**1. Introduction**

Soil moisture estimation across space and time has become possible with the advent of microwave remote sensing [1]. The amount of moisture in the soil is a function of physical, chemical, and management practices. Soil moisture is highly dynamic across space and correlated in time. The radar backscattering coefficient is a function of soil characteristics such as dielectric constant, texture, and surface roughness, and depends on the wavelength, polarization, and angle of incidence of the radar [1]. Shorter wavelength C-band radar backscatter has shown sensitivity to surface soil moisture at a depth of about 5 cm [2–4]. The launch of the Sentinel-1 mission of the European Space

Agency has made a huge amount of C-band data acquired since 2014 from all over the Earth's surface accessible. This opened up new perspectives on studying soil moisture in semi-arid regions, as was undertaken in Karnataka, India, in this work. Large scale soil moisture monitoring will provide greater insights into energy fluxes, which can result in improved meteorological and climatic projections [5] that will provide critical inputs for agriculture.

There have been studies based on physical, empirical, and semi-empirical models that estimate soil moisture over bare soils through radar remote sensing [6–8]. Physical approaches require many input parameters such as surface roughness and slope, which are not available under practical conditions [8]. Empirical models are only data driven, whereas semi-empirical models, while being data driven, also support theoretical considerations. In soil studies, they are site-specific and generally valid for specific soil characteristics [3]. Previous semi-empirical studies have considered single polarization to build a relationship between soil moisture and a backscatter model at 10 cm depth [9] and estimated ϑ*<sup>v</sup>* with a root mean square error (RMSE) of 3–6% [10–12] using C-band data. There have also been studies that have used the SAR interferometry technique and Sentinel-1 data to estimate soil moisture and compare them with in situ measurements [13]. Even though SAR interferometry is less frequently used in the remote sensing community to estimate soil moisture, its advantage lies in its ability to disentangle moisture and terrain roughness contributions. Most SAR-based soil moisture estimation studies have covered small areas limited to a few hundred square kilometers [11–17]. Estimating soil moisture over a wider area and at a higher resolution using SAR imagery will provide information on managing water resources and irrigation scheduling that can benefit a large number of farmers [14].

The aim of this study was to estimate soil moisture in bare rice agricultural soils. While SAR images have been used to estimate rice phenology using X-band TerraSAR-X images [15], there have been limited studies to estimate the soil moisture in bare rice agricultural soils using Sentinel-1 C-band images. Bare soils in Siruguppa are rice growing areas that lie bare after the rice crop has been harvested in March, with rice stubble and weeds that have dried up during summer (March–June). By the time the monsoon rains start, it is extremely critical to estimate the amount of soil moisture in the top 10 cm, which will help farmers decide when to start preparing the land and start sowing the next crop. Surface roughness, soil status, soil moisture, and crop residue distribution affect radar backscatter [16]. It is well established that σ<sup>0</sup> *VV* is more sensitive to variation in soils and <sup>σ</sup><sup>0</sup> *VH* is more suited to the identification of dry crop residue [17]. Utilizing both together can improve the accuracy of soil moisture estimates [18]. Nevertheless, soil moisture studies using σ<sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* together, especially using Sentinel 1 SAR data, are limited. The need for such studies over significantly large agricultural fields is very important to study agriculture, water, and food security. The major goal of this study was to estimate soil moisture over bare soils using both σ<sup>0</sup> *VV* and <sup>σ</sup><sup>0</sup> *VH* polarization and compare it with in situ measurements at a 10 cm (0–10 cm) depth. At the time of measurement, soil moisture to 10 cm is at the steady state and consistent across that top surface layer and therefore the C-band can be assumed to detect the top 10 cm layer. However, it is known that C-band SAR signals cannot penetrate to a 10 cm depth.

The contribution of standing stubble to total backscattering coefficient is comparable with that of the soil surface when the stubble has more than 75% water content. Backscatter coefficient decreases with a decrease in water content in the stubble. However, when the water content in the stubble is less than 40%, the contribution to the total backscattering coefficient is negligible [19]. We investigated both localized and generalized linear models to try to disentangle the stubble and soil moisture contributions. The linear coefficients of localized models were derived using in situ data acquired on a specific Sentinel-1 day. In contrast, generalized models were built using all in situ measurements acquired in the study period, thus adding the temporal dimension to the analysis of Sentinel-1 data. The question we wanted to answer is: can semi-empirical models estimate soil moisture, getting rid of the stubble contribution to the backscattering coefficient? We tried to answer this question by studying the effects of each variable, time, and polarization, separately. A localized model does not take into account the temporal evolution of backscattering, while a generalized model includes the time variable when

estimating the linear coefficients. Furthermore, for each model, it is possible to keep the polarimetric channels separated or merge them. In this work, we used a large dataset of in situ measurements of soil-moisture acquired across a 2-year period to answer the above question. The issues of the stability of results and of collinearity of data are crucial and will be used to assess the results of this experiment.

The rest of this paper is organized as follows: Section 2 is devoted to materials and methods, Section 3 to the results, and Section 4 presents the discussion. Finally, a few conclusions are drawn in Section 5.
