# Classification and Mapping of Paddy Rice by Combining Landsat and SAR Time Series Data
## 3 Methodology
Kernel functions are typically adopted to transform the data dimensionality to make it easy to identify optimum hyperplanes. There are various kernel functions including linear, polynomial, radial basis function (RBF), and sigmoid [64]. This study used RBF kernel, widely used in classification tasks, and a grid-search method was used to determine the optimum values of parameters (i.e., gamma in the kernel function and penalty parameter) [65; 66]. In this study, six schemes were tested to identify the improvement of classification performance when fusing multi-sensor time series data. Accuracy assessment was conducted under each scenario using test data (300 samples). Overall accuracies of multi-class classification (six classes for site A and eight classes for site B) and binary classification (i.e., paddy rice vs. non-paddy rice) were calculated for six schemes. The six schemes were designed considering sensor types and collection dates. * Scheme 1 (S1): only Landsat data on each date were used for classification. * Scheme 2 (S2): only Landsat data on all dates were used for classification. * Scheme 3 (S3): only SAR data on all dates were used for classification. * Scheme 4 (S4): Landsat, SAR, and DEM data during no growing season (November to March) were used for classification. * Scheme 5 (S5): Landsat, SAR, and DEM data during the growing season (April to October) were used for classification. * Scheme 6 (S6): Landsat, SAR, and DEM data on all dates were used for classification. In order to evaluate the significant difference between classifications, the McNemar test, a non-parametric test based on the proportion correct/incorrect was conducted. Large error matrices can be collapsed to a binary size (i.e., \(2\times 2\)) as the binary distinction between correct and incorrect class allocations should be focused for comparison [67; 68]. The standardized normal test statistics (z) from the McNemar test is calculated as:  
\[z=\frac{\mathrm{f}_{\mathrm{AB}}-\mathrm{f}_{\mathrm{BA}}}{\sqrt{\mathrm{f}_{ \mathrm{AB}}+\mathrm{f}_{\mathrm{BA}}}} \tag{4}\]  
where \(\mathrm{f}_{\mathrm{AB}}\) indicates the samples correctly identified in classification A, but is incorrectly classified in classification B; and, \(\mathrm{f}_{\mathrm{BA}}\) means the samples correctly identified in classification B, but incorrectly classified in classification A. The 5% level of significance (\(\alpha=0.05\)) was used for the McNemar test. Important spectral and temporal characteristics for paddy rice classification were identified from the temporal pattern of each variable and variable importance, as provided by RF. In this study, Paddy rice Mapping Index (PMI) was proposed by considering the phenological characteristics of paddy rice in NIR and SAR backscattering coefficients. NIR reflectance and SAR backscattering coefficients are low during the planting/transplanting season (May) and increase during the growing season (Figures 4 and 5). Paddy rice maps were produced from two classification models and PMI. The spatial distribution of the paddy rice maps was also compared with the reference paddy rice maps. PMI-based paddy rice mapping over a larger area (i.e., entire California State) was also conducted using Google Earth Engine. Figure 4: Phenological and spectral patterns of variables for each class (site A). Figure 5: Phenological and spectral patterns of variables for each class (site B).