Soil Moisture Estimation over Vegetated Agricultural Areas : Tigris Basin , Turkey from Radarsat-2 Data by Polarimetric Decomposition Models and a Generalized Regression Neural Network

Determining the soil moisture in agricultural fields is a significant parameter to use irrigation systems efficiently. In contrast to standard soil moisture measurements, good results might be acquired in a shorter time over large areas by remote sensing tools. In order to estimate the soil moisture over vegetated agricultural areas, a relationship between Radarsat-2 data and measured ground soil moistures was established by polarimetric decomposition models and a generalized regression neural network (GRNN). The experiments were executed over two agricultural sites on the Tigris Basin, Turkey. The study consists of four phases. In the first stage, Radarsat-2 data were acquired on different dates and in situ measurements were implemented simultaneously. In the second phase, the Radarsat-2 data were pre-processed and the GPS coordinates of the soil sample points were imported to this data. Then the standard sigma backscattering coefficients with the Freeman–Durden and H/A/α polarimetric decomposition models were employed for feature extraction and a feature vector with four sigma backscattering coefficients (σhh, σhv, σvh, and σvv) and six polarimetric decomposition parameters (entropy, anisotropy, alpha angle, volume scattering, odd bounce, and double bounce) were generated for each pattern. In the last stage, GRNN was used to estimate the regional soil moisture with the aid of feature vectors. The results indicated that radar is a strong remote sensing tool for soil moisture estimation, with mean absolute errors around 2.31 vol %, 2.11 vol %, and 2.10 vol % for Datasets 1–3, respectively; and 2.46 vol %, 2.70 vol %, 7.09 vol %, and 5.70 vol % on Datasets 1 & 2, 2 & 3, 1 & 3, and 1 & 2 & 3, respectively.


Introduction
Soil moisture is commonly defined as the amount of water in the soil particles, and is a very important parameter in minimizing the harmful effects of drought, preventing salinity caused by overwatering, protecting agricultural land, and using irrigation systems efficiently [1].Therefore, to determine the amount of water available in the soil used by plants, the soil moisture must be measured.
The retrieval of the soil moisture over large areas by gravimetric methods and digital probes is time-consuming, costly, and labor-intensive work [2].However, successful results can be obtained in a shorter time by using remote sensing techniques.Thus, significant work has been done towards the application of active microwave sensors to monitoring soil surface moisture content [3].Among the active microwave sensors, the Synthetic Aperture Radar (SAR) sensor plays an important role in agricultural monitoring, especially in plant growth, yield, mapping, and soil moisture estimation [4].With the aid of polarimetric SAR, far better information can be derived than with single polarized SAR.The polarimetric SAR is less susceptible to weather conditions and capable of generating suitable high-resolution images for the purpose of agricultural soil monitoring.It provides information by multiple polarizations (hh, hv, vh, and vv) and penetrates the vegetative canopies [5].Therefore, polarimetric SAR data can be used for soil moisture estimation over bare soil surface and vegetation-covered fields.In order to facilitate soil moisture estimation over vegetated agricultural areas, the contribution of the vegetation backscattering and ground scattering component must be separated from the observed backscattering [6].Thus, polarimetric decomposition models are used to discretize the backscattering from the different layers by decomposing a scattering matrix (covariance matrix) into the linear combinations of some specific scattering mechanisms, like the odd bounce scattering, the even bounce scattering, and the volume scattering.The polarimetric decomposition models are based on two main approaches covering coherent decompositions and incoherent decompositions [7].Among the decomposition techniques, H/A/α, Freeman-Durden, Krogager, Touzi, and Yamaguchi are the most widely used models and various works have been done in the literature with the aid of these models.For example, Jagdhuber et al. [8] used the multi-angular polarimetric decomposition model for retrieving soil moisture and found a very high estimation rate with low RMSE (root mean square error).Hajnsek et al. [2] suggested a surface inversion model by using different model-based decompositions under vegetation cover.Xiaodong et al. [9] improved an adaptive two-component decomposition to estimate the soil moisture for C band Radarsat-2.In this study, the eigenvector-eigenvalue based (H/A/α) and the model-based Freeman-Durden decomposition models were used for the feature extraction process since these models offer an efficient way to eliminate the effect of vegetation backscattering from the target backscattering in vegetated agricultural fields [10,11].
After the feature extraction process, a number of inversion models have been improved to estimate soil surface parameters from the texture features.The inversion models withstand three basic approaches in the literature, including the empirical/semi-empirical model [12][13][14], the theoretical model [10,15], and the machine learning model [4,[16][17][18][19][20].In the first approach, the empirical/semi empirical models are based on the scattering attitude of experimental measurements [16] and build a basic relationship between soil surface features and backscattering coefficients reflected from the target point [4].Among the empirical models, Oh [12] and Dubois [13] are the most used inversion models.However, these models have a restricted range of practicability since they depend on site-specific surface parameters and empirical equations are inadequate to solve complex and nonlinear problems.Therefore, theoretical models are preferred as a second approach for soil moisture inversion due to their ability to consider situations that have not been regarded by the empirical models [16].The Integral Equation Model (IEM) [15] is one of the most popular theoretical inversion models and can be used effectively over bare fields owing to its broad availability spectrum of surface roughness.However, this model is limited over vegetated areas since the vegetation causes complex volume backscattering.Moreover, the model requires some in situ measurements, such as surface morphology, which limits its applicability.Thus, the restraint of the model makes the inversions of such models highly complex and infeasible.To solve this problem, numerical inversion models such as machine learning must be considered as a third approach [18].
In machine learning models, soil surface moistures have been estimated successfully over bare and vegetated areas, and these models are used effectively in situations where both empirical and theoretical models are inadequate.Among the machine learning models, Support Vector Regression (SVR) [4,6], Bayes Theorem [21], and Artificial Neural Network (ANN) [21][22][23][24][25] are commonly used inversion techniques for soil moisture retrieval.In the literature, a number of studies have been done using machine-learning-based inversion models.For instance, Weimann et al. [22] derived simulated data from the theoretical backscattering model over bare fields and used this data for training of ANN.They also improved the ANN training system by using remotely sensed ERS-2/ESAR data and observed low RMSE values between estimated soil moisture and ground soil moisture.Paloscia et al. [21] investigated the capabilities of the ENVISAT/ASAR data to provide soil moisture maps over agricultural areas.They compared the performances of three inversion algorithms including a feedforward neural network (ANN), a statistical Bayes' theorem, and the iterative Nelder-Mead method.The results indicated that the estimated data of the three methods were very close to the measured data and the accuracy of ANN was slightly higher than the other methods.Zhang et al. [4] investigated TerraSAR-X and Radarsat-2 data for soil moisture retrieval over bare agricultural areas using both statistical (SVR) and semi-empirical (Modified Dubois) approaches.Their results indicated that the TerraSAR-X and Radarsat-2 were proper remote sensing tools for soil moisture estimation with a low RMSE value.Notarnicola et al. [16] employed the ANN and statistical Bayesian methods for retrieving soil moisture from the active and passive data.The results showed that each method has similar performance, but the performance of the ANN was enhanced with increasing input number.Pasolli et al. [18] proposed two non-linear machine learning methods containing MLP Neural Network and SVR to estimate soil moisture from active and passive microwave data.The performance of these methods was then compared and the results showed that SVR was an alternative approach to MLP since it indicated better accuracy values in the case of limited samples.Said et al. [17] used ANN to retrieve the soil moisture over bare and vegetated surfaces with the aid of ERS-2 SAR data.The results showed a good correlation between the estimated and measured soil moisture.Moreover, ANN produced more precise results than multiple statistical regressions.
The purpose of this study is to determine a relationship between the fully polarimetric Radarsat-2 data and the ground soil moisture measurements as well as estimate the soil moisture over both vegetated and bare agricultural areas based on the determined relationship.The Radarsat-2 data were acquired on different dates in order to extract the sigma backscattering coefficients (σhh, σhv, σvh, and σvv), which describe the soil surface content.Furthermore, the H/A/α and Generalized Freeman-Durden methods were applied on fully polarimetric Radarsat-2 data and various backscattering parameters (entropy, anisotropy, alpha angle, volume scattering, surface scattering, and double bounce) and were derived for the feature extraction stage.After this step, GRNN was used to evaluate the potential of C-band SAR data for soil moisture inversion.

Study Area
The study area is located at the Tigris Basin in Diyarbakır province, Turkey (40  04 N) and consists of two different agricultural lands that cover an average of 6 km 2 and 16 km 2 within the boundaries of the Dicle University campus (Figure 1).The mean slope of the study area is 3.05% and the mean elevation is 650 m.The average annual precipitation is approximately 496.0 mm/year and the average annual temperature is nearly 23.8 • C.This study area was dominated by cropland, which mostly includes wheat and barley during the period of SAR acquisitions (February 2015, April 2015, and June 2015).Hence, we concentrated on soil moisture estimation over vegetated agricultural areas.

Ground Measurements
The ground measurements in the Tigris Basin were organized during 27 February, 8 April, and 10 June 2015 and carried out over two experimental areas at the same time as the Radarsat-2 acquisition.The experimental areas were divided into 100 × 100 m grids and soil surface samples were taken from at least one point of each grid, at 3-5 cm depth.An average of 300 ground soil samples were collected simultaneously with the Radarsat-2 transition for each period.These soil samples were then placed in 100 cm 3 metal cylinders and the location of each sample point was recorded with the help of a global positioning system (GPS).The distance between the sample points was nearly 100 m and the soil moisture content (SMC) for each sample was measured using gravimetric methods at the Dicle University Science and Application Research Center (DUBTAM).The gravimetrical soil moisture measurements (SM) for each period are given in Table 1.

Ground Measurements
The ground measurements in the Tigris Basin were organized during 27 February, 8 April, and 10 June 2015 and carried out over two experimental areas at the same time as the Radarsat-2 acquisition.The experimental areas were divided into 100 × 100 m grids and soil surface samples were taken from at least one point of each grid, at 3-5 cm depth.An average of 300 ground soil samples were collected simultaneously with the Radarsat-2 transition for each period.These soil samples were then placed in 100 cm 3 metal cylinders and the location of each sample point was recorded with the help of a global positioning system (GPS).The distance between the sample points was nearly 100 m and the soil moisture content (SMC) for each sample was measured using gravimetric methods at the Dicle University Science and Application Research Center (DUBTAM).The gravimetrical soil moisture measurements (SM) for each period are given in Table 1.

SAR Data Collection
In this study, the Radarsat-2 data was used over the experimental areas.Radarsat-2 is a world observation satellite that was successfully launched by the Canadian Space Agency in December 2007.It has a SAR sensor that runs at the C-band (5.33 GHz) of the microwave spectrum.Furthermore, it is fully polarimetric and provides multiple imaging modes [26].In this study, three single-look complex (SLC) products that keep the resolution, phase, and amplitude information of the SAR data were used for estimating soil moistures [27].Three Radarsat-2 data with Fine-Quad mode polarization were obtained during the different periods of product development.Each Radarsat-2 has a spatial resolution of 5.83 m and coverage of 30 km × 30 km.

Preprocessing of SAR Data
The preprocessing to be applied to the RADARSAT-2 data was performed in the following steps.Sentinel-1 Toolbox (S1TBX) [28] was used to read the SAR data and extract backscattering coefficients.The data were calibrated to correct SAR images radiometrically and a Refined Lee filter with 7 × 7 windows was used to remove the speckle noise.The filtered data were then geocoded using a SRTM-3 Digital Elevation Model (DEM) and Geographical Latitude/Longitude (WGS84) was chosen as the default output map projection.The GPS values of the sample points were converted to shp-extended vectors by ARCGIS 10.2, then imported to the Radarsat-2 data with the aid of the Sentinel-I toolbox.The accurate geographical registration among the field measurements and Radarsat-2 data was accomplished by utilizing the corner reflectors in the study area.The preprocessed Radarsat-2 images are shown in Figure 2.

SAR Data Collection
In this study, the Radarsat-2 data was used over the experimental areas.Radarsat-2 is a world observation satellite that was successfully launched by the Canadian Space Agency in December 2007.It has a SAR sensor that runs at the C-band (5.33 GHz) of the microwave spectrum.Furthermore, it is fully polarimetric and provides multiple imaging modes [26].In this study, three single-look complex (SLC) products that keep the resolution, phase, and amplitude information of the SAR data were used for estimating soil moistures [27].Three Radarsat-2 data with Fine-Quad mode polarization were obtained during the different periods of product development.Each Radarsat-2 has a spatial resolution of 5.83 m and coverage of 30 km × 30 km.

Preprocessing of SAR Data
The preprocessing to be applied to the RADARSAT-2 data was performed in the following steps.Sentinel-1 Toolbox (S1TBX) [28] was used to read the SAR data and extract backscattering coefficients.The data were calibrated to correct SAR images radiometrically and a Refined Lee filter with 7 × 7 windows was used to remove the speckle noise.The filtered data were then geocoded using a SRTM-3 Digital Elevation Model (DEM) and Geographical Latitude/Longitude (WGS84) was chosen as the default output map projection.The GPS values of the sample points were converted to shp-extended vectors by ARCGIS 10.

Feature Extraction from SAR Data
After the pre-processing step, each GPS value of the sampling point, which corresponds to a SAR pixel, was represented by a cell (3 × 3 pixels) using a 3 × 3 window.These cells are different patterns of the training set and the backscattering coefficients of these patterns were calculated by taking the average of the coefficients in the cell.In order to form a feature vector for each pattern, three feature extraction models were used in this study.In the first approach, four sigma backscattering coefficients (σhh, σhv, σvh, and σvv) were derived from the patterns of different bands (hh, hv, vh, and vv) using standard SAR backscattering coefficients.In the second approach, six backscattering coefficients in total were extracted by using the Freeman-Durden (odd bounce, even bounce, and volume scattering) and H/A/α (entropy, anisotropy, and alpha angle) decomposition models.

Freeman-Durden Decomposition Model
The Freeman-Durden decomposition model is based on three independent scattering mechanisms including volume scattering, double bounce, and odd bounce, and they can be interpreted physically [29].Figure 3 shows the scattering mechanisms.

Feature Extraction from SAR Data
After the pre-processing step, each GPS value of the sampling point, which corresponds to a SAR pixel, was represented by a cell (3 × 3 pixels) using a 3 × 3 window.These cells are different patterns of the training set and the backscattering coefficients of these patterns were calculated by taking the average of the coefficients in the cell.In order to form a feature vector for each pattern, three feature extraction models were used in this study.In the first approach, four sigma backscattering coefficients (σhh, σhv, σvh, and σvv) were derived from the patterns of different bands (hh, hv, vh, and vv) using standard SAR backscattering coefficients.In the second approach, six backscattering coefficients in total were extracted by using the Freeman-Durden (odd bounce, even bounce, and volume scattering) and H/A/α (entropy, anisotropy, and alpha angle) decomposition models.

Freeman-Durden Decomposition Model
The Freeman-Durden decomposition model is based on three independent scattering mechanisms including volume scattering, double bounce, and odd bounce, and they can be interpreted physically [29].Figure 3 shows the scattering mechanisms.Among these components, the volume scattering expresses the canopy scattering generated by randomly oriented dipole clouds.It is supposed that the radar signal is backscattered from a cloud of randomly oriented scatterers, which are very thin and cylinder-like.In order to simulate such scatterers, it is assumed that an elementary dipole is oriented horizontally in the perpendicular linear x-y plane.Let the volume scattering be symbolized by the scatterers, which are in standard orientation, as shown in the scattering matrix in Equation (1) [29]: In this equation, SV and SH denote complex scattering coefficients and they are considered SV >> SH since the dipole is oriented horizontally.If a dipole is turning around the radar look direction under the θ angle, the scattering matrix of the oriented dipole (scatterer) is as in Equation ( 2):

S Cos S Sin S S Cos Sin Svv S S S S S S Cos Sin S Cos S Sin
Since the radar transmitter and receiver coordinate systems are the same, the created scattering matrix becomes symmetric; thus, SHV and SVH are considered equal.Scatterers (dipoles) can be randomly directed by the p(θ) probability density function (PDF) in the radar look direction.The expected value of any function f(θ) is given by Equation (3): Among these components, the volume scattering expresses the canopy scattering generated by randomly oriented dipole clouds.It is supposed that the radar signal is backscattered from a cloud of randomly oriented scatterers, which are very thin and cylinder-like.In order to simulate such scatterers, it is assumed that an elementary dipole is oriented horizontally in the perpendicular linear x-y plane.Let the volume scattering be symbolized by the scatterers, which are in standard orientation, as shown in the scattering matrix in Equation (1) [29]: In this equation, S V and S H denote complex scattering coefficients and they are considered S V >> S H since the dipole is oriented horizontally.If a dipole is turning around the radar look direction under the θ angle, the scattering matrix of the oriented dipole (scatterer) is as in Equation (2): Since the radar transmitter and receiver coordinate systems are the same, the created scattering matrix becomes symmetric; thus, S HV and S VH are considered equal.Scatterers (dipoles) can be randomly directed by the p(θ) probability density function (PDF) in the radar look direction.The expected value of any function f (θ) is given by Equation (3): The covariance matrix for volume (canopy) scattering is represented in Equation ( 4) and the matrix elements are generated using Equation (3): In order to simplify the equations, the uniformly distributed probability function is assumed to be p(θ) = 1 and the thin cylindrical scatterers are S V = 1 and S H = 0. Thus situated, the covariance matrix for volume (canopy) scatter is expressed in Equation ( 7) using the parameters of Equations ( 5) and ( 6): S HH S * HV = S HV S * VV = 0 (6) Here, f v represents the effect of volume scattering on the|Svv| 2 factor.The double bounce scattering is the second component of the Freeman-Durden decomposition, in which a dihedral corner reflector is used to model the scattering stage.For example, the surfaces of a tree trunk and the ground can be used as a dihedral reflector.The covariance matrix for this component is described in Equation (10) using Equations ( 8) and ( 9 where f d indicates the contribution of the double bounce scattering to the |Svv| 2 factor.Lastly, the odd bounce scattering refers to the backscattering from a rough surface and a first-order Bragg surface scattering model is used to represent the rough surfaces in this mechanism.The covariance matrix for this component is described in Equation ( 13) with the aid of Equations ( 11) and ( 12 where f s shows the contribution of surface scattering to the |Svv| 2 factor.On account of this, the measured covariance matrix of the Freeman-Durden decomposition can be defined as the summation of three covariance scattering matrices, as shown in Equation ( 14) [29]:

H/A/α Decomposition Model
The H/A/α decomposition model is built on the eigenvalue and eigenvector analysis of the coherency matrix T 3 , which is expressed as in Equation ( 15) [30]: where the coherency matrix T 3 is represented in Equation ( 16): Here, the λ matrix consists of the eigenvalues computed from T 3 .Additionally, the calculated eigenvectors u i are shown in Equation ( 17): Three eigenvectors (for i = 1, 2, 3) are then used to form the u 3 unitary matrix, as shown in Equation ( 18): where α is the incidence angle, β is the orientation angle, and γ and δ explain the relation of phases.One of the most important aspects of this decomposition model is that the parameters are invariant and constant for rotation around the radar line.Thus, three statistical features including polarimetric entropy (H), anisotropy (A), and alpha angle (α) have been described to make the analysis of this model easier, as shown in Equations ( 19)-( 21), respectively [30]: Here, P i represents the probability of each eigenvalue λ i .

GRNN Algorithm
The Generalized Regression Neural Network (GRNN) is a strong and nonlinear machine learning technique and it has the ability to retrieve complex, dynamic, and non-linear patterns from the data [31,32].It was used to estimate the soil moisture by way of a relationship between measured ground soil moisture and the backscattering coefficient.GRNN has input, pattern, summation, and output layers.The pattern and summation layers can be named hidden layers because they are inside the neural network and do not have any contact with the external surroundings.
The architecture of the GRNN model is indicated in Figure 4.Ten neurons corresponding to different backscattering parameters (σhh, σhv, σvh, σvv, entropy, anisotropy, alpha angle, volume scattering, surface scattering, and double bounce) are used in the input layer.Moreover, the pattern layer is attached to the input layer and the neurons of the pattern layer indicate training patterns.The nonlinear analysis of the input data is implemented in this layer and the distance between input and sample data is measured as the output data of the pattern layer.Then, all neurons of the pattern layer are connected to the summation layer, which has two types of summation neurons (one neuron and multiple neurons).The summation neurons are used to sum the weighted and unweighted outputs of the neurons in the pattern layer.Finally, the one neuron of the output layer computes the outputs of the summation layer to give the estimated result.
Remote Sens. 2017, 9, 395 9 of 22 the data [31,32].It was used to estimate the soil moisture by way of a relationship between measured ground soil moisture and the backscattering coefficient.GRNN has input, pattern, summation, and output layers.The pattern and summation layers can be named hidden layers because they are inside the neural network and do not have any contact with the external surroundings.
The architecture of the GRNN model is indicated in Figure 4.Ten neurons corresponding to different backscattering parameters (σhh, σhv, σvh, σvv, entropy, anisotropy, alpha angle, volume scattering, surface scattering, and double bounce) are used in the input layer.Moreover, the pattern layer is attached to the input layer and the neurons of the pattern layer indicate training patterns.The nonlinear analysis of the input data is implemented in this layer and the distance between input and sample data is measured as the output data of the pattern layer.Then, all neurons of the pattern layer are connected to the summation layer, which has two types of summation neurons (one neuron and multiple neurons).The summation neurons are used to sum the weighted and unweighted outputs of the neurons in the pattern layer.Finally, the one neuron of the output layer computes the outputs of the summation layer to give the estimated result.Assume that x and y become input and output variables, as seen in Equations ( 22) and ( 23 ( The target parameter y can be estimated from x variables by the GRNN regression model. Therefore, the estimated y can be computed as shown in Equation ( 24) [31]: Where n and ς indicate the number of training samples and the spread parameter, respectively.The spread parameter is an important parameter to affect the accuracy of the GRNN model and is used to arrange the kernel width of the Gaussian function [33].

Results
This section explains the results obtained from the standard sigma backscattering coefficients and polarimetric decomposition models.A nonlinear machine learning regression model was Assume that x and y become input and output variables, as seen in Equations ( 22) and ( 23), respectively: The target parameter y can be estimated from x variables by the GRNN regression model.Therefore, the estimated y can be computed as shown in Equation ( 24) [31]: Where n and ς indicate the number of training samples and the spread parameter, respectively.The spread parameter is an important parameter to affect the accuracy of the GRNN model and is used to arrange the kernel width of the Gaussian function [33].

Results
This section explains the results obtained from the standard sigma backscattering coefficients and polarimetric decomposition models.A nonlinear machine learning regression model was trained and tested on the basis of scattering components to estimate soil moisture content.Three datasets were generated in a new manner and the analysis of these datasets is shown below.

Experiments on Dataset 1
In this phase, Dataset 1 was constituted from Radarsat-2 data of 27 February 2015 in order to evaluate the impact of low vegetation cover over the study areas and the following steps were implemented to form Dataset 1.First of all, the standard sigma backscattering technique was applied to the Radarsat-2 data and four sigma backscattering coefficients were computed for each sampling cell.Then, Freeman-Durden and H/A/α decomposition models were employed and three physical three statistical parameters were extracted from the sampling cells.To process the fully polarimetric Radarsat-2 data, calibration, polarimetric matrix generation (generally T 3 Coherency matrix), polarimetric speckle filtering (typically Refined Lee Filter), and polarimetric decompositions steps are mandatory.The images that resulted after data processing are shown in Figure 5.
Remote Sens. 2017, 9, 395 10 of 22 trained and tested on the basis of scattering components to estimate soil moisture content.Three datasets were generated in a new manner and the analysis of these datasets is shown below.

Experiments on Dataset 1
In this phase, Dataset 1 was constituted from Radarsat-2 data of 27 February 2015 in order to evaluate the impact of low vegetation cover over the study areas and the following steps were implemented to form Dataset 1.First of all, the standard sigma backscattering technique was applied to the Radarsat-2 data and four sigma backscattering coefficients were computed for each sampling cell.Then, Freeman-Durden and H/A/α decomposition models were employed and three physical three statistical parameters were extracted from the sampling cells.To process the fully polarimetric Radarsat-2 data, calibration, polarimetric matrix generation (generally T3 Coherency matrix), polarimetric speckle filtering (typically Refined Lee Filter), and polarimetric decompositions steps are mandatory.The images that resulted after data processing are shown in Figure 5.The extracted parameters were then added in succession and the feature vector of 10 units in length (σhh, σhv, σvh, σvv, entropy, anisotropy, alpha angle, volume scattering, surface scattering, and double bounce) was generated from each sampling point.This process was repeated for 335 sampling points in this period and Dataset 1 with 335 × 10 lengths was formed.
In order to correlate the ground measurement data with the generated feature vectors as well as estimate the moisture value of sampling points not included in the calculation, GRNN was used as an inversion model.For computing the accuracy of the system, training and test sets were established from Dataset 1 and the moisture values of the agricultural areas included in the test set were estimated by the trained GRNN.Moreover, the spread parameter (ς) was set in the range (0.5-1.5) and was chosen as ς = 1 in this study since it provides the best performance at this value for all GRNN models.In order to determine the effect of the spread parameter, the result of one application example was shown in Table 2.The extracted parameters were then added in succession and the feature vector of 10 units in length (σhh, σhv, σvh, σvv, entropy, anisotropy, alpha angle, volume scattering, surface scattering, and double bounce) was generated from each sampling point.This process was repeated for 335 sampling points in this period and Dataset 1 with 335 × 10 lengths was formed.
In order to correlate the ground measurement data with the generated feature vectors as well as estimate the moisture value of sampling points not included in the calculation, GRNN was used as an inversion model.For computing the accuracy of the system, training and test sets were established from Dataset 1 and the moisture values of the agricultural areas included in the test set were estimated by the trained GRNN.Moreover, the spread parameter (ς) was set in the range (0.5-1.5) and was chosen as ς = 1 in this study since it provides the best performance at this value for all GRNN models.
In order to determine the effect of the spread parameter, the result of one application example was shown in Table 2.In the testing process, the leave-one-out cross validation method was used to validate the overall system accuracy and each of the patterns forming Dataset 1 was included in the test set alternately.Thus, the quantitative evaluation between measured and estimated soil moistures was determined by GRNN, as shown in Figure 6.In the testing process, the leave-one-out cross validation method was used to validate the overall system accuracy and each of the patterns forming Dataset 1 was included in the test set alternately.Thus, the quantitative evaluation between measured and estimated soil moistures was determined by GRNN, as shown in Figure 6.For the performance analysis, Root Mean Square Error (RMSE), Correlation Coefficient (r), and Mean Absolute Error (MAE) were chosen as the indicators.After a leave-one-out cross-validation process, the overall system accuracy was observed with the estimation error of around 2.84 vol % RMSE and 2.31 vol % MAE for Dataset 1.
On the other hand, four test areas (22 sampling points for each test area) were randomly selected on the basis of the Monte Carlo cross-validation method to validate the precision of the system over the local regions.Finally, the results (see Figure 7) showed estimation errors of 2.80 vol %, 2.79 vol %, 2.70 vol %, and 2.55 vol % MAE over testing areas 1-4, respectively.For the performance analysis, Root Mean Square Error (RMSE), Correlation Coefficient (r), and Mean Absolute Error (MAE) were chosen as the indicators.After a leave-one-out cross-validation process, the overall system accuracy was observed with the estimation error of around 2.84 vol % RMSE and 2.31 vol % MAE for Dataset 1.
On the other hand, four test areas (22 sampling points for each test area) were randomly selected on the basis of the Monte Carlo cross-validation method to validate the precision of the system over the local regions.Finally, the results (see Figure 7) showed estimation errors of 2.80 vol %, 2.79 vol %, 2.70 vol %, and 2.55 vol % MAE over testing areas 1-4, respectively.

Experiments on Dataset 2
For this stage, Dataset 2 was created from Radarsat-2 data of 8 April 2015 to analyze the effect of dense vegetation cover over the study areas.The same topology used in Section 4.1 was repeated in this stage to estimate soil moisture and then Dataset 2 with 285 × 10 lengths was generated.After the Radarsat-2 processing step, the resulting images are presented in Figure 8.In order to validate the applicability of the overall system, the leave-one-out cross-validation method was implemented in the testing stage, resulting in estimation errors of 2.65 vol % RMSE and 2.11 vol % MAE over the two experimental areas, as described in Figure 9.Moreover, the four test areas (25 sampling points for each test area) were randomly chosen for validation of local regions and their accuracy results are given in Figure 10.The experimental results indicated that the MAE was 2.78 vol %, 1.79 vol %, 2.61 vol %, and 1.98 vol % over test areas 1-4, respectively.

Experiments on Dataset 2
For this stage, Dataset 2 was created from Radarsat-2 data of 8 April 2015 to analyze the effect of dense vegetation cover over the study areas.The same topology used in Section 4.1 was repeated in this stage to estimate soil moisture and then Dataset 2 with 285 × 10 lengths was generated.After the Radarsat-2 processing step, the resulting images are presented in Figure 8 In order to validate the applicability of the overall system, the leave-one-out cross-validation method was implemented in the testing stage, resulting in estimation errors of 2.65 vol % RMSE and 2.11 vol % MAE over the two experimental areas, as described in Figure 9.Moreover, the four test areas (25 sampling points for each test area) were randomly chosen for validation of local regions and their accuracy results are given in Figure 10.The experimental results indicated that the MAE was 2.78 vol %, 1.79 vol %, 2.61 vol %, and 1.98 vol % over test areas 1-4, respectively.

Experiments on Dataset 3
In this period, Dataset 3 was generated from the Radarsat-2 data of 10 June 2015 for estimating the soil moisture over bare agricultural areas.A similar approach to that in the Sections 4.1 and 4.2 was employed for this phase and Dataset 3 with 272 × 10 lengths was constructed.After the decomposition process, we obtained the results shown in Figure 11.The overall system accuracy for this period was calculated with estimation error of 2.77 vol % RMSE and 2.10 vol % MAE, as displayed in Figure 12.Furthermore, four test regions (25 sampling points for each test area) were picked out randomly and the precision values of these sites are represented in Figure 13.Eventually, MAE of 2.10 vol % and 2.55 vol % was computed for test areas 1-2, respectively, with 2.11 vol % and 3.05 vol % for test areas 3-4, respectively.

Experiments on Dataset 3
In this period, Dataset 3 was generated from the Radarsat-2 data of 10 June 2015 for estimating the soil moisture over bare agricultural areas.A similar approach to that in the Sections 4.1 and 4.2 was employed for this phase and Dataset 3 with 272 × 10 lengths was constructed.After the decomposition process, we obtained the results shown in Figure 11.The overall system accuracy for this period was calculated with estimation error of 2.77 vol % RMSE and 2.10 vol % MAE, as displayed in Figure 12.Furthermore, four test regions (25 sampling points for each test area) were picked out randomly and the precision values of these sites are represented in Figure 13.Eventually, MAE of 2.10 vol % and 2.55 vol % was computed for test areas 1-2, respectively, with 2.11 vol % and 3.05 vol % for test areas 3-4, respectively.

Experiments on Dataset 3
In this period, Dataset 3 was generated from the Radarsat-2 data of 10 June 2015 for estimating the soil moisture over bare agricultural areas.A similar approach to that in the Sections 4.1 and 4.2 was employed for this phase and Dataset 3 with 272 × 10 lengths was constructed.After the decomposition process, we obtained the results shown in Figure 11.The overall system accuracy for this period was calculated with estimation error of 2.77 vol % RMSE and 2.10 vol % MAE, as displayed in Figure 12.Furthermore, four test regions (25 sampling points for each test area) were picked out randomly and the precision values of these sites are represented in Figure 13.Eventually, MAE of 2.10 vol % and 2.55 vol % was computed for test areas 1-2, respectively, with 2.11 vol % and 3.05 vol % for test areas 3-4, respectively.

Experiments on Combined Datasets
In order to prove the applicability and usefulness of the proposed algorithm for soil moisture estimation on different dates, the obtained datasets were merged in the following approaches.In the first instance, Datasets 1&2 were combined to determine the effect of low and dense vegetation cover at different dates and a new dataset with 620 × 10 lengths was formed.Then, the GRNN algorithm was used for soil moisture estimation on the basis of combined datasets.In testing stage, the leave-one-out cross-validation method was employed to test the overall system

Experiments on Combined Datasets
In order to prove the applicability and usefulness of the proposed algorithm for soil moisture estimation on different dates, the obtained datasets were merged in the following approaches.In the first instance, Datasets 1&2 were combined to determine the effect of low and dense vegetation cover at different dates and a new dataset with 620 × 10 lengths was formed.Then, the GRNN algorithm was used for soil moisture estimation on the basis of combined datasets.In the testing stage, the leave-one-out cross-validation method was employed to test the overall system

Experiments on Combined Datasets
In order to prove the applicability and usefulness of the proposed algorithm for soil moisture estimation on different dates, the obtained datasets were merged in the following approaches.In the first instance, Datasets 1&2 were combined to determine the effect of low and dense vegetation cover at different dates and a new dataset with 620 × 10 lengths was formed.Then, the GRNN algorithm was used for soil moisture estimation on the basis of combined datasets.In the testing stage, the leave-one-out cross-validation method was employed to test the overall system performance.Consequently, estimation errors of 3.23 vol % RMSE and 2.46 vol % MAE were computed, as displayed in Figure 14.
performance.Consequently, estimation errors of 3.23 vol % RMSE and 2.46 vol % MAE were computed, as displayed in Figure 14.In the second approach, Datasets 1&3 were combined to analyze the influence of low vegetation and bare soil surface on different dates and a dataset with 607 × 10 lengths was generated.After the training and testing process, the quantitative comparison between measured and estimated soil moistures (as indicated in Figure 15) was 9.76 vol % RMSE and 7.09 vol % MAE.In the next approach, Datasets 2&3 were combined to determine the effect of dense vegetation and bare soil surface on different dates and a dataset with 557 × 10 lengths was formed.The same topology as in the first approach was used in this stage for the validation and testing of the proposed model; the relationship between measured and estimated soil moistures is displayed in Figure 16.Consequently, estimation errors of 4.04 vol % RMSE and 2.69 vol % MAE were computed for this scenario.In the second approach, Datasets 1&3 were combined to analyze the influence of low vegetation and bare soil surface on different dates and a dataset with 607 × 10 lengths was generated.After the training and testing process, the quantitative comparison between measured and estimated soil moistures (as indicated in Figure 15) was 9.76 vol % RMSE and 7.09 vol % MAE.
performance.Consequently, estimation errors of 3.23 vol % RMSE and 2.46 vol % MAE were computed, as displayed in Figure 14.In the second approach, Datasets 1&3 were combined to analyze the influence of low vegetation and bare soil surface on different dates and a dataset with 607 × 10 lengths was generated.After the training and testing process, the quantitative comparison between measured and estimated soil moistures (as indicated in Figure 15) was 9.76 vol % RMSE and 7.09 vol % MAE.In the next approach, Datasets 2&3 were combined to determine the effect of dense vegetation and bare soil surface on different dates and a dataset with 557 × 10 lengths was formed.The same topology as in the first approach was used in this stage for the validation and testing of the proposed model; the relationship between measured and estimated soil moistures is displayed in Figure 16.Consequently, estimation errors of 4.04 vol % RMSE and 2.69 vol % MAE were computed for this scenario.In the next approach, Datasets 2&3 were combined to determine the effect of dense vegetation and bare soil surface on different dates and a dataset with 557 × 10 lengths was formed.The same topology as in the first approach was used in this stage for the validation and testing of the proposed model; the relationship between measured and estimated soil moistures is displayed in Figure 16.Consequently, estimation errors of 4.04 vol % RMSE and 2.69 vol % MAE were computed for this scenario.Finally, Datasets 1&2&3 were merged to examine the influence of low vegetation, dense vegetation, and bare soil surface on different dates and a dataset with 892 × 10 lengths was constituted.After the validation and testing process, the quantitative comparison between the measured and generated data (Figure 17) was shown to be 8.25 vol % RMSE and 5.69 vol % MAE.

Discussion
There are a small number of research studies estimating the soil moisture by polarimetric decomposition models and nonlinear machine learning techniques.In this study, two typical polarimetric decomposition models (Freeman-Durden, H/A/α) were picked out to obtain the different scattering components at different vegetation growth stages.The Freeman-Durden decomposition model was used in this study since it does not need any ground measurements like surface parameters.Moreover, the H/A/α method was employed as a second decomposition model because it covers all possible scenarios of scattering models, especially surface scattering.The regression analysis of the datasets was then implemented using the GRNN algorithm.In order to evaluate the results of three datasets, the statistical relationship between the measured and estimated soil moistures is given in Table 3 with a new parameter: coefficient of variation (CV).Finally, Datasets 1&2&3 were merged to examine the influence of low vegetation, dense vegetation, and bare soil surface on different dates and a dataset with 892 × 10 lengths was constituted.After the validation and testing process, the quantitative comparison between the measured and generated data (Figure 17) was shown to be 8.25 vol % RMSE and 5.69 vol % MAE.Finally, Datasets 1&2&3 were merged to examine the influence of low vegetation, dense vegetation, and bare soil surface on different dates and a dataset with 892 × 10 lengths was constituted.After the validation and testing process, the quantitative comparison between the measured and generated data (Figure 17) was shown to be 8.25 vol % RMSE and 5.69 vol % MAE.

Discussion
There are a small number of research studies estimating the soil moisture by polarimetric decomposition models and nonlinear machine learning techniques.In this study, two typical polarimetric decomposition models (Freeman-Durden, H/A/α) were picked out to obtain the different scattering components at different vegetation growth stages.The Freeman-Durden decomposition model was used in this study since it does not need any ground measurements like surface parameters.Moreover, the H/A/α method was employed as a second decomposition model because it covers all possible scenarios of scattering models, especially surface scattering.The regression analysis of the datasets was then implemented using the GRNN algorithm.In order to evaluate the results of three datasets, the statistical relationship between the measured and estimated soil moistures is given in Table 3 with a new parameter: coefficient of variation (CV).

Discussion
There are a small number of research studies estimating the soil moisture by polarimetric decomposition models and nonlinear machine learning techniques.In this study, two typical polarimetric decomposition models (Freeman-Durden, H/A/α) were picked out to obtain the different scattering components at different vegetation growth stages.The Freeman-Durden decomposition model was used in this study since it does not need any ground measurements like surface parameters.Moreover, the H/A/α method was employed as a second decomposition model because it covers all possible scenarios of scattering models, especially surface scattering.The regression analysis of the datasets was then implemented using the GRNN algorithm.In order to evaluate the results of three datasets, the statistical relationship between the measured and estimated soil moistures is given in Table 3 with a new parameter: coefficient of variation (C V ).From the results (see Table 3), we observed that the different test areas in this study area indicated different soil moisture content.This is because of the condition of the soil which might be plowed, unplowed, or irrigated.When we analyze Dataset 1 results; the average soil moisture of Dataset 1 was high at 29.72% and the Cv value of the ground soil moistures (SM) was around 0.16.Moreover, the soil surface was sparsely vegetated in this growth stage.This means that the data forming Dataset 1 were not uniformly distributed over the study area due to low vegetation.Therefore, the scattering parameters in Dataset 1 displayed a good R value, with slightly high error rates compared to other datasets.
Similarly, the average soil moisture value for Dataset 2 was near that of Dataset 1.Among the datasets, the lowest correlation coefficient R = 0.706 with the smallest estimation error was observed in this stage.The reason for the low R might be that the study area was densely vegetated on this date.Thus, the vegetation scattering decreased the correlation between the estimated and measured soil moisture.Furthermore, uniform data distribution was observed for Dataset 2 because of the dense vegetation impact, which caused low error rates at this stage.
In contrast to other datasets, the average soil moisture for Dataset 3 was low around 7%, which means that the surface was dry.However, a strong relationship between the measured and estimated soil moisture was established with the highest correlation coefficient: R = 0.919.This might be because the study area was bare in this growth stage, with high C V of SM, and Dataset 3 was not distributed uniformly over the study area.Here, partial irrigation might impact the distribution of the soil moisture and increase the C V of SM and R values.
By the time we considered all dataset combinations, the best estimation model was observed in Datasets 1 & 2 approach, with the smallest error rate.The reason for this might be that the C V of SM for both Datasets 1 and 2 is low and the data distribution of the Dataset 2 was uniform.Moreover, the variation of ground soil moisture for Datasets 1 and 2 is restricted, with high soil moisture values around saturation.For this reason, error could be limited due to the saturation of the radar signal for these levels [34].
However, the worst estimation models were examined in Datasets 1 & 3 and Datasets 1 & 2 & 3 approaches.This might be because of that the distribution of Datasets 1 & 3 was not uniform and the soil moisture vertical profile for Dataset 3 was heterogeneous.Thus, Datasets 1 and 3 induced high error rates when combined with other datasets [35].Furthermore, the roughness effect, which is an important parameter on bare soil conditions (Dataset 3), could generate significant error in soil moisture estimation [34].
The main contribution of the proposed system is that the datasets were constituted in a novel approach by combining the decomposed model parameters with the standard sigma backscattering coefficients.Then, the GRNN neural network was fed into by these parameters and estimated the soil moisture with a low error rate.Considering the literature studies, some of the main approaches for soil moisture estimation via SAR-based data are listed in Table 4.The overall accuracy of the proposed system indicated good results compared to the other approaches in the literature.

Figure 1 .
Figure 1.The location of the study area, presented as both (a) Radarsat-2 image and (b) Google Earth image.The black rectangular areas indicate the coverage of two experimental sites.

Figure 1 .
Figure 1.The location of the study area, presented as both (a) Radarsat-2 image and (b) Google Earth image.The black rectangular areas indicate the coverage of two experimental sites.

Figure 4 .
Figure 4.The architecture of the GRNN model.

Figure 4 .
Figure 4.The architecture of the GRNN model.

Figure 6 .
Figure 6.The relationship between the measured and estimated soil moistures (SM) for Dataset 1.

Figure 6 .
Figure 6.The relationship between the measured and estimated soil moistures (SM) for Dataset 1.

Figure 7 .
Figure 7.The relationship between the measured and estimated soil moistures (SM) over testing areas 1-4 for Dataset 1 (a-d), respectively.

Figure 7 .
Figure 7.The relationship between the measured and estimated soil moistures (SM) over testing areas 1-4 for Dataset 1 (a-d), respectively.

Figure 10 .
Figure 10.The relationship between measured and estimated SM over testing areas 1-4 for Dataset 2 (a-d), respectively.

Figure 10 .
Figure 10.The relationship between measured and estimated SM over testing areas 1-4 for Dataset 2 (a-d), respectively.

Figure 12 .Figure 13 .
Figure 12.The relationship between measured and estimated SM for Dataset 3.

Figure 12 .
Figure 12.The relationship between measured and estimated SM for Dataset 3.

Figure 12 .
Figure 12.The relationship between measured and estimated SM for Dataset 3.

Figure 13 .
Figure 13.The relationship between measured and estimated SM over testing areas 1-4 for Dataset 3 (a-d), respectively.

Figure 13 .
Figure 13.The relationship between measured and estimated SM over testing areas 1-4 for Dataset 3 (a-d), respectively.

Figure 14 .
Figure 14.The relationship between measured and estimated SM for combined Datasets 1&2.

Figure 15 .
Figure 15.The relationship between measured and estimated SM for combined Datasets 1&3.

Figure 14 .
Figure 14.The relationship between measured and estimated SM for combined Datasets 1&2.

Figure 14 .
Figure 14.The relationship between measured and estimated SM for combined Datasets 1&2.

Figure 15 .
Figure 15.The relationship between measured and estimated SM for combined Datasets 1&3.

Figure 15 .
Figure 15.The relationship between measured and estimated SM for combined Datasets 1&3.

Figure 16 .
Figure 16.The relationship between measured and estimated SM for combined Datasets 2&3.

Figure 17 .
Figure 17.The relationship between measured and estimated SM for combined Datasets 1&2&3.

Figure 16 .
Figure 16.The relationship between measured and estimated SM for combined Datasets 2&3.

Figure 16 .
Figure 16.The relationship between measured and estimated SM for combined Datasets 2&3.

Figure 17 .
Figure 17.The relationship between measured and estimated SM for combined Datasets 1&2&3.

Figure 17 .
Figure 17.The relationship between measured and estimated SM for combined Datasets 1&2&3.

Table 2 .
The effect of spread parameter on GRNN for testing Dataset 1.

Table 2 .
The effect of spread parameter on GRNN for testing Dataset 1.

Table 3 .
The statistical relationship between measured and estimated soil moistures (SM).