# Urban Flood Mapping Using SAR Intensity and Interferometric Coherence via Bayesian Network Fusion
## 1 Introduction
Nonetheless, the aforementioned studies only leveraged SAR intensity (\(\sigma^{\circ}\)) that provides limited information for flood mapping in urban environments for the following reasons. In principle, floodwater in front of buildings can be detected by the strengthened double-bounce effect in SAR intensity data. However, the increase of double-bounce effect is affected by the aspect angle \(\phi\) (i.e., the angle between the orientation of the wall and the SAR azimuth direction). According to the simulation experiments by [PERSON] et al. [31], the increase of intensity drops from 11.5 dB to \(\sim\)3.5 dB when \(\phi\) increases from \(0^{\circ}\) to greater than \(5\)-\(10^{\circ}\). Furthermore, the floodwater level is another factor which needs to be considered when detecting flooding via the double-bounce effect. The enhancement of this effect diminishes when the floodwater is on a high-level relative to the height of the surrounding buildings [32]. Several studies have shown that SAR interferometric coherence (\(\gamma\)) is valuable information for urban flood mapping and can reduce the abovementioned drawbacks [31; 33]. An urban settlement can generally be considered as a stable target with high coherence, and the coherence decorrelation is roughly irrelative to the temporal baseline (\(B_{t}\)) (time interval between two SAR acquisitions) while dominantly impacted by the spatial baseline (\(B_{p}\)) (spatial separation between repeat satellite orbits) [31; 34]. Standing floodwater between buildings causes changes in the spatial distribution of scatterers within a resolution cell, resulting in a drop-off in the co-event pair coherence (i.e., the interferometric coherence produced from one image acquired before and another during the flood) compared to pre-event pair coherence (i.e., the interferometriccoherence produced from two images both acquired before the flood). More details of SAR intensity and coherence response of floodwater over different land types in the urban environment can be found in [PERSON] et al. [35]. [PERSON] et al. [33] interpreted intensity and coherence characteristics of the Sendai (Japan) flood related to the tsunami of 2011 with high-resolution COSMO-SkyMed data and found a lower coherence of flooded urban areas than non-flooded ones. Also, with high-resolution COSMO-SkyMed data, in [PERSON] et al. [31], coherence was used complementary to intensity and substantially reduced missed alarms in flooded urban areas of the 2014 Secchia River flood (Italy). [PERSON] et al. [35] employed multi-temporal high-resolution TerraSAR-X intensity and coherence for urban flood detection of the 2017 Houston flood (US) accompanying Hurricane Harvey with an active self-learning Convolutional Neural Network (CNN) model, and suggested that both multi-temporal intensity and coherence are required to produce an accurate inundation map in urban areas. This work presented an active self-learning framework that improves classification results with limited training samples. However, the requirement of training samples limits its application in scenarios that no training samples are available. More recently, [PERSON] et al. [36] first applied mid-resolution Sentinel-1 intensity and coherence for urban flood detection for a case study of the 2017 Houston flood. In that study, the authors first extracted built-up areas with co- and cross-polarized (VV and VH) intensity time series and filtered false alarms with time series VV coherence. Subsequently, an adaptive thresholding-based change detection [16] was adopted to map flooded bare soils and flooded built-up areas with VV intensity and coherence, respectively. However, as noted by the authors, the influence of vegetation can lead to a decrease in coherence of built-up areas. This may result in an under-estimation of the flood extent in vegetated built-up areas. Intensity can complement coherence, in this case, to reduce under-estimation as flooded vegetation causes strong double-bounce scattering as well.