## 1 Introduction  
Changes in the water cycle may result in natural disasters such as flood, landslides and severe drought, thereby increasing the risk to human lives. Soil moisture is a key parameter regulating the earth water cycle since it is a function of the rates of soil evaporation and precipitation. The prediction of water cycle behaviors requires the frequent and spatially distributed estimation of soil moisture; this is provided at low resolution by several sensors including SMOS (resolution of ~30 km \(\times\) 30 km), SMAP (resolution ~36 km \(\times\) 36 km), and ASCAT (resolution ~25 km \(\times\) 25 km). However, this low spatial resolution may not be adequate for water cycle monitoring [1]. To overcome the spatial resolution limitation of the current soil moisture product, spatial disaggregation of the low resolution soil moisture product (SMOS, SMAP, and ASCAT) was performed [2; 3; 4; 5]. The new Sentinel-1A and -1B SAR (Synthetic Aperture Radar) sensors operating in the C-band will allow soil moisture mapping at high spatial resolution (up to the plot scale). SAR data in the C- and X-bands were widely and primarily used to estimate soil moisture (\(mv\)). Over bare soils (or soils with sparse vegetation cover), the estimation of soil moisture was realized by inverting the SAR signal using either physical [6; 7] or statistical models [8; 9; 10]. Unlike statistical models, physical models for soil moisture estimates do not require site-specific calibration and could always be used to simulate the backscattering coefficients from the radar configuration (frequency, polarization, and incidence angle) and soil parameters. The Integral Equation Model (IEM) [7] is the most commonly used physical model to invert the radar signal and estimate the soil moisture and/or soil roughness. The IEM developed by [PERSON] [7] shows a large difference between simulated and observed SAR data [11; 12; 13; 14] which leads to inaccurate soil moisture estimates. [PERSON] et al. [15; 16; 17; 18] attributed this difference mainly to the correlation length input parameter, which is difficult to measure with good accuracy. To improve the accuracy of simulated backscattering values from IEM, [PERSON] et al. [15; 16; 17; 18] proposed a semi-empirical calibration of the IEM. This semi-empirical calibration consists of replacing the in situ measured correlation length by a fitting parameter, called Lopt (depends on surface roughness and SAR parameters). The semi-empirical calibration has been performed and evaluated by using a large dataset at the X-band [16], C-band [15; 17] and L-band [18]. The accuracy of the soil moisture estimates for bare soils was approximately 3 vol % (volumetric unit expressed in percent) with SAR data in the X-band and approximately 6 vol % in the C-band [19; 20; 21; 22; 23; 24]. For soils covered with vegetation, the Water Cloud Model (WCM) developed by [PERSON] and [PERSON] [25] was used mainly to invert the radar signal to estimate the soil moisture. In the WCM, the total backscattered coefficient is modeled as the sum of direct vegetation contribution and soil contribution multiplied by the attenuation factor. The direct vegetation contribution and the attenuation are computed using one or more vegetation descriptors. Several studies showed that the use of the NDVI (Normalized Differential Vegetation Index) as the only vegetation descriptor allows for computation of the vegetation effects on the total backscattered coefficients with good accuracy [26; 27; 28]. The parametrization of the WCM was provided in several studies for different SAR configurations and crop types [27; 29]. Recently, [26] parameterized the WCM for a radar signal in the C-band and for various crop types (grassland, wheat, and cereals). Using the WCM, several studies estimated the soil moisture from the C- and X-band SAR with an accuracy better than 8 vol % [27; 28; 29; 30; 31; 32; 33].