## 3 Methods
### Multi-Temporal \(\sigma^{\circ}\) Rule-Based Rice Detection  
The multi-temporal stack of terrain-geocoded \(\sigma^{\circ}\) images was input to a rule-based rice detection algorithm in MAPscape-RICE. The temporal evolution of \(\sigma^{\circ}\) is analyzed from an agronomic perspective, which also requires _a priori_ knowledge of rice maturity, calendar and duration and crop practices from field information and knowledge of the study location. The temporal signature is frequency and polarization dependent and also depends on the crop establishment method and, to some extent, on crop maturity. This implies that general rules can be applied to detect rice, but that the parameters for these rules may need to be adapted according to the agro-ecological zone, crop practices and rice calendar. Figure 3 gives an overview of the developed rule-based detection algorithm. Details are expanded upon below. We derive rice area from the SAR temporal signature as follows. 1. The first rule is the rice exclusion condition. The following conditions are applied to the temporal signature for each pixel: 1. Is the average \(\sigma^{\circ}\) lower than expected (compared against parameter \(a\) = lowest mean)? This masks out areas with consistently low \(\sigma^{\circ}\) values that would be typical of stable water bodies. Figure 3: Rule-based rice detection algorithm for multi-temporal X-band \(\sigma^{\circ}\) in MAPscape-RICE. * Is the average \(\sigma^{\circ}\) higher than expected (compared against parameter \(b=\) highest mean)? This masks out areas of consistently high \(\sigma^{\circ}\) values that would be typical of settlements or infrastructure. * Does \(\sigma^{\circ}\) remain under a minimum value longer than expected (compared against parameter \(a=\) lowest mean and \(t_{2}-t_{1}=\) maximum time under water)? Agronomic flooding of a rice field occurs over a short period of time; any longer duration, but non-permanent flooding, such as fishponds, irrigation tanks or seasonal wetlands, should be removed by this condition. * Is the variation in \(\sigma^{\circ}\) larger than expected (compared against parameter \(c=\) maximum variation)? Rice, like other seasonal field crops, will show variation in \(\sigma^{\circ}\) over time. There is a maximum amount of variation that can be expected from growth in biomass over the season, and this condition removes any areas with unusually high variation. This exclusion or masking concept is similar to previous paddy mapping with optical time-series data [4], which also stresses the importance of using ancillary data, when available, to mask out non-rice areas _a priori_. Any pixel that meets one or more of these exclusion conditions is labeled non-rice and excluded from further processing. Any pixel that does not meet any of these conditions has exhibited a temporal signature that is consistent with a rice crop (see Section 1.2) and is retained for further processing. * We then apply a stepwise process looking at the temporal signature in more detail starting with a temporal series of data from the first image (\(t=0\)) in the time series to the last (\(t=t_{last}\)). The second rule looks for any evidence of agronomic flooding at the start of the season (_SoS_). Flooded paddy fields exhibit low \(\sigma^{\circ}\) values, so, starting with \(t=0\), if \(\sigma^{\circ}\) is less than a maximum value (\(d=\) maximum value at _SoS_) at this supposed _SoS_ date, then the pixel is retained for further analysis. If not, we move to the next image in the time series (\(t=t+1\)) and apply the same rule again. * If the above condition is not met on any \(t\) value between 0 and \(t_{last}\), we apply another rule to determine whether this pixel could be a rice crop that was established before the first date in the time series. In other words, despite not detecting the moment of agronomic flooding, is there enough evidence in the temporal signature to still classify this pixel as rice?