## 3 Methodology
### Flood Signal Detection  
Flood signal detection is performed to identify paddy rice for individual objects in their corresponding time windows. The flooding and rice transplanting signals are key features that identify paddy rice fields as this is the only crop that needs to be transplanted in a mixed water-soil environment [30]. The remote sensing recognition of transplanting signals is crucial to identifying paddy rice. Previous studies have revealed that the relationship between the LSWI and NDVI (or EVI) can effectively discriminate flooding/transplanting signals [6]. We performed temporal profile analyses at random paddy rice sites in the study region and found that all the paddy rice agriculture systems in the study area have flooding and transplanting signals in the early growing season that can be captured using vegetation indices. Here, we recognized flooding signals using the LSWI criteria as LSWI-min (EVI, NDVI) \(>\) 0. Different from pixel-based classification [11; 36], we calculate the signal in the object unit as the mean value of pixels within each object. Therefore, we detect the flooding and transplanting signals using vegetation indices during the rice transplanting phase. Specifically, the following equation is used [6]:  
\[\text{Flood}=\left\{ \begin{array}{ll}1&\text{if }\text{LSWI}_{\text{Ti}}- \text{min}(\text{EVI}_{\text{Ti}},\text{ NDVI}_{\text{Ti}})>0\\ 0&\text{if }\text{LSWI}_{\text{Ti}}-\text{min}(\text{EVI}_{\text{Ti}},\text{ NDVI}_{ \text{Ti}})\leq 0\end{array} \right.\text{(SOT}<T_{i}<\text{EOT)} \tag{3}\]  
where Flood is the status of the flooding/transplanting, and the starting (SOT) and ending (EOT) of the transplanting phase are as defined in Section 3.2, and \(T_{i}\) is the period when the observations are acquired. The spectral indices of NDVI [31], LSWI [7], are calculated using the following equations:  
\[\text{NDVI}=\frac{\rho_{NIR}-\rho_{Red}}{\rho_{NIR}+\rho_{Red}} \tag{4}\]  
\[\text{LSWI}=\frac{\rho_{NIR}-\rho_{SWIR}}{\rho_{NIR}+\rho_{SWIR}} \tag{5}\]  
where \(\rho_{Blue}\), \(\rho_{Rad}\), \(\rho_{NIR}\), and \(\rho_{SWIR}\) are the surface reflectance values of the blue, red, near-infrared, and shortwave-infrared bands from the Sentinel-2 sensor. SAR data provide complementary observations to optical data, especially in the monsoon season when clouds are prevalent [32; 33; 34]. The SAR backscattering coefficients  
Figure 6: The NDFI, raw and fitted EVI are in blue, orange, and green, respectively. The size of the red cycle (big/medium/small) denotes the quality of the associated observation (great/good/bad). for VH polarization over paddy rice fields decrease sharply when flooding occurs but remain relatively stable over non-rice fields throughout the year [35]. A threshold for the backscattering coefficient to divide flood and non-flood areas was successfully applied to SAR data over various frequencies ([PERSON] et al., 2006, [PERSON] et al., 2015, and [PERSON] et al., 2016). We selected fifty rice objects and fifty non-rice objects which are evenly distributed over the study area, calculated their minimum VH backscatter intensity during the time window, and applied linear discriminant analysis (LDA) to separate rice and non-rice objects using gamma-naught, which ultimately provides a threshold that separates the two classes [37]. A separation line between two classes can be established and the threshold can be obtained from the LDA with a threshold of \(-20.1\) dB. Paddy rice can be identified based on its unique flooding characteristics in the transplanting phase. However, variations in transplanting timing for different fields could bias the associated information from one specific image or one image composite [11]. We used a statistics-based approach to delineate the flooding signals by considering all flooding signals during the transplanting phase. The sum of the flooding signals in a given time window for each object (F) is calculated using Equation (6). The threshold for F to identify rice objects is also determined using the LDA approach.