**2. Materials and Methods**

#### *2.1. Study Area*

The study was conducted in Siruguppa *taluk* (sub-district) in the Bellary district of Karnataka state, India (Figure 1). Siruguppa is located between 15.35◦N to 15.83◦N latitudes and 76.69◦E to 76.71◦E longitudes covering an area of 1048 sq. km. Its climate is moderate and dry most of the year. It experiences high temperatures ranging from 23.2 ◦C to 42.4 ◦C from March to May and an annual rainfall of 645 mm. Irrigation from canal discharges cater to 60% of the cropped area, and the rest is either rainfed or irrigated through groundwater. Most of the crops are grown in predominantly black-clay, red-loamy, and red-sandy soils.

The River Tungabhadra runs diagonally across Siruguppa from the northwest, providing water for irrigation. The major crops grown are paddy, sorghum, pearl millet, sunflower, groundnut, cotton and sugarcane. The last decade saw a fall in kharif (rainy season) crop production due to deficit rainfall during the monsoon in some places in the *taluk*, leading to a shift from paddy and millets to cash crops such as cotton and sugarcane. The Deccan Plateau region is frequently prone to drought, making information on soil moisture critical for allocating water resources and scheduling irrigation. The date of sowing is a critical decision farmers make after the initial rainfall has occurred. This is done based on traditional knowledge and the physical assessment of soil moisture by hand or using a push probe. A scientific estimation of soil moisture can help farmers to decide the sowing date. This study was conducted on "bare agriculture fields" of Siruguppa to estimate soil moisture using radar remote sensing.

#### *2.2. In Situ Data*

#### 2.2.1. Soil Sampling and Ground Data Collection

The soils of Siruguppa are classified into Vertisols (covering 720.9 km2), Aridisols (146.8 km2), Inceptisols (65.1 km2), Alfisols (34.1 km2), and other land cover such as rock outcrops (21.5 km2). The locations for soil sample collection were based on random sampling, taking into account the fractions of different soil types. This mitigates the effects of variation from sampling error and increases the precision of the measured variable [20]. Soil samples were collected using a 10 cm standard metallic cylinder for a soil type to account for vertical and horizontal homogeneity [21], and weighed on site using a Mettler Toledo electronic balance. A handheld GPS (Garmin etrex) was used to georeference the locations immediately with an average accuracy of 2.5 meters as we collected it after a good almanac was received. Sixty-two locations were sampled spread across the four soil types. Forty-eight locations were sampled in Vertisols, eight in Inceptisols, four in Aridisols, and two in Alfisols. This was repeated for two years (2017 and 2018) over 13 dates of satellite overpasses, bringing the total data points to 806 (Figure 1).

Bulk density (BD) samples were collected simultaneously using standard cylindrical cores on site to estimate volumetric soil moisture (ϑ*v*). The sampling was carried out from March to May in bare agricultural soils with crop residue from paddy and weeds.

**Figure 1.** Map of the study area with sampling locations.

#### 2.2.2. Laboratory Analysis

Volumetric soil moisture was measured in two steps. First, the gravimetric method was used to estimate soil moisture from field samples over bare agricultural land [22]. Global Positioning System (GPS) coordinates were taken at each sample location to allow the approximate identification of the soil sample location with the image pixel. The soil collected from the ground after measuring the wet weight (ϑ*w*) was filled in airtight polythene bags and numbered with their corresponding GPS ID. The polythene bags were brought to the soil laboratory to measure their dry weight (ϑ*d*) using a standard drying process. Each sample was transferred to a microwave bowl and placed in the oven at 105 ◦C for 24 h, and the weight measured as dry weight. The following formula was used to estimate gravimetric soil moisture:

$$\mathfrak{G}\_0 = \frac{\mathfrak{G}\_w - \mathfrak{G}\_d}{\mathfrak{G}\_d} \left[ \frac{\mathcal{g}}{\mathcal{g}} \right] \tag{1}$$

The second step involved collecting the soil cores to estimate bulk density (BD). The drying process was repeated for each sample and the following formula was used to estimate BD:

$$\mathcal{S}\_0 = \frac{\mathcal{S}\_d}{V} \left[\frac{\mathcal{S}}{cm^3}\right] \tag{2}$$

where *V* is the volume of the core.

Volumetric soil moisture was expressed as:

$$\mathcal{S}\_v = \frac{\mathcal{S}\_0 \cdot BD}{\rho\_{H\_20}} \left[ \frac{cm^3}{cm^3} \right] \tag{3}$$

where ρ*H*20 is the water density.

#### *2.3. Data Collection and Pre-Processing*

Thirteen Sentinel-1 images were used, six acquired between 4 March 2017 and 27 May 2017 and seven between 11 March 2018 and 22 May 2018 (see Table 1). The incidence angle varied from 30◦ to 35◦ covering the study area in Co-Polarization (VV) and Cross-Polarization (VH) polarization. The frequency of the acquisition of imagery over India is very low, and a cycle of low and high number of acquisitions in alternating months was seen from the data portal (Table 1). Pre-processing of SAR imagery was carried out using SNAP software developed by the European Space Agency (ESA). Radiometric calibration, thermal noise removal, and terrain correction (using the Range Doppler terrain correction operator) algorithms were applied to obtain the backscattering coefficient (σ dB) [23]. A Lee speckle filter was applied to reduce speckle noise. Linear σ<sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* were converted to dB values.

Sentinel-2 Level-1C S2 imagery with less than 10% cloud cover was downloaded for the years 2016 to 2018. These were converted to Level 2A to obtain bottom of atmosphere reflectance using SNAP software provided by ESA under a GNU General Public License V3. Visible and Near Infrared Radiation (NIR) bands B4 and B8 were used to generate normalized difference vegetation index (NDVI) to delineate the agricultural area.

**Table 1.** Acquisition dates of Sentinel-1 images: Interferometric Wide (IW) swath mode, relative orbit 63, descending. Ground Range Detected (GRD) product type (VV and VH polarization). Images were downloaded from the European Space Agency (ESA) portal https://scihub.copernicus.eu/.


#### *2.4. Methodology*

The study began with pre-processing of Sentinel-1 C-band data (described in Section 2.3) to obtain σ◦ from both polarizations after applying appropriate corrections and speckle reduction. The in situ data collected during the field missions were used to extract σ<sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* values in dB from the respective images of different dates (Table 1). The in situ data and σ◦ data were compiled to analyze and build a semi-empirical model. Agricultural land was derived using band B4 and B8 of a time series of Sentinel-2 images used to calculate the NDVI for the date for which an image was available in the season during each year. Random forest (RF) classification was applied to the set of nine NDVI images covering the study area and training dataset. This is useful to mask out non-agricultural areas when visualizing soil moisture estimates. An evaluation of the semi-empirical model was conducted to assess the accuracy of soil moisture (Figure 2).

**Figure 2.** The process of estimating soil moisture using Sentinel-1 Co-Polarization (VV) and Cross-Polarization (VH) imagery.
