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The potentiality of polarimetric SAR data for the estimation of bare soil geophysical parameters (i.e., roughness and soil moisture) is investigated in this work. For this purpose, two forward models available in the literature, able to simulate the measurements of a multifrequency radar polarimeter, have been implemented for use within an inversion scheme. A multiplicative noise has been considered in the multidimensional space of the elements of the polarimetric Covariance Matrix, by adopting a complex Wishart distribution to account for speckle effects. An additive error has been also introduced on the simulated measurements to account for calibration and model errors. Maximum a Posteriori Probability and Minimum Variance criteria have been considered to perform the inversion. As for the algorithms to implement the criteria, simple optimization/integration procedures have been used. A Neural Network approach has been adopted as well. A correlation between the roughness parameters has been also supposed in the simulation as a priori information, to evaluate its effect on the estimation accuracy. The methods have been tested on simulated data to compare their performances as function of number of looks, incidence angles and frequency bands, thus identifying the best radar configuration in terms of estimation accuracy. Polarimetric measurements acquired during MAC Europe and SIR-C campaigns, over selected bare soil fields, have been also used as validation data.

The sensitivity of bare soil radar backscattering to soil moisture content and roughness has been demonstrated by several studies, both experimental and theoretical (e.g., [^{0}

Discriminating the contribution of soil moisture and surface roughness to the backscattered radar signal is a crucial aspect when dealing with the retrieval problem [

Different approaches have been adopted to deal with the retrieval problem both from single- and multiparameter SAR data. Generally, empirical/semi-empirical techniques and physical methods are distinguished [

Theoretical electromagnetic models physically describe the soil electromagnetic properties and the scattering mechanisms [

Despite the differences between retrieval approaches discussed above, the same statistical criteria should drive the retrieval process. Regression techniques are very often used to solve the problem, especially in the framework of empirical approaches when some linear relation between predictors and parameters to be retrieved can be always postulated [

The objective of this work is to investigate the potential of estimating bare soil parameters (soil moisture _{v}

We have applied the retrieval algorithms to both simulated and real data. The Integral Equation Model (IEM) [

The analysis of the simulated data has allowed us to identify the best system parameters (frequency, polarization and incidence angle) to estimate soil moisture and roughness. The experimental part of the work makes use of measured data available from airborne MAC Europe and from spaceborne SIR-C campaigns, both over the Italian test site of Montespertoli, Florence. Some bare soil fields have been selected in the images, whose roughness was determined by different rural tillage (ploughed, harrowed and rolled fields). The retrieval algorithms have been applied to the polarimetric radar signatures of the fields, where corresponding ground truth measurements were available for comparison.

The comparison of different estimation approaches, as well as the evaluation of the best sensor configuration, aims at yielding a contribution to find a reliable road to solve the problem of bare soil parameter retrieval from radar data. However, because of the numerous complications discussed at the beginning of this section, an ultimate solution to this problem is still far from being obtained.

The work is organized as follows. Section 2 provides a brief review on polarimetric radar data and on the direct models used to simulate them. Section 3 describes the methodologies we have used to estimate soil parameters, i.e, both the criteria followed for estimating the parameters and the algorithms implementing the criteria. Section 4 discusses the results and Section 5 reports the concluding remarks.

A polarimetric radar is able to measure the 2×2 Scattering Matrix _{hv}_{vh}

SAR data are usually multilook processed for speckle reduction. In this case, the Mueller matrix, which relates the scattered modified Stokes vector to the incidence Stokes vector, is generally introduced. It is well known that, instead of the Mueller matrix, it is possible to refer to the so called polarimetric Covariance Matrix

A multilook radar yields a maximum likelihood estimator of ^{0}_{hh}_{hh}s_{hh}^{2} distribution of order 2

A forward model maps the three soil moisture and roughness parameters, i.e., _{v}_{v}_{v}

A very fundamental aspect in the development of rough surface scattering models is the way the randomness of the surface is characterized. In this paper, we refer to the classic description of the roughness as a stationary bivariate random process, which is described by the autocorrelation function or, alternatively, by the power density spectrum. An exponential autocorrelation function has been adopted. The vertical scale of the roughness is described by the standard deviation

The first direct model considered here has been proposed by Oh _{hh}s_{vv}_{hh}s_{vv}

The second direct model is referred to in the literature as the Integral Equation Model (IEM), since it is a closed form solution of the integral equation applying to the surface electromagnetic field at the boundary between the air and a rough soil. The solution has been proposed by Fung

An exponential autocorrelation function (ACF) has been adopted in this work. The choice of the correct ACF is still object of discussion and it seems that the exponential ACF is better for small roughness, whilst the Gaussian one better predicts rough surface scattering. As for the soil permittivity, a model proposed in the literature that relates it to soil moisture and composition on a wide frequency spectrum has been used [

The logical scheme of the procedure adopted in this work is shown in ^{0}_{v}

The inversion method should be able to infer the soil parameters from the measurements. This requires knowledge about the direct mapping _{v}

From the computed covariance matrices _{v}

In order to take into account further sources of discrepancies (i.e., calibration errors, model errors, etc.), an additive error has been also introduced in the simulation, as described in a subsequent paragraph.

Whilst soil moisture _{v}_{v}

The Bayesian theory of parameter estimation has been considered to infer _{v}_{Θ}_{Θ}^{n−q}_{v}

If, instead of searching for the maximum _{Θ}) given by the Wishart distribution in

In the case of

In the absence of prior information on the soil parameters, apart from their ranges of variability, they are assumed statistically independent with uniform distribution, so that _{Δ}_{θ}

In order to compute MAP and MV estimates, minimization and integration techniques have to be implemented, respectively. We have used a simple method based on a Monte Carlo approach. It requires the statistical generation of a database {_{v}_{v}_{v}_{v}_{v}

As mentioned, Neural Network (NN) approaches have been widely used for soil parameter retrieval from radar data (e.g., [

A feed-forward NN has been considered, having, besides the input layer, a hidden layer of neurons with tan-sigmoid transfer functions and an output layer of neurons with linear transfer functions. The training process is able to produce a network that minimizes the mean square error between the output

Note that the NN does not account explicitly for prior information about soil parameter statistics. However, as the training set reflects such properties of the quantities to be retrieved, the NN should be able to extract this information from it. Finally, it is worth underlining that the NN basically implements a MV criterion without any assumption on the statistics of the data.

In this section we present the retrieval results using a simulated test set produced using both the IEM and the SEM direct models to simulate P (0.45 GHz), L (1.2 GHz), C (5.3 GHz), and X (9.66 GHz) band radar data. The accuracy of the estimation may be calculated in different ways. Here we have chosen to represent it in terms of the root mean square (rms) of the estimation error (the latter defined as the difference between the estimated and true values of the parameter to be retrieved), normalized to the prior standard deviation of the parameter, i.e. the standard deviation in the test database (hereafter normalized rms error). Evaluating the performances of the retrieval algorithms in terms of rms error, although fairly common, implicitly makes the MV- and NN-based estimators advantaged with respect to the MAP-based one, since the latter does not minimize the mean square error. It is interesting to compare the histograms of the error to analyze the effect of using different criteria. _{v}

Different numbers of looks are considered when dealing with speckle effects. When

_{v}_{v}

_{v}

To analyze the impact of other sources of discrepancies between ^{0}_{hh}^{0}_{vv}^{0}_{vh}_{hh}s_{vv}_{vv}s_{hh}

As expected, the accuracy generally decreases with the increase of the additive error. _{v}

The model outputs have been compared to the polarimetric data acquired by the AIRSAR sensor (developed by JPL/NASA) during the MAC Europe Campaign in 1991 [_{2}) soil masses and the volume (_{1}−_{2})/

The SEM simulation provides a good matching with the values of

The bias between SEM simulations and real ^{0}

The results obtained by using the MV criterion with the Monte Carlo integration are presented in _{v}_{v}

Different approaches for estimating bare soil parameters from multifrequency and polarimetric radar data have been described, to assess the potentiality of SAR polarimetry. They invert electromagnetic rough surface models in the framework of Bayesian criteria and Neural Network approaches. The methods have been tested on simulated data to compare their performances as function of number of looks, incidence angles and frequency bands. Neural Networks provide the best results when retrieval performances are measured by rms error (normalized to parameter standard deviation). MAP and MV criteria yield less accurate results, even though their clear theoretical framework and relatively small computer load can be appealing in some cases. By introducing

The analysis has also provided quantitative answers to some questions regarding the most profitable frequency band and incidence angle for accurate soil parameter retrieval. The L band provides best results when compared with other frequency bands. Lower incidence angles are better for _{v}

The application of the retrieval methods to a small set of real data shows results which are comparable to the predicted one for soil moisture and less satisfactory for roughness standard deviation. A small bias between radar data and SEM simulations had to be removed. The accuracy obtained for

This paper is intended to yield a contribution to find a reliable approach for bare soil parameter estimation from radar data, even though an ultimate solution to such a challenging problem is far to be obtained.

Logical scheme of the procedure adopted in this work.

Comparison between histograms of the _{v}

Accuracy estimation (in terms of normalized rms error) vs. frequencies and number of looks (reported between brackets) for IEM simulated measurements at

Same as

Accuracy estimation (in terms of normalized rms error) vs. incidence angle for SEM simulation, multifrequency (LCX) and multilook (

Scatterplot of SEM simulated versus measured backscattering coefficient (

MV estimated versus measured bare soil parameters for MAC and SIR-C campaigns. Upper, central and lower panel concern soil moisture, standard deviation of height and correlation length, respectively.

Comparison of retrieval results (in terms of normalized rms error) using MAP, MV and NN algorithms tested on a SEM-derived simulated database. Simulated data concern

_{v} |
_{v} |
_{v} |
||||||
---|---|---|---|---|---|---|---|---|

0.178 | 0.128 | 1.377 | 0.198 | 0.097 | 1.083 | 0.142 | 0.099 | 0.987 |

Same as

_{v} |
_{v} |
_{v} |
||||||
---|---|---|---|---|---|---|---|---|

0.114 | 0.086 | 0.561 | 0.101 | 0.082 | 0.397 | 0.138 | 0.096 | 0.516 |