AMS’04, Seattle, WA. January 12, 2004 Slide 1 HYDROS Radiometer and Radar Combined Soil Moisture Retrieval Using Kalman Filter Data Assimilation X. Zhan, UMBC-GEST P. Houser, NASA-GSFC, J. Walker, University of Melbourne, and HYDROS Science Team
Apr 01, 2015
AMS’04, Seattle, WA. January 12, 2004 Slide 1
HYDROS Radiometer and Radar Combined Soil Moisture Retrieval Using Kalman Filter Data
Assimilation
X. Zhan, UMBC-GESTP. Houser, NASA-GSFC,
J. Walker, University of Melbourne, andHYDROS Science Team
AMS’04, Seattle, WA. January 12, 2004 Slide 2
HYDROS: Hydrosphere States Mission
Spinning 6m dish
• NASA Earth System Science Pathfinder mission;• Surface soil moisture w/ 4%vol. accuracy and Freeze/Thaw state
transitions;• Revisit time: Global 3 days, boreal area 2 days• L-band Radiometer sensing 40km brightness temp. with H & V polarization;• L-band Radar measuring 3km backscatters with hh, vv, hv polarization;• Soil moisture products: 3km radar retrievals, 40km radiometer retrievals and
10km radar and radiometer combined retrievals.
AMS’04, Seattle, WA. January 12, 2004 Slide 3
36 km – Radiometer footprint
9 km Soil moisture product
3 km Radar footprint
1 2 3
4 5 61
7 8 9
2 3 4
7 865
9
13 14 15 16
121110
SM retrieval approaches:1) Fine scale radar;2) Coarse scale radiometer;3) Median scale combined;
Why combined method?
1) Account for missing data.2) Use noisy high-res radar to
downscale coarse radiometer.3) Use information in overlapped
observations.
Assimilation approach: Assimilate radar backscatter and
radiometer brightness observations into a combined soil moisture retrieval.
HYDROS OSSE: Observing System Simulation Experiment
To access the potential accuracy of HYDROS instruments in soil moisture retrievals using a set of 1km land surface states simulation data
AMS’04, Seattle, WA. January 12, 2004 Slide 4
TOPLATS 1km hydrological model input and output from Crow [2001] (SM, vegetation, soil, Tsoil, Tskin, Precip(Rf )) for the Red-Arkansas River Basin for 34 days from May 26 to June 28, 1994.
AVHRR NDVI composite from June 1995;
Vegetation and Soil parameters derived by HYDROS Science Team;
Data Domain Land Cover
OSSE Simulation Data Set
AMS’04, Seattle, WA. January 12, 2004 Slide 5
Update State estimate with observation:
Update the error Covariance:
Forecast steps:
Project the State ahead:
Project the error Covariance ahead:
)0,,ˆ(ˆ1 kkk uf
XX
kTkkkk QAPAP
1
Update steps:
Compute the Kalman gain:
))0,ˆ((ˆˆ kkkkk hK XOXX
kkkk PHKIP )(
Tkkkk
Tkk
k HPHR
HPK
Data Assimilation merges observations & model predictions to provide a superior state estimate:
Xa = Xb + K (O - Ô) Ô = h(Xb,0)
Extended Kalman Filter (EKF) tracks the conditional mean of a statistically optimal estimate of a state vector X through a series of forecast and update steps
Extended Kalman Filter Data Assimilation
AMS’04, Seattle, WA. January 12, 2004 Slide 6
1 km SM,LC, ST, Tsoil, Tskin, NDVI, rf
3/36 km Sigmas36 km Tbs
3/36 km Sigmas36 km Tbs
1 km Sigmas1 km Tbs
Radar forward model
Radiometer forward model
Gaussian NoiseGaussian Noise
3/9/36 km SM Retrievals
aggregate
3/9/36 km SM “Truth”
3/9/36 km SM Retrieval Errors
Resample or aggregate
EKF DA Retrieval Data Flow Chart
aggregate
3/36 km Precipitation
3/36 km SM Estimate
LSM
Aggregateforcing
EKF Data Assimilation Algorithms
AMS’04, Seattle, WA. January 12, 2004 Slide 7
144
3
2
1
...
SM
SM
SM
SM
X
144
144,3,
1
144,3,
144
1,3,
1
1,3,
1441
1441
...
.........
...
...
...
36,36,
36,36,
SMSM
SMSM
SM
T
SM
TSM
T
SM
T
H
kmhvkmhv
kmhhkmhh
bb
bb
kmvkmv
kmhkmh
)]([ VHXZKXX bba
EKF Data Assimilation Algorithm
144,3,
1,3,
36,
36,
...
kmhv
kmhh
kmv
kmh
b
b
T
T
Z
AMS’04, Seattle, WA. January 12, 2004 Slide 8
1. Do DA retrievals only at 3km scale and aggregate them up to 9km scale, use a former instrument error rate setup to compare the DA retrieval accuracy with mathematical inversion method:tb1: Use Tbv & Tbh onlyts1: Combine Tbv & Tbh with vv, hh & vh
Tbv & Tbh : 36km obs having 1.0K noise
vv, hh & vh: 3km obs having 0.5dB noise
2. Retrieve SM by using 36km Tb inversed SM rather than a LSM as Xb and assimilating sigmas into Xb with reproduced OSSE data: Kp = 0.15 and 3x3 moving average smoothing;
3. Retrieve SM by using 36km Tb inversed SM rather than a LSM as Xb and assimilating sigmas into Xb with various sigma noise levels: Kp = 0.05, 0.10, or 0.15
EKF Data Assimilation Retrieval Experiments
AMS’04, Seattle, WA. January 12, 2004 Slide 9
___ EKF DA Retrieval, ___ Math InversionPrevious OSSE data set with sigma noise = 0.5dB
0
1
2
3
4
5
6
7
8
0 5 10 15 20 25 30 35
RMSD_sda
RMSD_sdi
Day [DOY 146-179]
0
1
2
3
4
5
6
7
8
0 5 10 15 20 25 30 35
RMSD_sda
RMSD_sdi
Day [DOY 146-179]
tb1 ts1
RMSD of EKF DA SM Retrievals
AMS’04, Seattle, WA. January 12, 2004 Slide 10
RMSE of Different SM Retrievals
Reproduced OSSE data set with sigma noise Kp = 0.15
Sigma Inversion: Mathematically inverse sigmas
EKF Assimilation: 2D EKF 144 elements of X and 434 element Z
Tb Inversion: Mathematically inverse Tbh or Tbv0
2
4
6
8
10
12
145 150 155 160 165 170 175 180
Day of Year [1994]
Sigma Inversion
EKF Assimilation
Tb Inversion
AMS’04, Seattle, WA. January 12, 2004 Slide 11
Spatial Comparison of Different SM Retrievals
Reproduced OSSE data set with sigma noise Kp = 0.15
Sigma Inversion
EKF Assimilation
Tb Inversion
-50 -20 -10 -4 4 10 20 50 %VMSRMSE = 6.7%
RMSE = 6.5%
RMSE = 10.5%
AMS’04, Seattle, WA. January 12, 2004 Slide 12
Impact of Sigma Noise on SM Retrievals
Kp = 0.05
Kp = 0.10 Kp = 0.15
Dry area
0
2
4
6
8
10
12
145 150 155 160 165 170 175 180
Day of Year [1994]
Sigma Inversion
EKF AssimilationTb Inversion
0
2
4
6
8
10
12
145 150 155 160 165 170 175 180
Day of Year [1994]
Sigma Inversion
EKF AssimilationTb Inversion
0
2
4
6
8
10
12
145 150 155 160 165 170 175 180
Day of Year [1994]
Sigma Inversion
EKF AssimilationTb Inversion
AMS’04, Seattle, WA. January 12, 2004 Slide 13
Impact of Sigma Noise on SM Retrievals
Kp = 0.05
Kp = 0.10 Kp = 0.15
Wet area0
2
4
6
8
10
12
145 150 155 160 165 170 175 180
Day of Year [1994]
Sigma Inversion
EKF AssimilationTb Inversion
0
2
4
6
8
10
12
145 150 155 160 165 170 175 180
Day of Year [1994]
Sigma Inversion
EKF AssimilationTb Inversion
0
2
4
6
8
10
12
145 150 155 160 165 170 175 180
Day of Year [1994]
Sigma Inversion
EKF AssimilationTb Inversion
AMS’04, Seattle, WA. January 12, 2004 Slide 14
-50 -20 -10 -4 4 10 20 50 %VMS
Impact of Sigma Noise on SM Retrievals
Kp = 0.10 RMSE = 9.2%
Kp = 0.15 RMSE = 10.3%
Kp = 0.05 RMSE = 6.3%
AMS’04, Seattle, WA. January 12, 2004 Slide 15
Using Kalman Filter data assimilation algorithm may combine HYDROS passive and active observations to produce useful median resolution soil moisture data;
KF DA can also be used for SM retrieval with a more physically detailed land surface model for the background estimate Xb;
With EKF DA retrieving SM, VWC and Ts simultaneously may be possible by using all radar and radiometer observations.
Summary and Discussions