## 3 Methodology
### NN Sensitivity Tests
#### 3.3.3 Analyzing the Weight of Each NN Satellite Input  
To identify the most relevant inputs for the NN classification of the water surface, 15 NNs are trained based on all 15 different combinations of five input parameters, and their performances are evaluated following various criteria. Table 5 presents the best results with one to five inputs and illustrates how the overall accuracy of the NN classification increases when the number of satellite inputs increases, as compared to the reference Landsat-8 dataset. The NN trained with only the VH backscatter coefficient has a spatial correlation of 78% and a true positive accuracy (correctly detecting water pixels) of 77% compared to the reference data. The spatial correlation increases to 79%, and the true positive accuracy rises to 85% when the standard deviation of the VV backscatter coefficient is added as an input to the NN. The VV backscatter coefficient helps to increase the performance of the NN since both spatial correlation and true positive accuracy increase to 87% and 90%, respectively. The standard deviation of the VH backscatter coefficient does not significantly improve the accuracy of the NN classification. This is due to the strong linear correlation (88%) between the spatial standard deviations of the VH and the VV backscatter coefficients (the other linear correlations among the five input parameters of the NN are provided in Table 6). Similar to the standard deviation of the VH backscatter coefficient, the incidence angle does not have a strong impact on the performance of the NN since its accuracy remains nearly the same after adding the incidence angle as a new input. The input parameters of the NN classification are listed below, from the most important to the least important one in the NN processing:  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Non-water(0) (Predicted)** & **Water(1) (Predicted)** \\ \hline
**Non-water(0)** (Actual) & 99.7\% & 0.3\% \\
**Water(1)** (Actual) & 14\% & 86\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Confusion matrix of the NN without equalization of the training dataset, for an optimum threshold of 0.5 on the NN outputs.  
Figure 8: Histograms of the NN outputs, for water (blue) and non-water (dashed red) pixels separately, according to the corresponding Landsat-8 surface water maps. The NN uses the five initial inputs but the training dataset is not equalized. The y axis range is selected to illustrate the peak of the water histogram.  
* Backscatter coefficient VH polarization (BS_VH)
* Standard deviation of backscatter coefficient VV polarization (STD_VV)
* Backscatter coefficient VV polarization (BS_VV)
* Incidence angle
* Standard deviation of backscatter coefficient VH polarization (STD_VH)  
To conclude, the water detection ability of the proposed NN increased when the input parameters are carefully selected and when an optimal output threshold is selected. An equal number of water and non-water pixels should be used in the training dataset to ensure that the NN performs equally well in classifying water and non-water clusters. The STD_VH provides limited additional information to the NN due to its strong linear correlations with the other NN inputs. The incidence angle also plays a limited role in the NN performance. This is partly due to the rather narrow range of incidence angle, from 29\({}^{\circ}\) to 46\({}^{\circ}\).