# Detection of Frozen Soil Using Sentinel-1 SAR Data
## 1 Introduction  
Frost frequently causes serious crop damages and consequently loss of yield. A frozen soil map is a key tool to assess the extent of loss of yield in agricultural areas. This map requires a monitoring system that can map the frozen zones with fine spatial and temporal resolutions. The arrival of Sentinel-1 (S1) satellites encourages the analysis of Synthetic Aperture Radar (SAR) data for mapping agricultural frozen soils with a high revisit time and high spatial resolution (up to plot scale). Some studies have shown from SAR and radiometer-scatterometer data (e.g., ERS, ENVISAT/ASAR and RADARSAT) that the SAR backscattering coefficient decreases when soil freezes [1; 2; 3; 4; 5]. A decrease in the radar signal of approximately 3 dB was observed when the soil was frozen [2; 3]. [PERSON] [1] studied the effect of freezing and thawing on the microwave signatures of bare soil using radiometer-scatterometer system at frequencies between 3 and 11 GHz. His results showed that freezing increases the emissivity and decreases the backscattering coefficient. [PERSON] et al. [2] observed from temporal ERS-1 SAR images (C-band) pronounced temporal variations in radar backscattering coefficient in Taiga forests due to freezing events. They detected a 3 dB decrease when the soil and vegetation freeze. [PERSON] et al. [3] mapped agricultural frozen soils under snow cover using RADARSAT-1 images (C-band). They developed classification algorithm based onsoil-freezing threshold from the backscattering coefficient in HH polarization. [PERSON] et al. [4] used ENVISAT/ASAR images (C-band) to monitor freeze/thaw cycles of permafrost areas. A difference of 3-4 dB was observed between ASCAT signal in freezing condition and ASCAT signal in thawing condition. [PERSON] et al. [5] showed over a study site in Finland the high sensitivity of RADARSAT-2 signal (C-band) to soil freezing and thawing states even under dry snow cover. Under cold winter conditions, much of soil water freezes, which leads to a significant decrease of the soil dielectric constant. The decrease in the dielectric constant due to a decrease of the volumetric moisture content causes a decrease of the radar signal [6]. This variation in the radar signal due to the variation in the soil dielectric constant can be estimated using SAR images [1; 2; 3; 4; 5]. Currently, several high-resolution SAR images can be acquired at a given study site due to the availability of SAR data in the C-band (e.g., Radarsat-2 and Sentinel-1) and X-band (e.g., TerraSAR-X and COSMO-SkyMed). However, only Sentinel-1 satellites provide users with free and open access SAR data at high spatial and temporal resolutions (revisit time of six days over Europe and spatial resolution of 10 m). This high spatial resolution of SAR sensors will make it possible to follow the soil freezing at very fine spatial scales in agricultural areas (plot scale or sub-plot scale). Recently, a freeze/thaw product generated from SMAP data is available at low spatial resolution [7]. The product based on temporal change detection approach assumes that the high variation in the temporal dynamics of the normalized polarization ratio (NPR) of the brightness temperature is related to a large change in dielectric constant (passing from frozen to non-frozen condition, or reciprocally) [7]. The objective of this paper is to study the potential of Sentinel-1 SAR data for monitoring agricultural frozen soils. A SAR backscattering model combined with a dielectric mixing model was used to study the behavior of the SAR signal after freezing. Assuming that the soil moisture and the surface roughness were unchanged between the date of unfrozen soil condition and the date of frozen soil condition, a time series of Sentinel-1 images acquired on a study site in France was analyzed to identify frozen soils. After a detailed description of the semi-empirical frozen soil-water dielectric mixing model is presented in Section 2, Section 3 describes the data used (modeling settings, Sentinel-1 images and temperature data).