1. Retrieval of Soil Moisture under Vegetation using Polarimetric Scattering Cubes Motofumi Arii (motofumi@gmail.com) Mitsubishi Space Software Co., Ltd., 792 Kami-machiya, Kamakura, Kanagawa 247-0065 Jakob J. van Zyl and Yunjin Kim Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA

2. x,y : Polarization state for transmitting/receiving Many ways to invert soil moisture from radar backscattering from bare surfaces have been proposed as summarized in [1]. [1] J. J. van Zyl and Y. Kim, "A quantitative comparison of soil moisture inversion algorithms," Proc. of IGARSS01 , Sydney, Australia, Jul. 2001. Soil Moisture Retrieval from Bare Surface

3. p vi : Parameters to characterize vegetation More than 76% [2-3] of the earth surface is covered by vegetation. Surface Volume (Canopy) Double bounce (Ground-trunk, ground-canopy) Volume (Trunk) Soil Moisture Retrieval from Vegetated Terrain [2] R. T. Watson, I. R. Noble, B. Bolin, N. H. Ravindranath, D. J. Verado, and D. J. Dokken, Land use, land-use change and forestry , Cambridge, UK: Cambridge University Press, 2000. [3] E. Ezcurra, Global Desserts Outlook , Nairobi, Kenya: DEWA, UNEP, 2006.

4. Polarimetric Decomposition Soil Moisture One may try to decompose the Observation

5. - Inversion algorithm : A simple but robust technique proposed by Dubois et al .[4] for bare surfaces assuming L-band (24cm) Preparation for the Demonstration [4] P. C. Dubois, J. van Zyl, and T. Engman, “Measuring Soil Moisture with Imagin Radars,” IEEE Trans. Geosci. Remote Sensing , vol 33, no. 4, Jul. 1995. [5] J. J. van Zyl, M. Arii, and Y. Kim, “Model Based Decomposition of Polarimetric SAR Covariance Matrices Constrained for Non-Negative Eigenvalues,” IEEE Trans. on Geosci. Remote Sensing , 2010 (in press) - Polarimetric Decomposition : Non-Negative Eigenvalue Decomposition proposed by van Zyl et al.[5] assuming cosine squared distribution which is suitable for agricultural area After the decomposition, only HH and VV of the surface scattering component, C s , are utilized to estimate soil moisture by (1). (1) (2)

6. Iowa, at L-band Walnut creek watershed, Iowa observed by AIRSAR in July 2002. The area is widely covered by soy beans and corns. Residential area Densely vegetated area along the river Snapshot

7. Inversion Results -200 0 Maps of Negative  The more vegetation, the smaller  . Of course, negative  is not physically acceptable! Dubois et al. algorithm with decomposition Dubois et al. algorithm only

8. Discrete Scatterer Model (DSM) [6-7] [6] S. L. Durden, J. J. van Zyl, H. A. Zebker, “Modeling and Observation of the radar polarization signature of forested areas,” IEEE Trans. Geosci. Remote Sensing , vol. 27, no. 3, May 1989. [7] M. Arii, “Soil moisture retrieval under vegetation using polarimetric radar,” Ph.D. dissertation California Institute of Technology, Pasadena, CA, pp. 68-101, 2009. [8] M.Arii, J. J. van Zyl, and Y. Kim, "Adaptive decomposition of polarimetric SAR covariance matrices," Proc. of IGARSS09 , Cape Town, South Africa, Jul. 2009. [9] M. Arii, J. J. van Zyl and Y. Kim, “Adaptive model-based decomposition of polarimetric SAR covariance matrices,” IEEE Trans. on Geosci. Remote Sensing , 2010 (in press)   = 0.00 : Delta func. (methodical)   = 0.57 : Cosine squared (medium)    = 0.91 : Uniform (most complicated) Standard deviation of  [8-9]

9. Cosine squared distribution L-band (24cm) DSM for Grassland Variables

10. Inversion without Decomposition Backscatters from the grassland having specific soil moisture (10 to 60%) are generated as a test data in terms of vegetation water content. Then Dubois et al. ’s algorithm estimates dielectric constant using co-polarizations of the simulated data. m v (%)

11. What’s going on? Backscattering Cross Section [dB] m v = 40% Double-Bounce Volume

12. with Decomposition The ideal decomposition technique, which perfectly extracts the surface scattering component, makes the inversion even worse! Note that the DSM allows us to directly use the surface scattering. m v (%)

13. x = h , v Bare Surface Vegetated Terrain Attenuation coefficients are calculated by Optical Theorem as Then the scattering from bare surface are attenuated as Why?

14. Taking into account the attenuation, the inversion model is rewritten as For simplicity, let us take logarithm natural and assume same attenuation coefficients between co-polarizations. The inferred dielectric constant decreases in terms of the amount of vegetation. A new inversion algorithm which explicitly includes the attenuation effect is required!

15. From DSM, we can form the following cubes for backscattering cross sections. j = hhhv, hhvv, hvvv i = hh, hv, vv Polarimetric Scattering Cubes (PSC)

16. The same transformation is applied to measured data. Then the distance between the measured data and each point of the cubes are defined as where, w ’s are weighting functions. i = hh, hv, vv j = hhhv, hhvv, hvvv Minimum Distance Finally, we can determine the variables which minimize the distance.

17. RMSE( kh ) RMSE( m v )[%] RMSE( W c )[kg/m 2 ] The reference cubes (280x280x280 samples) for the grassland is applied to the area that has the same baseline parameters. The 300 test data sets for each plot are generated with randomly chosen m v , kh and W c . Note that the W c has a range between 0 and a number specified in the x axis. The error comes from the number of samples of the cubes. The HHVV plays an important role to remove the vegetation effect. Soil Moisture Vegetation water content Roughness Inversion by PSC

18. RMSE( m v )[%] Soil Moisture Vegetation water content Roughness RMSE( kh ) RMSE( W c )[kg/m 2 ] Sensitivity to Cylinder Radius

19. RMSE( kh ) RMSE( m v )[%] RMSE( W c )[kg/m 2 ] Soil Moisture Vegetation water content Roughness Sensitivity to Distribution,     = 0.00 : Delta func. (methodical)   = 0.57 : Cosine squared (medium)    = 0.91 : Uniform (most complicated)

20. Now noise equivalent  o = - 30 dB, is randomly added to the test data. The lower accuracy is achieved for smaller vegetation water content since smaller HV can be easily affected by the noise. RMSE( kh ) RMSE( m v )[%] RMSE( W c )[kg/m 2 ] Soil Moisture Vegetation water content Roughness Sensitivity to Noise

21. Cube Technique Cube Library Vegetation Type 1 Vegetation Type 2 Vegetation Type n Decomposition Technique Classification Inversion Vegetation Type Weighting Functions Cubes Comprehensive Inversion Strategy