(I) Copula Derived Observation Operators for Assimilating Remotely

Sensed Soil Moisture into Land Surface Models

Huilin Gao

Surface Hydrology GroupUniversity of Washington

03/26/2008

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

Outline

Role of Soil Moisture in Water and Energy Cycles

Condensation moist air

Condensation

Precipitation

TranspirationEvaporation from

soils,rivers,lakes

Precipitation

• Weather forecasting

• Flood forecasting

• Drought monitoring

• Climate modeling

Soil moisture

Field measurement ModelingRemote sensing

Soil Moisture Data Sources

240 245 250 255 260 265 270 275 280 285

Tb (K)

Soil moisture Emissivity Brightness temperature

Frequency Sensitivity

Soil Moisture from Passive Microwave Remote Sensing

TOA Brightness Temperature

Microwave emissions

Land Surface model

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

Uncertainty

Uncertainty

(Walker and Houser, 2001; Reichle et al., 2002; Crow et al., 2005)

Challenges for Assimilation of RS Soil Moisture

remote sensing<1cm

Measurement5cm

Modeling10cm

Measuring depth

mesurementpoint data

remote sensing

Modeling

Spatial resolution

Challenges for Assimilation of RS Soil Moisture

Generate ‘observation operators’ to transfer remotely sensed soil moisture to corresponding modeled soil moisture, while preserve the error structures associated with models and retrievals.

• “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

input

1|ˆ

ttYState prediction (LSM)

Filter

tKtZState update

Challenges for Assimilation of RS Soil Moisture

Surface soil moisture 10cm soil moisture?? Systematic biases

Sensor frequenciesRetrieval algorithms

Models

(RS)

Ensemble of state / output predictions

Ensemble of measurements

Ensemble filtering

(Model)

Soil Moisture from Different Sources

LSMEM

SGP99

NASA (NASA developed emission model)

LSMEM

SGP99

Soil Moisture from Different Sources

NASA (NASA developed emission model)

LSMEM

SGP99

Soil Moisture from Different Sources

LSMEMNASA

VICERA40

ERA40

VIC

NASA

Towards bias reduction for data assimilation

Previous solution: Compare the CDFs (Reichle and Koster, 2004, Drusch et al., 2005)

Proposed solution: Simulate the joint distributions─Correct bias, estimate error

Approach:Copula probability distribution

Figure 2, Drusch et al., 2005

Constraints: One to one mapping, not enough for data assimilation requirements

ERA40TMI

Joint Distributions of Training Data

LSMEM

LSM

EM

- V

IC

LSMEM NASA

VIC

NARR

ERA40

?

?

?

?

?

?

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?

Copulas

))(),((),( yFxFCyxF YXXY

Let FXY be a joint distribution function with marginals FX ,FY, there

exists a copula C such that

Dependency structures of Copulas

(Nelson, 1999)

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

))(),((),( yFxFCyxF YXXY

Let FXY be a joint distribution function with marginals FX ,FY, there

exists a copula C such that

Copulas

Joint distribution(x,y)

Copula simulatedJoint distributions of FX(x), FY(y)

Simulated joint distribution(x,y)

Fit distributions of X and Y independently

Obtain parameters

Kendall’s τDependency

Copula parameter δ

Flow Chart for Copula Simulation

Joint Distributions of Training Data

x

y

FX(x) FX(x)

Marginal Joint Distributions from Different Copulas

FX(x)

FY(y

)

F

Y(y

)

F

Y(y

)

F

Y(y

)

FX(x)

y xF Y

(y) F

X (x)

Copula Simulation Procedure

x

y

FX(x)

F Y(y

)

x

y

Red: Simulated data Black: Training data

Joint Distributions of Simulation Results

Red: Simulated data Black: Training data

?

Observation operators from Conditional Simulations

Observation operators from CDF matching and Copula

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, 413-429, 2007.

VIC

VIC

LSMEM

NASA

CDF

CDF

Observation operators from CDF matching and Copula

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, 413-429, 2007.

VIC

VIC

LSMEM

NASA

CDF

CDF

Copula

Copula

Observation operators from CDF matching and Copula

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, 413-429, 2007.

VIC

VIC

LSMEM

NASA

CDF

CDF

Copula

Copula

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.

(II) Estimating Continental-Scale Water Balance through

Remote Sensing and Modeling

Huilin Gao

Surface Hydrology GroupUniversity of Washington

03/26/2008

1. Constrains towards understanding large scale water balance

2. Scientific question and the research plan

3. Preliminary analysis of remote sensing data

Outline

∆S = P – R - ET

Constrains Towards the Closure of the Water Budget: Observation

Estimated water balance of a 200×200 km area over Oklahoma from observations(Pan and Wood, 2007)

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).

Problems1. 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.

Scientific Question

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 Plan1. 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)

Data 1: Precipitation from Satellite

CMORPH PERSIANN 3B42-RT 3B42-V6

Coverage 60S~60N 50S~50N 50S~50N 50S~50N

Resolution 0.25deg 0.25deg 0.25deg 0.25deg

Period Dec 02~cur Mar 00~cur Dec 02~cur Jan 98~cur

Time step 3hr 6hr 3hr 3hr

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

* Downloaded and processed Jan 2003~Dec 2006, global (50S~50N)

1. Arkansas-Red 5. East Coast 9. Lower Mississippi 13. Rio Grande2. California 6. Great Lakes 10. Mexico 14. Upper Mississippi3. Colorado 7. Great Basin 11. Missouri4. Columbia 8. Gulf 12. Ohio

Major River Basins within the U.S.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

CMORPH

PERSIANN

TRMM_RT

TRMM_V6

Observed

Precipitation from Remote Sensing v.s. Observation (by basin)

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

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.

GRACE storage changeVIC SWE+SM changeJan Apr Jul Oct Jan Apr Jul Oct

Comparison between GRACE data and VIC output

Columbia

California

Missouri

Arkensa

Data 3: Evaportranspiration (ET)

Summary

Some conclusions ......

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.

Questions?Thanks!!!