## 1 Introduction  
Studying the spatial and temporal distribution of surface water resources is critical, especially in highly populated areas and in regions under climate change pressure. With an increased number of Earth-observation satellites providing a large diversity of remote sensing data, there is now the potential to monitor the surface water at regional to global scale. However, mapping surface water is still challenging. It is difficult to provide products with the accuracy required for a large range of applications (e.g., agriculture, disaster management, and hydrology). Several methods have already been proposed to detect and monitor surface water with visible and Near-Infrared (NIR) images. Ref. [1] used positive values of the Normalized Difference Water Index (NDWI) to classify water bodies. Ref. [2] applied a threshold on NIR reflectances of the NOAA/AVHRR satellite to delineate lakes. Ref. [3] detected surface water by identifying the positive values of the Modification of Normalized Difference Water Index (MNDWI). Ref. [4] combined NIR data and the Normalized Difference Vegetation Index (NDVI) to detect surface water bodies. However, cloud contamination is a stringent constraint for these methods, limiting their application to cloud-free conditions which is very restrictive in some regions (e.g., in the Tropics). Vegetation can also mask the surface water partly or totally. This makes the water detection difficult or impossible under canopy. In addition, the NIR reflectance over highly turbid water can be higher than the red reflectance, introducing confusions in the indices used for the water detection. Synthetic Aperture Radar (SAR) have become an important source of data to detect flood or monitor surface water as they allow observations regardless of the cloud cover, day and night, with spatial resolution comparable to visible and near-infrared satellite images [5]. SAR instruments have been available on many sensors and platforms (Envisat ASAR, PALSAR, or RADARSAT, for example) providing observations for different areas all over the globe (but normally with a limited number of images available per year in some regions). Flood detection using different SAR observations has been studied by many authors, showcasing the advantages of SAR instruments compared to optical instruments in monitoring floods. Ref. [6] used a single decision tree classifier on two sets of JERS-1 SAR data to classify surface water within the states of North Carolina and South Carolina into five land cover types (water, marsh, flooded forest, field, and non-flooded forest). Although the classifier was simple, they reported an overall classification accuracy of nearly 90%. Ref. [7] showed the potential of the COSMO-SkyMed data for flood detection by showing case studies in several locations all over the globe (e.g., Tarano River overflow, Italy, April 2009; Pakistan inundation, July-September 2010; Thailand flood, October 2010; and Australia flood, January 2011). COSMO-SkyMed instruments provided very high resolution X-band SAR images, but covered limited areas (the highest spatial resolution is \(\sim\)1 m for an observation area of 10 km \(\times\) 10 km). X-band data from TerraSAR-X instrument were also reported suitable for flood mapping under forest canopy in the temperate forest zone in Estonia [8]. Ref. [9] compared four flood detection approaches over five areas (Vietnam, the Netherlands, Mali, Germany, and China) using SAR data from the TanDEM-X mission. Although these four approaches were designed according to different requirements, their performances were satisfactory over the studied areas (17 out of 20 water masks reaching an overall accuracy larger than 90%). Other studies using SAR data for water monitoring locally and regionally under different environments can be listed, such as [10; 11; 12]. Mapping water bodies at global scale using SAR data was limited due to the lack of global observations, and the fact that SAR data are not easy to access freely. Ref.