## 3 Method
### Random Forest Classifier  
Random Forest classifier was used to classify the fraction maps derived through MESMA into thematic land cover types. This supervised classifier was chosen due to its robustness and efficiency in \begin{table}
\begin{tabular}{c c c} \hline \hline
**Two-Endmember (35)** & **Three-Endmember (446)** & **Four-Endmember (2640)** \\ \hline water + shade & water + veg + shade & water + veg + imp + shade \\ veg + shade & water + imp + shade & water + veg + soil + shade \\ imp + shade & water + soil + shade & water + imp + soil + shade \\ soil + shade & veg + imp + shade & veg + imp + soil + shade \\  & veg + soil + shade & \\  & imp + soil + shade & \\ \hline \hline \end{tabular} Note: veg, vegetation; imp, impervious surface.  
\end{table} 
Table 2: Combinations of endmember models by land cover classes. remote sensing applications [29, 30, 31, 32, 33, 34, 35, 36, 37, 38]. Besides, Random Forest has been rarely used in flood mapping and its performance needs to be studied and verified. Random Forest is a machine learning based method proposed by [PERSON] [28] in 2001. It can be viewed as an ensemble of many decision trees and can be defined as Equation (2) [28],  
\[\{h(x,\theta_{k}),k=1,2...i...\} \tag{2}\]  
where \(h\) represents Random Forest, \(x\) represents input variables, and \(\{\theta_{k}\}\) stands for independently identically distributed random predictor variables which are used to split each decision tree. The final response of Random Forest is determined on the output of all the decision trees involved [29]. Two steps involving random selection are used to create each decision tree. First, a bootstrap strategy [28] is utilized to randomly select only 2/3 of the training samples with replacement to build each decision tree. The remaining 1/3 of the training samples are defined as out-of-bag (OOB) data [28], which are used for inner cross-validation to evaluate the performance of Random Forest. Second, only a subset of the predictor variables is randomly selected to split each tree using the Gini index [28]. Actually, the Gini index is the most frequently used attribute selection measure for splitting each decision tree, which measures the impurity of a given attribute with respect to the rest of the classes [28]. Both of the two random selection steps result in less correlation between the decision trees and thus a higher generalization capability of the Random Forest classifier. Besides, the importance of input variables can be measured, which indicates their contributions to the classification accuracy [28, 29]. The parameterization of Random Forest classifier is simple and can be carried out using the package _random Forest_ in \(R\) language [42, 43]. Only two parameters need to be specified including _ntree_ and _mty_. _ntree_ is the number of decision trees making up the whole forest. In general, the OOB error decreases with the growth of _ntree_ and the plot of OOB error _vs. ntree_ is always necessary to see whether the number of trees is sufficient in the grown forest [34]. _mty_ is the number of randomly selected predictor variables. Two methods [28] are commonly used to calculate _mty_, _i.e._, one-third or square root of the number of input variables. In this research, the four shade-normalized fraction images generated from MESMA, together with the five spectral bands were included as input for the Random Forest classifier. Besides, since the main interest of this study was with the extraction of inundated extent, an additional image of the normalized difference water index [44] was also included for image classification. In general, the Normalized Difference Spectral Indices (NDSIs) is suitable for detecting the open water surface and the inundated areas. [PERSON] _et al._[45] provided a useful review which summarized and compared dozens of NDSIs for detecting surface water in flooded rice fields, which also shed light on the inundated area detection.