## 3 Observational Data Description, Assimilation and Experimental Design
### Sentinel Observations for the Silvi Marina Test Case  
For the SST, the Sentinel-3 data acquired on 14 November 2017 at 20:24 UTC were used, while cloud free optical data to derive LST were not found for the Silvi Marina event. For what concerns SM, WD and WS, Sentinel-1 observed the area of interest area on 14 November 2017 at 05:10 UTC (descending orbit) and at 17:06 UTC (ascending orbit). To apply the multi-temporal SM retrieval algorithm, even the Sentinel-1 data acquired on 8 November, 2 November, 27 October and 21 October 2017 were gathered (both ascending and descending orbits). Figure 6 shows the available EO observational data. Looking at the SM maps, the area corresponding to the observed QPE maxima, over Marche and Abruzzo Apennines is well captured by the Sentinel data and it corresponds to SM values around 0.3 m\({}^{3}\)/m\({}^{3}\). The SST map shows valid values only two days ahead the observed event, mainly on the swat southern part on the Ionian Sea, as well as in front of the Abruzzo and Marche coastline. Also in this case an inverse square distance weighting interpolation of the Sentinel data on the WRF domains computational grids allowed to obtain the Sentinel maps (SM, SST, WIND) at the resolution of the innermost domain (1.5 km) before the assimilation. For the Silvi Marina case, also ZTD map retrieved from Sentinel-1 is available. In this work 49 Sentinel-1 images have been downloaded and processed by SqueezeSAR [38]. Details of the images processed are reported in Table 2.  
Atmospheric products have been subsampled, roughly at 100 \(\times\) 100 [m\({}^{2}\)]. In Figure 7 an example of the derived atmospheric product is given, depicting the Area of Interest (AOI). Along with the Atmospheric Phase Screen (APS) products a digital terrain model of the AOI used in data processing  
Figure 5: Sentinel observational data available for the Livorno test case. Soil moisture in panel (**a**), wind speed and direction in panel (**b**), Sea Surface Temperature in panel (**c**) and Land Surface Temperature in panel (**d**). This variable has been further under sampled for the assimilation due to the fact that the original resolution at 100 m increases the computational cost of the simulation and, most importantly, violates the assumption of spatially independent observation errors made in Section 2.3 for the **R** matrix [9; 10]. For this reason, Reference [10] applied a thinning procedure choosing the nearest available InSAR measurement to each model grid point to obtain a 1 km observed map (same resolution as the inner domain of their setup). With the same method, Reference [9] used a thinning distance of 15 km (for an inner domain resolution of 3 km). To choose the best thinning resolution we performed few sensitivity tests investigating the different observed and modeled ZTD in terms of BIAS and RMSE before and after the assimilation using various InSAR ZTD map resolutions. The thinning resolutions adopted for the sensitivity are 1.5 km, 4.5 km and 13.5 km (the three WRF nested domain grid spacings). For each experiment, the observed point nearest to the center of the corresponding grid cell is kept and the rest is discarded. Because of the differences between the WRF model orography and the InSAR Digital Elevation Model (DEM), a correction of the ZTD has to be introduced while comparing the WRF ZTD field and the InSAR-derived one. In particular, since the ZTD is the vertical integral of the refractivity \(N\)[39], which is a function of the pressure of dry air, the partial pressure of water vapour and the temperature [40; 41; 42], a simple ZTD correction based on the model variables can be implemented. Let \(Z_{obs}\) be the height of the DEM associated to the ZTD InSAR observation in a specific position. When it is lower than the WRF DEM, \(Z_{obs1}<Z_{0}\), a positive correction using the first model level refractivity \(N_{1}\),  
\[\Delta\text{ZTD}=10^{-6}\left[(Z_{0}-Z_{obs1})\cdot N_{1}\right] \tag{2}\]  
is introduced.