HYDROS Radiometer and Radar Combined Soil Moisture Retrieval Using Kalman Filter Data Assimilation

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