## 3 Results
### Meteorological Forecasting and Assimilation Performances
#### 3.1.2 Extreme Event Forecasting: Convective Storms
Moreover, the \"area ratio\", which quantifies overprediction or underpredictionof spatial extent, the \"intersection area\", which captures the overlap between forecast and observation, and the \"centroid dist\", which measures spatial displacement, all confirm the superior performance of DA over OL. Moving on to the second case study in France (20240619), it is evident that the afternoon thunderstorms were slightly more intense and widespread in the areas surrounding the site of interest. Figure 6: Detailed vertical profiles (**first two rows**) of temperature (T, **first column**), dew point temperature (TD, **second column**), wind speed (**third column**), and the cosine of the angle between wind vectors (**fourth column**). The comparison is made between Meteorones observations (black), background (orange), and DA analysis (red) to evaluate the impact of data assimilation on atmospheric variables at 21 UTC (**first row**) and 00 UTC (**second row**). Last two rows: Comparison of WRF model state in the OL (Open Loop, blue), BF (Background Forecast, orange), and DA (Data Assimilation, red) configurations against Meteorone observations (black) at predefined pressure levels (dots refers to the model values available at the different pressure levels). The panels show the vertical profiles of temperature (T, **first column**), dew point temperature (TD, **second column**), wind speed (**third column**), and the cosine of the angle between wind vectors (**fourth column**) at 21 UTC (**third row**) and 00 UTC (**fourth row**). Both model simulations, with and without data assimilation, successfully captured the spatial distribution and precipitation peaks. As a result, precipitation validation was conducted for two thresholds: 10 mm and 15 mm/12 h.  
Figure 8 (top) displays the objects identified by MODE, both observed and predicted, offering a graphical representation of the MODE output. The left columns display the objects for WRF OL, while the right columns show WRF DA for the 10 mm and 15 mm/12 h thresholds. In the figure, blue contour lines represent observed objects, brown areas indicate forecasted objects, and the red dot marks the Beaune site. A visual inspection reveals that both model runs accurately predicted the location of observed objects. However, DA demonstrates greater precision compared to OL, along with improved accuracy in terms of agreement between the forecast and actual observations. Additionally, the figure presents statistical indices computed using MODE. These show that while both runs overestimate precipitation at both thresholds, data assimilation helps to slightly reduce this overestimation. Since the PODY, FAR, and FBIAS indices should be interpreted together, it can be observed that in the OL run, where precipitation is more strongly overestimated, the probability of correctly predicting \"yes\" events is higher, resulting in a slightly greater PODY compared to DA. However, this also leads to a higher number of false alarms, as indicated by the greater FAR value for OL relative to DA. Figure 7: Graphical representation of MODE output: on the top WRF OL (left column) and WRF DA (right column) for thresholds 5 mm/12 h where blue line contours represent observation objects, brown patterns represent forecasted objects, the red dot represents Beaune site; in the middle are plotted main statistical indices with the red lines the best scores for each index; on the bottom are plotted main parameters with the red lines the best scores for each index. Figure 8: Graphical representation by MODE output: **(top)** WRF OL and WRF DA for thresholds 10 mm and 15 mm/12n where blue line contours represent observation objects, brown patterns represent forecasted objects, the red dot represents Beaune slice; **(middle)** are plotted main statistical indices with the red lines the best scores for each index; **(bottom)** are plotted main parameters with the red lines the best scores for each index.