## 3 Methods
### Multi-Temporal \(\sigma^{\circ}\) Rule-Based Rice Detection
This rule is critical in areas where there is considerable heterogeneity in crop establishment dates beyond that which was anticipated in the acquisition plan  
For the detected _SoS_, does the \(\sigma^{\circ}\) signature reach a suitable maximum value consistent with that expected from a rice crop between the detected _SoS_ date and the _fainlength_ date (compared against parameter \(e=\) minimum \(\sigma^{\circ}\) value at maximum peak)? For the detected _SoS_, does the variation in the \(\sigma^{\circ}\) signature reach a suitable minimum consistent with that expected from a rice crop between the detected _SoS_ date and the _fainlength_ date (compared against parameter \(f\)= minimum variation)? Again, this detection of rapid biomass increase after flood detection in the temporal series is similar to previous paddy mapping with optical time-series data [4]. Any pixel that meets both of these conditions is retained for further processing as a potential rice pixel. Like Rule 2b, it is also possible that the rice crop was established later than anticipated by the acquisition plan. In this case, agronomic flooding will have been detected late in the time series, and the full temporal signature for rice will not be present. This rule states that, if the duration between the detected _SoS_ date and the last date of the time series (\(t_{last}\)) is less than \(t_{minlength}\), then the pixel is labeled as late rice and excluded from further processing. The final rule looks for any unexpected drops in \(\sigma^{\circ}\) between \(t=\)_SoS_ + 1 and \(t=t_{maxlength}\) that would be evidence of either a flood or a new cropping season, depending on the elapsed time between this low-value detection and the _SoS_ detection (compared against \(a=\) lowest mean). If this condition is passed, the pixel is labeled as rice. Any pixel that exhibits an unexpected low \(\sigma^{\circ}\) value moves to \(t=t+1\), and Step 2 is applied again. Figure 4 shows the temporal signature for selected representative pixels to visualize the resulting classification from applying the rule-based system. Exemplar temporal signatures from the Leyte East site are shown for early rice, rice and late rice and other field crops in the top portion, while water bodies, urban areas, forest and fallow are shown in the lower portion. The top graph shows that, in the class \"rice,\" the crop shows significant temporal behavior and a large dynamic range (-15 to -9 dB) during its growth period. This is due to the interaction of microwave radiation with the crop canopy, increasing from the detection of \(\sigma^{\circ}\) minimum (field inundation) to the detection of \(\sigma^{\circ}\) maximum (around the tillering stage) between acquisitions four and six. In the case of \"early rice,\" the SAR series did not capture the \(\sigma^{\circ}\) minimum, since it occurred before the first acquisition; however, an increase in backscatter is observed during the growth period for the first four acquisitions that is typical of the seedling to tillering stage. In the case of \"late rice,\" the first four SAR acquisitions show a high backscatter value because, during that period, the fields were in fallow condition (as confirmed in the ground observations). The backscatter minimum was observed in the sixth acquisition, indicating flooded conditions, followed by an increase in backscatter in the succeeding acquisitions, indicating growth of the rice crop. The other field crop signal shows a distinctly different temporal evolution and the absence of any evidence of a water signal at the start of crop growth. In the bottom graph, the signatures for water bodies and fallow fields/bare soil show a consistently very low to low dB value and urban areas as consistently high, whereas areas with consistently dense vegetation over time (for instance, forest, banana plantations, _etc._) are characterized by a consistent medium to high backscattering coefficient.