## 1 Introduction  
Understanding the Earth's global water cycle requires the spatiotemporal monitoring of precipitation [1]. Moreover, precipitation monitoring is essential, since rainfall directly affects human life. Indeed, very high rainfall episodes may cause runoff, which damages life and property, whereas the absence of precipitation can produce droughts [2]. Thus, knowing the extent of rain helps us better understand the effect of climate and weather on agriculture and water availability. The registration of in situ rain gauges allows only the measurement of local precipitation amounts. Thus, these rain gauge instruments are not sufficient to provide robust continuous mapping of rainfall, because rainfall events can be very local. Moreover, in situ rain gauge registrations are not usually freely available. On the other hand, remote sensing metrological sensors enable the continuous mapping of precipitation in open access mode. Currently, several metrological sensors provide rainfall mapping with a high revisit time and low spatial resolution: the Tropical Rainfall Measuring Mission (TRMM) (resolution \(\sim\) 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\)) [3], the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network (PERSIANN) (resolution \(\sim\) 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\)) [4], the Climate Prediction Center Morphing (CMORPH) (resolution \(\sim\)8 km \(\times\) 8 km at the equator) [5]. The most recent sensor, Global Precipitation Measurement (GPM), provides precipitation mapping at 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) spatial resolution and a high revisit time (up to 30 minutes) [6]. The low spatial resolution makes the available metrological sensors not adequate for hydrological application, flood forecasting, and water resource management. For example, the spatial detection of extreme rainfall events remains difficult due to the low spatial resolution of available precipitation data. Extreme rainfall events can be defined as rainy episodes with high cumulative precipitation in short periods (24 to 48 hours), which is equal to that usually received in one month. An important variable affected by precipitation events is the surface soil moisture. In fact, surface soil moisture can be a key tool for detecting rain events, because soil moisture is a function of the precipitation rate, evaporation, runoff, irrigation, and snow melt. Eventually, an increase in the soil moisture values could be primarily associated with a precipitation event, assuming that no irrigation activity is performed. Currently, several satellite missions provide surface soil moisture estimations at different spatial resolutions such as the Soil Moisture Active Passive \"SMAP\" (level 3: 36 km \(\times\) 36 km, level 3 enhanced: 9 km \(\times\) 9 km, and Level 2 SMAP/Sentinel-1: 1 km \(\times\) 1 km) [7], the Advanced Scatterometer \"ASCAT\" (level 2 with three spatial resolutions: 25 km \(\times\) 25 km, 12.5 km \(\times\) 12.5 km, and 1 km \(\times\) 1 km) [8], and the Soil Moisture and Ocean Salinity \"SMOS\" (SMOS INRA-CESBIO level 3: 25 km \(\times\) 25 km) [9], the Advanced Microwave Scanning Radiometer 2 \"AMSR2\" [10] (with two spatial resolutions 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) and 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\)), and the Chinese Fengyun-3B \"FY3B\" (spatial resolution of 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\)) [11]. Using soil moisture information, [PERSON] et al. [12] proposed a simple method to correct the TRMM and PERSIANN precipitation estimations at low spatial resolution (\(\sim\) 0.25\({}^{\circ}\)\(\times\) 0.25\({}^{\circ}\)). However, in the last three decades, numerous approaches have been developed to retrieve soil surface parameters using synthetic aperture radar (SAR) remote sensing [13; 14; 15]. From soil surface parameters, Sentinel-1 gives soil moisture estimations at very high spatial resolution (plot scale).