# Urban Flood Mapping Using SAR Intensity and Interferometric Coherence via Bayesian Network Fusion
## 1 Introduction
Therefore, in practical urban flood mapping, the integrated information of intensity decrease, intensity increase, and coherence drop-off is required to account for different flood conditions in urban environments. In this paper, we introduce a method for flood detection in urban (and suburban) environments with synergistic use of SAR intensity and coherence based on Bayesian network fusion. It leverages SAR intensity and coherence time series to map non-obstructed-flood (e.g., flooded bare soils and short vegetation); obstructed-flooded non-coherent areas (e.g., flooded vegetation and vegetated built-up areas); and obstructed-flooded coherent areas (e.g., flooded predominantly built-up areas). The method is flexible with respect to the time spans of data sequences (at least one pre- and co-event intensity pair, and one pre- and co-event coherence pair are needed). As mentioned above, the growing number of SAR missions in orbit that offer a consistent observation scenario with short revisit times increases the chance of both observing a flood event and, at the same time, having a suitable pre-event scene acquired by the same sensor. This makes the method favorable for operational emergency responses. Bayesian networks are statistically well-founded methods with highly flexible structures for explicitly displaying relationships among different variables, combing expert knowledge and data, and characterizing uncertainties [37; 38; 39]. Bayesian networks have been widely used in risk analysis and management [40], uncertainty quantification [37], and classification with the incorporation of multi-source remote sensing data [41; 42]. [PERSON] et al. [43; 44] employed a Bayesian network for flood detection in rural areas combing SAR intensity, coherence, and ancillary data. In their study, they made use of coherence information with a very short temporal baseline (e.g., 1 day) to complement intensity for more robust inundation extent mapping in rural areas. However, their approach is difficult to transfer to more general cases with longer temporal baselines (e.g., 6 days with Sentinel-1A and Sentinel-1B constellation, and can be even longer for sensors such as TerraSAR-X and ALOS-2/PALSAR-2) as temporal decorrelation between subsequent acquisitions may outweigh the effect of coherence decrease due to flooding. For the scenario of flood mapping in an urban area, which comprises a variety of landscapes such as bare soil, vegetated areas, and man-made structures, it is essential to distinguish the variation in coherence from unstable scatterers and the changes caused by a flood event. Furthermore, in the work of [PERSON] et al. [43; 44] user-designed thresholding values are required, which are sensor and scene dependent. The stability of scatterers in urban areas is considered in the fusion of intensity and coherence in this paper, and the thresholding values are learned from the data, thus making the method automatic so that it is independent of sensors and study areas. To preserve the probability information of Bayesian network outputs and incorporate the global contexture information, considering the pairwise relationships on all pairs of pixels in the image, we adopted a fully-connected Conditional Random Field (CRF) [45] which has seen demonstrated success in flood mapping in our previous study [18]. The method is unsupervised and further provides a supplement to the current Sentinel-1 Flood Service [15] of the German Aerospace Center (DLR) to account for flood in urban areas. We show the effectiveness of the approach on the 2017 Houston flood (US) event with Sentinel-1 time series and the 2015 Joso flood (Japan) event with ALOS-2/PALSAR-2 time series. The remainder of this paper is structured as follows: Section 2 describes the details of methods. Details of the dataset and experiment setup are introduced in Section 3. Section 4 gives the results and discussions. Finally, Section 5 concludes this paper with some remarks.