huilin gao surface hydrology group university of washington 03/26/2008
DESCRIPTION
(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 - PowerPoint PPT PresentationTRANSCRIPT
(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!!!