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A new over-land rainfall retrieval algorithm using satellite microwave observations

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FLORIDA STATE UNIVERSITY
COLLEGE OF ARTS AND SCIENCES
A NEW OVER-LAND RAINFALL RETRIEVAL ALGORITHM USING SATELLITE
MICROWAVE OBSERVATIONS
By
YALEI YOU
A Dissertation submitted to the
Department of Earth, Ocean and Atmospheric Science
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Degree Awarded:
Fall Semester, 2013
c 2013 Yalei You. All Rights Reserved.
Copyright UMI Number: 3612535
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3612535
Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
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unauthorized copying under Title 17, United States Code
ProQuest LLC.
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P.O. Box 1346
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Yalei You defended this dissertation on November 17, 2013.
The members of the supervisory committee were:
Guosheng Liu
Professor Directing Dissertation
Eric Chicken
University Representative
Ming Cai
Committee Member
Robert Ellingson
Committee Member
Vasu Misra
Committee Member
Joseph Turk
Committee Member
The Graduate School has verified and approved the above-named committee members, and certifies
that the dissertation has been approved in accordance with university requirements.
ii
This thesis is dedicated to my parents.
iii
ACKNOWLEDGMENTS
First, I would like to thank my advisor, Dr. Guosheng Liu. He is a great mentor and has always
been smiling no matter how silly the questions I asked. His knowledge, patience and warm-hearted
personality make me enjoying my PhD time at FSU. This manuscript would have been impossible
without Dr. Liu’s guidance and support. I want to acknowledge Dr. Ming Cai, Dr. Eric Chicken,
Dr. Robert Ellingson, Dr. Vasu Misra and Dr. Joesph Turk for sitting on my committee. I would
also like to thank Dr. Joesph Turk and Dr. Ziad Haddad for giving me the opportunity to intern
at Jet Propulsion Laboratory, which is a wonderful experience. I want to give sincere thanks to Dr.
Eric Chicken, Dr. Fred Huffer and Dr. Wei Wu for many fruitful discussions about the Bayesian
statistical technique employed in this dissertation. In addition, I want to thank my friends at FSU,
Ben Schenkel, Steve Guimond, Yusheng Luo, Xiao Peng, Max Perron, Sergio Sejas, Amin Dezfuli
and many others. I would also like to thank the members in Dr. Liu’s lab, Holly Nowell, Beth
Sims, Gauher Shaheen, Bruce Veenhuis, John Smith, Ryan Honeyager, Yulan Hong and Yu Wang.
I thank Marianne Hightman for providing me countless helps and helping me to settle down when
I first got to United States. Finally, I would like to thank my parents and my wife, Guang Xing.
They have always been there to support and encourage me.
iv
TABLE OF CONTENTS
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
1 Introduction
1.1 Previous Work and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Objectives and Paper Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2 Data Sources and collocation scheme
2.1 TRMM Precipitation Radar and Microwave Imager . . . . . . . . . . . . . . . . . . .
2.2 Ancillary Environmental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Collocation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
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3 Sensitivity of Brightness Temperature to Rainfall Rates
3.1 Ranking Channel Sensitivity . . . . . . . . . . . . . . . . . .
3.2 Dependence on Cloud Microphysical Structures . . . . . . .
3.3 Rainfall Signatures at the V19-V37 Channel . . . . . . . . .
3.4 Influence of the Surface Temperature and Land Type . . . .
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Previous Rainfall Effect to Microwave Land Surface Emissivities
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Two Simultaneous Emissivity Datasets . . . . . . . . . . . . . . . . .
4.3 Influence of Previous Rainfall on MLSE . . . . . . . . . . . . . . . .
4.3.1 Correlation between Emissivities and Previous Rainfall . . .
4.3.2 Two Case Studies . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Emissivity Variations Caused by Previous Rainfall . . . . . .
4.4 Model Simulations Using Three Different Emissivity Datasets . . . .
4.4.1 Case Study from 12 August 2011 . . . . . . . . . . . . . . . .
4.4.2 Simulations over Entire Study Region . . . . . . . . . . . . .
4.5 Applications of Instantaneous PC-based Emissivity . . . . . . . . . .
4.5.1 Using Clear-Sky Emissivity to Retrieve Previous Rainfall . .
4.5.2 Adjusting Emissivities under Raining Conditions . . . . . . .
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 Relationship between Water Path and Surface Rainrate
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Spatial Variation of Ice Water Path . . . . . . . . . . . . . . . . . . . .
5.2.3 Correlation between Ice Water Path and Surface Rainrate . . . . . . . .
5.2.4 Relationship between Total Water Path and Surface Rainrate over Land
5.2.5 Relationship of Liquid Water Path and Surface Rainrate over Ocean . .
5.3 Implications to the Surface Rainrate Retrieval . . . . . . . . . . . . . . . . . . .
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 A Principal Component Analysis(PCA)-Based Bayesian Algorithm
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Estimation of the Atmospheric Variable x , given T . . . . . . . . . . . .
6.3 Monte Carlo Integration . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Implementation Details . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Likelihood PDF and Prior PDF . . . . . . . . . . . . . . . . . . .
6.4.2 Observational Database vs. Simulated Database . . . . . . . . .
6.5 Principal Components Analysis Based Bayesian Algorithm . . . . . . . .
6.6 Comparison between Regression-Based and Bayesian-Based Methods . .
6.7 Conclusions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . .
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7 Results from PCA based Bayesian Algorithm
7.1 Categorizing the Passive Microwave Signature . . . . . . . .
7.1.1 Effectiveness of the Physical Parameters . . . . . . .
7.2 Principal Component Analysis (PCA) . . . . . . . . . . . .
7.3 Rainfall Screening . . . . . . . . . . . . . . . . . . . . . . .
7.4 Rainfall Retrieval Results . . . . . . . . . . . . . . . . . . .
7.4.1 Comparison with One Database and TRMM Results
7.4.2 Overestimation Analysis . . . . . . . . . . . . . . . .
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .
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102
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8 Summary
8.1 Summary of the Physical Background in the Retrieval Algorithm . . . . . .
8.1.1 Sensitivity of Brightness Temperature to Rainfall Rates . . . . . . .
8.1.2 Previous Rainfall Effect to Microwave Land Surface Emissivities . .
8.1.3 Proportionality between Rainrate and Water Paths . . . . . . . . . .
8.2 Summary of the PCA-Based Bayesian Algorithm and the Retrieved Results
8.2.1 The PCA-Based Bayesian Algorithm . . . . . . . . . . . . . . . . . .
8.2.2 Results from the PCA-based Bayesian Algorithm . . . . . . . . . . .
8.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
vi
LIST OF TABLES
3.1
Correlation Coefficients (CC) Between NSR and TB of the Top 20 Channels/Combinations
for 1998, 1999, 2000, and three Years Combined . . . . . . . . . . . . . . . . . . . . . 23
3.2
Statistics of pixel number fraction (%) and rainfall amount fraction (%, in parenthesis)
grouped by FWI and RI indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3
Correlation coefficients between NSR and TBs of the top 5 channels/combinations
grouped FWI and RI indices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
7.1
Notation for Rain-No-Rain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
vii
LIST OF FIGURES
3.1
Correlation Coefficients (CC) between NSR and TBs of different channels/combinations
over land for data of 1998, 1999, 2000, and 3-year combined. For comparison, all the
correlation coefficients are in their absolute values. . . . . . . . . . . . . . . . . . . . . 25
3.2
Correlation Coefficients (CC) between NSR and TBs of different channels/combinations
over land for convective and non-convective clouds in 1998. For comparison, all the
correlation coefficients are in their absolute values. . . . . . . . . . . . . . . . . . . . . 26
3.3
The global distribution of correlation coefficients (CC) between TBs and NSR. Three
years of data are used in calculating the CCs. (a) CC between TBs at the V19-V37
channel and NSR (absolute value), (b) CC between TBs at the V85 channel and NSR
(absolute value), (c) CC between TBs at the V21-V85 channel and NSR (absolute
value), and (d) CC difference between (a) and (b). . . . . . . . . . . . . . . . . . . . . 27
3.4
Correlation coefficients (absolute value) between TBs at the V19-V37, V37, or V85
channel and NSR grouped by FWI and RI indices. Three years of data are used in
computing the correlation coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5
The CFADs of radar rainfall profiles for rain types of (a) Category 1, (b) Category 2,
and (c) Category 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6
The response of the V19-V37 (left panel) and the V85 (right panel) channels to Near
Surface Rain (NSR) for warm rain cases. Figs. (a) and (b) are for region of 70-65◦ W,
0-5◦ N in May of 1998, (c) and (d) are for region of 100-105◦ E, 20-25◦ N in July of 1998,
(e) and (f) are for regions of 105-110◦ E, 25-30◦ N in August of 1998, and (g) and (h)
are for region of 45-50◦ E, 15-20◦ S in December of 1998. . . . . . . . . . . . . . . . . . 30
3.7
TBs at the V19-V37 channel vs. near surface rain. (a) liquid drops only, (b) liquid
drops plus ice particles in the profile. The red (blue) curve denotes results with
(without) taking horizontal rain rate inhomogeneity within a pixel into account. Green
circles in (b) are observations over the S. Great Plain (95-90◦ W, 32-37◦ N) in July in
1998. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.8
Correlation Coefficients (CC) between TBs and NSR within each 5 ◦ latitudinal belt
from 35 ◦ S to 35 ◦ N for the months of (a) January, (b) April, (c) July, and (d) October. 32
3.9
Correlation Coefficients (CC) between TBs and NSR over seven 2-meter air temperature intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.10
The CFADS of radar rainfall profiles for observations (a) with 2-m air temperature
colder than 280K, (b) with 2-m air temperature warmer than 305K, (c) over bare
ground, (d) over evergreen forest, (e) with 2-m air temperature colder than 280K
viii
and over bare ground, and (f) with 2-m air temperature warmer than 305K and over
evergreen forest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.11
Correlation Coefficients (CC) between TBs and NSR over 12 different land surface
types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.12
(a) The distribution of observed raining pixel number fractions. (b) NSR variances
explained by the V19-V37 channel. (c) NSR variances explained by the V85 channel. (d) NSR variances explained by the V37 channel. (e) The difference between
NSR variances explained by the V19-V37 channel and by the V85 channel. (f) The
difference between NSR variances explained by the V37 channel and by the V85 channel. 35
3.13
Example for deriving the adjusted NSR-TBs relation. (a) Blue line: original regression
line from observations of NSR and the V19-V37 channel TBs; Green line: averaged
values in different rainfall bins. (b) Scatter plot of NSR vs. the V19-V37 channel TBs
using data from 1998 to 2000. The red curve is the original regression line and the
magenta curve is the adjusted line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.14
Comparison between retrieved rain rate and PR Near Surface Rain (NSR). (a) Retrievals from the V19-V37 channel over mixed forest where the temperature is between
290 and 295 K. (b) Same as (a) except for the V85 channel. (c) Retrievals from the
V19-V37 channel over bare ground where the temperature is between 280 and 285K.
(d) Same as (c) except for the V85 channel. . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1
Correlation coefficients between previous 1 to 24-hr rainfall and emissivity at H10
channel over closed shrub, crop and forest land, using PC-based emissivities. . . . . . 54
4.2
(a) Correlation between PC-based emissivity at H10 channel and previous 24-hrs accumulated rainfall. (b) Correlation between first principal component (PC1) and
previous 24- hrs accumulated rainfall. For comparison purposes, this correlation coefficient is multiplied by -1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3
PC-based emissivity over a closed shrub dominant location. (a) Emissivity at H10
channel response to previous 24-hr rainfall. (b) Emissivity at H19 channel response
to previous 24-hr rainfall. (c) Emissivity at H37 channel response to previous 24-hr
rainfall. (d) First principal component (PC1) response to 24-hr rainfall. (e) Third
principal component (PC3) response to 24-hr rainfall. (f) Fourth principal component
(PC4) response to 24-hr rainfall. (g) Previous 24-hr rainfall. The ’Number of obs.’
stands for the intermittent satellite observations over this specific area. . . . . . . . . 55
4.4
Same as Figure 3, except for over a forest dominant location. . . . . . . . . . . . . . . 56
4.5
(a) Difference between PC-based emissivities at the H10 channel when no rain occurred
in the previous 24-hr and that when it rained more than 20 mm in the previous 24hr. (b) Difference between PC-based emissivities at the H19 channel when no rain
occurred in the previous 24-hr and that when it rained more than 20 mm in the
previous 24-hr. (c) Difference between PC-based emissivities at the H37 channel
ix
when no rain occurred in the previous 24-hr and that when it rained more than 20
mm in the previous 24-hr. (d) Dominant land cover types over the study region. . . . 57
4.6
(a) Difference between brightness temperatures (TB) at the H10 channel when no
rain occurred in the previous 24-hr and that when it rained more than 20 mm in the
previous 24-hr. (b) Same as (a), but for at H19 channel. (c) Save as (a) but for at
H37 channel. (d) Difference between surface temperatures when no rain occurred in
the previous 24-hr and that when it rained more than 20 mm in the previous 24-hr. . 58
4.7
Emissivity analysis on 12 August 2011 over the Southern Great Plains (SGP) site between 32.5N to 36.5N latitude, and 100W to 97W longitude. (a) Scatter plot between
simulated and observed TB at V19 channel, using TELSEM climatological emissivity.
(b) Scatter plot between simulated and observed TB at V19 channel, using PC-based
instantaneous emissivity. (c) Scatter plot between simulated and observed TB at V19
channel, using physically-based instantaneous emissivity. (d) Scatter plot between
simulated and observed TB at V37 channel, using TELSEM climatological emissivity.
(e) Scatter plot between simulated and observed TB at V37 channel, using PC-based
instantaneous emissivity. (f) Scatter plot between simulated and observed TB at V37
channel, using physically-based instantaneous emissivity. (g) Scatter plot between
simulated and observed TB at V85 channel, using TELSEM climatological emissivity.
(h) Scatter plot between simulated and observed TB at V85 channel, using PC-based
instantaneous emissivity. (i) Geographical location for the case on 12 August 2011. . . 59
4.8
Same as Figure 8, except for the horizontally polarized channels. . . . . . . . . . . . . 60
4.9
TRMM emissivity analysis over the continental United States. (a) Scatter plot between simulated and observed TB at H19 channel, using TELSEM climatological
emissivity. (b) Scatter plot between simulated and observed TB at H19 channel, using
PC-based instantaneous emissivity. (c) Scatter plot between simulated and observed
TB at H19 channel, using physically-based instantaneous emissivity. (d) Scatter plot
between simulated and observed TB at H37 channel, using TELSEM climatological
emissivity. (e) Scatter plot between simulated and observed TB at H37 channel, using
PC-based instantaneous emissivity. (f) Scatter plot between simulated and observed
TB at H37 channel, using physically-based instantaneous emissivity. (g) Scatter plot
between simulated and observed TB at H85 channel, using TELSEM climatological
emissivity. (h) Scatter plot between simulated and observed TB at H85 channel, using
PC-based instantaneous emissivity. Black solid line is the 1:1 line. . . . . . . . . . . . 61
4.10
Analysis of previous rainfall and emissivity change over the region from 31N to 32N
latitude, and 99 to 100W longitude. (a) Scatter plot between emissivity at H10 and
previous 24-hr rainfall, using trained subset data. Solid curve denotes the least square
fitting line. (b) Scatter plot between predicted and observed previous 24-hr rainfall,
using validation subset data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
x
4.11
(a) Scatter plot between the first principal component (PC1) and previous 24-hr rainfall. (b) Same, but for the third principal component (PC3) and previous 24-hr rainfall.
(c) Same, but for the fourth principal component (PC4) and previous 24-hr rainfall. . 62
4.12
(a) Scatter plot between simulated TB and observed TB at H10 channel, before adjustment. (b) Scatter plot between simulated TB and observed TB at H10 channel,
after adjustment. (c) Same as (a) but for H19 channel. (d) Same as (b) but for H19
channel. (e) Same as (a) but for H37 channel. (f) Same as (b) but for H37 channel. . 63
4.13
Same as Figure 13, except for the vertically polarized channels. . . . . . . . . . . . . . 64
4.14
Calculated emissivity before (blue) and after (red) adjustment at H10, V10, H19, V19,
H37 and V37 channels, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1
(a) Scatter plot between TB at V85 and ice water path (IWP). (b)Scatter plot between
surface rainrate and ice water path (IWP). (c) Scatter plot between TB at V85 and
surface rainrate. (d) Scatter plot between TB at V19-V37 and total water path (TWP).
(e) Scatter plot between surface rainrate and total water path (TWP). (f) Scatter plot
between TB at V19-V37 and the surface rainrate. (g) Geographical location for the
case on January 19, 1998 over southeastern U.S.. . . . . . . . . . . . . . . . . . . . . . 80
5.2
(a) Scatter plot between TB at V19 and liquid water path (LWP). (b)Scatter plot
between surface rainrate and liquid water path (LWP). (c) Scatter plot between TB
at V19 and surface rainrate. (d) Scatter plot between TB at V85 and ice water path
(IWP). (e) Scatter plot between surface rainrate and ice water path (IWP). (f) Scatter
plot between TB at V85 and surface rainrate. (g) Geographical location for the case
on January 6, 1998 over South Pacific Ocean. . . . . . . . . . . . . . . . . . . . . . . . 81
5.3
(a) Spatial distribution of ice water path (IWP) corresponding to 1 mm h−1 surface
rainrate over TRMM covered areas.(b) Spatial distribution of total water path (TWP)
corresponding to 1 mm h−1 surface rainrate over land.(c) Spatial distribution of liquid
water path (LWP) corresponding to 1 mm h−1 surface rainrate over ocean. . . . . . . 82
5.4
Averaged precipitation rainfall profiles over four representative regions. Relative
height is the distance from the freezing level height. . . . . . . . . . . . . . . . . . . . 83
5.5
(a) Spatial distribution of correlation between ice water path and surface rainrate
over TRMM covered areas.The boxes delineate the six regions in subsequent studies.
(b) Spatial distribution of correlation between total water path and surface rainrate
over land. The boxes delineate the three regions in subsequent studies. (c) Spatial
distribution of correlation between liquid water path and surface rainrate over ocean.
5.6
84
Seasonal variation of ice water path, corresponding to 1,4,7 mm h−1 surface rainrate
over six selected regions in Fig. 5a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
xi
5.7
Averaged precipitation rainfall profiles in two months over (a) Central Africa, (b)
Central India, (c) Sahara desert. Relative height is the distance from the freezing
level height. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.8
(a) TB -variation at V85 in two months corresponding to similar surface rainrate over
central India region. (b) TB -variation at V85 in two months corresponding to similar surface rainrate over Indian Ocean region. Solid lines stand for TB -variation and
dashed lines represent water paths. TB -variation is the original TB minus the background TB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.9
(a) Correlation between TB -variation at V85 and ice water path. (b) Correlation
between ice water path and surface rainrate. (c) Correlation between TB -variation
at V85 and surface rainrate. (d) Spatial distriubtion of 4-type rain system regions.
TB -variation is the original TB minus the background TB . . . . . . . . . . . . . . . . . 87
5.10
(a) Correlation between TB -variation at V19 and liquid water path over ocean. (b)
Correlation between liquid water path and surface rainrate over ocean. (c) Correlation
between TB -variation at V19 and surface rainrate over ocean. TB -variation is the
original TB minus the background TB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.1
Corresponding to the same surface rainrate, the TBs response at V10 and V85 in two
distinct different category. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2
Corresponding to the same surface rainrate and the same freezing level height, the
TB response at V85 in low, medium and high storm height scenarios . . . . . . . . . . 109
7.3
Scatter plot between storm height (SH) and TB polarization between V21 and V85 . 110
7.4
The coefficients for TB at each channel in the three leading Principal Components . . 111
7.5
For critical values varying from -9 to 20, (a) the corresponding Ratio of True Detection
(Occurrence) and Ratio of False Alarm. (b)the corresponding Ratio of True Detection
(Amount) and Ratio of False Alarm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.6
Scatter plots between retrieved rainrates and observed rainrates from TRMM PR in
four months, January, April, July and October. The red curve stands for the 1:1 line . 113
7.7
Global distribution of monthly mean rainrates over 1◦ ×1◦ latitude-longitude grid box
in four months, January, April, July and October. . . . . . . . . . . . . . . . . . . . . 114
7.8
Same as Fig. 7.7 except for observations from TRMM PR . . . . . . . . . . . . . . . 115
7.9
Monthly rainfall difference between retrieved rainrates and observed rainrates over
1◦ ×1◦ latitude-longitude grid box in four months, January, April, July and October. . 116
7.10
Scatter plots between retrieved rainrates and observed rainrates (a) Using categorized
database (b) Using overall database (c) Using TRMM facility Algorithm . . . . . . . 117
xii
7.11
For a specific category, (a)Scatter plot between retrieved rainrates and observed rainrates using categorized database (b) Scatter plot between retrieved rainrates and observed rainrates using overall database (c) Corresponding to same surface rainrate,
the TBs’ response at V85GHz in categorized database and overall database. . . . . . 118
8.1
TB simulations using a microwave radiative transfer model at V10, V19, V37 and
V85GHz, blue curves represent the observations, red curves represent the simulated
TBs after emissivity and cloud ice/liquid adjustment, green curves stand for the simulated TBs after emissivity, cloud ice/liquid and beam-filling effects adjustment. . . . 128
xiii
LIST OF SYMBOLS
The following short list of abbreviations and symbols are used throughout the manuscript.
T
x
x|T
T)
f (x
T |x
x)
f (T
x
f (x )
Σ
E
[E]
r
Brightness temperature vector
Atmospheric variables
Posterior probability density function
Likelihood function
Prior probability density function
Covariance matrix
Expectation
Eigenvector
correlation coefficient
xiv
LIST OF ABBREVIATIONS
The following short list of abbreviations are used throughout the manuscript.
TB
TRMM
TMI
PR
NSR
SSM/I
AMSR-E
NMQ
FLH
SH
MLSE
PCA
MCI
PDF
ITCZ
TELSEM
Brightness Temperature
Tropical Rainfall Measurement Mission
TRMM Imager
TRMM Precipitation Radar
Near Surface Rainrate
Special Sensor Microwave/Imager
Advanced Microwave Scanning Radiometer for the Earth Observing System
National Mosaic and Multi-Sensor Quantitative Precipitation Estimates
Freezing Level Height
Storm Height
Microwave Land Surface Emissivity
Principal Component Analysis
Monte Carlo Integreation
Probability Density Function
Intertropical Convergence Zone
Tool to Estimate Land-Surface Emissivities at Microwave
xv
ABSTRACT
During the past two decades, the accuracy of rainfall retrieval based on passive microwave observations has been greatly improved, particularly over ocean. However, rainfall retrieval over
land remains to be problematic. The objective of this study is to develop a new rainfall retrieval
algorithm that provides better rainfall estimates over land.
Toward that end, in the first part of this study, we focus on better understanding three key
physical aspects which significantly influence the algorithm development, including signature from
both high and low frequencies, the surface emissivity effect and rainfall profile structure. Although
it has been long believed that the dominant signature of over land rainfall is the brightness temperature depression caused by ice scattering at high microwave frequencies (e.g., 85 GHz), our
results in chapter 3 showed that the brightness temperature combinations from 19 and 37 GHz,
i.e., V19-V37 (the letter V denotes vertical polarization, and the numbers denote frequency in GHz.
Similar notations are used hereafter) or V21-V37 can explain ∼10% more variance of near surface
rainfall rate than the V85 brightness temperature. A plausible explanation to this result is that in
addition to ice scattering signature, the V19-V37 channel contains liquid water information as well,
which is more directly related to surface rain than ice water aloft. In addition, to better utilized the
information from low frequency, we analyzed the instantaneous microwave land surface emissivity
(MLSE) and its response to the previous rainfall (Chapter 4). Current rainfall retrieval algorithm
over land has not yet taken the MLSE effect into consideration. Results showed that over grass,
closed shrub and cropland, previous rainfall can cause the horizontally-polarized 10 GHz brightness
temperature (TB) to drop by as much as 20 K with a corresponding emissivity drop of approximately 0.06, whereby previous rain exhibited little influence on the emissivity over forest due to the
dense vegetation. We developed a technique to estimate the emissivity underneath precipitating
radiometric scenes. Further, in chapter 5 the relationship between water paths and the surface
rain is evaluated. Results showed that corresponding to a similar surface rainrate ice water path
has large spatial variability, and the most prominent characteristic for the ice water path spatial
distribution is the contrast between land and ocean. On average, the correlation (R2 ) between ice
water path and surface rainrate is also larger over land than over ocean. Over the majority of land
areas, R2 is ∼0.36, with the exception of arid regions and the Indian subcontinent (∼0.25).
xvi
In the second part of this study (chapter 6 and chapter 7), a new Principal Component Analysis
(PCA) based Bayesian algorithm is proposed to take full advantage all the brightness temperature
observations. Results from this algorithm was compared with that from the TRMM facility algorithm. The unique features of the new retrieval algorithm are (1) physical parameters, including
surface temperature, land cover type, elevation, freezing level height and storm height, are used to
categorize the land surface conditions and rainfall profile structures. (2) the covariance matrix in
the Bayesian framework is calculated based on real observations and is perfectly diagonal through
the Principal Component Analysis transformation. It is demonstrated that the retrieved surface
rain rate agrees much better with observations from TRMM precipitation Radar, compared to the
results from TRMM facility algorithm over land. Particularly, no obvious over-estimations are
observed when rainrate is less than 10 mm/hr. Validation using one year data show that the correlation between retrieved rainrate and observations is 0.73, while it is 0.65 between retrieved rainrate
by TRMM facility algorithm and observations. The root mean square error (RMSE) is lowered by
about 35%. In terms of the computational time, this algorithm is several order faster than other
published Bayesian based algorithms. In addition, this algorithm can be conveniently adapted to
other satellite platforms (e.g., SSM/I) due to its location and season independent characteristics.
xvii
CHAPTER 1
INTRODUCTION
1.1
Previous Work and Motivation
Rainfall is one of the most challenging meteorological parameters to measure because of its
high spatial and temporal variability. It is widely accepted that rainfall monitoring by surface in
situ raingauge is inadequate for most applications in meteorology, hydrology, agronomy and many
other scientific disciplines. For example, rainfall rate measured by a raingauge at a given location
can be significantly different from that measured just a couple of hundred meters away. In some
areas of the world, e.g. the United States, Western Europe and Eastern China, the construction
of a reasonably dense network of weather radar stations provides us great capability to routinely
monitor local, regional, and even continental scale rainfall rate. Nevertheless, the vast majority of
the globe does not enjoy similar coverage by such meteorological radar or raingauge networks, and
will not in the foreseeable future. Further complicating the rainfall measurement, the inhospitable
weather/climate in certain areas around the world, such as, most parts of the Tibetan plateau as
well as polar regions, make it impossible to routinely collect rainfall data by in situ raingauge or
ground radar.
In view of the above, it is fortunate that meteorological satellite offers great opportunity to
monitor the spatial and temporal distribution of precipitation from space with much better resolution compared with in situ raingauge and radar networks. Along with the launching of the first
meteorological satellite (the Television and Infrared Observation SatelliteTIROS 1) in 1960, scientists started to pay attention to the possibility of retrieving rainfall rate utilizing infrared imagers.
Since then a large number of algorithm development activities based upon visible (VIS) and infrared
(IR) imagery have been seen. The physical bases of rainfall estimation from such imagery are well
explored and explained in detail (Barrett and Beaumont, 1994). Basically, such techniques depend
on assumptions that the surface rainfall can be inferred from analyzing the cloud top characteristics, either in the VIS (where the brightest clouds maybe represent those most likely to precipitate)
and/ or in the IR (where the clouds which can reach highest altitude, and therefore have the lowest
1
cloud top temperature are the most probably to precipitate). Unfortunately, all such algorithms
suffer from the drawback of the physical indirectness of the relationship between the characteristics
of the cloud tops and the processes which are taking place underneath them. That is, by no means,
all bright clouds precipitate, nor do all clouds having clod IR tops. Conversely, not all rain clouds
are bright or cold.
Passive microwave measurements provide more physically direct link between hydrometeors in
the atmosphere and radiances observed from a satellite. It was established as early as the mid1970s that passive microwave radiometers are capable of detecting precipitation over the oceans,
at least on a climatological time and space scales, owning to the radiatively cold, highly polarized
and homogeneous background of the oceans (e.g., Allison et al., 1974). Despite some partially
successful efforts to use 37 GHz channels to distinguish convective rainfall over land (e.g., Spencer
et al., 1983), it is only with the launch in 1987 of the first Special Sensor Microwave Imager (SSM/I),
which include channels at the comparatively high frequency of 85.5 GHz, that makes it possible to
distinguish rainfall over land with reasonable consistency.
During the past two decades, particularly with the success of TRMM (Tropical Rainfall Measuring Mission), the accuracy of rainfall retrieval based on passive microwave radiometers has been
greatly improved, particularly over ocean (Kummerow et al., 2001; McCollum and Ferraro, 2003).
However, rainfall retrieval over land remains to be problematic because land rainfall retrieval algorithms hinge mainly on the scattering signature from high microwave frequencies (Wilheit, 1986;
Spencer et al., 1989; Grody, 1991; Adler et al., 1993; Ferraro and Marks, 1995; Lin and Hou, 2008;
Wang et al., 2009; Gopalan et al., 2010), as opposed to ocean rainfall retrieval algorithms that make
full use of emission and scattering signatures from observations at multiple frequencies (Petty, 1994;
Smith et al., 1994b; Kummerow et al., 1996; Olson et al., 1996). The different philosophy for retrieving rainfall over land and ocean has been explained by many previous works (e.g., Stephens
and Kummerow, 2007).
Currently, to the authors best knowledge, all the land rainfall retrieval algorithms only make
use of the ice scattering signature. A few well-documented retrieval algorithms are highlighted as
follows. Spencer et al. (1989) introduced a polarization corrected temperature (PCT) to identify
rainfall over land. The PCT is a linear combination of the vertically and horizontally polarized
brightness temperatures at 85 GHz channel, which is designed to extract ice scattering signature
2
and to eliminate emissivity differences across land and ocean to get more continuous precipitation
field. It has also been used to identify severe convective systems (Zipser et al., 2006). An empirical
scattering index was proposed by Grody (1991), Ferraro et al. (1994) and Ferraro and Marks (1995)
to identify and estimate over-land rainfall. The basic idea is that brightness temperatures at lower
frequency channels, e.g., 19 and 22 GHz, can be used to estimate the nonscattering portion of the
85 GHz radiation. Subtracting the estimated nonscattering portion from actually observed 85 GHz
brightness temperature, one can obtain the ice scattering signature by raining clouds. This approach
has been used in the current TRMM facility over-land rain retrieval algorithm. Similarly, Adler
et al. (1993) used an empirical algorithm by retrieving the rainfall rate based on 85 GHz brightness
temperature colder than a fixed threshold of 247 K. Liu and Curry (1992) developed an algorithm
attempting to use both the emission and scattering signals, which relates rainfall rates to the
difference between the 19 and 85 GHz brightness temperatures. However, over land the algorithm
still relies on ice scattering signature at 85 GHz. Recently, Aonashi et al. (2009) described a
somewhat more elaborated empirical algorithm-Global Satellite Mapping of Precipitation(GSMaP).
While it is also based on ice scattering signals over land, a slightly different approach is attempted,
in which the 37 GHz channel is utilized as a supplemental scattering correction factor to the
85 GHz scattering signatures. The main consideration of using this correction is that the 85
GHz scattering signature reaches saturation when the rainfall become very heavy. In comparison
with the TRMM facility algorithm, they found that severe overestimation is mitigated for tall
precipitation cases (thickness between precipitation top level and freezing level larger than 4 km).
GSMaP, implemented at Japan Aerospace Exploration Agency (JAXA), together with TRMM
facility algorithm will be discussed in detail in Chapter 6.
While being different in details, the previous algorithms estimate rainfall rates over land fundamentally under the same principle: translating the scattering signature caused by ice water aloft
into a surface rainfall rate. The ice scattering signature, shown as a depression of brightness temperature relative to no-rain conditions, is very sensitive to the amount of ice particles aloft, as well
as their particle size distributions, shapes and densities (Bennartz and Petty, 2001). The frozen
hydrometeors population aloft often has an inconsistent and less direct relation with rainfall at the
surface, and varies significantly from region to region (Dinku and Anagnostou, 2005). Obviously,
3
rainfall retrieval algorithms only relying on the ice scattering signature will inevitably lead to a
large error for clouds that lack in ice particles (Ferraro et al., 2005; Huffman et al., 2007).
Another major obstacle to over land rainfall retrieval is the high and variable surface emissivity
which not only makes it difficult to distinguish rainfall signal from the complicated land background,
but also make the TBs at the lower frequency not so useful (Wilheit, 1986; Kummerow et al., 2001;
Ferraro et al., 2005). For example, an increase in surface wetness reduces its emissivity, which can
easily be mistaken as ice scattering, and therefore, rainfall signature. Adding to the complication,
rainfall itself increases the wetness of its underlying surface, which makes the emissivity values
estimated before or after a rain event not so useful. More importantly, Both the surface emissivity
and hydrometeors in the air will contributes to brightness temperature observed by the microwave
radiometer at the top of the atmosphere. This makes it rather difficult to estimate the surface
emissivity under raining scenario, and therefore makes the brightness temperature observations at
low frequencies less useful.
In addition, insufficiently used rainfall profile information in the previously published rainfall
retrieval algorithm also accounts for the large uncertainty in the retrieved surface rainrate, since
the retrieval of surface rainrate based on passive microwave observations from satellite always faces
the following unavoidable dilemma. On one hand, the brightness temperatures (TB) measured
by a passive microwave radiometer reflect the integrated effects of emission and scattering by the
surface, atmospheric gases, and hydrometeors in the atmospheric column. On the other hand, the
surface rainrate we intend to retrieve is the downward water flux at the very bottom layer (Haddad
and Park, 2009; You and Liu, 2012). Corresponding to similar rain rate, the water paths can differ
largely, therefore the observed brightness temperatures are rather different. Further, as pointed
by Hirose and Nakamura (2002) and Hirose and Nakamura (2004), the slope of the liquid water
below the freezing level varies depending on both location and season. It is worth mentioning that
brightness temperature responds much stronger to the ice particles than the liquid water over land
due to the high emissivity effect, which will pose great challenge to incorporate the liquid water
slope information into the algorithm development.
4
1.2
Objectives and Paper Organization
The objective of this study is to develop a new over-land rainfall retrieval algorithm by addressing the aforementioned three critical issues. At the same time, ancillary environmental parameters
(including surface temperature, land cover type, elevation) will also be utilized for the first time
in the development of the retrieval algorithm. The reminder of this manuscript is organized as
follows: in chapter two, the dataset used throughout this study is discussed. In chapter three,
we start to investigate the information contains in the low frequencies. In performing this study,
we intentionally do not limit ourselves to the common knowledge that the 85 GHz observations
contain the richest information on over-land rainfall. Instead, we start with searching the most
sensitive channels or channel combinations to over-land rainfall using actually observed TRMM
Precipitation Radar (PR) and Microwave Imager (TMI)data. In chapter four, the microwave land
surface emissivity (MLSE) was examined as a function of previous rainfall conditions using two
independent emissivity estimation techniques. By doing this, it is possible to incorporate the TBs
at lower frequency into the newly developed retrieval algorithm. At the same time, we will demonstrate how to estimate the emissivity underneath precipitating radiometric scenes. In chapter five,
the importance of the rainfall profile information for accurately retrieving the surface rainrate will
be demonstrated through investigating the relationship between surface rainrate and water paths.
Key parameters to characterize the vertical structure of the profiles will also been tested in this
chapter. In chapter six, the currently used Bayesian based algorithm will be revisited and several
unrealistic assumptions regarding this statistical method will be discussed. We will also briefly
discuss the differences and similarities between Bayesian based Algorithm and Regression based
Algorithm (e.g., simple regression and Look-Up-Table). A new Bayesian method based on Principal Component Analysis (PCA) will be proposed. In chapter seven, the newly developed rainfall
retrieval algorithm will be throughly tested. Summary and future work, including how to apply
this algorithm to other satellite sensors, will be discussed in the chapter eight.
5
CHAPTER 2
DATA SOURCES AND COLLOCATION SCHEME
2.1
TRMM Precipitation Radar and Microwave Imager
The TRMM Precipitation Radar (PR) and Mirowave Imager (TMI) data over TRMM satellite
covered area (38◦ S to 38◦ N) from 1998 to 2003 are used in this study. The TMI is a 9-channel,
5-frequency, linearly polarized, passive microwave radiometric system. The instrument measures
brightness temperatures (TB) at 10.7, 19.4, 21.3, 37.0, and 85.5 GHz. Each frequency has one
vertically (V) and one horizontally (H) polarized channel, except for the 21.3 GHz frequency,
which has only vertical polarization (hereafter referred to as V10, H10, V19, H19, V21, V37, H37,
V85 and H85). The swath width is about 760 km, covered by 104 low resolution pixels or 208 high
resolution pixels. The pixel size is dependent on the frequency, varying from about 5 km for 85
GHz to about 45 km for 10 GHz channels. The PR is a 13.8 GHz radar, receiving energy reflected
by atmospheric and surface targets. The PR electronically scans every 0.6 s with a swath width
of about 215 km, with respect to around 4.5 km horizontal resolution. Vertically, the PR is able
to detect targets from 0 to 20 km at a 250 m resolution. More details about TMI and PR are
provided by Kummerow et al. (1998). The PR rainfall rates are calculated from radar reflectivity
with corrections for attenuations based on Iguchi and Meneghini (1994). A surface rain (hereafter
referred to as SR) in the archived dataset is defined as the rainfall rate at the lowest point in the
clutter-free region. Since PR reflectivity measurements at the lowest 1.5 to 2 km above surface
are often contaminated by surface clutter, shallow rain events with tops lower than the clutter-free
region will be missed in our data analysis. In the present study, we use the TMI 1B11 version 6 for
the TBs data, PR 2A25 version 6 for the precipitation rate data, and PR 2A23 version 6 for the
rain type and storm height data. It is worth mentioning that storm height is defined as the top
altitude of the three highest consecutive range bins with significant radar echoes.
In addition, the archived dataset does not include water content variables; we calculate liquid
and ice water content profiles from PR reflectivities based on the method described by Iguchi et al.
(2000) and Masunaga et al. (2002). It should be noted that radar reflectivity is approximately
6
proportional to the sixth moment of rain drop size distribution, while water content is proportional
to the third moment. As a result, the radar reflectivity versus water path relation should depend
on rain drop size distribution, which cannot be assessed with a single-wavelength radar. Therefore,
the water path derived in this study may contain substantial uncertainties caused by the variability
of drop size distributions and may only be viewed as a proxy of water path (e.g., Chen et al.,
2007). It is worth mentioning that water content around the bright-band was replaced by linearly
interpolated data using data ±750 m from the bright-band peak to avoid possible contamination
by the bright band itself. The water content is considered liquid from the surface to freezing level
height, and ice above the freezing level height. No mixed phase particles are considered when
computing the water paths. Liquid water path, ice water path and total water path are then
computed by integrating the radar reflectivity-derived water contents.
2.2
Ancillary Environmental Data
Ancillary datasets employed in this study include land surface type, land elevation, Modern
Era Retrospective-analysis for Research and Applications (MERRA) reanalysis data, climatological
emissivity from Tool to Estimate Land-Surface Emissivities at Microwave(TELSEM) and National
Mosaic and Multi-sensor Quantitative gauge-adjusted precipitation (NMQ) data. Hansen et al.
(2000) classified global land surface into 14 categories at 1-km resolution using 1992-1993 Advanced
Very High Resolution Radiometer (AVHRR) data, including needleleaf evergreen forest, broadleaf
evergreen forest, broadleaf deciduous forest, mixed forest, woodland, wooded grassland, closed
shrubland, open shrubland, grassland, cropland, bared ground and urban and built-up. The Global
Land One-kilometer Base Elevation (GLOBE) was provided by National Geophysical Data Center
of National Oceanic and Atmospheric Administration (NOAA) (Hastings and Dunbar, 1998). The
relative humidity, geopotential height and temperature profiles from MERRA reanalysis data are
provided 8-times daily at an approximate 0.5-degree resolution from the 3-D instantaneous state
on pressure levels (inst 3d asm Cp) data product, and every hour for surface temperature data
from the 2-D surface and radiation fluxes (tavg1 2d rad Nx) data product (Rienecker et al., 2011).
TELSEM provides monthly mean emissivities at 0.25 degree resolution from 19GHz to 89GHz
frequency (Aires et al., 2011). The surface rainrate from NMQ data is at 1hr and 1km resolution,
provided by the National Severe Storms Laboratory of NOAA (Zhang et al., 2011).
7
The freezing level height provided by NASA-archived TRMM data is calculated through a
temporal and spatial interpolation of a climatological surface temperature at the sea level with a
constant lapse rate of 6 ◦ C per km, which can lead to significant biases, especially in winter and
high elevation areas (Harris et al., 2000; Berg et al., 2002; Ikai and Nakamura, 2003). Therefore,
we use MERRA reanalysis dataset to calculate the freezing level height instead. Similar to Harris
et al. (2000), linear interpolation of the temperature profile at each grid point is utilized to find the
geopotential height of the 0 ◦ C isotherm, and then the corresponding geopotential height is taken
as the freezing level height in this study.
2.3
Collocation Scheme
The spatial resolutions among various TMI channels are different, and they are also different
from that of PR. To analyze coincident data from all these channels, data collocation was performed
as follows. First, in order to avoid possible surface contamination and mismatch between PR and
TMI observations near the swath edges, only the 9 TMI pixels for 37 GHz near the center of the
TMI swath are kept. The 9 closest PR pixels to each 37 GHz pixel footprint are choen, and then
the rainfall rates related to the 9 PR pixels are averaged with weights to represent the rainfall
rate at the 37 GHz pixel resolution. Rainfall profile at this resolution is obtained by applying
this procedure at each layer. The same procedure is applied to the 85 GHz TBs to obtain the 85
GHz TB at the 37 GHz resolution. The weight assigned to a selected PR pixel decreases with the
distance of its center to the center of the TMI pixel following the function exp(−r2 /σ 2 ), where r is
the distance and σ is a constant that can be determined by letting the weight reduce to one-half
when r increases from 0 to one-half of the effective field of view at 37GHz (i.e., 12.6km). For lower
frequency channels (i.e., 10 GHz, 19 GHz, and 21 GHz) their original coarser spatial resolution
has been used in this study. Several investigators have proposed methods for spatial resolution
enhancement for some of these channels (e.g., Farrar and Smith, 1992; Bauer and Bennartz, 1998;
Rapp et al., 2009). While their approach brings better matching resolution among all the channels,
it also introduces noise by the resolution enhancement. In this study, we decided to work with the
original resolution for data at the lower frequencies. This collocation process is similar to Fu and
Liu (2001).
8
Spatially, for the land type, land elevation, MERRA reanalysis and TELSEM emissivity dataset,
we use the closet grid data to mach the TMI pixels at 37GHz. The 1-km native NMQ precipitation
pixels are averaged to match this resolution. Temporally, surface temperature, temperature profile,
relative humidity profile and geopotential height profile are linearly interpolated to match the time
of the TB observation.
9
CHAPTER 3
SENSITIVITY OF BRIGHTNESS TEMPERATURE
TO RAINFALL RATES
3.1
Ranking Channel Sensitivity
Unlike TB-rain relation over ocean at low microwave frequencies, which is highly nonlinear with
TBs increasing initially and decreasing as rainfall rate increases (with the exception for TBs at 10
GHz or lower frequencies), the degree of linearity of the TB-rain relation over land is not well known.
It may depend on many variables, such as the rainfall location, rain types or regimes, etc. (Ferraro
and Marks, 1995; Dinku and Anagnostou, 2005). Therefore, in the following correlation analysis,
we use the more robust Spearman rank correlation, rather than the conventional Pearson productmoment correlation that cannot recognize the nonlinear relationship between two variables and is
sensitive to the outlying points. To compute the Spearman correlation coeeficients, the ranks of the
data points rather than the data values themselves are used, as shown in the following equation:
1
n−1
rxy =
1
[ n−1
n
P
n
P
(xi − x̄)(yi − ȳ)
i=1
1
1
(xi − x̄)2 ] 2 × [ n−1
i=1
n
P
1
(3.1)
(yi − ȳ)2 ] 2
i=1
where x and y denote the ranks of data pairs, n is the sample size, and x̄ and ȳ are the means of
x and y, respectively. Through such transformation, the Spearman correlation is able to be applied
to both linearly and non-linearly related data pairs and has a higher tolerance to outliers (Wilks,
2011).
Utilizing the Spearman rank correlation (Eq.3.1), the sensitivity of the TMI channels or channel
combinations to rainfall over land was investigated using collocated TMI and PR data, in an effort
to gauge the rainfall information content within brightness temperatures of these channels. The
sensitivities of both the 9 original TMI channels and their combinations are studied. Here we
consider only addition and subtraction when combining brightness temperatures from two channels.
The possible channel combinations from the 9 original TMI channels is 72, resulting in totally 81
10
new brightness temperatures. For simplicity, in the following discussions, we will call the channel
combinations channels as well.
Using data from 3 years (1998 to 2000) of global observations of the TRMM covered land areas,
the correlation coefficients between NSR and TBs for the 81 channels are computed. Only pixels
that are identified rain by PR are included in the calculations. The number of the collocated
pixels is 1,620,274, 1,665,948 and 1,649,498 for 1998, 1999 and 2000, respectively. The results are
shown in Fig. 3.1, in which the channels are ordered by their magnitude of (the absolute value of)
correlation coefficients. The channels with the top 20 correlation coefficients are listed in Table 3.1.
The magnitude of correlation coefficients among the different channels varies considerably from 0 to
0.6. That is, TBs at some channels (channel combinations) can explain 40% of the variances of NSR,
while TBs at other channels are completely uncorrelated with NSR. The results show that there is
little year-to-year change in the orders of the channel sensitivity as determined by the magnitude
of their correlation coefficients, and the manners by which the sensitivity decreases with channels
are almost identical among the three years. The channels that possess the highest correlation
with NSR are V19-V37 and V21-V37, with a correlation coefficient of 0.6. In comparison, the
correlation coefficient for the V85 channel is about -0.5, which means that TBs at the V85 channel
explain 10% less NSR variances than those at the V19-V37 or the V21-V37 channels. Statistical
test indicates that the difference between the correlation coefficients of the V85 and the V19-V37
(or the V21-V37) channels is significant at 99% confidence level. It is worth mentioning that the
individual responses from the V19, V21 or V37 channel alone is much weaker than the V85 channel.
In particular, there is almost no correlation with NSR at all for the V19 or the V21 channel alone.
It is the combination of the two lower frequency channels with the V37 channel that responds more
sensitively to NSR than the 85 GHz channel. The correlations of the V19-V37 and the V21-V37
channels with NSR are almost identical (ref. Table 3.1). In the following, we only use the V19-V37
channel as the most sensitive channel for discussions. Alternatively, using the V21-V37 channel
does not change any conclusion. To investigate the dependence of the TB - NSR correlation on rain
types, the collocated data are divided into convective and non-convective pixels. Similar to Seo
et al. (2007), if more than 5 of the 9 original PR pixels within a TMI 37 GHz pixel footprint are
classified as convective in 2A23, the collocated pixel is called convective, otherwise non-convective.
The correlation coefficients between NSR and TBs are then calculated, and shown in Fig. 3.2. The
11
results indicate that the V19-V37 (V21-V37) channel has the strongest response to NSR regardless
of rain type, while both the V19-V37 and the V85 channels have higher correlation with NSR for
convective rainfall.
To investigate the geographical distribution of the responses of the V19-V37 and the V85 channels to NSR, the correlation coefficients between TBs at the V19-V37, the V85 or the V21-V85
channel and NSRs are calculated for each 5◦ (latitude) × 5◦ (longitude) grid box. The distributions
of the correlation coefficients and their differences (i.e., the magnitude of correlation coefficients
for the V19-V37 channel minus that for the V85 channel) are shown in Fig. 3.3. The response to
rainfall at the V19-V37 channel is stronger than that at the V85 channel for most of the tropical
land areas, except for the northern part of the African continent, the Middle East and southern
Australia. What is interesting is that the signal from both the V19-V37 and the V85 channels is
weaker in the aforementioned regions than in other areas, indicating that these are the areas being
the most challenging for rainfall retrieval. It is worth noting that for almost all (∼99%) the grid
boxes, the correlation coefficients and their differences passed the 99% significance level. Since the
V21-V85 channel combination has been used in TRMM facility algorithm (Ferraro et al., 2005),
the correlation coefficients between TBs at the V21-V85 channel and NSRs are also calculated and
shown in Fig. 3.3. It is found that the characteristics for the V21-V85 channel are similar to those
for the V85 channel, implying that the radiative signature for the V21-V85 channel combination is
dominated by the signature at the V85 channel.
The above results seem to be counter-intuitive because it is commonly believed that over land
rainfall signature generally originates from the scattering by ice particles aloft, which is the strongest
at 85 GHz and has some appreciable magnitude at 37 GHz when the rainfall becomes heavy.
However, our analysis as shown above indicates that the combination of two lower frequencies
provides better information for over-land rainfall. Understanding this apparent contradiction and
examining the usefulness of the low frequency channel combination in over-land rainfall retrievals
are the main goals of this study.
3.2
Dependence on Cloud Microphysical Structures
To quantify the abundance of liquid and ice hydrometeors in a raining cloud, the following two
indices are defined: the frozen water index (hereafter referred to as FWI) and the liquid-to-frozen
12
water ratio index (hereafter referred to as RI). FWI is defined as the summation of the rain rates
retrieved from PR over all levels above -10◦ C (in mm h−1 as unit). RI is defined by the ratio of
the summation of rain rates below -10◦ C level to the summation of rain rates above -10◦ C level.
The -10◦ C level height is assumed to be located 1.75 km above freezing level height that is given
in the 2A25 dataset. While the use of -10◦ C as a threshold for liquid-ice separation is somewhat
arbitrary, choosing a different threshold a few degrees higher or lower than -10◦ C does not change
the main conclusions to be derived below. Based on this definition, the larger the FWI is, the more
ice particles there are in the vertical atmospheric column. Similarly, a larger RI value indicates
greater liquid water amount in the column compared to ice water.
First, all raining pixels are divided into 9 groups based on their FWI and RI values, i.e., dividing
both FWI and RI into three ranges: 0 to 3, 3 to 6 and greater than 6. For convenience, each of the 9
groups is given a name consisting of a F- and a R-number, so that the group name F1− R1 represents
those data with FWI=0∼3 and RI=0∼3, F1− R2 with FWI=0 3 and RI=3 6, and so on. The pixel
number and rainfall amount fractions of the so-divided groups within all raining clouds are shown in
Table 3.2. It is noted that the group F1− R3, which contains the least amount of ice but relatively
large amount of liquid water, makes up 2/3 of the raining pixels and 1/3 of total rainfall amount.
Next, in each group, the eighty-one correlation coefficients between NSR and different channels as
done in the previous section are computed (not shown). The channels with the top 5 correlation
coefficients in each group are shown in Table 3.3. Largely, the correlation characteristics may be
divided into 3 categories according to these top responding channels. The first category (F1− R1,
F1− R2) is represented by a negative correlation and the top responding channels are either 85
GHz alone or 85 GHz plus a lower frequency channel (Note that signatures from horizontal and
vertical polarization channels are nearly identical over land surface). The main rainfall signature in
this category is the brightness temperature reduction at 85 GHz. The second category (F1− R3) is
represented by a positive correlation and the top responders radiometric signature is the difference
between brightness temperatures at two frequencies. The main response is the increase in brightness
temperature differences between the two channels as rainfall rate increases. The third category
(F2− R1, F2− R2, F2− R3, F3− R2, F3− R3) is also represented by a negative correlation, but the
top responding channels are a lower frequency channel (21 or 37 GHz) or a lower channel plus
another lower frequency channel. The main rainfall signature is again the reduction of brightness
13
temperature but at lower frequency channels. The group F3− R1 is a mixture of the categories 2
and 3. To simplify the discussion while not losing the generality of the problem, we will use V85,
V19-V37, or V37 to discuss the dominant rainfall signatures in these 3 categories, respectively.
Note that using a slightly different channel set, for example, H85, V21-V37, or V21+V37 does not
change our conclusions. The correlation coefficients between NSR and the aforementioned three
channels are compared in Fig. 3.4 for the 9 groups of raining clouds. For the F1− R1 and F1− R2
groups, although they are weak, there are measurable rainfall signatures contained in the V37 and
V85 channels, in comparison to almost no response by the V19-V37 channel. Based on Table 3.2,
these two groups contain 7% of the total raining pixels, which contribute to ∼1.3% of the total
rainfall amount. In group F1− R3, the V19-V37 channel responds to rainfall the strongest among
the 3 channels. This group makes up ∼65% of raining pixels and ∼35% of rainfall amount. Because
of the large number fraction and the stronger response at the V19-V37 channel in this group, the
correlation coefficient between the V19-V37 channel and NSR for all raining pixels is the highest
among all the channels as shown in Fig. 3.1. For the rest six groups, the common feature is that
the V37 channels response is stronger than the other two channels, except for F3− R1 in which the
V37 and the V19-V37 channels have a similar degree of response. To further explore the physical
causes of the different responses, the characteristics of the vertical structures are analyzed using
the contoured frequency by altitude diagrams (CFADs) [Yuter and Houze, 1995] as shown in Fig.
3.5. Specifically, the data are re-grouped into three categories based on the above analysis, i.e.
F1− R1 and F1− R2 as Category 1, F1− R3 as Category 2, and the other six groups as Category
3. The CFADs are generated using all raining data over the global tropics during the 3 years. In
generating the CFADs, we used the -10C altitude at reference level (i.e., relative height = 0 at
-10◦ C), so that radar returns above this level are to be considered as frozen water and those below
this level are to be considered as liquid water. Fig. 3.5a for Category 1 (F1− R1 and F1− R2) clouds
shows that both the amounts of frozen and liquid water are quite low. Consequently, only the
relative high frequency channels, especially V85, are sensitive enough to capture the frozen water
scattering information. Shown in Fig. 3.5b is the CFADs for raining clouds in Category 2 (F1− R3).
While the amount of frozen water is small (close to that for Category 1 in Fig. 3.5a), the amount
of liquid water is much larger. In other words, the vertical distribution of hydrometeors in this
category is dominated by the bottom-heavy liquid water, which is more directly related to the NSR.
14
Recalling that for this category the V19-V37 channel demonstrates the highest response to NSR,
suggesting that this channel combination may have the ability to capture liquid water information.
In Fig. 3.5c (Category 3), both frozen and liquid water amounts are large, and the large amount of
hydrometers makes the brightness temperatures at all the three channels (V19-V37, V37 and V85)
have a relatively high response to NSR, although the 37V channel tops the other two. In other
words, when the vertical column contains high amounts of frozen and liquid hydrometeors, it is the
37 GHz channel, not the 85 GHz channel, that has the strongest response to surface rainfall. This
finding is consistent with Aonashi et al. (2009) and Seo et al. (2010).
3.3
Rainfall Signatures at the V19-V37 Channel
The ice scattering signatures at the 85 GHz or even the 37 GHz channel have been well described
in the literature and used in retrieval algorithms (e.g., Adler et al., 1993; Aonashi et al., 2009).
However, the nature of the rainfall signature at the V19-V37 (or likewise the V21-V37) channel has
not been well understood so far. As mentioned above, this channel combination responds to rainfall
more closely for Category 2 clouds, in which liquid water drops are the dominant hydrometeors,
suggesting that it contains information on the amount of liquid water in the atmospheric column.
Because liquid water is more directly related to surface rainfall than frozen water aloft, this channel
combination is potentially very useful in improving rainfall retrieval over land.
Let us first examine several cases in which frozen water amount is minimal as indicated by
FWI=0 (belonging to group F1− R3). Fig. 3.6 presents the scatterplots of 4 such cases in 1998,
with the V19-V37 channels response in the left panel and the V85 channels response in the right
panel. While brightness temperatures at both channels do not have strong response to NSR,
the V19-V37 channel does show some skills with correlation coefficients ranging from 0.2 to 0.3,
compared to no measurable correlation for the V85 channel. Note that the correlation coefficient
for the V19-V37 channel drops to 0.1 if it is computed using all raining data in the global dataset
(instead of individual cases). The reason is that rainfall rates (and the rainfall signature) for the
FWI=0 cases are weak, and including all cases with various surface and atmospheric conditions
leads to the rainfall signature being swallowed by the variations of the background.
The liquid water information possibly contained in the V19-V37 channel may be further examined by using radiative transfer simulations (Liu, 1998). In these simulations, we assume 1.0 for
15
surface emissivity, a tropical standard atmosphere, and rainfall profiles as derived from PR data
by Liu and Fu (2001). Additionally, we conducted the simulations with and without taking into
account of the horizontal inhomogeneity within a radiometers field-of-view (Varma et al., 2004;
Varma and Liu, 2006). The simulation results are shown in Fig. 3.7, together with TRMM observed data over the southern Great Plain regions. In Fig. 3.7a, we show the liquid-only results,
in which all hydrometeors are assumed to be raindrops. It shows that even without ice particles
in the atmospheric column, there is still a response on the order of 20 K by the V19-V37 channel
to surface rain rate. The simulations (red curve) matches reasonably well with observations (green
circles) derived from pixels with almost no PR radar echo above -10C altitude. If ice particles
are added in the simulations to the hydrometeors profiles (Fig. 3.7b), the dynamic range of the
V19-V37 channel expends to 35 K, and the simulation results (red curve) still captures the trend
of the real observations (green circles). Based on the above results, we argue that the V19-V37
channel contains not only ice, but liquid water information in the atmospheric column as well. An
effective use of it can potentially improve rain retrieval over land, since liquid water is more directly
related to surface rain than ice water aloft.
While it is difficult to verify, we suspect that the better correlation between NSR and V19V37 (or V21-V37) may be also benefited from the reduction of surface-emissivity-variation-induced
uncertainties because of the subtraction of brightness temperatures at two channels. In this case,
as surface wetness changes, emissivities for 19 and 37 GHz channels vary in a similar fashion so
that its net impact on V19-V37 channel combination is small. If the above speculation is true, the
V19-V37 channel not only extracts liquid water information in the atmosphere, but also reduces
surface noise, which makes it the most favorable candidate for over-land rainfall retrieval.
3.4
Influence of the Surface Temperature and Land Type
The correlation coefficients between TBs at the V19-V37, V37 and V85 channels and NSR are
computed within each 5◦ latitudinal belt from 35◦ S to 35◦ N for the months of January, April, July
and December, by using the data from 1998 to 2000. The results are shown in Fig. 3.8. Fig. 3.8a
shows that in January the V19-V37 channel responses strongly from 35◦ S to 10◦ N, while to north
of 10◦ N the correlation between TBs at the V19-V37 channel and NSR decreases dramatically,
and the signal at the V85 channel becomes the strongest instead. The trend in July (Fig. 3.8c)
16
is almost the opposite to that in January. That is, the V85 channel responded the strongest from
35◦ S to 20◦ S, while the V19-V37 channel becomes the top responder to the north of 10◦ S. In April
(Fig. 3.8b) and October (Fig. 3.8d), the V19-V37 channel better captures rainfall signature over
the vast majority of the latitudes, except in the area of 30◦ − 35◦ at both hemispheres. These results
imply that the TBs response to NSR closely relates to seasons, or the change of temperatures. That
is, the V85 channel responds to NSR better between 20◦ and 35◦ over the winter hemisphere, while
the V19-V37 channel responds better in the summer hemisphere and near the equator.
To examine the influence of surface temperature on the TB NSR relation, we use the 24-times
daily 2-meter air temperature obtained from MERRAR reanalysis. Correlation coefficients for the 3
channels (V19-V37, V37, and V85) are calculated over the following seven 2-meter air temperature
intervals: <280K, 280K∼285K, . . . , 300K∼305K, and >305K (Fig. 3.9). The V19-V37 channel
responds stronger (weaker) than the V85 channel when the 2-meter air temperature is warmer
(colder) than 290 K. Interestingly, even the V37 channel becomes a better responder than the V85
channel when the temperature is higher than 290 K, although the signal at the V37 channel is
weaker than those of the other two channels when the 2-meter air temperature is colder than 290
K. The CFADs (Fig. 3.10a and Fig. 3.10b) from the rainfall profiles in air temperature <280 K and
>305 K show that liquid water amount in the warmer temperature group is much higher than that
in the colder temperature group. Since the V19-V37 channel is thought to combine the liquid and
frozen water information, the rainfall signal strength at this channel is expected to increase as the
surface temperature (therefore freezing level height) increases.
The influence of land type on the TB NSR relation is studied using the land type classification
of Hansen et al. (2000), in which land types are given by 12 indices over TRMM covered areas:
needleleaf evergreen forest (1), broadleaf evergreen forest (2), broadleaf deciduous forest (4), mixed
forest (5), woodland (6), wooded grassland (7), closed shrubland (8), open shrubland (9), grassland(10), cropland (11), bared ground (12) and urban and built-up (14), where the value in the
parenthesis stands for the land surface type index. The global distribution of these land types can
be found in Hansen et al. (2000). It is noticed that the vegetation cover becomes less and less with
the land type index increases from 1 to 12. For each land type, the relationship between TBs at
the V19-V37, V37 and V85 channels and NSR are computed and the results are shown in Fig. 3.11.
It can be seen that the V19-V37 channel responds the strongest over all the land types except for
17
over bare ground (index 12), for which the V85 channel has the highest correlation with NSR. As
can be seen from Fig. 3.10c and Fig. 3.10d, the rainfall vertical structures over bare ground and
evergreen forest do not show obvious differences, indicating that rainfall can also become relatively
heavy even over bare ground when the air temperature is high. Therefore, the different response to
NSR by V19-V37 and V85 shown in Fig.11 is most likely due to the fact that colder temperatures
are more often to occur at bare ground regions.
The influence of both surface type and surface air temperature on the TB NSR relations is
summarized by their correlations displayed in the 2-dimensional space of 2-meter air temperature
and surface type index as shown in Fig. 3.12. In Fig. 3.12a, we show the distribution of observed
raining pixel frequency (in percentage), which indicates that rainfall occurs most frequently when
the 2-meter air temperature is between 290 and 300 K and land types are needleleaf evergreen
forest and wooded grassland. The NSR variances (R2) explained by the V19-V37, V37 and V85
channels are shown in Fig. 3.12b,Fig. 3.12c and Fig. 3.12d, respectively. The differences between
these explained NSR variances are shown in Fig. 3.12e and Fig. 3.12f. All three channels can explain
more NSR variances where 2-meter air temperature is around 290 K and vegetation is relatively
dense, such as needleleaf evergreen forest, broadleaf evergreen forest, broadleaf deciduous forest or
mixed forest. Even if there is little vegetation, as long as the 2-meter air temperature is warmer than
290 K, the NSR variances explained by the V19-V37 channel still surpasses that by the V85 channel.
Similar conclusion can also be drawn for the V37 channel. The V85 channel, on the other hand, can
explain more NSR variances where there is not much vegetation and the air temperature is colder
than 290K, especially over the bare ground. The CFADs (Fig. 3.10e) for rainfall profiles over bare
ground at low temperatures showed that only small amounts of frozen and liquid hydrometeors
exist under this condition. It seems that the V85 channel is advantageous over other channels
at this low hydrometeor condition. In contrast, the CFADs (Fig. 3.10f) showed that abundant
frozen and liquid hydrometeors exist in rainfall profiles over evergreen forest at warm temperatures.
Therefore, the V19-V37 channel is superior to other channels under such scenario. Evidently, the 2meter air temperature and surface land type, which indirectly provide information on the potential
depth of rain drops (related to freezing level) and surface emissivity, are two useful indicators for
the precipitation structures overland. Using them to select and prioritize channels in retrieval
algorithms can potentially improve rainfall retrieval over land. The usefulness of the 2-meter air
18
temperature and land surface type in selecting or prioritizing channels for retrieval algorithms may
be demonstrated by a mock-retrieval experiment under the following two cases: 1. warm vegetated
case - rainfall events over mixed forest when the 2-meter temperature is between 290K and 295K,
and 2. cold bare ground case - rainfall events over bare ground when the temperature is between
280 and 285 K. From Fig. 3.12, it is seen that the two cases correspond to the situations where
V19-V37 and V85 channels are more responsive to NSR, respectively.
To perform the retrieval, under each of the above two conditions we first use the collocated PR
NSR and TMI TB data from 1998 to 2000 to derive a NSR TB regression equation, separately for
the V19-V37 and the V85 channels. Because data points are heavily populated at the lower end
of rainfall rate, a NSR-TB relation from a simple regression cannot fit well to the data points at
the higher end of the rainfall rates. To mitigate this problem, we conduct a procedure as explained
below to form the adjusted NSR −TB relation. Taking the NSR and the V19-V37 channel data as
an example, the blue line in Fig. 3.13a is the least-square regression line between NSR and V19V37 channel using original data point, while the green dots are the mean TB values averaged over
different rainfall rate bins. Clearly, using the original regression line will significantly underestimate
rainfall rate when it is heavier than 8 mm h−1 . Instead of using the original regression line for
retrieval, we regenerate an adjusted curve by fitting data points derived from the original regression
line when rainfall rate is lower than 8 mm h−1 and those bin-averaged when rainfall rate is higher.
The original regression line and the adjusted fitting curve are shown in Fig. 3.13b along with
observational data points; the adjust curve fits better to the observations at the higher end of the
rainfall rates. Similar adjustment is done to the V85 TB versus NSR relation as well.
Utilizing the adjusted NSR−TB curve, rainfall rates are retrieved from TBs at the V19-V37
or the V85 channel for the year of 2001. The retrieved rainfall rates are then compared to PR
derived NSRs. Note that we do not have a rain detection algorithm yet; therefore comparisons
are only done for those pixels designated as rain by the PR. The results are shown in Fig. 3.14.
For the warm vegetated case (Fig. 3.14a and Fig. 3.14b), the correlation coefficient and the rootmean-square error are 0.65 and 3.88 mm h−1 for the V19-V37 channel, and 0.48 and 5.60 mm h−1
for the V85 channel, respectively. Therefore, the V19-V37 channel can deliver a better retrieval
where land type is mixed forest and when the 2-meter air temperature is between 290K and 295K.
In contrast, for the cold bare ground case (Fig. 3.14c and Fig. 3.14d), the correlation coefficient
19
and root-mean-square error are -0.09 and 2.06 mm h−1 for the V19-V37 channel, and 0.45 and
2.28 mm h−1 for the V85 channel, respectively. Therefore, over cold bare grounds there is modest
skill to retrieve rainfall by the V85 channel while no retrieval skill is demonstrated by the V19-V37
channel. Based on the above results, we argue that multiple channels or channel combinations are
needed for over-land algorithms. In the algorithms, appropriate weights need to be set to different
channels to reflect their superiority in responding to rainfall under a certain condition or rain
regime. As noticed above, land surface type and 2-meter air temperature are two good parameters
to characterize the rain regimes.
3.5
Conclusions
Using collocated TRMM PR and TMI data, we first investigated the sensitivity of TMI channels
or their combinations to over-land rainfall. To our surprise, the results show that instead of the 85
GHz channel, it is the V19-V37 or the V21-37 channel combination that has the highest sensitivity
to over-land rainfall over the global tropical areas covered by TRMM satellite observations. The
V19-V37 or the V21-V37 channel combination can explain 10% more of the rainfall rate variances
than the V85 GHz channel. Furthermore, the global distribution of channel sensitivity indicates
that the V19-V37 channel combination has a stronger response to rainfall than the V85 channel
for most of tropical land regions, except for those over desert, arid and semi-arid areas, such as
northern part of the African continent, the Middle East and southern Australia.
To understand the underlying physics of the different responses of TMI channels or channel
combinations to over-land rainfall, we introduced two parameters derived from PR vertical rainfall
profiles: the frozen water index and the liquid-to-frozen water ratio index. The two parameters
represent the amounts of frozen water and liquid water in the raining clouds, respectively. Grouping
all raining pixels by the two indices, we found that the most sensitive channel varies with cloud
groups, and all raining clouds may be largely divided into 3 categories with the following 3 most
favorable channels: V19-V37, V37 and V85. For clouds with modest amount of liquid water and
low amount of frozen water, the V19-V37 channel can capture information from both liquid and
frozen water, leading to the strongest response to near surface rainfall. A large majority of raining
clouds belongs to this category, resulting in that the V19-V37 channel is the most sensitive channel
if all rain clouds are used in the analysis. The V85 channel, on the other hand, is the most sensitive
20
channel for clouds being low in both liquid and frozen water amounts. Because of the low amount of
hydrometeors, the rainfall signal in this category even at the V85 channel remains weak. For clouds
with large amount of hydrometers (liquid and ice), the V37 GHz channel becomes the strongest
responder to surface rainfall, with the V19-V37 channel being the close second.
In searching for routinely observable parameters that are related to rain cloud microphysical
structures, and therefore have bearing on channel selections in retrieval algorithms, we found that
land surface type and 2-meter air temperature are helpful. The V19-V37 channel often responds
the most closely to surface rainfall where vegetation is denser and 2-meter air temperature is
warmer, while the V85 channel responds closer to surface rainfall over less vegetated ground with
relative cold 2-meter air temperatures, especially over cold bare ground. We argue that 2-meter
air temperature and land surface type provide information on the potential depth of rain drops
(related to freezing level) and surface emissivity, which can be used to select and prioritize channels
in retrieval algorithms to improve rainfall retrieval over land. As a confirmation to this argument, we
performed retrievals under warm vegetated and cold bare ground conditions using regressed formula
separately for the V19-V37 and the V85 channels. As expected, the V19-V37 channel substantially
outperforms the V85 channel in the warm vegetated case and the V85 channel performs better in
the cold vegetated case.
Because of the high and highly variable emissivity of land surface, it has been long believed that
the only useful information from passive microwave observations for over-land rainfall retrieval is
the ice scattering at high frequency channels (i.e., 85 GHz). This study challenges this common
belief and concludes that it is the channel combination of two lower frequencies, i.e., V19-V37, that
has a stronger response to over-land rainfall for majority of the conditions. Its better response
is likely resulted from that this combination contains both liquid and ice information, and liquid
water has a more direct linkage to surface rainfall rate. Additionally, this study further indicates
that the best channel for over-land rainfall retrieval is dependent on the microphysical structures
of the rain clouds, and two routinely observable parameters, i.e., land surface type and 2-meter
air temperature, are good predictors to the cloud structures. The implication of this finding is
that retrieval algorithms may be developed to use the above two parameters to prioritize and set
different weights to satellite observations at different channels, so that the channel that has the best
rainfall sensitivity under a given condition receives the highest weight in the retrieval algorithm.
21
Such a practice in future land precipitation algorithms is highly recommended. Finally, it should be
mentioned that the spatial resolution of 85 GHz is finer than those for 19 and 37 GHz. Therefore,
while there is a high potential to improve the accuracy of rainfall rate estimation by including lower
frequency channels in retrieval algorithms, it will result in a coarser spatial resolution than when
only 85 GHz data are used.
22
Table 3.1: Correlation Coefficients (CC) Between NSR and TB of the Top 20 Channels/Combinations for 1998, 1999, 2000, and three Years Combined
Channels/Combinations
1998
V21 - V37
V19 - V37
V21 - V85
V19 - V85
H19 - V85
H19 - H85
H19 - H37
V19 - H85
V21 - H85
V10 - V85
V10 - H85
H19 - V37
H37 - V85
H37 - H85
V37 - V85
V85
V10 - V37
H10 - H85
H85 + V85
H10 - V85
Channels/Combinations
2000
V21 - V37
V19 - V37
H19 - H37
V10 - V85
V10 - V37
V19 - V85
V21 - V85
V10 - H85
V19 - H85
H19 - V85
V21 - H85
H19 - H85
V85
V19 - H37
H85 + V85
V37 + V85
V10 - H37
H85
H85 + V37
H37 + V85
CC
Channels/Combinations
1999
V21 - V37
V19 - V37
V21 - V85
V19 - V85
H19 - H37
H19 - V85
H19 - H85
V19 - H85
V10 - V85
V21 - H85
V10 - H85
H19 - V37
V10 - V37
H37 - V85
H37 - H85
V37 - V85
H10 - H85
V85
V19 - H37
H10 - V85
Channels/Combinations
3-yrs combined
V21 - V37
V19 - V37
V21 - V85
V19 - V85
H19 - H37
H19 - V85
H19 - H85
V19 - H85
V10 - V85
V21 - H85
V10 - H85
H19 - V37
H37 - V85
V10 - V37
H37 - H85
V37 - V85
V85
H10 - H85
H10 - V85
H85 + V85
0.56
0.55
0.51
0.51
0.51
0.51
0.50
0.49
0.49
0.49
0.48
0.47
0.46
0.46
0.45
-0.45
0.45
0.44
-0.44
0.44
CC
0.59
0.59
0.53
0.52
0.52
0.52
0.51
0.51
0.50
0.50
0.50
0.50
-0.49
0.49
-0.48
-0.48
0.48
-0.48
-0.47
-0.46
23
CC
0.57
0.57
0.52
0.52
0.52
0.51
0.51
0.50
0.50
0.50
0.49
0.49
0.47
0.46
0.46
0.45
0.45
-0.45
0.45
0.45
CC
0.57
0.56
0.52
0.52
0.51
0.51
0.51
0.50
0.50
0.49
0.48
0.48
0.47
0.46
0.46
0.45
-0.45
0.45
0.44
-0.44
Table 3.2: Statistics of pixel number fraction (%) and rainfall amount fraction (%, in
parenthesis) grouped by FWI and RI indices.
RI1
RI2
RI3
FWI 1
3.80(0.53)
3.42(0.78)
64.74(35.02)
FWI 2
2.48(0.70)
1.98(1.21)
5.55(11.76)
FWI 3
7.04(10.88)
4.80(12.94)
6.18(26.18)
Table 3.3: Correlation coefficients between NSR and TBs of the top 5 channels/combinations grouped FWI and RI indices.
F1 R1
F1 R2
F1 R3
F2 R1
F2 R2
F2 R3
F3 R1
F3 R2
F3 R3
V85
-0.1898
V37 + V85
-0.2614
V21 - V37
0.3961
V37
-0.3514
V21
-0.3563
V21 + V37
-0.3733
V10 - V37
0.5014
V37
-0.5155
V21 + V37
-0.4281
V37+V85
-0.1835
V21 + V85
-0.2520
V19 - V37
0.3914
V21 + V37
-0.3511
V21 + V37
-0.3539
V37
-0.3720
V37
-0.4804
V21 + V37
-0.5065
V21
-0.4222
H85+V85
-0.1790
H85 + V37
-0.2511
V21 - V85
0.3808
V21
-0.3455
V19 + V21
-0.3415
V21
-0.3568
V19 - V37
0.4759
H37 + V37
-0.4982
V37
-0.4131
24
V21+V85
-0.1788
V85
-0.2511
V19 - V85
0.3710
V19 + V37
-0.3419
V37
-0.3397
H37 + V37
-0.3430
V21 - V37
0.4600
H37 + V21
-0.4841
V19 + V37
-0.3999
V19+V85
-0.1748
V19 + V85
-0.2467
V21 - H85
0.3615
V19 + V21
-0.3372
V19 + V37
-0.3391
V19 + V37
-0.3394
V10 - H37
0.4577
V19 + V37
-0.4792
H37 + V21
-0.3972
V21−V37
0.6
V19−V37
0.6
1998
V19−V37
V21−V37
0.5
1999
V85
0.5
V85
R (absolute value)
R (absolute value)
V37
V37
0.4
0.3
V21
0.2
0.4
0.3
V21
0.2
V19
0
0.6
V19
0.1
0.1
1
11
21
31
41
51
Channel Combination
61
0
81
2000
V19−V37
V21−V37
71
1
11
21
31
41
51
Channel Combination
V21−V37
0.6
V85
61
71
81
3yrs combined
V19−V37
0.5
0.5
V85
R (absolute value)
R (absolute value)
V37
0.4
0.3
0.2
V21
V37
0.4
0.3
V21
0.2
V19
V19
0.1
0
0.1
1
11
21
31
41
51
Channel Combination
61
71
0
81
1
11
21
31
41
51
Channel Combination
61
71
81
Figure 3.1: Correlation Coefficients (CC) between NSR and TBs of different channels/combinations over land for data of 1998, 1999, 2000, and 3-year combined. For
comparison, all the correlation coefficients are in their absolute values.
25
0.6
0.5
CC (absolute value)
1998
V21−V37
V19−V37
non−convective
V85
0.4
V37
0.3
V21
0.2
V19
0.1
0
1
0.6
11
31
41
51
Channel Combination
61
71
81
1998
V21−V37
V19−V37
0.5
CC (absolute value)
21
non−convective
V85
0.4
V37
0.3
V21
0.2
V19
0.1
0
1
11
21
31
41
51
Channel Combination
61
71
81
Figure 3.2: Correlation Coefficients (CC) between NSR and TBs of different channels/combinations over land for convective and non-convective clouds in 1998. For comparison, all the correlation coefficients are in their absolute values.
26
0.4
o
15 S
0.2
30oS
120oW
60oW
0o
response of V85
60oE
120oE
(b)
30oN
Latitude
180oW
0o
0.4
15oS
0.2
30oS
120oW
60oW
0o
60oE
response of V21−V85
120oE
Latitude
180oW
(c)
30oN
0o
15 S
0.2
30oS
120oW
60oW
0o
60oE
120oE
180oW
response difference between V19−V37 and V85
(d)
30oN
Latitude
0.8
0.4
o
15oN
0o
15oS
30oS
180oW
0
0.6
15oN
180oW
0.8
0.6
15oN
180oW
0
120oW
60oW
0o
Longitude
60oE
120oE
180oW
0
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
correlation coefficient
0o
correlation coefficient
Latitude
0.6
15oN
180oW
0.8
correlation coefficient
(a)
30oN
correlation coefficient difference
response of V19−V37
Figure 3.3: The global distribution of correlation coefficients (CC) between TBs and NSR.
Three years of data are used in calculating the CCs. (a) CC between TBs at the V19-V37
channel and NSR (absolute value), (b) CC between TBs at the V85 channel and NSR
(absolute value), (c) CC between TBs at the V21-V85 channel and NSR (absolute value),
and (d) CC difference between (a) and (b).
27
CC (absolute value)
0.5
0.4
0.3
0.2
0.1
0
3
2
Ratio Index (RI)
V19−V37
1
V85
3
V37
2
Frozen Water Index (FWI)
1
Figure 3.4: Correlation coefficients (absolute value) between TBs at the V19-V37, V37,
or V85 channel and NSR grouped by FWI and RI indices. Three years of data are used
in computing the correlation coefficients.
28
60 %
(a)
6
55
50
45
Relative Height (km)
4
40
35
2
30
25
0
20
15
−2
10
5
−4
−1
10
0
1
10
10
2
10
0
Rain Rate (mm h−1)
60 %
(b)
6
55
50
45
Relative Height (km)
4
40
35
2
30
25
0
20
15
−2
10
5
−4
−1
10
0
1
10
10
2
10
0
Rain Rate (mm h−1)
60 %
(c)
6
55
50
45
Relative Height (km)
4
40
35
2
30
25
0
20
15
−2
10
5
−4
−1
10
0
1
10
10
2
10
0
Rain Rate (mm h−1)
Figure 3.5: The CFADs of radar rainfall profiles for rain types of (a) Category 1, (b)
Category 2, and (c) Category 3.
29
10
295
(a)
(b)
8
6
V85 (K)
V19−V37 (K)
285
4
275
265
2
CC=0.30
0
0
1
2
3
4
NSR (mm h−1)
5
10
CC=0.05
255
0
6
1
2
3
4
NSR (mm h−1)
5
290
(c)
6
(d)
280
6
V85 (K)
V19−V37 (K)
8
4
270
2
260
0
CC=0.17
−2
0
1
2
3
4
NSR (mm h−1)
5
8
250
0
6
CC=−0.10
1
2
3
4
NSR (mm h−1)
5
295
(e)
6
(f)
285
4
V85 (K)
V19−V37 (K)
6
2
275
0
265
−2
CC=0.17
−4
0
1
2
3
4
NSR (mm h−1)
5
255
0
6
CC=0.04
1
2
3
4
NSR (mm h−1)
5
6
Figure 3.6: The response of the V19-V37 (left panel) and the V85 (right panel) channels
to Near Surface Rain (NSR) for warm rain cases. Figs. (a) and (b) are for region of
70-65◦ W, 0-5◦ N in May of 1998, (c) and (d) are for region of 100-105◦ E, 20-25◦ N in July
of 1998, (e) and (f) are for regions of 105-110◦ E, 25-30◦ N in August of 1998, and (g) and
(h) are for region of 45-50◦ E, 15-20◦ S in December of 1998.
30
40
(a)
V19−V37 (K)
30
20
10
0
0
5
10
NSR (mm h−1)
15
40
20
(b)
V19−V37 (K)
30
20
10
0
0
5
10
NSR (mm h−1)
15
20
Figure 3.7: TBs at the V19-V37 channel vs. near surface rain. (a) liquid drops only, (b)
liquid drops plus ice particles in the profile. The red (blue) curve denotes results with
(without) taking horizontal rain rate inhomogeneity within a pixel into account. Green
circles in (b) are observations over the S. Great Plain (95-90◦ W, 32-37◦ N) in July in 1998.
31
0.7
0.7
0.6
0.65
V19−V37
0.6
V85
CC (absolute value)
CC (absolute value)
0.5
0.4
0.3
V37
0.2
V19−V37
0.55
V85
0.5
0.1
0.4
(b) April
(a) January
0
−35 −30 −25 −20 −15 −10 −5 0 5
Latitude
0.35
10 15 20 25 30 35
0.7
0.65
10 15 20 25 30 35
V37
V19−V37
V19−V37
0.6
CC (absolute value)
CC (absolute value)
0.65
0.55
0.5
0.45
0.4
V37
0.35
0.3
−35 −30 −25 −20 −15 −10 −5 0 5
Latitude
0.7
V85
0.6
0.25
V37
0.45
0.55
0.5
V85
0.45
0.4
0.35
0.3
(c) July
−35 −30 −25 −20 −15 −10 −5 0 5
Latitude
0.25
10 15 20 25 30 35
(d) October
−35 −30 −25 −20 −15 −10 −5 0 5
Latitude
10 15 20 25 30 35
Figure 3.8: Correlation Coefficients (CC) between TBs and NSR within each 5 ◦ latitudinal
belt from 35 ◦ S to 35 ◦ N for the months of (a) January, (b) April, (c) July, and (d) October.
0.7
R (absolute value)
0.6
V19−V37
V85
0.5
0.4
0.3
0.2
0.1
0
240
280
285
290
295
300
2−meter Air Temperature (K)
305
310
Figure 3.9: Correlation Coefficients (CC) between TBs and NSR over seven 2-meter air
temperature intervals.
32
40 %
(a)
6
35
35
30
4
2
Relative Height (km)
25
20
15
0
25
2
20
15
0
10
10
−2
−2
5
−4
10−1
100
101
102
5
0
−4
Rain Rate (mm h−1)
(c)
100
101
40 %
102
30
Relative Height (km)
20
15
0
25
2
20
15
0
10
−2
5
10−1
100
101
102
5
−4
0
10−1
Rain Rate (mm h−1)
100
101
102
0
Rain Rate (mm h−1)
(e)
6
40 %
30
Relative Height (km)
20
15
0
40 %
35
30
4
25
2
(f)
6
35
4
25
2
20
15
0
10
10
−2
−2
5
−4
40 %
30
10
−2
−4
0
35
4
25
2
(d)
6
35
4
Relative Height (km)
10−1
Rain Rate (mm h−1)
6
Relative Height (km)
40 %
30
4
Relative Height (km)
(b)
6
10−1
100
101
102
5
−4
0
Rain Rate (mm h−1)
10−1
100
101
102
0
Rain Rate (mm h−1)
Figure 3.10: The CFADS of radar rainfall profiles for observations (a) with 2-m air temperature colder than 280K, (b) with 2-m air temperature warmer than 305K, (c) over bare
ground, (d) over evergreen forest, (e) with 2-m air temperature colder than 280K and over
bare ground, and (f) with 2-m air temperature warmer than 305K and over evergreen
forest.
33
0.7
R (absolute value)
0.6
V19−V37
V85
0.5
0.4
0.3
0.2
0.1
1
2
4
5
6
7
8
9 10
Land Surface Type Index
11
12
14
Figure 3.11: Correlation Coefficients (CC) between TBs and NSR over 12 different land
surface types.
34
0.5
0.5
5
0.5
1
1
0.1
0.5
5
30
25
25
290
0
−15
−10
−20
11
−5
−10
−15
−20
−1
Land Surface Type Index
300
5
15
10
0
12
10
0
5
0
−1
−5
10
15
5
20
5
2
30
0
−1
5
−1
−10
−15
285
290
295
300
(f)
−5
0
9
0
−1
8
−1
5
6
5
2
2−meter Air Temperature (K)
305
0
5
−10
10
5
5
5
−10
−10
15
280
300
0
−5
5
1
240
10
30
295
4
15
5
10
25
10
4
0
290
0
5
285
2−meter Air Temperature (K)
10
7
1
240
305
15
25
35
280
0
0
0
20
35
−1
6
0
−2
−15
−10
−5
7
35
40
35
11
10
10
8
25
14
(e)
5
−5
0
−5
−15
9
5
1
240
305
15
0
−1
35
295
5
−10
25
30
0
−1
5
10
35
2
Land Surface Type Index
15
5
285
2−meter Air Temperature (K)
−5
7
20
35
−10
12
20
25
15
15
14
30
30
280
10
30
4
20
1
240
30
25
25
5
2
30
35
35
10
30
35
40
40
45
5
25
30
30
8
6
(d)
20
25
30
20
30
30
305
25
20
25
6
9
300
25
30
30
10
45
295
35
40
20
30
7
4
25
10
290
15
15
5
25
20
285
2−meter Air Temperature (K)
30 35
20 25
11
25
8
280
15
30
40
45
25
25
10
9
30
12
30
25
14
(c)
40
0
20
305
45
50
45
−5
15
10
Land Surface Type Index
35
25
20
40
35
20
1
240
0.1
300
25
11
Land Surface Type Index
0.5
295
2−meter Air Temperature (K)
30
15
1
45
30
10
5
12
290
40
0
14
285
40
30
−1
280
35
35
25
15
2
0.
5
1
5
1
240
4
0.1
1
5
10
0.1
30
40
1
0.5
2
20
6
0.5
4
5
7 10
35
35
20
10
8
30
35
25
0.5
5
30
35
(b)
25
25
15
5
9
25
6
25
35
1
5 5
0.5
7
40
35
30
20
40
1
0.5
8
10
25
1
25
15
15
Land Surface Type Index
9
35
30
10
1
0.5
1
10
40
30
25 20
10
5
10
15
20
15
5
5
11
0.5
35
25 30
20
10
12
45
14
(a)
0.5
1
1
Land Surface Type Index
11
0.1
0.1
0.5
25
0.5
20
0.1
12
15
14
280
285
290
5
295
2−meter Air Temperature (K)
300
305
Figure 3.12: (a) The distribution of observed raining pixel number fractions. (b) NSR
variances explained by the V19-V37 channel. (c) NSR variances explained by the V85
channel. (d) NSR variances explained by the V37 channel. (e) The difference between
NSR variances explained by the V19-V37 channel and by the V85 channel. (f) The
difference between NSR variances explained by the V37 channel and by the V85 channel.
35
21
50
(b)
(a)
18
40
NSR (mm h−1)
NSR (mm h−1)
15
12
9
30
20
6
10
3
0
0
3
6
9
12
V19−V37 (K)
15
18
0
0
21
10
20
30
V19−V37 (K)
40
50
Figure 3.13: Example for deriving the adjusted NSR-TBs relation. (a) Blue line: original
regression line from observations of NSR and the V19-V37 channel TBs; Green line: averaged values in different rainfall bins. (b) Scatter plot of NSR vs. the V19-V37 channel
TBs using data from 1998 to 2000. The red curve is the original regression line and the
magenta curve is the adjusted line.
36
15
10
5
0
0
5
10
15
Observed Rain Rate (mm h−1)
10
6
4
2
2
4
6
8
Observed Rain Rate (mm h−1)
10
5
5
10
15
Observed Rain Rate (mm h−1)
10
(c)
8
0
0
(b)
15
0
0
20
Retrieved Rain Rate (mm h−1)
−1
Retrieved Rain Rate (mm h )
20
(a)
Retrieved Rain Rate (mm h−1)
−1
Retrieved Rain Rate (mm h )
20
(d)
8
6
4
2
0
0
10
20
2
4
6
8
Observed Rain Rate NSR (mm h−1)
10
Figure 3.14: Comparison between retrieved rain rate and PR Near Surface Rain (NSR).
(a) Retrievals from the V19-V37 channel over mixed forest where the temperature is
between 290 and 295 K. (b) Same as (a) except for the V85 channel. (c) Retrievals from
the V19-V37 channel over bare ground where the temperature is between 280 and 285K.
(d) Same as (c) except for the V85 channel.
37
CHAPTER 4
PREVIOUS RAINFALL EFFECT TO MICROWAVE
LAND SURFACE EMISSIVITIES
4.1
Introduction
In this chapter, detailed analyis will be performed regarding the reponse of the Microwave Land
Surface Emissivities (MLSE) to the previous rainfall. MLSE is a fundamental parameter in physical
over-land rainfall retrieval algorithm development involving space-based passive microwave (PMW)
radiometer observations, since it influences the thermal emission and scattering of radiation at the
surface.
Currently, most MLSE estimations are performed under clear sky conditions, as discriminated
by satellite-based cloud products or numerical model cloud analysis fields. The estimation approaches can be broadly grouped into three categories: (1) brightness temperature (TB) based
retrievals that estimate the emissivity by matching radiative transfer model (RTM) simulations
and satellite observed TB for each PMW radiometer channel, (2) land surface model (LSM) based,
where LSM models are coupled to bulk land surface RTM models, and (3) physical emissivity retrieval methods based on PMW TB observations, originally developed for PMW-based soil moisture
retrievals (Ferraro et al., 2013). Using a TB-based technique, Jones and Vonder Haar (1990) examined early Special Sensor Microwave Imager (SSM/I) data and estimated the MLSE between 19
and 85 GHz over Colorado. They pointed out that the emissivity at horizontally polarized 19 GHz
can decrease to 0.8 due to previous heavy precipitation events or irrigated lands, which significantly
wet the surface. Jones and Haar (1997) further presented a composite emissivity map for a 70-day
period over the central United States, which showed that the emissivity over parts of the central
Great Plains appeared to be more sensitive to previous heavy rain events, compared with that over
other areas in the continental United States. Prigent et al. (1997, 1998) investigated the MLSE at
continental and global scale also using SSM/I data under clear sky. They found that the emissivity
characteristics vary greatly over different land surface types; For example, compared with less vegetated areas, the microwave emissivity is not strongly polarized over forest. And the horizontally
38
polarized emissivity over forest is generally lower, while the vertically polarized one is higher. Such
a phenomenon, i.e., vegetation is able to depolarize the emissivity−relative to bare soil, has been
realized by numerous studies (e.g., BRUNFELDT and ULABY, 1986; Tian et al., 2012). Prigent
et al. (2005) showed that the PMW emissivities at frequencies of 19 GHz and higher are more
sensitive to vegetation than to soil moisture over dense vegetated regions. Their findings were
recently condensed into the Tool to Estimate Land-Surface Emissivities at Microwave frequencies
(TELSEM) (Aires et al., 2011). TELSEM can interpolate the climatological monthly mean emissivity database from a collection of multi-year SSMI, Advanced Microwave Scanning Radiometer
(AMSR-E) and Advanced Microwave Sounding Unit (AMSU) TB at 0.25◦ × 0.25◦ resolution. Aires
et al. (2011) showed that the use of TELSEM produced an overall positive impact upon numerical
weather prediction model forecasts.
Even under clear sky, there exist large errors and uncertainties in the emissivity estimation. Ruston and Vonder Haar (2004) analyzed the SSMI-based MLSE over the continental United States
during three summer seasons and pointed out that the dominant error sources in the MLSE retrieval include inaccurate land surface temperature, subpixel impacts and undetected clouds. Yang
and Weng (2011) showed that the land surface temperature is the primary source of error in emissivity estimation for frequencies lower than 19 GHz. Instead of using surface skin temperatures in
the MLSE retrieval algorithm, Norouzi et al. (2012) developed a lookup table of surface effective
temperatures, which take the TB diurnal cycle into consideration. Results showed that the differences between day and night emissivities are reduced to less than 0.01 by integrating such a lookup
table. By evaluating several MLSE datasets, Tian et al. (2012) demonstrated that there exist large
discrepancies among the estimates from different sensors and from different investigators for the
same targeted region.
Furthermore, it has been realized that MLSE at different channels are highly correlated. Using data from the Atmospheric Radiation Measurement (ARM) program Southern Great Plains
(SGP) site, Lin and Minnis (2000) noticed that the correlation coefficients between emissivity at
19 GHz vertical polarization and emissivities at all other channels on SMM/I are 0.98. Therefore,
they suggested that only two or three independent components are needed to determine all other
emissivities at SSM/I channels. Based on this premise, Bytheway and Kummerow (2010) proposed
an empirical model to estimate emissivities at other AMSR-E channels by using the emissivity at
39
horizontally polarized 10.7 GHz. They also utilized the calculated emissivity at 89 GHz to perform
the precipitation detection over three regions in United States and noted improved results.
Once precipitation has been flagged or deemed certain, physically-based precipitation estimation from PMW radiometers requires the MLSE under raining conditions. As mentioned, current
estimation methods and their subsequent estimates are performed almost exclusively for clear sky
conditions. In part 1 of this study, Turk et al. (2013)utilized a principal component (PC) analysis
of a multi-year set of clear-sky, over-land AMSR-E emissivity retrievals collected over all latitudes
and seasons, and showed that the clear-sky PC structure can be reasonably well estimated by
linear and nonlinear TB combinations. Their study focused on instantaneous conditions and did
not analyze any previous-time (antecedent) surface conditions. In this part 2 of this study, the
PC-based emissivity method of Turk et al. (2013) is further analyzed under clear-scene conditions,
where these data are separated by the amount, location and duration of previous-time precipitation. Therefore, the objective is to quantify how previous rainfall affects MLSE at AMSR-E and
similar channels on the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI)
(i.e., between 10 and 85 GHz). By doing this, one is able to obtain the emissivity over wet land
surfaces, which may be considered as proxy for the emissivity under raining conditions. Recent
investigations (Ferraro et al., 2013) noticed that the impact of previous precipitation on the emissivity at one site over the SGP region is most noticeable only after moderate rainfall events (more
than 10 mm day−1 ). In this study, the emissivity response to previous rainfall is performed over
a portion of the continental United States using hourly rainfall estimations from the National Mosaic and Multi-sensor Quantitative gauge-adjusted precipitation (NMQ) data (Zhang et al., 2011).
Additionally, we compare these instantaneous MLSE with the climatological TELSEM emissivity
(Aires et al., 2011) to illustrate how they differ under various surface wetness conditions, and utilize
a RTM to evaluate the performance of climatological and instantaneous emissivities under different
surface wetness circumstances and under different land cover types. Lastly, the study explores two
unique applications of the instantaneous PC-based emissivity. The first is a means to retrieve some
measure of the amount of previous rainfall from the relative time history change of the MLSE.
The second is a method to estimate the emissivity underneath precipitating scenes, by first adjusting the surface-sensitive principal components that were derived under clear-sky scenes, and then
reconstructing the joint MLSE (all channels simultaneously) in the presence of precipitation.
40
4.2
Two Simultaneous Emissivity Datasets
Central to this study are two simultaneous emissivity datasets.
The first of these is the
physically-based soil moisture dataset and emissivity retrieval technique developed for the WindSat
sensor at the Naval Research Laboratory (Li et al., 2010) that was adapted to TMI data (Turk
et al., 2012a). This dataset provides joint retrievals of the soil moisture, vegetation water content,
surface temperature, and emissivity at 6 channels (H/V at 10.7, 19.35 and 37 GHz) under nonprecipitating and non snow-covered surfaces on a daily 25-km Equal Area Scalable Earth (EASE)
grid, identical to the grid used for AMSR-E land products. Although this physically-based MLSE
dataset was produced on daily ascending and descending swath composites, each grid point carries
the overpass time of the TMI scan that was used, enabling close time alignment with previous
time NMQ precipitation data. Specifically, in this retrieval algorithm, the vegetation is represented
as a single-scattering layer above the soil. The effective microwave land surface emissivity can be
approximately expressed by the following tau-omega model (Njoku and Li, 1999)
p = 1 − sp exp(−τc ) + (1 − ωp )(1 − exp(−τc ))(1 + rsp exp(−τc ))
(4.1)
Where p and rsp = 1−p are the soil emissivity and reflectivity at polarization, p, respectively;ωp
is the vegetation single scattering albedo; τc is the slant vegetation optical depth. The first term
accounts for soil emission attenuated by vegetation. The second term represents emission contribution from vegetation. It is noted that the contribution of sp to p decreases with increasing optical
depth τc , and that τc itself increases with vegetation water content and frequency.
The second is the Jet Propulsion Laboratory’s (JPL) PC-based MLSE dataset based on an
AMSR-E clear-scene principal component (PC) analysis (Turk et al., 2013), that provides the
nine-channel (e.g., TMI-like) MLSE on an instantaneous basis. This PC-based MLSE dataset is
based upon first estimating the PC structure from the observed AMSR-E TB, and then reconstructing the MLSE vector. The advantage of this technique is that emissivities at all channels are
computed simultaneously and without the need for ad-hoc (e.g., clustering-based) surface classifications. Briefly summarized, the PC-based technique used a PC analysis from an extensive set of
clear-scene AMSR-E MLSE, whereby the MLSE vector (denoted by ) was broken down into its nine
E ], whose columns are
PCs (denoted by u ) via a transformation expressed by an orthogonal matrix [E
S ] . Since u is not known and the factors that
the eigenvectors of the emissivity covariance matrix [S
41
control the MLSE are nonlinear processes, each PC element u1 , u2 , . . . , u9 was estimated (estimates
denoted by primes) by nonlinear combinations of the nine TMI-like TB and the polarization ratios
0
at 10, 18, 36 and 89 GHz, e.g. for u1 ,
0
2
2
u1 = a0 + a1 T10H + a2 T10V + · · · + a1 T10H
+ a2 T10V
+ · · · + a19
T10V − T10H
T89V − T89H
+ · · · + a22
(4.2)
T10V + T10H
T89V + T89H
Least squares regression was used to determine the above 23 (9+9+4, plus the constant term)
coefficients for each PC. The MLSE can then be jointly estimated from subsequent TMI or AMSR-E
data by the PC reconstruction equation,
0
E ]u
u
e = [E
4.3
(4.3)
Influence of Previous Rainfall on MLSE
All emissivity datasets described above were taken from satellite overpasses under non-precipitating
conditions.However, different surface and vegetation types may respond very differently depending
upon how much rainfall had fallen prior to the satellite overpass.Therefore, in this section, we will
analyze how previous-time accumulated precipitation affects MLSE over different land covers, using
the hourly NMQ precipitation data described above.
4.3.1
Correlation between Emissivities and Previous Rainfall
The correlation between emissivity at H10 and previous 1 to 24-hr rainfall amount is calculated
at three locations (Fig. 4.1), whose land cover types are closed shrubland, crop land and forest,
respectively. The purpose of performing this analysis is to investigate whether there exists temporalresolution dependence for the emissivity response to previous rainfall over different land cover types.
That is, how do the duration, timing and accumulation of the previous time rainfall affect the
current emissivity? Over closed shrubland, the correlation between previous rainfall and emissivity
at H10 could be as large as -0.6, using either PC-based or physically-based emissivity (Fig. 4.1a
and Fig. 4.1d). It is also noticed that correlation coefficients peak at previous 13- and 18-hours for
physically-based and PC-based emissivity, respectively. Different from over shrubland, for cropland
it is the previous 24-hour accumulated rainfall that has the largest correlation with emissivity at
H10, though the magnitude of such correlation differs slightly using PC-based and physicallybased emissivity datasets (-0.3 for physically-based emissivity and -0.2 for PC-based emissivity).
42
Interestingly, when using PC-based emissivity, there indeed exists a positive correlation between
H10 emissivity and previous 1- and 8-hr rainfall over cropland dominated location, with correlation
as large as 0.2. Similar to over forest, this phenomenon may be caused by the water intercepted
by crop leafs, to increase the optical depth and therefore cause the ”bulk” emissivity increase.
Over forest, previous 8-hr rainfall has the largest correlation with emissivity at H10, though such
correlation is quite weak.
Clearly, the correlation between the number of hours of accumulated rainfall and the emissivity
at H10 depends on land cover types. It is also noticed that previous 1-hr rainfall always has the
smallest correlation with emissivity at H10 in this case study, which is rather counter-intuitive.
We hypothesize that previous 1-hr rainfall should have the largest influence on surface emissivity ,
compared with previous other hours accumulated rainfall. The reasoning behind this phenomenon
is presently unclear. In addition, the correlations between emissivity at other channels and previous
rainfall have similar characteristics over these three locations. In summary, the influence of the
duration of the previous rainfall differs amongst the land cover types. Throughout the remainder of
this study, the previous 24-hr accumulated rainfall is used, since the correlation coefficient between
emissivity and previous 24-hr accumulated rainfall is close to the largest correlation coefficient
between emissivity and previous 1 to 24-hr accumulated rainfall, regardless of land cover type.
Next, the correlation between emissivity at H10 and previous 24-hr rainfall is calculated over
each 1-degree latitude by 1-degree longitude grid box using both physically-based and PC-based
estimates, and is shown in Fig. 4.2a and Fig. 4.2b. It is noted that the largest correlation locates
over Southern Great Plains and a small region over central United States, which are approximately
-0.6. Over these regions, the dominant land cover types are grass, closed shrub and crop. Over
New Mexico and Arizona, there also exist some scattered areas with large correlations. In contrast,
over the more vegetated eastern United States, the correlation is about -0.1 for physically-based
emissivity and 0.1 for PC-based emissivity. The opposite sign of this correlation coefficient may due
to the fact that the PC-based emissivity, being purely observationally-based, inherently accounts for
any effects of intercepted rain drops by tree leaves, whereas the simple one-layer model used in the
physically-based emissivity does not. In Fig. 4.2c, it is showed the correlation between emissivity
at H10 and the first PC. For comparison purposes, this correlation coefficient is multiplied by -1.
Obviously, the correlation pattern is very similar to those calculated by using physically-based and
43
PC-based emissivities, though the magnitude of this correlation coefficient is slightly smaller. It is
worth mentioning that using emissivities at other channels will lead to similar results.
To summarize, the previous 24-hr accumulate rainfall has largest correlation with emissivity
over closed shrub and crop dominated regions, such as Southern Great Plains. On the other hand,
over forest region, previous rainfall has little impact on the emissivity, thus resulting in a much
weaker correlation between previous rainfall and emissivity.
4.3.2
Two Case Studies
As an example, two locations over different land cover types are chosen to demonstrate how
the MLSE responds to previous rainfall. The center latitude-longitude for these two locations are
(31.83N, 85.44W) and (32.06N, 100.81W), where dominant land cover types are forest and closed
shrubland, respectively. For every TRMM satellite overpasses under clear sky conditions, the TMI
physically-based and TMI PC-based emissivities are compared to the previous 24-hr rainfall from
NMQ at these two locations. The results are shown in Fig. 4.3 and Fig. 4.4. Over closed shrubland
(Fig. 4.3), the physically-based emissivities at H10 GHz to H37 GHz show noticeable decrease when
it previously rained. Especially, emissivity at H10 GHz can drop as large as 0.1 after previously
heavy rain (Fig. 4.3a). For the PC-based emissivity, the magnitudes of emissivity decrease at H10
and H19 channels are similar to that of physically-based emissivity corresponding to previous 24hr heavy rainfall (¿ 20 mm), while essentially no response is observed when the previous 24-hr
rainfall is under 10 mm. Additionally, there exists little response at H37 channel for the PC-based
emissivity. The first and third PCs show a large increase corresponding to periods of previous
heavy rainfall, whereas the fourth PC varies little at this location.
In contrast to the emissivity response to previous rainfall over shrubland, both emissivities
from H10 to H37 and PCs show little variation over forest land, regardless of previous rain amounts
(Fig. 4.4). It is worth mentioning that emissivities at vertically polarized channels respond similarly
to the previous rainfall, though the magnitude is smaller. In summary, over shrubland dominant
location the emissivities decrease greatly corresponding to periods of previous heavy rainfall, while
little variation is observed over forest area regardless of previous raining conditions.
44
4.3.3
Emissivity Variations Caused by Previous Rainfall
Next, using the PC-based instantaneous emissivities, we calculate the difference between emissivities when no rain occurred in the previous 24-hr and that when it rained more than 20 mm in
the previous 24-hr, in each 1 ◦ ×1◦ degree grid box in the study region, as shown in 4.5. The largest
difference ( 0.05 at H10) is located over the Southern Great Plains (SGP) region and Mississippi
Alluvial Plain, where the dominant land cover types are grass and crop land, respectively ( 4.5d).
Such a characteristic is apparent at all frequencies. In contrast, over more vegetated regions in the
Eastern United States, previous rainfall causes a much smaller emissivity variation (less than 0.01).
The magnitude of emissivity difference caused by previous rainfall is larger at H10 channel than
that at H19 and H37 channels, due to its stronger sensitivity to wet/dry soil changes. It is noticed
that previous rainfall may result in a small emissivity increase ( 0.01) over forest dominant areas.
Such increase probably stems from the optical depth increase due to water covered leaf structure
(Li and Min, 2013), though other possible explanations cannot be excluded and deserves further
investigation in the future.
The TB difference caused by the emissivity change has been computed and is shown in Fig. 4.6.
Not surprisingly, the large TB decrease is located over Southern Great Plains and Mississippi
Alluvial Plain, where the emissivities decrease is most obvious. Over the aforementioned two
regions, the magnitude of the TB decrease at H10 could be as large as 25 K. However, the
surface temperature may also decrease by 5 K over such regions along with previous rainfall
(Fig. 4.6d). Therefore, the net TB decrease at H10 caused by emissivity drop over these two
regions is approximately 20 K. At H19 and H37 channel, the net TB decrease is 5 to 10 K. Though
not shown, both emissivity and TB variations at H85 channel caused by previous 24-hr rainfall (¿
20 mm) is less than 0.01 and 5 K, respectively. Indeed, when using a larger previous 24-hr rainfall
as criteria (e.g., 40 mm), the corresponding emissivity and TB variation will increase.
To summarize, the large emissivity and TB decrease caused by previous 24-hr heavy rainfall (>
20 mm) appears over Southern Great Plain and Mississippi Alluvial Plain, though the magnitude
of emissivity decrease is different using PC-based and physically-based emissivities. The different
response to previous rainfall over shrub land and over forest has been explained by previous works
(Jackson, 1993; Li et al., 2010, e.g.,), which can be summarized in two major reasons. First, the soil
moisture is generally higher over forest region than that over shrub dominated land, which will lead
45
to a relatively weaker response over forest for the same amount previous rainfall. Additionally, the
larger optical depth of forest canopy will more effectively attenuate emission from soil, as shown in
Eq. 4.1.
Finally, we would like to mention that similar analysis has also been conducted using the
physically-based emissivity. The major conclusions still hold though the numerical value is somewhat different.
4.4
Model Simulations Using Three Different Emissivity
Datasets
Since the in-situ MLSE cannot be measured at such a large spatial scale, it is difficult to directly
evaluate or verify different MSLE datasets. As an alternative, RTM simulations are used to simulate
the observed TB corresponding to TRMM satellite overpasses using these three emissivity datasets
(i.e., TELSEM, PC-based emissivity and physically-based emissivity), and then these emissivity
datasets are evaluated by comparing the simulated TB with TMI observations. The microwave
RTM used in this study was developed by Liu (1998) and updated later with improved ice particle
handling by incorporating results from single-scattering properties of ice particles (Liu, 2008). The
model applies a discrete ordinate method to solve microwave radiation transfer for the plane parallel
atmosphere at specified frequencies, using profiles of the atmosphere (e.g., relative humidity and
temperature profiles) and hydrometeors (e.g., snow and rain drops, etc.). Additionally, this RTM
itself does not account for the soil and vegetation properties. These properties are taken into
consideration through varying surface emissivities.
The surface temperature plays an important role in the process of retrieving the surface emissivity under clear-sky condition. We are aware that different surface temperature products are used in
the emissivity calculations for the different emissivity databases. Specifically, International Satellite
Cloud Climatology Project (ISCCP) skin temperature and Atmospheric Infrared Sounder (AIRS)
temperature are used for TELSEM and PC-based emissivities, respectively. For the physicallybased emissivity, the surface temperature is directly retrieved from microwave brightness temperatures together with emissivity, soil moisture and vegetation water content. We compared these
products by calculating the differences among them (not shown). It is found that approximately
90% of the ISSCP, AIRS and physically-based surface temperatures are within 5 K of those from
46
MERRA reanalysis which is employed in this study. There indeed exist large temperature differences over dessert areas that may be caused by the temperature gradient in the soil emitting layer.
This feature has also been noticed by previous investigators (e.g., Prigent et al., 2005; Mathew
et al., 2008), which is possibly caused by the temperature gradient in the soil layer. We focus on
the previous rainfall impact on surface emissivity. The large differences over dessert areas will not
change our major conclusions since it rarely rains over dessert regions.
4.4.1
Case Study from 12 August 2011
A clear-sky scene on 12 August 2011 was selected where heavy rain had occurred in the previous 24-hours, over the area of 32.5◦ to 36.5◦ N latitude and 100◦ W to 97◦ W longitude (Fig. 4.7i),
since it has already been demonstrated in section 3 that over this region the previous rainfall can
greatly impact the surface emissivity. Because it is clear sky in this case, there are no hydrometers
or clouds are taken into consideration in the model simulation, only the temperature, humidity
and surface temperature information from the MERRA data (Section 2) interpolated in time and
space to the TMI locations. Only the surface emissivity varies in the simulations; all the other
parameters (surface temperature, temperature and humidity profiles) are exactly the same in these
simulations. TB simulations at V19, V37 and V85 channels are shown at Fig. 4.7a to Fig. 4.7h. The
root mean square error (RMSE) for simulated TB at V19 channel is 5.33, 3.68 and 4.82 when using
the TELSEM, PC-based and the physically-based emissivities, respectively (Fig. 4.7a, Fig. 4.7b and
Fig. 4.7c). Clearly, the RMSE using the PC-based emissivity is the smallest. Furthermore, the correlation coefficient between the simulated and observed TB at V19 is the largest (0.92, see Fig. 4.7b)
when utilizing the PC-based emissivity. It is worth mentioning that the simulated TB at V19 using
the TELSEM emissivity is almost a straight line because being a climatological value, there are
only a few different emissivity values in this case. For all three emissivity datasets, the simulated
TB at V37 agree well with the observed TB when the surface is relative dry (corresponding to
observed TB between 280 and 290 K). However, when it rained heavily previously (corresponding
to observed TB less than 280 K), the simulated TB at V37 using the TELSEM emissivity vary little
(Fig. 4.7d). The simulated TB at V37 using the PC-based emissivity (Fig. 4.7e) agree much better
with observations than when using the TELSEM emissivity dataset, though there is a slight overestimation when it previously rained heavily. Simulated results at V37 using the physically-based
47
emissivity (Fig. 4.7f) are in-between the TELSEM and the PC-based results. For the simulated results at V85 (Fig. 4.7g and Fig. 4.7h), the TELSEM emissivity seems better in terms of correlation
coefficient and RMSE because there exist several outliers in the simulations using the PC-based
emissivities. All the simulations for the corresponding horizontal polarized channels (H19, H37 and
H85) are illustrated at Fig. 4.8. Similarly, the simulations using the PC-based emissivity are the
closest to observations in terms of correlation and RMSE.
In summary, for this case, the simulated TB using the PC-based emissivity tends to agree best
with observations, and the TELSEM emissivity does not represent wet surface very well. The
physically-based MLSE performs better than TELSEM, but worse than the PC-based MLSE.
4.4.2
Simulations over Entire Study Region
Employing the same procedure as in the above case study, simulations are carried out over
the whole study area, and the results are shown in Fig. 4.9. The simulated TB at H19 channel
(Fig. 4.9a) shows two tails using the TELSEM emissivity, which leads to a large RMSE (13.57 K)
and smaller correlation (0.42). Further examination shows that the upper left tail is caused by
wet surface (i.e., previous heavy rain conditions). The vast majority of the points at the bottom
right tail are located over coastal regions. The simulated results at H19 channel (Fig. 4.9b) using
the PC-based emissivity agree much better with observations, with RMSE and correlation being
4.86 K and 0.87. It is worth mentioning that simulated TB using the PC-based emissivity are
slightly positively biased, especially when the surface is wet. Simulations at H19 channel using the
physically-based emissivity also shows clear upper left tails, indicating that this emissivity does
not perform well under wet surface conditions. For the simulations at H37 channel using all three
emissivity datasets, similar characteristics as for H19 channels are observed (Fig. 4.9d and Fig. 4.9e
Fig. 4.9f). Interestingly, the upper left tails are evident for both simulations using the TELSEM
and the PC-based emissivities at H85 channel (Fig. 4.9g and Fig. 4.9h), which probably caused
by cloud contamination within the (assumed clear-sky) scene. Simulations at vertically polarized
channels show very similar characteristics (not shown). In summary, simulated TB using the PCbased instantaneous MLSE dataset shows the best agreement with observations. The simulations
using the TELSEM climatological emissivity dataset does not perform well under wet surface and
over coastal regions. In addition, the physically-based emissivity dataset does not perform well
over wet surfaces, either.
48
4.5
Applications of Instantaneous PC-based Emissivity
In section 3, we showed that over Southern Great Plains (SGP) the previous 24-hr rainfall is
able to significantly impact the MLSE, especially at low frequencies (e.g., 10 GHz). Therefore, in
this section, we examine whether it is possible to employ this correlation to retrieve previous 24-hr
rainfall. If possible, this implies that one could estimate precipitation accumulations directly from
individual TMI-like satellite overpasses, and alleviates the sampling issues associated with merging intermittent, sometimes widely-spaced satellite overpasses, especially in the tropical latitudes
(Huffman et al., 2007).
4.5.1
Using Clear-Sky Emissivity to Retrieve Previous Rainfall
A case study over the area from 31N to 32N and from 99W to 100W is conducted to show
the ability of using H10 emissivity to retrieve previous 24-hour rainfall. Over this selected area,
there are 220 data points of both PC-based emissivity at H10 and previous 24-hour rainfall. These
observations are randomly separated into two subsets, each including half of the data (110 observations). The first subset is used to train a curve between emissivity at H10 and previous 24-hr
rainfall, shown in Fig. 4.10a. The solid line depicts the fitting curve using a power-law relationship.
Using this relation, the previous 24-hr rainfall in the second subset is predicted, and the results are
shown in Fig. 4.10b, as compared with observed previous 24-hr rainfall. The predicted values agree
reasonably well with the observations, with the correlation coefficient and RMSE being 0.59 and
11.39 K, respectively. It is also noticed that there exists noticeable underestimation for previous
24-hr heavy rainfall (greater than 40 mm), which could be due to the minimal number of observations in this range, or to effects stemming from the saturation of the soil conditions. However
this limited study showed that it is possible to use clear sky emissivity to retrieve previous 24-hr
rainfall over particular regions where there exists a good correlation between previous rainfall and
emissivity.
It is worth mentioning that studies have already been performed to use soil moisture information to improve the accumulated rainfall accuracy (e.g., Crow, et al. 2009). In our case study,
emissivity at H10 channel derived from clear-sky brightness temperature is used to directly retrieve
the previous 24-hr accumulated rainfall amount. This approach has the potential to increase the
utility of brightness temperature since approximately 85
49
4.5.2
Adjusting Emissivities under Raining Conditions
As stated in the introduction, currently all the emissivity datasets are developed under clear
sky. In this section, we will explore the possibility of using the relation between the surface-sensitive
PCs and the amount of previous rainfall to adjust the clear sky emissivity, and use this as a proxy
for the emissivity under precipitating scenes. Turk et al. (2012b) in Part 1 of this manuscript
showed that three PCs (1st, 3rd and 4th) are the most sensitive components to surface conditions,
Therefore, the equations [2] are employed to estimate PCs under raining scenarios, though this
equation is developed under clear sky, and then further adjust or modify three PCs prior to the
emissivity reconstruction in Equation [3]. The underlying assumption for this adjustment technique
is that, regardless of clear sky or raining conditions, the relationship between PCs and surface
wetness is similar. That is equivalent to say, under clear sky or under raining condition, the
relationship between emissivities and surface wetness is similar, since the PCs and emissivities are
directly related through equation [3]. The adjustment procedure developed in this study is based
on matching simulated and observed multichannel TB.
An area (31◦ N to 33◦ N latitude, 97◦ W to 99◦ W longitude) over the Southern Great Plains was
selected to demonstrate how this emissivity adjustment is performed under raining conditions. The
scatter plots between three PCs (1st, 3rd and 4th) and previous rainfall over the selected area are
shown in Fig. 4.11, where red lines denote the least-square linear fitting curves. When it is raining
over this area, in most cases this emissivity estimation is positively biased since equation [2] is
developed under clear sky. Therefore, an adjustment procedure is needed. To do the adjustment,
we choose a fairly heavy previous rainfall amount (20 mm day-1) from x-axis of Fig. 4.11, and then
three corresponding PCs on the red curves from Fig. 4.11a, Fig. 4.11b and Fig. 4.11c are taken (e.g.,
-24.2, 0.1 and 3.3). Instead of using directly estimated PC1, PC3, and PC4, these three new PCs are
used in their place when applying Equation [3]. By doing this, nine new emissivities are obtained,
but for this study only the emissivity at H10 channel is chosen to do the simulation. If the difference
between simulated and observed TB at H10 channel is less than 10 K, the nine emissivities are
taken as estimated emissivities under raining condition. Otherwise, the same procedure is repeated
by randomly choosing three other PCs (corresponding to the same previous rainfall amount) until
the difference between simulated and observed TB at H10 channel is less than 10 K.
50
Between May to August 2011, there exist 112 observed raining pixels in this area. The hydrometeor profiles for these 112 pixels are taken from the TRMM 2A25 Version 7 Precipitation
Radar (PR) water content retrievals. For RTM inputs, hydrometers are assumed to be snow above
and rain under the freezing level. All other variables, such as surface temperature, temperature
and relative humidity profiles, are taken from MERRA reanalysis dataset. Fig. 4.12a shows the
simulated TB at H10 before applying such an adjustment procedure (i.e., using clear sky emissivity). Clearly, the vast majority of the simulated TB are larger than those observed, due to using
the clear sky emissivities. After the adjustment, the difference between simulated and observed
TB is less than 10 K at H10 (Fig. 4.12b). Similarly, Fig. 4.12d shows that simulated TB at H19
using the adjusted emissivity agree much better with observations than those when using clear sky
emissivities (Fig. 4.12c). For H37 channel (Fig. 4.12e and Fig. 4.12f), the adjusted emissivity has
little impact on the majority of simulations. However, it is noticed that the simulations are closer
to the observations when the observed TB are greater than 280 K, corresponding to rainfall less
than 6 mm/hr. When the rainfall is 10 mm/hr, the emissivity adjustment may have very little
influence to the simulated TB. Due to the high sensitivity to the hydrometers, not surprisingly,
the emissivity adjustment has little influence to the simulations at H85 (not shown). Fig. 4.13
shows the simulations at vertically polarized channels with and without applying this adjustment.
Similarly, without such adjustment, there exist obvious positive biases for most of the simulations,
particularly for TB simulations at V10 and V19 channels.
The emissivities with and without adjustments (blue and red curves, respectively) at 10, 19
and 37 GHz are shown in Fig. 4.14 for data over the selected box. The mean value of raining
scene emissivity at H10 (Fig. 4.14a) is 0.09 lower than the mean of non-adjustment emissivities,
which leads to a 25 K decrease of the associated TB. For the emissivities at V10, the mean value
drops 0.05 with respect to the non-adjusted emissivities. On several occasions, the raining V10
emissivities become lower than 0.9 due to heavy rain (>10 mm/hr). Under such circumstances,
this adjustment technique will lead to an inaccurate emissivity due to strong absorption by the rain
media. In fact, when it is raining heavily (>10 mm/hr), the surface emissivity has little influence
to the eventual observed TB. Similar characteristics are observed for emissivities at 19 and 37
channels.
51
In summary, using the relationship between PCs and previous rainfall, we dynamically and
consistently adjust nine emissivities, and a proxy for the emissivity under raining conditions is
obtained. Results showed applying such adjusted emissivities will greatly reduce the positive biases
in simulated TB (resulting from using clear sky emissivities in the rain), and bring the simulated
TB closer to observations. It is worth mentioning that rainfall will make the horizontally polarized
channel emissivities decrease in a larger extent than that of vertically polarized channel. It is also
noticed that this adjustment technique does not perform well under heavy rainfall (¿ 10 mm/hr),
probably because the heavy rainfall will obscure the surface emission. Additionally, under raining
scenario, the land surface is much prone to be saturated; therefore more previously heavily rained
data are needed to investigate how the PCs behave when surface is saturated. In addition, we
understood that there exists large uncertainty in the hydrometeor profiles employed in this study
(e.g., Munchak and Kummerow, 2006). Therefore, the estimated emissivity can only be taken
as approximation. In essence, our major objective for this case study is to show that the nine
TMI emissivities can be reconstructed simultaneously through only varying three PCs, even under
raining scenario.
4.6
Conclusions
Using NMQ hourly rainfall and the PC-based and the physically-based instantaneous microwave
land surface emissivity (MLSE) datasets, we investigate the response of the MLSE to previous
rainfall duration, timing and amount. It was found that previous rainfall produced a large emissivity
decrease over the Southern Great Plains and Mississippi Alluvial Plain. Over these two regions,
the dominant land cover types are grass, closed shrub and crop. In particular, previous 24-hr heavy
rainfall (¿ 20 mm) could lead to a 0.06 emissivity decrease at H10, corresponding to a 20 K net
TB decrease. In addition, corresponding to the same previous rainfall, the higher the frequency,
the smaller such emissivity decrease will be. In contrast, over forest dominant areas (e.g., Eastern
United States), emissivities do no vary much ( 0.1 at H10 channel) corresponding to previous
rainfall. The correlation between emissivity and previous rainfall has also been investigated. Large
correlations were located over the Southern Great Plains and a small region over central United
States. The correlation coefficients over Southern Great Plains were as large as -0.6. On the other
52
hand, the correlation over forest regions is much weaker, indicating that the emissivity over forest
responds weakly to previous rainfall.
The comparison among the PC-based MLSE, physically-based MLSE and the TELSEM climatological MLSE datasets was conducted over continental United States. Results show that
the simulated brightness temperatures (TB) using the PC-based emissivities agree the best with
TRMM satellite observations, with correlation and RMSE being 0.80 and 5.0 K for all channels.
For the climatological TELSEM emissivity, there exist two major biases. One is that it overestimates the wet surface emissivity, leading to higher simulated TB relative to the TMI observed
TB. The other is that it underestimates the coastal region emissivity, resulting in lower simulated
multichannel TB than observed. These biases lead to a lower correlation ( 0.45) between simulated
and observed TB. The overestimation under wet surface in the physically-based emissivity dataset
is also noticeable. We note that while the NMQ data was used to screen precipitating scenes, there
is likely non-precipitating cloud contamination that may contribute significantly to the emissivity
estimation errors especially at the 85 GHz channels.
Two potential applications of the instantaneous emissivity were investigated. First, it was
demonstrated that clear sky emissivity at low frequency (e.g., H10) is well correlated with previous 24-hour rainfall over Southern Great Plains. Using such a relationship, we estimated the
previous 24-hour rainfall that is needed to produce this same emissivity, and which agreed fairly
well with the observed previous 24-hour rainfall (correlation coefficient of0.59). Additionally, using
the relationship between PCs and previous rainfall, the raining scene emissivities at 10, 19 and 37
GHz are estimated. The applications of proper raining scene emissivities will greatly reduce the
positive biases in simulated TB (resulting from using clear sky emissivities in the rain), and bring
the simulated TB closer to observations. This emissivity adjustment technique does not work well
under moderate to heavy rain (¿ 10 mm hr-1), since the rain media almost completely obscures the
surface. Due to the promising results in these case studies, further application of these techniques
over a much large scale is under current development.
Finally, we would like to emphasize that the primary objective of this study is to investigate
the emissivity response to the precipitation in the summer over a portion of United States. Investigation of the emissivity response in other seasons is underway currently. Such an analysis will be
particularly beneficial for the physical rainfall retrieval algorithm development in the GPM era.
53
Corr. Coef.
0.3
0.3
Closed Shrub
PC−based emis.
0.3
Crop
PC−based emis.
0
0
0
−0.3
−0.3
−0.3
−0.6
(a)
0
4
8
12
16
Previous hours
20
24
−0.6
(b)
0
4
8
12
16
Previous hours
20
24
−0.6
Forest
PC−based emis.
(c)
0
4
8
12
16
Previous hours
20
24
Figure 4.1: Correlation coefficients between previous 1 to 24-hr rainfall and emissivity at
H10 channel over closed shrub, crop and forest land, using PC-based emissivities.
40oN
(a)
30oN
20oN
Using PC-based emissivity
40 N
o
(b)
30 N
o
20oN Using PC1
130oW
120oW
-0.6
-0.5
110oW
-0.4
100oW
-0.3
-0.2
90oW
-0.1
80oW
0
70oW
0.1
Figure 4.2: (a) Correlation between PC-based emissivity at H10 channel and previous
24-hrs accumulated rainfall. (b) Correlation between first principal component (PC1) and
previous 24- hrs accumulated rainfall. For comparison purposes, this correlation coefficient
is multiplied by -1.
54
0.9
0.85
PC−based emis.
0.8
−2.3
1
(b)
0.95
PC−based emis.
0.9
0.1
(d)
1
Emissivity at H37
(a)
Emissivity at H19
Emissivity at H10
0.95
(c)
0.95
PC−based emis.
0.9
0.4
(e)
(f)
PC4
PC3
PC1
0.05
−2.4
0.35
0
Pre. 24−hr rainfall (mm)
−2.5
−0.05
30
(g)
0
30
60
90 120
Number of Obs.
150
0.3
0
30
60
90 120
Number of Obs.
150
20
10
0
0
30
60
90 120
Number of Obs.
150
Figure 4.3: PC-based emissivity over a closed shrub dominant location. (a) Emissivity at
H10 channel response to previous 24-hr rainfall. (b) Emissivity at H19 channel response
to previous 24-hr rainfall. (c) Emissivity at H37 channel response to previous 24-hr rainfall. (d) First principal component (PC1) response to 24-hr rainfall. (e) Third principal
component (PC3) response to 24-hr rainfall. (f) Fourth principal component (PC4) response to 24-hr rainfall. (g) Previous 24-hr rainfall. The ’Number of obs.’ stands for the
intermittent satellite observations over this specific area.
55
0.95
PC−based emis.
−2.5
(g)
1
30
60
Number of Obs.
0.95
PC−based emis.
0.4
(e)
0
(c)
0.9
0
−0.05
30
PC−based emis.
0.05
(d)
−2.4
Pre. 24−hr rainfall (mm)
0.95
0.9
PC3
PC1
−2.3
(b)
PC4
0.9
1
Emissivity at H37
(a)
Emissivity at H19
Emissivity at H10
1
90
(f)
0.35
0.3
0
30
60
Number of Obs.
20
10
0
0
30
60
Number of Obs.
90
Figure 4.4: Same as Figure 3, except for over a forest dominant location.
56
90
40oN
(a)
30 N
o
20oN
Emissivity difference at H10
40oN
(b)
30oN
20oN
Emissivity difference at H19
40 N
o
(c)
30oN
20oN Emissivity difference at H37
130oW
120oW
110oW
-0.01
0
0.01
100oW
0.02
0.03
90oW
0.04
80oW
0.05
70oW
0.06
40oN
(d)
30oN
20oN Dominant land cover type
130oW
120oW
110oW
Forest
Wooded Grassland
100oW
Grassland
Closed shrub
90oW
80oW
Crop
70oW
Bare ground
Figure 4.5: (a) Difference between PC-based emissivities at the H10 channel when no rain
occurred in the previous 24-hr and that when it rained more than 20 mm in the previous
24-hr. (b) Difference between PC-based emissivities at the H19 channel when no rain
occurred in the previous 24-hr and that when it rained more than 20 mm in the previous
24-hr. (c) Difference between PC-based emissivities at the H37 channel when no rain
occurred in the previous 24-hr and that when it rained more than 20 mm in the previous
24-hr. (d) Dominant land cover types over the study region.
57
40oN
(a)
30 N
o
TB difference at H10
20oN
40oN
(b)
30oN
TB difference at H19
20oN
40 N
o
(c)
30oN
TB difference at H37
20oN
40 N
o
(d)
30oN
20oN Surface temperature difference
130oW
120oW
110oW
0
5
10
100oW
15
90oW
20
80oW
25
30
70oW
35
Figure 4.6: (a) Difference between brightness temperatures (TB) at the H10 channel when
no rain occurred in the previous 24-hr and that when it rained more than 20 mm in the
previous 24-hr. (b) Same as (a), but for at H19 channel. (c) Save as (a) but for at
H37 channel. (d) Difference between surface temperatures when no rain occurred in the
previous 24-hr and that when it rained more than 20 mm in the previous 24-hr.
58
295
290
285
(a)
PC−based emis.
280
280
300
RMSE=6.25
corr=0.53
290
280
300
Simulated TB at V37
300
285
290
295
Observed TB at V19
Simulated TB at V19
285
300
RMSE=3.68
corr=0.92
285
290
295
Observed TB at V19
(b)
290
280
TELSEM
(d)
270
270
280
290
300
Observed TB at V37
PC−based emis.
(e)
270
270
280
290
300
Observed TB at V37
295
295
RMSE=2.67
corr=0.68
290
285
TELSEM
(g)
280
280
285
290
295
Observed TB at V85
295
290
285
300
RMSE=3.93
corr=0.87
RMSE=4.82
corr=0.77
Phys−based emis.
(c)
280
280
285
290
295
300
Observed TB at V19
300
Simulated TB at V37
290
280
280
Simulated TB at V37
Simulated TB at V19
295
TELSEM
Simulated TB at V85
300
RMSE=5.33
corr=0.71
Simulated TB at V85
Simulated TB at V19
300
RMSE=6.19
corr=0.67
290
280
Phys−based emis.
(f)
270
270
280
290
300
Observed TB at V37
RMSE=3.84
corr=0.57
40° N
290
30° N
285
20° N °
130 W
PC−based emis.
100° W
(i)
70° W
(h)
280
Observed TB at V85
Figure 4.7: Emissivity analysis on 12 August 2011 over the Southern Great Plains (SGP)
site between 32.5N to 36.5N latitude, and 100W to 97W longitude. (a) Scatter plot between simulated and observed TB at V19 channel, using TELSEM climatological emissivity. (b) Scatter plot between simulated and observed TB at V19 channel, using PC-based
instantaneous emissivity. (c) Scatter plot between simulated and observed TB at V19
channel, using physically-based instantaneous emissivity. (d) Scatter plot between simulated and observed TB at V37 channel, using TELSEM climatological emissivity. (e)
Scatter plot between simulated and observed TB at V37 channel, using PC-based instantaneous emissivity. (f) Scatter plot between simulated and observed TB at V37 channel,
using physically-based instantaneous emissivity. (g) Scatter plot between simulated and
observed TB at V85 channel, using TELSEM climatological emissivity. (h) Scatter plot
between simulated and observed TB at V85 channel, using PC-based instantaneous emissivity. (i) Geographical location for the case on 12 August 2011.
59
Simulated TB at H19
285
275
295
RMSE=3.72
corr=0.95
Simulated TB at H19
295
RMSE=7.42
corr=0.27
285
275
RMSE=5.68
corr=0.68
285
275
TELSEM
(a)
265
265
275
285
295
Observed TB at H19
PC−based emis.
(b)
265
265
275
285
295
Observed TB at H19
Phys−based emis.
(c)
265
265
275
285
295
Observed TB at H19
300
295
300
290
280
RMSE=3.11
corr=0.87
Simulated TB at H37
Simulated TB at H37
RMSE=8.64
corr=0.36
290
285
TELSEM
(d)
270
270
280
290
300
Observed TB at H37
PC−based emis.
(e)
280
280
285
290
295
Observed TB at H37
295
295
RMSE=4.8
corr=0.52
Simulated TB at H85
Simulated TB at H85
Simulated TB at H37
Simulated TB at H19
295
290
285
TELSEM
280
RMSE=7.61
corr=0.66
290
280
Phys−based emis.
(f)
270
270
280
290
300
Observed TB at H37
RMSE=2.51
corr=0.72
40° N
290
30° N
285
(g)
20° N °
130 W
PC−based emis.
100° W
(i)
70° W
(h)
280
Observed TB at H85
Observed TB at H85
Figure 4.8: Same as Figure 8, except for the horizontally polarized channels.
60
260
2
240
TELSEM
(a)
220
220 240 260 280 300 320
Observed TB at H19
320
300
3
6
4
260
2
240
TELSEM
(d)
220
220 240 260 280 300 320
Observed TB at H37
300
0
3
8 ×10
RMSE=10.72
corr=0.48
6
280
4
260
240
0
8 ×10
RMSE=14.72
corr=0.39
280
320
1
2
TELSEM
(g)
220
220 240 260 280 300 320
Observed TB at H85
0
5
4
280
3
260
2
240
PC−based emis. (b)
220
220 240 260 280 300 320
Observed TB at H19
320
300
3
6
4
260
2
240
PC−based emis. (e)
220
220 240 260 280 300 320
Observed TB at H37
300
0
300
6
4
260
2
PC−based emis.
(h)
220
220 240 260 280 300 320
Observed TB at H85
0
3
6 ×10
RMSE=11.16
corr=0.21
5
4
280
3
260
2
240
Phys−based emis. (c)
220
220 240 260 280 300 320
Observed TB at H19
320
300
1
0
3
8 ×10
RMSE=11.03
corr=0.26
6
280
4
260
2
240
Phys−based emis. (f)
220
220 240 260 280 300 320
Observed TB at H37
3
8 ×10
RMSE=4.86
corr=0.87
280
240
0
8 ×10
RMSE=4.68
corr=0.78
280
320
1
320
0
320
Simulated TB at H85
3
300
3
6 ×10
RMSE=4.86
corr=0.87
Simulated TB at H19
280
320
Simulated TB at H37
4
Simulated TB at H19
5
Simulated TB at H37
300
3
6 ×10
RMSE=13.57
corr=0.42
Simulated TB at H85
Simulated TB at H19
Simulated TB at H37
Simulated TB at H85
320
300
280
260
NA
240
220
220 240 260 280 300 320
Observed TB at H85
Figure 4.9: TRMM emissivity analysis over the continental United States. (a) Scatter
plot between simulated and observed TB at H19 channel, using TELSEM climatological
emissivity. (b) Scatter plot between simulated and observed TB at H19 channel, using
PC-based instantaneous emissivity. (c) Scatter plot between simulated and observed TB
at H19 channel, using physically-based instantaneous emissivity. (d) Scatter plot between
simulated and observed TB at H37 channel, using TELSEM climatological emissivity. (e)
Scatter plot between simulated and observed TB at H37 channel, using PC-based instantaneous emissivity. (f) Scatter plot between simulated and observed TB at H37 channel,
using physically-based instantaneous emissivity. (g) Scatter plot between simulated and
observed TB at H85 channel, using TELSEM climatological emissivity. (h) Scatter plot
between simulated and observed TB at H85 channel, using PC-based instantaneous emissivity. Black solid line is the 1:1 line.
61
60
Predicted previous 24−hr rainfall (mm)
Previous 24−hr rainfall (mm)
60
50
40
30
20
10
0
0.8
(a)
0.85
0.9
0.95
Emissivity at H10
1
50
RMSE=11.39
Corr=0.59
40
30
20
10
0
0
(b)
10
20
30
40
50
Observed previous 24−hr rainfall (mm)
60
Figure 4.10: Analysis of previous rainfall and emissivity change over the region from 31N
to 32N latitude, and 99 to 100W longitude. (a) Scatter plot between emissivity at H10
and previous 24-hr rainfall, using trained subset data. Solid curve denotes the least square
fitting line. (b) Scatter plot between predicted and observed previous 24-hr rainfall, using
validation subset data.
−23
0.6
3.6
−24
PC4
PC3
PC1
0.4
0.2
3.4
0
(a)
−25
1
20
40
60
Previous 24−hr rainfall (mm)
(b)
80
−0.2
1
20
40
60
Previous 24−hr rainfall (mm)
(c)
80
3.2
1
20
40
60
Previous 24−hr rainfall (mm)
80
Figure 4.11: (a) Scatter plot between the first principal component (PC1) and previous
24-hr rainfall. (b) Same, but for the third principal component (PC3) and previous 24hr rainfall. (c) Same, but for the fourth principal component (PC4) and previous 24-hr
rainfall.
62
320
Simulated TB at H10
Simulated TB at H10
320
300
280
260
240
Before adjustment
220
220
(a)
240 260 280 300
Observed TB at H10
320
260
240
320
Simulated TB at H19
Simulated TB at H19
280
After adjustment
(b)
220
220 240 260 280 300 320
Observed TB at H10
320
300
280
260
240
Before adjustment
220
220
(c)
240 260 280 300
Observed TB at H19
300
280
260
240
After adjustment
(d)
220
220 240 260 280 300 320
Observed TB at H19
320
320
Simulated TB at H37
320
Simulated TB at H37
300
300
280
260
240
Before adjustment
220
220
(e)
240 260 280 300
Observed TB at H37
300
280
260
240
After adjustment
(f)
220
220 240 260 280 300 320
Observed TB at H37
320
Figure 4.12: (a) Scatter plot between simulated TB and observed TB at H10 channel,
before adjustment. (b) Scatter plot between simulated TB and observed TB at H10
channel, after adjustment. (c) Same as (a) but for H19 channel. (d) Same as (b) but for
H19 channel. (e) Same as (a) but for H37 channel. (f) Same as (b) but for H37 channel.
63
320
Simulated TB at V10
Simulated TB at V10
320
300
280
260
240
Before adjustment
220
220
(a)
240 260 280 300
Observed TB at V10
320
260
240
320
Simulated TB at V19
Simulated TB at V19
280
After adjustment
(b)
220
220 240 260 280 300 320
Observed TB at V10
320
300
280
260
240
Before adjustment
220
220
(c)
240 260 280 300
Observed TB at V19
300
280
260
240
After adjustment
(d)
220
220 240 260 280 300 320
Observed TB at V19
320
320
Simulated TB at V37
320
Simulated TB at V37
300
300
280
260
240
Before adjustment
220
220
(e)
240 260 280 300
Observed TB at V37
300
280
260
240
After adjustment
(f)
220
220 240 260 280 300 320
Observed TB at V37
320
Figure 4.13: Same as Figure 13, except for the vertically polarized channels.
64
1
Emissivity at V10
Emissivity at H10
1
0.95
0.9
0.95
0.9
(a)
0.85
0
20
40
60
80
100
(b)
0.85
120
20
40
60
80
100
0.95
0.9
0
20
40
60
80
100
0.95
0.9
(c)
(f)
0.85
0
20
40
60
80
100
(d)
0.85
120
120
1
Emissivity at V37
Emissivity at H37
1
0.95
0.9
0.95
0.9
(e)
0.85
120
1
Emissivity at V19
Emissivity at H19
1
0
0
20
40
60
80
Number of Obs.
100
(f)
0.85
120
0
20
40
60
80
Number of Obs.
100
120
Figure 4.14: Calculated emissivity before (blue) and after (red) adjustment at H10, V10,
H19, V19, H37 and V37 channels, respectively.
65
CHAPTER 5
RELATIONSHIP BETWEEN WATER PATH AND
SURFACE RAINRATE
5.1
Introduction
Retrieval of surface rainrate based on passive microwave observations from satellite always faces
the following unavoidable dilemma. On one hand, the brightness temperatures (TB s) measured by a
passive microwave radiometer reflect the integrated effects of emission and scattering by the surface,
atmospheric gases, and hydrometeors in the atmospheric column. On the other hand, the surface
rainrate we intend to retrieve is the downward water flux at the very bottom layer. Excluding the
influence by the surface and atmospheric gases, the microwave TB s largely respond to the variation
of the vertically-integrated water amount, in particular, to liquid water path for emission signatures
at low frequencies (Wilheit, 1986), to ice water path for scattering signatures at high frequencies
(Smith et al., 1994b), and to total water path for combined signatures when using TB differences
(You et al., 2011). Consequently, the rainfall retrieval accuracy based on passive microwave satellite
observations relies heavily on the natural correlation between the above water paths and rainrate.
Indeed, in some algorithms, ice water path and/or liquid water path are estimated from brightness
temperatures first, and then rainrate is linked to the water paths through predetermined statistical
relations (Iturbide-Sanchez et al., 2011). Clearly, the accuracy of this type of approach depends
implicitly on the natural relationship between rainrates and water paths.
The non-uniqueness between rainrate and condensed water aloft has long been recognized,
mostly based on analysis of Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar
(PR) data. Petersen and Rutledge (2001) investigated regional variability of precipitation profiles
in tropical convections. They observed large variability in precipitation vertical structure both
spatially and seasonally in the interior tropical continental regions and pointed out that the largest
systematic variability in vertical structures occurs above the freezing level. By dividing precipitation
profiles into different groups according to emission signatures at 19 GHz and scattering signatures
at 85 GHz, Fu and Liu (2001) demonstrated that precipitation clouds could have high, average and
66
low amounts of liquid and ice water contents given a similar surface rainrate. Therefore, given the
same surface rainrate, different profiles result in a large spread of brightness temperatures. Liu and
Fu (2001) showed that the rainfall profile displays a clear seasonal variation in the mid-latitudes for
the same surface rainrate, regardless of convective or stratiform clouds. The seasonal characteristics
of precipitation profiles are further demonstrated by Fu et al. (2003). Berg et al. (2002) noticed that
precipitation systems over the eastern Pacific exhibit a number of significant differences from those
over the western Pacific warm pool, e.g., less ice for similar amounts of rainwater and a melting
layer significantly farther below the freezing level. Hirose and Nakamura (2004) investigated the
vertical gradient of precipitation profiles by grouping them into downward-decreasing or downwardincreasing rainrate in the bottom portion of the profiles. Their results demonstrated that downwarddecreasing profiles dominate tropical interior landmasses. By comparing the vertical structures of
storms, Xu et al. (2009) showed that during Mei-Yu season (i.e., East Asian rainy season) mesoscale
convective systems have significantly different vertical structures compared to their counterparts
during the break period, e.g., lower echo tops and much less liquid or ice content around mixedphase regions (∼6 km).
As implications to rainrate retrieval, Haddad and Park (2009) pointed out that it is no more
or less credible to estimate the rainrate at the surface than it is to estimate the rainrate at any
discrete altitude from brightness temperatures, due to the fact that the radiance measured by a
passive microwave radiometer depends on the vertical distribution of precipitation water, surface
wind, surface temperature, vertical distribution of water vapor, etc. Seo et al. (2010) found that the
relationship between the amounts of rain below freezing level height and ice above is quite variable
depending on cloud types. However, to the authors’ knowledge, neither the relationship between
water paths and surface rainrate nor the spatial and temporal variations of this relationship have
been studied systematically over the whole globe.
In this chapter, we investigate the relationship between surface rainrate and water paths over the
TRMM satellite covered regions. The central questions we intend to answer are: Where and why
do the surface rainrates have good correlation with water paths? How do these correlations vary
depending on location and season? What are the implications of the variation of these correlations
to satellite remote sensing of surface rainrate when using microwave radiometer observations?
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5.2
Results
In this section, we first show two cases, one over land and the other over ocean, to demonstrate
that microwave TB s are indeed more strongly correlated to water paths than surface rainrate. Using a year-long (1998) TRMM data set, correlations between surface rainrates and water paths are
then investigated over both land and ocean by calculating the Spearman correlation coefficients (as
shown in Eq.3.1), where x and y denote the ranks of data pairs, n is the sample size, and x̄ and
ȳ are the means of x and y, respectively. The Spearman correlation, rather than the traditional
Pearson correlation, is utilized in this study to compute correlation coefficients, to alleviate influences by outliers in the data and to take possible non-linear relations into consideration (Wilks,
2011). Seasonal and spatial variations of water paths have also been shown in various regions. As
mentioned previously, we focus on ice water path over both land and ocean, total water path over
land and liquid water path over ocean.
5.2.1
Case Studies
The first case (Fig. 5.1) shows a rain event on January 19, 1998 in southeast U.S. over the land
area of 34 ◦ N to 36 ◦ N and 78 ◦ W to 84 ◦ W. Over land, it has been believed that ice scattering
signature at 85 GHz is a major indicator of surface rainrate. Therefore, we first examine how V85
TB responds to surface rainrate. In Fig. 5.1, the results show that although the correlation (R2 )
between V85 TB and ice water path (Fig. 5.1a) is large (0.74), the correlation between V85 TB
and surface rainrate (Fig. 5.1c) is much weaker (0.38), due to the low correlation between surface
rainrate and ice water path (0.28) as shown in Fig. 5.1b. You et al. [2011] pointed out that over
land V19-V37 TB (brightness temperature difference between 19 and 37 GHz vertically-polarized
channels) possesses a better relation to surface rainrate since it can capture both solid and liquid
water’s signatures (i.e., response to total water path). In Fig. 5.1, the scatterplots of V19-V37
TB versus total water path, surface rainrate versus total water path, and surface rainrate versus
V19-V37 TB have also been shown. The correlation between V19-V37 TB and total water path is
0.67 (Fig. 5.1d), which is weaker than that between V85 TB and ice water path (0.74). However,
total water path versus surface rainrate correlation (0.38, Fig. 5.1e) is larger than the ice water path
versus surface rainrate correlation (0.28, Fig. 5.1b). As a result, the relationship between V19-V37
TB and surface rainrate is stronger (0.53) than that between V85 TB and surface rainrate (0.38).
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This case is a clear example to illustrate the importance of the relationship between water paths
and surface rainrates in retrieving surface rainrate by passive microwave observations.
The second case (Fig. 5.2) is a rain event over the South Pacific Ocean (20 ◦ S to 23 ◦ S and 168 ◦ E
to 173 ◦ E) on January 6, 1998. In this case, we use both liquid water emission and ice scattering
signatures to illustrate the importance of the relationship between water path and surface rainrate.
The correlation (R2 ) between V19 TB and liquid water path is 0.80 (Fig. 5.2a), which is much larger
than that between V19 TB and surface rainrate (Fig. 5.2c). Also, the correlation (R2 ) between
V85 TB and ice water path is 0.59, while it is only 0.27 between V85 TB and surface rainrate.
Similar to the over land case shown in Fig. 5.1, the less-perfect relationship between water paths
and surface rainrate weakens the correlation between surface rainrate and TB at V19 or V85.
In summary, since TB inherently reflects the integrated effects of hydrometers vertically distributed in the atmospheric column, the less-perfect relationship between surface rainrates and
water paths complicates the relation between satellite received radiances and surface rainrates,
thus increasing the degree of difficulty to retrieve surface rainrate from TB s, regardless of over land
or over ocean. The correlation between surface rainrates and TB s is commonly much weaker than
that between water paths and TB s. Without a good correlation between water paths and surface
rainrate, surface rainrates cannot be correctly retrieved even if we have accurate radiometric observations and a good knowledge of surface emissivity. Therefore, understanding this correlation
is of importance to rainrate retrievals. In the next section, we start to discuss the geographical
distribution of water paths distribution and their relationship with surface rainrate.
5.2.2
Spatial Variation of Ice Water Path
In performing the data analysis, we first divide the globe into 5 ◦ ×5 ◦ grid boxes. In each
grid box, we calculate the averaged ice water path in 1998 corresponding to surface rainrate of
around 1 mm h−1 (0∼3 mm h−1 ), 4 mm h−1 (3∼5 mm h
−1 ),
and 7 mm h−1 (5∼12 mm h−1 ),
which represents light, moderate and heavy rainfall, respectively. These three surface rainrate
intervals cover ∼95% of all rainy pixels. Although the rainrate intervals are chosen somewhat
arbitrarily, choosing slightly different values will not change our major conclusions. In each grid
box, if there are less than 50 rainy pixels observed in the three previously defined rainrate intervals,
averaged ice water path is not calculated due to the low sampling size. The averaged ice water path
corresponding to 1 mm h−1 surface rainrate is shown in Fig. 5.3a. It is immediately apparent that
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given 1 mm h−1 surface rainrate, ice water path over land is generally larger than that over ocean.
In particular, there exist large areas with ice water path being less than 20 g m−2 depicted as blue
color in Fig. 5.3a over shallow convection dominant regions over ocean. In contrast, larger values
of ice water path are observed over desert areas and semi-arid regions (e.g., the Sahara desert and
its surrounding areas, the Arab peninsula and northwestern Australia). It is also noticed that ice
water path over maritime regions and oceanic regions surrounded by land (the Gulf of Mexico,
the East China sea and the South China Sea) is larger than that over other ocean surfaces. For
example, given ∼1 mm h−1 surface rainrate, ice water path is ∼ 100 g m−2 over the East China
Sea, which is similar to that over its neighboring land. Similar characteristics are observed for ice
water path spatial distribution corresponding to 4 and 7 mm h−1 surface rainrates (not shown). To
further explore the spatial variation of ice water path, rainfall vertical structures over the eastern
tropical Pacific (130 ◦ W∼140 ◦ W, 5 ◦ S∼5 ◦ N), the Gulf of Mexico (84 ◦ W∼89 ◦ W,25 ◦ N∼30 ◦ N),
southeastern Atlantic (25 ◦ W∼30 ◦ W,15 ◦ S∼20 ◦ S) and central Africa (25 ◦ E∼30 ◦ E,5 ◦ S∼5 ◦ N) are
shown in Fig. 5.4. These four locations are chosen to represent rainfall systems over the ITCZ, the
maritime region, the shallow convection dominant region and the deep convection region over land,
respectively. It is found that given a similar surface rainrate, there exists the largest amount of ice
particles over land with deep convection, and then over the maritime region and the ITCZ, then
with the smallest ice particles being over the shallow convection dominant region. In summary,
corresponding to a similar surface rainrate, ice water path is large over land, small over the shallow
convection dominant regions, and its magnitude over maritime regions and the ITCZ is in between.
5.2.3
Correlation between Ice Water Path and Surface Rainrate
In this section, we investigate the spatial distribution of correlation (R2 ) between ice water path
and surface rainrate. Similar to section 3.2, we first divide the globe into 5 ◦ ×5 ◦ grid boxes. In each
grid box, the correlation (R2 ) between ice water path and surface rainrate is calculated, and the
result is shown in Fig. 5.5. The correlation (R2 ) varies from ∼0 to ∼0.8 over the TRMM satellite
covered area. On average, R2 is larger over land than over ocean. Specifically, over the majority
of land areas R2 is ∼0.6 with the exception over the Sahara desert region, the Indian subcontinent
and western Australia, where R2 is only ∼0.45. Over ocean, relatively large correlations are found
over the ITCZ, the maritime region and mid-latitude regions, while small values are over shallow
convection dominant regions, e.g., southeastern Pacific, southeastern Atlantic and oceanic regions
70
around the Hawaiian islands. In order to explain why R2 varies so dramatically over both land
and ocean, we select six regions (three over land and three over ocean, delineated with black boxes
in Fig. 5.5a) to show how ice water path varies given a similar surface rainrate. These six regions
include areas over central Africa, the Sahara desert, central India, the ITCZ, mid-latitudes and
shallow convection dominant areas. Letters A to F are assigned to those aformentioned six regions
to make the subsequent discussion easier to follow (see Fig. 5.5a). In each region, we calculate
monthly averaged ice water path during 1998 corresponding to surface rainrate around 1, 4, and 7
mm h−1 . In each month, if there are less than 50 pixels observed in a certain region for a rainrate
interval, ice water path is not calculated because of the small sample size. The results are shown
in Fig. 5.6. It is noticed that the seasonal variation of ice water path over central Africa (area
A) is small, particularly for clouds corresponding to 1 mm h−1 surface rainrate. This leads to
a relatively large correlation between surface rainrate and ice water path. In contrast, ice water
path varies quite largely over the Sahara desert region (area B) and the Indian subcontinent (area
C). Over the Sahara desert region, corresponding to 1 mm h−1 surface rainrate, ice water path is
∼300 g m−2 in July while it is only ∼100 g m−2 in September. Over central India, given a similar
surface rainrate, ice water path in the pre-monsoon season (April and May) is about twice as large
as that in the monsoon season (June to August). Previous studies [e.g., Liu and Fu, 2001; Hirose
and Nakamura, 2004] offered two possible explanations for this phenomenon. One possible reason
is that the evaporation process is stronger in the pre-monsoon season (e.g., May) due to a drier
lower atmosphere, which reduces rainrate near the surface. Another explanation is that during
the monsoon season the vertical motion is not as strong as that in the pre-monsoon season, which
results in less ice water above the freezing level. Given a similar surface rainrate, the strong seasonal
variation of ice water path contributes to the weak correlation between ice water path and surface
rainrate over the Sahara desert region and the Indian subcontinent. Similarly, seasonal variation of
ice water path over three ocean regions has also been shown in Fig. 5.6. It is found that over the
central Pacific ITCZ region (area D) the ice water path varies little from January to May, and then
decreases almost to 0 from June to December of 1998, which reflects the movement of the ITCZ.
Fortunately, from June to December there are only 7% of rainfall pixels in that region. Therefore,
it has little influence to the overall correlation between ice water path and surface rainrate. It is
shown that the North Pacific shallow convection dominant region (area E) is highly influenced by
71
shallow convective rain events, i.e., there exists no ice water path in certain month (e.g., January),
compared with ∼20 g m−2 in February of 1998. Ice water path over the mid-latitude North Atlantic
(area F) exhibits noticeable seasonal variation. Given 1 mm h−1 surface rainrate, ice water path
over the mid-latitude North Atlantic is much larger than that over the ITCZ regions. However,
corresponding to the larger (∼4 mm h−1 and ∼7 mm h−1 ) surface rainrates, ice water path over
the central Pacific, the ITCZ regions and the mid-latitude North Atlantic is similar.
To summarize, given similar surface rainrate, the smaller seasonal variation of ice water path
over tropical land, the ITCZ and the mid-latitude ocean accounts for a larger correlation between
surface rainrate and ice water path, while the larger seasonal variation over arid regions, the Indian
subcontinent and shallow convection dominant ocean areas leads to a smaller correlation between
ice water path and surface rainrate.
5.2.4
Relationship between Total Water Path and Surface Rainrate over Land
The averaged total water path corresponding to 1 mm h−1 surface rainrate is shown in Fig. 5.3b.
It is noted that given 1 mm h−1 surface rainrate, total water path over arid regions (e.g., the Sahara
desert and its surrounding areas) is larger, compared with that over coast regions and inland China.
The correlation (R2 ) between total water path and surface rainrate is shown in Fig. 5.5b. It is
found that over the majority of the land regions the correlation is ∼0.7, such as over central to
southern Africa and South America. Similar to ice water path, corresponding to a similar surface
rainrate, the smaller seasonal variation of vertical rain/ice water structure contributes to the larger
correlation between total water path and surface rainrate over the majority of the land regions. The
lowest value (∼0.45) is located over the Sahara desert region. Over other arid regions, including
the Arab peninsula, the Iran Plateau, western Australia and western United States, R2 (∼0.55)
is also relatively small. The strong evaporation over arid regions is believed to be the cause that
greater total water path does not necessarily produce a greater surface rainrate [e.g., McCollum
et al., 2000], and thus reduces the correlation over such regions. It is also worth mentioning that
given a similar surface rainrate, total water path over the Indian subcontinent has a strong seasonal
variation (not shown). Therefore, over the majority of the Indian subcontinent the correlation (R2 )
between total water path and surface rainrate is ∼0.65, smaller than that over central to southern
Africa. In particular, there exists a greater total water path in the pre-monsoon season (e.g., April
and May), compared with that in the monsoon season (e.g., August).
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In order to show the seasonal vertical rain/ice water structure variation, we select three regions
(delineated with black boxes in Fig. 5.5b): central Africa, central India and the Sahara desert. In
each region, we choose two distinctively different months based on rainy pixel number and ice water
path amount; the vertical rainrate profiles are shown in Fig. 5.7. Over central Africa (Fig. 5.7a),
the rainfall profiles are very similar between these two months; only small differences appear when
surface rainrates are larger than 7 mm h−1 . In contrast, over central India (Fig. 5.7b), rainfall
profiles in May (pre-monsoon season) and August (monsoon season) are distinctively different, i.e.,
corresponding to a similar surface rainrate, there exists much more water in the atmospheric column
in May than that in August. The echo top is ∼6 km above the freezing level in May, compared to
only ∼4 km in August. Similarly, the rainrate profiles over the Sahara desert (Fig. 5.7c) also differ
significantly between July and September; the rain system in July is deeper with the echo top over
∼6 km above the freezing level, compared to ∼4 km in September.
In summary, the correlation (R2 ) between total water path and surface rainrate varies from
∼0.3 to ∼0.8 over land. Seasonal variation of total water path given a similar surface rainrate
largely accounts for the variation of such correlation.
5.2.5
Relationship of Liquid Water Path and Surface Rainrate over Ocean
Given a similar surface rainrate, strong seasonal variation of liquid water path (not shown)
largely contributes to the weak correlation between liquid water path and surface rainrate and vice
versa. Given 1 mm h−1 surface rainrate, the spatial variation of liquid water path is shown in
Fig. 5.3c. It is noted that the large liquid water path is over the tropical ocean. More interestingly,
it seems that the largest liquid water path corresponding to ∼1 mm h−1 surface rainrate is over
maritime regions (e.g., the oceanic area around Malaysia and Indonesia) and oceanic regions surrounded by land (e.g., Gulf of Mexico, South China Sea, northeast Indian Ocean and the west coast
of Mexico). Similar characteristics are observed under surface rainrates of 4 and 7 mm h−1 . These
results imply that for a similar surface rainrate liquid water layers are deeper in these regions than
over other open ocean regions, probably due to stronger convective activity. Shown in Fig. 5.5c
is the spatial distribution of the correlation (R2 ) between liquid water path and surface rainrate
over ocean. The largest correlation value (∼0.8) is observed over central to eastern tropical Pacific
regions (80 ◦ W∼180 ◦ W; 20 ◦ S∼20 ◦ N) and over a small portion of the Atlantic (20 ◦ W∼40 ◦ W;
10 ◦ S∼5 ◦ N). Much weaker correlation is observed over shallow convection dominant regions, such
73
as off the western coast of U. S. and the western coast of southern Africa. Previous studies indicated
that surface rainrate generated by shallow convective systems remains difficult to retrieve even by
exploiting multi-channel brightness temperatures (e.g.,Chen et al., 2011). In addition to the weak
radiometric response to these shallow systems, we argue that the small correlation between surface
rainrate and liquid water path makes the retrieval problem even harder. Given a similar surface
rainrate, strong seasonal variation of liquid water path (not shown) largely contributes to the weak
correlation between liquid water path and surface rainrate and vice versa.
5.3
Implications to the Surface Rainrate Retrieval
It is the water path that is more directly related to the brightness temperature observed by
microwave radiometers than is the surface rainrate. In this section, we first choose two cases to
illustrate water path’s influence on brightness temperature over land and ocean. Then we categorize
the relationship between surface rainrate and TB -variation into different groups based on two pairs
of relationships, i.e., between water paths and surface rainrate, and between water paths and TB variation. TB -variation is defined as the original TB minus the background TB . The background
TB database is created under a no-rain condition with resolution of 5 days and 2◦ longitude × 2◦
latitude using TMI data observed during 1998. These resolutions are determined by considering
the tradeoff between sample size and TB ’s temporal-spatial variations. By doing this, the surface
emissivity influence is largely alleviated.
As shown previously, given a similar surface rainrate the water path can be very different
depending on season and location; thus TB is expected to be different, too. First, we choose a
5◦ ×5◦ region (75 ◦ E∼80 ◦ E; 15 ◦ N∼20 ◦ N) over central India and calculate the TB -variation (solid
curves) at V85 for two months (May and August) under a similar surface rainrate. The result is
shown in Fig. 5.8a, along with the corresponding ice water path by dashed curves. It is noticed
that over the Indian subcontinent given a similar surface rainrate the difference of TB -variation
at V85 between August and May is 15 K on average. Ice water path in May is about twice as
much as that in August, leading to the large difference of TB -departure at V85 between the two
months. It is worth mentioning that we also observe a noticeable discrepancy of TB -variation at
V19-V37 between August and May (not shown) due to the difference in total water path in these
two months, although the discrepancy in these two months at V19-V37 is not as large as that at
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V85 caused by ice water path. Similarly, we choose a 10◦ ×10◦ region (80 ◦ E∼90 ◦ E; 5 ◦ S∼15 ◦ S)
over the Indian Ocean to investigate the ice water path’s influence to TB -variation at V85. We
find that the difference of TB -variation at V85 between January and July changes from 5 K to
20 K corresponding to surface rainrate varying from 1 mm h−1 to 10 mm h−1 (Fig. 5.8b), due to
the fact that ice water path in July is ∼150 g m−2 more than that in January. Additionally, the
difference of TB -variation at V19 (not shown) between January and July is relatively constant at
∼10 K, because liquid water path difference is relatively constant at ∼200 g m−2 between these
two months. In summary, the above results show that given a similar surface rainrate TB -variation
can differ by several tens of K due to water path differences in the atmospheric column.
To further illustrate the importance of the relationship between surface rainrate and water paths,
we calculate three pairs of correlations, i.e., correlations between ice water path and TB -variation,
between ice water path and surface rainrate, and between TB -variation and surface rainrate. The
results are shown in Fig. 5.9. For the correlation between ice water path and TB -variation, it is
noticed that R2 is ∼0.75 over the vast majority of land regions with exception over the Iran plateau
and areas surrounding the Tibetan plateau (Fig. 5.9a). Over ocean, R2 is ∼0.75 over the ITCZ
(∼10◦ S to ∼10◦ N) region. Correlation between ice water path and surface rainrate is ∼0.60 over
most of the land regions except for over the Indian subcontinent and the Sahara desert regions.
In contrast, over the ITCZ region, the correlation between ice water path and surface rainrate is
much lower (∼0.45) than that over land (Fig. 5.9b). Consequently, R2 between surface rainrate and
brightness temperature over the ITCZ region (∼0.20) becomes lower than that over the majority of
the land regions (∼0.35), which is particularly evident over the Indian Ocean (Fig. 5.9c). In addition
to TB at V85, scattering index (SI) as defined by by Grody (1991) has also been examined for its
correlation with ice water path and surface rainrate. While SI shows slightly better correlation
with ice water path at some regions, it, too, suffers the same reduction of correlation to surface
rainrate as does TB at 85V when ice water path versus surface rainrate are not well correlated. To
simplify the presentation while not losing the points of our conclusion, in the following we will use
TB at V85 and omit discussions using SI.
Clearly, the strength of the correlation between TB -variation and surface rainrate depends on
the closeness of the following two relations: TB -variation versus water paths and water paths versus
surface rainrate. The former is determined by the radiative response to the variation of condensed
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water, and the latter is related to the vertical structure of hydrometeors themselves. To demonstrate
the relative importance of the above two relations in affecting rainfall retrievals at different regions,
we divide the whole globe into 4 types of regions based on whether the two correlations in it are
large or small. Here we use the median among all R2 values as a separator for large and small
correlation. The so-determined region types are shown in Fig. 5.9d. Over Type 1 regions, both
correlation between ice water path and TB -variation and correlation between ice water path and
surface rainrate are large. Thus, the correlation between surface rainrate and TB -variation is large,
too. That is, the scattering signature at V85 TB can be utilized to retrieve surface rainrate (the very
bottom layer of the water flux) with the fewest challenges. Over Type 2 regions, although ice water
path strongly responds to TB -variation, ice water path is not well correlated with surface rainrate,
leading to a weak response of TB -variation to surface rainrate. Conversely, over Type 3 regions,
surface rainrate is well correlated to ice water path. However, ice water path is not well correlated
to TB -variation, which also leads to a weak correlation between surface rainrate and TB -variation.
It is worth mentioning that although the relationship between surface rainrate and TB -variation
is weak over both Type 2 and Type 3 regions, the reasons of causing such a weak correlation are
different. Over Type 2 regions, it is the lack of proportionality between surface rainrate and ice
water path that leads to the weak correlation between surface rainrate and TB -variation, while
over Type 3 regions it is because TB itself cannot well represent the integrated effect of ice water.
Finally, over Type 4 regions, neither the correlation between ice water path and TB -variation nor
the correlation between ice water path and surface rainrate is strong. Rain systems over such
regions will pose the greatest challenges to surface rainrate retrieval using scattering signatures.
The majority of the land region is determined as Type 1. Not surprisingly, the ITCZ regions, the
Indian subcontinent and part of the Sahara desert are categorized as Type 2 regions due to their
small correlation between ice water path and surface rainrate as shown in the previous section.
Type 3 regions are scattered over the Iran plateau, areas surrounding the Tibetan plateau and the
mid-latitude oceans. Type 4 regions are located mainly over shallow convection dominant areas
over ocean and part of the Sahara desert regions. The percentage of rain systems belonging to
types 1 through 4 are 23%, 27%, 10% and 40%, respectively, in terms of rain pixel number, and
30%, 34%, 11% and 25%, respectively, in terms of rainfall amount.
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For liquid water path over ocean, relationships between liquid water path and TB -variation
at V19, between liquid water path and surface rainrate, and between TB -variation at V19 and
surface rainrate are shown in Fig. 5.10. Instead of grouping them into different categories based
on the first two-pair correlations, we focus on the difference between these three figures and the
first three figures shown in Fig. 5.9. Interestingly, it is found that over the ITCZ region correlation
between ice water path and TB -variation at V85 is ∼0.75 (Fig. 5.9a). In contrast, correlation
between liquid water path and TB -variation at V19 is only ∼0.50 (Fig. 5.10a) over this region.
However, this does not result in surface rainrate having a better correlation to TB -variation at V85
than to TB -variation at V19 (compare Fig. 5.9c and Fig. 5.10c over the ITCZ region). In fact,
over the ITCZ region the correlation (R2 ) between surface rainrate and TB -variation at V85 is
only ∼0.25, compared to ∼0.45 between surface rainrate and TB -variation at V19. This seemingly
contradictory phenomenon is largely due to the fact that surface rainrate is more closely related to
liquid water path than to ice water path, as shown in Fig. 5.9b and Fig. 5.10b.
While not shown, similar results have be found for total water path over land. Ice water path
responds much more strongly to TB -variation at V85 (R2 ∼0.75) than total water path responds to
TB -variation at V19-V37 (R2 ∼0.5) over land. However, correlations between total water path and
surface rainrate (0.80) are much larger than that between ice water path and surface rainrate (0.55).
Therefore, on average surface rainrate is better correlated with TB -variation at V19-V37 than with
TB -variation V85 (not shown). These results again support the conclusion that the relationship
between water paths and surface rainrate will greatly influence the relationship between surface
rainrate and TB -variation, and therefore will influence the ability to retrieve surface rainrate from
brightness temperatures.
5.4
Conclusions
Using precipitation radar and microwave radiometer data observed by the TRMM satellite
during 1998, the relationships between water paths and surface rainrate are investigated. Based on
previous sensitivity studies on microwave radiation to water paths over different surface types, we
investigate the relationships between ice water path and surface rainrate over both land and ocean,
between total water path and surface rainrate over land, and between liquid water path and surface
rainrate over ocean. Results show that corresponding to a similar surface rainrate ice water path
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has large spatial variability, and the most prominent characteristic for the ice water path spatial
distribution is the contrast between land and ocean. That is, given a similar surface rainrate, larger
ice water path is observed over land than over ocean. Specifically, for a similar surface rainrate
ice water path is large over arid regions (e.g., the Sahara desert), small over shallow convection
dominant regions (e.g., oceanic area near Hawaii), and in-between over maritime and ITCZ regions.
On average, the correlation (R2 ) between ice water path and surface rainrate is also larger over
land than over ocean. Over the majority of land areas, R2 is ∼0.40, with the exception of arid
regions and the Indian subcontinent (∼0.25). Relatively large R2 is also found over ITCZ regions
over ocean, while it decreases to nearly 0 over shallow convection dominant regions over ocean.
The cause of the correlation difference is investigated by analyzing the seasonal variation of ice
water path and rain systems’ vertical structures. It is found that given a similar surface rainrate,
a larger R2 corresponds to a smaller seasonal variation of ice water path and vice versa. For
example, over central India, given a similar surface rainrate, ice water path in the pre-monsoon
season (April and May) is about twice as large as that in the monsoon season (June to August)
due to a stronger low-level evaporation in the pre-monsoon season. Strong low-level evaporation
also causes low correlation between ice water path and surface rainrate over arid regions, which is
particularly evident over the Sahara desert.
Over ocean, we investigated the spatial distribution of liquid water path and its relationship
with surface rainrate. It is noticed that corresponding to a similar surface rainrate, liquid water
path over ITCZ and maritime regions is larger than that in other oceanic regions. The correlation
between liquid water path and surface rainrate is small over shallow convection dominant regions,
but large over ITCZ and maritime regions. Over land, low values of correlation between total water
path and surface rainrate are found over the Sahara desert regions and the Indian subcontinent.
The relations between water path and surface rainrate are shown to have significant implications
to surface rainrate retrieval by using microwave brightness temperatures. That is, given the same
surface rainrate, depending on the closeness of the water path versus surface rainrate relationships,
the degree of brightness temperature response is very different. In particular, over the ITCZ, the
Indian subcontinent and arid regions (e.g., the Sahara desert), although ice water path responds
well to brightness temperatures, since the correlation between ice water path and surface rainrate is
weak, it leads to a relatively weak response of brightness temperature at 85 GHz to surface rainrate.
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Additionally, it is worth mentioning that liquid water path over ocean as well as total water path
over land, always possess a better relationship with surface rainrate than that between ice water
path and surface rainrate. It implies that channels or channel combinations that can capture liquid
water signal over ocean (or total water signal over land) are preferable to those capturing ice water
information for retrieving surface rainrate.
Finally, we would like to clarify that a weak correlative relationship between water paths and
surface rainrate is not the only challenge posed to surface rainrate retrieval; it is in addition to
other outstanding problems, such as uncertainties in surface emissivity, etc. In fact, considerable
efforts have already been made to better understand the land surface characteristics [e.g., Prigent
et al., 2006; Liu et al., 2011]. Knowledge of the surface emissivity is crucial for quantifying the
contribution from the surface to the brightness temperatures observed by a radiometer. However,
even if surface emissivity is perfectly known, the surface rainrate retrieval accuracy will still suffer
from a weakly coupled relation between surface rain and columnar water path.
79
V85 (K)
R2=0.74
240
220
200
0
200
400
600
6
800
(b)
4
3
2
4
0
0
200
400
600
800
0
0
6
1000 1200
TWP (g m−2)
36
240
220
200
400
600
200
800
0
1
(e)
R2=0.38
5
4
3
2
3
4
(f)
12
5
6
R2=0.53
8
4
0
1
0
2
Surface rainrate (mm h−1)
V19−V37 (K)
V19−V37 (K)
R2=0.67
8
−4
R2=0.38
IWP (g m−2)
Surface rainrate (mm h−1)
(d)
(c)
260
1
IWP (g m−2)
12
270
R2=0.28
5
V85 (K)
(a)
260
Surface rainrate (mm h−1)
270
0
200
400
600
800
TWP (g m−2)
1000 1200
−4
0
1
2
3
4
5
6
Surface rainrate (mm h−1)
(g)
01/19/1998 South Carolina
latitude
35
34
pixel with rain
pixel without rain
33
−84
−82
−80
longitude
−78
Figure 5.1: (a) Scatter plot between TB at V85 and ice water path (IWP). (b)Scatter
plot between surface rainrate and ice water path (IWP). (c) Scatter plot between TB at
V85 and surface rainrate. (d) Scatter plot between TB at V19-V37 and total water path
(TWP). (e) Scatter plot between surface rainrate and total water path (TWP). (f) Scatter
plot between TB at V19-V37 and the surface rainrate. (g) Geographical location for the
case on January 19, 1998 over southeastern U.S..
80
240
230
220
0
100 200 300 400 500 600 700
LWP (g m−2)
275
(d)
R2=0.59
V85 (K)
265
255
245
235
0
100
200
300
400
500
600
IWP (g m−2)
−20
(b)
260
R2=0.73
2
1
0
R2=0.54
240
230
0
100 200 300 400 500 600 700
LWP (g m−2)
(e)
220
0
R2=0.41
1
2
3
Surface rainrate (mm h−1)
275
(f)
R2=0.27
265
2
1
0
(c)
250
3
Surface rainrate (mm h−1)
V19 (K)
250
3
V19(K)
R2=0.80
V85(K)
(a)
Surface rainrate (mm h−1)
260
255
245
0
100
200
300
400
IWP (g m−2)
500
600
235
0
1
2
3
Surface rainrate (mm h−1)
01/06/1998 Pacific
latitude
−21
−22
pixel with rain
pixel without rain
(g)
−23
168
169
170
171
longitude
172
173
Figure 5.2: (a) Scatter plot between TB at V19 and liquid water path (LWP). (b)Scatter
plot between surface rainrate and liquid water path (LWP). (c) Scatter plot between TB
at V19 and surface rainrate. (d) Scatter plot between TB at V85 and ice water path
(IWP). (e) Scatter plot between surface rainrate and ice water path (IWP). (f) Scatter
plot between TB at V85 and surface rainrate. (g) Geographical location for the case on
January 6, 1998 over South Pacific Ocean.
81
40oN
(a)
20oN
0o
20oS
40oS
180o
120oW
20
40
60oW
60
90
0o
120
150
60oE
180
210
120oE
240
270
180o
-2
300 (g m )
40oN
(b)
20oN
0o
20oS
40oS
180o
120oW
150
60oW
0o
250
60oE
350
120oE
450
40 N
o
180o
(g m-2)
(c)
20oN
0o
20oS
40oS
180o
120oW
40
60oW
0o
80
60oE
120
120oE
160
180o
(g m-2)
Figure 5.3: (a) Spatial distribution of ice water path (IWP) corresponding to 1 mm h−1
surface rainrate over TRMM covered areas.(b) Spatial distribution of total water path
(TWP) corresponding to 1 mm h−1 surface rainrate over land.(c) Spatial distribution of
liquid water path (LWP) corresponding to 1 mm h−1 surface rainrate over ocean.
82
6
Over deep−convection land
Relative Height (km)
Over maritime region
Over shallow−convection ocean
4
Over ITCZ
2
0
−2
−4
0
1
4
Rainrate (mm h−1)
7
Figure 5.4: Averaged precipitation rainfall profiles over four representative regions. Relative height is the distance from the freezing level height.
83
40oN
20 N
E
0o
D
o
F
(a)
B
C
A
20oS
40oS
180o
120oW
60oW
0o
60oE
120oE
40oN
180o
(b)
20oN
0o
20oS
40oS
180o
120oW
60oW
0o
60oE
120oE
40oN
180o
(c)
20oN
0o
20oS
40oS
180o
120oW
0.1
0.2
60oW
0.3
0o
0.4
0.5
60oE
0.6
120oE
0.7
0.8
180o
0.9
Figure 5.5: (a) Spatial distribution of correlation between ice water path and surface rainrate over TRMM covered areas.The boxes delineate the six regions in subsequent studies.
(b) Spatial distribution of correlation between total water path and surface rainrate over
land. The boxes delineate the three regions in subsequent studies. (c) Spatial distribution
of correlation between liquid water path and surface rainrate over ocean.
84
1 mm h−1 surface rainrate
300
4 mm h−1 surface rainrate
600
LAND
Area A
7 mm h−1 surface rainrate
900
LAND
LAND
IWP (g m−2)
Area B
Area C
200
600
400
100
0
1
IWP (g m−2)
80
4
7
10
12
1
40
200
20
100
0
0
4
7
month
10
Area C
7
10
12
12
0
1
4
7
10
12
10
12
OCEAN
600
300
Area F
1
4
OCEAN
Area D
Area E.
Area A
Area C
400
OCEAN
60
300
Area A
200
400
Area D
Area D
200
Area F
Area F
1
4
7
month
10
12
0
1
4
7
month
Figure 5.6: Seasonal variation of ice water path, corresponding to 1,4,7 mm h−1 surface
rainrate over six selected regions in Fig. 5a.
85
4
2
0
−2
−4
0
Relative Height (km)
January
April
(a)
Relative Height (km)
Relative Height (km)
6
Central Africa (25°E~35°E,5°S~5°N)
May
August
(b)
4
2
0
−2
−4
0
5
10
Rainrate (mm h−1)
6
6
Central India (75°E~80°E,15°N~12°N)
5
10
Rainrate (mm h−1)
July
September
(c)
4
2
0
−2
−4
0
Sahara desert (0°~10°E,12°N~30°N)
1
2
Rainrate (mm h−1)
3
Figure 5.7: Averaged precipitation rainfall profiles in two months over (a) Central Africa,
(b) Central India, (c) Sahara desert. Relative height is the distance from the freezing level
height.
−20
800
600
May
−30
400
May
−40
−50
200
August
0
2
Indian Subcontinent
4
6
−1
8
0
10
0
January
500
−10
July
−20
250
−30
−40
Surface rainrate (mm h )
750
(b)
July
January
0
2
Indian ocean
4
6
−1
8
LWP (g m−2)
August
−10
10
TB−Variation (K) at V85
1000
(a)
IWP (g m−2)
TB−Variation (K) at V85
0
0
10
Surface rainrate (mm h )
Figure 5.8: (a) TB -variation at V85 in two months corresponding to similar surface rainrate
over central India region. (b) TB -variation at V85 in two months corresponding to similar
surface rainrate over Indian Ocean region. Solid lines stand for TB -variation and dashed
lines represent water paths. TB -variation is the original TB minus the background TB .
86
40oN
(a)
20oN
0o
20oS
40oS
180o
120oW
0.1
0.2
60oW
0o
0.3
0.4
60oE
0.5
120oE
0.6
40oN
180o
0.7
(R2)
(b)
20oN
0o
20oS
40oS
180o
120oW
0.1
0.2
60oW
0o
0.3
0.4
60oE
0.5
120oE
0.6
40oN
180o
0.7
(R2)
(c)
20oN
0o
20oS
40oS
180o
120oW
0.05
0.1
60oW
0o
0.15
0.2
60oE
0.25
120oE
0.3
40oN
180o
0.35 (R2)
(d)
20oN
0o
20oS
40oS
180o
120oW
TYPE 1
60oW
0o
TYPE 2
60oE
TYPE 3
120oE
180o
TYPE 4
Figure 5.9: (a) Correlation between TB -variation at V85 and ice water path. (b) Correlation between ice water path and surface rainrate. (c) Correlation between TB -variation
at V85 and surface rainrate. (d) Spatial distriubtion of 4-type rain system regions. TB variation is the original TB minus the background TB .
87
40oN
(a)
20oN
0o
20oS
40oS
180o
120oW
0.1
60oW
0.2
0o
0.3
60oE
0.4
120oE
0.5
180o
0.6
40 N
o
(b)
20oN
0o
20oS
40oS
180o
120oW
60oW
0.4
0o
0.5
60oE
0.6
120oE
0.7
180o
0.8
40 N
o
(c)
20oN
0o
20oS
40oS
180o
120oW
0.1
60oW
0.2
0o
0.3
60oE
0.4
120oE
0.5
180o
0.6
Figure 5.10: (a) Correlation between TB -variation at V19 and liquid water path over
ocean. (b) Correlation between liquid water path and surface rainrate over ocean. (c)
Correlation between TB -variation at V19 and surface rainrate over ocean. TB -variation is
the original TB minus the background TB .
88
CHAPTER 6
A PRINCIPAL COMPONENT
ANALYSIS(PCA)-BASED BAYESIAN ALGORITHM
6.1
Introduction
There exist a large number of rainfall retrieval algorithms in literature (Spencer et al., 1989;
Liu and Curry, 1992; Petty, 1994; Smith et al., 1994a; Ferraro and Marks, 1995; Evans et al., 1995;
Kummerow et al., 1996; Panegrossi et al., 1998; Grecu and Anagnostou, 2001; Evans et al., 2002;
Viltard et al., 2006; Chiu and Petty, 2006; Aonashi et al., 2009; Gopalan et al., 2010; Kummerow
et al., 2011; Liu and Seo, 2013). Although, they are seemingly very different in both theory and
implementation process, in fact, these algorithm are closely related and usually generates similar
results. Mathematically, these algorithms can be grouped into two categories, i.e., regression based
algorithm and Bayesian based algorithm.
Regression Based Algorithm (e.g., Liu and Curry, 1992; Ferraro and Marks, 1995; Gopalan et al.,
2010) has been widely utilized in the rainfall retrieval community since it is easy to understand and
straightforward to implement. In the version7 TRMM facility algorithm over land, two regression
curves, one for stratiform cloud and the other for convective clouds, are proposed (eq. 6.1). Where
RRconv and RRstrat are the estimated rainfall rate for convective and stratiform pixels, respectively.
Tb85V is the brightness temperature at the 85GHz. Clearly, in order to consider the nonlinearity
between rainfall rate and TB in convective clouds, the cubic line is used.
RRconv = −0.00001177 × T b385V + 0.008027 × T b285V + 1.946 × T b85V + 182.68
RRstrat = −0.0708 × T b85V + 19.7
(6.1)
One special case of the regression based algorithm is the Look-Up-Table (LUT) technique (e.g.,
Aonashi et al., 2009). Instead of using regression equation between rainfall rate and TB, this
technique generates a database, where each TB corresponds to certain rainfall rate. Since there is
no analytic form of the regression line, the LUT naturally take the nonlinearity between rainfall
rate and TB into consideration. Similar technique has also been employed by Liu and Seo (2013).
89
The current Bayesian based algorithm in rainfall retrieval community can date back at least to
Rodgers (1976) and Lorenc (1986). We would like to emphasize that the following equations in this
chapter are not original, nor are the derivations.
Bayes’ theorem itself is simple and can be easily obtained as follows. Suppose P(A) and P(B)
are the probability of A occurring and B occurring, respectively. P (A ∩ B) is the probability that
both A and B has occurred. P (A|B) is the probability that the event A occurs given that B has
already occurred. Similarly, P (B|A) is the probability that the event B occurs given that A has
already occurred. There are two ways to express the joint probability P (A ∩ B),
P (A ∩ B) = P (A) × P (B|A) = P (B) × P (A|B)
(6.2)
A simple mathematical manipulation leads directly to the Bayes’ theorem:
P (A) × P (B|A)
P (B)
P (A) × P (B|A)
=P
P (Ai ) × P (B|Ai )
P (A|B) =
(6.3)
Clearly, Bayes’ theorem gives the relationship between the probabilities of A and B, P(A) and
P(B), and the conditional probabilities of A given B and B given A, P (A|B) and P (B|A). The
denominator in Eq. 6.3 is a constant. Therefore, Eq. 6.3 can be re-written as:
P (A|B) ∝ P (A) × P (B|A)
(6.4)
In Bayesian theory, the P (A|B), P(A) and P (B|A) are often called posterior, prior and likelihood probability, respectively. Following this name convention, the Eq. 6.4 states that posterior is
proportional to prior times likelihood. It is worth mentioning that from the pure probability point
of view, P (A|B) and P (B|A) are often called conditional probability, P(A) and P(B) marginal
probability, and P (A ∩ B) joint probability.
To be consistent with the symbols used in the rainfall retrieval community, we will use x to
represent the atmospheric variable we are intended to obtain (e.g., rain rate or profile), T to the
brightness temperatures. The bold symbols stands for a vector. In order to obtain the atmospheric
90
variable x , one can apply the Bayes’ theorem (Eq. 6.3):
T |x
x) × f (x
x)
f (T
T)
f (T
T |x
x) × f (x
x)
f (T
=R
T |x
x) × f (x
x)dx
x
f (T
x|T
T) =
f (x
(6.5)
x|T
T ) stands for the posterior probability density function (PDF) of the atmospheric
Where f (x
x) is the prior PDF of the atmospheric
variable x given the measured brightness temperature, f (x
T |x
x) is the likelihood function. Eq. 6.5 serves the foundation of current popular
variable x and f (T
Bayesian algorithm (Evans et al., 1995; Kummerow et al., 1996; Chiu and Petty, 2006). In the
following section, we will discuss two ways of calculating the atmospheric variable x from the
x|T
T ). In addition, several common misconception will also be clarified.
posterior probability f (x
6.2
Estimation of the Atmospheric Variable x , given T
From Eq. 6.5, there are two ways to obtain and estimation of the atmospheric variable x ,
given T , in the literature. One way (e.g., Evans et al., 1995; Chiu and Petty, 2006) to obtain an
estimation of atmospheric variable x , given T , is: both the prior PDF and likelihood function are
assumed to be in certain analytical form, then one can obtain a analytical form for the posterior
PDF. In some situations, when no analytical form exists, samples from the posterior PDF can be
obtained by drawing samples from prior PDF and likelihood function. Because both prior PDF and
likelihood function are in analytical forms, there exist many techniques to draw samples from these
distributions (e.g., Monte Carlo and importance sampling techniques). Once the posterior PDF is
known, there are two common estimator can be used to obtain a estimation of the atmospheric
R
x|T
T )dx
x and the Maximum A Posterior (MAP), which
variable x , given T , i.e., the mean x f (x
basically take the atmospheric variable x , given T , corresponding to the maximum of the posterior
PDF.
Another way to obtain an estimation of the atmospheric variable x , given T , is, directly use the
likelihood function and the prior PDF to calculate the mean of the atmospheric variable x , given
pmbT , without knowing the form of the posterior PDF (e.g., Kummerow et al., 1996; Evans et al.,
2002; L’ecuyer and Stephens, 2002). The details of this process can be mathematically stated as
follows:
91
Z
x|T
T] =
E[x
x|T
T )dx
x
x f (x
R
T |x
x) × f (x
x)dx
x
x × f (T
R
T |x
x) × f (x
x)dx
x
f (T
x × f (T
T |x
x)]
E[x
=
T |x
x)]
E[f (T
=
(6.6)
x|T
T ) is the expectation of the atmospheric variable x , given T . Based on law of large
Where E(x
numbers, the sample mean will converge to the expectation when the sample size grows to infinity.
In practice, a large number of samples will be drawn based on the distribution of x to obtain the
mean, which is an approximation of the expectation.
x|T
T ). This
In Eq. 6.6, to obtain the second integration, we simply use the Eq. 6.5 to replace the f (x
replacement seems mediocre, however, it fundamentally changes the way to obtain the expectation
x|T
T ). In fact, the fundamental difference between the two previously mentioned method to
E(x
T lies in Eq. 6.6. To fully understand this point,
estimate the mean of the atmospheric variable x|T
knowledge of the Monte Carlo integration is necessary.
6.3
Monte Carlo Integration
Monte Carlo Integration (MCI) is a simple and powerful technique for estimating the integration
without analytical form. Suppose our goal is to estimate the following integration:
Z
x) × f (x
x)dx
x
g(x
x)) =
E(g(x
(6.7)
x) is the density function. g(x
x) can be any function as long as E(g(x
x)2 ) is bounded.
Where f (x
Using the MCI technique, Eq. 6.7 can be re-written as follows:
Z
x)) =
E(g(x
x) × f (x
x)dx
x
g(x
n
1X
xi )
g(x
≈
n
(6.8)
i=1
x).
Where x 1 , x 2 , · · · , x n are independent and identically distributed (iid) samples from f (x
Based on the definition of the MCI, if one uses the first integration in the Eq. 6.6, i.e.,
92
Z
x] =
E[x
x|T
T )dx
x
x × f (x
(6.9)
to calculate the mean of the atmospheric variable x , the iid samples must be drawn from the
x|T
T ). One the other hand, if one uses the second integration in the Eq. 6.6, i.e.,
posterior PDF f (x
R
x] =
E[x
T |x
x) × f (x
x)dx
x
x × f (T
T |x
x)]
x × f (T
E[x
R
=
T |x
x)]
T |x
x) × f (x
x)dx
x
E[f (T
f (T
(6.10)
x). Using samples from prior PDF can be
the iid samples must be drawn from the prior PDF f (x
particularly convenient when there exist a pre-defined database, either from observations or model
simulations.
x), a common measure of the uncertainty, can also be
Using MCI technique, the variance of g(x
calculated.
2
Z
x) − E(g(x
x)))2 × f (x
x)dx
x
(g(x
Z
Z
x)2 f (x
x)dx
x − 2E(g(x
x)) g(x
x)f (x
x)dx
x + E(g(x
x))2
= g(x
Z
x)2 f (x
x)dx
x − E(g(x
x))2
= g(x
x)) =
σ (g(x
≈
n
n
i=1
i=1
1X
1X
xi )2 − (
xi ))2
g(x
g(x
n
n
6.4
6.4.1
(6.11)
Implementation Details
Likelihood PDF and Prior PDF
In precipitation/cloud retrieval community, the likelihood PDF is usually assumed to follow a
multivariate normal distribution (Eq. 6.12).
1
0
−1
T − µ ) |Σ
Σ| (T
T − µ)
T |x
x) = p
exp − (T
f (T
2
Σ|
(2π)k |Σ
1
x)
µ = g(x
(6.12)
Σ| is the determinant of
Where Σ is the covariance matrix of the brightness temperature, |Σ
the Σ , µ is the mean vector of the brightness temperature, which is related to the atmospheric
93
variable x through the function g. In Evans et al. (1995)’s work, the mean vector of the brightness
temperature is assigned as the model simulated values, and the covariance matrix is assumed to
be diagonal with given values and varies along with each model simulated mean vector. In Chiu
and Petty (2006)’s work, g is in an exponential form. And other experimental forms have also been
attempted in the same work. The full matrix instead of the diagonal one is used, but it is assumed
to be constant.
One can further assume that each component in the vector T is uncorrelated. Based on this
assumption, the covariance matrix Σ becomes a diagonal matrix. Then, without much effort,
Eq. 6.12 can be simplified into the following form:
M
Y
T − µ )2
1 (T
q
T |x
x) =
f (T
exp −
2
σj2
2πσj2
j=1
1
!
x)
µ = g(x
(6.13)
The uncorrelatedness assumption in the likelihood PDF has been utilized widely since Rodgers
(1976) (e.g., Evans et al., 1995; Kummerow et al., 1996; Austin et al., 2009; Evans et al., 2012).
However, this assumption is problematic, especially for the rainfall retrieval, since the brightness
temperatures at different channel often are highly correlated, for example, the correlation between
the TBs at 37 GHz and 85GHz can be as high as 0.9. We will propose a Principal Component
Analysis (PCA)-based method which will solve this problem (see next section).
Regarding the Prior PDF for the atmospheric variable x (e.g., rain rate and rainfall profile),
both log-normal and Gamma distribution have been commonly used (Houze Jr and Cheng, 1977;
Kedem and Chiu, 1987; Wilks and Eggleston, 1992; Cho et al., 2004). In fact, when using the Eq.
6.6, no analytical form for the Prior PDF is needed if there exists pre-defined database. One can
directly use the already discretized values of x, as demonstrated by Kummerow et al. (1996) and
Evans et al. (2002).
94
6.4.2
Observational Database vs. Simulated Database
When employing a pre-defined database, where the atmospheric variable x has already been in
discrete form, the expectation of x , given T ,is usually calculated in the following way:
R
T |x
x) × f (x
x)dx
x
x × f (T
x|T
T) = R
E(x
T |x
x) × f (x
x)dx
x
f (T
x × f (T
T |x
x)]
E[x
=
T |x
x)]
E[f (T
M
N
Q
P
T −µ
µi )2
(T
1
1
q
xi ×
exp − 2 σ2
2
≈
2πσj
j=1
i=1
N Q
M
P
j
T −µ
µi )2
1 (T
exp − 2 σ2
2
q1
i=1 j=1 2πσj
j
N
M
P
Q
T −µ
µi )2
1 (T
xi ×
exp − 2 σ2
=
i=1
j
j=1
N Q
M
P
T −µ
µ i )2
1 (T
exp − 2 σ2
j
i=1 j=1
N
P
=
xi × exp
i=1
j=1
N
P
i=1
N
P
=
i=1
N
P
χ =
M
X
j=1
exp
M
P
j=1
T µ i )2
− 12 (T −µ
σj2
!
!
T −µ
µi )2
1 (T
− 2 σ2
j
x i × exp(− 12 χ2 )
i=1
2
M
P
exp(− 12 χ2 )
T − µ i )2
(T
σj2
!
(6.14)
This is the exact equation used by Kummerow et al. (1996) and Evans et al. (2002).
When apply this equation, using observational database or simulated database by models will
have a non-trivial influence on the final result through affecting the mean TB vector µ . Using model
x) is simply replaced by the brightness temperatures
simulated database, the mean vector µ = g(x
corresponding to each x i . This simplification may be reasonable since in the simulated database,
each x (e.g., rainfall profile) corresponds only to one brightness temperature vector T . Assuming
this T is the mean value of certain normal distribution may be reasonable.
However, when using observational database, corresponding to each atmospheric variable x ,
there exists a large number of different brightness temperature vector T . One cannot simply assume
95
all the T are the mean value µ . Otherwise, uniform distribution, instead of normal distribution,
seems more appropriate.
The following mock example will demonstrate why choosing the right mean value µ is of importance. To simplify the discussion while not losing the generality, we will assume both x and T are
one dimensional variables. We can think x to be the surface rain rate, and T to be the brightness
temperature at 85GHz. Suppose the database for T is (280,280,260,240,240,260), corresponding to
each value in T , the x is (1,1,1,20,20,20). Further, we assume the variance σ 2 of the TB, given x,
is a constant, and it is a fixed constant for any surface rain rate (σ = 10).
When new TB observation is obtained, say, T1=280K. It is of interest to know what is the
rainrate, i.e., E(x|T = 280). Follow the procedure used by Kummerow et al. (1996) and Evans
et al. (2002), where it assumed that each T value in the database approximately equals the mean
value in the normal distribution, E(x|T = 280) is:
6
P
E(x|T 1 = 280) ≈
i=1
2
i)
xi × exp − 12 (T 1−T
2
σ
6
P
i=1
= 1.95
(6.15)
2
i)
exp − 12 (T 1−T
σ2
Clearly, given certain surface rainrate x, the mean value µ for the likelihood function should be
a fixed value. If we assume the mean value µ1 = µ2 = µ3 = (280 + 280 + 260)/3, given x = 1, and
µ4 = µ5 = µ6 = (240 + 240 + 260)/3, given x = 20, the estimation of E(x|T = 280) should be:
6
P
E(x|T 1 = 280) ≈
i=1
2
i)
xi × exp − 12 (T 1−µ
2
σ
6
P
= 1.07
exp
i=1
2
i)
− 12 (T 1−µ
σ2
(6.16)
Generally, these two calculation processes lead to different final results. The degree of the
difference depends on how scattered the database is, given x, and how large the variance σ is. As
mentioned previously, when using the real observations to form the database, these two method
will generate very different results since given same surface rainrate, the TBs are largely scattered.
6.5
Principal Components Analysis Based Bayesian Algorithm
T |x
x). It is
There are two ways to estimate the covariance matrix Σ of the likelihood PDF p(T
either assume that it is a diagonal matrix (e.g., Evans et al., 2002), which is unrealistic since the TBs
96
at some channels are highly correlated. On the other hand, Chiu and Petty (2006) estimated the
full matrix without this assumption. It is worth mentioning that three TB-like variables are used
in Chiu and Petty (2006), therefore, the covariance matrix Σ is a 3 × 3 matrix. When employing
more variables, estimation of the full covariance matrix is not an easy task. For example, using
TBs at nine TRMM channels will require to estimate 81 elements in the covariance matrix.
Principal Components Analysis (also known as Empirical Orthogonal function) reduces a data
set containing many variables to a dataset containing many fewer new variables. These new variables are linear combinations of the original ones. Further, these new variables (Principal Components) are uncorrelated to each other. Therefore, using PCs, instead of using TBs directly,
will make the covariance matrix diagonal, which will significantly reduce the number of elements
needed estimated in the covariance matrix. In this study, we will use u to represent the principal
components, [E] to represents the eigenvector matrix and T to the brightness temperature matrix.
Details regarding the PCA technique is referred to Wilks (2011). The PCs are calculated by the
following equation:
0
u = [E] T
0
(6.17)
where ”0 ” stands for transpose.
To simplify the description without losing generality, we assume the atmospheric variable x is
surface rain rate. In our new method, the already discrete x has been used. The log transformation
has been applied to x. Then, the x is binned into n small bins. Depending on the sample size in the
dataset, the number of bins (n) can be adjusted. In each small bin, we use L1 , · · · , Ln to represent
the sample size, and x1 , · · · , xn to represent the mean value of the rainrate.
In each small bin (i.e., corresponding to each xi ), the PCA technique is applied to the T matrix.
Once PCs are obtained, we further assume that PC follows the normal distribution. If evidences
show that PC does not follow normal distribution, Gaussian mixture model will be used to fit the
PC.
97
T ) by Principal
Next, we use the Eq. 6.14 by replacing the brightness temperature variables (T
u), assuming the PCs follow normal distribution:
Components(u
R
u|x) × f (x)dx
x × f (u
u) = R
E(x|u
u|x) × f (x)dx
f (u
u|x)]
E[x × f (u
=
u|x)]
E[f (u
N
P
xi × exp(− 12 χ2i )
= i=1 N
P
exp(− 12 χ2i )
i=1
=
=
(xa1 + · · · + xb1 ) × exp(− 21 χ21 ) + · · · + (xan + · · · + xbn ) × exp(− 12 χ2n )
(b1 − a1 + 1) × exp(− 12 χ21 ) + · · · + (bn − an + 1) × exp(− 12 χ2n )
n
P
Lj × xj × χ2jk
j=1
n
P
j=1
χ2jk
Lj × χ2jk
K
Y
1
1 (u − µjk )2
√
=
exp −
2
2
σjk
2πσjk
k=1
N=
n
X
!
Lj
j=1
Lj = bj − aj + 1
(6.18)
Where xj and Lj are the sample mean and sample size in each bin, respectively. K is the
number of the PCs. The number of bins (n) is usually several order smaller than the overall sample
size (N). In the current study, n is assigned to be 10. Therefore, the calculation using Eq. 6.18
requires very little time.
If the normal distribution assumption for the PCs are not appropriate, we will use Gaussian
mixture model to estimate the likelihood function.A Gaussian mixture model is a weighted sum of
M components Gaussian densities as given by the equation:
f (z) =
M
X
wi × g(z|µi , σi )
i=1
M
X
wi = 1
(6.19)
i=1
98
Where z stands for any PC. The parameters (µ, σ and w) can be estimated using ExpectationMaximization method.
u|x) is given by the equation:
Using the Gaussian mixture model, the likelihood function f (u
u|x) = f (u1 |x) × · · · × f (uK |x) =
f (u
K X
M
Y
wij × g(z|µij , σij )
(6.20)
i=1 j=1
6.6
Comparison between Regression-Based and Bayesian-Based
Methods
As mentioned in the introduction, the retrieval algorithm is essentially either regression based
or Bayesian based. In this section, we will compare these two methods briefly.
For simplicity, we only consider the one-dimensional case. To be consistent with the previous
discussion, we will use x to represent the surface rainrate and T to the brightness temperature at
any channel. Suppose our goal is to obtain an estimation of x when new T is observed. Following
the Bayesian procedure, we will use the following equation to achieve the goal:
f (T |x) × f (x)
f (T )
f (T |x) × f (x)
=R
f (T |x) × f (x)dx
f (x|T ) =
= C × f (T |x) × f (x)
(6.21)
Where C is the denominator, which is usually a fixed values. In most cases, one will further
assume the likelihood function f (T |x) follows normal distribution, i.e.,
f (T |x) ∼ N (µ1 , σ12 )
µ1 = f (x) = β1 × x + β0
(6.22)
On the other hand, the commonly used simple linear regression x = a×T +b can be equivalently
formulated in probabilistic notation:
f (x|T ) ∼ N (µ2 , σ22 )
µ2 = g(T ) = a × T + b
99
(6.23)
Generally the relationship between x and T is not linear. However, it can be easily transformed
into a linear form.
Clearly, the mean function g(T ) in the linear regression is just the inverse of the f (x) in the
likelihood function. The real difference between these methods is from the prior information.
If the prior PDF is normal distribution, and we already assumed that the mean value of the
likelihood PDF (µ1) is linearly related to x, it can be proven that the joint distribution f (x, T )
is normal distribution. Therefore, each conditional distribution is also normal distribution. That
is, f (x|T ) from the Bayesian procedure will be the same form with the equation from regression
method (Eq. 6.23). In reality, the rainrate is close to the log-normal distribution. Therefore, these
two methods almost always generate very similar results.
6.7
Conclusions and Discussions
In this chapter, a detailed review of the widely used Bayesian algorithm in rainfall retrieval
community was provided. It is found that the fundamental difference between two popular Bayesian
framework lies in the choice of either using the samples from posterior probability density function
(PDF) or using samples from the prior PDF. Using the posteriors probability, the analytical forms
of the prior probability function and likelihood function is needed. And then one can obtain an
analytical form for the posterior PDF. If there exists no analytical form for the posterior PDF,
techniques, such as Monte Carlo integration and importance sampling, could be used to draw
many samples from prior PDF and likelihood function. Then the numerical form of the posterior
density function is obtained. On the other hand, when there exists an already discrete database
for the prior PDF, one can conveniently draw samples from the prior PDF and the expectation of
the atmospheric variable (e.g., rainrate, rainfall profile) can be obtained.
It is also found that both the covariance being constant and the uncorrelatedness assumption
for the brightness temperature among different channels are unrealistic. In view of this, the rainfall
rate is first binned into several small bins. In each bin, the Principal Component Analysis (PCA)
is used to transform the brightness temperatures into principal components (PC). By doing this,
only a few PCs are need to account for approximately 99% of the total variable. More importantly,
the PCs are uncorrelated to each other, therefore the covariance matrix becomes diagonal. On the
other hand, the current Bayesian retrieval algorithm is very time consuming, especially when the
100
sample size is huge. However, the sample size needed in our new PCA-based algorithm is several
order smaller than that needed in the current method, which makes it particularly suitable to the
operational use.
We would like to emphasize that in our algorithm, the PCA are applied to the brightness
temperatures, corresponding to certain rainfall rate. In this way, the covariance matrix in the
T |x
x)) is transformed to a perfectly diagonal matrix. While, when the PCA
likelihood function (f (T
is applied to the overall brightness temperature, both theoretically and practically, the covariance
matrix in the likelihood function will not be a diagonal matrix.
One should always keep in mind that Bayesian-Based algorithm is justified when one conditional
probability is more difficult (sometimes impossible) to obtain than the other. Sometimes, it may
be not even possible to obtain one conditional probability. For example, when it is of interest to
know the probability that one get killed when Driving Under the Influence (DUI), that is, to know
f (death|DU I). It is impossible and immoral to hire people and let them drive under the influence,
and then figure out what is this probability. One possible way is using historical data to obtain
what is the probability of DUI when somebody get killed, i.e., f (DU I|death). Then, one can apply
the Bayes’ theorem to obtain the f (death|DU I).
T |x
x) using
Without TRMM Precipitation Radar observations, one can easily calculate the f (T
x|T
T ). This
the radiative transfer model, but it will be much more difficult to calculate the f (x
is particularly true when x stands for the rainfall profile. After fifteen years data collection by
TRMM, one can easily calculate both probabilities. Therefore, in practice, both methods can
be easily implemented. Unless one assumes that there is no enough observations, or the prior
information is dominated, there is no reason to believe one method is preferential to the other.
Overall, no fancy statistical method will ever replace good physics.
101
CHAPTER 7
RESULTS FROM PCA BASED BAYESIAN
ALGORITHM
7.1
Categorizing the Passive Microwave Signature
As we have discussed in the previous chapters, the current over-land rainfall retrieval algorithms
seem very different. However, in essence, they all estimate rainfall rates fundamentally under the
same principle: translating the scattering signature caused by ice water aloft into a surface rainfall
rate.
In practice, for TRMM facility algorithm, Eq. 6.1 is utilized to retrieve the surface rainfall rate.
Clearly, only the scattering information from 85GHz is exploited. Realizing that one equation
(Eq. 6.1) may not work well globally everywhere or for any season, a more complicated algorithm,
named Global Satellite Mapping of Precipitation project (GSMaP), has been developed (Kubota
et al., 2007; Aonashi et al., 2009). In GSMaP, The globe was divided into 2.5◦ by 2.5◦ latitudelongitude grid boxes. In each 2.5◦ grid box, a Look-Up-Table (LUT) based mainly on scattering
signature from 85GHz is created trimonthly using the TRMM observations. By doing this, GSMaP
algorithm takes account of the local and seasonal variation of the precipitation characteristics. In
addition, the TB at 37 GHz is utilized as a secondary signature when the very heavy rainfall makes
the TB at 85GHz saturated.
In our newly developed algorithm, we will take the full advantage of the TB at all channels,
including both scattering signature from high frequency and emission signature from low frequency
combination. We have also realized that one equation does not apply to any scenario. Therefore,
land cove type, land elevation and surface temperature are used to largely categorize the TB signature at low frequency. The effectiveness of these parameters capturing different surface conditions
have been demonstrated by You et al. (2011) and Gebregiorgis and Hossain (2013). On the other
hand, freezing level height and storm height are used to separate the rainfall profiles with different
amount of ice in the air. The effectiveness of these five parameters are shown in the following
section.
102
7.1.1
Effectiveness of the Physical Parameters
In this section, we will investigate that corresponding to same surface rainrate how the TB
responds under different surface conditions and with different rainfall profiles.
According to the surface temperature (ST), the TBs are grouped into four different categories,
i.e., ST1(273.15∼285K), ST2(285∼295K), ST3(295∼305K) and ST4(>305K). We regroup the land
cover types into four categories, named as evergreen forest, deciduous forest, grassland and bare
ground. The regrouped evergreen forest includes evergreen needleleaf forest and evergreen broadleaf
forest, deciduous forest includes deciduous needleleaf forest, deciduous broadleaf forest, and mixed
forest; Grassland includes woodland, wooded Grassland, closed shrubland, open shrubland, grassland and crop land; Bareground includes original bareground and urban-built. The land elevation is
categorized as low-elevation-land (ranging from 0 to 100 m), medium-elevation-land (ranging from
100 m to 1500 m) and high-elevation-land (elevation greater than 1500 m). The freezing level height
(FLH) is grouped into three categories. They are low-FLH (FLH is less then 4km), medium-FLH
(FLH ranging from 4 to 5km) and high-FLH(FLH greater than 5km). The storm height (SH) has
also been divided into three categories, including low-SH (SH lower than 7km), medium-SH (SH
ranging from 7km to 9km) and high-SH (SH greater than 9km). The boundary values are chosen
by considering the tradeoff between sample size in each category and the number of the categories.
Though these values are somewhat arbitrary, choosing other boundary values will not change our
major conclusions.
We calculated the TB’s response corresponding to same surface rainrate in two very different surface conditions. One surface condition is over evergreen forest at low-elevation land when
the surface temperature is greater than 305K. The other surface condition is over bareground at
high-elevation land when the surface temperature is low (from 273.15 to 285K). As we expected,
corresponding to the same surface rainrate, the TB at 10GHz differs about 20K in these two scenarios (Fig. 7.1a). The TB’s difference at 85 GHz is also large in these two situations when the
surface rainrate is smaller than 5 mm/hr (Fig. 7.1b). One the other hand, the TB difference is
almost negligible when the surface rainrate is greater than 5 mm/hr. That is, TB at 85 GHz is
blind to the surface conditions when it heavily rains. Interestingly, it is noted that the TB at
85GHz responds to surface rainrate almost linearly in the latter scenario, while the non-linearity
between TB at 85 GHz and surface rainrate is obvious in the former scenario (Fig. 7.1b).
103
Corresponding to same surface rainrate, the TB response at 85 GHz in three different SH
categories is calculated when the FLH is ranging from 4km to 5km under same surface condition,
i.e., surface temperature being 295 to 305K, land surface type being evergreen forest and land
elevation from 0 to 100m. The result is shown in Fig. 7.2. Clearly, the higher the SH is, the lower
the TB at 85 GHz reaches. The TB difference at 85GHz in these three categories could be as large
as 50K, corresponding to same surface rainrate.
It is worth mentioning that the storm height is estimated using the TB polarization between
21GHz and 85GHz (referred to as V21-V85), since it is an unknown parameter in the rainfall
retrieval algorithm based on radiometers only. To make a better estimation, both the storm height
and V21-V85 has been transformed using box-cox technique to make sure they are close to normal
distribution. The regression curve is shown in Fig. 7.3.
Using these five physical parameters, the overall dataset (TBs and rainrate) can be grouped into
432 categories. We only choose the categories with 2500 samples or more, which accounts for 99%
of the overall samples. The Principal Component Analysis based Bayesian algorithm developed
in the previous chapter will be applied in each category. It is worth mentioning that only the
TBs at vertical polarized channels are used in the PCA analysis and in the actual rainfall retrieval
algorithm. Adding the TBs at horizontally polarized channels will generate almost identical results.
7.2
Principal Component Analysis (PCA)
In each category, we first divide the log-transformed surface rainrate into 10 equally sampled
bins. In each bin, the surface rainrate can be considered as approximately same. Corresponding to
the same surface rainrate, the Principal Component Analysis (PCA) is applied to the brightness
T |x)) will become a
temperatures. By doing this, the covariance of the likelihood function f (T
diagonal matrix. The Fig. 7.4b shows amplitudes of the first three leading principal component,
corresponding to 2 mm/hr surface rainrate in a random category. The first three PCs explains
99.15% of the total variance from the TBs. It is noted that the largest contribution to the first
PC is from the TB at 85GHz, which presumably represents the ice scattering signature. The TB
at the lowest frequency (10GHz) contributes most to the second PC, which probably stands for
the emission signature. Interestingly, the two lower frequency polarization (V10-V37) is the major
source for the third PC, which are highly likely to represent some liquid information. Corresponding
104
to other surface rainrate and in other categories, the amplitudes pattern of the first three PC are
similar, though values differs.
7.3
Rainfall Screening
Commonly, the rainfall screening is performed for each pixel before the actual retrieval being
applied. Numerous rainfall detection techniques have been proposed in the past several decades
(Grody, 1991; Ferraro et al., 1994; Adler et al., 1994; Conner and Petty, 1998; Seto et al., 2005;
Kacimi et al., 2013). Though they differs greatly in details, yet they all utilized the ”scattering
index (SI)” concept proposed by Grody (1991). In essence, the SI represents the hydrometeors
scattering effect in the air, which is usually calculated by estimated TB at 85GHz subtracting the
observed TB. Regarding the estimated TB at 85GHz, a number of the regression equations are
employed in practice (Seto et al., 2005). The simplest form using by Kummerow et al. (2001) is
adopted in this project. That is, it is assumed the estimated TB at 85GHz equals to simultaneously
observed TB at 21 GHz. Therefore, the SI in this dissertation simply equals to V21-V85.
After obtaining the SI, a critical value is needed to determine whether it is raining or not when
new observation is obtained. In the TRMM facility algorithm over land, the observation is judged
as rain-pixel when SI is greater than 8K. Since TBs at both V21 and V85 varies under different
surface conditions, this critical value should be a different value in the different surface conditions.
By changing the critical values from -9 to 20, the different ratio of true detections (occurrence
and amount) is shown in Fig. 7.5, along with the ration of false alarms. The critical values are
determined by considering the tradeoff between ratio of true detection (RTDO) and the ratio of the
false alarm (RFAO). The definition of the RTDO and RFAO is adapted from (Seto et al., 2005),
shown in Table 7.1.1. Specifically, the value corresponding to RTDO being 0.7 is chosen as critical
value if the RFAO is smaller than 0.1. Otherwise, the value corresponding to RFAO being 0.1 is
chosen as critical value.
7.4
Rainfall Retrieval Results
Scatter plots between retrieved instantaneous rainrate and TRMM PR observations in four
months (January, April, July and October) are shown in Fig. 7.6. The retrieved rainrate agrees
remarkably well with the observations, especially when the rainrate is less than 10 mm/hr. Clear
105
underestimation is observed when rainrate is greater than 10 mm/hr. The underestimation phenomenon has also been noted by Aonashi et al. (2009) in GSMaP retrieved rainrates. On average,
the correlation and root mean square error (RMSE) is approximately 0.73 and 0.97, respectively.
Next, the retrieved rainrate in the same four months is averaged over 1◦ ×1◦ latitude-longitude
box, shown in Fig. 7.7. Compared with TRMM PR observations (Fig. 7.8), the retrieved results
captured all the major rainfall regimes, including the rainband and its movement in the Intertropical
Convergence Zone (ITCZ) over South America and Central Africa areas, the monsoon rainfall over
Asia, over North America and over Southeast areas of South America. The difference between
retrieved and observed rainfall is shown in Fig. 7.9. The magnitude of the vast majority of the
difference is less than 0.5 mm/hr. It is noted that the newly developed rainfall algorithm tends to
overestimate the rainfall in the ITCZ band, while underestimate the rainfall over monsoon regions.
The reason behind this phenomenon is presently unknown, which deserved further analysis in the
future. We hypothesized that this bias is related to do with the slope of the liquid water from the
freezing level height to the surface, though other explanations cannot be ruled out.
7.4.1
Comparison with One Database and TRMM Results
In this section we will briefly compared the retrieved rainrate using the categorized database
and overall database. The retrieved rainrate using overall database is shown in Fig. 7.10b. The
overestimation when rainrate is less than 5 mm/hr is obvious. On the other hand, there exists no
clear overestimation when using categorized database. Detailed analysis will be demonstrated in
the next section.
Compared with the results from TRMM facility algorithm (Fig. 7.10c), our retrieved rainrate is
better correlated with the observations, with the correlation coefficient being 0.73, compared with
that being 0.65 from TRMM facility algorithm. More importantly, the root mean square error is
only 0.97, while it is 1.47 from TRMM facility algorithm. There exists clear overestimation when
the rainrate is less than 5 mm/hr in the results from TRMM facility algorithm. It is high likely
that the inaccurate convective-stratiform separation employed in the TRMM facility algorithm
contributes significantly to this overestimation.
106
7.4.2
Overestimation Analysis
The retrieved rainrate in one category is chosen to demonstrate why there exists overestimation
when using overall database for relatively light rainfall (less than 5 mm/hr). The results using
categorized database and overall database are shown in Fig. 7.11a and Fig. 7.11b. Curves in
Fig. 7.11c show the relation between surface rainrate and TB at 85GHz. Corresponding to the
same TB, using the overall database curve will always generate a larger rainfall rate. This is the
reason why there exists large overestimations when using overall-database. It is worth mentioning
that although we use all the TBs in our retrieval algorithm, the TB from 85GHz contributes the
most to the first PC.
7.5
Conclusions
For the first time, the newly developed rainfall retrieval algorithm effectively combines both
emissivity information and rainfall profile information using three external environmental parameters (including surface temperature, land cover type, elevation) and two rainfall profile-related
parameters (freezing level height and storm height). In addition, the rainfall retrieval algorithm
over land takes full advantage of all the brightness temperature observations from both high and
low frequencies, using the newly developed PCA-based Bayesian technique. Results demonstrate
that the retrieved surface rain rate agrees much better with observations from TRMM precipitation
Radar, compared with the results from TRMM facility algorithm over land. Particularly, no obvious over-estimations is observed when rainrate is less than 10 mm/hr. Validation using one year
data shows that the correlation between retrieved rainrate and observations is 0.73, while it is 0.65
between retrieved rainrate by TRMM facility algorithm and observations. The root mean square
error (RMSE) is lowered by about 35%. The retrieved result well captures the major rainfall characteristics, e.g., the heavy rainfall over ITCZ in central Africa and South America, and its seasonal
movement, the monsoon rainfall, etc. Since this algorithm is location- and season-independent, it
can be conveniently adapted to other satellite platforms (e.g., SSM/I and AMSR-E)
107
Table 7.1: Notation for Rain-No-Rain
No rain judged
by TMI
B
D
290
280
280
260
TB at V85 (K)
TB at V10 (K)
Rain judged by PR
No rain judged by PR
Rain judged
by TMI
A
C
270
260
240
220
(a)
250
0
(b)
5
10
15
20
Surface rain rate(mm/h)
200
0
25
5
10
15
20
Surface rain rate(mm/h)
Figure 7.1: Corresponding to the same surface rainrate, the TBs response at V10 and V85
in two distinct different category.
108
25
280
TB at V85 (K)
260
240
220
200
0
Low SH
5
Medium SH
10
15
Surface rain rate(mm/h)
High SH
20
25
Figure 7.2: Corresponding to the same surface rainrate and the same freezing level height,
the TB response at V85 in low, medium and high storm height scenarios
109
20
Storm Height (km)
15
10
5
0
0
30
60
V21−V85 (K)
90
120
Figure 7.3: Scatter plot between storm height (SH) and TB polarization between V21 and V85
110
V85
Channels
V37
PC1 (88.29%)
PC2(9.15%)
PC3(1.70%)
V21
V19
V10
−0.8
−0.6
−0.4
−0.2
0
0.2
Amplitudes
0.4
0.6
0.8
1
Figure 7.4: The coefficients for TB at each channel in the three leading Principal Components
111
Ratio of True Detection(Occurence)
1
0.8
0.6
0.4
0.2
(a)
0
0
0.2
0.4
0.6
Ratio of False Alarm
0.8
1
Ratio of True Detection(Amount)
1
0.8
0.6
0.4
(b)
0.2
0
0.2
0.4
0.6
Ratio of False Alarm
0.8
1
Figure 7.5: For critical values varying from -9 to 20, (a) the corresponding Ratio of True
Detection (Occurrence) and Ratio of False Alarm. (b)the corresponding Ratio of True
Detection (Amount) and Ratio of False Alarm.
112
20
RMSE=0.90
6
January
corr=0.74
×102
20
6
April
corr=0.72
5
15
4
10
3
2
5
5
4
10
3
2
5
1
1
(a)
0
0
20
5
10
Observed rainfall
RMSE=1.03
15
(b)
20
6
July
corr=0.71
0
0
0
×102
20
10
Observed rainfall
RMSE=0.98
15
20
0
6
October
×102
5
15
4
10
Retrieved rainfall
Retrieved rainfall
5
corr=0.74
5
15
3
2
5
4
10
3
2
5
1
1
(c)
0
0
×102
15
Retrieved rainfall
Retrieved rainfall
RMSE=0.98
5
10
Observed rainfall
15
(d)
20
0
0
0
5
10
Observed rainfall
15
20
0
Figure 7.6: Scatter plots between retrieved rainrates and observed rainrates from TRMM
PR in four months, January, April, July and October. The red curve stands for the 1:1
line
113
40oN
(a)
20oN
0o
20oS
January
40oS
180o
40 N
o
120oW
60oW
0o
60oE
120oE
180o
120oW
60oW
0o
60oE
120oE
180o
120oW
60oW
0o
60oE
120oE
180o
60oW
0o
60oE
120oE
180o
(b)
20oN
0o
20oS
April
40oS
180o
40 N
o
(c)
20oN
0o
20oS
July
40oS
180o
40 N
o
(d)
20oN
0o
20oS
October
40oS
180o
120oW
0
0.5
1
1.5
2
4
6
8
10 (mm/hr)
Figure 7.7: Global distribution of monthly mean rainrates over 1◦ ×1◦ latitude-longitude
grid box in four months, January, April, July and October.
114
40oN
(a)
20oN
0o
20oS
January
40oS
180o
40oN
120oW
60oW
0o
60oE
120oE
180o
120oW
60oW
0o
60oE
120oE
180o
120oW
60oW
0o
60oE
120oE
180o
60oW
0o
60oE
120oE
180o
(b)
20oN
0o
20oS
April
40oS
180o
40oN
(c)
20oN
0o
20oS
July
40oS
180o
40oN
(d)
20oN
0o
20 S
o
October
40oS
180o
120oW
0
0.5
1
1.5
2
4
6
8
10 (mm/hr)
Figure 7.8: Same as Fig. 7.7 except for observations from TRMM PR
115
40oN
(a)
20oN
0o
20oS
January
40oS
180o
40 N
o
120oW
60oW
0o
60oE
120oE
180o
120oW
60oW
0o
60oE
120oE
180o
120oW
60oW
0o
60oE
120oE
180o
60oW
0o
60oE
120oE
180o
(b)
20oN
0o
20oS
April
40oS
180o
40 N
o
(c)
20oN
0o
20oS
July
40oS
180o
40 N
o
(d)
20oN
0o
20oS
October
40oS
180o
120oW
-4
-2
-1
-0.5
0
0.5
1
2
4 (mm/hr)
Figure 7.9: Monthly rainfall difference between retrieved rainrates and observed rainrates
over 1◦ ×1◦ latitude-longitude grid box in four months, January, April, July and October.
116
20
RMSE=0.97
×103
20
RMSE=0.17
7
corr=0.73
15
15
6
5
10
4
3
5
5
10
4
3
2
1
0
0
(a)
5
10
Observed rainfall
20
15
20
RMSE=1.47
(b)
5
10
Observed rainfall
15
20
0
×103
7
corr=0.65
15
Retrieved rainfall
1
0
0
0
8
×103
6
5
2
8
7
corr=0.65
Retrieved rainfall
Retrieved rainfall
8
6
5
10
4
3
5
2
1
0
0
(c)
5
10
Observed rainfall
15
20
0
Figure 7.10: Scatter plots between retrieved rainrates and observed rainrates (a) Using
categorized database (b) Using overall database (c) Using TRMM facility Algorithm
117
20
RMSE=1.88
35
corr=0.73
15
15
30
25
10
20
15
5
10
30
25
10
20
15
5
10
5
(a)
0
0
5
10
Observed rainfall
15
20
40
35
corr=0.60
Retrieved rainfall
Retrieved rainfall
20
40
RMSE=1.18
5
0
0
0
(b)
5
10
Observed rainfall
15
20
0
280
Categorized Database
Overall Database
TB at V85 (K)
260
240
220
(c)
0
5
10
15
Surface rain rate(mm/h)
20
25
Figure 7.11: For a specific category, (a)Scatter plot between retrieved rainrates and observed rainrates using categorized database (b) Scatter plot between retrieved rainrates
and observed rainrates using overall database (c) Corresponding to same surface rainrate,
the TBs’ response at V85GHz in categorized database and overall database.
118
CHAPTER 8
SUMMARY
The objective of this study is to develop a better rainfall retrieval algorithm over land. To this
end, in the first part of this study, we focus on better understanding three key physical aspects
which significantly influence the algorithm development, including signature from both high and
low frequencies, the surface emissivity effect and rainfall profile structure. In the second part of this
study, a detailed analysis regarding the currently widely used Bayesian method and its assumptions
has been conducted. A new Principal Component Analysis based Bayesian algorithm is proposed
to take full advantage of all the brightness temperature observations. Results from this algorithm
was compared with that from the TRMM facility algorithm.
The unique features of the new retrieval algorithm are (1) physical parameters are used to
categorize the land surface conditions and rainfall profile structures; (2) the covariance matrix in
the Bayesian framework is calculated based on real observations and is perfectly diagonal through
the Principal Component Analysis transformation. The major results of this study have been
condensed into four papers published in Journal of Geophysical Research (Atmospheres) and Journal
of Hydrometeorology.
8.1
Summary of the Physical Background in the Retrieval
Algorithm
In this section, we summarized our major results regarding the physical background in the
newly developed retrieval algorithm. They are (1) signatures from both low and high frequencies,
the surface emissivity effects and the proportionality between rainfall rate and water paths.
8.1.1
Sensitivity of Brightness Temperature to Rainfall Rates
In Chapter 3, using collocated TRMM PR and TMI data, we investigated the sensitivity of
TMI channels or their combinations to over-land rainfall. To our surprise, the results show that
instead of the 85 GHz channel, it is the V19-V37 or the V21-37 channel combination that has the
119
highest sensitivity to over-land rainfall over the global tropical areas covered by TRMM satellite
observations. The V19-V37 or the V21-V37 channel combination can explain 10% more of the
rainfall rate variances than the V85 GHz channel. Furthermore, the global distribution of channel
sensitivity indicates that the V19-V37 channel combination has a stronger response to rainfall than
the V85 channel for most of tropical land regions, except for those over desert, arid and semi-arid
areas, such as northern part of the African continent, the Middle East and southern Australia.
To understand the underlying physics of the different responses of TMI channels or channel
combinations to over-land rainfall, we introduced two parameters derived from PR vertical rainfall
profiles: the frozen water index and the liquid-to-frozen water ratio index. The two parameters
represent the amounts of frozen water and liquid water in the raining clouds, respectively. Grouping
all raining pixels by the two indices, we found that the most sensitive channel varies with cloud
groups, and all raining clouds may be largely divided into 3 categories with the following 3 most
favorable channels: V19-V37, V37 and V85. For clouds with modest amount of liquid water and
low amount of frozen water, the V19-V37 channel can capture information from both liquid and
frozen water, leading to the strongest response to near surface rainfall. A large majority of raining
clouds belongs to this category, resulting in that the V19-V37 channel is the most sensitive channel
if all rain clouds are used in the analysis. The V85 channel, on the other hand, is the most sensitive
channel for clouds being low in both liquid and frozen water amounts. Because of the low amount of
hydrometeors, the rainfall signal in this category even at the V85 channel remains weak. For clouds
with large amount of hydrometers (liquid and ice), the V37 GHz channel becomes the strongest
responder to surface rainfall, with the V19-V37 channel being the close second.
It is also found that two ancillary parameters, land surface type and 2-m air temperature
are helpful to indicate rain cloud microphysical structures. The V19-V37 channel often responds
the most closely to surface rainfall where vegetation is denser and 2-meter air temperature is
warmer, while the V85 channel responds closer to surface rainfall over less vegetated ground with
relative cold 2-meter air temperatures, especially over cold bare ground. We argue that 2-meter
air temperature and land surface type provide information on the potential depth of rain drops
(related to freezing level) and surface emissivity, which can be used to select and prioritize channels
in retrieval algorithms to improve rainfall retrieval over land.
120
Because of the high and highly variable emissivity of land surface, it has been long believed that
the only useful information from passive microwave observations for over-land rainfall retrieval is
the ice scattering at high frequency channels (i.e., 85 GHz). This study challenges this common
belief and concludes that it is the channel combination of two lower frequencies, i.e., V19-V37, that
has a stronger response to over-land rainfall for majority of the conditions. Its better response
is likely resulted from that this combination contains both liquid and ice information, and liquid
water has a more direct linkage to surface rainfall rate.
To better utilized the information from low frequency, we further analyzed the instantaneous
microwave land surface emissivity (MLSE) and particularly its response to the previous rainfall
(Chapter 4)
8.1.2
Previous Rainfall Effect to Microwave Land Surface Emissivities
In chapter 4, using NMQ hourly rainfall and two instantaneous microwave land surface emissivity (MLSE) datasets, we investigate the response of the MLSE to previous rainfall duration,
timing and amount. It was found that previous rainfall produced a large emissivity decrease over
the Southern Great Plains and Mississippi Alluvial Plain. Over these two regions, the dominant
land cover types are grass, closed shrub and crop. In particular, previous 24-hr heavy rainfall (>
20 mm) could lead to a 0.06 emissivity decrease at H10, corresponding to a 20 K net TB decrease.
In addition, corresponding to the same previous rainfall, the higher the frequency, the smaller such
emissivity decrease will be. In contrast, over forest dominant areas (e.g., Eastern United States),
emissivities do no vary much (∼0.01 at H10 channel) corresponding to previous rainfall. The correlation between emissivity and previous rainfall has also been investigated. Large correlations were
located over the Southern Great Plains and Mississippi Alluvial Plain. The correlation coefficients
over Southern Great Plains were as large as -0.6. On the other hand, the correlation over forest regions is much weaker, indicating that the emissivity over forest responds weakly to previous
rainfall.
The comparison among the Principal Component Analysis (PCA) based MLSE, physically based
MLSE and the TELSEM climatological MLSE datasets was conducted over continental United
States. Results show that the simulated brightness temperatures using the PC-based emissivities
agree the best with TRMM satellite observations, with correlation and RMSE being 0.80 and ∼
5.0 K for all channels. For the climatological TELSEM emissivity, there exist two major biases.
121
One is that it overestimates the wet surface emissivity, leading to higher simulated TB relative to
the TMI observed brightness temperature. The other is that it underestimates the coastal region
emissivity, resulting in lower simulated multichannel TB than observed. These biases lead to a lower
correlation ( 0.45) between simulated and observed TB. The overestimation under wet surface in
the physically-based emissivity dataset is also noticeable. We note that while the NMQ data was
used to screen precipitating scenes, there is likely non-precipitating cloud contamination that may
contribute significantly to the emissivity estimation errors especially at the 85 GHz channels.
Two potential applications of the instantaneous emissivity were investigated. First, it was
demonstrated that clear sky emissivity at low frequency (e.g., H10) is well correlated with previous 24-hour rainfall over Southern Great Plains. Using such a relationship, we estimated the
previous 24-hour rainfall that is needed to produce this same emissivity, and which agreed fairly
well with the observed previous 24-hour rainfall (correlation coefficient of0.59). Additionally, using
the relationship between PCs and previous rainfall, the raining scene emissivities at 10, 19 and 37
GHz are estimated. The applications of proper raining scene emissivities will greatly reduce the
positive biases in simulated TB (resulting from using clear sky emissivities in the rain), and bring
the simulated TB closer to observations. This emissivity adjustment technique does not work well
under moderate to heavy rain (> 10 mm/hr), since the rain media almost completely obscures the
surface. Due to the promising results in these case studies, further application of these techniques
over a much large scale is under current development.
8.1.3
Proportionality between Rainrate and Water Paths
In chapter 5, the relationships between water paths and surface rainrate are investigated. Based
on previous sensitivity studies on microwave radiation to water paths over different surface types,
we investigate the relationships between ice water path and surface rainrate over both land and
ocean, between total water path and surface rainrate over land, and between liquid water path and
surface rainrate over ocean.
Results show that corresponding to a similar surface rainrate ice water path has large spatial
variability, and the most prominent characteristic for the ice water path spatial distribution is the
contrast between land and ocean. That is, given a similar surface rainrate, larger ice water path
is observed over land than over ocean. Specifically, for a similar surface rainrate ice water path is
large over arid regions (e.g., the Sahara desert), small over shallow convection dominant regions
122
(e.g., oceanic area near Hawaii), and in-between over maritime and ITCZ regions. On average,
the correlation (R2 ) between ice water path and surface rainrate is also larger over land than over
ocean. Over the majority of land areas, R2 is ∼0.40, with the exception of arid regions and the
Indian subcontinent (∼0.25). Relatively large R2 is also found over ITCZ regions over ocean, while
it decreases to nearly 0 over shallow convection dominant regions over ocean. The cause of the
correlation difference is investigated by analyzing the seasonal variation of ice water path and rain
systems’ vertical structures. It is found that given a similar surface rainrate, a larger R2 corresponds
to a smaller seasonal variation of ice water path and vice versa. For example, over central India,
given a similar surface rainrate, ice water path in the pre-monsoon season (April and May) is
about twice as large as that in the monsoon season (June to August) due to a stronger low-level
evaporation in the pre-monsoon season. Strong low-level evaporation also causes low correlation
between ice water path and surface rainrate over arid regions, which is particularly evident over
the Sahara desert.
The relations between water path and surface rainrate are shown to have significant implications
to surface rainrate retrieval by using microwave brightness temperatures. That is, given the same
surface rainrate, depending on the closeness of the water path versus surface rainrate relationships,
the degree of brightness temperature response is very different. In particular, over the ITCZ, the
Indian subcontinent and arid regions (e.g., the Sahara desert), although ice water path responds
well to brightness temperatures, since the correlation between ice water path and surface rainrate is
weak, it leads to a relatively weak response of brightness temperature at 85 GHz to surface rainrate.
Additionally, it is worth mentioning that liquid water path over ocean as well as total water path
over land, always possess a better relationship with surface rainrate than that between ice water
path and surface rainrate. It implies that channels or channel combinations that can capture liquid
water signal over ocean (or total water signal over land) are preferable to those capturing ice water
information for retrieving surface rainrate.
123
8.2
8.2.1
Summary of the PCA-Based Bayesian Algorithm and the
Retrieved Results
The PCA-Based Bayesian Algorithm
In chapter 6, a detailed review of the widely used Bayesian algorithm in rainfall retrieval community was provided. It is found that the fundamental difference between two popular Bayesian
framework lies in the choice of either using the samples from posterior probability density function (PDF) or using samples from the prior PDF. Using the posteriors probability, the analytical
forms of the prior probability function and likelihood function is needed. And then one can obtain
an analytical form for the posterior PDF. If there exists no analytical form for the posterior PDF,
techniques, such as Monte Carlo integration and importance sampling, could be used to draw many
samples from prior PDF and likelihood function. Then the numerical form of the posterior density
function is obtained. On the other hand, when there exists an already discrete database for the
prior PDF, one can conveniently draw samples from the prior PDF and the expectation of the
atmospheric variable (e.g., rainrate, rainfall profile) can be obtained.
It is also found that both the covariance being constant and the uncorrelatedness assumption
for the brightness temperature among different channels are unrealistic. In view of this, the rainfall
rate is first binned into several small bins. In each bin, the Principal Component Analysis is used
to transform the brightness temperatures into principal components. By doing this, only a few
PCs are need to account for approximately 99% of the total variable. More importantly, the PCs
are uncorrelated to each other, therefore the covariance matrix becomes diagonal. On the other
hand, the previously-published Bayesian retrieval algorithm is very time consuming, especially when
the sample size is huge. In contrast, the sample size needed in our new PCA-based algorithm is
several order smaller than that needed in prevous methods, which makes it particularly suitable to
operational use.
We would like to emphasize that in our algorithm, the PCA is applied to data points that only
corresponding to a certain rainfall rate. In this way, the covariance matrix in the likelihood function
T |x
x)) is transformed to a perfectly diagonal matrix. Meanwhile, when the PCA is applied to
(P (T
data points in the entire database, both theoretically and practically, the covariance matrix in the
likelihood function will not be a diagonal matrix.
124
We also briefly compare the Bayesian based and regression based method for the rainfall retrieval algorithm. It was showed that in reality these two methods generally produce very similar
results, unless the prior information dominates. One should always keep in mind that Bayesian
based algorithm is justified when one conditional probability is more difficult to obtain than the
T |x
x) usother. Without TRMM Precipitation Radar observations, one can easily calculate the P (T
x|T
T ). This
ing the radiative transfer model, but it will be much more difficult to calculate the P (x
is particularly true when x stands for the rainfall profile. After fifteen years data collection by
TRMM, one can easily calculate both probability. Therefore, in practice, both methods can be
easily implemented. Unless one assumes that there is no enough observations, or the prior information is dominated, there is no reason to believe one method is preferential to another. Overall,
no fancy statistical method will ever replace good physics.
8.2.2
Results from the PCA-based Bayesian Algorithm
For the first time, the newly developed rainfall retrieval algorithm effectively combines both
emissivity information and rainfall profile information using three external environmental parameters (including surface temperature, land cover type, elevation) and two rainfall profile-related
parameters (freezing level height and storm height). In addition, the rainfall retrieval algorithm
over land takes full advantage of all the brightness temperature observations from both high and
low frequencies, using the newly developed PCA-based Bayesian technique. Results demonstrate
that the retrieved surface rain rate agrees much better with observations from TRMM precipitation
Radar, compared with the results from TRMM facility algorithm over land. Particularly, no obvious over-estimations is observed when rainrate is less than 10 mm/hr. Validation using one year
data showed that the correlation between retrieved rainrate and observations is 0.73, while it is 0.65
between retrieved rainrate by TRMM facility algorithm and observations. The root mean square
error (RMSE) is lowered by about 35%. The retrieved result well captures the major rainfall characteristics, e.g., the heavy rainfall over ITCZ in central Africa and south America, and its seasonal
movement, the monsoon rainfall, etc. Since this algorithm is location- and season-independent, it
can be conveniently adapted to other satellite platforms (e.g., SSM/I and AMSR-E)
125
8.3
Future Work
There are at least two important topics regarding this rainfall retrieval algorithm should be
investigated in the future. First, applying the rainfall retrieval algorithm to other radiometers for
which there is no instantaneous radar observations, e.g., Special Sensor Microwave/Imager (SSM/I)
and Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E). To this end,
the radiative transfer model is needed due to different frequencies used in these observational
satellite platforms. In each category, one only need the several (10 in the current algorithm) mean
TBs at each frequency, since we already have the surface temperature, relative humidity, rainfall
profiles available.
As an example, the mean TB values (blue curve) in one randomly chosen category are demonstrated in Fig. 8.1. The red curves stand for the simulations using a radiative transfer model. In
the simulation, it is assumed that the hydrometeors are snow above freezing level height (FLH)
and rainfall below FLH. There exists no grauple in the profile. The surface emissivity is assumed
to be 0.9.
Using the emissivity adjustment technique developed by You et al. (2013), we first adjust the
principal components of the emissivity to make sure that the simulated TBs and observed TBs
at 10GHz are less than 2K, then emissivities at all five channels are reconstructed simultaneously.
Next, cloud ice and cloud liquid are added to make sure that the observed TB at 85GHz corresponding to the lightest rainfall and simulated TB at 85GHz is less than 2K. The simulations after
these two steps are shown in red curves. In this particular case, the cloud ice and cloud liquid is 0.6
g/m3 . Then the beam-filling effects are taken into consideration using the techniques developed by
Varma and Liu (2006). The green curves represent the results after considering emissivity, cloud
ice/liquid and beam-filling effects. Obviously, TBs at 85GHz and 10GHz are in excellent agreement
with observations, while there are warm biases in the simulated TBs at 19GHz and 37GHz. Specifically, the simulated TBs at 19GHz and at 37GHz are 5K and 4K greater than the observations,
respectively. These warm biases are possibly caused by the inaccurate emissivity estimations, which
is the second topic deserving the further study.
Regarding the emissivity adjustment, further study is needed to obtain better emissivity estimations suitable for each category. Current technique is only validated over a specific area over
Oklahoma, United States. It is expected that by categorizing the emissivity adjustment, the warm
126
biases in the simulated TBs can be alleviated. In addition, the standard deviation of the estimated
emissivity should also been calculated in the future.
127
290
TB at V19 (K)
TB at V10 (K)
280
275
270
0
Observed
Simulated
Adjusted
5
10
15
Surface rain rate(mm/h)
TB at V85 (K)
TB at V37 (K)
Observed
Simulated
Adjusted
5
10
15
Surface rain rate(mm/h)
20
280
275
260
230
0
270
260
0
20
290
245
280
Observed
Simulated
Adjusted
5
10
15
Surface rain rate(mm/h)
240
200
160
0
20
Observed
Simulated
Adjusted
5
10
15
Surface rain rate(mm/h)
20
Figure 8.1: TB simulations using a microwave radiative transfer model at V10, V19, V37
and V85GHz, blue curves represent the observations, red curves represent the simulated
TBs after emissivity and cloud ice/liquid adjustment, green curves stand for the simulated
TBs after emissivity, cloud ice/liquid and beam-filling effects adjustment.
128
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BIOGRAPHICAL SKETCH
Yalei You was born on April 20, 1982 in Henan, China. Yalei has always been very interested in the
weather since it often significantly affects the produce of the family’s farm land, and occasionally
makes the wheat and corn unharvestable. He enrolled at Yunan University in September, 2001 and
earned the Bachelor of Atmospheric Science in July, 2005. Shortly thereafter he started working
on his Master degree under Dr. Jie Cao at Yunnan University. He received the Master degree
in Atmospheric Science in July, 2008. He entered Florida State University in September, 2008,
and started working on his Doctoral degree under the supervision of Dr. Guosheng Liu. He will
graduate with the Doctor of Philosophy degree in Meteorology in December, 2013.
138
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