# Inundation Extent Mapping by Synthetic Aperture Radar: A Review
## 3 Relative Strengths and Limitations of Existing Techniques
### Selected Studies of Combined Approaches
Over vegetated areas with naturally distributed scatterers, as modeled by the Freeman-Durden three-component decomposition [38, 81], volume scattering contributes significantly to both co- and cross-polarized intensities while the dihedral scattering only contributes to co-polarizations. Whereas over built-up areas, modeled by the Yamaguchi four-component decomposition [38, 82], the helix component contains the correlated contribution from dihedral scattering to both co- and cross-polarizations. For coherence, buildings show persistent strong values, while vegetation does not. Toward automation, [PERSON] et al. [51] developed the M2a algorithm to determine the threshold that makes the non-water pixels (below the threshold) best fit a gamma distribution--a theoretical distribution of any given class in a SAR image. They then extended flooded areas using RGA from detected water pixels using a larger threshold--99 percentile of the \"water\" backscatter gamma distribution--arguing that flood maps resulting from region growing should include all \"open water\" pixels connected to the seeds. Then they applied a change detection technique to backscattering to reduce over-detection within the identified water bodies caused by water-like surfaces, as well as to remove permanent water pixels. Based on the same concept, [PERSON] et al. [49] developed an iterative approach to calibrate the segmentation threshold, distribution parameter, and region growing threshold (M2b). They applied the same segmentation threshold to the dry reference SAR image to obtain the permanent water area. They claimed, however, that if the intensity distribution of the SAR image were not bimodal, the automated threshold determination might not work. [PERSON] et al. [57] used a changed detection approach, first to detect a core flood area that contained a more plausible but incomplete collection of flood pixels, and then to derive the statistical curve of the water class to segment water pixels. The major advantage of this approach is that a bimodal distribution is not compulsory. In practice, a non-bimodal distribution often occurs. The change detection threshold might be difficult to determine and globalize. Assuming even prior probability of flooded and non-flooded conditions, [PERSON] et al. [83] computed probabilistic flood maps that characterize the uncertainty of flood delineation. The probability reported in this study, however, related to the uncertainty neither in extent nor in time. Rather, it was the uncertainty of a SAR image classification based on backscattering. Taking advantage of big earth observation (EO) data, the two most recent studies--[PERSON] et al. [67] and [PERSON] et al. [59]--implemented full automation of inundation retrieval. With the CD principle underpinning both methods, they employed multiple dry references instead of one supported by operational satellite SAR data for multiple years. [PERSON] et al. [67] developed two CD-based flood indices, the Normalized Difference Flood Index (NDFI) and the Normalized Difference Vegetated Flood Index (NDVFI), assuming a number of revisits for each pixel in dry conditions was available:  
\[\text{NDFI}=\frac{mean\langle\sigma^{0}_{ref}\rangle-min\langle\sigma^{0}_{ref},~{}\sigma^{0}_{flood}\rangle}{mean\langle\sigma^{0}_{ref}\rangle+min\langle \sigma^{0}_{ref},~{}\sigma^{0}_{flood}\rangle} \tag{1}\]  
\[\text{NDFVI}=\frac{mean\langle\sigma^{0}_{ref}\rangle-max\langle\sigma^{0}_{ ref},~{}\sigma^{0}_{flood}\rangle}{mean\langle\sigma^{0}_{ref}\rangle+max\langle \sigma^{0}_{ref},~{}\sigma^{0}_{flood}\rangle} \tag{2}\]  
Empirical thresholds 0.7 and 0.75 were reported sufficiently stable for generating the inundation mask from NDFI and NDFVI, respectively. In the post-processing, [PERSON] et al. [67] applied dilation and closing morphological operators, a larger than 10-pixel size limit, and a smaller than 5-degree slope limit to the inundation mask to further reduce speckle-caused noise. They concluded the potential for detecting inundation under vegetation was limited. [PERSON] et al.