## 3 Results  
### Pearson Correlation Coefficient, Anomaly Correlation, and Taylor Diagram  
In this section, we consider the comparison between the WRF 3 h forecast and the corresponding IMERG precipitation. For this purpose, the WRF 3 h forecasts for the whole period were regridded onto the IMERG \(0.1^{\circ}\times 0.1^{\circ}\) grid by a remapping procedure that conserves, to a desired degree of accuracy, the total precipitation forecast of the WRF native grid [83; 84]. The average precipitation over the whole period is shown in Figure 2. Comparing the results for CTRL and LIGHT, the precipitation increase given by LDA both over the sea and over land is apparent. This increase is larger over the Tyrrhenian Sea, especially close to the Italian mainland, and over northern and southern Adriatic Sea. The IMERG dataset shows higher precipitation values over the sea compared to CTRL and LIGHT, revealing rainfall underestimation for both model configurations. This underestimation is reduced in LIGHT, showing the positive contribution of LDA to the short-term precipitation forecast. Even if better than CTRL, LIGHT substantially underestimates the rainfall compared to IMERG, especially over the Tyrrhenian Sea (west of Sardinia) and over the Ionian Sea. An opposite behavior is observed over land, where CTRL and LIGHT show larger precipitation than IMERG. In particular, the IMERG dataset is not able to represent the impact of orography on the precipitation (western and north-eastern Italian mainland), which is evident in both CTRL and LIGHT. The Pearson correlation coefficient for each grid point of the domain was computed:  
\[r=\frac{\sum_{i=1}^{N}(y_{i}-\overline{y})(o_{i}-\overline{o})}{\left(\sum_{i=1} ^{N}(y_{i}-\overline{y})^{2}\sum_{i=1}^{N}(o_{i}-\overline{o})^{2}\right)^{1/2}} \tag{2}\]  
In Equation (2), \(y_{i}\) is the precipitation 3 h forecast, \(o_{i}\) is the corresponding observation given by IMERG dataset, \(N\) is the total number of data for each grid point (\(N=232\)), and \(\overline{y}\) and \(\overline{o}\) are, respectively, the forecast and observed averages for each grid point. The correlation results are shown in Figure 3.  
The result for CTRL (Figure 3a) shows a good performance of the WRF forecast over Italy and the central Mediterranean because for most of the grid points (more than 98%, both for CTRL and LIGHT, on a total of 27,602 grid points), the correlation between the forecast and the observed precipitation is positive. About 1.5% of the grid points have a negative correlation coefficient for both LIGHT and CTRL. Performance is improved by LDA (Figure 3b). A comparison of Figure 3a,b shows that LIGHT performs better, especially over the Adriatic and Ionian Seas. Differences between LIGHT and CTRL Pearson correlations (Figure 3c) help to visualize these results. From Figure 3c, the improvement of LIGHT forecast over CTRL is apparent both over sea and over land. Figure 3: Pearson correlation coefficient of the WRF precipitation forecast over the central Mediterranean domain: (**a**) CTRL forecast, (**b**) LIGHT forecast, and (**c**) correlation coefficient differences between LIGHT and CTRL. The positive values (green-yellow) in panel (**c**) show a better performance of the LIGHT forecast. Figure 2: Mean precipitation over the month of November 2019 for (**a**) CTRL forecast, (**b**) LIGHT forecast, and (**c**) Integrated Multi-satellite Retrievals for Global Precipitation Mission (IMERG). To highlight the added value of the LIGHT forecast compared to CTRL, we considered the correlation coefficient values over a reference threshold of 0.5. For the CTRL forecast, the correlation coefficient is above 0.5 for 5476 grid points, while for the LIGHT forecast, the correlation coefficient is over the 0.5 threshold for 8067 grid points. The same behavior is shown for different correlation thresholds (Table 1). In addition, the average of the correlation coefficient over the domain of Figure 3 is 0.59 for CTRL and 0.67 for LIGHT.