GPROF6 is the decrease in
random error (increase o f efficiency by 0.4) and bias by about 60%. The random
98
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error reduction observed here is about the same as that reported comparing PR-TMI to
GPROF6 algorithm applied on TMI data over the same region. The bias reduction on
the other hand is more significant in SSM/I data compared to TMI improvement.
Comparing TMI retrieval (from PR-TMI algorithm) with ALG10 based SSM/I
retrieval, we observe an increase o f 0.1 in correlation, and a relative increase o f 46%
and 19% in efficiency and HSS statistics, respectively. The decrease in random error
(i.e., 46% increase in efficiency) is particularly notable.
The 2D HSS plots o f Figure 4.4 compare the overall agreement between the
various PM estimates (SSM/I estimates from algorithms ALG10 and GPROF6, and
TMI estimates from PR-TMI) and PR rain products.
Better correspondence is
observed between ALG10 and PR relative to GPROF6 and PR. GPROF6 tends to
overestimate at all rain rate ranges, and the overestimation increases with rainfall
intensity. On the other hand, ALG10 shows a larger spread at higher rain rate
thresholds compared to GPROF6. Nevertheless, as shown in Table 4.2, ALGlO’s
overall variance is significantly lower than that o f GPROF6. This contradiction arises
from the fact that the contribution from the higher rain rate ( > 1 0 mm/hr) to the
overall statistics is relatively small (25%). The TMI estimates are better than both
SSM/I estimates. The 1D-HSS plot in Fig. 4.4 presents the HSS values along the
diagonal o f the 2D HSS plots.
algorithms.
This plot provides a clearer comparison o f the
It is evident that ALG10 has higher HSS than GPROF6 at rain rates
greater than lmm/hr, which contributes the most to the cumulated rainfall (90%). The
1D-HSS plot also shows the superior performance o f estimates from the higher
resolution TMI sensor. Figure 4.5 shows that the cumulative distribution function
(CDF) o f ALG10 rain rate estimates is closer to the corresponding PR-based CDF
99
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than G PR 0F6, while the CDF o f TMI estimates exhibit the best agreement with the
PR-based CDF.
Figure 4.6 shows sample images o f instantaneous rain fields derived from PR,
TMI (PR-TMI algorithm) and SSM/I (ALG10 and GPROF6 algorithms). This is the
same system shown in Fig. 4.3. The PR image shows only part o f the system because
o f its narrower swath. The PR rainfall field is at original resolution (5-km), while the
TMI and SSM/I fields are at 10-km and 25-km resolutions, respectively. The TMI
estimates exhibit rain rate patterns very similar to those o f PR. Yet the effect o f
spatial averaging is apparent in the data. The effect o f spatial averaging is even more
evident in the SSM/I estimated rainfall fields.
ALGlO’s rainfall patterns exhibit
better similarity with the PR compared to GPROF6. For the given case, GPROF6
overestimated low rain rate areas, and underestimated higher rain rate areas.
For
instance, the >16 mm/hr rain cluster is hardly visible in the GPROF6 derived rain
field, while light rain rate areas located between the maxima are estimated at higher
values compared to the other sensor estimates. Another important observation is that
the error structure o f ALG10 is less spatially correlated than GPROF6 (see Fig. 4.7).
Error being defined as the difference o f SSM/I estimates from PR. It is noted that the
spatial error correlation o f ALG10 is below 0.2 at all spatial lags, while GPROF6
drops below 0.2 at lags greater than 50 km (-0.5 deg). This spatial dependence o f
error for GPROF6 can introduce additional biases in aggregated fields at coarser
resolutions.
b) AMZ
The error statistics for this region are given in Table 4.3. Values for ALG25
are not included here because the point has already been made, and the results are
100
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similar to that o f AFC. Comparison o f ALG10 and GPROF6 shows that ALG10 has a
much better correspondence with PR.
The significant improvements are the E ff
statistics (-0.43 for GPROF versus 0.35 for ALG10) and bias (74% overestimation by
GPRPF versus 3% underestimation by ALG10).
Table 4.3 also shows significant
differences between ALG10 and TMI estimates from the PR-TMI algorithm.
The
random error decreases by 71% while the linear correlation coefficient increases by
28%. There is also a 15% increase in the HSS value. However, the TMI estimates
have slightly higher bias. Figures 4.8 and 4.9 present the HSS and CDF plots for the
AMZ box.
The overestimation by GPROF is evident from the 2D-HSS plot o f
Fig.4.8. This figure also confirms the better performance o f the TMI estimates. The
difference between ALG10 and GPROF from the 1D-HSS plot (bottom right panel o f
Fig.4.8) is moderate. TMI is much better than both SSM/I algorithms. In CDF plot o f
Fig.4.9, only GPROF stands out while the other estimates are closer to the PR curve.
c) SAS
Table 4.4 compares the error statistics. Comparisons for TMI are not included
here because the SAS box used here is significantly different from the one used in
PR-TMI. Here the box is moved away from the mountains and is made larger in
order to have enough validation data sample.
The significant difference between
GPROF and ALG10 is that ALG10 has less random error (Eff increases by 0.24) and
better HSS (increase by 0.11) as compared to GPROF. The 2D-HSS plot in Fig.4.10
shows overestimation by GPROF. The 1D-HSS plot (lower left panel o f Fig. 10)
shows better performance for ALG10 for rain rates over 5 mm/hr. However both
ALG10 and GPROF do not offer reliable assessment above rain rates o f about 15
mm/hr. The CDF plot (Fig.4.10 lower right panel) shows that ALG10 corresponds
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better with PR rain than GPROF.
Though it is clear that ALG10 is better than
GPROF, the performance o f ALG10 is relatively poor for this region as compared to
the other two regions.
Summary and Conclusions
The objective o f this research has been to calibrate SSM/I passive microwave
data using TRMM-PR rain estimates as reference.
The algorithm used here was
originally developed for TMI overland rainfall estimation.
Its parameters were
determined based on TRMM data over central Africa. A challenge o f this study has
been that SSM/I and PR sensors fly onboard two different satellite platforms with
varying field-of-view, geometry and overpass times. As a result, it is difficult to
obtain adequate data samples required for calibration. Two indirect approaches were
investigated to overcome this problem. In the first, we re-mapped TMI channel data
to the spatial resolutions o f the corresponding SSM/I channels to produce “SSM/Ilike” data. Then we calibrated the algorithm parameters using PR and the “SSM/Ilike” data at 0.25° resolution. In the second approach we did not do re-mapping, but
the original PR-TMI algorithm was recalibrated at 0.25° resolution.
Although the remapping procedure produced reasonable “SSM/I-like”
brightness temperature fields, the second approach gave much better validation error
statistics against PR. This was mainly ascribed to the coarser resolution o f the
remapped data. It is also possible that remapping o f data had some secondary effect.
Best performance was achieved when the rain delineation and C/S classification
parameters were evaluated at 0.25° and the regression parameters at 0.1° resolution.
This shows that the calibration o f the Tb-rain rate relationship may be performed at
higher resolution than the observational satellite dataset used in rain estimation. This
102
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calibration approach is particularly attractive as it does not rely on the availability o f
matched PR and SSM/I data. It can readily use TRMM-PR and TMI observations to
derive SSM/I algorithm parameters for the various tropical/sub-tropical continental
regimes and seasons.
In this paper, this is demonstrated for the summer season
convections.
Comparison with GPROF6 shows that the PR-TMI algorithm applied to
SSM/I observations may improve rain estimation error statistics. The most significant
improvements are significant decreases in both systematic and random errors. For the
AFC region there was 60% reduction in bias and an increase o f 0.4 in efficiency. For
AMZ the efficiency increased by 0.78, while bias is deceased by 0.71.
The
improvements for the SAS region are moderate but still significant (efficiency
increases by 0.24 and HSS by 0.11). We also compared our SSM/I rain estimates
with those from TMI (based on PR-TMI algorithm). The higher resolution TMI rain
rates exhibited better agreement with PR rain rates.
The most important
improvements were the decrease in random error and increase in linear correlation.
The efficiency increased by 46% and 71% for AFC and AMZ, respectively. The
increases in correlation coefficients were 0.1 and 0.18 for AFC and AMZ,
respectively. Part o f this improvement is attributed to the fact that the TMI sensor is
onboard the same satellite (TRMM) with PR, consequently it is associated with less
sensor sampling difference effects than SSM/I.
Acknowledgements: This study was supported by NASA’s Global Water and Energy
Cycle program (NAG5-11527). TRMM and GPROF6 data were provided by NASA
DAAC. SSM/I data were obtained from NASA/GHRC.
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References
Adler R. F., J Huffman, and P. R. Keehn, 1994: Global tropical rain estimates from
microwave-adjusted geosynchronous IR data. Remote Sens. Rev., 11,125-152.
Bamstone, A. G., 1992: Correspondence among the correlation, RMSE, and Heidke
forecast verification measures; refinement o f the Heidke score. Weather and
forecasting, 7, 699-709.
Conner, M. D., and G. R. Petty, 1998: Validation and intercomparison o f SSM/I rainrates retrieval methods over the continental Unites States. J. Appl.
Meteor.,37,
679-700.
Dinku T., and E.N. Anagnostou, 2005: Regional Differences in Overland Rainfall
Estimation from PR-Calibrated TMI Algorithm. J. Appl. Meteo., 44(2), 189-205.
Ferraro, R. R., and G. F. Marks, 1995: The Development o f SSM/I rain-rate retrieval
algorithms using ground-based radar measurements. J. Atmos. Oceanic Technol.,
12,755-770.
Ferraro, R. R., 1997: Special sensor microwave imager derived global rainfall
estimates for climatological applications. J. Geoephys. Res., 102,16715-16735.
Grody, N.C., 1991: Classification o f snow cover and precipitation using the Special
Sensor Microwave Imager. J. Geoephys. Res., 96, 7423-7435.
Heidke, P, 1926: Berechnung des Erfolges und der Gute der Windstarkevorhersagen
im Sturmwamungsdienst. Geogr. Ann. 8, 301-349.
Manohar G. K., S. S. Kandalgaonkar, and I. R. Tinmaker (1999): Thunderstorm
activity over India and the Indian southwest monsoon. J. Geoephys. Res., 104(D4),
4169-4188
McCollum, J. R. and R. R. Ferraro, 2003: Next generation o f NOAA/NESDIS TMI,
SSM/I, and AMSR-E microwave land rainfall algorithms. J. Geoephys. Res.,
108(D8), doi: 10.1029/2001JD001512.
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Mohr, K. I. and E. J. Zipser, 1996: Mesoscale convective systems defined by their 85GHz ice scattering signature: size and intensity comparisons over tropical oceans
and continents. Mon. Weather Rev., 124, 2417-2437.
Olson, W. S., 1989: Physical retrieval o f rainfall rates over the ocean by multispectral
microwave radiometry: Application to tropical cyclones . J. Geophys. Res., 94,
2267-2280.
Petersen, W.A., and S.A. Rutledge, 2001: Regional variability in tropical convection:
observations from TRMM. J. Clim., 14, 3566-3586.
Simpson, J., R. F. Adler and G.R. North (1988): Aproposed Tropical Rainfall
Measuring Mission(TRMM) Satellite. Bull. Amer. Met. Soc., 69(3), 278-295.
Spencer, R.W., H.M. Goodman, R.E. Hood, 1989: Precipitation Retrieval over Land
and Ocean with the SSM/I: Identification and Characteristics o f the Scattering
Signal. J. Atmos. Oceanic Technol., 6,254-273.
Toracinta, E. H. and J. Zipser, 2001: Lightening and SSM/I-Ice-scattering mesoscale
convective systems in the global tropics. J. Appl. Meteo., 40, 983-1002.
105
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List o f Tables
Table 4.1: Contingency table used for computing the Heidke skill score(HSS) PM, PR
and Rthre are passive microwave rain estimate, PR rain and the rain threshold,
respectively.
Table 4.2: Validation statistics HSS, Correlation (Cor), Efficiency (Eff), and Bias as
defined in Section 4, for the AFC region. GPROF6 is the SSM/I surface rain
rates derived from the NASA/GSFC Goddard profiling algorithm. ALG25 and
ALG10 stand for regressions parameters derived at 25-km and 10-km grid
resolutions, respectively. TMI is TMI estimates from DA05 algorithm
averaged to 25-km.
Table 4.3: Validation statistics for the AMZ region.
Table 4.4: Validation statistics for the SAS region.
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Table 4.1: Contingency table used for computing the Heidke skill score(HSS)
PM, PR and Rthre are passive microwave rain estimate, PR rain and the rain
threshold, respectively
PR > Rthre
PR < Rthre
PM > Rthre
A
B
PM < Rthre
C
D
107
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Table 4.2: Validation statistics HSS, Correlation (Cor), Efficiency (Eff), and Bias as
defined in Section 4, for the AFC region. GPROF6 is the SSM/I surface rain
rates derived from the NASA/GSFC Goddard profiling algorithm. ALG25 and
ALG10 stand for regressions parameters derived at 25-km and 10-km grid
resolutions, respectively.
TMI is TMI estimates from DA05 algorithm
averaged to 25-km.
GPROF6
ALG25
ALG10
TMI
HSS
0.70
0.64
0.62
0.74
Cor
0.67
0.66
0.70
0.80
Eff
-0.03
0.12
0.37
0.54
Bias
1.64
1.43
1.03
1.16
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Table 4.3: Validation statistics for the AMZ region.
GPROF6
ALG10
TMI
HSS
0.63
0.62
0.71
Cor
0.64
0.65
0.83
Eff
-0.43
0.35
0.60
Bias
1.74
0.97
1.22
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Table 4.4: Validation statistics for the SAS region.
GPROF6
ALG10
HSS
0.49
0.60
Cor
0.58
0.62
Eff
-0.03
0.21
Bias
1.13
1.15
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List of figures
Figure 4.1:
The study region.
Figure 4.2:
Brightness temperature (T37) versus rain rate values o f common
exceedance probabilities (quantiles) overlaid by a fitted regression line.
The left and right panels are for stratiform and convective rain type,
respectively.
Figure 4.3:
Comparison o f original TMI, remapped TMI (Remap) and actual SSMI
brightness temperatures at 85 GHz and 19 GHz channels.
The
histograms and scatter plots are based on matched Remapped and
SSM/I pixels. The rain fields are from 02/10/2002 at 18:45.
Figure 4.4:
HSS plots as function o f rain threshold. The bottom right panel shows
HSS values along the diagonal as function o f rain threshold.
Figure 4.5:
Cumulative density function o f rain rates estimated from PR, TMI and
SSM/I.
Figure 4.6:
Sample cases o f coincident instantaneous rain rate maps o f PR, TMI
(PR-TMI algorithm) and SSM/I (ALG10 and GPROF6 algorithms)
estimates. Lines show the PR swath.
The rain fields are from
02/10/2002 at 18:45.
Figure 4.7:
Spatial error correlation o f ALG10 and GPROF6 SSM/I estimates.
Error is defined as the difference o f SSM/I versus PR estimates.
Figure 4.8:
Same as Fig.44, for AMZ region
Figure 4.9:
Same as Fig.45, for AMZ region
Figure 4.10:
HSS and CDF plots as function o f rain threshold for the SAS region.
The bottom left panel shows HSS values along the diagonal, and
bottom left panel is the CDF.
Ill
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Fig.4.1
112
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S tratifo rm
50
20
PR rami
15
10
5
10
0
oL.
250
220
260
T37[k]
240
260
T 37[k]
Fig.4.2
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280
300
12
Frequency[X]
12
Ftakatiw
Ll
19 GHz
85 GHz
150
200
2 50
25 0
500
270
50C
2S0
Tb [K]
Tt» [K]
300
300
.................... M
,,,r
CC = 0.99
CC = 0.98
200
250
ja r .,;
£
280
K
I
g 200
|
2™
150
26 0
19 GHz
85 GHz
ioo
100
25 0
150
200
SSM/I[K]
250
500
.................... 1 ...................... i . . .
250
260
, , . . , , 1 . , . . .......... 1 .......................
270
280
SSM/I[K]
Fig.4.3
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290
*
500
ALG10
PR r a i n [ m m / h r ]
PR rain [ m m / h r ]
ALG10
GPROF
PR r a i n [ m m / h r ]
Rain [m m /h r]
Fig. 4.4
115
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1 .0 0 1
D .9 0 |
PR
CDF
TMI
A LG 10
GPROF
0
5
10
15
Rain [mm /hr]
Fig.4.5
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A L G 10
G P R O F 6
Fig.4.6
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0 .5 0
0 .4 0
GPRQF6
ALG1Q
0.20
0,10
20
40
60
SO
Distance [km]
Fig.4.7
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100
P M [m m /hr]
ALG1 0
10
15
10
PM [ m m / h r ]
PR r a i n [ m m / h r ]
15
PR n a i n [ m m / h r ]
in
sp 0,4
10
15
5
PR n a in [m m /h r]
10
15
Rain [m m /h r]
Fig.4.8
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PR
CDF
TMI
ALG10
GPROF
0
5
10
15
25
Rain [mm /hr]
Fig.4.9
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G rR Q r
P W [ m m /h r ]
A LG 10
10
15
20
25
10
15
20
25
P r ram [ m m /h r ]
1.00
0.8
0.6
GPROF
PR
ALG10
ALG1
u_
C
oi
0
GPROF
0,2
0
5
10
15
Rain [mm/hr]
20
0
25
5
10
15
Rain [mm/hr]
F ig .4 .1 0
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20
25
V.
Summary, conclusions and future research directions
Summary
An algorithm for calibrating the TRMM passive microwave channels(TMI)
using the precipitation radar(PR) was developed in Chapter 2. This algorithm (PRTMI algorithm) uses multi-channel rain screening and convective/stratiform (C/S)
classification schemes. The relationship between brightness temperature and rain rate
was found to be non-linear (linear) for stratiform (convective) rain regimes. The
significance o f using regionally dependent calibrations was investigated over four
geographic regions, namely central Africa (AFC), Amazon (AMZ), USA and the
India/South Asia (SAS).
Two calibration strategies were used: calibration for each
region and ‘global’ calibration (where 25% o f the data from each region were
combined).
In addition to evaluating the significance o f regional calibration, this
study also assessed the performance o f the current algorithm with respect to TRMM2A12 Versions 5 and 6 overland rain retrievals.
The study also stressed the
importance o f convective/stratiform rain type classification in the accuracy o f PM
retrievals.
The objective for Chapter 3 has been to investigate the effects o f using
calibration parameters specific to a given season versus using one set o f parameters
for the whole year(seasonal versus annual calibration).
The PR-TMI algorithm
developed in Chapter 2 was used for this study. Three the above four regions, namely
AFC, AMZ and SAS were used for this study. For each region three relatively wet
seasons were selected. These are the respective summer seasons o f each region and
the two seasons preceding and following the respective summer season. Two types o f
comparisons were undertaken.
In the first case calibration parameters derived for
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each season and all-seasons data combined were used to estimate rainfall rates from
the validation dataset. Difference statistics were evaluated separately for each season
by comparing the retrieved rain rates with PR rain estimates.
In the second
comparison, parameter sets from MAM and SON were applied to the validation
dataset from the summer season and compared to the calibration parameter o f the
summer season.
Chapter 4 investigated the possibility o f calibrating SSM/I passive microwave
data using TRMM-PR rain estimates as reference. The PR-TMI algorithm was used
here too. A major challenge o f this study has been that SSM/I and PR sensors fly
onboard two different satellite platforms with varying field-of-view, geometry and
overpass times. As a result, it is difficult to obtain adequate data samples required for
calibration. Two indirect approaches were investigated to overcome this problem. In
the first approach, TMI channel data were re-mapped to the spatial resolutions o f the
corresponding SSM/I channels to produce “SSM/I-like” data. In the second approach,
the PR-TMI algorithm developed in Chapter 2 was recalibrated at a nominal grid
resolution o f 0.25°. Although the remapping procedure produced reasonable “ SSM/Ilike” brightness temperature fields, the second approach gave much better validation
error statistics against PR. This was mainly ascribed to the coarser resolution o f the
remapped data. It is also possible that remapping o f data had some secondary effect.
Best performance was achieved when the rain delineation and C/S classification
parameters were evaluated at 0.25° and the regression parameters at 0.1° resolution.
This shows that the calibration o f the Tb-rain rate relationship may be performed at
higher resolution than the observational satellite dataset used in rain estimation. This
calibration approach is particularly attractive as it does not rely on the availability o f
matched PR and SSM/I data. It can readily use TRMM-PR and TMI observations to
123
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derive SSM/I algorithm parameters for the various tropical/sub-tropical continental
regimes and seasons.
Conclusions
Comparison o f regional versus global calibration did not show significant
difference over AFC, AMZ and USA regions. For all practical purposes, the global
calibration can be used over these regions. Over SAS, where T85 was used instead o f
T37, there was some difference between the global and regional calibrations. This
was ascribed to unique convective characteristics and effect o f mountains over this
region.
The algorithm developed in Chapter 2 outperformed the TRMM-2A12 V6,
and consequently V5.
random error. The
The major improvement was shown to be the decrease in
values were shown to increase by 24%, 36%, 57% and 165%
for USA, AFC, AMZ, and SAS, respectively. It was also shown that TMI-2A12 V6 is
superior to the corresponding V5 in terms o f all the validation criteria used here. The
largest difference between V5 and V6 is over the AFC region and the least
improvement is over GMB.
Validation statistics were also performed for the case
where PR-2A23 rain type classification was used in place o f our algorithm’s C/S
classification scheme. This resulted in improvements in terms o f rain estimation. The
decrease in random error was 29%, 31%, 32% and 84% for AFC, USA, AMZ and
SAS, respectively. The greatest improvement was shown to be over regions where
the algorithm performance was relatively poor, and in particular in stratiform rain
regimes.
Comparisons o f individual season calibrations with the annual calibration did
not show any significant differences. The application o f one season’s parameters sets
to another has been found to reduce the accuracy o f the retrieval, but the degree o f
124
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reduction in accuracy varies by region. In AFC the random error increased by 24% as
a result o f using SON calibration parameters on the summer data. Over SAS, bias
doubles when pre-monsoon season calibration parameters are applied to the validation
dataset over the monsoon season. No significant effect was observed over Amazon.
The performance o f the PM algorithm with respect to PR has bee found to vary
among the different seasons for all regions. In AFC, the best agreement between PM
estimates and PR rain rates are observed during SON, while the least performance is
during MAM. The pre-monsoon season performs better in SAS region. In Amazon
region the MAM calibration performs the worst. However, the difference between
SON and DJF is not significant.
Comparison o f the current SSM/I rain estimates with that o f GPROF6 has
shown that the current algorithm performs better The most significant indication for
improvement was with respect to the systematic (~60% bias reduction) and random
(increase o f 0.4 in efficiency) error for the AFC region. For AMZ the efficiency
increased by 0.78, while bias is deceased by 0.71. The improvements for the SAS
region are moderate but still significant. Algorithm rain estimates based on SSM/I
observations were also compared with those from TMI. The higher resolution TMI
rain rates exhibited better agreement with PR rain rates.
The most important
improvement were decrease in random error and increase in correlation coefficients.
The efficiency increased by 46% and 71% for AFC and AMZ, respectively. The
increases in correlation coefficients were 0.1 and 0.18 for AFC and AMZ,
respectively. Part o f this improvement is attributed to the fact that the TMI sensor is
onboard the same satellite (TRMM) with PR, consequently it is associated with less
sensor sampling difference effects than SSM/I.
125
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Further research areas
The conclusions o f the study on regional calibration differences were based
only on four geographic regions.
These regions may not represent all possible
climatic regimes. Future work aims at including more climatic regimes. Another
issue is the fact that the selected regions may not be homogenous in terms o f the
characteristics o f the convection ice microphysics. The main problems are the coastal
areas. Furthermore, these regions could further be classified according to the flow
regime and storm meteorology (maritime vs. continental systems).
Another
shortcoming o f this study is that it is limited to three summer months. Thus, it does
not address the issue o f seasonal variability. Further research needs to address these
issues.
The findings o f Chapter 3 have been a useful one. However, more detailed
investigation (say at monthly level) may be required to come to a general conclusion
about seasonal differences. This would be one o f the follow-ups to this research.
Even monthly calibration may not bring about a big difference for areas like Amazon
where different rain characteristics are observed within a matter o f weeks. In such
cases one may need to use wind information in order to determine the convective
regimes.
Another future direction o f the current investigation is to go outside the
tropics, where more significant seasonal differences are expected.
126
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VI.
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