## 1 Introduction  
Flooding causes significant death, injury, displacement, homelessness and economic loss all over the world every year. The risks to people and the economic impacts of flooding are greatest for urban flooding [1, 2, 3, 4]. For example, regarding riverine floods in the UK, over 2 million properties (the majority of them in urban areas) are located in floodplains. An estimated 200,000 of these properties are at risk because they do not have protection against a 1-in-75-year flood event [5]. The number of floods and the number of properties affected by them are likely to increase in the future, due to the growing population exposure in floodplains and the impact of climate change [6]. In economically strong and populated areas, global economic losses due to floods are projected to reach 5597 billion over the period 2016-2035 [7]. High-resolution SAR sensors are now commonly used for flood detection because of their ability (unlike visible-band sensors) to penetrate the clouds that are often present during flooding and to image at night as well as during the day. A number of very-high-resolution (VHR) SARs with spatial resolutions as high as 3 m or better are capable of detecting urban flooding, including TerraSAR-X, ALOS-2/PALSAR-2, the 3-satellite RADARSAT-2 constellation, the four satellites of the COSMO-SkyMed constellation, and the three satellites of the IceEye constellation [8; 9]. In the absence of significant surface water turbulence caused by wind, rain or currents, floodwater generally appears dark in a SAR image due to specular reflection from the water surface away from the antenna. In addition, an attractive option for flood studies is the high-resolution (HR) Sentinel-1 constellation, which provides open-access satellite data at 10 m spatial resolution in near real-time, acquired according to a preplanned schedule. In common with RADARSAT-2, Sentinel-1 provides the user with processed multilook georegistered SAR images about one hour after image reception at the ground station. An important use of the flood extent from a near real-time SAR image is as a tool for operational flood incident management [10]. Rapid response to flooding is essential to minimise loss of life and reduce suffering. Knowledge of the flooding situation is crucial for personnel deployment, resource allocation and rescue operations. The English Environment Agency (EA) now uses SAR images to detect the extent and depth of flooding as floods evolve [11]. The data may also be used for assimilation into urban flood inundation models, improving the model state and providing estimates of the model parameters and external forcing [12; 13; 14; 15; 16; 17; 18; 19]. The problem of automated flood detection in rural areas has received a substantial amount of attention in the literature [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. The Copernicus Emergency Management Service (EMS) and the EA are among several organisations that have developed semi-automatic systems to extract flood extents from a SAR image. Fully automated systems have also recently been developed using deep learning methods [35; 36]. All these systems tend to work well in rural areas but have difficulty detecting urban flooding, primarily because SAR is a side-looking instrument. As a result, substantial areas of urban ground may not be visible to the SAR due to radar layover and shadow caused by buildings [37]. As shadows will appear dark, they may be misclassified as water if the ground in shadow is dry, whereas layover will generally appear bright and may possibly be misclassified as unflooded when, in reality, the ground is flooded. In addition, double scattering between ground surfaces and adjacent buildings often causes strong returns that confuse the image [37]. A further difficulty is that unflooded roads and tarmac areas also exhibit low backscatter, though often not as low as undisturbed water [25].