Soil Parameter Retrieval from Backscattering Measurements by using a Bayesian Approach combined with IEM simulations

In this paper, a procedure for the retrieval of the soil moisture values from SAR measurements, based on a Bayesian approach, is shown. This method offers a rigorous probabilistic framework to face up to the inversion problem. The followed procedure consisted first in evaluating the discrepancies between an analytical e.m. model simulations and the measured backscattering data useful for the calculation of the probability density function (pdf). In this first step the Integral Equation Model (IEM) was used to generate reference values of backscattering coefficient from direct measurements of soil parameters. The Bayesian model was then applied to retrieve the dielectric constant from SAR data, and, lastly, the results obtained by using the inversion procedure were compared with the experimental data set. Section 1 The correlation of backscattering coefficient at different frequencies with soil parameters was widely demonstrated in many theoretical and experimental investigations, in particular at C and Lbands and at low incidence angles. However, the obtained relationships vary very much according to the combinations of soil parameters and to the different observation conditions. Multi-sensor techniques are able to discriminate different contributions of the soil features to the global system response and, in fact, by using different frequencies, polarization and incidence angle, it is possible to improve the accuracy in the extraction of information. The development of inversion algorithms is extremely challenging and strongly dependent on environmental factors. In general, the retrieval of soil and vegetation parameters from radar measurements is a typical illposed problem, generally because more than one combination of soil parameters (soil moisture, roughness etc.) has the same electromagnetic response. In order to univocally retrieve the soil parameters (in particular the soil moisture content) from SAR data, a Bayesian approach was chosen, because this method offers a rigorous probabilistic framework to face up to the inversion problem. This technique, based on the Bayes theorem (1793), updates the likelihood of a event, given a previous likelihood estimate and an additional evidence. One of the advantages of this method is the ability to incorporate a priori information on the target, also through the use of casual/direct models; thus, it provides additional constraints to overcome the ill-poseness of the problem. In the present work, the bayesian approach was applied to the retrieval of soil parameters from radar measurements at C band in H and V polarization. In particular the attention was focused on the retrieval of dielectric constant of soil from backscattering coefficients, since moisture content of soil can be estimated from this parameter by means of the inversion of theoretical models such as Dobson model. Applying the Bayes theorem, the conditional density function P(ε,s,lc|σVV ,σHH ), which represents the probability to have these values of ground parameters once given the measured backscattering, can be expressed as: P(ε,s,lc |σVV ,σHH )= ) , ( ) , , | , ( ) , , ( 0 0 0 0 HH VV HH VV post prior P lc s P lc s P σ σ ε σ σ ε