## 1 Introduction
The results indicated that flooding could be detected in urban areas with reasonable accuracy but also that this accuracy was limited by the VHR SAR's poor visibility of the urban ground due to shadow and layover and the backscatter similarity between urban floodwater and unflooded urban surfaces. This paper considers the merits of an alternative method of improving the accuracy of rapid post-event flood mapping in urban areas by merging precomputed flood return period (FRP) maps with VHR SAR-derived flood inundation maps [43] and compares the method with that of [42]. [PERSON] et al. (2017) mapped river flooding in urban areas using RADARSAT-2 backscatter intensities together with FRP data produced by a hydrodynamic model [43]. The flood level was estimated in rural areas using a post-flood SAR image, and this rural flood level was used with the FRP data to calculate where the flooding should be in the adjacent urban areas. A high accuracy of urban flood detection (87%) was achieved on the test cases studied, with a false alarm rate of 14%. Because the SAR data are used only in rural areas, the method has the advantages that there is no need to calculate shadow/ layover maps in the urban areas, and that false alarms from unflooded urban surfaces with responses similar to water are eliminated. The advantage of the FRP maps is that, if there are urban areas that are either higher than the flooding or lower than it but defended (e.g., by embankments), this information should be contained in the maps, which would associate high return periods with such areas. A disadvantage is that it is necessary that the FRP data be accurate. The model predicts only flooding that is fluvial in origin, and it must be assumed that the rainfall pattern across the catchment that caused a particular flood is the same as that used to calculate the FRP maps. However, if a flood event was due to pluvial as well as fluvial flooding, the rural SAR water level observations should be able to correct errors in model water elevations in their immediate neighborhoods at least. The paper extends that of [43] by estimating urban flooding in image sequences. The inputs are dynamic flood inundation extent and depth maps (updated every 3 h) produced by the Flood Foresight system [50], together with a contemporaneous SAR image sequence. Real-time flood modelling may often be carried out during a flood event, and the combination of the SAR and model flood extents may allow the model to be kept on track to make future predictions more accurately. The linking of the SAR and model data in this way allows a two-way symbiosis, whereby currently available SAR urban flood extent improves future model flood predictions, while flood hazard maps obtained after the SAR overpass improve the SAR estimate of the urban flood extent. The present study and those of [42; 43] require both VHR SAR and accurate high-resolution DSM data to be available. The method employs a LiDAR DSM, which limits its use to urban regions that have been mapped using airborne LiDAR. However, most major urban areas in flood plains in the UK and other developed countries have now been mapped. The hydrodynamic model used to estimate the FRP data also requires an accurate DSM, though this need not be as high-resolution as LiDAR. The object of the paper is to investigate whether, given contemporaneous SAR, model FRP and flood inundation data, urban flooding can best be predicted using  
1. SAR in rural areas,
2. SAR in rural areas and precomputed FRP maps in urban areas,
3. SAR in rural areas and FRP maps and dynamic model flood inundation in urban areas,
4. SAR in both rural and urban areas (with associated urban shadow/layover maps).