# Potential of Sentinel-1 Radar Data for the Assessment of Soil and Cereal Cover Parameters
## 4 Simulation of S1 Data with Backscattering Models
### Validation of the Water Cloud Model  
The water cloud model developed by [PERSON] and [PERSON] (42) was used to model the radar signal backscattered by covered surfaces. At an incidence angle \(\theta\), the backscattering coefficient in this model is given by the following expression:  
\[\sigma^{0}=\sigma^{0}_{canopy}+\sigma^{0}_{canopy+soil}+\tau^{2}\sigma^{0}_{soil} \tag{4}\]  
where \(\tau^{2}\) is the two-way vegetation transmissivity. The first term represents scattering due to the vegetation, whereas the second term is related to multiple scattering effects, and the third term represents soil scattering attenuated by the vegetation cover. The second term, which can be neglected in the case of wheat scattering, is used to account for double-bounce scattering, the effects of which are stronger in the VV than in the VH polarization. Expression (4) can thus be simplified to:  
\[\sigma^{0}=\sigma^{0}_{canopy}+\tau^{2}\sigma^{0}_{soil} \tag{5}\]  
With  
\[\tau^{2}=\exp(-2\,B\,V1\,\sec\theta) \tag{6}\]  
And  
\[\sigma^{0}_{canopy}=A\,V1\,\cos\theta\left(1-\tau^{2}\right) \tag{7}\]  
where \(V1\) is a parameter related to the vegetation. In the present case we consider the NDVI, which is strongly related to the vegetation parameters. The parameters A and B depend on the type of canopy. This formulation represents a first-order solution for the radiative transfer equation through a weak medium, where multiple scattering is neglected. As in the case of bare soils, we consider two datasets, with the first being used for the calibration of A and B, and the second for validation of the retrieved model.  
The empirical model proposed in expression (2) was used to represent the soil contribution.  
In the present study, two different data sets were used, with different soil and vegetation conditions (moisture, roughness, vegetation index (NDVI)). The first of these contains data recorded from 110 reference fields, and is used to determine the parameters A and B, which are then used to calibrate the model. The second dataset describes a different set of 110 reference fields, which are used to validate the calibrated model. As the results described in Section 3.2 reveal a very low sensitivity of VH signals to vegetation cover, which is probably due to a volume scattering effect, in the water cloud model we consider the VV polarization only. The calibration process allows the empirical parameters A and B to be determined as: A = 0.06; B = 0.42.  
In Figure 11, the modeled VV radar strength is compared with the measured values taken from the second validation dataset. These are based on measurements made over reference fields, which are different to those used for the calibration. The modeled signal strengths can be seen to be in very good agreement with the real radar signal. This agreement was observed for a large range of vegetation types (NDVI between 0.14 and 0.69), soil moistures (ranging from 6.4 vol. % to 37.1 vol. %) and soil roughness values (ranging between 0.94 cm and 2.02 cm). The RMSE is equal to 0.84 dB and the bias is equal to 0.08 dB.