# Mapping Rice Fields in Urban Shanghai, Southeast China, Using Sentinel-1A and Landsat 8 Datasets
## Methodology
### Image Classification  
A decision tree classification algorithm is implemented in this study based on the spatial and temporal distribution of backscatter coefficients obtained from Sentinel-1A data and optical indices derived from the single Landsat image. A decision tree classifier is independent of data probability distributions [23]. It employs tree-structured rules which recursively divide the initial input dataset into increasingly homogeneous subsets based on well defined splitting criteria [49]. At each split or node, the values of each explanatory variable are examined and a particular threshold of a single variable that produces the largest reduction in a deviance measure is chosen to partition the data [50]. Decision tree classifiers are advantageous in that they are less sensitive to nonlinearities in the input data than classification methods that require an assumption of Gaussian distributions [50; 51]. As the Sentinel-1A data used in this study are in dual polarization of VV and VH, we have attempted to propose the most optimal polarization for mapping the targeted land-cover types. We have decided to use a single polarization in order to reduce data redundancy and dimensionality, as Landsat 8 optical indices are also utilized. In [52], similar to using multiple or dual polarization data, a corresponding increase in accuracy is expected when the inputs to the classification algorithm consist of measurements acquired at different dates. Two criteria were considered in the selection of the optimal polarization. The first criterion is based on the temporal increase of paddy rice backscatter, whereas the second exploits a two-class separability measure. The optimal polarization is assumed to be the one which exhibits the most sustained increase in paddy rice backscatter, while at the same time producing the best results with the two-class separability measure. In other words, a polarization has to satisfy both conditions to be considered optimal or else both polarizations will be used as inputs in the decision tree classifier. According to the concept of feature separability [53], two classes are said to be well separated if the distance between their respective class means is larger than that of their standard deviations. The separability criteria between classes \(a\) and \(b\) is measured by the Bahattacharrya distance [54] as:  
\[S_{ab}=\frac{|\mu_{a}-\mu_{b}|}{s_{a}+s_{b}} \tag{2}\]  
where \(\mu\) and \(s\) are the mean and standard deviation of the features to be separated, respectively. The Bahattachayrrya distance is theoretically sound as it is directly related to the upper bound of classification error probabilities [23]. It measures the real values between 0 and 2, where 0 indicatesa complete overlap between two classes, and 2 indicates a complete separation between them [55]. The larger the separability values among class pairs, the better the final classification results [23; 49]. The normalized difference vegetation index (NDVI) and the normalized difference water index (NDWI) were the two optical indices generated from the PAN-sharpened (10 m) Landsat 8 image for combination with the temporal Sentinel-1A data. NDVI has been widely applied in monitoring various vegetation cover, and is frequently used as a proxy of plant growth and productivity, as the amount of solar radiation reflected by the vegetation canopy is related to wavelength, chlorophyll, leaf interior tissues and plant water content [56]. NDWI is as important to the monitoring of water bodies as NDVI is to the monitoring of vegetation canopies. In this study, we have employed the modified NDWI (MNDWI) proposed by [57] which cannot only enhance information about water and restricting the one from vegetation and soil, but can also significantly distinguish built-up features from water bodies. These optical indices have been derived using the following equations:  
\[NDVI=\frac{b_{nir}-b_{rd}}{b_{nir}+b_{rd}} \tag{3}\]  
where \(b_{nir}\) is the near infrared band and \(b_{rd}\) is the red band.