1. A BayesianMethodology for Soil Parameters Retrieval from SAR Images M. Barber1, M. Piscitelli2, P. Perna1, C. Bruscantini1, F. Grings1, J. Jacobo-Berlles3, H. Karszenbaum1 1Grupo de Teledetección Cuantitativa, Instituto de Astronomía y Física del Espacio (IAFE), Buenos Aires, Argentina. 2 Facultad de Agronomía, Universidad Nacional del Centro de la Provincia de Buenos Aires (UNCPBA), Azul, Argentina. 3 Departamento de Computación, Facultad de Ciencias Exactas y naturales, Universidad de Buenos Aires (UBA), Buenos Aires, Argentina. Session TU2.T03: Soil Moisture Remote Sensing II 24-29 July, Vancouver, Canada.

3. Hydrological applications (water dynamics and runoff, both closely related with water erosion, risk of floods).

5. In this context the goal of this work is to develop a soil moisture retrieval algorithm.As previous work a 3D laser profiler was developed and tested as part of the thesis done to complete my degree in Physics (Licenciatura en Física). SAC-D SAOCOM Launched in 2011 To be Launched in 2015

7. Leads to a grain-like appearance of SAR images.

8. Decreases the contrast and radiometric quality of SAR images.

9. It is usually reduced by spatial averaging at the expense of spatial resolution.SAC-D SAOCOM Launched in 2011 To be Launched in 2015

11. Relates soil parameters

12. volumetric soil moisture m (cm3/cm3),

14. Presented in an algebraic, explicit way.

17. It takes into account no speckle effects at all (i.e. achieved by averaging)These facts will implicitly be in any retrieval scheme that uses Oh model as the forward model. Through a minimization procedure, Oh [Oh 2004] establishes an algorithm for retrieving soil moisture and roughness from a set of measured backscattering coefficients hh, vv and vh. Shaded area encloses the Oh Model validity region SAC-D SAOCOM Launched in 2011 To be Launched in 2015

19. Which soil moisture estimate should be chosen in case of a measured (hh,vv) pair laying outside the validity region? A minimum-distance criterion could be an option but would yield to strongly noisy estimations.In this sense a retrieval scheme based only in Oh Model is not suitable for real applications (i.e. those involving coherent imaging as from SAR systems). Then, we should deal with the speckle noise affecting SAR images. SAC-D SAOCOM Launched in 2011 To be Launched in 2015

20. Multiplicative Model for speckle The Multiplicative Model includes terrain backscatter and speckle noise Z=X.Y X and Y are assumed to be independent return speckle backscatter If target is modeled without considering speckle, then Z=X.1 How can we develop a model that includes terrain features as well as speckle noise in order to achieve a suitable retrieval for soil parameters, mainly for soil moisture? SAC-D SAOCOM Launched in 2011 To be Launched in 2015

21. Bayes’ theorem Likelihood Prior Posterior Evidence The Posterior is conditional probability of measuring m and ks given measured SAR backscattering coefficients hh, vv, vh. The Likelihood involves forward model as well as speckle model. In the Prior is included all a priori information about m and ks. The Evidence is an overall normalization factor. Providing the conditional density function the optimal unbiased estimators are: D={0.04<m<0.297 cm3/cm3,0.13<ks<3.5). SAC-D SAOCOM Launched in 2011 To be Launched in 2015

22. In our case the Oh Model is rewritten in terms of the multiplicative model as hh =f1(m,ks) vv =f2(m,ks) vh=f3(m,ks) Z1=X1Y1 Z2=X2Y2 Z3=X3Y3 Model hypotheses Xi=fi(M,KS) (i=1,2,3), so that fi represents the deterministic “typical” or average way in which the random variable Xi depends on the random variables M and KS (which represent target's m and ks). It is sound to state E[Xi]=fi(E[M],E[KS]), (i=1,2,3). Speckle adds only a multiplicative noise of mean value E[Yi]=1, (i=1,2,3). Under these hypotheses E[Zi]=E[Xi]E[Yi]=fi(E[M],E[KS]), (i=1,2,3) getting the proper average behavior for the returns in terms of the chosen forward model. SAC-D SAOCOM Launched in 2011 To be Launched in 2015

23. Model parameters In ordertoperform a numerical simulation, the following functions and model parameters are required: Probability density function for M and KS. Prior. Number of looks n. For the purpose of the simulation, it will be assumed that: M and KS are normally distributed with sm=0.005 and sks=0.01. the Prior is uniformly distributed: U[0.01-0.35] for m and U[0.1-4.0] for ks. n=3 and n=64 will be used for the number of looks. SAC-D SAOCOM Launched in 2011 To be Launched in 2015

24. Results Case n=3 One-sigma standard deviation contour lines Estimated m Units of m in cm3/cm3 SAC-D SAOCOM Launched in 2011 To be Launched in 2015

25. Results Case n=64 One-sigma standard deviation contour lines Estimated m Units of m in cm3/cm3 SAC-D SAOCOM Launched in 2011 To be Launched in 2015

27. When significant multi-looking is present the Bayesian retrieval looks more compact around the corresponding contour lines of Oh Model indicating a correct asymptotical behavior.

28. In the same way, the one-sigma contour lines are also computed yielding an estimator for the retrieval errors.

30. Such a Bayesian methodology:

31. Needs only a forward model (no retrieval model required) and a speckle model.

32. Gives an estimator of soil parameters as well as their associated error.

34. Studying the sensitivity of the retrieval in terms of terrain heterogeneity parameters sm and sks.