**5. Conclusions**

**Figure 11.** Comparison of SM estimates under different roughness hypothesis with ground measurements. "LR" stand for low roughness, "HR" for high roughness, "Whole" for the whole range of roughness and adaptive for adaptive

58 Dynamic Programming and Bayesian Inference, Concepts and Applications

**Figure 12.** Taylor diagram showing the comparison under different prior hypotheses on roughness. A refers to ground measurements; B to low roughness; C to high roughness; D to whole range of roughness; E adapted rough‐

values of roughness.

ness ranges.

The main objective of this chapter is to present the capability of Bayesian approach to estimate SM values starting from SAR backscattering coefficients. Two case studies are presented where SAR acquisitions took place over agricultural fields. The first case study was related to an Argentinean test site developed and equipped for acquisitions of airborne L band SAR called SARAT. The acquisitions were carried out in preparation of the SAOCOM mission. The second case study was related to the experiment SMEX'02 carried out in IOWA in 2002. In this experiment airborne AirSAR images were available and for this reason the retrieval was applied to C band, L band and C+L band data.

Based on the retrieval results, the main goal was then to verify the sensitivity of the SM estimates from the set prior information on roughness and vegetation. All the prior PDFs are set a uniform, non-informative but the set limits of the interval in the integration procedure can determine variation in the final SM estimates. This behavior is expected because the electromagnetic models used in the retrieval approach contain explicitly the dependence of backscattering coefficients on roughness and vegetation parameters.

The effect of prior information ranges from few percentages up to 25% where the highest sensitivity is found in both case studies when too specific and narrow intervals for roughness are used. The highest performances were found for both case studies when the range of roughness is large enough to include most roughness measurements. Moreover, if a prelimi‐ nary assessment on the roughness level is available, the algorithm determines the highest performances with respect to the ground reference data.

An interesting feature observed in the case of Argentinean test site is the reduction of errors on the SM estimates when the retrieval is performed on average values of backscattering coefficients from each field. This behavior can be due to the reduction of noise present in the SAR signal.

As main conclusion of this analysis and suggestions in using the proposed the Bayesian algorithms for SM estimation, the following considerations emerge:

