## 3 Materials and Methods
### Soil Salinity Prediction and Accuracy Assessment  
The corrected ECe modeling dataset of HH and VV modes was used separately to interpolate a continuous surface for soil salinity prediction using IDW, OK, CCK, and RK methods. Firstly, the IDW interpolation determines cell values using a linearly weighted combination of sample points. The weight is a function of inverse distance. The surface being interpolated should be that of a locationally dependent variable. This method assumes that the mapped variable decreases influence with distance from its sampled location [38]. The general equation of IDW by [PERSON] [49] is shown below. \[\hat{Z}(\text{u}_{0})=\sum_{i=1}^{N}w_{i}Z(\text{u}_{i}) \tag{3}\]  
Here, \(\hat{Z}(\text{u}_{0})\) is the value being predicted for the target location \(\text{u}_{0}\); N is the number of measured data points in the search window; \(\text{w}_{i}\) represents the weights assigned to each measured point, and \(Z(\text{u}_{1})\) is the observed value at location \(\text{u}_{i}\). \(\text{u}_{i}=(\text{x}_{i}\text{y}_{i})\)[49]. Secondly, the OK method is a geostatistical interpolation method that weights the surrounding measured values to predict an unsampled location by incorporating the spatial dependence expressed by the semi-variogram in the estimation procedure [50]. The general equation of OK is displayed in the followings. \[Z(\text{x}_{0})=\sum_{i=1}^{N}\lambda_{i}Z(\text{x}_{i}) \tag{4}\]  
Here, \(Z(\text{x}_{0})\) is the value of variable \(Z\) at the unsampled location \(\text{x}_{0}\); \(\lambda_{i}\) represents the weights associated with the data points, which consider the spatial relationship of the sampled points, and \(Z(\text{x}_{i})\) is the observed value of \(Z\) at sampled locations \(\text{x}_{i}\)[50]. Thirdly, the CCK method is a variation of the OK, which considers a secondary variable related to the primary variable that wants to estimate, in which additional observed variables (which are often correlated with each other and the variable of interest) are used to enhance the precision of the interpolation of the variable of interest at each location [51]. The general equation of CCK by [PERSON] and [PERSON] [52] is presented in the following Equation (5). \[Z(\text{x}_{0})=\sum_{i=1}^{n}w_{1i}Z_{1}(\text{x}_{i})+\sum_{i=1}^{p}w_{2i} z_{2}\big{(}\text{x}_{i}\big{)} \tag{5}\]  
Here, \(Z(\text{x}_{0})\) is the position of the sample point, \(w_{1i}\) and \(w_{2i}\) are two regionalized variables, and \(z_{1}(\text{x}_{i})\) and \(z_{2}(\text{x}_{i})\) are weight coefficients [52]. In this study, the covariable factor of the CCK is soil moisture content applied for HH and VV modes. For soil moisture content measurement, some collected soil samples for ECe extraction in 30 locations were used to calculate soil moisture content based on a gravimetric basis. The soil moisture content (\(\theta_{g}\)) is measured by weighting a soil sample (m\({}_{wet}\)), drying the sample to remove the water, then weighting the dried soil (m\({}_{dry}\)) [53] as:  
\[\theta_{g}=\frac{m_{water}}{m_{soil}}=\frac{m_{wet}-m_{dry}}{m_{dry}} \tag{6}\]  
Figure 5 displays the spatial distribution of soil moisture content data, which was interpolated using IDW. The interpolated soil moisture content delivered a mean prediction error (ME) of 0.6403 percent by mass and root mean square error (RMSE) of 3.1008 percent by mass under the cross-validation of IDW. Fourthly, the RK method is a spatial interpolation technique that combines a regression of dependent variables on predictors with Kriging of the prediction residuals [54]. The general equation of RK by [PERSON] et al. [55] is shown in Equation (7). \[S(x)=\ f(Q,x)+e^{\prime}(x) \tag{7}\]  
Here, f(Q,x) is a function describing the structural component of \(S\) as a function of Q at x, and e\(\prime\)(x) is the locally varying, spatially dependent residual from f (Q,x). In regression Kriging, the soil property S at an unvisited site is first predicted by f (Q,x), followed by Kriging of the model's residuals [55].