## 1 Introduction
### A Summary of SAR Research and Applications for Rice Mapping  
SAR data have a proven ability to detect lowland rice systems (both irrigated and rainfed) through the unique temporal signature of the backscatter coefficient (also termed sigma naught or \(\sigma^{\circ}\)) exhibited by the crop. In the past three decades, a significant number of publications have been dedicated to better understanding this relationship and applying it to rice detection and rice monitoring [14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. In summary, these studies have shown that:* Lower frequencies (L- and C-band) penetrate deeper into the rice plant than higher frequencies, while only higher frequencies (X-band) interact with grain water content and grain weight sufficiently to show a dual-peak signal in \(\sigma^{\circ}\) during the rice season [15, 16, 18, 19]. * The maximum \(\sigma^{\circ}\) date at the X-band precedes those of the C- and L-band. Moreover, short wavelengths (X-, Ka-, Ku-band), especially at large incident angles, are sensitive enough to detect even very small rice seedlings just after transplanting [15, 19]. * The correlation between \(\sigma^{\circ}\) and rice biophysical parameters shows that lower frequencies are more closely related to total fresh weight, leaf area index (LAI) and plant height than other parameters [15, 19]. * Although \(\sigma^{\circ}\) from X-band is poorly correlated with LAI, it is best correlated with panicle biomass. This means that the X-band can be used for a direct assessment of rice grain yield [22, 23]. * When using C-band HV polarization, \(\sigma^{\circ}\) is most strongly correlated with the fraction of absorbed photosynthetically-active radiation (fAPAR), which is strongly determined by the amount and structure of leaf elements in a canopy. This means that C-band \(\sigma^{\circ}\) can provide information equivalent to the normalized difference vegetation index (NDVI) [23]. * The \(\sigma^{\circ}\) from VV polarization increases only during the vegetative stage; it is quite stable at the reproductive stage, and it decreases at the ripening stage because of canopy attenuation [14, 18]. * The \(\sigma^{\circ}\) from HH polarization increases at the reproductive stage and is quite stable at the ripening stage. The temporal trend of \(\sigma^{\circ}\) from HV is similar to HH [18]. * The HH/VV polarization ratio at the C- and L-band decreases significantly throughout the season and is thus a good descriptor of rice plant age [18]. * The frequency ratios for HH and VV (C-VV/L-VV and C-HH/L-HH) are significantly lower in the latter part of the rice season when thick vegetation canopy hampers wave penetration [18]. * For X-band, the HH/VV polarization ratio continuously changes as a function of phenology during the vegetative and reproductive stages [20]. * For X-band, the HH-VV phase difference is sensitive to early rice plant emergence. Moreover, the use of four polarimetric features derived from coherence coplanar dual-polarization X-band enables the estimation of five phenological stages from a single date scene [15, 20, 21]. It is clear from the literature that well-understood relationships exist between rice crop characteristics and backscatter coefficients from different wavelengths, and these relationships have been used to derive different types of algorithms for estimating rice crop characteristics from SAR data. In particular, rice signature interpretation has been proposed based on theoretical models [14, 18], and supervised classification algorithms [16] or image ratio methods have been used for rice mapping purposes [14, 24]. Another approach for sparse time series is to extract temporal features from the data, such as the minimum, maximum or range of values on a pixel-by-pixel basis, relate those to the known temporal dynamics of the rice crop and use that knowledge to classify areas as rice or non-rice [25]. All of these approaches have been demonstrated successfully in the literature.