# 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
#### 5.1.2 Impact of Soil Roughness Spatial Homogeneity  
A wide in-situ surface soil roughness dataset (defined by the root mean square surface height _Hrms_), collected over several agricultural study sites [24; 30], was used to analyze the distribution of _Hrms_ values in agricultural areas (around 500 samples). Measurements of soil roughness were carried out using a needle profilometer 1 m in length with 2 cm sampling intervals. Ten roughness profiles were established in each plot. From these profiles, two surface roughness parameters were then calculated: the average root mean square surface height (_Hrms_), which specifies the vertical scale of the roughness, and the correlation length (_L_), representing the horizontal scale. In general, the _Hrms_-values of cultivated winter crops (wheat, barley, oat, rapeseed... ) are between 1 and 1.5 cm, whereas they fall between 1 and 3 cm for 90% of the measurements carried out on agricultural bare plots (Figure 11). Figure 10: Impact of 5 vol.% vegetated plots SSM underestimation on VOD estimations: Bias (noisy VOD—reference VOD) and RMSE are plotted as a function of NDVI. Figure 9: Impact of 5 vol.% vegetated plots SSM underestimation on VOD estimations: Noisy VOD as a function of reference VOD. In the present study, it was assumed that the \(Hrms\) for all agricultural plots located within an area of 5 km \(\times\) 5 km is similar. However, in some places the \(Hrms\) values are not homogeneous in an area of 5 km \(\times\) 5 km because some plots are plowed (in general, higher \(Hrms\)) and others are cultivated (in general, lower \(Hrms\)). Thus, in some cases, the \(Hrms\) of plots with vegetation cover may be lower than the averaged \(Hrms\) over an area of 5 km \(\times\) 5 km. An analysis on the impact of this overestimation of \(Hrms\) on the calculation of VOD was carried out by using the calibrated Integral Equation Model combined with the Water Cloud Model [23; 30]. The C-band radar signal was simulated as a function of \(Hrms\) for a \(\theta\) of 35\({}^{\circ}\) (S1 incidence angle) and a SSM of 20 vol.% (Figure 12). Results show that an overestimation of \(Hrms\) by about 1 cm on average for the plots with vegetation cover (assuming that \(Hrms\) of plots with vegetation = average \(Hrms\) of bare soils) would lead to an overestimation of the soil contribution of 1 dB maximum (Figure 12). The impact of a 1 cm \(Hrms\) overestimation of vegetated plots on VOD estimates was investigated through a sensitivity analysis of Equation (3). As done for analyzing the impact of SSM errors on VOD estimation, a synthetic database of \(\sigma^{0}_{\rm soil}\) and of \(\sigma^{0}_{\rm tot}\) was computed using the calibrated IEM combined  
Figure 11: Distribution of \(Hrms\) values measured over several agricultural plots in several study sites. Figure 12: Behavior of radar signal according to \(Hrms\) using C-band, \(\theta\) of 35\({}^{\circ}\), SSM of 20 vol.% and VV polarization. The calibrated Integral Equation Model was used for these simulations. with the Water Cloud Model [23; 30] for _Hrms_ values between 1 and 3.5 cm (step of 0.1 cm), NDVI between 0.4 and 0.8, SSM fixed to 20 vol.%, and \(\theta\) was fixed to 35\({}^{\circ}\). From each reference element of the synthetic database composed of \(\theta\), _Hrms_, SSM, and NDVI, 1000 elements containing _Hrms_-values noisy with a Gaussian noise of 1 cm mean and 1 cm standard deviation were generated. Figure 13 shows the reference VOD values (without bias on _Hrms_) and noisy VOD values (1 cm _Hrms_ overestimation). Results show that a 1 cm _Hrms_ overestimation leads to a slight overestimation of VOD of 0.03 (with an RMSE of 0.04). In addition, the impact of 1 cm _Hrms_ overestimation on VOD estimation was analyzed according to the NDVI for values between 0.4 and 0.8. The overestimation of VOD as well as the RMSE increase as the NDVI increases (Figure 14). The overestimation on VOD increases from 0.02 for NDVI = 0.4 to 0.05 for NDVI = 0.8.