## 3 Methodology
### A Neural Network-Based Classification  
Here, we propose training a NN to produce surface water maps from SAR images, over the Mekong Delta. In the remote sensing field, NNs are often used as a regression tool to estimate a quantity. For each pixel, NN input satellite observations are represented by a vector \(x\), and the network outputs (i.e., the retrieval) is represented by a vector \(y\). However, NNs can also be used as classifiers. In this case, when trained with binary output values (\(y\) = 0 for non-water, 1 for water surfaces), the NN becomes a statistical model for the conditional probability \(y=P(surface=water/x)\), i.e., the probability of the surface being covered by water knowing the satellite observations \(x\). The NN output can then directly be used as an index for water presence probability, but a threshold can also be applied to classify the state as being covered by water or not. The threshold needs to be optimized in order to satisfy some quality criteria, such as overall accuracy or false alarm rates. The NN classifier needs to be trained in order to perform an optimal discrimination between water and non-water states. A supervised learning is chosen: the NN will be designed to reproduce an already existing classification. A dataset including a collection of SAR information \(x\) and associated surface water state \(y\) is first built. Part of it is then used during the training stage in order to determine the optimal parameters of the NN model. The reference dataset in the selected area is provided here by  
Figure 4: The SAR backscatter coefficients (VH and VV polarizations) from the Sentinel-1 as a function of the incidence angle over water bodies. The linear regression lines are also plotted. a Landsat-8 surface water map (NN outputs), in spatial and temporal coincidence with the Sentinel-1 SAR data (NN inputs). A maximum time difference of 3 days is tolerated, as the two satellites do not fly in phase. Six Landsat-8 surface water maps are selected, along with the corresponding Sentinel-1 SAR observations (see Table 1 for more details on the training dataset). The selection process for the Landsat-8 images has been described in Section 2.2.1. The images cover parts of the lower Mekong Delta in Vietnam and Cambodia. For each image in the training dataset, the number of non-water pixels is much higher than the number of water pixels. To avoid giving too much weight to the non-water pixels, an equalization of the training dataset is performed: an equal number of non-water and water pixels is selected in the training dataset. For this purpose, non-water pixels are selected randomly in the images, to match the number of water pixels. The total number of training samples is \(\sim\)10 million pixels, half water pixels, half non-water pixels. It takes \(\sim\)5 h to train the NN (with the use of a personal computer), but when the training is completed, a surface water map can be produced quickly (after \(\sim\)3-4 min) from any new set of satellite inputs \(x\). A test dataset is chosen to measure the performance of the NN retrieval scheme with data not used in the training process. The NN methodology is summarized in Figure 5.  
Several tests were necessary to determine the optimum inputs to the NN, in addition to the obvious ones, i.e., the backscatter coefficients for both polarizations. To limit ambiguities between flat arid surfaces and surface water, and to better capture small rivers, the spatial homogeneity of the backscatter coefficients appeared to be a relevant parameter. The standard deviation of the backscatter coefficients are computed locally over 100 m \(\times\) 100 m boxes.