**2.1. Argentinean study area**

polarizations should, in theory, improve the SM estimate. The general consensus of the literature indicates that low incidence angles, long wavelengths (such as L-band) and both HH and HV polarization settings are the most appropriate sensor for an accurate SM estimate [1]. Another effective approach to mitigate the ambiguity introduced by the vegetation and roughness is to focus attention on the temporal variations through time series of radar images. In this case the basis is to assume that the average roughness characteristics and vegetation remain almost unaltered while variations in moisture content affect backscatter signal along the time [21, 22]. In this regard, methods have been developed using change detection series, as in the recent study [23] Hornacek et al. (2012) used data from the wide swath Envisat/ASAR acquisition mode as part of an evaluation of the potential of algorithms for estimating SM for

In remote sensing, researchers have to deal with two problems: the direct problem and the inverse problem. The direct problem refers to the development of electromagnetic models that can correctly characterize ground backscatter coefficient by using as input the sensor param‐

These models provide a solid physical description of the interactions between the electromag‐ netic waves and the objects on the Earth's surface (e.g., bare soil or vegetation), allowing to simulate numerous experimental settings in terms of sensor configurations and soil charac‐ teristics. The generality of models is a property essential to avoid dependence on local site conditions and characteristics of the sensor, a situation that often occurs when working with

Once the models have been validated, it is possible to develop algorithms to invert these models and predict soil surface properties using radar observations as inputs, which is the

Numerous backscattering models have been developed in recent decades to help determine the relationship between the measured signal at the sensor and biophysical parameters, with particular emphasis on understanding the effects of surface roughness [11, 25, 27]. Considering the inversion of the direct models many approaches have been developed through numerical simulations of forward models which include Look Up Tables, Neural Networks, Bayesian

For example, the potential of some of these approaches to provide accurate maps of SM has been investigated by Pampaloni et al. (2004) [28]. They conducted a performance comparison of the three inversion algorithms using time series of Envisat ASAR cross-and co-polarized images on a farm site in Italy. The algorithms evaluated for accuracy, error rate and compu‐ tational complexity were: multilayer perceptron neural network, a statistical approach based on the Bayesian theorem and iterative optimization algorithm based on the Nelder-Mead

Among the different methods, the Bayesian approach has been deeply investigated for its capability to provide an evaluation of the uncertainties on the variable estimates as well as the possibility to create hierarchical models with different sources of information [11, 21, 29, 30].

configuration, as well as soil parameters, such as dielectric constant and roughness.

), the wavelength (λ) and a specified polarization

Sentinel-1 mission of ESA.

evidence-based algorithms.

method.

eters, such as the angle of incidence (θ<sup>i</sup>

42 Dynamic Programming and Bayesian Inference, Concepts and Applications

solution to the inverse problem [24,25,26].

approaches, and minimization techniques.

The procedure adopted here was applied to data from SARAT L Band active sensor. The SARAT SAR is an airborne sensor (figure 2) used to simulate the SAOCOM images to be analyzed in feasibility studies. The SAR Airborne instrument works in L band (λ=23cm) and is fully polarimetric.

The data set consists of field soil moisture content measurements with the corresponding backscattering coefficients at HH, HV, VH and VV polarizations and 25° incidence angle acquired with a L-band SARAT sensor. SARAT project includes an airborne sensor and an experimental agricultural site. It is part of the SAOCOM mission of Argentinean Space Agency (CONAE). The main aim of the SARAT project is to provide full polarimetric SAR images to develop and validate different applications before the launch of the first satellite SAOCOM, the SAOCOM 1A, estimated for the year 2014. The SAR instrument is installed on a Beechcraft Super King Air B-200 from the Fueza Aérea Argentina (FAA) which has a nominal range of flight altitudes between 4000 and 6000 meters above the Earth's surface, resulting in the formation of images with angles of incidence between 20° and 70°.

Argentina, was selected. Its central geographic coordinates are 31°31'15.08''S-64°27'16.32''W.

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45

The experimental site, chosen for SM, vegetation and surface roughness measurements, has 10 fields with dimension of 50 m x 120 m which contain different kinds of crop and bare soil, as depicted in Fig. 4. All fields were intensively sampled during the SARAT acquisitions.

Plots with crops contain soybean, sunflower, corn and wheat crops. Figure 5 depicts crops

Some plots were left without vegetation to better investigate the interaction of microwave signal with roughness surfaces. The bare soil plots (1N, 2N, 1S and 2S) were ploughed with two roughness levels (low and high roughness) to evaluate the roughness impact on soil

The roughness parameters, namely standard deviation of heights, s, and correlation length, l,

The SARAT images for this study (resolution: 9 m ground range) were acquired on February 2012 and all the data was provided by CONAE. Soil moisture varied between 4% and 40%,

were calculated as indicated in [31]. These parameters are listed in Table 2.

Figure 3 shows the location of the test site.

**Figure 3.** Location of the test site at Conae, in Argentina.

stage at the moment of the SARAT acquisition time.

moisture retrieval at plot level, as shown in Fig. 6.

even though most plots showed medium-dry conditions.

**Figure 2.** SARAT instrument and Aircraft of the FAA.

This SAR system has the same characteristics of the upcoming SAOCOM. These characteristics are described on Table 1.


**Table 1.** Technical characteristics of the SARAT sensor.

SARAT project also includes a validation sites in agricultural areas. For this study, an area inside the CETT (Teófilo Tabanera Space Center of CONAE) located in Cordoba province, Argentina, was selected. Its central geographic coordinates are 31°31'15.08''S-64°27'16.32''W. Figure 3 shows the location of the test site.

**Figure 3.** Location of the test site at Conae, in Argentina.

**Figure 2.** SARAT instrument and Aircraft of the FAA.

Central frequency 1.3 GHz (L band)

44 Dynamic Programming and Bayesian Inference, Concepts and Applications

Azimuth resolution 1.2 m (nominal)

Spatial resolution 6 m (nominal)

Polarization Quad-Pol (HH, HV, VH y VV)

Incidence angle 20° - 70° (nominal to 4200 m of height)

SARAT project also includes a validation sites in agricultural areas. For this study, an area inside the CETT (Teófilo Tabanera Space Center of CONAE) located in Cordoba province,

Swath 9 km (nominal to 4200 m of height)

Chirp bandwidth 39.8 MHz

Pulse duration 10 μm

Pulse Repetition Frequency 250 Hz

Slant Range resolution 5.5 m

Dynamic Range 45 dB

PSLR -25 dB

Noise equivalent σ<sup>0</sup> -36.9 dB

**Table 1.** Technical characteristics of the SARAT sensor.

are described on Table 1.

This SAR system has the same characteristics of the upcoming SAOCOM. These characteristics

The experimental site, chosen for SM, vegetation and surface roughness measurements, has 10 fields with dimension of 50 m x 120 m which contain different kinds of crop and bare soil, as depicted in Fig. 4. All fields were intensively sampled during the SARAT acquisitions.

Plots with crops contain soybean, sunflower, corn and wheat crops. Figure 5 depicts crops stage at the moment of the SARAT acquisition time.

Some plots were left without vegetation to better investigate the interaction of microwave signal with roughness surfaces. The bare soil plots (1N, 2N, 1S and 2S) were ploughed with two roughness levels (low and high roughness) to evaluate the roughness impact on soil moisture retrieval at plot level, as shown in Fig. 6.

The roughness parameters, namely standard deviation of heights, s, and correlation length, l, were calculated as indicated in [31]. These parameters are listed in Table 2.

The SARAT images for this study (resolution: 9 m ground range) were acquired on February 2012 and all the data was provided by CONAE. Soil moisture varied between 4% and 40%, even though most plots showed medium-dry conditions.

**Parameter Symbol High roughness value Low roughness value**

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SMEX'02 is a remote sensing experiment that was carried out in Iowa in 2002. The main site, chosen for soil moisture, vegetation and surface roughness measurements, was the Walnut Creek watershed, where 32 fields, 10 soybean and 21 corn fields, were sampled intensively [32]. The field and sensor data acquired during this experiment are particularly suitable thanks to the significant number of surveyed fields and wide range of soil conditions. The AirSAR images (resolution: 8-12 m ground range) were acquired on 1, 5, 7, 8, 9 July 2002. The five P-, L-and C-band images were processed by the AirSAR operational processor providing

The retrieval algorithm for SM is based on a Bayesian approach. Bayesian data analysis determines methods to make inference from data by using probabilities models for quantities.

The main characteristic of Bayesian methods is the explicit use of probability for quantifying

**•** Calculate the posterior distribution which provides information on the unobserved

Prior distributions can express our knowledge and uncertainty about the target variable. In this case the target variable could be thought as a random realization from the prior distribu‐

The application of Bayesian approach implies passing from a prior distribution to a posterior distribution. Based on this concept, a relationship is expected between these two distributions [29, 30, 33]. A general feature of Bayesian inference is that the posterior distribution is centered at a point which represents a compromise between the prior information and the data. This

A prior distribution may not have a population basis and for this reason it is desirable to have a prior which plays a minor role in the posterior distributions. These prior distribu‐

Rms height s 3.22 cm 1.55 cm Correlation length l 8.17 cm 5.03 cm

**Table 2.** Mean roughness values inside the bare soil plots.

calibrated data sets.

**2.2. Iowa study area in the SMEX'02 experiment**

**3. Description of the methodology for SM estimation**

The process of Bayesian data analysis consists of three main steps:

**•** Definition of a joint probability model for all variables under evaluation;

compromise is strongly controlled by the data as the sample size increase.

uncertainty in inference based on statistical data analysis.

quantities, given the observed data;

**•** Evaluation of the fit model.

tion.

**Figure 4.** Detail of the sampled plots during SARAT campaign acquisitions. N and S indicate North and South test fields.

**Figure 5.** Soybeans, wheat (winter development), corn and sunflower.

**Figure 6.** Bare plot with induced low (left) and high roughness (right).


**Table 2.** Mean roughness values inside the bare soil plots.
