Huilin Gao Surface Hydrology Group University of Washington 03/26/2008

(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

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

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

Field measurement Remote sensing Modeling Soil Moisture Data Sources

Soil moistureEmissivity Brightness temperature Frequency Sensitivity Soil Moisture from Passive Microwave Remote Sensing 240 245 250 255 260 265 270 275 280 285 Tb (K)

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

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

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.

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

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

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

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 Proposed solution: Simulate the joint distributions─ Correct bias, estimate error Approach: Copula probability distribution ERA40 TMI Figure 2, Drusch et al., 2005

Joint Distributions of Training Data ? ? ? ? ? ? LSMEM NASA VIC LSMEM - VIC LSMEM 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 LetFXYbe a joint distribution function with marginals FX ,FY, there exists a copula C such that Dependency structures of Copulas (Nelson, 1999)

Copulas LetFXYbe 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

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

Joint Distributions of Training Data y x

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

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

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

Observation operators from Conditional Simulations

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, 413-429, 2007.

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, 413-429, 2007.

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 Group University of Washington 03/26/2008

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

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)

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.

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? 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)

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

Major River Basins within the U.S. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 12. Ohio

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

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.

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

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!!!

Huilin Gao Surface Hydrology Group University of Washington 03/26/2008