*2.6. RAINBOW Algorithm*

The RAINBOW algorithm is composed by a static module, which has been developed using historical data, and a dynamic module, which continuously updates the data to be used.

Both static and dynamic modules of RAINBOW have been developed for each of the five geographical boxes in which the area of interest has been divided (Figure 3). The choice to divide the area of study in geographical boxes is mainly related to the fact that precipitations with different microphysics properties can occurred over the Italian territory (e.g., a precipitation over the Alps may have different characteristics of a simultaneous precipitation over sea and/or in proximity of the coast). In addition, the precipitation occurring at the same time in different locations could be at different stage of its evolution. Dividing the area of study in geographical boxes mitigates the problems deriving from the situations just above described. In general, the smaller the box the better is the characterization of the precipitation. However, the box size has to be large enough to ensure an adequate number of samples in order to perform a reliable calibration. At the same time, an excessive number of geographical boxes can create discontinuities in the transition zones (i.e., on the line connecting two adjacent boxes). It was found that a good trade-off for the Italian country was to divide the country in five boxes.

**Figure 3.** Geographical boxes division of the area of study.

The RAINBOW algorithm works with data at SEVIRI spatial and temporal resolution and provides the output at the same spatial and temporal resolution. Thus, the first step is to downscale the SRI data at SEVIRI resolution. The SRI pixels selected for each SEVIRI IFOV have to satisfy two different thresholds:

The mean QI is calculated considering all the IT GR pixels within a SEVIRI IFOV. To consider the IFOV useful, the mean QI has to be higher than 60%.

If the threshold of 60% for the mean QI is overcome, the mean SRI (i.e., the mean precipitation rate for a SEVIRI IFOV) is calculated by considering only the pixel with QI ≥ 80%. The threshold at 80% allows to discard the pixels affected by any possible spurious signal (e.g., noise, beam blockage, etc.). At the same time, the maximum SRI value is stored.

At this point, RAINBOW decides if to use the static or dynamic part of the algorithm. The decision is based on the number of useful IFOVs in each geographical box (i.e., the IFOVs with both RR and TB data) collected both in the last hour with respect to the running time and in the last SEVIRI acquisition (we recall that GR data have higher temporal resolution than SEVIRI, ten versus 15 min, respectively). In particular, if the number of useful IFOVs in the last hour is higher (or equal) than 50% and, the number of useful IFOVs in the last acquisition is higher (or equal) than 10% or lower than 10% but the maximum RR exceed 3 mmh<sup>−</sup>1, the dynamic module of RAINBOW algorithm is applied. On the other hand, if these conditions are not satisfied, the static module of RAINBOW algorithm is used. The thresholds are defined through sensitivity tests changing both the percentage of useful IFOVs and the maximum RR value. The final output of both dynamic and static part of RAINBOW is a RR-TB10.8 relationship, for each geographical box, to be applied to the SEVIRI data in order to give precipitation estimation. The main difference between the two modules is that the dynamic one updates and changes the RR-TB10.8 relationship at each new SEVIRI acquisition, while the static one makes use of RR-TB10.8 relationships obtained by considering the whole dataset available (i.e., from 1 July, 2015 to 31 December, 2017). Furthermore, a RR-TB10.8 relationship for each meteorological season is derived in the static module. The RR-TB10.8 relationship is obtained by sampling the TB10.8 between 200 K and 270 K in 35 bins 2 K width. For each bin, the mean rainfall rate and the mean of maxima rainfall rates are calculated. More specifically, the TB10.8 spectrum is split in two parts, one between 200 K and 220 K and one between 220 K and 270 K, and two RR-TB10.8 relationships are derived. A second degree polynomial RR-TB10.8 relationship is derived for the first part of TB10.8 spectrum (200 ≤ TB10.8 ≤ 220 K), while a first degree polynomial RR-TB10.8 relationship is derived for the first part of TB10.8 spectrum (220 < TB10.8 ≤ 270 K).

Figure 4 shows, as an example, the RR-TB10.8 relationship obtained from the whole dataset for each season and each box used by the static module of the algorithm. It outlines how the higher rainfall rates are associated to the lower TB10.8. Fall and summer (Figure 4a–d) are the seasons where this relationship is more straightforward for all the considered geographical boxes. At the same time, winter (Figure 4b) is the season with the lowest precipitation rate (as could be expected) and with a very light relationship between RR and TB10.8. Together to the RR-TB10.8 relationship, the probability of precipitation (POP) is calculated for each TB10.8 bin and the corresponding POP-TB10.8 relationship is derived. The POP is defined as the ratio between the number of SEVIRI IFOVs with precipitation (RR <sup>≥</sup> 0.25 mmh−1) and the number of SEVIRI IFOVs with no precipitation (RR < 0.25 mmh−1). As for the RR-TB10.8 relationship, the dynamic module of RAINBOW updates and changes the POP-TB10.8 relationship at each SEVIRI acquisition, while the static module again takes advantages of the POP-TB10.8 relationship (for each box and each season) built by using the whole available dataset.

**Figure 4.** RR-TB10.8 relationship obtained from the whole dataset (i.e., from 1 July, 2015 to 31 December, 31, 2017) for each box for (**a**) fall, (**b**) winter, (**c**) spring, and (**d**) summer season, respectively.

Figure 5 reports the POP-TB10.8 relationships derived for each season and each box. The POP clearly increases decreasing the TB10.8 during fall and summer season (Figure 5a–d), reaching the 100% for TB10.8 as low as 210 K (boxes 2 and 3 show a decrease of POP for TB10.8 < 210 K during fall season—Figure 5a). Not as straightforward as for fall/summer is the POP-TB10.8 relationship for spring/winter (Figure 5b–c). There is a sharp decrease of POP at TB10.8 higher than 255 K. At the same time, POP increases decreasing TB10.8 up to 220 K about; then, the trend diversifies among the boxes, with most of them showing a marked decrease of POP for TB10.8 lower than 220 K. Among these, someone present a sharp increase when TB10.8 reaches values lower than 210K. The decrease of POP at lower TB10.8 values is mainly related to the presence of cirrus clouds, which are no-precipitating clouds with very low cloud top temperature. The occurrence of cirrus clouds reaches a maximum (minimum) in winter (summer) [86]. This aspect is related to the lower temperature in the troposphere during winter that favors both the formation and the maintenance of ice crystals, which are the constituents of this type of clouds [87].

**Figure 5.** POP-TB10.8 relationship obtained from the whole dataset (i.e., from 1 July, 2015 to 31 December, 2017) for each box for (**a**) fall, (**b**) winter, (**c**) spring, and (**d**) summer season, respectively.

#### **3. Results**

The methodology described above has been applied to several case studies. The algorithm performances were analyzed by comparing the RAINBOW precipitation retrievals with the outputs of GRISO and P-IN-SEVIRI on a regular grid (0.25◦ × 0.25◦) for ten selected case studies (occurred in 2016 and 2017). Furthermore, the potentialities and limitations of RAINBOW are discussed for two outputs of the algorithm considering two different case studies.

The first considered event occurred in the night between 9 and 10 September, 2017, causing a flash flood which hit the coastal city of Livorno (43.5◦N, 10.3◦E), in the Tuscany region. In the area around the city, three rain gauges measured more than 230 mm of accumulated precipitation in six hours (00:00–06:00 UTC), with peaks of 150 mm h−<sup>1</sup> registered between 01:00 and 03:00 UTC.

Regarding the event observed on 10 September 2017, Figure 6 shows the TB10.8 as measured by SEVIRI (Figure 6a), the instantaneous rainfall rate as estimated by IT GR network at SEVIRI spatial resolution (Figure 6b) and by RAINBOW (Figure 6c) at 01:12 UTC, respectively. The SEVIRI TB10.8 (Figure 6a) highlights the presence of a V-shaped thunderstorm hitting mainly the north part of Tuscany region. The updraft core developed over sea, just offshore of the coastal line remained stationary for several hours (roughly between 18:00 UTC of 9 September and the 03:00 UTC of 10 September). Values of TB10.8 as low as about 210 K are measured in the updraft core corresponding to a cloud top height around 12 km. The plot also outlines the presence of a storm line across the Sardinia region. The IT GR network estimated rainfall rate values up to 50 mmh−<sup>1</sup> (Figure 6b) within a SEVIRI IFOV (i.e., round 4 km × 4 km). At the same time, the spatial extension of the storm is quite limited both in terms of cloud and precipitation coverage. The same can be said for the precipitation across

the Sardinia even if the estimated rainfall rates reach lower values up to 40 mmh−1. Finally, lighter precipitation is detected in the northern part of Italy. The RAINBOW rainfall rate estimation (Figure 6c) captures well the two most intense precipitation zones (i.e., the area around Livorno and over Sardinia) but tends to detect precipitation over a larger area than radar. At the same time, the precipitation peak is well identified in both location and intensity, with a slight underestimation of the most intense cells.

**Figure 6.** Snapshot relative to the 01:12 UTC of 10 September, 2017. Panel (**a**) shows the TB10.8 as measured by Spinning Enhanced Visible and InfraRed Imager (SEVIRI), (**b**) the instantaneous rainfall rate as estimated by Italian ground radar network (IT GR) network at SEVIRI spatial resolution and (**c**) by RAdar INfrared Blending algorithm for Operational Weather monitoring (RAINBOW).

Figure 7 shows a snapshot relative to the 04:12 UTC for the case study of 14 October, 2016. Although the storm involved the same region (at least at that time), different properties of RAINBOW can be highlighted by the analysis if this case study. The case study reported in Figure 7 presents different characteristics showing two convective cells, one between Tuscany and Emilia Romagna regions, and one out of the Italian territory over south France (partially over sea and partially over land). Both convective cells have bigger spatial extension and even colder TB10.8 values up to 205 K about (Figure 7a). To the big cloud extension does not correspond an equal precipitation extension; in fact, the IT GR network shows scattered and small precipitation clusters with a quite wide range of intensity from few mmh−<sup>1</sup> to almost 50 mmh−<sup>1</sup> (Figure 7b). Analyzing the precipitation estimated by RAINBOW, it is possible to note significant differences with respect to SRI (Figure 7c):

**Figure 7.** Snapshot relative to the 04:12 UTC of 14 October, 2016. Panel (**a**) shows the TB10.8 as measured by SEVIRI, (**b**) the instantaneous rainfall rate as estimated by IT GR network at SEVIRI spatial resolution and (**c**) by RAINBOW.

The rainfall rate peak estimated by RAINBOW is weaker than that estimated by IT GR, with maximum values around 20 mmh−1. This can be mainly attributed to the limited number of IFOVs with intense rainfall rate considered in the calibration process.

RAINBOW is able to estimate precipitation for the convective cell over France and for the small cell on the border between Tuscany and Umbria region (red circle in Figure 7c). However, the precipitation corresponding to this latter cell is slightly overestimated, in terms of spatial extension, by RAINBOW. On the other hand, the precipitation cluster centered on the coastal line of Tuscany is well detected by RAINBOW. In the operational frame in which the algorithm is intended, this case study highlights the potentialities of RAINBOW. The precipitation detection of the two cells can be considered as warning of a possible event moving toward the Italian territory and as complementary to the SRI estimation, respectively.
