1. (I) Copula Derived Observation Operators for Assimilating Remotely Sensed Soil Moisture into Land Surface Models
Huilin Gao
Surface Hydrology Group
University of Washington
03/26/2008

2. Outline
1. Background
2. Deriving observation operators for data assimilation using Copula
Challenges for assimilating satellite data
Copula and its flexibility in simulating joint distributions
Observation operators from conditional Copula simulations

3. Role of Soil Moisture in Water and Energy Cycles
Weather forecasting
Flood forecasting
Drought monitoring
Climate modeling
Soil moisture
Condensation
moist air
Precipitation
Transpiration
Evaporation from
soils,rivers,lakes

4. Soil Moisture Data Sources
Field measurement
Remote sensing
Modeling

5. Soil Moisture from Passive Microwave Remote Sensing
Soil moisture Emissivity Brightness temperature
Frequency Sensitivity
Tb (K)

6. Data Assimilation of RS Soil Moisture
Update the land surface model with remotely sensed REAL TIME soil moisture using data assimilation techniques.
Uncertainty
Want best estimates of the land surface states
(Walker and Houser, 2001; Reichle et al., 2002; Crow et al., 2005)
TOA Brightness Temperature
Microwave emissions
Land Surface model

7. Challenges for Assimilation of RS Soil Moisture
remote sensing
<1cm
Measurement
5cm
Modeling
10cm
Measuring depth
mesurement
point data
remote sensing
Modeling
Spatial resolution

8. Challenges for Assimilation of RS Soil Moisture
“The analysis of available in situ soil moisture data does not allow us to determine whether remotely sensed or model data are closer to the truth”
“transferring soil moisture data from satellite to models and between models is fraught with risk.” —Reichle et al (2004)
Figure 1, Drusch et al., 2005
Objective
Generate ‘observation operators’ to transfer remotely sensed soil moisture to corresponding modeled soil moisture, while preserve the error structures associated with models and retrievals.

9. Challenges for Assimilation of RS Soil Moisture
Surface soil moisture
10cm soil moisture
?? Systematic biases
Sensor frequencies
Retrieval algorithms
Models
Ensemble of state / output predictions
Ensemble of measurements
Ensemble filtering
input
Filter
State update
State prediction
(LSM)
(RS)
(Model)

10. Soil Moisture from Different Sources
LSMEM
NASA (NASA developed emission model)
SGP99

11. Soil Moisture from Different Sources
LSMEM
NASA (NASA developed emission model)
SGP99

12. Soil Moisture from Different Sources
LSMEM
NASA
VIC
ERA40
VIC
ERA40
LSMEM
NASA
SGP99

13. Towards bias reduction for data assimilation
Previous solution:
Compare the CDFs (Reichle and Koster, 2004, Drusch et al., 2005)
Constraints:
One to one mapping, not enough for data assimilation requirements
ERA40
TMI
Proposed solution:
Simulate the joint distributions─
Correct bias, estimate error
Approach:
Copula probability distribution
Figure 2, Drusch et al., 2005

14. Joint Distributions of Training Data
LSMEM
NASA ?
VIC
LSMEM - VIC
LSMEM
NARR
ERA40

15. Copula Approach What is a Copula?
Why do we choose Copulas to simulate joint distributions?
How to run Copula simulations?
What are the benefits of doing conditional Copula simulation?

16. Dependency structures of Copulas
Let FXY be a joint distribution function with marginals FX ,FY, there exists a copula C such that
Dependency structures of Copulas
(Nelson, 1999)

17. Copulas
Let FXY be a joint distribution function with marginals FX ,FY, there exists a copula C such that
What makes copulas favorable?
Extract the dependence structure from the joint distribution function
“Separate out” the dependency structure from the marginal distribution functions
There are many choices for fitting distributions of single variables, but few for fitting multiple variables

18. Flow Chart for Copula Simulation
Fit distributions of X and Y
independently
Obtain parameters
Kendall’s τ
Dependency
Copula parameter δ
Simulated joint distribution
(x,y)
Joint distribution
(x,y)
Copula simulated
Joint distributions of FX(x), FY(y)

19. Joint Distributions of Training Datay x

20. Marginal Joint Distributions from Different Copulas
FY(y)
FY(y)
FX(x)
FX(x)
FY(y)
FY(y)
FX(x)
FX(x)

21. Copula Simulation Procedure
y x
FY(y)
FX(x) x y
Red: Simulated data
Black: Training data y x
FY(y)
FX(x)

22. Joint Distributions of Simulation Results?
Red: Simulated data
Black: Training data

23. Observation operators from Conditional Simulations

24. Observation operators from CDF matching and Copula
VIC
CDF
LSMEM
VIC
CDF
NASA
Gao, H., E. F. Wood, M. Drusch, M. McCabe, Copula Derived Observation Operators for Assimilating TMI and AMSR-E Soil Moisture into Land Surface Models , J. Hydromet., 8, , 2007.

25. Observation operators from CDF matching and Copula
VIC
CDF
Copula
LSMEM
VIC
CDF
Copula
NASA
Gao, H., E. F. Wood, M. Drusch, M. McCabe, Copula Derived Observation Operators for Assimilating TMI and AMSR-E Soil Moisture into Land Surface Models , J. Hydromet., 8, , 2007.

26. Observation operators from CDF matching and Copula
VIC
CDF
Copula
LSMEM
VIC
CDF
Copula
NASA
Gao, H., E. F. Wood, M. Drusch, M. McCabe, Copula Derived Observation Operators for Assimilating TMI and AMSR-E Soil Moisture into Land Surface Models , J. Hydromet., 8, , 2007.

27. Conclusions
Understanding the systematic biases between satellite and model soil moistures is essential for improving assimilation of soil moisture;
Copula is selected for the study because of its flexibility in simulating joint distributions;
Observation operators from conditional Copula simulations include the mean and the standard deviation of the biases, which are sufficient in helping generate ensembles for data assimilation purpose;
Operators are further regressed using 2nd order polynomial (with all R2>0.99), making them especially user friendly;
The observation operators capture the characteristics of the models, retrievals, and their relationships.

28. (II) Estimating Continental-Scale Water Balance through
Remote Sensing and Modeling
Huilin Gao
Surface Hydrology Group
University of Washington
03/26/2008

29. Outline 1. Constrains towards understanding large scale water balance
2. Scientific question and the research plan
3. Preliminary analysis of remote sensing data

30. Constrains Towards the Closure of the Water Budget: Observation
∆S = P – R - ET
Estimated water balance of a 200×200 km area over Oklahoma from observations
(Pan and Wood, 2007)

31. Constrains Towards the Closure of the Water Budget: Modeling
Advantage
LSMs close the water budget by constructing the water balance terms, with reanalysis model used mostly due to the good forcings (e.g., NCEP-NCAR and ECMWF ERA40).
Problems
1. Reanalysis models assimilate data that are primarily atmospheric profiles, rather than land surface fluxes and state variables;
2. For most cases, LSMs are forced by precipitations from model output, therefore model errors are transferred to surface fields (e.g., ET, SM).
3. The 'nudging' of LSMs often times causes unrealistic SM, ET, and a loss of seasonal runoff cycle.
4. LSMs forced by gridded surface observations do not allow for incorporation of time and space discontinuous observation from remote sensing.

32. Scientific Question Research Plan
How can in-situ and satellite data be combined with LSM predictions, using data assimilation techniques, to produce improved, coherent merged products that are space-time continuous over the land areas of the globe?
Research Plan
1. Collecting and selecting satellite and in-situ data
2. Constructing a simple model to simulate the water balance and test it over
the U.S.
3. Using data assimilation technique to close the water balance
4. Applying the approach globally
R (in-situ) ?=? P – ∆S – ET (remote sensing)

33. Data 1: Precipitation from Satellite
CPC Morphing Technique (CMORPH) ─ NCAR
Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) ─ UCI
TRMM-Adjusted Merged-Infrared Precipitation 3B42 Real Time ─ NASA
TRMM-Adjusted Merged-Infrared Precipitation 3B42 Version 6 ─ NASA
CMORPH
PERSIANN
3B42-RT
3B42-V6
Coverage
60S~60N
50S~50N
Resolution
0.25deg
Period
Dec 02~cur
Mar 00~cur
Jan 98~cur
Time step
3hr
6hr
* Downloaded and processed Jan 2003~Dec 2006, global (50S~50N)

34. Major River Basins within the U.S.
1. Arkansas-Red 5. East Coast 9. Lower Mississippi 13. Rio Grande
2. California 6. Great Lakes 10. Mexico 14. Upper Mississippi
3. Colorado 7. Great Basin 11. Missouri
4. Columbia 8. Gulf Ohio

35. Precipitation from Remote Sensing v.s. Observation (by basin)
CMORPH
PERSIANN
TRMM_RT
TRMM_V6
Observed

36. Correlation Coefficients between Observed & Remotely Sensed Precipitation by Basin (monthly)

37. Data 2: Water Storage Change from GRACE
The Gravity Recovery and Climate Experiment (GRACE) mission detects changes in Earth’s gravity field by monitoring the changes in distance between the two satellites as they orbit Earth. The twin satellites were launched in March, 2002.
Data: Aug 2002 ~ July 2007 at 1degree resolution, global coverage
The GRACE has helped the science community to understand the change of fresh water storage over land.

38. Comparison between GRACE data and VIC output
Columbia
California
Missouri
Arkensa
GRACE storage change
VIC SWE+SM change
Jan Apr Jul Oct
Jan Apr Jul Oct

39. Data 3: Evaportranspiration (ET)

40. Summary Some conclusions ...... Near future ......
1. TRMM 3B42-V6, which has been calibrated by guage data, is selected for precipitation input;
2. GRACE water storage change agrees with LSM output over most basins in the U.S., offering insight for selecting studied basins.
Near future
1. the ET and runoff data;
2. select research domain (preferably whole U.S., separated by basin) and construct a simple LSM for water balance;
3. A simple scheme for modelling SWE in the LSM.

41. Questions?
Thanks!!!