**3. Results**

A well distributed sampling scheme and data collected over two years yielded a well calibrated model to estimate soil moisture in the bare agricultural soils during the dry season (March–May). Linear and multi-linear regression was used to find the relationship between observed soil moisture and backscatter coefficients by deriving the model constants for each date and a combination of dates.

#### *3.1. Field Measurements and Laboratory Analysis*

Soil moisture was estimated using the gravimetric method for all 62 samples spread over Siruguppa *taluk* (Figure 1) for each date of satellite pass. Mean volumetric soil moisture (ϑ*v*) in the samples ranged from 0.22 m3/m<sup>3</sup> to 0.28 m3/m<sup>3</sup> from 4 March 2017 to 27 May 2017. Minimum ϑ*<sup>v</sup>* varied from 0.12 m3/m3 to 0.17 m3/m<sup>3</sup> from March 2017 to May 2017 and the maximum ϑ*<sup>v</sup>* varied from 0.30 m3/m3 to 0.34 m3/m3, respectively (Table 2). Figure 3 illustrates the range of values that each point in the population takes above and below the mean for six dates of satellite passes during 2017. It is worth noting that Figure 3 displays the soil moisture values measured the day of the satellite passes and for this reason, the ranges of the variation of soil moisture appeared as different from those reported in Table 2. Similarly, measurements were made during 2018 at the same locations. The minimum ϑ*<sup>v</sup>* varied from 0.11 m3/m3 to 0.15 m3/m3 and the maximum varied from 0.32 to 0.34 m3/m<sup>3</sup> from March 2018 to May 2018, respectively. The mean ϑ*<sup>v</sup>* was measured between 0.23 m3/m<sup>3</sup> and 0.26 m3/m<sup>3</sup> (Table 2). Figure 4 shows the range of values during 2018 for the seven dates of satellite passes during 2018.

**Figure 3.** Observed soil moisture of each point during six passes of the satellite estimated using the gravimetric method during 2017.

**Figure 4.** Observed soil moisture of each point during seven passes of the satellite estimated using the gravimetric method during 2018.

**Table 2.** Observed soil moisture of all 62 samples combined during each pass of the satellite during 2017 and 2018 collected at Siruguppa *taluk*.


#### *3.2. Localized and Generalized Relationships*

The concepts of localized and generalized relationships were used in the in situ measurements of soil moisture and SAR estimates. A relationship was localized if it was obtained using single date data points in the study area, collected both in 2017 and 2018. A generalized relationship was obtained when all the dates data points were considered in the study area (Figure 5).

The relationship for localized models showed R<sup>2</sup> ranging from 0.62 to 0.75 between σ<sup>0</sup> *VV* and ϑ*v*, revealing a significantly strong relationship in 2017 (Table 3). As far as σ<sup>0</sup> *VH* is concerned, it was found to have a lower R2, ranging from 0.43 to 0.70. During 2018, R2 values ranged from 0.56 to 0.69 for σ0 *VV* and from 0.31 to 0.62 for <sup>σ</sup><sup>0</sup> *VH*. The linear combination of <sup>σ</sup><sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* showed higher R2 values, ranging from 0.71 to 0.88 during 2017, and from 0.60 to 0.86 during 2018 (see Table 3).

Generalized relationships attempted to study the impact of seasonal effects observed in the study area due to different agroecologies (i.e., the different management and practices in a homogenous landscape). Table 4 summarizes the R2 values obtained in the individual years 2017 and 2018 along with a combination of two years for σ<sup>0</sup> *VV*, <sup>σ</sup><sup>0</sup> *VH* and their linear combination (σ<sup>0</sup> *VV* <sup>+</sup> <sup>σ</sup><sup>0</sup> *VH*). The individual

and combined backscatter coefficients in the two VV and VH polarizations over 2017 and 2018 pointed out a clear relationship with the in situ measurements of soil moisture.

**Figure 5.** Localized and generalized linear models between soil moisture and backscatter. (**Top**) Examples of localized models refer to the Sentinel-1 acquisition of 15 May 2017. The remaining rows refer to the generalized models obtained using all Sentinel-1 images acquired in 2017, 2018, and in the total study from 2017 to 2018. The images from left to right represent Sentinel-1 images VV, VH, and VV + VH backscattering coefficients.


**Table 3.** Localized relationship between soil moisture and backscatter.

**Table 4.** Generalized relationship between soil moisture and backscatter.


#### *3.3. Soil Moisture Evaluation*

Multi-linear regression and linear regression were applied to determine the value of empirical constants (A, B, and T) in both the localized and generalized models. Tables 5 and 6 summarize the results. Each localized model comprises images from one date of pass over of the study area, totaling 39 equations from March 2017 to May 2018, and considering individual σ<sup>0</sup> *VV*, <sup>σ</sup><sup>0</sup> *VH*, and their linear combination σ<sup>0</sup> *VV* <sup>+</sup> <sup>σ</sup><sup>0</sup> *VH*. Each generalized model combines all images acquired during a year for individual σ<sup>0</sup> *VV*, <sup>σ</sup><sup>0</sup> *VH* and linear combination <sup>σ</sup><sup>0</sup> *VV* <sup>+</sup> <sup>σ</sup><sup>0</sup> *VH*. Three models were obtained for each year 2017 and 2018 and three additional models using all the images used in the study, making it a total of nine generalized models. For the localized model, 40 samples for calibration and 22 samples for validation were used during 2017 and 2018 (N = 62). The model calibration for individual dates (localized models) with combined backscatter coefficient (σ<sup>0</sup> *VV* <sup>+</sup> <sup>σ</sup><sup>0</sup> *VH*) during the study years of 2017 and 2018 estimated an R<sup>2</sup> ranging from 0.91 to 0.70 and RSE ranging from 0.03 to 0.01.

As far as generalized models are concerned, N = 368 points were used in 2017, 258 for calibration, and 110 for validation, and N = 427 in 2018, with 299 for calibration and 128 for validation. The total number of points for both years was N = 795, with 557 used for calibration and 238 for validation. The nine linear equations modeled each backscatter coefficient σ<sup>0</sup> *VV*, <sup>σ</sup><sup>0</sup> *VH* and a linear combination of both (σ<sup>0</sup> *VV* <sup>+</sup> <sup>σ</sup><sup>0</sup> *VH*) for each year (2017, 2018) and 2017 and 2018 put together. Table <sup>6</sup> summarizes the R<sup>2</sup> values modeled from σ<sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* as a function of (ϑ*v*) during 2017 and 2018. RSE was 0.03 for 2017, 2018 from σ<sup>0</sup> *VV*, and 0.03 and 0.04 from <sup>σ</sup><sup>0</sup> *VH* for 2017 and 2018, respectively. A linear combination of both backscatter coefficients during 2017 and 2018 showed an R<sup>2</sup> of 0.80 and 0.70, respectively. The RSE values were 0.02. The backscatter coefficient from each polarization and a linear combination of both

polarizations put together for two years were also attempted. The R<sup>2</sup> from σ<sup>0</sup> *VV* was 0.60 with a RSE of 0.03 and from σ<sup>0</sup> *VH* it was 0.50 with a RSE 0.03. The R2 from a linear combination of both polarizations (σ<sup>0</sup> *VV* <sup>+</sup> <sup>σ</sup><sup>0</sup> *VH*) was 0.70 with a RSE of 0.02.

Model validation was done for individual dates from a linear combination of the two polarizations. Table 5 and Figure 6 summarize the RMSE values for 2017 and 2018. The nine generalized models were also validated and the RMSE values are reported in Table 6 and Figure 7.

**Figure 6.** *Cont*.

**Figure 7.** Generalized models. Validation between the estimated and observed soil moisture.
