GMAO Seminar March 3, 2008 Soil moisture data assimilation: Soil moisture data assimilation: Error modeling, adaptive filtering, and the Error modeling, adaptive filtering, and the contribution of soil moisture retrievals to land data contribution of soil moisture retrievals to land data assimilation products assimilation products R. Reichle 1,2 , W. Crow 3 , R. Koster 1,2 , C. Keppenne 2 , S. Mahanama 1,2 , and H. Sharif 4 [email protected]1 − Goddard Earth Sciences and Technology Center, UMBC 2 − Global Modeling and Assimilation Office, NASA-GSFC 3 − Hydrology and Remote Sensing Lab, USDA-ARS 4 − Civil Engineering Dept., University of Texas, San Antonio
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Soil moisture data assimilation: Error modeling, … assimilation of AMSR-E soil moisture retrievals Assimilation product agrees better with ground data than satellite or model alone.
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GMAO SeminarMarch 3, 2008
Soil moisture data assimilation:Soil moisture data assimilation:Error modeling, adaptive filtering, and theError modeling, adaptive filtering, and the
contribution of soil moisture retrievals to land datacontribution of soil moisture retrievals to land dataassimilation productsassimilation products
R. Reichle1,2, W. Crow3, R. Koster1,2, C. Keppenne2,S. Mahanama1,2, and H. Sharif4
1 − Goddard Earth Sciences and Technology Center, UMBC2 − Global Modeling and Assimilation Office, NASA-GSFC3 − Hydrology and Remote Sensing Lab, USDA-ARS4 − Civil Engineering Dept., University of Texas, San Antonio
• Motivation• Soil moisture data assimilation
• Part 1 (doi:10.1029/2007WR006357)
• Impact of input error parameters on soil moisture estimates
• Adaptive filtering
• Part 2 (doi:10.1029/2007GL031986)
• Contribution of soil moisture retrievals to land assimilation products
http://userpages.umbc.edu/~reichle/
OutlineOutline
IntroductionIntroduction
Large-scale soil moisture is needed, for example, for water cycle studies and forinitializing weather/climate models. It is available from:
Model soilmoisture
(subject toerror)
Soilmoistureretrievals(subjectto error)
“Optimal”soil
moisture
Assimilation
Weights basedon respectiveuncertainties.
Catchment land surface model forced w/observed meteorology. Complete space-time coverage, incl. root zone.
Repeat for many different sets ofmodel and retrieval error cov’s.
Investigate impact of wrong model and obs. error inputs on assimilation estimates:
Reichle et al., doi:10.1029/2007WR006357
1200
900
600
300
Annual Precipitation
(mm)
Red-Arkansas river basinRed-Arkansas river basin
West: Dry withsparse vegetation
East: Wet withdense vegetation
Red-Arkansas river basin (308 catchments)
Hourly forcing data (1981−2000)
NASA Catchment land surface model(identical twin experiment)
Sharif et al., JHM, 2007
Impact of Q and R on assimilation estimatesImpact of Q and R on assimilation estimates
RMSE of assimilation estimates v. truth for:
Each “+” symbolrepresents one19-year assim.experiment overthe Red-Arkansaswith a uniquecombination ofinput model andobservation errorparameters.
Surface soil moisture m3/m3
input obs error std-dev
Q = model error(includingerrors in precip,radiation, andsoil moisturetendencies)
P = P(Q)= soil moistureerror variancefo
reca
st e
rror
std
-dev
Reichle et al., doi:10.1029/2007WR006357
sqrt(P(Q_true))
Impact of Q and R on assimilation estimatesImpact of Q and R on assimilation estimates
RMSE of assimilation estimates v. truth for:
Surface soil moisture m3/m3
• “True” input error covariances yield minimum estimation errors.• Wrong model and obs. error covariance inputs degrade assimilation estimates.• In most cases, assimilation still better than open loop (OL).
Reichle et al., doi:10.1029/2007WR006357
sqrt(P(Q_true))
Impact of Q and R on assimilation estimatesImpact of Q and R on assimilation estimates
Root zone soil moisture m3/m3
• Root zone more sensitive than surface soil moisture.
RMSE of assimilation estimates v. truth for:
Surface soil moisture m3/m3
Reichle et al., doi:10.1029/2007WR006357
Impact of Q and R on assimilation estimates (fluxes)Impact of Q and R on assimilation estimates (fluxes)
• Fluxes more sensitive to wrong error parameters than soil moisture.• Sensible/latent heat more sensitive to model error cov than obs error cov
(probably related to ensemble propagation).
Reichle et al., doi:10.1029/2007WR006357
• Motivation• Soil moisture data assimilation
• Part 1 (doi:10.1029/2007WR006357)
• Impact of input error parameters on soil moisture estimates
• Adaptive filtering
• Part 2 (doi:10.1029/2007GL031986)
• Contribution of soil moisture retrievals to land assimilation products
http://userpages.umbc.edu/~reichle/
OutlineOutline
Diagnostics of filter performance and adaptive filteringDiagnostics of filter performance and adaptive filtering
innovations ≡ obs – model prediction(internal diagnostic)
state err cov + obs err cov(controlled by inputs)
Find true Q, R by enumeration?• RMSE plots require “truth” (not usually available).• Too expensive computationally.Use diagnostics that are available within the assimilation system.
Filter update: x+ = x− + K(y – x−)K = P (P + R)−1 = Kalman gain
Diagnostic: E[(y − x−) (y – x−)T] = P + R
time
soil
moi
stur
e Example: Average “obs.minus model prediction”distance is much largerthan assumed inputuncertainties
Ry±
Px ±!
!x-y
x− = model forecastx+ = “analysis”y = observation
state err cov + obs err cov(controlled by inputs)
Find true Q, R by enumeration?• RMSE plots require “truth” (not usually available).• Too expensive computationally.Use diagnostics that are available within the assimilation system.
Filter update: x+ = x− + K(y – x−)K = P (P + R)−1 = Kalman gain
Diagnostic: E[(y − x−) (y – x−)T] = P + R
Contours: misfit between diagnosticand what it “should” be.Adaptive filter: Nudge input errorparameters (Q, R) during assimilationto minimize misfit.
Diagnostics of filter performance and adaptive filteringDiagnostics of filter performance and adaptive filtering
innovations ≡ obs – model prediction(internal diagnostic)
Reichle et al., doi:10.1029/2007WR006357
x− = model forecastx+ = “analysis”y = observation
innovations ≡ obs – model prediction(internal diagnostic)
state err cov + obs err cov(controlled by inputs)
Find true Q, R by enumeration?• RMSE plots require “truth” (not usually available).• Too expensive computationally.Use diagnostics that are available within the assimilation system.
Filter update: x+ = x− + K(y – x−)K = P (P + R)−1 = Kalman gain
Diagnostic: E[(y − x−) (y – x−)T] = P + R
Contours: misfit between diagnosticand what it “should” be.Adaptive filter: Nudge input errorparameters (Q, R) during assimilationto minimize misfit.
Diagnostics of filter performance and adaptive filteringDiagnostics of filter performance and adaptive filtering
Reichle et al., doi:10.1029/2007WR006357
x− = model forecastx+ = “analysis”y = observation
1. EnKF propagation and update
2. Moving average of filterdiagnostics
3. Adaptive scaling coefficients
Adaptive algorithmAdaptive algorithm
Reichle et al., doi:10.1029/2007WR006357
• Adapted Dee et al. for land• Cheap• Need parameters
• Adaptive scaling factors generally converge to true values (thick lines).• Convergence is slow (order of years).• Spatial variability (thin lines) much greater for alphaQ than for alphaR.
sqrt(R0)=0.02 sqrt(R0)=0.08
Reichle et al., doi:10.1029/2007WR006357
Convergence of adaptive scaling factorsConvergence of adaptive scaling factors
True values
_ AlphaQ
_ AlphaR
sqrt(P0 )=0.050
sqrt(P0 )=0.012
Adaptive v. non-adaptive EnKF (soil moisture)Adaptive v. non-adaptive EnKF (soil moisture)
Non-adaptive Adaptive Difference
Surfacesoilmoisturem3/m3
Rootzone soilmoisturem3/m3
• Adaptive filter: Map experiment onto contour plot based on initial guess of R, P(Q).• Adaptive filter yields improved assimilation estimates for initially wrong model andobservation error inputs (except for R0=0).
Contours:RMSE ofassim.estimatesv. truth
Reichle et al., doi:10.1029/2007WR006357
Adaptive v. non-adaptive EnKF (fluxes)Adaptive v. non-adaptive EnKF (fluxes)
• Assimilation of soil moisture retrievals adds skill (relative to model product).• Even retrievals of poor quality contribute information to the assimilation product.
Skill (R) of retrievals (surface soil moisture)
Skill
(R) o
f mod
el (s
urfa
ce s
oil m
oist
ure)
Skill (R) of retrievals (surface soil moisture)
Skill improvement of assimilation over model (ΔR)(surface soil moisture)
Skill improvement of assimilation over model (ΔR)(root zone soil moisture)
• Assimilation of soil moisture retrievals adds skill (relative to model product).• Even retrievals of poor quality contribute information to the assimilation product.• Published AMSR-E and SMMR assimilation products are consistent with expected
skill levels for surface soil moisture, to a lesser degree also for root zone soilmoisture.
Skill (R) of retrievals (surface soil moisture)
Skill
(R) o
f mod
el (s
urfa
ce s
oil m
oist
ure)
Skill (R) of retrievals (surface soil moisture)
Skill improvement of assimilation over model (ΔR)(surface soil moisture)
Skill improvement of assimilation over model (ΔR)(root zone soil moisture)
AMSR-E (Δ): ΔR=0.07 ΔR=0.06
SMMR (□): ΔR=0.07 ΔR=0.03
Reichle et al., doi:10.1029/2007GL031986
Skill improvement (ET)Skill improvement (ET)
• Assimilation of surface soil moisture retrievals yields, on average, modestimprovements in ET estimates.
• Negative ΔR related to technicalities (EnKF bias issues and adaptive filtering).
Skill (R) of retrievals (surface soil moisture)
Skill
(R) o
f mod
el
(m
onth
ly E
T)
Skill improvement of assimilation over model (ΔR)(monthly ET)
Reichle et al., doi:10.1029/2007GL031986
DA-OSSE summaryDA-OSSE summary
• General DA-OSSE framework developed:• Quantify the information added to land assimilation products by satelliteretrievals for detailed and comprehensive error budget analyses for dataassimilation products.
• Adaptive filtering is major component of the DA-OSSE.• Success of DA-OSSE depends on realism of imposed model errors.
• Soil moisture assimilation study for the Red-Arkansas:• Even retrieval data sets of poor quality contribute information to theassimilation product.
• Published AMSR-E and SMMR assimilation products are consistent withexpected skill levels for surface soil moisture, to a lesser degree also forroot zone soil moisture.
• Future applications:• Extending the DA-OSSE to continental/global scales is straightforward butcomputationally demanding.
• Same applies for higher-resolution soil moisture retrievals (e.g. fromactive/passive MW sensor).