# First Vegetation Optical Depth Mapping from Sentinel-1 C-band SAR Data over Crop Fields
## 5 Discussion  
### Impact of Our Assumption of Spatial Homogeneity of Soil Moisture and Roughness on VOD Calculation  
#### 5.1.1 Impact of Soil Moisture Spatial Homogeneity  
In this study, it is assumed that the surface soil moisture (SSM) for vegetated plots is similar to the averaged SSM of all bare soils in the surrounding 5 km \(\times\) 5 km. However, in some places the SSM is not homogeneous in a pixel of 5 km \(\times\) 5 km due to many factors related, and not limited to, meteorological context and soil texture. In-situ SSM measurements performed between 2016 and 2018 over non-irrigated plots (mainly non-irrigated wheat and grassland), located in a flat area with  
Figure 7: Maps of VOD derived from S1 images at VV polarization in Ascending mode for the dates of 12/02/2018 (**a**), 02/03/2018 (**b**), 07/04/2018 (**c**), 25/04/2018 (**d**), and 13/05/2018 (**e**). In addition, maps of NDVI for the dates of 10/02/2018 (**f**,**g**), 30/03/2018 (**h**), 26/04/2018 (**i**), and 15/05/2018 (**j**). Coordinates are in UTM (Universal Transverse Mercator) ZONE 31 North. dimension of 15 km \(\times\) 15 km around Montpellier region of France, were analyzed. Within this area, the SSM values of plots with vegetation cover were close to the averaged SSM values of all bare plots in the 15 km \(\times\) 15 km area. The histogram displayed in Figure 8 (established using 165 samples) shows the distribution of the difference between the SSM of each vegetated plot (Height \(>\) 15 cm) and the averaged SSM of all bare plots (vegetation height \(<\) 15 cm). The mean of the difference distribution is about 1.1 vol.% with a standard deviation (std) of 3.0 vol.%. This result signifies that the SSM values of non-irrigated plots (bare or with vegetation cover) were homogeneous (up to a certain limit) within the area of 15 km \(\times\) 15 km. However, even though most in-situ SSM points show a high consistency between the SSM measured on plots with vegetation cover and the average SSM calculated using all the SSM measurements made on the bare soil plots in an area of 15 km \(\times\) 15 km, Figure 8 also shows that for a small part of the data, the SSM of plots with vegetation are 5 vol.% higher than the SSM of the bare soils. Furthermore, a sensitivity analysis was performed to assess the impact of 5 vol.% SSM underestimation for vegetated soil on VOD estimation from Equation (3). Indeed, we assume in our method that the SSM of vegetated plots is similar to that of bare soils whereas in fact the SSM of vegetated plots could be in some cases higher than the SSM of bare soils (about 5 vol.% as shown in Figure 8). First, the impact of the error on the SAR backscattering coefficients \(\sigma^{0}_{\text{tot}}\) and \(\sigma^{0}_{\text{soil}}\) due to an 5 vol.% underestimation for the SSM of vegetated plots is quantified. Then, the impact of the errors on \(\sigma^{0}_{\text{tot}}\) and \(\sigma^{0}_{\text{soil}}\) on VOD estimation was investigated through sensitivity analysis of Equation (3). A synthetic database of \(\sigma^{0}_{\text{soil}}\) and of \(\sigma^{0}_{\text{tot}}\) was generated using the calibrated IEM combined with the Water Cloud Model [23; 30] for SSM values between 10 and 30 vol.% (step of 5 vol.%), NDVI between 0.4 and 0.8, soil roughness defined by the root mean surface height \"_Hrms_\" fixed to 1.5 cm, and SAR incidence angle \"9\" was fixed to 35\({}^{\circ}\) (S1 incidence angle). From each reference element of the synthetic database (composed of \(\theta\), _Hrms_, SSM and NDVI), 1000 elements containing SSM values noisy with a Gaussian noise with a mean of 5 vol.% and std of 5 vol.% were generated. Using the calibrated Integral Equation Model and the Water Cloud Model, \(\sigma^{0}_{\text{soil}}\) and \(\sigma^{0}_{\text{tot}}\) were computed for each reference element (reference \(\sigma^{0}_{\text{soil}}\) and \(\sigma^{0}_{\text{tot}}\)) and for the corresponding 1000 noisy elements (noisy \(\sigma^{0}_{\text{soil}}\) and \(\sigma^{0}_{\text{tot}}\)).