**1. Introduction**

Soil moisture (SM) is an important state variable that significantly affects the water cycle, ecosystem, and energy exchange between the land and the atmosphere. SM information is important in different fields, such as agriculture, meteorology, hydrology, weather, and evapotranspiration forecasting [1–7]. In recent decades, in the large-scale domain, the development of remote sensing technology has provided more opportunities. Specifically, surface SM inversion based on remote sensing technology has become a hotspot of research [8–11]. Optical remote sensing cannot penetrate clouds and rain and is easily restricted by weather and solar illumination conditions. Therefore, it is impossible to

**Citation:** Gao, Y.; Gao, M.; Wang, L.; Rozenstein, O. Soil Moisture Retrieval over a Vegetation-Covered Area Using ALOS-2 L-Band Synthetic Aperture Radar Data. *Remote Sens.* **2021**, *13*, 3894. https://doi.org/ 10.3390/rs13193894

Academic Editors: Takeo Tadono and Masato Ohki

Received: 19 August 2021 Accepted: 24 September 2021 Published: 29 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

perform an all-weather observation of the Earth in the optical and thermal spectral regions. However, microwave remote sensing is not subject to weather and light conditions and can monitor surface SM under all weather conditions at all hours of the day [12]. Moreover, it has a certain penetrating ability for vegetation and, therefore, it has the potential for the continuous monitoring of surface SM over a large area [13–20].

In the past few decades, synthetic aperture radar (SAR) has been the primary active microwave remote sensing means of monitoring SM [6,21]. However, in vegetation-covered areas, the signal includes direct scattering from plant cover and attenuated backscatter from the ground. As a result, the observed backscattering signal includes the vegetation, the surface, and the interaction between vegetation and the surface simultaneously [22], making it extremely difficult to retrieve SM under the vegetation coverage. Therefore, the main challenge to estimating SM vegetation coverage is the elimination of the impact of surface roughness and vegetation [1,23–25]. Many scholars have proposed different solutions to the impact of vegetation on radar backscattering in vegetation-covered areas. In many studies, the WCM is applied in an inversion method to estimate SM in vegetationcovered areas. In the WCM, the total reflected radar signal is modeled as a function of soil and vegetation contributions. The direct contribution of the vegetation's scattering and attenuation is mainly calculated by using biophysical parameters representing vegetation. Optical data can be used to estimate biophysical parameters [12,26]. Therefore, combining optical and SAR data is beneficial for SM retrieval in vegetation-covered areas [27–38].

However, due to the topography, the actual measurement (SM, soil roughness, etc.), and other factors, the lack of soil roughness and other relevant information will affect the inversion accuracy. In order to solve this problem, the purpose of this study is to evaluate the potential of combining L-band SAR data and optical data to estimate SM under vegetation. Research on the basics of the inversion of the WCM using GA-BP neural networks was developed to solve the problem of the lack of soil roughness and other factors. This study consists of four main parts: (1) the parameterization of WCM; (2) a learning simulation of synthetic SAR data; (3) training of a GA-BP neural network; (4) applied training and the verification of the results of the inversion method on real datasets. Section 2 of the paper describes the study area and in situ measurements. Section 3 investigates the methods. Section 4 features the results. Section 5 presents the discussion. Finally, Section 6 outlines the main conclusions.

#### **2. Study Area**

#### *2.1. Study Area*

The area of interest, situated in the Liuzhi Special District of Guizhou province (centered at 105.159◦E, 26.541◦N), was selected for SM estimation research (Figure 1). The Liuzhi Special Zone is marked by a warm and humid subtropical monsoon climate with abundant rainfall. It is located between mountains with steep terrain and a high altitude. In addition, it is characterized by high vegetation cover, with a forest coverage rate of 51.05%, rich crop species, and a wide grassland range. Because of the influence of topography and vegetation, natural disasters, such as landslides and debris flow, are prone to occur in this area. Therefore, the motivation to estimate SM in this region is very high since disasters are driven by soil water content changes that significantly affect the economy, the environment, and people's lives.

**Figure 1.** The study region of the land use patterns in Liuzhi (left), and a district map (right). **Figure 1.** The study region of the land use patterns in Liuzhi (**left**), and a district map (**right**).

0 σ

#### *2.2. Radar Data*

radar backscatter coefficient (

*2.4. In Situ Measurements* 

*2.2. Radar Data* 

In this research, the ALOS-2 SAR data was utilized for SM inversion research. The ALOS-2 is the only L-band SAR satellite currently in orbit. Its frequency is 1.2 GHz. This study uses fine dual-polarization modes (HH and HV) with a nominal spatial coverage resolution of 3 m. Using an algorithm to calibrate SAR images by the Japan Aerospace Exploration Agency (JAXA), the digital number (DNi) of each pixel was converted to the In this research, the ALOS-2 SAR data was utilized for SM inversion research. The ALOS-2 is the only L-band SAR satellite currently in orbit. Its frequency is 1.2 GHz. This study uses fine dual-polarization modes (HH and HV) with a nominal spatial coverage resolution of 3 m. Using an algorithm to calibrate SAR images by the Japan Aerospace Exploration Agency (JAXA), the digital number (*DNi*) of each pixel was converted to the radar backscatter coefficient (*σ* 0 *pq*) by radiation calibration. The calculation formula for radiation calibration of the ALOS-2 data is:

$$
\sigma\_{pq}^0 = \text{K} \cdot \text{DN}\_i^2 \tag{1}
$$

radiation calibration of the ALOS-2 data is: 0 2 σ *pq i* =*K DN* ⋅ (1) The absolute calibration constant is represented by *K*. Following radiometric calibration, the backscattering coefficient had linear units, which was then converted to dB units for convenience [35] using Equation (2):

$$
\sigma\_{d\mathcal{B}}^{0} = 10 \cdot \log\_{10} \left( \sigma\_{pq}^{0} \right) \tag{2}
$$

tion, the backscattering coefficient had linear units, which was then converted to dB units for convenience [35] using Equation (2): SARscape, an advanced radar image processing software developed by SARmap (Purasca, Switzerland), was used to process the ALOS-2 data by performing multilooking, filtering, geocoding, and radiometric calibration.

> σ

#### *2.3. Optical Data*

( ) 0 0 <sup>10</sup> 10 log *dB pq* = ⋅ (2) SARscape, an advanced radar image processing software developed by SARmap (Purasca, Switzerland), was used to process the ALOS-2 data by performing multilooking, filtering, geocoding, and radiometric calibration. The operational land imager (OLI) sensor, and the thermal infrared sensor (TIRS), are two instruments on NASA's Landsat-8 satellite [39]. Landsat-8 and Landsat 4–7 products have similar spatial resolution and spectroscopic characteristics. There is a total of 11 bands in Landsat-8 imagery. The spatial resolution of bands 1–7 and 9–11 is 30 m. The spatial resolution of band 8 is 15 m. The satellite achieves global coverage every 16 days (https://earthexplorer.usgs.gov/, accessed on 19 August 2021).

*2.3. Optical Data*  The operational land imager (OLI) sensor, and the thermal infrared sensor (TIRS), are The NDVI is a significant measure reflecting crop growth and nutrition information [40]. The NDWI is an important index for evaluating vegetation water status [41]. The NMDI was calculated based on a near-infrared and two short wave infrareds [42,43].

two instruments on NASA's Landsat-8 satellite [39]. Landsat-8 and Landsat 4–7 products

spatial resolution of band 8 is 15 m. The satellite achieves global coverage every 16 days

[40]. The NDWI is an important index for evaluating vegetation water status [41]. The

NMDI was calculated based on a near-infrared and two short wave infrareds [42,43].

The NDVI is a significant measure reflecting crop growth and nutrition information

While acquiring ALOS-2 SAR data, the field measurements were performed in the

study area from 26 September 2020 to 27 September 2020. During this period, there was

(https://earthexplorer.usgs.gov/, accessed on 19 August 2021).

σ

## *2.4. In Situ Measurements*

While acquiring ALOS-2 SAR data, the field measurements were performed in the study area from 26 September 2020 to 27 September 2020. During this period, there was no precipitation or significant temperature changes in the experimental area. In the research field, the appropriate sampling points were selected to collect soil samples. The terrain of the Liuzhi Special Zone in Guizhou Province is complex and there are many mountains, which increases the difficulty of sampling. Therefore, the areas we sampled were all flat areas, such as farmland and grassland. At the same time, in order to make the samples diverse, we tried to distribute them as widely as possible. A handheld GPS was used to record the longitude and latitude of each sample point, take photos of the sampling point (one photo), and take pictures of the surrounding environment (four photos from the front, back, left, and right). We finally selected 120 sampling points. 119 samples were taken at depths of 0–10 cm, and 120 samples were taken at depths of 20–30 cm. Figure 2 shows the distribution of sampling points. no precipitation or significant temperature changes in the experimental area. In the research field, the appropriate sampling points were selected to collect soil samples. The terrain of the Liuzhi Special Zone in Guizhou Province is complex and there are many mountains, which increases the difficulty of sampling. Therefore, the areas we sampled were all flat areas, such as farmland and grassland. At the same time, in order to make the samples diverse, we tried to distribute them as widely as possible. A handheld GPS was used to record the longitude and latitude of each sample point, take photos of the sampling point (one photo), and take pictures of the surrounding environment (four photos from the front, back, left, and right). We finally selected 120 sampling points. 119 samples were taken at depths of 0–10 cm, and 120 samples were taken at depths of 20–30 cm. Figure 2 shows the distribution of sampling points.

**Figure 2.** Distribution map of sampling points in the study area. **Figure 2.** Distribution map of sampling points in the study area.

The determination of the soil moisture content was obtained by the laboratory weighing and drying of soil samples. Water content can be expressed as gravimetric water content and volumetric water content. The ratio of the quantity of water in the soil and the dry The determination of the soil moisture content was obtained by the laboratory weighing and drying of soil samples. Water content can be expressed as gravimetric water content and volumetric water content. The ratio of the quantity of water in the soil and the dry soil is gravimetric water content (*Mg*). It is represented by Formula (3).

$$M\_{\mathcal{S}} = \frac{M\_w}{M\_s} \tag{3}$$

$$M\_{\mathcal{S}} = \frac{M\_w}{M\_s} \tag{4}$$

$$M\_{\mathcal{S}} = \frac{M\_w}{M\_s} \tag{5} \qquad \text{and} \qquad M\_{\mathcal{S}} = \frac{M\_w}{M\_s} \tag{6} \qquad \text{and} \qquad M\_{\mathcal{S}} = \frac{M\_w}{M\_s} \tag{7}$$

*g s <sup>M</sup>*<sup>=</sup> (3) where *M<sup>w</sup>* represents the quality of water in the soil, and *M<sup>s</sup>* represents the mass of dry soil. The volumetric water content (of *Mv*) is the ratio of the volume of the soil water in soil.

$$M\_{\upsilon} = \frac{V\_w}{V} \tag{4}$$

*w*

*<sup>V</sup>* <sup>=</sup> (4)

(5)

*v <sup>V</sup> <sup>M</sup>*

*M M v g* =

The relationship between soil volumetric water content and mass water content can

ρ

The volumetric water content (of *Mv*) is the ratio of the volume of the soil water in soil. where *V<sup>w</sup>* is the volume occupied by water in the soil, and *V* is the total volume of the soil.

where *ρ* represents the bulk density.

soil.

be expressed as:

The relationship between soil volumetric water content and mass water content can be expressed as:

$$M\_{\upsilon} = M\_{\circledast} \rho \tag{5}$$

where *ρ* represents the bulk density.

119 samples from a 0–10 cm depth were collected, and 120 samples were collected at a depth of 20–30 cm. The values of soil volumetric water content less than 20% and greater than 62% were removed. A total of 116 sample points remained. Following outlier removal, the measured range of SM at a 0–10 cm depth was between 22.90 and 60.82 vol%, and the average SM was 39.49 vol%. The measured range of SM at a 20–30 cm depth was between 21.17 and 61.92 vol%, and the average SM was 37.28 vol%.

#### **3. Methods**

The research is divided into two parts, the WCM and GA-BP, which are used for SM estimation. The GA-BP algorithm is used to analyze the empirical model, 3.1. radar signal modeling.

In 1978, Attema and Ulaby took crops as the research object and proposed a semiempirical vegetation backscattering model ground on the first-order solution of the radiation transfer equation, namely, the WCM [44]. The intensity of radar backscattering is easily affected by the surface roughness and vegetation [22]. This is accounted for in the WCM, due to the joint scattering contribution of the vegetation and the underlying surface scattering to determine the total backward canopy scattering coefficient. The vegetation layer reduces the contribution of the underlying surface scattering to a certain extent. When the influence of the radar shadow and terrain undulation is neglected, the WCM can be expressed as Equation (6):

$$
\sigma^0 = \sigma^0\_{\text{reg}} + \tau^2 \sigma\_{\text{soil}} \tag{6}
$$

The total backscattering coefficient is represented by *σ* 0 in the vegetation coverage area; *σ* 0 *soil* represents the backscattering coefficient for the soil surface; *σ* 0 *veg* shows the backscattering coefficient produced by the surface plants; *τ* 2 is the two-way attenuation coefficient; *σ* 0 *veg* and *τ* <sup>2</sup> are expressed in Equations (7) and (8):

$$
\sigma\_{\text{reg}}^0 = AV\_1 \cos \theta \left(1 - \tau^2\right) \tag{7}
$$

$$
\tau^2 = \exp(-2BV\_2/\cos\theta) \tag{8}
$$

$$\sigma\_{\text{soil}}^{0} = \frac{\sigma^{0} - AV\_{1} \* \cos\theta [1 - \exp(-2 \* B \* V\_{2} \* \sec\theta)]}{\exp(-2 \* B \* V\_{2} \* \sec\theta)} \tag{9}$$

where *θ* is the angle of radar incidence; *V*<sup>1</sup> represents the direct scattering of vegetation; and *V*<sup>2</sup> represents the attenuation of vegetation. The common feature is that optical vegetation parameters are needed to parameterize the scattering component of the vegetation. In this study, *V*<sup>1</sup> and *V*<sup>2</sup> were replaced by the NDWI, the NDVI, and the NMDI, calculated from Landsat-8 imagery; *A* and *B* are empirical constants. The values of *A* and *B* are obtained by nonlinear least-square fitting.

#### *3.1. GA-BP Neural Network*

#### 3.1.1. Genetic Algorithm (GA)

GA is a computational model simulating the natural selection and genetic mechanisms of Darwinian biological evolution. This is a method used to find the optimal solution according to the natural evolutionary process. The core content of the genetic algorithm is divided into five steps: parameter coding, initial population setting, fitness function design, genetic operation design, and control parameter setting.

The basic operation of the genetic algorithm is split into three steps: selection, crossover, and mutation operation [45–47]. Selection is the operation of selecting superior individuals from the group and eliminating inferior individuals. Crossover refers

to replacing and recombining the partial structures of two parent individuals to generate new individuals. The basic content of the mutation operator is to change the gene value on some loci of the individual string in the population.

#### 3.1.2. Back Propagation (BP) Neural Network

The BP neural network is divided into an input layer, a hidden layer, and an output layer. It is a multilayer feedforward neural network.

The learning process of the algorithm was divided into two stages: the first stage was the forward propagation process, in which the actual output values of nodes in each layer were calculated layer by layer from the input layer through the hidden layer. The nodes in each layer only accepted the input from the nodes in the previous layer and influenced only the state of nodes in the next layer. The second stage was the process of back propagation. If the output layer failed to get the expected output value, the error between the actual output and the expected output was calculated recursively layer by layer. The weight of the previous layer was corrected according to the error to minimize the error signal. In the direction of the decline of the error function slope, the network weight and threshold changes were constantly adjusted to gradually approach the objective function. Each time, the weight and error changes were proportional to the influence of the network error [48,49].

#### *3.2. Soil Moisture Retrieval*

SM was estimated using a GA-BP algorithm. In order to study the performance of the inversion method, the BP neural network was trained and verified on the synthetic dataset. The specific steps were as follows:

(1) The BP neural network consists of three layers. The layers are completely interconnected, with each layer having layers of simple processing units (neurons). The input data information is assigned to the input layer, multiplied, and forwarded through a weighting factor, and a deviation is added to the hidden layer. The output layer neurons obtained by the control are considered the input values of the output layer [27]. In this study, based on the data, we will set two inputs and one output. The soil backscattering coefficient under different polarizations (HH, HV), excluding the influence of vegetation, was used as input. These synthetic SAR backscatter datasets are obtained from the WCM. The parameterization uses soil volumetric moisture, vegetation descriptors, and incident angle values as input variables to simulate the backscatter coefficient of HH and HV polarization. Only parameters that can be easily estimated from optical images, such as the NDVI, the NDWI, and the NMDI, were considered in the generation of the synthetic dataset. When the WCM was coupled with the surface scattering model used to retrieve SM under vegetation cover, the separation of the vegetation-scattering contribution was mainly through synchronous optical data or auxiliary data measured on the ground. However, there is no unified standard for vegetation parameterization at present, and there is no theoretical basis to support which vegetation parameter can effectively and accurately represent vegetation scattering. Therefore, different vegetation parameters are used to characterize the contribution of vegetation scattering. This paper aims at the estimation of SM under vegetation cover. Therefore, before the active microwave method is used to retrieve SM, the data should be firstly downscaled. According to the resampling method, the radar backscattering coefficient, with a resolution of 3 m, is downscaled to the backscattering coefficient with a resolution of 30 m, and the total backscattering coefficient *δtot* of the vegetation-covered surfaces under HH and HV polarization is obtained, respectively. The WCM model is parameterized. Firstly, the least-square method was used to estimate parameters *A* and *B* by fitting the model based on the ground-truthed measurements (Equations (7)–(9)). Among them, the parameters of *V*<sup>1</sup> and *V*<sup>2</sup> were described by the NDVI, the NDWI, and the NMDI, and the incident angle was obtained from the radar image. With parameters *A* and *B*, it becomes possicomponents (

ficient ( *tot* δ

WCM.

0 *veg* δ , <sup>2</sup> τ

*Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 7 of 20

ments (Equations (7)–(9)). Among them, the parameters of V1 and V2 were described by the NDVI, the NDWI, and the NMDI, and the incident angle was obtained from

ble to predict the WCM components (*δ* 0 *veg*, *τ* 2 , and *δ* 0 *soil*) and, consequently, the total backscattering coefficient (*δtot*) using one vegetation descriptor and the SM values as inputs in the WCM. the radar image. With parameters A and B, it becomes possible to predict the WCM , and <sup>0</sup> δ *soil* ) and, consequently, the total backscattering coef-) using one vegetation descriptor and the SM values as inputs in the


**Figure 3.** Soil moisture inversion method flow. (**A**) is a flow chart for establishing a data set based on WCM, and (**B**) shows the detailed process of the GA-BP algorithm. Figure 3B (**left**) is the GA algorithm part, and Figure 3B (**right**) is the BP algorithm part. **Figure 3.** Soil moisture inversion method flow. (**A**) is a flow chart for establishing a data set based on WCM, and (**B**) shows the detailed process of the GA-BP algorithm. (**B**, **left**) is the GA algorithm part, and (**B**, **right**) is the BP algorithm part.

#### **4. Results**

**4. Results**  *4.1. Sensitivity Analysis of the Radar Signal*

the total backscatter.

*4.1. Sensitivity Analysis of the Radar Signal*  4.1.1. Water Cloud Model Parameterization

4.1.1. Water Cloud Model Parameterization The WCM parameterization results were calculated and analyzed according to Sec-The WCM parameterization results were calculated and analyzed according to Section 3.2. Table 1 details the WCM input parameters.

> **Parameter Min Value Max Value Mean Unit**  NDVI 0 0.76 0.08 - NDWI 0.3 0.94 0.72 -

The backscatter coefficient of soil without vegetation influence was calculated from the WCM. The HH polarization and HV polarization backscatter values were lower than

By comparison, because of the higher sensitivity of the HH polarization to the dihedral angular reflection effect, the backscattering coefficient was higher than that of the HV polarization. This is because the branches and shapes of the surface vegetation have more influence on crosspolarization than on copolarization. The inclination angle of branches and leaves affected the degree of response of different polarizations. Thus, the HH polar-

The relationship with the soil backscattering coefficient and SM, presented in Table 2, was obtained by replacing the vegetation water content with different vegetation indices. At depths of 0–10 cm, the quality of the fit was approximately the same for all the vegetation descriptors used, with an MAE of the predicted backscattering coefficients between 2.792 and 3.142 dB in HH, and between 3.083 and 3.469 dB in HV polarization. The RMSE of the predicted backscattering coefficients was between 3.606 and 4.053 dB in HH, and between 3.755 and 4.226 dB in HV polarization. The MAPE of the predicted backscattering coefficients was −0.25 dB in HH, and −0.16 dB in HV polarization. At depths of 20–

ization and HV polarization of the radar scattering were affected differently.

4.1.2. The Sensitivity of ALOS-2 Data to SM Under Vegetation Cover

**Table 1.** The input parameters of the WCM.

tion 3.3. Table 1 details the WCM input parameters.


**Table 1.** The input parameters of the WCM.

The backscatter coefficient of soil without vegetation influence was calculated from the WCM. The HH polarization and HV polarization backscatter values were lower than the total backscatter.

By comparison, because of the higher sensitivity of the HH polarization to the dihedral angular reflection effect, the backscattering coefficient was higher than that of the HV polarization. This is because the branches and shapes of the surface vegetation have more influence on crosspolarization than on copolarization. The inclination angle of branches and leaves affected the degree of response of different polarizations. Thus, the HH polarization and HV polarization of the radar scattering were affected differently.

#### 4.1.2. The Sensitivity of ALOS-2 Data to SM under Vegetation Cover

The relationship with the soil backscattering coefficient and SM, presented in Table 2, was obtained by replacing the vegetation water content with different vegetation indices. At depths of 0–10 cm, the quality of the fit was approximately the same for all the vegetation descriptors used, with an MAE of the predicted backscattering coefficients between 2.792 and 3.142 dB in HH, and between 3.083 and 3.469 dB in HV polarization. The RMSE of the predicted backscattering coefficients was between 3.606 and 4.053 dB in HH, and between 3.755 and 4.226 dB in HV polarization. The MAPE of the predicted backscattering coefficients was −0.25 dB in HH, and −0.16 dB in HV polarization. At depths of 20–30 cm, the quality of the fit was approximately the same for all the used vegetation descriptors, with an MAE of the predicted backscattering coefficients between 2.843 and 3.199 dB in HH, and between 3.085 and 3.472 dB in HV polarization. The RMSE on the predicted backscattering coefficients was between 3.67 and 4.13 dB in HH, and between 3.743 and 4.13 dB in HV polarization. The MAPE of the predicted backscattering coefficients was −0.25 dB in HH, and −0.16 dB in HV polarization. Therefore, the copolarizations of the ALOS-2 were found to be more sensitive to SM than the crosspolarizations. In addition, the sensitivity to SM at a depth of 0–10 cm was higher than at a depth of 20–30 cm.

**Table 2.** The results of the relationship between the backscattering coefficient and SM.


#### *4.2. Modeling Results*

#### 4.2.1. GA-BP Results Analysis

In order to improve the sensitivity of the radar signal, HH and HV were used as inputs in the BP neural network model. The GA-BP parameter settings are displayed in Table 3.


**Table 3.** GA-BP preferences.

Figure 4 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (*V*<sup>1</sup> = *V*<sup>2</sup> = NDVI in Equation (9)) at a depth of 0–10 cm. The GA-BP network became stable, as seen in the fitness curve region, after 160 generations, and the GA algorithm can search the appropriate weight and threshold at this time (Figure 4A). The error percentage of the BP neural network ranges from −0.4 to 0.6. (Figure 4B). The prediction of BP is between −0.25 and 0.2 (Figure 4C). The BEST dotted line indicates that the BP training result is ideal when the BP network is trained to the sixth generation (Figure 4D). *Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 10 of 20

**Figure 4.** GA-BP training results of the vegetation description in the WCM (V1=V2=NDVI in Equation (9)), sampling depth is 0–10 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of **Figure 4.** GA-BP training results of the vegetation description in the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NDVI in Equation (9)), sampling depth is 0–10 cm. (**A**) shows the fitness curve, (**B**) shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**).

result is ideal when the BP network is trained to the second generation (Figure 5D).

tion, which is the result of BP calculation and training (**D**).

the MSE index in the BP testing process in each generation. The red line represents the test condi-

cients (HH, HV) as inputs in the WCM model (V1=V2=NDVI in Equation (9)) at a depth of 20–30 cm. The GA-BP network is stable in the fitness curve region after 60 generations, and the GA can search the appropriate weight and threshold at this time (Figure 5A). The error percentage of the BP neural network ranges from −0.4 to 0.5 (Figure 5B). The prediction of BP is −0.15 to 0.2 (Figure 5C). The BEST dotted line indicates that the BP training

Figure 5 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (*V*<sup>1</sup> = *V*<sup>2</sup> = NDVI in Equation (9)) at a depth of 20–30 cm. The GA-BP network is stable in the fitness curve region after 60 generations, and the GA can search the appropriate weight and threshold at this time (Figure 5A). The error percentage of the BP neural network ranges from −0.4 to 0.5 (Figure 5B). The prediction of BP is −0.15 to 0.2 (Figure 5C). The BEST dotted line indicates that the BP training result is ideal when the BP network is trained to the second generation (Figure 5D). cients (HH, HV) as inputs in the WCM model (V1=V2=NDVI in Equation (9)) at a depth of 20–30 cm. The GA-BP network is stable in the fitness curve region after 60 generations, and the GA can search the appropriate weight and threshold at this time (Figure 5A). The error percentage of the BP neural network ranges from −0.4 to 0.5 (Figure 5B). The prediction of BP is −0.15 to 0.2 (Figure 5C). The BEST dotted line indicates that the BP training result is ideal when the BP network is trained to the second generation (Figure 5D).

*Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 10 of 20

**Figure 4.** GA-BP training results of the vegetation description in the WCM (V1=V2=NDVI in Equation (9)), sampling depth is 0–10 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condi-

Figure 5 shows the training results obtained by using the soil backscattering coeffi-

tion, which is the result of BP calculation and training (**D**).

**Figure 5.** GA-BP training results of the vegetation description in the WCM (V1=V2=NDVI in Equation (9)), sampling depth is 20–30 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of **Figure 5.** GA-BP training results of the vegetation description in the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NDVI in Equation (9)), sampling depth is 20–30 cm. (**A**) shows the fitness curve, (**B**) shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**).

the MSE index in the BP testing process in each generation. The red line represents the test condi-

6A). The error percentage of the BP neural network ranged from −0.5 to 0.5 (Figure 6B). The prediction of BP was −0.25 to 0.25 (Figure 6C). The BEST line indicates that an ideal

tion, which is the result of BP calculation and training (**D**). Figure 6 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (V1=V2=NDWI in Equation (9)) at a depth of 0–10 cm. The GA-BP network was stable in the fitness curve region after 105 generations, and the GA can search for the appropriate weight and threshold at this time (Figure Figure 6 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (*V*<sup>1</sup> = *V*<sup>2</sup> = NDWI in Equation (9)) at a depth of 0–10 cm. The GA-BP network was stable in the fitness curve region after 105 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 6A). The error percentage of the BP neural network ranged from −0.5 to 0.5 (Figure 6B). The prediction of BP was −0.25 to 0.25 (Figure 6C). The BEST line indicates that an ideal BP training result was reached at the 11th generation (Figure 6D).

 **Figure 6.** GA-BP training results of the vegetation description in the WCM (V1=V2= NDWI in Equation (9)), sampling depth is 0–10 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in

BP training result was reached at the 11th generation (Figure 6D).

tion, which is the result of BP calculation and training (**D**).

BP training result was reached at the 11th generation (Figure 6D).

**Figure 5.** GA-BP training results of the vegetation description in the WCM (V1=V2=NDVI in Equation (9)), sampling depth is 20–30 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condi-

Figure 6 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (V1=V2=NDWI in Equation (9)) at a depth of 0–10 cm. The GA-BP network was stable in the fitness curve region after 105 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 6A). The error percentage of the BP neural network ranged from −0.5 to 0.5 (Figure 6B).

**Figure 6.** GA-BP training results of the vegetation description in the WCM (V1=V2= NDWI in Equation (9)), sampling depth is 0–10 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in **Figure 6.** GA-BP training results of the vegetation description in the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NDWI in Equation (9)), sampling depth is 0–10 cm. (**A**) shows the fitness curve, (**B**) shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**).

Figure 7 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (*V*<sup>1</sup> = *V*<sup>2</sup> = NDWI in Equation (9)) at a depth of 20–30 cm. The GA-BP network was stable in the fitness curve region after 75 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 7A). The error percentage of the BP neural network ranges from −0.5 to 0.5 (Figure 7B). The prediction of BP was −0.2 to 0.2 (Figure 7C). The BEST dotted line indicates that the BP training result was ideal in first generation (Figure 7D).

Figure 8 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (*V*<sup>1</sup> = *V*<sup>2</sup> = NMDI in Equation (9)) at a depth of 0–10 cm. The GA-BP network was stable in the fitness curve region after 120 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 8A). The error percentage of the BP neural network ranges from −0.5 to 0.5 (Figure 8B). The prediction of BP was −0.2 to 0.2 (Figure 8C). The BEST dotted line indicates that the BP training result was ideal in the third generation (Figure 8D).

the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condi-

Figure 7 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (V1=V2=NDWI in Equation (9)) at a depth of 20–30 cm. The GA-BP network was stable in the fitness curve region after 75 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 7A). The error percentage of the BP neural network ranges from −0.5 to 0.5 (Figure 7B).

tion, which is the result of BP calculation and training (**D**).

BP training result was ideal in first generation (Figure 7D).

**Figure 7.** GA-BP training results of the vegetation description in the WCM (V1=V2= NDWI in Equation (9)), sampling depth is 20–30 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index **Figure 7.** GA-BP training results of the vegetation description in the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NDWI in Equation (9)), sampling depth is 20–30 cm. (**A**) shows the fitness curve, (**B**) shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**). *Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 13 of 20

**Figure 8.** *Cont*.

 **Figure 8.** GA-BP training results of the vegetation description in the WCM (V1=V2= NMDI in Equation (9)), sampling depth is 0–10 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condi-

Figure 9 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (V1=V2=NMDI in Equation (9)) at a depth of 20–30 cm. The GA-BP network was stable in the fitness curve region after 75 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 9A). The error percentage of the BP neural network ranges from −0.4 to 0.6 (Figure 9B). The prediction of BP was −0.2 to 0.15 (Figure 9C). The BEST dotted line indicates that the

tion, which is the result of BP calculation and training (**D**).

BP training result was ideal at the third generation (Figure 9D).

*Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 13 of 20

**Figure 8.** GA-BP training results of the vegetation description in the WCM (V1=V2= NMDI in Equation (9)), sampling depth is 0–10 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of **Figure 8.** GA-BP training results of the vegetation description in the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NMDI in Equation (9)), sampling depth is 0–10 cm. (**A**) shows the fitness curve, (**B**) shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**). **Figure 8.** GA-BP training results of the vegetation description in the WCM (V1=V2= NMDI in Equation (9)), sampling depth is 0–10 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process.The three

the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**). Figure 9 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (V1=V2=NMDI in Equation (9)) at a depth of 20–30 cm. The GA-BP network was stable in the fitness curve region after 75 genera-Figure 9 shows the training results obtained by using the soil backscattering coefficients (HH, HV) as inputs in the WCM model (*V*<sup>1</sup> = *V*<sup>2</sup> = NMDI in Equation (9)) at a depth of 20–30 cm. The GA-BP network was stable in the fitness curve region after 75 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 9A). The error percentage of the BP neural network ranges from −0.4 to 0.6 (Figure 9B). The prediction of BP was −0.2 to 0.15 (Figure 9C). The BEST dotted line indicates that the BP training result was ideal at the third generation (Figure 9D). solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**). Figure 9 shows the training results obtained by using the soil backscattering coeffi-

#### tions, and the GA can search for the appropriate weight and threshold at this time (Figure 9A). The error percentage of the BP neural network ranges from −0.4 to 0.6 (Figure 9B). 4.2.2. Soil Moisture Retrieval cients (HH, HV) as inputs in the WCM model (V1=V2=NMDI in Equation (9)) at a depth

The prediction of BP was −0.2 to 0.15 (Figure 9C). The BEST dotted line indicates that the BP training result was ideal at the third generation (Figure 9D). As stated in Section 3.2, different datasets were used to retrieve SM using the GA-BP neural network: (1) using the radar signal in both HH and HV (*V*<sup>1</sup> = *V*<sup>2</sup> = NDVI in Equation (9)); (2) using the radar signal in both HH and HV, which come from the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NDWI in Equation (9)); (3) the radar signal in both HH and HV (*V*<sup>1</sup> = *V*<sup>2</sup> = NMDI in Equation (9)). Estimates of SM and SM reference scores were compared to assess the accuracy of the SM inversion. of 20–30 cm. The GA-BP network was stable in the fitness curve region after 75 generations, and the GA can search for the appropriate weight and threshold at this time (Figure 9A). The error percentage of the BP neural network ranges from −0.4 to 0.6 (Figure 9B). The prediction of BP was −0.2 to 0.15 (Figure 9C). The BEST dotted line indicates that the BP training result was ideal at the third generation (Figure 9D).

**Figure 9.** *Cont*.

ure 10B).

ure 12B).

tail.

for ALOS-2 data.

**Figure 9.** GA-BP training results of the vegetation description in the WCM (V1=V2= NMDI in

of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in

*Remote Sens.* **2021**, *13*, x FOR PEER REVIEW 14 of 20

**Figure 9.** GA-BP training results of the vegetation description in the WCM (V1=V2= NMDI in Equation (9)), sampling depth is 20–30 cm. (**A**)shows the fitness curve, (**B**)shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance **Figure 9.** GA-BP training results of the vegetation description in the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NMDI in Equation (9)), sampling depth is 20–30 cm. (**A**) shows the fitness curve, (**B**) shows error percentage of BP neural network, (**C**) is prediction error of BP network, and (**D**) is BP training process. The three solid colored lines in the figure: the blue line represents the performance of the MSE index in the BP training process in each generation; the green line shows the performance of the MSE index in the BP crossvalidation process in each generation; and the red line represents the performance of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (**D**). To calculate the SM, use two-thirds of the data as the training set, and the rest as the validation set. Figures 10–12 show the results of the GA-BP method. These two backscattering coefficients (HH and HV) were used in GA-BP (WCM, V1=V2=NDVI in Equation (9)) analysis of the ALOS-2. According to the GA-BP results, the MAE, RMSE, and MAPE values were calculated as 2.248 vol%, 3.146 vol%, and 0.056

of the MSE index in the BP testing process in each generation. The red line represents the test condition, which is the result of BP calculation and training (D). To calculate the SM, use two-thirds of the data as the training set, and the rest as the validation set. vol% at the depth of 0–10 cm, respectively (Figure 10A). At a 20–30 cm depth, the MAE, RMSE and MAPE values were 2.481 vol%, 3.196 vol%, and 0.065 vol%, respectively (Fig-

Figures 10–12 show the results of the GA-BP method.

Figures 10–12 show the results of the GA-BP method. These two backscattering coefficients (HH and HV) were used in GA-BP (WCM, **Figure 10.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the **Figure 10.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the vegetation description in the WCM model is the NDVI (0–10 cm (**A**), 20–30 cm (**B**)). and MAPE values were calculated as 2.389 vol%, 2.834 vol%, and 0.06 vol%, respectively (Figure 11B).

vegetation description in the WCM model is the NDVI (0–10 cm (**A**), 20–30 cm (**B**)).

**Figure 11.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the vegetation description in the WCM model is the NDWI (0–10 cm (**A**), 20–30 cm (**B**)). **Figure 11.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the vegetation description in the WCM model is the NDWI (0–10 cm (**A**), 20–30 cm (**B**)).

vegetation description in the WCM model is the NMDI (0–10 cm (**A**), 20–30 cm (**B**)).

**Figure 12.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the

**Table 4.** The results of the MAE, RMSE, and MAPE between the GA-BP-based Mv and in situ Mv

 **0–10 cm (Vol.%) 20–30 cm (Vol.%)** 

V1=V2=NDVI 2.248 3.146 0.056 2.481 3.195 0.065 V1=V2=NDWI 2.883 3.495 0.069 2.389 2.834 0.06 V1=V2=NMDI 2.417 3.096 0.062 2.333 2.883 0.067

Figures 10 to 12 show the scatter plots between the measured and inverted soil moisture. It can be seen from the scatter plots that the retrieved soil moisture was underestimated in relatively humid regions because of the sensitivity of radar signals to soil mois-

**MAE RMSE MAPE MAE RMSE MAPE** 

Combined with the data analysis, the experiments show that, at a depth of 0–10 cm, the accuracy of the results obtained by the NDVI as a description of vegetation is higher than that obtained by other parameters.. The findings were better when vegetation was described as the NDWI at depths of 20–30 cm. Table 4 presents the MAE, RMSE, and MAPE analyses between the GA-BP-based Mv and the in situ Mv for ALOS-2 data in de-

vegetation description in the WCM model is the NDVI (0–10 cm (**A**), 20–30 cm (**B**)).

values' calculated results were 2.333 vol%, 2.882 vol%, and 0.067 vol%, respectively (Fig-

It follows that two backscattering coefficients were used in GA-BP (WCM, V1=V2=NMDI in Equation (9)). Underlying the GA-BP results, the MAE, RMSE, and

The results of the backscattering coefficients were used in GA-BP (WCM, V1=V2=NDWI in Equation (9)). Correspondingly, at the depth of 0–10 cm, based on the GA-BP results, the MAE, RMSE and MAPE values were calculated as 2.883 vol%, 3.495 vol%, and 0.069 vol%, respectively (Figure 11A). At a 20–30 cm depth, the MAE, RMSE ure 12B).

tail.

for ALOS-2 data.

(Figure 11B).

vegetation description in the WCM model is the NDWI (0–10 cm (**A**), 20–30 cm (**B**)).

**Figure 11.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the

It follows that two backscattering coefficients were used in GA-BP (WCM, V1=V2=NMDI in Equation (9)). Underlying the GA-BP results, the MAE, RMSE, and MAPE values were calculated as 2.417 vol%, 3.096 vol%, and 0.062 vol%, respectively, at

and MAPE values were calculated as 2.389 vol%, 2.834 vol%, and 0.06 vol%, respectively

**Figure 12.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the **Figure 12.** The relationship between the estimated Mv of GA-BP and reference Mv, in which the vegetation description in the WCM model is the NMDI (0–10 cm (**A**), 20–30 cm (**B**)).

vegetation description in the WCM model is the NMDI (0–10 cm (**A**), 20–30 cm (**B**)).

Combined with the data analysis, the experiments show that, at a depth of 0–10 cm, the accuracy of the results obtained by the NDVI as a description of vegetation is higher than that obtained by other parameters.. The findings were better when vegetation was described as the NDWI at depths of 20–30 cm. Table 4 presents the MAE, RMSE, and MAPE analyses between the GA-BP-based Mv and the in situ Mv for ALOS-2 data in de-These two backscattering coefficients (HH and HV) were used in GA-BP (WCM, *V*<sup>1</sup> = *V*<sup>2</sup> = NDVI in Equation (9)) analysis of the ALOS-2. According to the GA-BP results, the MAE, RMSE, and MAPE values were calculated as 2.248 vol%, 3.146 vol%, and 0.056 vol% at the depth of 0–10 cm, respectively (Figure 10A). At a 20–30 cm depth, the MAE, RMSE and MAPE values were 2.481 vol%, 3.196 vol%, and 0.065 vol%, respectively (Figure 10B).

**Table 4.** The results of the MAE, RMSE, and MAPE between the GA-BP-based Mv and in situ Mv The results of the backscattering coefficients were used in GA-BP (WCM, *V*<sup>1</sup> = *V*<sup>2</sup> = NDWI in Equation (9)). Correspondingly, at the depth of 0–10 cm, based on the GA-BP results, the MAE, RMSE and MAPE values were calculated as 2.883 vol%, 3.495 vol%, and 0.069 vol%, respectively (Figure 11A). At a 20–30 cm depth, the MAE, RMSE and MAPE values were calculated as 2.389 vol%, 2.834 vol%, and 0.06 vol%, respectively (Figure 11B).

 **0–10 cm (Vol.%) 20–30 cm (Vol.%) MAE RMSE MAPE MAE RMSE MAPE**  V1=V2=NDVI 2.248 3.146 0.056 2.481 3.195 0.065 V1=V2=NDWI 2.883 3.495 0.069 2.389 2.834 0.06 It follows that two backscattering coefficients were used in GA-BP (WCM, *V*<sup>1</sup> = *V*<sup>2</sup> = NMDI in Equation (9)). Underlying the GA-BP results, the MAE, RMSE, and MAPE values were calculated as 2.417 vol%, 3.096 vol%, and 0.062 vol%, respectively, at the depth of 0–10 cm (Figure 12A). At a 20–30 cm depth, the MAE, RMSE, and MAPE values' calculated results were 2.333 vol%, 2.882 vol%, and 0.067 vol%, respectively (Figure 12B).

V1=V2=NMDI 2.417 3.096 0.062 2.333 2.883 0.067 Figures 10 to 12 show the scatter plots between the measured and inverted soil moisture. It can be seen from the scatter plots that the retrieved soil moisture was underesti-Combined with the data analysis, the experiments show that, at a depth of 0–10 cm, the accuracy of the results obtained by the NDVI as a description of vegetation is higher than that obtained by other parameters.. The findings were better when vegetation was described as the NDWI at depths of 20–30 cm. Table 4 presents the MAE, RMSE, and MAPE analyses between the GA-BP-based Mv and the in situ Mv for ALOS-2 data in detail.

mated in relatively humid regions because of the sensitivity of radar signals to soil mois-**Table 4.** The results of the MAE, RMSE, and MAPE between the GA-BP-based Mv and in situ Mv for ALOS-2 data.


Figures 10–12 show the scatter plots between the measured and inverted soil moisture. It can be seen from the scatter plots that the retrieved soil moisture was underestimated in relatively humid regions because of the sensitivity of radar signals to soil moisture. In drier areas, the retrieved soil moisture was overestimated because the soil moisture content in the surface layer was lower than that in the deep layer. At the same time, the consistency of the soil moisture gradient also led to an overestimation of moisture. Because the soil moisture range in this study area was too extensive, the estimated value was underestimated or overestimated to a certain extent because of the actual local conditions. A large number of experimental analyses have verified this result.

Considering the GA-BP inversion analysis of the ALOS-2, the MAE, RMSE, and MAPE values were computed with different inputs (WCM, Equation (9)): Figures 10–12, respectively. The results show that the WCM (*V*<sup>1</sup> = *V*<sup>2</sup> = NDVI, NDWI, NMDI) can effectively eliminate the backscattering effect of vegetation, and the results of the GA-BP inversion using ALOS-2 data to estimate SM are satisfactory.

#### **5. Discussion**

This novel study shows the sensitivity of ALOS-2 radar data to SM. Only a few studies have performed SM inversion using ALOS-2 data [7,35,50,51]. Sekertekin et al. compared the potentials of ALOS-2 L-band and Sentinel-1 C-band data for SM estimation in bare and vegetation-covered agricultural fields using the WCM. The NDVI and plant coverage (PC) were considered the vegetation description, and the NDVI performed better than PC. The results show that the WCM can effectively eliminate the backscattering effect of vegetation, and the inversion of WCM presented satisfactory results in estimating SM with the ALOS-2 and Sentinel-1 data. Table 5 is a summary of the above methods. These findings show that the WCM method could effectively remove the influence of vegetation backscattering, which is consistent with our conclusion.

**Table 5.** The methods summary.


The potential of the C-band and L-band in SM retrieval is compared by El Hajj et al. However, for both frequencies, they only examine the potential of a copolarized HH HV C-band and L-band to estimate the SM because they believe that previous studies show that the use of crosspolarized (HV or VH) and copolarized SM data does not improve the estimation accuracy. Nevertheless, they did not consider crosspolarization [52,53]. This study, however, used ALOS-2 dual-polarization radar data and considered both polarization modes (HH and HV) while overcoming the lack of soil roughness.

The method used by Zribi et al. for estimating SM using ALOS-2 L-band radar data was compared for different types of crops (turmeric, marigold, and sorghum). In areas covered by vegetation, soil roughness measurements are rare. Accordingly, only the WCM has been considered to simulate the relationship between SM and the radar backscattering coefficient to retrieve the SM. Zribi et al. obtained moderately accurate estimates of SM for turmeric and marigold fields, with errors equal to 6.7 vol% and 7.9 vol% for HH and HV polarization, respectively, for turmeric, and 8.7 vol% and 11 vol%, in the HH and HV polarizations, respectively, for marigold. This result can be explained by the fact that the multiscattering effect is not considered in the simplified first-order radiation transfer equation of the WCM. The method presented in this paper also encountered challenges, such as the lack of measured soil roughness data. Therefore, we propose a GA-BP neural network algorithm, which overcomes the above problems to a certain extent while considering all polarization (HH and HV) modes. Even if there is a lack of measured data, such as soil roughness, an error analysis is carried out each time according to the results obtained from the training, and the expected results according to the nature of the BP neural network. Then, the weights and thresholds are modified step by step to get the model that can output the same as the expected result.

However, in this study, with the WCM model, different vegetation descriptions were established. When the vegetation index was the NDVI, the accuracy analysis results of the SM estimated by the GA-BP method, and the SM measured, were the best. The MAE, RESE, and MAPE results were 2.248 vol%, 3.146 vol%, 0.056 vol%, respectively, at a 0–10 cm depth. When the vegetation index was the NDWI, the accuracy analysis results of SM estimated by the GA-BP method, and the SM measured, were the best at a 20–30 cm depth. The MAE, RESE, and MAPE results were 2.389 vol%, 2.834 vol%, and 0.06 vol%, respectively. We can also see from the results that when the SM is less than about 30 vol%, the inversion results are slightly higher than the measured values. When the SM was higher than approximately 45 vol%, the inversion result was slightly lower than the measured value. The reason is that the sensitivity of the backscatter coefficient to the SM increases in relatively low and dry areas. The sensitivity of the backscattering coefficient to the SM decreases in the relatively humid area. In the following research, the method will be analyzed and verified according to different humidity gradients to discuss the applicability of the method.

By using the three vegetation indices as the vegetation input in the algorithm, we can observe the following conclusions. When the soil moisture is less than about 34%, we find that the slope of the scatter plot of the measured and inverted soil moisture is higher. At this time, it was in a relatively dry area, and the retrieved soil moisture was overestimated because the soil moisture at this time was lower than the deeper part. When the soil moisture is greater than 44%, the slope of the scatter plot of the measured and inverted soil moisture is low. At this time, it is in a relatively humid area. This is because the sensitivity of the radar signal to soil moisture is reduced in the humid area. A large number of experimental analyses have verified this result.

This study has some limitations. Because the sampling area has many hillsides, sampling is more difficult. Because of the influence of the topography of the sampling points, the distribution of the sampling points should choose flat areas as much as possible. However, the distribution should be as uniform as possible throughout the study area. At the same time, only soil samples were collected. Soil roughness, soil type, etc., can be considered in future research. In addition to these limitations, further research is needed to obtain better results for SM estimation using SAR data. We believe that the results of this study provide a new idea for future research.

Future studies should look at the following:


#### **6. Conclusions**

According to this study, the potential of ALOS-2 L-band radar data for SM calculation was investigated over vegetation-covered fields.


**Author Contributions:** Conceptualization, Y.G., M.G.; Methodology, Y.G., M.G.; Formal analysis, M.G., L.W.; Data curation, Y.G.; Writing—original draft, Y.G.; Writing—review & editing, M.G., L.W., O.R.; Valuable advice, M.G., L.W., O.R.; Funding acquisition, M.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (grant number 41871282, 62071084, 62001434).

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**

