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Passive microwave remote sensing of surface soil moisture: Methods, results, and applications

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PASSIVE MICROWAVE REMOTE SENSING OF SURFACE SOIL
MOISTURE: METHODS, RESULTS, AND APPLICATIONS
Huilin Gao
A DISSERTATION
PRESENTED TO THE FACULTY
OF PRINCETON UNIVERSITY
IN CANDIDACY FOR THE DEGREE
OF DOCTOR OF PHILOSOPHY
RECOMMENDED FOR ACCEPTANCE
BY THE DEPARTMENT OF
CIVIL AND ENVIRONMENTAL ENGINEERING
November 2005
i
UMI Number: 3188649
Copyright 2005 by
Gao, Huilin
All rights reserved.
UMI Microform 3188649
Copyright 2005 by ProQuest Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
300 North Zeeb Road
P.O. Box 1346
Ann Arbor, MI 48106-1346
© Copyright by Huilin Gao, 2005. All rights reserved.
ii
Abstract
This study investigates passive microwave remote sensing of surface soil
moisture from three aspects: retrieval science, its application to the retrieval of soil
moisture from satellite measurements, and the application of retrieved soil moisture
for land surface models assimilation. A land surface microwave emission model
(LSMEM) has been implemented to retrieve soil moistures using passive remote
sensing data. Chapter 2 introduces the physics and parameterization of the LSMEM
algorithm. Based on this framework, soil moisture is estimated from L band synthetic
radiometry during the Southern Great Plains 1999 experiment. Results show a RMS of
1.8-2.8% volumetric soil moisture. To conduct operational retrievals from space-borne
radiometry, LSMEM is further parameterized at large scales in Chapter 3. A five-year
(1998-2002) surface soil moisture product is derived across the southern United States
from TRMM/TMI X band horizontally polarized brightness temperatures. Because of
the limited information content on soil moisture in the observed brightness
temperatures over regions characterized by heavy vegetation, active precipitation,
snow, and frozen ground, quality control flags for the retrieved soil moisture are
provided. The product is validated by Oklahoma Mesonet field measurements, and its
spatial patterns also demonstrate consistencies with precipitation fields. This is the
first time that a fully validated approach and product is implemented at continental
scales, and the product will be made available through the NASA Goddard Space
Flight Center Distributed Active Archive Center (NASA/GSFC DAAC). Chapter 4
explores the potential of assimilating space-borne remote sensing soil moisture
product into land surface models through the development of “observational
iii
operators”. Besides the TMI product, soil moisture from AMSR-E using the
operational NASA retrieval algorithm is also evaluated. The focus is to use Copulabased bivariate probability distributions to generate observation operators so that the
systematic bias between remotely sensed and modeled soil moisture can be reduced
and the error structure can be provided for generation of assimilation ensembles.
Observation operators are derived from different remote sensing products for two land
surface models: Variable Infiltration Capacity (VIC) and ECMWF reanalysis (ERA40)
land surface model.
iv
Table of Contents
page
Abstract ......................................................................................................................iii
Chapter 1: Overview of the Research....................................................................... 1
1.1 Introduction ...................................................................................................... 1
1.2 LSMEM and its Sensitivity Tests .................................................................... 5
1.3 Retrieving Soil Moisture from Space-borne Observations and Related Issues6
1.4 Generate Observation Operators for Data Assimilation .................................. 9
References ............................................................................................................. 12
Chapter 2: Using a Microwave Emission Model to Estimate Soil Moisture from
ESTAR Observations During SGP99 ................................................................... 19
2.1 Introduction .................................................................................................... 19
2.2 Land Surface Microwave Emission Model (LSMEM ) ................................. 22
2.3 1999 Southern Great Plains Experiment (SGP99) ......................................... 26
2.3.1 SGP99 Data Collection............................................................................. 26
2.3.2 Meteorological Conditions during the Experiment .................................. 27
2.3.3 ESTAR Airborne L-band Instrument ....................................................... 27
2.4 Input State Variables and Parameters for the LSMEM.................................. 29
2.4.1 Soil and Vegetation Temperatures ........................................................... 29
2.4.2 Soil Texture .............................................................................................. 30
2.4.3 Surface Roughness, Bulk Density, and Land Cover Classification ......... 31
v
2.4.4 Estimation of the Vegetation Optical Depth ............................................ 31
2.5 Soil Moisture Retrievals ................................................................................. 32
2.5.1 SGP99 Regional Results........................................................................... 32
2.5.2 Comparisons with Ground Validation Sites ............................................. 33
2.6 Discussion and Conclusions ........................................................................... 37
References ............................................................................................................. 40
Chapter 3: Using TRMM/TMI to Retrieve Surface Soil Moisture over the
Southern United States from 1998 to 2002........................................................... 61
3.1 Introduction .................................................................................................... 62
3.2 Methodology and Data Sources ..................................................................... 67
3.2.1 Land Surface Microwave Emission Model (LSMEM) ............................ 68
3.2.2 LSMEM Model Resolution and Inputs .................................................... 69
3.3 Results ............................................................................................................ 74
3.3.1 Surface Soil Moisture Retrieved for Each TMI Orbit .............................. 74
3.3.2 Daily Surface Soil Moisture Composites ................................................. 75
3.4 Quality Control Masks ................................................................................... 75
3.4.1 Precipitation Mask.................................................................................... 76
3.4.2 Vegetation Sensitivity Mask..................................................................... 76
3.4.3 Snow Cover, Frozen Soil and Surface Water Contamination Mask ........ 78
3.4.4 Data Availability ...................................................................................... 78
3.5 Initial Comparisons with Oklahoma Mesonet in-situ Measurements ............ 79
3.6 Summary ........................................................................................................ 81
Appendix A: Available Data Product.................................................................... 84
vi
References ............................................................................................................. 85
Chapter 4: Copula Derived Observation Operators for Assimilating TMI and
AMSR-E Soil Moisture into Land Surface Models ........................................... 102
4.1 Introduction .................................................................................................. 103
4.2 Copula-Based Joint Probability Distribution ............................................... 110
4.3 Data Sources................................................................................................. 113
4.3.1 Soil Moisture from Satellite Observations ............................................. 113
4.3.2 Comparisons between Remotely Sensed Soil Moisture and Field
Measurements................................................................................................ 115
4.3.3 Soil Moisture from Land Surface Model Outputs.................................. 115
4.4 Generation of Observation Operators .......................................................... 117
4.4.1 Fitting Single Variable Distributions...................................................... 118
4.4.2 Using Copula to Simulate the Joint Distributions .................................. 119
4.4.3 Observation Operators Based on Conditional Simulation Results......... 120
4.5 Discussions and Summary ........................................................................... 122
References ........................................................................................................... 125
vii
List of Tables
page
2.1
SGP99 satellite observing systems, aircraft remote sensing instruments, ground
data collection, and regional networks ............................................................... 47
2.2
Land cover classification statistics over SGP99 experiment region .................. 48
2.3
Land cover classification for field sampling sites at CF, ER, and LW .............. 49
3.1
LSMEM model inputs ........................................................................................ 90
3.2
Seasonal and annual statistics for Oklahoma Mesonet and TMI retrieved soil
moisture averaged over the 72 Mesonet sites....................................................... 91
4.1
TMI and AMSR instrument characteristics...................................................... 130
4.2
Regression coefficients for estimating the mean (y1) and standard deviation (y2)
of the systematic bias from observed soil moisture (x) for different observationmodel combinations, with y1=a1+b1×x+c1×x2 and y2=a2+b2×x+c2×x2 ............. 131
viii
List of Figures
Page
1.1
Standard deviation of soil moisture retrieval uncertainties ................................ 16
1.2
Surface soil moisture retrieved from AMSR-E observations on Jan. 10, 2003
using (a) LSMEM and (b) NASA/JPL algorithm respectively .......................... 17
1.3
Time series of daily averaged soil moistures over the Southern Great Plains from
VIC and ERA40 model outputs.......................................................................... 18
2.1
Flow chart of the LSMEM soil moisture retrieval algorithm............................ 50
2.2
Sample Observed total daily precipitation on July 10, 1999 over the SGP99 area
based on NESDIS stage IV radar-gage precipitation products ......................... 51
2.3
Horizontal component of ESTAR observed brightness temperature on July 8,
July 9, July 14, July 15, July 19, and July 20 .................................................... 52
2.4
(a) VIC surface temperature validation compared to all ARM/CART solar and
infrared observing systems (SIROS) sites for July, 1999; (b) and (c) the time
series of soil temperatures at different layers from VIC and Oklahoma Mesonet
observations at Apache (34.91° N, 98.29°W) ................................................... 53
2.5
(a) Sand fraction and (b) clay fraction for the SGP99 region............................ 54
2.6
(a) Surface roughness, (b) bulk density, (c) NDVI and (d) vegetation parameter b
for the SGP99 region ......................................................................................... 55
2.7
LSMEM retrieved soil moisture from ESTAR images during SGP99 ............. 56
2.8
Validation results for full sampling sites during SGP99 ................................... 57
ix
2.9
Validation of the soil moisture averaged over the sampling sites for the CF, ER,
and LW areas ..................................................................................................... 58
2.10 WS Field measurements at each sampling location in field LW12 during days
with ESTAR measurements .............................................................................. 59
2.11 0.25° retrieved soil moisture as compared to soil moisture averaged from 0.125°
retrieved soil moisture over the ESTAR observed region during SGP99 ...... 60
3.1
The LSMEM output sensitivity to water fraction at the surface temperature of
288K .................................................................................................................. 92
3.2
Examples of LSMEM model data and inputs.................................................... 93
3.3
Fractional area covered by water for the grid boxes within the study area ....... 94
3.4
Daily total precipitation (mm) and the second-day soil moisture increment (%)
from July 8th to July 14th, 1999.......................................................................... 95
3.5
TMI 10.7 GHz polarization ratio for July 1999 over the southern U.S. a)
monthly average TbV/TbH; b) monthly standard deviation of TbV/TbH ............... 96
3.6
TMI 10.7 GHz polarization ratio for January 1999 over the southern U.S. a)
monthly average TbV/TbH; b) monthly standard deviation of TbV/TbH ............... 97
3.7
Mask for frozen ground, snow-covered, and water contamination ................... 98
3.8
Retrieved surface volumetric soil moisture (%) for January 1, 1999 with all
quality masks applied ........................................................................................ 99
3.9
Rain Percentage of time by season that the retrieved soil moisture passed all data
quality flags; a) MAM, b) JJA, c) SON, and d) DJF........................................ 100
x
3.10 Retrieved soil moisture from TMI and Oklahoma Mesonet with observed
precipitation for the period June through October 2002 for a) the El Reno
Mesonet site and b) averaged over the 72 Oklahoma Mesonet sites reporting soil
moisture ............................................................................................................ 101
4.1
Comparison between soil moisture retrieved from the LSMEM and the JPL
algorithm........................................................................................................... 132
4.2
Comparison between soil moisture from the LSMEM retrieval and their
differences from Oklahoma Mesonet field measured data............................... 133
4.3
Comparison between soil moisture from the JPL algorithm retrieval and their
differences from Oklahoma Mesonet field measured data...............................134
4.4
Comparison between soil moisture from the LSMEM retrieval and their
differences from VIC model outputs................................................................ 135
4.5
Comparison between soil moisture from the JPL algorithm retrieval and their
differences from VIC model outputs................................................................ 136
4.6
Comparison between TMI soil moisture from the LSMEM retrieval and their
differences from ERA40 model outputs (from 1998 to 2002) .........................137
4.7
Comparison between TMI soil moisture from the JPL algorithm retrieval and
their differences from ERA40 model outputs (from 1998 to 2002).................138
4.8
Comparison between TMI soil moisture from the LSMEM retrieval and their
differences from NARR model outputs (from 1998 to 2003) .......................... 139
4.9
Comparison between TMI soil moisture from the JPL algorithm retrieval and
their differences from NARR model outputs (from 1998 to 2003)..................140
xi
4.10 Fitted single distributions for LSMEM SM, JPL SM, LSMEM-VIC, and JPLVIC. .................................................................................................................. 141
4.11 Fitted single distributions for LSMEM SM, JPL SM, LSMEM-ERA40, and JPLERA40 .............................................................................................................. 142
4.12 An example that compares empirical CDF with CDFs simulated from three types
of copulas: Clayton, Gumbel, and Frank.......................................................... 143
4.13 Copula simulated joint distributions between observations from LSMEM
retrievals and their biases from VIC model outputs ......................................... 144
4.14 Copula simulated joint distributions between observations from JPL algorithm
retrievals and their biases from VIC model outputs ......................................... 145
4.15 Copula simulated joint distributions between observations from LSMEM
retrievals and their biases from ERA40 model outputs.................................... 146
4.16 Copula simulated joint distributions between observations from JPL algorithm
retrievals and their biases from ERA40 model outputs....................................147
4.17 Observed soil moisture and the mean of their biases from modeled soil moisture
.......................................................................................................................... 148
4.18 Observed soil moisture and the standard deviation of their biases from modeled
soil moisture ..................................................................................................... 149
4.19 Comparisons of soil moisture increments due to rainfall (lager than 10mm/day) .
.......................................................................................................................... 150
xii
Acknowledgements
This dissertation is a summary of the research accomplished during my five
years at Princeton, and represents a significant part of my life. I have been blessed to
be supervised and helped in my research, and developed friendships with so many
people that it is almost impossible to find a proper way to fully express my gratitude
towards them.
First of all, I want to thank my advisor, Professor Eric F. Wood., without
whom the dissertation would not have been possible. Eric has been a committed
advisor who makes developing the student from a passive learner to an active
researcher his main priority - in a strict but always encouraging way. Most
importantly, Eric sets me an example by his passion and devotion to research. I am
sure that I will continue to be influenced and learn from him in the future.
I also owe many thanks to the members of our Land Surface Hydrology Group,
some of whom have left Princeton. Dr. Matthias Drusch generously shared the land
surface microwave emission model and contributed many good ideas to my research.
Dr. Wade Crow is owed credit for introducing me to microwave remote sensing and
offering valuable feedbacks whenever I approached him for suggestions. Besides these
contributions, both Matthias and Wade served on my committee diligently. I am
indebted to Dr. Justin Sheffield for the most efficient technical support and help
through all these years. I’m grateful to Dr. Matthew McCabe for the wonderful
collaborations both in the field and in the lab. Dr. Lifeng Luo has helped me with
xiii
some of the figures and data. I especially appreciate Ming Pan and Hongbo Su, for the
countless favors they offered, both in my work and daily life.
In addition, I want to thank Professor Ignacio Rodriguez-Iturbe and Professor
James A. Smith for giving valuable feedbacks at my committee meetings each year.
My research was helped greatly by people outside of Princeton as well. Dr.
Thomas J. Jackson, as a committee member and a coauthor, shared his research
experiences and ideas - always as a top priority, regardless of how busy he was at the
time. Dr. Rajat Bindlish has provided me with the satellite data essential for the
dissertation. Dr. Eni Njoku kindly offered the NASA developed algorithm for the
research carried out in Chapter 4. The frozen soil data in Chapter 3 were made
available by Dr. T. Zhang of NSIDC.
Accompanied to my research explorations is my growing understanding about
life. I would not have survived the tough graduate experience without my dear friends’
encouragement. Some of them I have mentioned, but many of them are not listed here.
I wish them all the best.
Finally, my deepest appreciation goes to my parents and my family. My
parents have given me all the supports they possibly can. They do not know how
proud I am of them. Now they do.
xiv
Chapter 1
Overview of the Research
1.1 Introduction
Advances in remote sensing have provided the means for observing state
variables from space at large scales, improving our understanding of many
hydrological processes (Schmugge et al., 2002). By taking advantages of the land
surface emission characteristics, many state variables such as the land surface
temperature, surface soil moisture, snow cover, evapotranspriation, etc., can be
monitored by radiometers installed on satellites. Amongst these applications, passive
microwave remote sensing of surface soil moisture is particularly important because of
the many limitations on obtaining soil moisture through traditional field
measurements. For instance, soil moisture is so spatially heterogeneous that point
measurements are generally unable to characterize the wetness conditions at land
surface modeling resolutions unless tremendous quantities of data were collected
(Entin et al., 2002).
Passive microwave frequencies have been adopted for monitoring surface
moisture conditions because of two unique advantages. Firstly, as the soil water
content increases, dielectric conductivity of the soil decreases, resulting in reduced
surface emission (or brightness temperature). The lower is the frequency; the higher is
the sensitivity to soil moisture. Secondly, atmospheric contributions are minimal at
many microwave frequencies such that land surface emission can penetrate through
1
the atmosphere and thin clouds unaffected by atmospheric attenuation (Ulaby et al.,
1986). As a result, surface soil moisture information can be retrieved globally at real
time from space-borne remote sensing.
Since soil moisture is one of the key variables in land atmospheric interactions,
operational soil moisture information would certainly contribute to improving
hydrological modeling and numerical weather forecasting (NWF), drought/flood
monitoring, flood forecasting, and climate studies. By incorporating real time indirect
(i.e. remotely sensed) observations into hydrological models, errors associated with
both the modeling and the observations can be accounted for when updating model
outputs. For example, forcing errors (primarily precipitation errors) can be reduced by
knowledge of the soil wetness monitored in real time using data assimilation
techniques (Entekhabi et al., 1999), hence preventing temporal propagation of these
errors through the model space.
Although the microwave radiation observed from space is sensitive to soil
moisture, retrieving soil moisture operationally and employing the results into various
applications are complicated due to a number of constraints. These include:
1) Incomplete parameterization
While electromagnetic and radiative transfer theories have offered enough
support for modeling brightness temperatures at the top of atmosphere (TOA),
many parameters (especially those concerning vegetation) involved in the
scheme are unavailable at continental scales. Furthermore, even for those
available parameters, their uncertainties have different impact on modeling
results, and are often dependent on modeling sensitivities (Gao et al., 2005).
2
2) Differences among soil moisture products
To solve or avoid the parameterization problem, most algorithms
developed for retrieving soil moisture at microwave frequencies are to some
extent empirical, largely fitting into three categories (Wigneron et al., 2003):
statistical techniques; forward model inversion; and explicit inverse (Kerr and
Njoku, 1990; Njoku and Li, 1999; Bindlish et al., 2003; De Jeu and Owe,
2003; Gao et al., 2005). Although these soil moisture results share primary
dynamics such as rainfall responses and seasonal cycles (De Jeu and Owe,
2003; Gao et al., 2005), very often their means and variances differ
considerably. Therefore, users are often confused in choosing the proper
product before any potential applications.
3) Limited validation data
One reason those remotely sensed soil moisture products having different
means and variances is that validation cannot be carried out at large scales over
a long time period. The main challenge results from scale inconsistencies: field
measurements are at point scale, while the resolutions of satellite remote
sensing products are often more than 40 km (Mohanty and Skaggs, 2001).
Since soil moisture is a state variable with high spatial heterogeneity,
performing intensive field campaigns is the only solution to provide
representative data for evaluating the products and algorithms at limited spatial
and temporal scales (Famiglietti et al., 1999; Jackson and Hsu, 2001; McCabe
et al., 2005). Soil moisture from airborne remote sensing at L band or C band
is an indirect data source for validation (Saleh et al., 2004; McCabe et al.,
3
2005), but it is restricted to field campaign scale due to high cost. Operational
field measurements like the Oklahoma Mesonet provide valuable time series
(years) of soil moisture data at point scale, but their contribution to validation
is yet to be thoroughly explored.
4) Low sensing depth
Apart from product differences between algorithms, another restriction for
applications is that the remotely sensed radiation from current space based
sensors only contains surface soil moisture information from less than about
1cm of soil depth (Ulaby et al., 1986; Owe and Van de Griend, 1998), rather
than the lower layer soil moisture which is more meaningful in most studies.
For instance, in most hydrological models, the top layer is about 5cm to 10cm
thick. To simulate the remotely sensed surface soil moisture, the systematic
bias between these layers has to be corrected (Reichle and Koster, 2004;
Drusch et al., 2005).
To contribute to the science questions stated above, this dissertation contains
three chapters (Chapter 2 to Chapter 4) based on three first authored papers that
investigate passive microwave remote sensing from the following perspectives:
Algorithm development; Model parameterization for conducting operational soil
moisture retrieval at large scales; and Application in data assimilation: deriving
observation operators to reduce systematic bias from modeled soil moisture. A land
surface microwave emission model (LSMEM, Gao et al., 2004), which has been
developed and employed to retrieve soil moisture from both airborne and space-borne
4
observations, is a key component of this dissertation. Soil moistures retrieved using
LSMEM involve observations from both airborne radiometers and space based
sensors.
The remainder of this chapter provides an overview of the research undertaken,
focusing on those topics specifically addressed in the following chapters. Additional
results and analysis that will provide the reader with necessary background knowledge
is also presented.
1.2 LSMEM and its Sensitivity Tests
Chapter 2 is derived from the published work “Using a Microwave Emission
Model to Estimate Soil Moisture from ESTAR Observations during SGP99” (Gao et
al., J. Hydromet., (5), 49-63, 2004). The Chapter explains the modeling components
and radiative transfer scheme of LSMEM in detail. LSMEM is based on a solution for
the radiative transfer equation as outlined in Kerr and Njoku (1990), combining
literature results on soil and vegetation microwave radiation properties. The forward
model of LSMEM simulates polarized brightness temperatures at the top of the
atmosphere, using soil moisture and soil and vegetation parameters as inputs. By
inverting LSMEM numerically, surface soil moisture can be retrieved from a single
polarized brightness temperature.
LSMEM is also used to retrieve soil moistures from airborne L-band ESTAR
data during the Southern Great Plains field experiments in 1999. The soil moisture
product has been made available at
5
http://disc.gsfc.nasa.gov/fieldexp/SGP99/estar11.shtml. This retrieval is important
because of two reasons.
1) The airborne L band ESTAR radiometer plays a significant role in passive
microwave remote sensing. Its high resolution (800m) and long wavelength (21cm)
have made it the optimal airborne radiometer for retrieving surface soil moisture. Due
to its high resolution, the validation constraints can be reasonably resolved by
intensive field measurement. Therefore, ESTAR measurements during field
campaigns provide the best environment for algorithm evaluation (Jackson et al.,
1995; Le Vine et al., 2001). Here the LSMEM retrieved soil moisture had a RMS
range for the area-averaged soil moisture of 1.8-2.8% volumetric soil moisture,
demonstrating excellent model performance.
2) An operational soil temperature rather than an interpolated field
measurement is used in this retrieval. The effective soil temperature is calculated from
the surface and deep soil temperatures obtained from the Variable Infiltration Capacity
(VIC) land surface model (Liang et al., 1994), running as part of the North American
Land Data Assimilation System (NLDAS) (Mitchell et al., 2004). The success of this
approach has made significant progress towards retrieving soil moisture operationally
using LSMEM. When the algorithm is applied for retrievals from spaceborne
radiometers in Chapter 3, the same soil temperature data source is employed.
1.3 Retrieving Soil Moisture from Space-borne Observations and Related Issues
In Chapter 3, based on “Using TRMM/TMI to Retrieve Surface Soil Moisture
over the Southern United States from 1998 to 2002” (Gao et al., J. Hydromet., in
6
press, 2005), the LSMEM is further parameterized across the southern United States at
1/8th degree and then employed for retrieving surface soil moisture conditions from the
TRMM Microwave Imager (TRMM/TMI) from 1998 to 2002. The five year soil
moisture product is to be provided to NASA/GSFC Distributed Active Archive Center
(DAAC).
As discussed in Section 1.1, validating remotely sensed soil moisture at large
scales is challenging. Although the results have been compared with field
measurements collected from Oklahoma Mesonet and shown to produce good
correlations, this section includes additional research results to tackle validation
approaches. By using the same modeling scheme, soil moisture was retrieved from the
Advanced Microwave Scanning Radiometer (AMSR-E) coinciding with SMEX02, a
comprehensive field experiment designed for the purpose of pixel scale validation of
remotely sensed soil moisture estimates. Using data collected from SMEX02, results
were presented in a collaborative paper, “An evaluation of AMSR-E derived soil
moisture retrievals using ground based and airborne data during SMEX 02” (McCabe
et al., J. Hydromet., in press, 2005), the first such validation of AMSR-E results to
appear in a peer reviewed publication. Validation strategies based on these two papers
are summarized as following.
1) Comparison of daily soil moisture changes with precipitation patterns.
Precipitation is the cause for soil moisture increment. Pattern consistency
between soil moisture changes and precipitation is expected. Otherwise the soil
moisture product should be questioned.
2) Comparison of retrieved soil moisture with in situ data.
7
Although the scale or heterogeneity problem cannot be avoided, spatial averages
of point measurements will have an improved representation of soil wetness
condition. Therefore, the averaged Oklahoma Mesonet data across 72 stations
are used to evaluate the seasonality of TMI product at regional scale through
their correlations; and the more densely collected ground data from SMEX02,
though only comparable to a few satellite footprints, are used to check AMSR-E
results accuracies directly.
3) Comparison of spaceborne soil moisture with airborne soil moisture.
The airborne polarimetric scanning radiometer (PSR) operating at C-band was
employed during SMEX02. The PSR offers high resolution detail of the soil
moisture distribution which can be used to analyze heterogeneity at the scale of
the AMSR-E pixel. The PSR data provides an excellent intermediary source of
validation information between the scales of the AMSR-E pixel and ground
based measurements, and offers the only feasible means of comparing
predictions with a reasonable spatial equivalence and measurement
characteristics to AMSR-E.
Although the validation options mentioned above have provided valuable
results at the regional scale, they are spatially and temporally limited. If the
operational retrieval is to be executed globally, knowledge on the degree of
uncertainty are associated with the algorithm and parameterization is critical.
In passive microwave remote sensing, the observed radiation at the top of
atmosphere is a function of soil moisture, soil temperature, soil texture, vegetation
8
parameters, frequency, and polarization. However, these variables or parameters effect
observations differently. There has been considerable literature concerning modeling
sensitivity effects from single parameter by fixing the remaining variables (Njoku and
Entekhabi, 1996; Du et al., 2000; Devenport et al., 2005). In operational retrievals
such as LSMEM and similar algorithms, parameters are not always independent and
all have a range of uncertainty associated with them. Thus a more detailed
understanding of the retrieval error is required.
Further detailed experiments to characterize modeling errors associated with
various algorithms and parameterizations are required. Here a preliminary exploration
of LSMEM retrieval uncertainty using Monte-Carlo simulation is presented. For a
single orbit of TMI observed brightness temperatures, multiple (100) sets of inputs,
with each parameter or variable randomly perturbed by a certain percentage of noise
was run using LSMEM. As a result, 100 different scenarios were produced, with each
model reproduction compared to a single fixed parameterization, enabling the
calculation of the standard deviation at each observation point. The results are
presented in Figure 1.1, which indicate that considerable modeling errors occur over
heavily vegetated areas, consistent with the analysis of polarization ratios presented in
Chapter 3. Since LSMEM represents more detailed model physics than many other
algorithms, such uncertainty studies aid in gaining further insights not only for the X
band but also L band sensors. Such knowledge is particularly important in assisting
the performance of future missions such as the yet to be launched Hydrosphere State
(HYDROS) satellite.
9
1.4 Generate observation operators for data assimilation
Chapter 4 relates to the paper entitled “Copula Derived Observation Operators
for Assimilating TMI and AMSR-E Soil Moistures into Land Surface Models in the
Southern Great Plains” (to be submitted to Monthly Weather Review). It explores the
application potential of assimilating space-borne remote sensing soil moisture product
into land surface models through the development of “observational operators”.
As discussed in Section 1.1, current soil moisture products from space-borne
observations differ significantly. Figure 1.2 gives an example of soil moistures from
AMSR-E using the LSMEM and operational NASA retrieval algorithm respectively.
Although the soil moisture patterns are similar, the absolute values differ significantly:
LSMEM results have a much larger dynamic range than results from the NASA
algorithm. In terms of assimilating remotely sensed soil moistures into land surface
models, the modeling side suffers from similar problems due to modeling physics.
Figure 1.3 compares soil moisture time series from VIC and the European Center for
Medium-range Weather Forecasts (ECMWF) reanalysis (ERA40). Again the non
uniform offset between these two data sets can be observed. Besides these
uncertainties, the different representative depth, less than 1cm for remote sensing
compared to 10cm for land surface modeling, adds complexities to assimilating
remotely sensed soil moistures into land surface models.
In order to best use the remote sensing information and correct the systematic
biases, Chapter 4 attempts to address this problem by generating observation
operators. Remotely sensed soil moistures from LSMEM and NASA/JPL algorithms,
and modeled soil moistures from VIC and ERA40 outputs are classified by seasons
10
and paired up to address four types of combinations. A statistical approach based on
the copula, is employed for simulating the joint distributions between observations and
their biases from model outputs. By separating marginals of multi-variables from their
dependency structures, copulas demonstrate flexibility in modeling joint distributions
over traditional methods. Furthermore, copula conditional simulations based on
parameters representing single distributions and their dependencies, estimate potential
biases for given observation. Statistics from these results, such as the mean and
standard deviation of the biases over a range of observations, serve as observation
operators for data assimilation practices. These operators are good abstractions of the
models, the observations, and their inter-relationship. It is a relatively straightforward
procedure to implement this approach in models to generate ensembles, increasing
their broader application in the hydrological community.
11
References
Bindlish, R., T. J. Jackson, E. Wood, H. L. Gao, P. Starks, D. Bosch, and V. Lakshmi,
2003: Soil moisture estimates from TRMM Microwave Imager observations over the
Southern United States. Remote Sensing of Environment, 85, 507-515.
Davenport, I. J., J. Fernandez-Galvez, and R. J. Gurney, 2005: A sensitivity analysis
of soil moisture retrieval from the Tau-Omega microwave emission model. Ieee
Transactions on Geoscience and Remote Sensing, 43, 1304-1316.
De Jeu, R. A. M. and M. Owe, 2003: Further validation of a new methodology for
surface moisture and vegetation optical depth retrieval. International Journal of
Remote Sensing, 24, 4559-4578.
Drusch, M., E. Wood, and H. Gao, 2005: Observation operators for the direct
Assimilation of satellite retrieved soil moisture into land surface models. Geophysical
Research Letters, Geophysical Research Letters, 32, L15403,
doi:10.1029/2005GL023623, 2005.
Du, Y., F. T. Ulaby, and M. C. Dobson, 2000: Sensitivity to soil moisture by active
and passive microwave sensors. Ieee Transactions on Geoscience and Remote
Sensing, 38, 105-114.
Entekhabi, D., G. R. Asrar, A. K. Betts, K. J. Beven, R. L. Bras, and C. J. e. a. Duffy,
1999: An agenda for land-surface hydrology and a call for the Second International
Hydrologic Decade. Bulletin of American Meteorological Society, 80, 2043-2058.
Entin, J. K., A. Robock, K. Y. Vinnikov, S. E. Hollinger, S. X. Liu, and A. Namkhai,
2000: Temporal and spatial scales of observed soil moisture variations in the
extratropics. Journal of Geophysical Research-Atmospheres, 105, 11865-11877.
12
Famiglietti, J. S., J. A. Devereaux, C. A. Laymon, T. Tsegaye, P. R. Houser, T. J.
Jackson, S. T. Graham, M. Rodell, and P. J. van Oevelen, 1999: Ground-based
investigation of soil moisture variability within remote sensing footprints during the
Southern Great Plains 1997 (SGP97) Hydrology Experiment. Water Resources
Research, 35, 1839-1851.
Gao, H., E. F. Wood, T. J. Jackson, M. Drusch, and R. Bindlish, 2005: Using
TRMM/TMI to retrieve surface soil moisture over the southern United States from
1998 to 2002. Journal of Hydrometeorology, in press.
Gao, H. L., E. F. Wood, M. Drusch, W. Crow, and T. J. Jackson, 2004: Using a
microwave emission model to estimate soil moisture from ESTAR observations
during SGP99. Journal of Hydrometeorology, 5, 49-63.
Jackson, T. J. and A. Y. Hsu, 2001: Soil moisture and TRMM microwave imager
relationships in the Southern Great Plains 1999 (SGP99) Experiment. Ieee
Transactions on Geoscience and Remote Sensing, 39, 1632-1642.
Jackson, T. J., D. M. Levine, C. T. Swift, T. J. Schmugge, and F. R. Schiebe, 1995:
Large-Area Mapping of Soil-Moisture Using the Estar Passive Microwave Radiometer
in Washita92. Remote Sensing of Environment, 54, 27-37.
Kerr, Y. H. and E. G. Njoku, 1990: A Semiempirical Model for Interpreting
Microwave Emission from Semiarid Land Surfaces as Seen from Space. Ieee
Transactions on Geoscience and Remote Sensing, 28, 384-393.
Le Vine, D. M., T. J. Jackson, C. T. Swift, M. Haken, and S. W. Bidwell, 2001:
ESTAR measurements during the Southern Great Plains experiment (SGP99). Ieee
Transactions on Geoscience and Remote Sensing, 39, 1680-1685.
13
Liang, X., D. P. Lettenmaier, E. F. Wood, and S. J. Burges, 1994: A Simple
Hydrologically Based Model of Land-Surface Water and Energy Fluxes for GeneralCirculation Models. Journal of Geophysical Research, 99, 14415-14428.
McCabe, M. F., E. F. Wood, and H. Gao, 2005: Initial soil moisture retrievals from
AMSR-E: Multiscale comparison using in situ data and rainfall patterns over Iowa.
Geophysical Research Letters, 32, L06403, doi:10.1029/2004GL021222.
McCabe, M. F., H. Gao, and E. F. Wood, 2005: An evaluation of AMSR-E derived
soil moisture retrievals using ground based, airborne and ancillary data during SMEX
02. Journal of Hydrometeorology, in press.
Mitchell, K. E. and others, 2004: The multi-institution North American Land Data
Assimilation System (NLDAS): Utilizing multiple GCIP products and partners in a
continental distributed hydrological modeling system. Journal of Geophysical
Research, 109, Art. No. D07S90.
Mohanty, B. P. and T. H. Skaggs, 2001: Spatio-temporal evolution and time-stable
characteristics of soil moisture within remote sensing footprints with varying soil,
slope, and vegetation. Advances in Water Resources, 24, 1051-1067.
Njoku, E. G. and D. Entekhabi, 1996: Passive microwave remote sensing of soil
moisture. Journal of Hydrology, 184, 101-129.
Njoku, E. G. and L. Li, 1999: Retrieval of land surface parameters using passive
microwave measurements at 6-18 GHz. Ieee Transactions on Geoscience and Remote
Sensing, 37, 79-93.
14
Owe, M. and A. A. Van de Griend, 1998: Comparison of soil moisture penetration
depths for several bare soils at two microwave frequencies and implications for remote
sensing. Water Resources Research, 34, 2319-2327.
Reichle, R. H. and R. D. Koster, 2004: Bias reduction in short records of satellite soil
moisture. Geophysical Research Letters, 31, (19), Art. No. L19501.
Saleh, K., J. P. Wigneron, J. C. Calvet, E. Lopez-Baeza, P. Ferrazzoli, M. Berger, P.
Wursteisen, L. Simmonds, and J. Miller, 2004: The EuroSTARRS airborne campaign
in support of the SMOS mission: first results over land surfaces. International Journal
of Remote Sensing, 25, 177-194.
Schmugge, T. J., W. P. Kustas, J. C. Ritchie, T. J. Jackson, and A. Rango, 2002:
Remote sensing in hydrology. Advances in Water Resources, 25, 1367-1385.
Ulaby, F. T., R. K. Moore, and A. K. Fung, 1986: Microwave Remote Sensing III:
From theory to applications. Artech House,Dedham, MA, 1065-2162 pp.
Wigneron, J. P., J. C. Calvet, T. Pellarin, A. A. Van de Griend, M. Berger, and P.
Ferrazzoli, 2003: Retrieving near-surface soil moisture from microwave radiometric
observations: current status and future plans. Remote Sensing of Environment, 85, 489506.
15
Figure 1.1 Standard deviation of soil moisture retrieval uncertainties. The example is
based on parameterization for TMI overpass on July 14, 1999 at 15 UTC. Standard
deviations of the randomly generated parameters are: 4K for surface temperature; 10%
for soil texture; 2K for horizontally polarized brightness temperature; 10% for
vegetation coverage; and 20% for vegetation water content.
16
Figure 1.2 Surface soil moisture retrieved from AMSR-E observations on Jan. 10,
2003 using (a) LSMEM and (b) NASA/JPL algorithm respectively.
17
40
VIC
ERA40
35
Soil moisture
30
25
20
15
10
01-02-1999
03-03-1999
05-02-1999
07-01-1999
Date
08-30-1999
10-29-1999
12-28-1999
Figure 1.3 Time series of daily averaged soil moistures over the Southern Great Plains
from VIC and ERA40 model outputs.
18
Chapter 2
Using a Microwave Emission Model to Estimate Soil Moisture from ESTAR
Observations During SGP99
Abstract
The 1999 Southern Great Plains Hydrology Experiment (SGP99) provides
comprehensive data sets for evaluating microwave remote sensing of soil moisture
algorithms that involve complex physical properties of soils and vegetation. The Land
Surface Microwave Emission Model (LSMEM) is used to retrieve soil moisture from
brightness temperatures collected by the airborne ESTAR L-band radiometer, where
ESTAR refers to the Electronically Scanned Thinned Array Radiometer. Soil moisture
maps for the SGP99 domain are retrieved using LSMEM, surface temperatures
computed using the VIC land surface mode, standard soil data sets and vegetation
parameters estimated through remote sensing. The retrieved soil moisture is validated
using field-scale and area-averaged soil moisture collected as part of the SGP99
experiment, and had a RMS range for the area-averaged soil moisture of 1.8-2.8%
volumetric soil moisture.
2.1 Introduction
Soil moisture is a key factor in understanding land-atmosphere feedbacks.
Operational large-scale soil moisture observational products would likely enhance the
19
accuracy of Numerical Weather Prediction (NWP) products (e.g. Koster and Suarez,
2001), hydrological flood forecasting, agricultural drought monitoring as well as water
cycle research related to climate studies. Observations based on standard in-situ
instrumentation can only measure local values and may not adequately sample land
surface heterogeneity. In addition, dense ground networks are expensive to install and
maintain.Space borne microwave radiomtery has been recognized as an effective
method for monitoring soil moisture at large scales (Owe et al., 1999). In theory, the
dielectric constant of the soil- water medium is raised by increases in soil water
content. These variations are detectable by remote microwave sensors (Njoku 1977).
The sensitivity of surface dielectric measurements to soil moisture is higher at lower
microwave frequencies. Currently operating and scheduled microwave satellite
missions that have been applied to soil moisture retrievals include: the Scanning
Multichannel Microwave Radiometer (SMMR) at 6.63 GHz on Nimbus-7, which was
launched in 1978, with data available until 1987 (Owe et al., 1992); the Defense
Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I)
at 19.3 GHz, which was launched in 1987 (Jackson, 1997); Tropical Rainfall
Measuring Mission (TRMM) Microwave Imager (TMI) at 10.65 GHz, which was
launched in 1997 (Jackson and Hsu, 2001); the Advanced Microwave Scanning
Radiometer (AMSR) on the EOS Aqua satellite
(AMSR-E) at 6.9 GHz, which was launched in May 2002 and the ADEOS-II AMSR,
which was launched in December 2002; and the European Soil Moisture and Ocean
Salinity Mission (SMOS) at 1.4 GHz, which has an anticipated launch in 2007 (Kerr et
al., 2001).
20
Algorithm development and validation are essential before global application
of soil moisture retrieval algorithms. The dielectric properties of wet soil have been
widely investigated (Wang and Schmugge, 1980; Dobson et al., 1985; Ulaby et al.,
1986), as well as the radiative characteristics of vegetation (Kirdyashev et al, 1979;
Wegmuller et al, 1995). Using these results and data from airborne remote sensing
field studies, soil moisture retrieval algorithms have continued to be refined (e.g.
Jackson et al., 1995, 1999). However, operational application of these algorithms at
regional scales using
satellite sensor measurements faces two major challenges: the shortage of information
regarding the numerous parameters involved in radiometry physics at large scales and
the high within- footprint spatial heterogeneity of land surface variables relative to the
low resolution of spaceborne microwave radiometers (> 10 km). This chapter
contributes to the refinement of soil moisture retrieval approaches through application
of an algorithm based on modeling microwave emissions from the surface and
information available from large scale SVAT modeling.
There are two major objectives of this chapter. The first objective is to apply a
new soil moisture retrieval approach that utilizes a Land Surface Microwave Emission
Model (LSMEM) for the soil-vegetation-atmospheric system with surface temperature
data from a SVAT model that utilizes high resolution remotely sensed vegetation and
soil data. The second objective is to apply the approach to retrieve soil moisture fields
from the airborne Electronically Scanned Thinned Array Antenna (ESTAR) sensor
1.413 GHz brightness temperatures collected during the 1999 Southern Great Plains
Hydrology Experiment (SGP99) experiment, and making them available to the
21
scientific community. Such a data product has not yet been developed. Underlying
these objectives is the objective to develop a soil moisture retrieval approach suitable
for satellite measured brightness temperatures collected at regional to continental
scales. At these scales, the detailed meteorological and vegetation data are
unavailable, so operational products need to be utilized. Validation of the LSMEM
algorithm, using the detailed ground observations available during SGP99, is an
important step. Section 2.2 presents the soil moisture retrieval approach based on the
LSMEM model, section 2.3 describes the SGP99 field experiment including the Lband
brightness temperature measurements from ESTAR, and section 2.4 describes the
LSMEM model input variables used for the ESTAR-based soil moisture retrievals.
The retrieved soil moisture fields for the SGP99 domain and validation results for the
LSMEM for the SGP99 ground observation sites and presented in section 2.5,
followed by a discussion and conclusions in section 2.6.
2.2 Land Surface Microwave Emission Model (LSMEM )
In the reviewed literature, a number of models for the computation of
microwave emission from land surfaces exist (Ulaby et al., 1986; Wang and
Choudhury, 1995; Njoku and Entekhabi, 1996). Depending on the specific application
and frequency range they represent more or less complex approximations of the vector
radiative transfer equation and distinguish themselves through different
parameterizations for the key processes describing the interaction between radiation
and matter. The LSMEM model used in this study is based on a solution for the
22
radiative transfer equation as outlined in Kerr and Njoku (1990). Following this
article, the brightness temperature of vegetation covered soils Tbv,p can be written as:
Tbv = Tau + e −τ at (Tad + Tsky e −τ at )(1 − ε )e −2τ +
*
e
−τ at
[εT e
s
−τ *
+ TV (1 − ω )(1 − e
*
−τ *
)(1 + (1 − ε )e
−τ *
)
]
(1)
where Tau and Tad are the upward and downward contributions from the atmosphere,
Ts is the effective soil temperature, Tv the vegetation temperature, Tsky the cosmic
radiation, τat the optical depth of the atmosphere, and εp the rough soil emissivity. For
vegetation with cylindrical structure, ω* is the single scattering albedo, τ* is the
optical depth of the vegetation (Chang et al., 1980). For non-isotropic conditions, ω*
and τ* are effective single scatter albedo and effective optical depth of vegetation (Mo
et al., 1982; Jackson et al., 1982). Subscript p indicates polarization dependency in the
model configuration for this study.
Within the LSMEM code multiple options exist to compute the key parameters
εp, and τ*, which provide a flexible interface to various input data sources and makes
the model an appropriate tool for combined hydrological / data assimilation studies
(e.g. Drusch et al., 1999; Crow et al.; 2001, Drusch et al., 2001; Seuffert et al., 2003).
To get rough-soil emissivity εp in LSMEM, the saline dielectric constant is calculate
after Klein and Swift (1977), and the wet soil dielectric constant can be calculated
either after Wang and Schmugge (1980) or after Dobson et al. (1985). Then, using the
Fresnel equation, the reflectivity of a smooth surface is derived, and the effect of soil
roughness is parameterized using the equations presented in Wang and Choudhury
23
(1981). In this investigation, we used the approach by Wang and Schmugge (1980) to
compute the soil dielectric constant.
Two choices within LSMEM are available to get the vegetation optical depth
τ*: Effective Medium theory for low frequencies by Kirdyashev et al. (1979) and
Geometrical Optics approach as described by Wegmüller et al. (1995). For the
Effective Medium theory, τ* depends on a vegetation structure parameter, the
imaginary part of the dielectric constant of saline water, frequency, the vegetation
water content and the viewing angle. The superiority of Geometrical Optics approach
over Effective Medium theory is that it's not restricted by frequency, and it can also
estimate ω*, the single scattering albedo. The drawback is that additional parameters
(dry mass fraction, leaf thickness, and polarization dependant structure parameters) are
needed. As this study is for the L band, the simple algorithm by Kirdyashev is used.
The single scattering albedo ω* is assigned constant (0.1) based on literature reviews (
Ulaby et al., 1983; Pampaloni and Paloscia, 1986; Wegmüller, et al. 1995).
For bare soil the brightness temperature Tbs,p can be obtained from Equation
(1) by setting τ* equal 0. For partly vegetated surfaces the brightness temperature Tb,p
can be calculated introducing the fractional vegetation cover c:
Tb = (1 − c)Tbs + cTbv (2)
In this study, fractional vegetation cover was set to unity. Since it is not realistic to
assume homogeneity at ESTAR resolution, the parameters involved in the retrieval are
effective parameters for the specific resolution. Aggregation effects due to the nonlinearities in radiative transfer were found to be negligible at L- band in the SGP area
24
(Drusch et al., 1999). Consequently, Tb,p reduces to Tbv,p . The modeling approach
used in previous studies on ESTAR soil moisture retrievals (e.g. Jackson et al. 1999)
requires further approximations. Under the assumption that the contributions of the
atmosphere, the cosmic background radiation and the single scattering albedo are zero
Equations (1) and (2) yield:
Tb = εTs e −τ + Tv (1 − e −τ )(1 + (1 − ε )e −τ ) (3)
*
*
*
If vegetation temperature is set equal soil temperature, then
*
Tb
= 1 + (ε − 1)e −2τ (4)
Ts
Equation (4) forms the basis for the soil moisture retrieval scheme introduced in
Jackson et al. (1982; 1995; 1999).
It has been shown in various applications that Equation (4) leads to very good
results when applied to areas with sparse vegetation (e.g. Jackson et al., 1982; Jackson
et al., 1995; Jackson et al., 1999). However, in areas characterized by different
vegetation types the assumptions outlined above may not hold (Ferrazzoli et al., 2002).
A second critical assumption in the earlier modeling approaches is to ignore the
temperature difference between the soil and vegetation, which can exceed a maximum
of 7 K, as reported in Jackson et al. (1982). The LSMEM distinguishes between an
effective soil temperature, which takes the radiation emission depth into account, and
vegetation/surface temperature. In both approximations, soil roughness effects are
parameterized using the equations presented in Wang and Choudhury (1981). The
optical depth of vegetation is computed following Kirdyashev et al. (1979). As a
result, both rely on the correct calibration with respect to the soil roughness parameter
25
and the vegetation structure coefficient. These quantities cannot be obtained from
large-scale measurements, since at these scales they represent an equivalent effect
rather than geophysical parameters (Choudhury et al., 1979).
For a better comparison with previous retrieval studies (e.g. Jackson et al.,
1999) the effect of errors in the observations on the derived soil moisture are
neglected. For the application presented in this study, it is not necessary to retrieve soil
moisture through a variational method, which would require the adjoint model of the
LSMEM. Since the LSMEM is ‘cheap’ in terms of computational resources, it can be
inverted numerically. Starting from a first guess value for volumetric soil moisture,
brightness temperature can be computed using the specified vegetation, soil properties,
and computed atmospheric contributions, which can be done with an atmospheric
radiative transfer model. The optimal soil moisture value is then retrieved through a
simple iterative procedure. Figure 2.1 shows the flowchart of LSMEM soil moisture
retrieval algorithm.
2.3 1999 Southern Great Plains Experiment (SGP99)
2.3.1 SGP99 Data Collection
The 1999 Southern Great Plains Hydrology Experiment was carried out from
July 8 to July 21, 1999 in central Oklahoma. The boundaries for the SPG99
experimental region (see http://hydrolab.arsusda.gov/sgp99) were defined by the flight
path for the airborne measurements and include three sub-regions where intensive
ground-based sampling was focused. The experimental plan, including the remote
sensing, ground-based, and ancillary data collection activities is available at
26
http://hydrolab.arsusda.gov/sgp99 and the reader is referred to this URL for further
details. Table 2.1 provides a listing of the detailed measurements taken during the
experiment. The three ground validation sub-regions are the USDA Agriculture
Research Service (ARS) Little Washita watershed (LW) southwest of Chickasha, OK,
the USDA ARS Grazinglands Research Laboratory at El Reno (ER), OK, and the
Department of Energy Atmospheric Radiation Measurement (ARM) Cloud and
Radiation Testbed (CART) Central Facility (CF) near Lamont, OKlahoma.
2.3.2 Meteorological Conditions during the Experiment
At the beginning of SGP99, the experimental region was generally dry except
for the northern portion of the area. On July 10th, a large, warm season rain event
occurred over the northern two-thirds of the region. Figure 2.2 shows observed total
daily precipitation of the experimental region based on National Environment
Satellite, Data, and Information Service (NESDIS) stage IV radar- gage precipitation
products. The rainfall totals at Oklahoma Mesonet stations at El Reno, Little Washita,
and Central Facility were 107mm, 49mm and 37mm respectively. These two data
sources show the rainfall pattern and the high spatial variability of this summer rainfall
event. No other rainfall events occurred during the experiment, which resulted in a
strong dry-down from the 10th through the 20th of July and a large dynamic range in
observed soil moisture.
2.3.3 ESTAR Airborne L-band Instrument
27
ESTAR is an airborne passive microwave L-band radiometer centered at 1.413
GHz and with a bandwidth of 20 MHz. It has been widely used in soil moisture remote
sensing studies, includingWashita’92 (Jackson et al., 1995) and SGP97 (Jackson et al.,
1999). ESTAR is a hybrid radiometer; its along track measurement is obtained by real
aperture and across track is by synthetic aperture (Le Vine et al., 1990; 2001a). The
instrument was installed on a P-3B aircraft operated by the NASA Wallops Flight
Facility. Flights were conducted at an altitude of 7.5 km. The instrument takes a
complete cross-track scan every 0.25 seconds. A data record consists of the measured
brightness temperature from each beam location, the corresponding time, the GPSbased aircraft geoposition, and aircraft pitch, roll and yaw data. The field of view is
restricted to ± 45o to avoid any distortion of the synthesized beam with incidence
angle.
As described in the SGP99 campaign documents
(http://daac.gsfc.nasa.gov/CAMPAIGN_DOCS/SGP99/), post processing of the
ESTAR data consisted of refining the brightness temperature calibration, radio
frequency interference (RFI) removal, georegistration, and an incidence angle
correction. Instrument calibrations included a pre- mission laboratory blackbody
measurement and a post-mission open-ocean water measurement, the latter flown with
salinity and sea-surface temperature ground truth supplied by shipboard
measurements. As in the case of SGP97 (Jackson et al. 1999) the planned four parallel
lines were modified to compensate for strong RFI in the vicinity of Oklahoma City.
This was a critical problem because of the potential impact on the El Reno study area.
The flight- line reconfiguration eliminated the strong RFI for measurements over El
28
Reno. (See the experimental plan and campaign documents for additional discussion
of the RFI.) The data were normalized to nadir using methods described in Jackson et
al. (1995) and Le Vine et al (1994,2001b), and georeferenced to 0.005 degrees latitude
by 0.005 degrees longitude grid (approximately 555 m X 450 m). The grid value is the
unweighted average of all brightness temperatures falling within the grid.
During SGP99, ESTAR measured the horizontal polarized brightness
temperature on July 8th, July 9th, July 14th, July 15th, July 19th, and July 20th. Figure
2.3 shows images of these data. A linear soil moisture regression was reported by Le
Vine et al (2001b) to evaluate the ESTAR observations during SGP99.
2.4 Input State Variables and Parameters for the LSMEM
Besides the horizontal polarized brightness temperature, the LSMEM inputs
include effective soil temperature, vegetation temperature, soil texture, surface
roughness, soil bulk density, vegetation water content, and a vegetation structure
parameter. For soil moisture retrievals from the ESTAR airborne sensor during
SGP99, all input data were processed onto grids of 0.005 degree resolution for the area
encompassed by 34° N to 38° N in latitude and –97° W to –98.5°W in longitude.
2.4.1 Soil and Vegetation Temperatures
The effective soil temperature needed for the soil moisture retrievals is a
function of surface temperature, deep soil temperature, and frequency (Choudhury et
al., 1982). For SGP97 Jackson (1999) used interpolated Oklahoma Mesonet soil
temperatures. However, over continental areas lacking intensive ground-based
29
networks, sparse measurements of soil temperature may neglect spatial heterogeneity
due to soils and land cover, and lead to excessively smooth soil temperature fields.
Operational products from land surface models (LSM) offer an alternative to ground
based measurements. In this study, the surface and deep soil temperatures were
obtained from the Variable Infiltration Capacity (VIC) land surface model (Liang et
al., 1994; Cherkauer et al, 2002), running as part of the North American Land Data
Assimilation System (NLDAS) (Mitchell et al., 2000; Mitchell et al., 2002). As part of
the NLDAS validation activities, VIC modeled states were compared to observations.
Figure 2.4a shows VIC surface temperature validation when compared to the
ARM/CART solar and infrared observing system (SIROS) sites for July, 1999; Figure
2.4b and Figure 2.4c show the time series of soil temperatures from VIC and
Oklahoma Mesonet observations at Apache (34.91° N, 98.29°W) (see
http://climate.envsci.rutgers.edu/luo/research/LDAS/models.vic.php). Based on the
VIC NLDAS validation (see also Robock et al., 2002), we believe that the VICderived surface temperature and soil temperatures are suitable for LSMEM soil
moisture retrievals. As with the effective soil temperature, the effective vegetation
temperature used in the model varies with vegetation structure, vertical canopy
temperature profile, and frequency. The VIC land surface model has a single surface
layer, with the soil temperature computed beneath the vegetation (Liang et al., 1999.)
For the vegetation temperature, it is approximated using the VIC radiometric surface
temperature, adjusted for the vegetation emissivity based on its classification.
2.4.2 Soil Texture
30
Sand fraction and clay fraction data are used in calculating the soil dielectric
constant. Soil texture classifications of the SGP99 domain were obtained from the
state soil geographic database (STATSGO), which was developed by the USDA’s
Natural Resources Conservation Service (Miller and White, 1998), and resampled to a
800 m grid by the SGP99 data team. In this investigation, we further processed the
data into grids of 0.005 degree so to be compatible with ESTAR brightness
temperatures.
This data is shown in Figure 2.5.
2.4.3 Surface Roughness, Bulk Density, and Land Cover Classification
The surface roughness and bulk density are from the SGP99 database (ftp://
daac.gsfc.nasa.gov/data/sgp99). Following the approach used by Jackson et al. (1999)
for the SGP97 data, the SGP99 data team extended the ground measured values using
a Landsat Thematic Mapper (TM) derived land cover classification to get surface
roughness and bulk density across the SGP99 region (Figure 2.6a and 2.6b). The
classification was made with available “cloud free” Landsat-5 (March 9, May 12, and
July 15) and Landsat-7 scenes (July 7 and July 23) from March 9 to July 23
(Jackson, personal communication). Using multiple images typically provides more
information to increase the accuracy of the supervised classification, if there was no
land cover change during the experimental period. Table 2.2 shows the land cover
statistics for the SGP99 domain.
2.4.4 Estimation of the Vegetation Optical Depth
31
The product of the vegetation water content and vegetation structure parameter
b gives the vegetation optical depth for calcula ting the microwave emission
attenuated by vegetation (Kirdyashev, 1979). During SGP99, vegetation water content
was measured at the ground sampling sites as indicated in Table 2.1. Normalized
Differential Vegetation Index (NDVI), derived from TM data collected on July 15,
1999 (Figure 2.6c) provides a measure of the vegetation greenness for the domain. For
the ground sampling sites, NDVI values were regressed against vegetation water
content resulting in the following relationship:
VWC ( kg / m 2 )=1.75*NDVI
(5)
Using NDVI from remote sensing and (5), the vegetation water content was estimated
over the region.
The vegetation structure parameter for vegetation, other than winter wheat, is
assigned a value of 0.5, the average value for short and long grass according to Wang
et al. (1980,1982) and used by Jackson and Schmugge (1991). Since much of the
winter wheat had been harvested and cons isted of ~10 cm high stubble (similar to the
height of short grass), its vegetation parameter is probably larger than that of short
grass, which Wang (1980, 1982) estimates to 0.30. Thus a value of 0.6 (twice the
value for short grass) is assigned for winter wheat stubble. The land cover
classification, derived from Landsat TM images, is used to estimate b across the
region (Figure 2.6d).
2.5 Soil Moisture Retrievals
2.5.1 SGP99 Regional Results
32
ESTAR brightness temperature data, and other input variable and parameters
(as described in sections 2.3 and 2.4) were used in LSMEM algorithm to retrieve soil
moisture on a pixel-by-pixel basis for SGP99. Figure 2.7 shows the results.
On July 8th and July 9th, the area was mainly dry except in the northern part,
which experienced a total precipitation of 40 mm to 80 mm from June 29th to July 1st.
Though no ESTAR data were collected from July 10th to July 13th, the effect of the
rainfall on July 10th was still significant on July 14th, with the soil moisture being on
average 12% higher as compared to July 9th. The soil moisture map is consistent with
the rainfall pattern as shown in Figure 2.2. Images for July 14th, 15th, 19th, and 20th
illustrate the dry down process. At the end of the SGP99 experiment, the soil moisture
across the study area was below 10%. From July 14th to July 20th, soil moisture
decreased more than 30% (volumetric soil moisture) in the northern part of the SGP99
domain, decreased about 20% in the middle, and less than 10% in the southern part.
The soil moisture patterns agree with the following hydrologic characteristics: soils
with a high clay fraction and low hydrologic conductivity had relatively higher soil
moisture, showing less drainage; and areas with high vegetation coverage remained
with higher soil moisture, suggesting less soil evaporation perhaps due to reduced
radiation through the canopy and higher humidity beneath the vegetation.
2.5.2 Comparisons with Ground Validation Sites
The LSMEM retrieved soil moisture results were validated by comparisons
with volumetric soil moisture derived from SGP99 field sampling. During SGP99, the
most intensive ground sampling was in the LW area, with less sampling sites at ER
33
and CF. For the validation results presented here, only sampling sites that covered an
area comparable to the ESTAR footprints (approximately 800 m by 800 m) are
considered.
The field sampling protocols developed for the experiment are as follows: For
each site, fourteen samples were collected along two transects separated by 400 m
with a sample every 100 m. Each sample was split in half to provide 0-2.5 cm and 2.55.0 cm gravimetric soil moisture data. From these measurements, site average and
standard deviation were then calculated. The product of the gravimetric soil moisture
and bulk density determines volumetric soil moisture. Since only four bulk density
samples were collected at each field site, bulk density measurements were averaged,
when appropriate, to provide more representative values. Specifically, for nearby
fields with similar soil properties (LW3-5, LW12-13, LW21-23), an average bulk
density was computed. For fields not adjacent to other sites, the SGP99 measured bulk
density data was averaged with measurements from SGP97 for the same field. The 0-5
cm averaged volumetric soil moisture data were used to compare with the ESTAR
retrieved soil moistures, since the moisture sensing depth at this frequency (1.4 GHz)
is typically in the 2- to 5-cm range (Ulaby et al., 1986). We feel that this sampling
protocol provides a reliable dataset for validating the ESTAR retrieved soil moisture.
The LSMEM input parameters for the validation sites were first compared with
SGP99 field observations. Vegetation classification and soil texture were, in some
cases, inconsistent with site survey data, and were corrected. For example, the wheat
sites (CF05, LW21, and LW23) were misclassified, which could cause an
underestimation of vegetation attenuation in these sites. This happened because the
34
winter wheat fields were in different stages of harvest during the experimental period.
The SGP regional soil texture data (Miller and White, 1998) classified the LW winter
wheat sites as silt loam (15% clay and 20% sand), while SGP99 field observations
suggested more clay in these sites. Thus a silty- clay classification (10% sand and 45%
clay) was substituted. Table 2.3 shows the input parameters for all sites, with the sites
with adjusted data marked with an asterisk.
For the retrieval validation, soil moisture values for sites without any
misclassification were extracted from the ESTAR retrieved soil moisture images,
while for the corrected sites the LSMEM was re-run with modified parameters. Figure
2.8 shows the validation results for each of the sites, and Figure 2.9 shows the
validation of the averaged soil moisture for the sites in each region. The root mean
square errors are: CF=2.8%, ER=2.3%, LW=1.8%, with an average of 2.1% across all
sites. As compared to other ESTAR soil moisture retrieval algorithms, the LSMEM
retrieved soil moisture results are excellent for most of the sites. For instance, Jackson
et al. (1999) reported root means square errors of: CF=2.7%, ER=3.3%, LW=2.1%.
Site LW12 had the largest detected inconsistency. For July 8th and July 9th, the
retrieved soil moistures were 8.5% and 5.6% lower than field measurement
respectively. Analysis of the field data shows that part of these errors could be due to
the high heterogeneity of this site. The standard deviations of observed soil moisture
for LW12 on July 8th and July 9th is the highest among all the LW sampling sites:
9.95% and 8.77%. Figure 2.10 shows the field data for each sampling location for this
site during ESTAR data collecting days. Using July 8th as an example, the highest
sample value for this site was 36.9% and the lowest value was 5.0%, sample ID 1 and
35
sample ID 2 were only 100 meters apart while the reported field values were 6.6% and
31.9%. Values for sample ID 2 on other days differed significantly from those on the
first days of the experiment, suggesting even higher heterogeneity around that
location. The average value used for validation at LW12 was 19.5%, much larger than
that for the adjacent field LW13 (8.2%). For areas with significant heterogeneity, due
to soils, topography, drainage and so forth, accurate retrievals of remote sensing soil
moisture data will be challenging. For more discussion on sub- grid soil moisture
heterogeneity the reader is referred to Charpentier and Groffman (1992), Famiglietti et
al. (1999) and Crow and Wood, (1999).
As a test, and because the heterogeneity in the SGP99 domain is quite small,
the second approach was used to test the retrieval of soil moisture at 0.25-degree
spatial resolution, and compare these values to soil moisture values retrieved at 0.125degree NLDAS resolution--the resolution that the VIC surface temperature data were
available. Figure 2.11 presents the results, which shows that using low-resolution
brightness temperatures gives almost the same results as averaging the soil moisture
from higher resolution brightness temperatures. This indicates that for this region and
period, the non- linearity and heterogeneity has a small impact. Comprehensive tests
are outside the scope of this chapter, but these initial tests gives confidence that a
retrieval algorithm based on LSMEM, a land surface model to provide surface
temperatures, and operational soil and vegetation data sets can provide a strong basis
for satellite soil moisture retrieval. It is currently being tested using TRMM
Microwave Imager and AMSR-E data (Wood et al, 2003.)
36
2.6 Discussion and Conclusions
The use of passive microwave remote sensing for soil moisture estimation is
well established, yet most studies rely on empirical and semi- empirical relationships
to retrieve soil moisture from microwave brightness temperatures (e.g. Wang, 1983;
Owe et al., 1992). A Land Surface Microwave Emission Model (LSMEM) is
presented that computes the surface emissions based on the equations of soil emission
and vegetation attenuation at microwave frequencies. LSMEM is used to retrieve soil
moisture from L-band brightness temperature measurements during SGP99, collected
from the airborne ESTAR instrument, surface temperatures from a land surface model
and vegetation parameters estimated from remote sensing. This approach allows us to
explore LSMEM's potential in satellite remote sensing retrievals at coarser resolution
using a mix of remote sensing and operational hydrological modeling products (Wood
et al., 2003).
The SGP99 field campaign provided a comprehensive data set for this
investigation. Full site field observations of gravimetric soil moisture offered
validation data at the ESTAR footprint resolution. The vegetation and soil parameters
were compiled as part of the SGP99 experiment and the VIC land surface model
provided the surface temperatures as part of the North American Land Data
Assimilation System (NLDAS) model output. At the same time, the meteorology
background during the experimental period was excellent for testing the retrieval over
a large dynamic range of moisture conditions.
LSMEM retrieved soil moisture, validated by field observations at the three
main field sites (CF, ER, and LW), have RMS errors in volumetric soil moisture of
37
2.8%, 2.3%, and 1.8% respectively. Compared to other microwave soil moisture
retrieval algorithms, the LSMEM performs well (Jackson et al, 1999). This encourages
further application of this physical model in retrieving soil moisture from space-borne
platforms such as AMSR- E.
To test out the potential of applying hydrological modeling to represent spatial
heterogeneity within the footprints of coarse resolution spaceborne retrievals, the
LSMEM model was run with interpolated Oklahoma Mesonet surface temperature
observations. The validated results by field observations at CF, ER, and LW sites,
have RMS errors in volumetric soil moisture of 3.1%, 2.6%, and 2.0% respectively.
This shows that using a LSM- based surface temperature provides accuracy
comparable to using interpolated temperatures from a dense operational network. It
further supports the development of offline land data assimilation systems and their
data products for applications beyond initial surface conditions for weather prediction
models. Since networks of the density of the Oklahoma Mesonet are unavailable at
continental to global scales, the use of LSM-based surface temperatures for satellite
soil moisture retrievals is recommended.
The results presented here offer support that the LSMEM algorithm and
approach should work well for satellite-based measurements of microwave brightness
temperatures. Because of the low resolution of these sensors, it remains a challenge to
determine the most effective way of combining higher resolution soil, vegetation and
surface temperature data to retrie ve soil moisture, and for strategies for downscaling
either through active sensors or model-based data assimilation. An additional
challenge is to validate satellite products, when significant scale-disparity exists
38
among the point-scale ground measurements, LSM-based estimates and satellite-based
retrievals.
The SGP99 retrieved soil moisture fields developed in this study have been
made available to the community through the SGP99 data center
(ftp://daac.gsfc.nasa.gov). The retrieved ESTAR soil moisture products can be
compared with soil moisture products derived from C-band and X-band radiometers,
whose penetration depth is less, and sensitivity to vegetation is greater, than at L-band.
During SGP99, these higher frequency products include soil moisture from the
airborne PSR C-band passive radiometer and the satellite X-band TMI radiometer.
Intercomparison studies among L, C and X bands are important due to the launch of
the Advanced Microwave Scanning Radiometer on board NASA Aqua platform
(AMSR-E) and NASDA ADEOS-II, which includes both C and X bands as well as the
X-band on TMI, which has flown since 1997 (Wood et al., 2003), and the anticipated
L-band sensor on the Soil Moisture Ocean Salinity (SMOS) satellite.
39
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46
Table 2.1 SGP99 satellite observing systems, aircraft remote sensing instruments,
ground data collection, and regional networks (details are available from
http://hydrolab.arsusda.gov/sgp99/sgp99b.htm)
Aircraft observations
Measurement
Passive radiometer (7.3 GHz)
Passive radiometer (1.4 GHz)
Passive radiometer(1.4 and 2.7
GHz);
Active radar (1.2 and 3.1GHz)
Ground measurements
Platform
Measurement
Soil moisture
Gravimetric
Soil and surface temperature
Infrared thermometers (IRT)
Soil properties
Bulk density, roughness
Vegetation properties
Land cover type
Vegetation water content
Surface heat fluxes
Eddy correlation estimates of
latent, sensible and ground heat
flux
Regional meteorological networks
Platform
Measurement
Oklahoma Mesonet
Air temperature, soil
temperature, soil moisture,
wind speed
ARM CART
Radiometric observations,
wind, temperature and
humidity sounding systems;
Platform*
PSR
ESTAR
PALS
ARS Micronet
Bowen ration, eddy correlation,
surface meteorology
observation, soil temperature
and moisture.
rainfall, relative humidity, air
temperature, solar radiation,
soil temperature
Frequency during SGP99
July 8, 9, 11, 14, 15, and 19
July 8, 9, 14, 15, 19, and 20
July 8, 9, 11, 12, 13, and 14
Frequency during SGP99
July 8 to July 20
July 8 to July 20
Once in fields
Once in fields
Once in fields
Continuously, in four fields
in Little Washita area
Frequency during SGP99
Every five minutes
Continuously, at the
ARM/CART Central
Facility site.
Little Washita, every 5
minutes for climate data, 15
minutes for soil
temperature
SSM/I: Special Sensor Microwave Imager; TMI: TRMM Microwave Imager; Landsat TM: Landsat Thematic
Mapper; AVHRR: Advanced Very High Resolution Radiometer; GOES: Geostationary Operational Environmental
Satellites; PSR: Polarimetric Scanning Radiometer; PALS: Passive and Active L and S Band System.
47
Table 2.2 Land cover classification statistics over SGP99 experiment region
Land cover classification
%
alfalfa
1.7
bare soil
8.1
corn
2.3
pasture grazed
45.1
legume
1.2
pasture ungrazed
8.6
trees
7.4
urban
3.5
water
1.0
wheat stubble
6.9
bare ground w/wheat stubble
6.9
bare ground w/green vegetation.
3.0
shrubs
3.8
sand bars and quarries
0.3
outcrops
0.3
48
Table 2.3 Land cover classification for full sampling sites at CF, ER, and LW
Site ID
Land Cover
Estimated
NDVI
Vegetation
water
content
Soil classification
Bulk
Density
Roughness
Estimated
vegetation
structure
parameter
( g / cm 3 )
( Kg / m 2 )
CF-04
Winter wheat
0.22
0.39
Silt loam
1.23
0.31
0.6
CF-05
Winter
wheat*
0.25
0.44
Silt loam
1.26
0.30
0.6
ER-01
Rangeland
0.57
1.00
Silt loam
1.29
0.30
0.5
ER-05
Rangeland
0.55
0.96
Silt loam
1.29
0.30
0.5
LW-03
Rangeland
0.49
0.86
Fine sandy loam
1.29
0.30
0.5
LW-04
Rangeland
0.52
0.91
Fine sandy loam
1.27
0.30
0.5
LW-05
Rangeland
0.48
0.84
Fine sandy loam
1.28
0.30
0.5
LW-12
Rangeland
0.50
0.88
Loam
1.29
0.30
0.5
LW-13
Rangeland
0.37
0.65
Loam
1.28
0.30
0.5
LW-21
Winter
wheat*
0.26
0.46
Silty clay*
1.20
0.30
0.6
LW-22
Winter wheat
0.15
0.26
Silty clay*
1.24
0.30
0.6
LW-23
Winter wheat
0.31
0.54
Silty clay*
1.21
0.34
0.6
49
Sensor information
(Incident angle, frequency)
Atmospheric forcing
State variables
(vegetation temperature,
and effective soil
temperature)
Initial soil
moisture
Inputs to LSMEM
LSMEM
Parameters
(soil texture, soil roughness, soil
bulk density, vegetation water
content, vegetation structure
parameter)
Adjust controlled
soil moisture
Predicted brightness
temperature ( TˆB )
Observed brightness
temperature ( TB )
| TˆB − TB |< ε
No
Yes
Final soil moisture
Figure 2.1 Flow chart of the LSMEM soil moisture retrieval algorithm.
50
Figure 2.2 Sample Observed total daily precipitation on July 10, 1999 over the SGP99
area based on NESDIS stage IV radar-gage precipitation products
51
Figure 2.3 Horizontal component of ESTAR observed brightness temperature on July
8, July 9, July 14, July 15, July 19, and July 20
52
315
a)
VIC (K)
310
305
300
295
290
290
295
300 305 310
ARM/CART (K)
o
soil temperature ( C)
40
35
Mesonet (5cm)
VIC (0-10cm)
b)
30
25
20
15
10
5
0
-5
Jan-1998
Apr-1998
Jul-1998
Oct-1998
Feb-1999
40
o
soil temperature ( C)
315
35
May-1999
Aug-1999
Mesonet (25cm)
VIC (10-40cm)
c)
30
25
20
15
10
5
0
-5
Jan-1998
Apr-1998
Jul-1998
Oct-1998
Feb-1999
May-1999
Aug-1999
Figure 2.4 (a) VIC surface temperature validation compared to all ARM/CART solar
and infrared observing systems (SIROS) sites for July, 1999; (b) and (c) the time
series of soil temperatures at different layers from VIC and Oklahoma Mesonet
observations at Apache (34.91° N, 98.29°W)
53
Figure 2.5 (a) Sand fraction and (b) clay fraction for the SGP99 region.
54
Figure 2.6 (a) Surface roughness, (b) bulk density, (c) NDVI and (d) vegetation
parameter b for the SGP99 region
55
Figure 2.7 LSMEM retrieved soil moisture from ESTAR images during SGP99.
56
0
10
0
0
10
20
30
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Figure 2.8 Validation results for full sampling sites during SGP99.
57
40
Retrieved Soil Moisture (%)
CF
ER
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40
Figure 2.9 Validation of the averaged soil moisture for the CF, ER, and LW areas.
58
40
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Observed Soil Moisture (%)
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Figure 2.10 Raw data for each of the sample locations in field LW12 during days with
ESTAR imaging.
59
1/4 degree retrieved soil moisture (%)
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1/8 degree retrieved soil moisture (%)
Figure 2.11 0.25° retrieved soil moisture as compared to soil moisture averaged from
0.125° retrieved soil moisture over the ESTAR observed region during SGP99
60
Chapter 3
Using TRMM/TMI to Retrieve Surface Soil Moisture over the Southern United
States from 1998 to 2002
Abstract
Passive microwave remote sensing has been recognized as a potential method
for measuring soil moisture. Combined with field observations and hydrological
modeling brightness temperatures can be used to infer soil moisture states and fluxes
in real-time at large scales. However, operationally acquiring reliable soil moisture
products from satellite observations has been hindered by three limitations: suitable
low-frequency passive radiometric sensors that are sensitive to soil moisture and its
changes; retrieval model (parameterization) that provides operational estimates of soil
moisture from top-of-atmosphere (TOA) microwave brightness temperature
measurements at continental-scales; and suitable, large-scale validation data sets. In
this chpater, we retrieve soil moisture across the southern United States using
measurements from the Tropical Rainfall Measuring Mission (TRMM) Microwave
Imager (TMI) X-band (10.65 GHz) radiometer with a land surface microwave
emission retrieval model (LSMEM) developed by the authors. Surface temperatures
required for the retrieval algorithm were obtained from the Variable Infiltration
Capacity (VIC) hydrological model using North American Land Data Assimilation
System (NLDAS) forcing data. Because of the limited information content on soil
61
moisture in the observed brightness temperatures over regions characterized by heavy
vegetation, active precipitation, snow, and frozen ground, quality control flags for the
retrieved soil moisture are provided. The resulting retrieved soil moisture database
will be available through the NASA Goddard Space Flight Center Distributed Active
Archive Center (NASA/GSFC DAAC) at a 1/8° spatial resolution across the southern
U.S. for the 5-year period of January 1998 through December 2002. Initial
comparisons with in-situ observations obtained from the Oklahoma Mesonet resulted
in seasonal correlation coefficients exceeding 0.7 for half of the time covered by the
data set. The dynamic range of the satellite derived soil moisture data set is
considerably higher compared to the in-situ data. The spatial pattern of the TMI soil
moisture product is consistent with the corresponding precipitation fields.
3.1 Introduction
Soil moisture is one of the key variables for studying the terrestrial water and
energy cycles because of its role in controlling the partitioning of available radiative
energy into latent and sensible heat, and controlling the partitioning of precipitation
into infiltration and runoff. Soil moisture integrates precipitation and evaporation over
periods of days to weeks and introduces a significant element of memory in the
atmosphere/land system. Soil moisture observations at large scales are critical for a
variety of applications, including assimilation into weather forecasting (4DDA
models), crop and drought monitoring, for initial conditions in flood forecasting, and
to quantify the Earth’s water budget. There is strong climatological and modeling
62
evidence that the fast recycling of water through evapotranspiration and precipitation
is a primary factor in the persistence of dry or wet anomalies over large continental
regions during summer (Koster and Suarez, 2004). On this account, soil moisture is
the most significant boundary condition that controls summer precipitation over the
central U.S. and other large mid-latitude continental regions, and essential initial
information for seasonal predictions (Koster et al., 2000, 2003, 2004; Salvucci et al.,
2002).
To date there have been very few in situ soil moisture observing systems that
could provide direct estimates of regional or continental soil moisture fields. Even in
seemingly large networks, precise in situ measurements of soil moisture are sparse,
often infrequently measured at a single point, which is only representative of a small
area. The Oklahoma Mesonet system is amongst the largest networks, since 1996 a
total number of 114 automated stations have been set up to measure soil moisture
every 30 min (http://www.mesonet.org/). Robock et al. (2000) describe their global
soil moisture data bank, which archives much of the available soil moisture
measurements from a disperse set of networks. Soil moisture measurements at
regional to continental scales could be used to address the following science questions,
that are central to research programs like the World Climate Research Program
(WCRP) Global Energy and Water Experiment (GEWEX), regional studies like the
North American Monsoon Experiment (NAME), or agency research programs such as
those in NASA related to the water cycle (see
http://earth.nasa.gov/visions/researchstrat/). These science questions include;
•
Is there a feedback mechanism between soil moisture and atmospheric boundary
63
layer that can be verified?
This has been explored somewhat by Betts et al. (2000, 2003) and Berbery et al.,
(2003) with modeled data and assumptions, but needs observations for more definitive
results.
•
Do climate and weather prediction models accurately represent the land surface
partitioning of precipitation into infiltration and runoff? Can they be improved by
the assimilation of surface soil moisture observations?
The North American Land Data Assimilation System (NLDAS) (Mitchell et al.,
2004) has evaluated how well land surface models compare to observed soil moisture
(Robock et al., 2003), while Berbery et al. (2003) has investigated the relationship
between soil moisture and atmospheric processes from the coupled Eta model.
•
Can spatial and temporal surface soil moisture observations provide new
information on soil hydrological processes and properties?
Investigations have used soil moisture data to estimate soil properties (Hollenbeck
et al., 1996), hydrologic processes (Jackson, 2002; Salvucci 2001; Saleem and
Salvucci 2002) and land atmospheric coupling (Betts, 2000.). To date, scientific
investigations related to these questions have often relied on model-based soil
moisture fields, or on limited in-situ data.
For remote sensing of soil moisture, microwave frequencies have some
distinctive advantages over other spectral regions (Schmugge et al., 2002).
Microwave emission at frequencies below about 10 GHz can penetrate through grass
and short crops, and is essentially unaffected by atmospheric water vapor. Also, the
top of atmosphere microwave brightness temperature measurement is independent of
64
sun illumination. Soil moisture can be retrieved from the microwave brightness
temperature (TB) because of the strong relationship between TB and wet soil
emissivity: Increased soil moisture leads to a decrease in soil emissivity and
consequently observed brightness temperature. The sensitivity of the relationship is
frequency dependent, with the lower the frequency, the higher the sensitivity to soil
moisture. Lower frequencies are also less affected by vegetation and surface
roughness. Within the same frequency, horizontally polarized emission is more
sensitive to soil wetness as compared to the vertical component.
It has been shown that low frequency passive microwave data have the
potential to improve operationally produced soil moisture fields from numerical
weather prediction models (e.g. Drusch et al., 2004; Seuffert et al., 2004). The
challenge is whether such remotely sensed soil moisture data sets can be achieved with
sufficient accuracy and reliability from space on the continental scale for observation
periods exceeding typical field experiments. For the Tropical Rainfall Measuring
Mission (TRMM) Microwave Imager (TMI), the sensor characteristics include a dualpolarized passive radiometer for frequency of 10.65 GHz, with a spatial resolution of
38 km, that measures microwave emissions over the top ~0.5 cm surface depth. The
TMI has been in operation since December 1997, and its 10.65 GHz (X-band)
radiometer is better than previous instruments in terms of radiometric frequency,
repeat coverage (where available) and resolution (38 km). Before TMI, low frequency
passive microwave, space-borne sensors included a 1.4 GHz (L-band) sensor with a
110 km footprint on Skylab (Jackson et al., 2004), and a 6.63 GHz (C-Band) sensor on
the Scanning Multichannel Microwave Radiometer (SMMR), with a 159 km footprint,
65
from October 1978 to August 1987. More recently, the lowest frequency available
radiometric measurement was at 19.3 GHz from the Special Sensor
Microwave/Imager (SSMI), which has been a part of the U.S. Defense Meteorological
Satellite Program (DMSP) since 1987. Currently the EOS Aqua satellite, launched in
May 2002, has both 6.9 GHz and 10.65 GHz channels as part of its Advanced
Microwave Scanning Radiometer (AMSR-E), but severe radio frequency interference
(RFI) at 6.9 GHz has been detected, leaving its 10.65 GHz and TMI as the only readily
available, low frequency microwave instruments.
This chapter presents a 5-year retrieval (January 1998 through December
2002) of soil moisture from the TRMM Microwave Imager 10.65 GHz band sensor. It
is our expectation that this data set, with its accompanying data quality flags will
provide a unique data set for the research community in addressing the above, and
similar, science questions. Furthermore, this data set will assist in evaluating retrieved
soil moisture from AMSR-E.
Section 3.2 discusses the retrieval approach used in the study, and it utilizes the
Land Surface Microwave Emission Model (LSMEM) of Drusch et al. (1999). The
results of the retrievals are presented in section 3.3, with fields of soil moisture across
the southern United States between 25° and 38° north latitude for each TMI orbit.
Because of the swath width of the TMI sensor, complete coverage is not provided on
each orbit, and because of the TRMM orbit characteristics, the overpass time and time
between overpasses varies for a particular location. In fact, since this portion of the
U.S. is near the top of the TRMM orbit, locations are observed with different number
of times during a 24-hour period. Thus, we also provide a daily soil moisture field
66
where the retrieved soil moisture from each orbit (with precipitated areas masked out)
is averaged. Section 3.4 discusses sources of uncertainty in the retrieved soil
moisture, and conditions under which retrievals are not possible. Within the database
these are indicated by a series of quality control masks. The soil moisture data set is
to be available through NASA Goddard Space Flight Center Distributed Active
Archive Center (NASA/GSFC DAAC).
3.2 Methodology and Data Sources
Despite comprehensive laboratory measurements and field experiments,
knowledge of retrieval model parameters (e.g. fractional vegetation cover, vegetation
water content) and inputs on the continental scale are incomplete. Problems
associated with collecting these parameters and inputs include: (i) Vegetation
parameters vary significantly with classification and season. In contrast, available
measurements were obtained from field experiments and are limited to only a few
vegetation types (Jackson and Schmugge, 1991); (ii) Satellite sensor resolution is large
compared to the heterogeneity in the landscape. Nonlinear scaling results in the need
for ‘effective parameters’ values rather than measured physical values. (iii) Ancillary
data, specifically a source of surface temperature information, as required for
retrievals from single channel and single polarization microwave sensors are
incomplete. Although remotely sensed infrared techniques are a sufficiently accurate
source of surface temperature data at a variety of resolutions, surface temperature
products are only available under cloud-free conditions, while microwave soil
moisture retrievals are possible and desirable under cloudy conditions. In this section,
67
we review the retrieval algorithm used in this study and introduce required data
sources.
3.2.1 Land Surface Microwave Emission Model (LSMEM)
The retrieval algorithm is based on a semi-empirical model for passive microwave
brightness temperatures observed at the top of the atmosphere (TOA) as proposed by
Kerr and Njoku (1990). The LSMEM comprises a set of alternative parameterizations
for the key components, e.g. the dielectric constant of the soil, surface roughness, or
vegetation opacity (Drusch et al., 1999). A detailed description of the actual model
configuration and the components used for the TMI soil retrieval presented in this
study can be found in Gao et al. (2004). Beginning with an initial estimation of soil
moisture, the LSMEM iteratively searches for the soil moisture value that matches the
observed brightness temperature best (Gao et al., 2004). In the LSMEM formulation,
the total brightness temperature (Tb,p) is a weighted average of radiation originating
from bare soil (Tbs, p) and from vegetation covered soils (Tbv, p):
(
)
Tbv , p = Tau + e −τ at Tad + Tsky e −τ at (1 − ε p )e −2τ +
*
e −τ at {ε pTs e −τ + Tv (1 − ω * )(1 − e −τ )[1 + (1 − ε p )e −τ ]}
*
(
*
)
*
(1)
Tbs , p = Tau + e −τ at Tad + Tsky e −τ at (1 − ε p ) + e −τ at ε pTs
(2)
Tb, p = (1 − Cv )Tbs , p + CvTbv , p
(3)
In these equations, Tau and Tad denote the upward and downward contributions
from the atmosphere, Ts is the soil temperature, Tv the vegetation temperature, Tsky the
cosmic radiation, εp the rough soil emissivity, and ω* the vegetation single scattering
68
albedo. τat and τ* represent the optical depth of the atmosphere and the effective
optical depth of the vegetation. Cv is the fractional vegetation coverage. Subscript p
indicates polarization dependency in the model representation.
For continental applications, open water has to be included. The brightness
temperature of water (Tbw,p) is computed using equation (4) with εw,p being the water
emissivity and Tw the water temperature. As a result, the simulated TOA brightness
temperature has been computed from:
(
)
Tbw, p = Tau + e −τ at Tad + Tsky e −τ at (1 − ε w, p ) + e −τ at ε w, pTw
(4)
Tb, p = (1 − Cv − C w )Tbs , p + CvTbv , p + C wTbw, p
(5)
with CW the fractional coverage of water. A sensitivity test was carried out to simulate
the brightness temperatures for footprints characterized by different water fractions
and soil moisture conditions. Figure 3.1 shows the decrease in microwave brightness
temperature as the fraction of surface water within a footprint increases. A decrease is
expected because the horizontally polarized water emissivity (εw,h) can be well below
0.5 while soil emissivity (εh) at X-band normally ranges from 0.85 to 0.95. These
results demonstrate that the microwave emission contributions from water bodies must
be taken into account in order not to overestimate volumetric soil moisture.
3.2.2 LSMEM Model Resolution and Inputs
The -3dB footprint for TMI at X-band is ~38 km over the southern U.S., with
an over-sampling rate that results in adjacent footprint centers, which are
approximately 8 to 13 km apart, depending on the location within the swath and the
69
orbit. Since the supporting data base from the NLDAS project (Mitchell et al., 2004)
is produced at 1/8° spatial resolution, the TMI brightness temperatures have been resampled to the NLDAS grid using the nearest neighbor technique. Due to the over
sampling, interpolation would reduce the observed spatial variability. The LSMEM
model inputs are listed in Table 3.1. All parameters and variables have been resampled to the NLDAS grid. Figure 3.2 shows some input fields across the U.S., with
Figure 3.2h displaying one TMI overpass. The most relevant geophysical input
parameters are discussed in the following paragraphs.
1) TMI X-band brightness temperature
The TRMM satellite was launched in Nov. 1997. One of the instruments on the
satellite is TMI, a dual-polarization passive microwave conical scanning radiometer
with an incidence angle of 52.8°, which operates at 10.65, 19.4, 21.3, and 85.5 GHz.
In this study, the 10.65 GHz horizontally polarized brightness temperature has been
used to retrieve soil moisture. The TRMM orbit and sensor swath result in spatial
coverage between +/-38° latitudes. For each day, about five orbits overpass the
southern U.S. at various times (Bindlish et al., 2003).
2) Atmospheric contributions
At X-band, the atmospheric contributions (optical depth and atmospheric
emission) are comparably small with low temporal variability (Drusch et al., 2001).
Consequently, it is sufficient to apply a constant atmospheric correction for the soil
moisture retrieval presented in this study. A set of 3472 atmospheric temperature and
humidity profiles acquired from the NCEP Eta Model Location Time Series (MOLTS)
data set have been analyzed. They were collected at 56 sites within Oklahoma (34°N
70
to 38°N in latitude and –97°W to –98.5°W in longitude) during July 1999. This
region and period were used because of the large number of available MOLTS data
and because of the generally highly variable summertime humidity for which the
atmospheric affects would be most noticeable. For each of the profiles, the optical
depth and the brightness temperature of the atmosphere were calculated at 10.65 GHz,
19.35 GHz and 22.235 GHz based on the gas absorption scheme described in Drusch
et al. (2001). Averaged values for Tad and Tau from this data set were used as LSMEM
inputs for the TMI retrieval.
3) Surface roughness parameter
For this parameter there is no robust data source over large spatial domains. A
constant value of 0.3, which is typical for a medium rough surface, was selected
(Choudhury et al., 1979). The constant value does not take into account the fact that h
should scale with wavelength (Choudhury et al., 1979) and vary with surface type.
However, setting a constant value is the most widely used approach for accounting for
the effects of surface roughness on the modeled brightness temperatures (Drusch et al.,
2004). A sensitivity test over a rangeland land cover shows that 10% uncertainty in
surface roughness will result in an error of about 3% volumetric soil moisture.
4) Vegetation structure parameter and vegetation single scattering albedo
The effective optical depth of the vegetation (τ*) in equation (1) is the product
of the vegetation structure parameter (b) and vegetation water content (Wc) (Jackson
and Schmugge, 1991). The b parameter is a function of the canopy type/structure,
polarization, and wavelength. However, studies in the literature on these
71
dependencies are far from being complete. An approximate parameterization over the
U.S. was made for the current investigation by assigning b values to different
vegetation classes according to Table 1 in Jackson and Schmugge (1991). For
vegetation types without available b values (forest, woodland, and shrub), the value of
0.7 at X-band was assigned based upon Figure 4 in Jackson and Schmugge (1991).
In equation (1), the soil emission from below the canopy is affected by the
vegetation single scattering albedo (ω*). According to the literature (Pampaloni and
Paloscia, 1986; Ulaby et al., 1983), ω* varies from 0.04 to 1.0. An average value of
0.07, which is assumed to be polarization independent, was used for LSMEM model
input.
5) Water fractional coverage
Figure 3.3 shows the statistics of fractional water coverage for NLDAS grid
boxes within our study area. It has been derived from the NLDAS land cover database,
which draws from the 1-km Moderate Resolution Imaging Spectroradiometer
(MODIS) land
cover data developed at the University of Maryland (Hansen, et. al.,
2000). This data was then reprocessed so that the grid box value represents the water
fraction of a TMI X-band footprint. Although most areas have less than 1% water
coverage, 11% of the total number of grid boxes has a substantial water fraction of
more than 5%. According to Figure 3.1, if the microwave emissions from water bodies
are ignored for grid boxes with 5% fractional water, then the overestimation of the
retrieved soil moisture will be approximately 5%. Figure 3.2d shows the fraction as a
spatial map across the U.S.
6) Soil texture
72
Soil texture information (sand fraction, clay fraction, and bulk density) is
required for calculating the dielectric constant of wet soils. These data are obtained
from the state soil geographic database (STATSGO) (Miller and White, 1998) and
were re-sampled to the 1/8° grid. Both, the water fraction and the soil parameters (see
fig 2a-d) are spatially heterogeneous but invariant with time.
7) Vegetation fractional coverage and vegetation water content
The monthly vegetation fractional coverage is available from the NLDAS
database, and was calculated from the normalized difference vegetation index (NDVI)
using (Chang and Wetzel, 1991):
1.5 ( NDVI − 0.1),
f veg = 
3.2 ( NDVI ) − 1.08,
NDVI ≤ 0.547
NDVI > 0.547,
(6)
One example of vegetation fractional coverage is plotted in Figure 3.2e.
Vegetation water content (Wc), which contributes to vegetation optical depth
(τ*), was derived from the land cover classification and monthly leaf area index (LAI),
using MODIS C-4 LAI available through Boston University. The vegetation water
content was computed using general relationships between LAI, foliar and stem
biomass, and estimates of their relative water content (Rodell et al., 2005). The
vegetation water content for July is shown in Figure 3.2f.
8) Surface temperature
As explained in the introduction to section 3.2, the retrieval algorithm used in
this chapter is based on a single frequency, single polarization. Thus, physical surface
temperatures are required. To avoid the constraints of only clear sky retrievals (i.e. if
surface temperatures derived from infrared measurements would be used), the surface
73
temperatures that will be used for the retrieval is based on the VIC land surface
scheme (Liang et al., 1994; Liang et al., 1999). Mitchell et al. (2004) provides a
comparison among NLDAS modeled surface temperatures, estimates based on GOES,
and instruments deployed as part of the Atmospheric Radiation Measurement, Cloud
and Radiation Test bed (ARM/CART) facility in the Southern Great Plains region of
the U.S. This comparison showed absolute bias between the models and the GOES or
ARM/CART data in the range of 0.3 to 6.5 K and RMS difference around 3.5 K. For
VIC, the absolute bias ranged from 0.5 to 2.8 K depending on the season and the RMS
of the difference ranged from 3.3 to 4.3 K. A sensitivity test over rangeland land cover
shows that 1 K error in surface temperature results in an error about 1% in the
retrieved volumetric soil moisture. , The NLDAS system is run hourly and the
surface temperature that matched the TMI overpass times was used in the retrievals for
both the soil temperature and vegetation temperature because the VIC LSM only has a
single surface layer (see Figure 3.2g for an example field).
3.3 Results
3.3.1 Surface Soil Moisture Retrieved for Each TMI Orbit
Using the LSMEM model and the parameters and inputs described in section
3.2, soil moisture fields were retrieved on an orbit overpass basis from January 1, 1998
through December 31, 2002. As described earlier, up to five overpasses may occur
over the southern U.S. on any particular day. Although the overpass time varies during
the day, the patterns and retrieved soil moisture values from the different orbits are
74
consistent. Data quality masks, which help to indicate locations where we have low
confidence in the retrieved product, will be discussed in section 3.4.
3.3.2 Daily Surface Soil Moisture Composites
For many hydrological applications (e.g. providing initial conditions for stream
flow forecasting, crop monitoring, etc.) soil moisture information is needed on a daily
basis. Since the TRMM orbits cover different portions of the study area, a daily
composite was made by combining the retrieved soil moisture values from all the
overpasses occurring during a day. When multiple overpasses occurred for a grid box,
its daily average was computed from the multiple retrieved values.
Figure 3.4 presents a one-week period (July 8th to July 14th, 1999) of the daily
change in estimated soil moisture (dayn – dayn-1) compared to the daily precipitation
from NLDAS forcing during dayn-1. The main conclusions from this comparison are:
1) The soil moisture changes are hydrologically consistent with the precipitation in
most areas except for portions of the southeastern U.S.; 2) The soil moisture dry-down
in areas without precipitation is clearly evident; and 3) The effects of large-scale
irrigation can be seen in areas like the central valley in California, where high values
of soil moisture are observed, without rainfall occurring.
3.4 Quality Control Masks
We recognize that there are conditions under which soil moisture cannot be
accurately retrieved due to the X-band sensor sensitivity, weather conditions, or
surface features. In this section, these error sources are analyzed and masks
75
developed for quality control. This allows the users of the data set to access the final
soil moisture product and to apply the quality control masks.
3.4.1 Precipitation Mask
At X-band, the sensor observed brightness temperature is affected by falling
precipitation (liquid or solid) (Tsang et al., 1977). To avoid the complex impact of
falling precipitation, retrievals for grid boxes where it is precipitating were removed
using hourly Stage IV precipitation data from the NLDAS data system. The mask
uses a 1mm threshold for the hour of the satellite overpass to determine whether it was
precipitating. This mask is applied to the orbit retrievals.
3.4.2 Vegetation Sensitivity Mask
In analyzing the retrieved soil moisture, we noted that in some regions,
particularly in the southeastern U.S., the soil moisture dynamics are not consistent
with the precipitation dynamics. Specifically, most of these areas have consistently
low soil moisture values (less than 10% most of the time) with little variability. These
results warranted further investigations.
To do the analysis, the 10.65 GHz polarization ratio (Tb,V/Tb,H) was studied.
This ratio is almost independent of surface temperature and thus its soil moisture
sensitivity mainly depends on land cover conditions. The monthly average of the ratio
for July 1999 is plotted in Figure 3.5a and the standard deviation is presented in Figure
3.5b. These images indicate that the polarization ratios for the ‘consistently dry’ areas
in Figure 3.5 are low (high Tb,H) and vary slightly.. The low variability confirms that
76
the dynamics of the precipitation (and of the subsequent soil moisture) is not being
captured in the brightness temperatures or polarization ratio and thus the soil moisture
cannot be retrieved accurately.
A comparison between the above areas and a vegetation classification shows
that the areas of low polarization sensitivity and dynamics are over forested regions.
In forested regions the vegetation optical depth is large, and causes a high TOA
brightness temperature with little polarization (Ulaby, et. al., 1986). Consequently,
over the forests, the soil microwave 10.7 GHz emission cannot penetrate the canopy
and the vegetation brightness temperatures that are observed by the satellite sensor are
high due to the high emissivity of the forest canopy (Ulaby et al., 1986). In the
absence of vegetation information, the retrieval model would estimate consistently low
soil moisture from the constantly high observed brightness temperature. A reasonable
consistency is also observed between the polarization pattern (Figure 3.5a) and the
vegetation water content map (Figure 3.2f). Accordingly, it is our assessment that soil
moisture retrievals for areas with heavy vegetation are not reliable and should be
masked out. As an aside, the emission from heavy vegetation also suggests that subgrid, small-scale patches of large trees, if ignored as is the usual practice, will tend to
increase the average brightness temperature in a scene resulting in a lower mean
retrieved surface moisture. This may explain part of the differences between the mean
retrieved soil moisture and observation in Figure 3.10.
Since vegetation mass varies seasonally, the polarization ratio sensitivity
analysis was computed for each month. The results for January 1999 are shown in
Figure 3.6, and a comparison of the Figures 3.5a and 3.6a shows an expanded area
77
with potentially good retrievals in January when compared to July. We have used a
monthly averaged polarization ratio of below 1.02 and a standard deviation less than
0.005 to determine areas where we feel the vegetation effects prevent reliable
retrievals.
3.4.3 Snow Cover, Frozen Soil and Surface Water Contamination Mask
The current version of the LSMEM does not consider the emission from snowcovered or frozen soil, and cannot be used to retrieve soil moisture under these
conditions. Basically, when the soil is frozen the algorithm for calculating wet soil
dielectric constant no longer holds. Thus, a daily frozen soil and snow cover
classification dataset, provided by the National Snow and Ice Data Center (NSIDC)
(Zhang et al., 2003), was reprocessed to the NLDAS 1/8° grid and used as the mask.
This data set, based on processing SSM/I data, also identifies coastal areas (including
those of large lakes) where water contamination degrades any retrievals. These areas
are masked out in our TMI data set. Figure 3.7 presents a image of the snow, frozen
soil and water contaminated areas for January 1, 1999.
3.4.4 Data Availability
Figure 3.8 presents an example (for January 1, 1999) of the retrieved soil
moisture with all areas screened out where the retrievals are suspect. In order to
provide a synoptic description of the data availability over the five years, Figure 3.9
presents the percentage of days within a season when the retrieved soil moisture
passed all quality flags. In the summer, the major factor influencing the retrieved soil
78
moisture is heavy vegetation; in the winter, the major factor is snow cover and frozen
soil. A full description of the available data product is presented in Appendix A.
3.5 Initial Comparisons with Oklahoma Mesonet in-situ Measurements
Historically the ‘validation’ of remote sensing products consisted of
comparisons to ground-based measurements with the goal of having the former match
the latter. This approach to validation needs to be revised, since too often the groundbased observations are taken at different spatial and temporal scales than the remote
sensing measurements rendering them inappropriate for direct comparison.
Nonetheless, it seemed appropriate that some comparisons to in-situ be provided here.
The Oklahoma Mesonet (http://www.mesonet.org ) is an operational
environmental monitoring network that consists of 114 stations, with at least one in
each of the 77 Oklahoma counties. From 1998, soil moisture point values at 72
stations at depths of 5, 25, 60 and 75 centimeters are available. The volumetric soil
moisture is estimated using a calibrated change in soil temperature over time after a
heat pulse is introduced (heat dissipation sensor).
Figure 3.10 presents the Oklahoma Mesonet and TMI retrieved soil moisture
for the period June – October 2002, with Figure 3.10a comparing the retrieved soil
moisture from the El Reno Mesonet site with the corresponding grid box and Figure
3.10b comparing the average ‘Mesonet-wide’ soil moisture from the reporting sites
with the average TMI soil moisture of the grid boxes overlaying those sites. Also
shown is the El Reno (Figure 3.10a) or Mesonet average (Figure 3.10b) daily
precipitation values. Qualitatively the comparison show the following: 1) In general at
79
both scales, TMI and the Oklahoma Mesonet soil moisture show good responses to
precipitation, while there are a couple of rainfall events captured by TMI but not in
Mesonet at El Reno: e.g. rainfall at the end of June and around the July 20th; 2) TMIretrieved soil moisture has a lower mean value and larger dynamic range and a faster
dry-down, which can be attributed to its shallower (~0.5-cm) sensing depth as
compared to the Mesonet 5-cm depth; and 3) The El Reno data shows that the sensor
appears to have a lower bound on reported soil moisture of about 22%, and that
moisture saturation occurs in the Mesonet but not in the TMI-retrieved values.
The daily average of the 72 Mesonet sites and TMI data for the grid overlaying
the Mesonet site was computed to obtain a ‘Mesonet-wide’ daily average soil moisture
value. This provides a regional daily soil moisture estimate that should be more
consistent with the observing scale of TMI. Basically the comparison between the
Mesonet-wide and TMI soil moisture times series displays the same characteristics as
the comparison for El Reno, except that the time series are ‘damped’ due to the
averaging of the 72 sites.
Table 3.2 provides for each year and over the 5-year data set seasonal statistics
for both the Mesonet-wide average (OK_M) and for the TMI averaged (TMI) soil
moisture time series. These statistics include means, coefficients of variation and
correlation between OK_M and TMI. Table 3.2 confirms the low variability in the
Oklahoma Mesonet data, whose seasonal coefficients of variation varies from a low of
0.018 in the DJF season to a high of 0.045 in JJA, with MAM being 0.030 and SON
being 0.040. For TMI these corresponding seasonal statistics are 0.15 (DJF), 0.20
(MAM), 0.21 (JJA) and 0.18 (SON). The correlation between the Mesonet-wide soil
80
moisture and TMI average shows a strong seasonal trend as well as large inter-annual
variability. The seasonal trend has the lowest correlation in winter (0.41 for DJF) and
highest in the autumn (0.74 in SON). It is encouraging that for the three non-winter
seasons, the correlations are greater than 0.50 for all years, with the autumn (SON)
being higher than 0.69. This shows a remarkable correlation between the two data sets
whose observing techniques and scales are so different, and between two data sets that
may appear at first glance are not comparable. There is some concern regarding the
large inter-annual variability in the correlations, which will require further
investigation. In a similar manner, the correlations between the monthly soil moisture
anomalies (monthly soil moisture subtracted from its monthly average from the five
years) were computed between TMI and Mesonet as 0.78, which confirms that at the
monthly temporal scale they co-vary well. Similar correlations between the Mesonet
monthly rainfall anomalies and Mesonet (TMI) soil moisture anomalies resulted in
correlations of 0.68 (0.54), again demonstrating the good correspondence between the
TMI retrieved soil moisture and Mesonet soil moisture. From these evaluations, we
conclude that the two data sets are comparable.
3.6 Summary
This chapter describes the retrieval of soil moisture across the southern U.S.
from TRMM/TMI X-band brightness measurements using the LSMEM of Drusch et
al. (1999), augmented by including microwave emissions from surface water bodies.
Determining the retrieval model parameters such that quasi-operational retrievals can
be obtained is important if routine estimates are to be retrieved. The chapter describes
81
the available sources of information from which these parameters can be estimated, as
well as the reliability of the data. For data such as soil texture, extensive databases are
available for the U.S. For parameters such as the soil roughness parameter or the
vegetation single scattering albedo, representative values were used based on studies
and field measurements reported in the literature. Some parameters and inputs, such
as the land surface temperatures and atmospheric microwave contribution to the TOA
measurements were derived from other models. In the case of land surface
temperature, this allowed the retrieval of soil moisture under cloudy conditions when
satellite-IR based estimates are unavailable. The accuracy of surface temperatures
(Mitchell et al., 2004) is sufficient for their use in the soil moisture retrieval algorithm.
Finally, some parameter values are calculated from other remote sensing products,
such as monthly vegetation water content and monthly vegetation fractional coverage.
For this investigation, all these inputs were re-sampled to 1/8° grids to be consistent
with the NLDAS data assimilation data system.
Using the LSMEM retrieval model, a five year soil moisture dataset for each
TMI orbit across the southern U.S. was derived, and is provided as the Level 1 data
product. To make the data more suitable for general applications, a Level 2 product
consisting of daily fields compiled using the Level 1b data, with averaged soil
moisture values for locations with multiple TMI overpasses. The highest quality data
product is the Level 3 product, in which areas of poor retrievals due to heavy
vegetation, snow cover, frozen ground, and water contamination are masked out. In
analyzing the soil moisture sensitivity over various vegetation types, we conclude that
82
only forested regions resulted in failed retrievals, which is a better result than we
initially expected.
Initial comparisons with soil moisture estimates from the Oklahoma Mesonet
heat dissipation sensors, averaged across 72 Mesonet sites, shows that the retrieved
TMI soil moisture product is comparable to the in-situ estimated soil moisture values,
with seasonal correlations as high as 0.86, and with an average seasonal correlation of
0.59. Comparisons during the DJF season were poorest and SON the best in term of
overall seasonal compatibility. Though evaluating remote sensing results is rather
challenging, considering the different scales, representative depths of the two datasets,
the preliminary comparisons indicate the TMI retrievals to be encouraging.
The TMI X-band retrieved soil moisture described in this chpater serves as a
long-term, continental-scale data product available to the community for use in
weather and climate studies. Its use by the community will help address science
questions central to global water and energy studies, will provide experimental data to
test soil moisture data assimilation systems and to explore the usefulness in water
resource applications like flood forecasting and agriculture. Through such use, the
community will better understand the potential uses for soil moisture products based
on NASA/AQUA’s AMSR-E and the planned Hydrosphere State (HYDROS) L-band
microwave mission.
83
Apendix A:
Available Data Products.
The following retrieved soil moisture and related data quality products are
being provided to the NASA/GSFC DAAC:
•
Level 1: Level 1 are the retrievals for each orbit, with Level 1a being the soil
moisture retrieved for each TMI overpass, using the LSMEM (Gao et al., 2004),
without consideration of the retrieval quality considerations discussed in section 3.4.
Level 1b is the same as level 1a but with the precipitation masks applied. Size of each
is ~1.9 GB.
•
Level 2: Daily averaged fields using Level 1 data with averaged soil moisture
values for locations with multiple TMI overpasses on that day that passed the active
precipitation quality flag (see section 3.4.1. Size ~377 MB.
•
Level 3: Daily averaged, quality screened fields. Level 2 data fields with areas
screened out due to retrieval concerns from heavy vegetation, snow cover and frozen
soil (see sections 3.4.2 and 3.4.3). Size ~377 MB. The quality control data for each
condition (heavy vegetation, snow cover, frozen soil and water contamination) is
provided. The size for the each heavy vegetation masks is 207 KB, and there is one
for each month. The size for the snow cover, frozen soil and water contamination
mask files is 377 MB.
The data format is binary Little-Endian, 4-bytes for each grid box, 464
columns by 112 rows. Areas masked out have a value of 0; areas where there are no
TMI retrievals have a value of 9.999×e+20. All retrieved soil moisture values are
greater than 0 so no conflict with the mask files will occur.
84
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89
Table 3.1 LSMEM model inputs
Input class
Parameter/variable
Value
Sensor
information
Incident angle
52.8°
10.65 GHz
TMI
observation
Horizontal Tb
Orbit data
Atmospheric
Optical depth
0.014
contribution
Emitted Tb
6.0K
Sand fraction, clay
fraction and soil
bulk density
Spatially
distributed
constants
Soil surface
roughness
0.3
parameters
State
variable
Reference
Jackson and Hsu, 2001
Modeling frequency
Surface
Data source
USDA
Bindlish et
al., 2003
MOLTS/radiatvie Drusch,
transfer
2001
STATSGO
Miller and
White,
1998
Choudhury et al., 1979
Vegetation coverage
Spatially
distributed,
monthly
NLDAS
greenness
fraction (based
on NDVI)
Chang and
Wetzel,
1991
Vegetation water
content
Spatially
distributed,
monthly
Calculated results Rodell et
based on MODIS al., 2005
LAI and land
cover types
Water coverage
Spatially
distributed
constants
MODIS
classification
Vegetation structure
parameter
Constants
based on
classification
Hansen,
et. al.,
2000
Jackson and Schmugge, 1991
Vegetation single
scattering albedo
0.07
Average value according to
Pampaloni and Paloscia, 1986;
Ulaby et al., 1983
Surface temperature
Spatially
distributed,
hourly
NLDAS/VIC
output
90
Liang et
al., 1994;
1999
Table 3.2 Seasonal and annual statistics for Oklahoma Mesonet and TMI retrieved soil
moisture averaged over the 72 Mesonet sites.
1998
1999
2000
2001
2002
Mean soil
moisture
(OK_M)
29.4
30.9
29.5
27.9
30.9
27.7
Coefficent of
Variation
(OK_M)
0.018
0.008
0.021
0.029
0.010
0.024
Mean soil
moisture
(TMI)
12.2
13.9
11.9
10.1
14.1
11.1
1998
1999
2000
2001
2002
28.5
27.8
29.1
28.6
28.7
28.5
0.030
0.035
0.034
0.032
0.029
0.021
14.5
14.9
15.6
13.5
14.8
13.7
0.20
0.23
0.18
0.18
0.17
0.22
0.60
0.74
0.62
0.48
0.59
0.58
1998
1999
2000
2001
2002
24.6
22.6
25.5
25.9
23.8
25.3
0.045
0.034
0.047
0.066
0.039
0.039
11.9
10.1
11.4
12.3
11.5
14.3
0.21
0.22
0.21
0.18
0.22
0.21
0.62
0.42
0.86
0.52
0.76
0.56
1998
1999
2000
2001
2002
25.5
27.0
24.5
25.1
24.9
26.1
0.040
0.041
0.054
0.031
0.038
0.035
11.9
13.2
9.5
12.0
10.5
14.2
0.18
0.22
0.18
0.16
0.14
0.19
0.74
0.75
0.80
0.73
0.69
0.71
DJF
MAM
JJA
SON
91
Coefficent
of Variation Correlation
(TMI)
(OK_M, TMI)
0.15
0.41
0.17
0.75
0.12
0.70
0.13
0.24
0.20
0.24
0.12
0.13
300
0% water
5% water
10% water
15% water
Tb (K)
280
260
240
220
200
10
20
30
Volumetric soil moisture (%)
40
Figure 3.1 LSMEM output sensitivity to water fraction at the surface temperature of
288K
92
Figure 3.2 Examples of LSMEM model data and inputs.
93
0% water: 11113 pixels
>5% water: 1226 pixels
4~5% water: 202 pixels
3~4% water: 312 pixels
2~3% water: 501 pixels
1~2% water: 997 pixels
0~1% water: 6800 pixels
Figure 3.3 Fractional area covered by water for the grid boxes within the study area
94
Figure 3.4 Daily total precipitation (mm) (left column) and the second-day soil
moisture increment (%) (right column) from July 8th to July 14th, 1999
95
Figure 3.5 TMI 10.7 GHz polarization ratio for July 1999 over the southern U.S. a)
monthly average TbV/TbH; b) monthly standard deviation of TbV/TbH.
96
Figure 3.6 TMI 10.7 GHz polarization ratio for January 1999 over the southern U.S.
a) monthly average TbV/TbH; b) monthly standard deviation of TbV/TbH.
97
Figure 3.7 Mask for frozen ground (dark gray), snow-covered (gray), and water
contamination (bright gray)
98
Figure 3.8 Retrieved surface volumetric soil moisture (%) for January 1, 1999 with all
quality masks applied
99
Figure 3.9 Percentage of time by season that the retrieved soil moisture passed all data
quality flags; a) MAM, b) JJA, c) SON, and d) DJF.
100
Volumetric soil moisture (%)
40
50
40
30
30
20
20
10
10
0
2002-06-1
2002-07-1
2002-08-1
2002-09-1
2002-10-1
0
b)
60
50
40
60
daily precipitation
TMI soil moisture
Mesonet soil moisture
50
40
30
30
20
20
10
10
0
2002-06-1
2002-07-1
2003-08-01
2002-09-1
2002-10-1
0
Daily total precipitation (mm)
Volumetric soil moisture (%)
50
60
daily precipitation
TMI soil moisture
Mesonet soil moisture
Daily total precipitation (mm)
a)
60
Date
Figure 3.10 Retrieved soil moisture from TMI and Oklahoma Mesonet with observed
precipitation for the period June through October 2002 for a) the El Reno Mesonet site
and b) averaged over the 72 Oklahoma Mesonet sites reporting soil moisture.
101
Chapter 4
Copula Derived Observation Operators for Assimilating TMI and AMSR-E Soil
Moisture into Land Surface Models
Abstract
Assimilating soil moisture from satellite remote sensing into land surface
models has great potential for improving model predictions by providing real time
information at large scales. However, to date such research has been constrained to
using either airborne data or synthetic observations. One problem is that satellite
retrieved and modeled soil moisture have systematic differences in their mean values
and dynamic ranges, and these systematic differences vary with satellite sensors,
retrieval algorithms, land surface model. This investigation focuses on generating
observation operators for assimilating soil moisture into land surface models, using a
number of satellite-model combinations. The remotely sensed soil moisture products
are from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI)
and the NASA/EOS Advanced Microwave Scanning Radiometer (AMSR-E); and the
land surface modeled soil moisture outputs are from the Variable Infiltration Capacity
(VIC) hydrological model; the land surface model from European Center for Mediumrange Weather Forecasts (ECMWF) reanalysis (ERA40); and land surface model from
the NCEP North American Regional Reanalysis (NARR). For this analysis, the
satellite and model data is over the southern Great Plains region, using data from
102
1998-2003. A bivariate statistical approach, based on copula distributions, is
employed for simulating the joint distribution between retrieved and modeled soil
moisture. The copula-based joint distribution allows for the separate estimation of the
two marginal distribution and their dependency structure, permitting greater flexibility
over traditional approaches. Furthermore, copula conditional simulations allows for
ensemble generation of modeled soil moisture for a given satellite retrieval that
preserves the systematic differences between the satellite and modeled soil moisture.
Statistics from the bivariate copula, basically the mean and standard deviation, can
also serve as the observation operator for data assimilation.
4.1 Introduction
Soil moisture plays a unique role in land-atmosphere interactions by directly
coupling both both the water and energy cycles through its control on
evapotranspiration and runoff. Additionally, its coupling with precipitation and
boundary layer cloud formation has been well documented (e.g. Schär, 1999; Betts,
2004; Koster et al., 2004). Although it is well recognized that an accurate knowledge
of real time soil moisture conditions will enhance the performance of hydrological
numerical weather forecasting, these data have not been collected at continental scales
through traditional operational networks. Even their collection through regional
networks, like the Oklahoma mesonet, or from short-duration field measurements
presents a challenge to obtain accurate and representative values due to spatial
heterogeneity, inherent variability and measurement problems (Vinnikov et al., 1999;
Illston et al., 2004; Reichle et al., 2004; Prigent et al., 2005; Gao et al., 2005).
103
Therefore, most of the time soil moisture remains a model output whose accuracy
depends exclusively on the quality of the forcing data and model physics.
The sensitivity of surface radiation at microwave frequencies to surface soil
wetness and the availability of space-borne passive microwave sensors in the 6-11
GHz range has offered the potential for observing surface soil wetness at large scales
operationally (Jackson and Schmugge, 1989; Jackson, 1993; Owe et al., 1999.) The
lowest frequency passive space-borne microwave sensor was 6.6 GHz on the Scanning
Multichannel Microwave Radiometer (SMMR) operated on NASA's Nimbus-7
satellite for more than eight years, from 26 October 1978 to 20 August 1987,
transmitting data every other day. The 79 cm diameter conical scanning parabolic
antenna resulted in an incidence angle of 50.3 degrees at Earth's surface and provided
a 780 km swath with a
-3dB footprint of 148x95 km at 6.6 GHz and 91 x 59 km at
10.7 GHz, the two lowest frequencies. Studies of soil moisture retrieved by SMMR
(Owe et al., 1999; Vinnikov et al., 1999; Owe et al., 2001; and Reichle et al., 2004)
have tended to conclude that higher resolutions and lower microwave frequencies are
needed to make the data useful for hydrometeorological studies. While Vinnikov et al.
(1999) recognize the potential of satellite retrieved soil moisture for climate studies,
the observation by Reichle et al (2004)—“The analysis of available in situ soil
moisture data does not allow us to determine whether SMMR or model data are closer
to the truth and shows that transferring soil moisture data from satellite to models and
between models is fraught with risk.”—is more reflective of a broad concern within
the hydrologic community. After August 1987, the lowest frequency passive
microwave sensor was 19.7 GHz on SMM/I until the TRMM Microwave Imager
104
(TMI) was launched in 1998. This was followed by the Advanced Microwave
Scanning Radiometer on the NASA Aqua platform (AMSR-E), which was launched in
2002.
For hydrologic and hydrometeorologic applications, it has been recognized that
higher spatial resolutions and lower frequency are needed (e.g. Jackson and
Schmugge, 1989, Jackson, 1993), resulting in a series of soil moisture field
experiments with airborne sensors, such as the L-band electronically scanned thinned
array radiometer (ESTAR) (Jackson et al., 1995; Jackson et al, 1999) and the C-band
Polarimetric Scanning Radiometer (PSR) (Jackson et al., 2002). These efforts have
culminated in the NASA Earth System Science Pathfinder (ESSP) Program
Hydrosphere State Mission (Hydros), with a planned launch date of 2010 and whose
observational goals include mapping soil moisture at a 10km footprint using combined
information from multi-polarized L-band passive (1.26 GHz) and active (1.41 GHz)
sensors (Entekhabi et al., 2004).
The usefulness of soil moisture observations in weather prediction was
highlighted by the analysis of Beljaars et al., (1996) and Viterbo and Betts (1999),
which analyzed the sensitivity of short- and medium-range precipitation forecasts for
the central United States to land surface parameterization and modeled soil moisture
anomalies in the European Centre Medium range Weather Forecast (ECMWF) model
during the July 1993 Mississippi River basin floods. Related work (Betts et al., 1996;
Betts 2004) using observations from two North American field experiments (First
International Satellite Land Surface Climatology Project Field Experiment (FIFE) and
Boreal Ecosystem Atmosphere Study (BOREAS) and a South American field
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experiment (Large Scale Biosphere-Atmosphere Experiment in Amazonia (LBA))
demonstrated that soil moisture plays a central role in coupling the land surface and
the atmospheric boundary layer, determining cloud base heights and in the partitioning
of net surface radiation into sensible and latent heat fluxes. These and similar results
(e.g. Koster et al., 2003) demonstrate the need for global-scale soil moisture
observations that are useful for weather prediction model.
Koster and Suarez (2001, 2003) analyzed the role of soil moisture in the
seasonal prediction of summertime precipitation. They found that predictability
increased in selected regions when accurate soil moisture states were used for
initializing the land states. Koster et al (2004a) carried out seasonal model intercomparisons under the GEWEX Land Atmospheric Coupling Experiment (GLACE) to
determine, for a suite of seasonal forecast models, areas of strong coupling between
soil moisture and precipitation.
Thus it is now recognized that there is a need for global-scale fields of soil
moisture that can be merged with short-term weather prediction and seasonal climate
forecast models, which will result in improved weather prediction and seasonal
climate forecast skill. To fulfill this need, two approaches have been taken. The first
approach is to use observed fields of precipitation, radiation, and near-surface
meteorology to force land surface model (LSM) offline to generate fields of soil
moisture, surface temperature, and other land surface states that can be assimilated
into weather models (Mitchell et al., 2004) and used to initialize seasonal climate
models (Koster et al., 2004b). This approach has been referred to as ‘land data
assimilation’, and its challenge is the assemblage of accurate forcings and the inherent
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modeling errors from incorrect parameterizations, calibrations and/or data sets used by
the model. The second approach is to assimilate satellite-based soil moisture or
brightness temperature directly into the forecast models. The challenge with the
second approach is the spatial resolution of the satellite data, especially over
heterogeneous terrain, the thinness of the surface layer that is being sensed, which is
between 1 and 5 cm depending on the sensor frequency, and the accuracy of the soil
moisture retrieval algorithm.
The focus of this chapter is to advance the second approach through the
development and testing of ‘observation operators’ (Reichle and Koster 2004; Drusch
et al, 2005) using two different retrieval algorithms and three land surface models with
five years of TMI and one year of AMSR-E 10.7 GHz brightness temperature
measurements. There have been a number of studies that demonstrate the potential of
assimilating satellite-derived soil moisture into land surface models (e.g. Walker and
Houser, 2001; Reichle et al., 2002; Crow et al., 2005), but the promising results from
these studies were obtained using synthetic observations that may not represent actual
retrievals. Reichle et al. (2004) in their analysis of SMMR retrievals, and Gao et al
(2005) in their analysis of TMI-based retrievals, have noted that systematic biases
exist between satellite-retrieved soil moisture and either in-situ observations or
modeled soil moisture. Part of this difference is due to scale mismatches in both the
sensing depth to the observing/modeling depth, part is due to models and retrieval
algorithms having their own ‘climatology’ (Koster and Milly, 1997), and part is due to
sub-grid contamination within the satellite footprint from small water bodies, trees,
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roads and buildings that affect the brightness temperature but are ignored in the
retrievals.
To overcome this systematic bias, Reichle and Koster (2004) and Drusch et al.
(2005) developed observation operators that removed the systematic bias between
retrieved and modeled soil moisture by matching the values of the cumulative
distribution functions (CDF). Thus, for example, the 90th quantile from the
distribution of retrieved soil moisture is matched with the 90th quantile of modeled soil
moisture.
One shortcoming of this approach is that it ignores the statistical dependency
between the two data sets, and makes the assumption that their ranked values are
uniquely related. In reality, there is uncertainty in the retrieved and observed/modeled
soil moisture due to the various factors discussed earlier, resulting in a statistical
dependency between the time series of retrieved and observed/modeled soil moisture
that is less than perfect. Therefore an alternative approach is to model the joint
probabilitistic behavior that includes both the dependency between and the uncertainty
within in the soil moisture data sets. In this chapter we use probabilistic models based
on the family of Copula distributions (Nelsen, 1999; De Michele and Salvadori, 2003;
Favre et al., 2004) to develop the observational operators using two satellite soil
moisture retrieval algorithms (Gao et al., 2004, 2005; Njoku, personal communication)
applied to 10.7 GHz brightness temperature measurements from the TRMM
Microwave Imager (TMI) and NASA’s AMSR-E satellite, and three land surface
model soil moisture products—one from the Variable Infiltration Capacity LSM used
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in the NLDAS project (Mitchell et al., 2004), one from the ECMWF reanalysis ERA40 and one from the NCEP North American Regional Reanalysis (NARR) project.
Section 4.2 describes the Copula family of probability distributions and their
applicability for determining observational operators, while sections 4.3 introduces the
data used in the study: both the satellite retrieved soil moisture, the modeled soil
moisture and a comparison of the remotely sensed soil moisture to 10-cm, field
measured Oklahoma Mesonet. In terms of remotely sensed and modeled data
sources, this investigation focuses on deriving observation operators in the Southern
Great Plains from two remote sensing soil moisture products: the Tropical Rainfall
Measuring Mission (TRMM) Microwave Imager (TMI) (Gao et al., 2005) and
Advanced Microwave Scanning Radiometer (AMSR-E) (Njoku, personal
communication). Both products are from X-band brightness temperatures and are
available to the general public, with TMI soil moisture covering a longer time period
due to its earlier launch. The main difference between the two products comes from
the retrieval algorithms.
In section 4.4 we briefly compare the retrieved soil moisture and then generate
the observation operators by associating each to outputs from three independent land
surface models: the Variable Infiltration Capacity (VIC) hydrological model; the
European Center for Medium-range Weather Forecasts (ECMWF) reanalysis
(ERA40); and NCEP North American Regional Reanalysis (NARR). The operators
are separated by season. For each satellite ‘observation’, a mean and variance of the
model output can be calculated through simple equations based on the simulated
conditional joint distributions. The objective of using the derived observation
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operators is for the assimilation of the satellite products into the land surface models.
The last section discusses and summarizes the results.
4.2 Copula Based Joint Probability Distribution
For continuous bivariate distributions, separating the functional form of the
univariate marginals can often be problematic unless the joint distribution is Bivariate
Normal. An alternative approach is to construct the bivariate joint distribution from
the marginals plus the dependence structure between the variates through a copula
function (Nelsen, 1999). Consider a bivariate distribution of two continuous random
variables X and Y , with cumulative marginal distribution functions FX , FY , and joint
distribution function FXY . According to the Sklar’s theorem (Sklar, 1959), there exists
a unique 2-D function C, such that:
FXY ( x, y ) = C ( FX ( x), FY ( y ))
(1)
Here the C is the copula, defined as I 2 → I , where I = [0,1] . Note that FX , FY are
uniformly distributed on the interval [0,1], which implies that the function C( FX , FY )
must satisfy C(0, t) = C(t,0) = 0 and C(1, t) = C(t,1) = 1 for all t ∈ I . FX and FY are
the marginals representing individual behaviors of the random variables X and Y, and
C represents the dependency structure between them.
A commonly used copula family is the Archimedean family (Kimberling,
1974), a large parametric family that fits into the following form:
Cφ (u, v; δ ) = φ −1{φ (u;δ ) + φ (v; δ )} ,
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0 < u, v < 1
(2)
Here for notational ease, u≡ FX , v≡ FY and δ is the copula parameter that increases as
the dependency increases. The variable φ is referred to as the copula generator. The
copula parameter δ is related to the Kendall’s tau (τ), a measure of correlation by
φ (u, δ )
du
φ ' (u, δ )
0
1
τ = 1 + 4∫
where φ’(u, δ) is the derivative of φ(u, δ). The particular type of copula to be applied
in this study is the Gumbel copula, whose generator is φ (u; δ ) = {− log(u )}δ +1 .
In general, the following steps are needed to simulate a bivariate joint distribution
using the copula function. Given a time series of paired observations of X and Y:
1) Fit the marginal distributions for the two variables of interest; they do not have
to share the same type of distribution;
2) Calculate Kendall’s tau (τ), which is a non-parametric correlation coefficient;
3) Calculate the dependency parameter δ by solving equation (3) (codes are
available in MathLab for solving for δ.)
4) For the generation of random variables from the joint copula distribution, first
generate u as a uniform [0,1] random variable; i.e. generate the value of the
marginal FX. Conditional on the value of u, generate a random value of v by
using the inverse cumulative distribution function (CDF) of the conditional
distribution of v\u. This is calculated by taking the partial of C(u, v, δ) with
respect to u; i.e. C v|u (v | u , δ ) =
∂
[C (u , v, δ )] .
∂u
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(3)
5) The inverse of u and v (i.e. F-1X and F-1Y ), the variables x and y can be
calculated
6) For conditional simulation, say the generation of y given observed x, the
procedure is similar except u is determined from u=FX(x). Then as described
in step 4), generate a random value of v by using the inverse cumulative
distribution function (CDF) of the conditional distribution of v\u. Following
5), the variable y is determined by inverting FY.
The conditional simulation is especially important for this investigation,
because we want to understand that given a soil moisture observation from remote
sensing what the modeled soil moisture might be. Statistics of these conditional
modeled soil moisture will help to generate better ensembles in data assimilation.
Compared to traditional methods to simulate joint distributions, copula offers
considerable flexibility. While there are plenty of choices available for fitting
distributions of single random variables, there are few options for multivariable
distributions, and often same type of distribution has to be used for each random
variable. The copula approach solves this problem by separating the dependency
structure for the joint distribution from its marginals. The scale of dependency is
characterized by the copula parameter, which is related to Kendall’s non-parametric
correlation tau (τ). The structure of dependency is described within copula, with many
parametric types available. Consequently, based on the simulated marginals, each
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random variable can be generated independently according to its best-fit distribution
type, while the joint properties are still maintained.
4.3 Data Sources
4.3.1 Soil Moisture from Satellite Observations
Since its launch in November 1997, TRMM/TMI has been measuring
microwave emissions from the earth at multiple frequencies between 38°S and 38°N
latitude. TRMM has a sun asynchronous orbit type and it provides 16 orbits per day
(Bindlish et al., 2003). AMSR-E, which was launched in May 2002, shares the same
frequencies with TMI with an additional C-band radiometer. It operates in a polar,
sun-synchronous orbit with equator crossings at 1:30A.M. /P.M. (Njoku et al., 2003).
Table 4.1 lists the major instrument characteristics for the two sensors. Because of
radio frequency interference (RFI) with the C-band frequency, the remote sensing
ability of AMSR-E is basically the same as that of TMI. Retrieved soil moisture
products from both sensors have been made available to the public, with TMI soil
moisture from the NASA/GSFC Distributed Active Archive Center (DAAC) based on
the retrievals presented in chapter 3 of this thesis (also as Gao et al., 2005) and
AMSR-E soil moisture from the NASA-USGS Land Process Distributed Active
Archive Center (LP DAAC) (http://edcimswww.cr.usgs.gov/pub/imswelcome/). The
TMI soil moisture has been retrieved from horizontally polarized X-band brightness
temperatures using a land surface microwave emission model at 1/8° spatial resolution
(Gao et al., 2005), while the AMSR-E soil moisture at 1/4° spatial resolution is
derived by an algorithm developed at the NASA Jet Propulsion Laboratory (JPL).
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This algorithm uses multi-frequency and multi-polarization measurements within a
statistical framework, whose coefficients are regressed from simulation results (Njoku,
personal communication).
Inspection of the retrieved soil moisture shows that they have qualitatively
different characteristics, with the dominant feature being that they have different
dynamic ranges. Since the TMI measurements extend since 1998 (and AMSR-E since
2003), the retrieval algorithm LSMEM was used to retrieve soil moisture from the
2003 AMSR-E measurements and the NASA/JPL algorithm was applied to the TMI
measurements (January 1998 to December 2003); thus extending these two datasets.
Therefore, four datasets for the two sensors are involved in this study.
As part of the evaluation of the retrieved soil moisture products, the pixel
values overlying 30 Oklahoma mesonet sites were extracted. These 30 sites were
chosen because they appeared through visual inspection to have soil moisture values
that didn’t have obvious instrumental errors. Figure 4.1 shows the two retrievals
averaged over the 30 sites. According to Figure 4.1, despite the difference of the
absolute values, the dependency between the two retrieved data sets can be seen. The
difference between the two retrieval algorithms is larger compared to the differences
between the sensors. We thus decide to consider the soil moisture from LSMEM
(using both AMSR-E and TMI) as one product (to be referred to in the remainder of
the chapter as LSMEM soil moisture), and the soil moisture from the NASA/JPL
algorithm (again from AMSR-E and TMI) as the other product (referred to as JPL soil
moisture). By doing so, the temporally limited AMSR-E soil moisture from the DAAC
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is expanded such that observation operator with a more general representation can be
developed.
4.3.2 Comparisons between Remotely Sensed Soil Moisture and Field
Measurements
Before relating the remotely sensed soil moisture to those from land surface
modeling outputs, we first compare them to field measured data from Oklahoma
Mesonet operational environmental monitoring network (http://www.mesonet.org).
Soil moisture data collected from 1998 to 2003 at 30 Oklahoma Mesonet sites are
averaged spatially (to represent the Southern Great Plains) on daily basis; remotely
observed soil moisture from the corresponding pixels are scaled up as well. The
mesonet soil moisture have been measured at 5cm depth, while TMI and AMSR-E
only get surface soil moisture at less than 1cm. Very often the lower layer tends to be
wetter when the surface is dry and drier when the surface is wetted by significant
amount of precipitation (Gao et al., 2005). Thus, the soil moisture differences, rather
than the Mesonet soil moisture itself, are plotted against the retrieved soil moisture
from TMI and AMSR-E (Figure 4.2 and Figure 4.3). LSMEM derived soil moisture
demonstrates a strong correlation to the soil moisture difference, though it is less
significant with JPL derived soil moisture, especially in summer and fall.
4.3.3 Soil Moisture from Land Surface Model Outputs
Using North American Land Data Assimilation System (NLDAS) forcing data,
VIC hydrological model simulates state variable hourly at 1/8° spatial resolution
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(Mitchell et al., 2004). It offers soil moisture outputs are at the depth of 10cm, 40cm,
and 1m respectively. The top layer (10cm) soil moisture from 1998 to 2003 are
selected for the operator generation, and values averaged across the 30 selected
Mesonet locations at daily basis as well as those at 18UTC (AMSR-E day overpass
time) are prepared for the investigation.
The reanalysis of the European Center for Medium Range Weather Forecasting
(ECMWF), ERA40 (Simmons and Gibson, 2000) is the second land surface model for
this study, and is available globally at a resolution of 120km with outputs given at 00,
06, 12, and 18UTC respectively. Its top layer (7cm) soil moisture from 1998 to 2002
(2003 is not available) are averaged to a daily value. The same spatial up-scaling is
carried out as with the other data sources such that the time series will be a better
representation of the Southern Great Plains region and the resolution inconsistencies
among various data sources will be reduced. The third modeled soil moisture is from
the North American Regional Reanalysis (NARR) system. Its output variables are
available at a 3-hourly, 32km resolution, with a top soil moisture layer being 7cm.
The soil moisture output was processed in the same way as with the soil moisture from
the other two models.
Considering the similarities between the depths of the modeled soil moisture
and that from Oklahoma Mesonet measurements, the training data for generating
observation operators and its preparation is described in section 4.2. Six sets of
combinations (Figure 4.4 to Figure 4.9) are made by comparing each of the remotely
observed soil moisture to its systematic differences from the model output. Despite the
seasonal variations, the demonstrated disparities of the systematic difference patterns
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are mainly related to the problems addressed in the introduction: remotely sensed soil
moisture vary with retrieval algorithms, and model simulated soil moisture vary with
model physics, forcings, etc. The soil moisture have not been adjusted through
calibration or other techniques, because soil moisture validation across scales remains
unsolved. On the other hand, the motivation for this study, to improve the efficiencies
of using remotely sensed soil moisture information within different land surface
models, is reinforced by these comparisons.
In terms of retrieved soil moisture, the differences introduced by the different
algorithms are rather significant, while the sensor differences (TMI or AMSR-E) does
not have a great affect. In Figure 4.4, Figure 4.6 and Figure 4.8, there is no bias
between TMI and AMSR-E soil moisture. It is actually within expectation because the
incident angle, a major difference between the sensors, is considered one of the inputs
for LSMEM. When it comes to the JPL algorithm, a slight systematic bias is observed
from Figure 4.5, Figure 4.7, and Figure 4.9. The coefficients are originally regressed
from simulation results suitable for AMSR-E instrumental characteristics, copying
them over by ignoring the sensor differences leads to the inconsistencies. If the same
approach had been carried out to generate coefficients for TMI, the bias should not
occur. Nevertheless, soil moisture from these two sensors still fall into the same
clusters. Therefore, to increase generality, we classify the observation data by the way
they are derived and refer them as LSMEM soil moisture and JPL soil moisture
respectively. Observation operators from LSMEM soil moisture will serve users of the
TMI product, and those who are interested in AMSR-E soil moisture should refer to
operators from JPL soil moisture.
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4.4 Generation of Observation Operators
This section describes the detailed procedures of using the Copula to simulate
the joint distributions between modeled and observed soil moisture and thus to
generate observation operators for data assimilation applications. There are two
observation datasets (LSMEM soil moisture and JPL soil moisture) and three modelbased soil moisture data sets, making a total of six combinations. To reduce
redundancy, we will focus on explaining how the LSMEM-VIC and JPL-VIC
operators are derived, and lay out the results for the other combinations briefly.
Further discussions about the operators are made in Section 4.5.
4.4.1 Fitting Single Variable Distributions
Copula function describes the dependency structure of bi-variables through the
joint distributions of their marginal CDFs. Therefore, proper fitting of each
distribution is of great importance: It transfers the random variables to their marginals
as copula inputs; and it maps the copula simulated outputs back into the random
variable space. The fittings of each random distribution are independent, which allow
maximum choices in finding the best fit.
Experiments with the data show that a Gamma distribution fits the remotely
sensed soil moisture best (both with the LSMEM and JPL product). Gamma
distribution also fits the difference between LSMEM and models (VIC, ERA40, and
NARR), while normal distribution is selected for describing difference between JPL
and the models. The marginal CDFs of the training data and those of the fitted
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distributions are plotted in Figure 4.10 to Figure 4.11. According to these figures, two
characteristics of these distributions can be summarized: 1) LSMEM soil moisture has
larger dynamic ranges than the others, especially in the summer season; 2) Difference
between LSMEM and JPL is most pronounced in the spring and least obvious in the
winter.
4.4.2 Using Copula to Simulate the Joint Distributions
Kendall’s tau (τ), also known as Kendall’s rank correlation coefficient,
provides a distribution free test of independence and a measure of the strength of
dependence between two variables. Consider two samples, x and y, each of size n. The
total number of possible pairings of x with y observations is n(n-1)/2. Now consider
one pair of the data (x1, y1) and (x2, y2), if (x1-x2) (y1-y2)>0 then the pair is concordant,
otherwise the pair is discordant. Then the Kendall’s tau of the two data sets is:
τ=
nc − nd
n(n − 1) / 2
(4)
Where nc represents the number of concordant pairs and nd is the number of discordant
pairs.
Within the bi-variant function of copula, the scale of dependency is described
by its parameter δ, which is transformed from the Kendall’s tau (τ) according to
Equation (3). Different type of copula represents different dependency structure.
Knowing the parameter δ for a certain type of copula, the joint distribution of
marginals thus can be simulated (see Section 4.2 for details). Various copula-derived
119
distributions should be compared with the joint distribution of the empirical marginals
such that the type of copula whose dependency structure characterizes the training
data best will be selected. Based on experimental results, we choose Gumbel copula
for generating operators in this study. Figure 4.12 shows an example of the results
from several copulas.
As described above, for each joint distribution addressed from Figure 4.4 to
Figure 4.9 Gumbel copula simulation is made using corresponding dependency
parameter δ. Then the fitted distribution parameters from Section 4.1 are used to
reverse the CDFs from copula results, offering the pairs of simulated variables
(observe soil moisture and the soil moisture difference). Figure 4.13 to Figure 4.16 are
the simulation results.
4.4.3 Observation Operators Based on Conditional Simulation Results
In this study, we are interested in understanding the statistics of the systematic
bias between observed and modeled soil moisture, which will be useful for improving
data assimilation performance. By doing conditional copula simulation, numerous
random values of soil moisture systematic biases (observed soil moisture - modeled
soil moisture) can be generated for a given observed soil moisture. Accordingly, the
mean and standard deviation of the soil moisture differences can be calculated. The
procedure is largely the same as described in Section 4.2, except that the following
modifications.
First, for a range of potential soil moisture observations, calculate their CDFs
using distribution parameters from Section 4.1. For instance, since most of the times
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LSMEM soil moisture is between 2% to 37%, we can create a series of 100 LSMEM
soil moisture with an interval of 0.35% and calculate each of the CDF using the
Gamma parameters.
When copula is employed to simulate the joint distribution of the marginals,
instead of using a ‘u’ randomly generated from uniform distribution, a ‘u’ from above
CDF series will be selected sequentially. By running the conditional simulation 1000
times at each ‘u’, 1000 ‘v’ values are created, fairly representing most of the
possibilities of v. Then through reversing these ‘v’ values, 1000 possible soil moisture
differences (observed soil moisture - modeled soil moisture) are found at the chosen
observed soil moisture.
Finally, statistical mean and standard deviation of soil moisture differences can
be calculated for each observation. The means and standard deviations are further
regressed against observations using second-order polynomials. All R2 values are
larger than 0.99 for these regressions and the coefficients are provided in Table 4.2.
Thus a set of observation operators have been generated, and they are plotted
from Figure 4.17 to Figure 4.18. Following summarizes major features of these
operators.
1) As observed soil moisture increases, the mean of soil moisture difference
increases. This is true except for the summer season with JPL soil moisture. The
physics supporting this has been explained in Section 4.3, and it has been well
captured by the operators.
2) Operators from LSMEM soil moisture and JPL soil moisture are almost the
same in the spring and the winter.
121
3) Since there is a relatively constant bias between VIC soil moisture and
ERA40 soil moisture, their mean values of soil moisture differences tend to be parallel
to each other.
4) The standard deviations of the soil moisture differences vary with modelobservation combinations and seasons, offering a flexible error structure that has been
ignored by previous data assimilation applications.
4.5 Discussions and Summary
Besides the features of the operators addressed in previous section, some
phenomena warrants further discussion. In the summer the mean values of soil
moisture differences associated with JPL observations do not seem to be selfexplainable and this also happens with the JPL-ERA40 operator in the autumn. Scatter
plots of the original data suggests that for these cases the observations are barely
correlated to the differences (their Kendall’s τ are -0.073, -0.022, and -0.025
respectively). On the other hand, the autumn JPL-VIC operator has a much better
representation and is coherent with that from LSMEM. These results indicate that
potential efficiencies of the operators may well rely on both the properties of the soil
moisture product itself and how well it connects to specific land surface model.
The objective of assimilating remotely sensed soil moisture information into
land surface models is to reduce output errors from bad forcing (primarily
precipitation) by updating the model with real-time observations. Therefore, one way
to compare the remotely sensed soil moisture is to compare their responses to
precipitation. We set daily total precipitation of 10mm as a threshold for defining ‘big’
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and ‘small’ rainfall events. We then pick the big rainfall events from 1998 to 2003 and
calculated the soil moisture increments after these rainfalls for both LSMEM and JPL
derived products. In Figure 4.19a, the LSMEM soil moisture increments are plotted
against JPL soil moisture increments. Many times LSMEM soil moisture add to more
than 5% but JPL soil moisture tend to have moderate increments. Figure 4.19b shows
the increment rates of the two data sets, similar results are observed. Although the
rainfall responses differ, the consistencies between the two products are obvious and
reasonable, supported by earlier illustrations in Figure 4.1.
As addressed in the Introduction, there are handful choices of remotely sensed
soil moisture from different sensors or retrieval algorithms, and there are land surface
models with various modeling physics at a range of scales driven by various forcings.
The goal of this investigation is not to evaluate these products; rather, it is to resolve
the complexities involved in assimilating operational space-borne soil moisture
through easy-to-use observation operators that reduce systematic bias and offer
realistic observation error structures for generating ensembles. Copula approach has
been selected because of its flexibility in simulating joint distributions, which is
accomplished by separating the dependency structure from the marginal distributions.
With the abstracted distribution characteristics and dependencies from real data sets,
statistics from conditional copula simulation results are able to construct operators
suitable for specific observation-model combinations.
The released X-band soil moisture from TMI and AMSR-E serve as
observations, expanded to six-year time series by switching the two algorithms.
Selected land surface models are VIC and EAR40, at different spatial and temporal
123
resolutions. Considering the fact that the change of canopy and climate tend to affect
the relationship between remotely sensed surface soil moisture and the modeled lower
layer soil moisture, observation operators are classified by season. Gamma
distributions are found to fit the observations and the soil moisture differences
between LSMEM and modeled soil moisture best, while normal distribution is applied
for the differences between JPL and modeled soil moisture. Gumbel copula is used to
simulate the dependency structures, and the output marginals are reversed to model the
joint distributions, which leads to the operators. The means and standard deviations of
the system biases are further regressed using second order polynomials, saving the
effort for employing the results into data assimilation practices.
Besides its application benefits, these observation operators summarize the
characteristics of different model outputs and their biases from observations through
statistical abstraction. For instance, the ERA40 soil moisture is often about 5%-10%
lower than VIC soil moisture, and the offsets vary with season and surface wetness
conditions. The LSMEM and JPL operators agree with each other well in the spring
and winter; JPL operators in the summer and autumn do not imply effective model
updates unless additional effort is made to use the informative part of the observations.
Although operators from this study are restricted in terms of observations,
models, and spatial representations, they are expected to help initiate investigations
using real satellite data in data assimilation, and the shared methodology can be
applied to various cases.
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129
Table 4.1 TMI and AMSR instrument characteristics
TMI
Center frequencies
(GHz)
AMSR
10.7 19.4 21.3 37.0 85.5
6.9
10.7 18.7 23.8 36.5 89.0
Polarization
V,H
V,H
H
V,H
V,H
V,H
V,H
V,H
V,H
V,H
V,H
Horizontal
resolution (km)
38
18
16
10
4
75
48
27
31
14
6
Orbit altitude (km)
401
705
Incident angle (°)
52.8
54.8
Inclination angle (°)
35
98.2
Swath (km)
790
1445
130
Table 4.2 Regression coefficients for estimating the mean (y1) and standard deviation
(y2) of the systematic bias from observed soil moisture (x) for different observationmodel combinations, with y1=a1+b1×x+c1×x2 and y2=a2+b2×x+c2×x2.
Season
Model
Observation
a1
b1
c1
a2
b2
c2
LSMEM
-30.0
0.99
-0.0053
2.0
-0.021
-0.0003
JPL
-27.9
0.50
0.0095
2.3
-0.019
-0.0017
LSMEM
-17.1
0.48
0.0076
1.8
0.096
-0.0019
JPL
-13.4
-0.14
0.024
2.6
-0.062
0.0033
LSMEM
-26.8
0.75
-0.0022
2.4
-0.012
-0.0005
JPL
-20.4
0.17
-0.011
2.9
-0.24
0.013
LSMEM
-13.9
0.20
0.012
2.6
0.07
0.0002
JPL
-13.0
0.63
-0.042
3.9
-0.41
0.023
LSMEM
-26.1
0.67
-0.0023
2.2
-0.018
-0.0004
JPL
-19.3
-0.26
0.021
2.7
-0.15
0.0084
LSMEM
-13.7
0.23
0.0050
1.9
0.04
-0.0004
JPL
-11.3
0.11
-0.006
2.6
-0.14
0.0067
LSMEM
-27.3
0.78
-0.0026
1.9
-0.034
0.000
JPL
-25.3
0.38
0.014
2.0
0.012
-0.0027
LSMEM
-15.7
0.13
0.015
1.8
0.08
-0.001
JPL
-13.223
-0.37
0.032
3.3
-0.16
0.009
VIC
MAM
ERA40
VIC
JJA
ERA40
VIC
SON
ERA40
VIC
DJF
ERA40
131
SM using JPL algorithm (%)
40
30
20
10
0
0
10
20
SM using LSMEM (%)
30
40
Figure 4.1 Comparison between soil moisture retrieved from the LSMEM and the JPL
algorithm. Results from TMI (1998 to 2003) are in black) and results from AMSR-E
(2003) are in red.
132
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
40
Figure 4.2 Comparison between soil moisture from the LSMEM retrieval and their
differences from Oklahoma Mesonet field measured data. Results from TMI (1998 to
2003) are in black) and results from AMSR-E (2003) are in red.
133
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.3 Comparison between soil moisture from the JPL algorithm retrieval and
their differences from Oklahoma Mesonet field measured data. Results from TMI
(1998 to 2003) are in black) and results from AMSR-E (2003) are in red.
134
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.4 Comparison between soil moisture from the LSMEM retrieval and their
differences from VIC model outputs. Results from TMI (1998 to 2003) are in black)
and results from AMSR-E (2003) are in red.
135
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.5 Comparison between soil moisture from the JPL algorithm retrieval and
their differences from VIC model outputs. Results from TMI (1998 to 2003) are in
black) and results from AMSR-E (2003) are in red.
136
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.6 Comparison between TMI soil moisture from the LSMEM retrieval and
their differences from ERA40 model outputs (from 1998 to 2002)
137
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.7 Comparison between TMI soil moisture from the JPL algorithm retrieval
and their differences from ERA40 model outputs (from 1998 to 2002)
138
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.8 Comparison between TMI soil moisture from the LSMEM retrieval and
their differences from NARR model outputs (from 1998 to 2003)
139
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.9 Comparison between TMI soil moisture from the JPL algorithm retrieval
and their differences from NARR model outputs (from 1998 to 2003)
140
40
40
0.8
0.8
0.6
0.6
0.4
0.2
0
-40
CDF
CDF
1
-20
0
20
soil moisture (%)
0.4
0.2
MAM
0
-40
40
1
1
0.8
0.8
0.6
0.6
CDF
CDF
1
0.4
0.2
0
-40
-20
0
20
soil moisture (%)
40
40
0.4
0.2
SON
-20
0
20
soil moisture (%)
JJA
0
-40
DJF
-20
0
20
soil moisture (%)
Figure 4.10 Fitted single distributions for LSMEM SM (black), JPL SM (blue),
LSMEM-VIC (red), and JPL-VIC (purple). The CDFs of original data are in gray.
141
40
0.8
0.8
0.6
0.6
0.4
0.2
0
-40
CDF
CDF
1
-20
0
20
soil moisture (%)
0.4
0.2
MAM
0
-40
40
1
1
0.8
0.8
0.6
0.6
CDF
CDF
1
0.4
0.2
0
-40
-20
0
20
soil moisture (%)
40
40
0.4
0.2
SON
-20
0
20
soil moisture (%)
JJA
0
-40
DJF
-20
0
20
soil moisture (%)
Figure 4.11 Fitted single distributions for LSMEM SM (black), JPL SM (blue),
LSMEM-ERA40 (red), and JPL-ERA40 (purple). The CDFs of original data are in
gray
142
40
0.6
0.4
0.2
Original
0
Soil moisture difference (%)
Soil moisture difference (%)
0.8
0
0.8
0.6
0.4
0.2
Clayton
0
0.2 0.4 0.6 0.8
1
Retrieved soil moisture (%)
1
1
0.8
0.6
0.4
0.2
Gumbel
0
1
0
0.2 0.4 0.6 0.8
1
Retrived soil moisture (%)
Soil moisture difference (%)
Soil moisture difference (%)
1
0
0.8
0.6
0.4
0.2
Frank
0
0.2 0.4 0.6 0.8
1
Retrieved soil moisture (%)
0
0.2 0.4 0.6 0.8
1
Retrieved soil moisture (%)
Figure 4.12 An example that compares empirical CDF with CDFs simulated from
three types of copulas: Clayton, Gumbel, and Frank. LSMEM soil moisture and its
bias from VIC outputs in the spring ( refer to Figure 4) are used to derive these results.
143
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
40
Figure 4.13 Copula simulated joint distributions (in red) between observations from
LSMEM retrievals and their biases from VIC model outputs. The original data are in
black.
144
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.14 Copula simulated joint distributions (in red) between observations from
JPL algorithm retrievals and their biases from VIC model outputs. The original data
are in black.
145
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
40
Figur 4.15 Copula simulated joint distributions (in red) between observations from
LSMEM retrievals and their biases from ERA40 model outputs. The original data are
in black.
146
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
Figure 4.16 Copula simulated joint distributions (in red) between observations from
JPL algorithm retrievals and their biases from ERA40 model outputs. The original
data are in black.
147
40
40
Soil moisture difference (%)
0
-10
-20
MAM
-30
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
10
10
0
-10
-20
SON
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
JJA
-30
0
10
20
30
Retrieved soil moisture (%)
40
10
0
-10
-20
DJF
-30
0
10
20
30
Retrieved soil moisture (%)
40
Figure 4.17 Observed soil moisture and the mean of their biases from modeled soil
moisture. Solid black lines represent pairing of LSMEM and VIC; solid gray lines are
for JPL and VIC; dashed black lines are for LSMEM and ERA40; and dashed gray
lines are for JPL and EAR40.
148
Soil moisture difference (%)
4
2
MAM
0
0
10
20
30
Retrived soil moisture (%)
40
Soil moisture difference (%)
Soil moisture difference (%)
Soil moisture difference (%)
6
6
4
2
SON
0
0
10
20
30
Retrieved soil moisture (%)
40
6
4
2
JJA
0
0
10
20
30
Retrieved soil moisture (%)
40
6
4
2
DJF
0
0
10
20
30
Retrieved soil moisture (%)
40
Figure 4.18 Observed soil moisture and the standard deviation of their biases from
modeled soil moisture. Solid black lines represent pairing of LSMEM and VIC; solid
gray lines are for JPL and VIC; dashed black lines are for LSMEM and ERA40; and
dashed gray lines are for JPL and EAR40.
149
SM increment after rainfall events
daily rain > 10mm, with slight/no rain (<10mm) previous day
20
SM increment of JPL product
15
10
5
0
0
10
5
15
SM increment of LSMEM product
20
(a)
SM increment rate after rainfall events
daily rain > 10mm
SM increment rate (%/mm) of JPL product
2
1.5
1
0.5
0
0
1
0.5
1.5
SM increment rate (%/mm) of LSMEM product
2
(b)
Figure 4.19 Comparisons of soil moisture increments due to rainfall (lager than
10mm/day).
150
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