## 4 Validation and Results  
To validate all the modeling experiments and identify the best performing WRF setup for each case study, the Method for Object-Based Evaluation [(43; 44)] [MODE] is applied by comparing the Quantitative Precipitation Forecast (QPF) of WRF with the raingauges QPE. MODE identifies precipitation structures in both forecast and observed fields and performs a spatial evaluation of the model capability of reproducing the identified observed objects. Such validation method overcomes the so-called \"double-penalty\" issue [(45)], that traditional verification methods suffer from. This is particularly true when comparing high-resolution observational data analysis and cloud-resolving meteorological forecasts in case of deep moist convective and highly localized phenomena. Since traditional methods cannot provide a measure of spatial and temporal match between the forecast and the observed rainfall patterns, it is preferable to use feature-based verification techniques, such as MODE. In this paper 13 different indices provided by MODE validation are considered. They include both pairs of objects attributes and classical statistical scores: centroid distance, angle difference, area ratio, symmetric difference and percentile intensity (in this work above the 90 th percentile threshold), Frequency BIAS (FBIAS), Probability of Detection Yes (PODY), False Alarm Ratio (FAR), Critical Success Index (CSI), Hanssen and Kuipers discriminant (HK), Heidke Skill Score (HSS). For a complete description of the indices refer to References [(23; 24)]. The setup of all MODE parameters (except the rainfall threshold) is taken as it is by default. This means that in this work it is used a convolution radius of 1 grid square and a merging threshold above or equal to 1.25.  
The main goal of this meteorological validation, from a QPF standpoint, is to select the best meteorological forecast out of the whole set of the sensitivity experiments performed to investigate the impact of assimilating Sentinel and GNSS derived products. The outputs of the MODE validation tool are calculated for three different rainfall thresholds, namely 24, 48 and 72 mm. The evaluation metrics to assess the most reliable meteorological forecast in each set of experiments is performed as in Reference [(23)]: all the indices and statistical scores described above are calculated for each sensitivity experiment, then the times in which a simulation has been the best for each score is counted. Finally, the simulation ranking as the best for the highest number of times is identified.  
Additionally, the behavior of the experiments performed is discussed in the following sections both in terms of spatial indices and in terms of cumulated rainfall thresholds, to infer as many physical insights as possible. For a given experiment or a given index, the MODE spatial indices are compared to the OL ones to see if the assimilation has a positive impact on the forecast. The most relevant results are then highlighted and explained on a physical basis. This twofold approach (number of best scores and discussion on the indices with respect to the OL) is suggested as an alternative to the standard MODE approach [(43; 44)]. This is done because, in its original formulation, MODE makes use of an interest function that depends on a certain number of parameters that are not simple to define. Thus, to avoid extracting partial or wrong information, we decided to follow our simple and physically-oriented approach, as in References [(12; 24)].