## 3 Observational Data Description, Assimilation and Experimental Design
### Sentinel Observations for the Livorno Test Case  
The following data were available directly through the Sentinel catalogues: (1) land and sea surface temperatures derived from the Sea and Land Surface Temperature Radiometer (SLSTR) on board of Sentinel-3, generated on a 1 \(\times\) 1 km\({}^{2}\) grid; (2) wind vector (speed and direction at 10 m a.s.l.) included in the Ocean Wind Field (OWI) component of the Sentinel-1 Level-2 Ocean (OCN) product (again generated on a 1 \(\times\) 1 km\({}^{2}\) grid). In particular, for the SST, the Sentinel-3 data acquired on 9 September 2017 at 20:36 UTC were gathered, while for LST, the Sentinel-3 data acquired on 9 September 2017 at 09:50 UTC were used. For what concerns SM, WD and WS, Sentinel-1 observed the Livorno area on 8 September 2017 at 17:14 UTC. To apply the multi-temporal SM retrieval algorithm, even the Sentinel-1 data acquired on 2 September, 27 August, 21 August and 15 August 2017 were used. Sentinel-1 ground range detected products were collected to estimate SM; these data were multi-looked (10 \(\times\) 10), calibrated and geocoded using the 30 m SRTM DEM.  
Figure 5 shows the maps of soil moisture (a), wind field (b), sea surface temperature (c) and land surface temperature (d). The SM map shows that the area corresponding to the observed QPE maxima is well captured by the Sentinel-1 data and corresponds to quite high SM values, around 0.3 m\({}^{3}\)/m\({}^{3}\). As for the wind field, the map shows that an intense Scirocco wind was blowing along the southern Tuscany and northern Lazio coastline, while the pattern of the wind over the sea in front of northern Tuscany was more disorganized and chaotic. Additionally, an intense wind jet was blowing near the Strait of Bonifacio, between Corsica and Sardinia. The Sentinel-3 derived SST map shows valid values (without cloud coverage) mainly on the southern part of the area of interest around Sicily Island, while not valid observations are available in front of the Tuscany coastlines. The problem of the scarcity of valid observations when severe weather events occur is common for optical data. For what concerns the Sentinel-3 derived LST data, it can be seen that the northern part of Tuscany, near the area mostly affected by the observed torrential rainfall phenomenon, shows a significantly lower LST than the surrounding areas, especially along the Adriatic coastlines and the eastern portion of Pianura Padana.  
Figure 4: Italian Global Navigation Satellite System (GNSS) receivers (yellow dots) and EPN (European Permanent Network) GNSS receivers (red triangles) used in the present work.  
An inverse square distance weighting interpolation of the Sentinel data on the WRF domains computational grids allowed obtaining the Sentinel maps into to the resolution of the innermost domain (1.5 km) before the assimilation. As mentioned in Section 2.3, the SM maps are also propagated in all the model soil layers (refer to Figure 3 in Reference [12]). Concerning ZTD measurements, for the Livorno test case the ZTD from InSAR was not available, thus only GNSS data were assimilated.