2.4.1. Semi-Empirical Model

A semi-empirical model was proposed to estimate soil moisture over bare soils in agricultural areas from the backscatter coefficient based on a linear relationship. The linear equation captures the backscatter from bare soil, which constitutes soil moisture and surface roughness (as crop residue) and includes both VV and VH backscattering coefficients as:

$$f(\mathfrak{s}\_{\text{v}}) = A \,\sigma \, VV + B \,\sigma(VH) + T \tag{4}$$

where ϑ*<sup>v</sup>* is the volumetric soil moisture; A, B, and T are empirical constants; and σ<sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* are the VV and VH backscattering coefficients, respectively.

On bare soil, σ<sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* are mainly influenced by soil moisture. Since the major crop in the study area is rice, there is a crop residue as rice stubble on the ground. The rice stubble at 75% water content also contributes to the σ<sup>0</sup> *VV*, but decreases as the water content decreases and is negligible in both polarizations [19,24]. A linear combination including both polarizations was found to better estimate soil moisture from bare soil.

#### 2.4.2. Delineation of Agricultural Fields

The estimation of soil moisture is more meaningful when linked to the purpose for which it is used. The ideal domain for use of such information is agricultural lands. Ideally, NDVI [25] is used to understand changes in crop phenology as the growing season progresses. Since the target class was only agricultural land, time series NDVI during the cropping season was best suited for the delineation using Sentinel-2 imagery. A set of nine NDVI images during the three crop seasons was used to estimate land cover using the RF algorithm [26]. The training dataset included land use in the soil sample locations (62). Additionally, 200 training samples were used: 100 from agricultural land and 100 from non-agricultural land. This product was used as a base for mapping soil moisture in agricultural lands.

#### 2.4.3. Evaluation of Semi-Empirical Model

Basic information like maximum, minimum and mean in situ soil moisture were generated (Table 2). Linear regression was used to understand the relationship between Sentinel-1 backscattering coefficients and in situ soil moisture data. The P value, which indicates the significance of the accuracy assessment was significant (≤0.05) and not significant (≥0.05). The RMSE of the modeled soil moisture was estimated using the equation:

$$RMSE = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} \left( Y\_{\text{mcs}} - Y\_{\text{cst}} \right)^2} \tag{5}$$

To understand the contribution of each polarization and sum of both polarizations to the accuracy of the model, residual standard error (RSE) of the estimated soil moisture was calculated using equation:

$$\text{Residual standard error (RSE)} = \sqrt{\frac{\sum \left(y\_0 - y\_\epsilon\right)^2}{n-2}}\tag{6}$$

where *y*<sup>0</sup> is the observed soil moisture; *ye* is the predicted soil moisture; and n is the degree of freedom.
