**4. Discussion**

The algorithm performances were assessed by comparing the RAINBOW outputs with the GRISO data (taken as reference) on a regular 0.25◦ × 0.25◦ grid for 10 case studies. Since both RAINBOW and GRISO are provided at higher but different spatial resolutions, they are up-scaled to a regular 0.25◦ × 0.25◦ grid. Both categorical scores (Probability of Detection (POD), False Alarm Ratio (FAR), Heidke Skill Score (HSS)) and continuous scores (mean error (ME) and root mean square error (RMSE)) have been considered [88]. The analysis has been done on an hourly basis (mm of rain fell in this time interval) considering the entire event of each case study. Furthermore, a minimum cumulative hourly rainfall threshold of 0.25 mm and three different intervals of cumulated rain are considered: light 0.25–1 mm, moderate 1–10 mm, and heavy 10–100 mm. The statistical scores above reported have been calculated even between P-IN-SEVIRI and GRISO in order to compare the RAINBOW and P-IN-SEVIRI performances.

The results shown in Figure 8 evidence excellent algorithm performance especially for moderate and heavy precipitation intensity. The Probability of Detection (POD)—Figure 8a) ranges between 0.8 and 1, except for light precipitation (0.25–1 mm); the False Alarm Ratio (FAR)—Figure 8b) has a specular trend with respect to the POD, with higher values for light precipitation and lower for the other rain intervals, while the Heidke Skill Score (HSS)—Figure 8c) follows the trend of the POD with values up to 0.8. It should be noted that the values of POD, FAR, and HSS are almost constant for all 10 case studies, underlining an excellent stability of the algorithm. In particular, HSS increases with time, highlighting that the continuous update of DPR GR network plays a crucial role in the RAINBOW performance by supplying ever-higher quality data input.

**Figure 8.** (**a**) Probability of Detection (POD), (**b**) False Alarm Ratio (FAR), and (**c**) Heidke Skill Score (HSS) scores calculated by comparing the RAINBOW outputs with the Random Generator of Spatial Interpolation from uncertain Observations (GRISO) data (taken as reference) on a regular 0.25◦ × 0.25◦ grid for 10 case studies. A minimum cumulated rain threshold is set at 0.25 mm and three different intervals of cumulated rain are considered: light 0.25–1 mm, moderate 1–10 mm, and heavy 10–100 mm.

The algorithm error in estimating the precipitation rate is quantified with respect to GRISO by calculating the mean error (ME) and the root mean square error (RMSE). Figure 9a shows that the ME oscillates around 0 mm for all cases and for all precipitation intervals except for heavy intensity where the values range between −7 and −9 mm indicating a clear underestimation of the higher intensities by the algorithm. The good results are confirmed by the RMSE (Figure 9b), which never exceeds 3 mm except for intense rainfall.

**Figure 9.** (**a**) Mean error (ME) and (**b**) root mean square error (RMSE) scores calculated by comparing the RAINBOW outputs with the GRISO data (taken as reference) on a regular 0.25◦ × 0.25◦ grid for 10 case studies. A minimum cumulated rain threshold is set at 0.25 mm and three different intervals of cumulated rain are considered: light 0.25–1 mm, moderate 1–10 mm, and heavy 10–100 mm.

A sensitivity study has been conducted in order to evaluate the performance of RAINBOW as a function of the resolution of the regular grid. To this end, four different grids have been chosen ranging from 0.1◦ × 0.1◦ to 0.25◦ × 0.25◦. The analysis has been always done on an hourly basis considering only the minimum cumulative hourly rainfall threshold of 0.25 mm.

The results shown in Figure 10 evidence very stable values for the categorical scores as a function of the resolution of the grid. In particular, POD (Figure 10a) has constant values slightly higher than 0.8, while both FAR and HSS (Figure 10b,c, respectively) show a more irregular trend only for the 0.1◦ × 0.1◦ grid with higher and lower values, respectively, than the other grids.

**Figure 10.** (**a**) POD, (**b**) FAR, and (**c**) HSS scores calculated by comparing the RAINBOW outputs with the GRISO data (taken as reference) on different regular grids for 10 case studies. A minimum cumulated rain threshold is set at 0.25 mm.

The continuous scores in Figure 11 confirm the results shown in Figure 10. The ME (Figure 11a) is always negative, around −0.4 mm, except for the first two case studies of 0.1◦ × 0.1◦ grid. On the other hand, the RMSE (Figure 11b) has very limited variations around 3.2 (mm), while for 0.1◦ × 0.1◦ grid, it shows an irregular trend with values dropping down up to 1.8 mm.

**Figure 11.** (**a**) ME and (**b**) RMSE scores calculated by comparing the RAINBOW outputs with the GRISO data (taken as reference) on different regular grids for 10 case studies. A minimum cumulated rain threshold is set at 0.25 mm.

The same analyses, shown in Figures 8 and 9, have been carried out by comparing the statistical scores calculated for RAINBOW with those one calculated for P-IN-SEVIRI product (always taking GRISO as reference). The results are ported in Figures 10 and 11 for categorical and continuous scores, respectively.

Figure 12 evidences the better performances of RAINBOW in detecting precipitation. The PODRAINBOW is always higher than PODP-IN-SEVIRI (Figure 12a) regardless the intensity of precipitation (different marker shape in the plot) and the different events (labeled by different colors). For light precipitation (circle markers), the PODP-IN-SEVIRI does not exceed 0.3, while PODRAINBOW ranges between 0.5 and 0.7. At moderate and heavy precipitation (and even not considering any rain intervals), while PODRAINBOW is always above 0.8, PODP-IN-SEVIRI shows a wide range of values between 0.2 and 1. At the same time, the FAR is very similar between the two algorithms with most of the points on the one-to-one line and at values generally lower than 0.4 (Figure 12b). The combination of POD and FAR results in constantly higher values oh HSSRAINBOW with respect to P-IN-SEVIRI (Figure 12c). The very good performances of RAINBOW in detecting the precipitation are confirmed by continuous scores, which refer to the precipitation rate estimation.

**Figure 12.** Comparison of (**a**) POD, (**b**) FAR, and (**c**) HSS scores calculated for RAINBOW and P-IN-SEVIRI outputs with respect to the GRISO data (taken as reference) on a regular 0.25◦ × 0.25◦ grid for 10 case studies. A minimum cumulated rain threshold is set at 0.25 mm and three different intervals of cumulated rain are considered: light 0.25–1 mm, moderate 1–10 mm, and heavy 10–100 mm.

Figure 13a shows that MERAINBOW and MEP-IN-SEVIRI are very similar for heavier precipitation intensity, while MERAINBOW and MEP-IN-SEVIRI assume values around 0 mm and slightly negative, respectively, for light to moderate precipitation intensity. On the other hand, RMSERAINBOW is generally lower than RMSEP-IN-SEVIRI regardless the precipitation rate (Figure 13b).

**Figure 13.** Comparison of (**a**) ME and (**b**) RMSE scores calculated for RAINBOW and P-IN-SEVIRI outputs with respect to the GRISO data (taken as reference) on a regular 0.25◦ × 0.25◦ grid for 10 case studies. A minimum cumulated rain threshold is set at 0.25 mm and three different intervals of cumulated rain are considered: light 0.25–1 mm, moderate 1–10 mm, and heavy 10–100 mm.

#### **5. Conclusions**

A new algorithm (RAINBOW) based on the combination of the data collected by SEVIRI onboard of MSG) and by the Italian ground-based radars network (IT GR) to provide precipitation estimation over Italy has been described. The algorithm, consisting of two main modules and operating over five geographical boxes in which the study area is divided, derives and updates (whenever it is possible) second degree polynomial RR-TB10.8 relationships. These relationships are applied to each acquisition of SEVIRI in order to provide a precipitation map. The results, based on a number of case studies, show good performance of the algorithm when it is compared with ground reference (i.e., GRISO precipitation pattern and intensity derived from rain gauge measurements), with high/low values for POD/FAR especially for light to moderate precipitation range. At the same time, the ME values are close to 0 mmh<sup>−</sup>1, while RMSE is about 2 mmh−1, highlighting a remarkable accuracy of RAINBOW estimates, whereas the capability to detect the precipitation pattern and intensity decreases for severe phenomena. It has to be remarked that severe events could be characterized by high spatial variability, which cannot be accomplished by RAINBOW (due to the SEVIRI instrument characteristics). It is worth noting that the performance of RAINBOW are quite constant through the different case studies with a slight improvement of the performance over time. This is related to the fact that RAINBOW relies on the high quality precipitation rate estimates from IT GR network, which are constantly maintained and upgraded. Furthermore, RAINBOW shows better performance than P-IN-SEVIRI (i.e., the H SAF product based on IR-derived precipitation estimation) when both products are compared to GRISO.

RAINBOW was conceived as an operational product to supply data where the IT GR coverage is absent or it presents low QI values. In this regard, the main aim of RAINBOW is the detection of extreme events that are barely observed by IT GR network in order to support the pre-alarm system for the hydro-geological risks and the life threatening conditions related to the incoming extreme events. Furthermore, the algorithm has to comply with short running time and with ease of management, which are fundamental aspects in a pre-alarm system. RAINBOW ensures running time comparable (or even shorter) with the IT GR running time and significantly shorter than P-IN-SEVIRI running time.

The next launch (scheduled in December 2021) of Flexible Combined Imager (FCI) on board of Meteosat Third Generation (MTG), will be useful to further improve the performance of RAINBOW. The higher number of channels available, the higher spatial and temporal resolution will provide higher quality data to characterize, also, very local severe events.

**Author Contributions:** Conceptualization, L.P.D. and S.D.; Methodology, L.P.D., P.S., and S.D.; Validation, L.P.D.; Formal Analysis, L.P.D.; Investigation, L.P.D.; Resources, S.D., S.P., G.V., and M.P.; Data Curation, L.P.D. and M.P.; Writing—Original Draft Preparation, L.P.D.; Writing—Review & Editing, P.S., S.D., G.V., and M.P.; Visualization, L.P.D.; Supervision, L.P.D. and S.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partially funded by the agreement between CNR-ISAC and the Italian Department of Civil Protection.

**Conflicts of Interest:** The authors declare no conflict of interest.
