Regional precipitation index: Method analysis and application over Greece

The current work focuses on the development of a regional precipitation index (RPI) to rank precipitation events in Greece, with the goal of identifying the most severe weather events in terms of their potential to cause socioeconomic impacts. The study is motivated by the increasing occurrence of extreme weather events and accompanying hydrogeological phenomena worldwide, which have caused significant infrastructure damage and loss of life. The analysis is based on the exploitation of the ERA‐Land high‐resolution rainfall dataset, covering the period from 1991 to 2020, while it considers both the area and the population affected by each rainfall event. The study provides a categorization of the ranked storms based on the percentiles of all non‐zero RPI values and highlights the socioeconomic impacts of the most severe weather events. The findings suggest that the developed RPI can be a useful tool for early warning systems and risk management strategies, particularly for emergency preparedness and response. The resulting ranking procedure has been applied operationally by the METEO unit of the National Observatory of Athens since fall 2021.


| INTRODUCTION
Heavy precipitation events and accompanying hydrogeological phenomena lead to major disruptions, significant infrastructure damages, and loss of life worldwide (e.g., see Petrucci et al., 2019;Hochman et al., 2022 andPapagiannaki et al., 2022 for the Mediterranean region).According to MunichRe (2022), flooding accounts for 40% of all insurance loss-related natural catastrophes since 1980.In Europe, economic losses from thunderstorms, including heavy storms and flash floods, have substantially increased in the same period (MunichRe, 2022).
Based on a published and systematically updated database (Papagiannaki et al., 2013), the analysis of weatherrelated disasters that affected Greece between 2000 and 2020 revealed that rainfall-related events (floods and flash floods) accounted for 64% of the total number of cases.The resulting adverse effects include the loss of 132 lives (61% of the total losses of lives) and severe damage to buildings, vehicles, other infrastructure, and the road network.
Increasing awareness of society before a severe rainfall event is of paramount importance.For example, the procedure of naming storms in Greece has been proven to be an efficient way to communicate the potential risk (Kotroni et al., 2021) and increase the citizens' awareness.Another approach, in line with storm naming, is storm ranking.So far, only mesoscale features, such as tropical cyclones/hurricanes (The Saffir-Simpson Team, 2021), and micro-scale features, such as tornadoes, are ranked, following a ranking which is based on the wind intensity and severity of the damage.Therefore, there is a need to start discussing procedures and methodologies to rank synoptic-scale features such as low-pressure weather systems and fronts, based on the accumulated rainfall produced by these phenomena.
The discussion on ranking mid-latitude storms was initiated about 20 years ago, by Kocin and Uccellini (2004) with emphasis on snowstorms that affect the eastern coasts of the continental USA during winter.The authors proposed a five-scale categorical ranking (from 1 to 5), which is a measure of the impact of snowstorms.The proposed ranking was based on observed snowfall accumulations, in conjunction with the population of the areas affected by these accumulations.This pioneering work was pursued by Cerruti and Decker (2011) based on the so-called "storm element scores" that comprise maxima of sustained wind and wind gusts, snow and ice accumulation, as well as visibility.They proposed a scale for the classification of winter storms and they related the values of the proposed index to the disruption observed in a limited area over the eastern USA (Newark airport).More recently, Squires et al. (2014) refined the work of Kocin and Uccellini (2004) and proposed a regional snowfall index (RSI) which is based on the spatial extent of a winter storm, the amount of snowfall, and the affected population.The area of application was the entire continental USA, but it is now used operationally by the National Centers for Environmental Information on smaller regions of the United States (https://www.ncei.noaa.gov/access/monitoring/rsi/).
In Europe, the ranking of daily precipitation extremes has been performed by Ramos et al. (2014), focusing on the Iberian Peninsula.The authors used a relatively highresolution rainfall dataset (with 0.2 spatial resolution) and ranked all rainfall events within the period 1950-2008.As in the previous studies, the area affected by rainfall was considered as a factor of ranking, but no population density data were taken into account.
The motivation for this work stems from the lack of any storm ranking procedure in the Mediterranean region.The present work exploits the concept of the RSI, developed by Squires et al. (2014), but focuses only on rainfall since in Greece snowstorms are not a frequent adverse weather event, while excessive rainfall is.Based on the climatology of daily accumulated rainfall provided by a reanalysis dataset for the period 1991-2020, the density of the population, and the area affected, a regional precipitation index (RPI, hereafter) was developed and used for ranking the rainy days of the period 1991-2020.The events with the highest ranks are also discussed in relation to the occurrence of socioeconomic impacts.This ranking procedure has been applied operationally since fall 2021 by the authors who are members of the METEO unit of the National Observatory of Athens (hereafter NOA).
The rest of the paper is structured as follows: Section 2 presents the dataset used as well as the methodology applied to calculate the RPI for Greece.Application of the RPI to the events that occurred in the period 1991-2020 is discussed in Section 3, together with a short analysis of the seasonal variability and tendencies.Section 4 is devoted to the potential application of RPI methodology in operational mode and an example of a severe flooding episode that occurred in Greece in the fall of 2021 is presented.Finally, Section 5 summarizes the work and provides some prospects for the future.

| DATA AND METHODOLOGY
For this study, the state-of-the-art land component of the fifth generation of the European ReAnalysis (ERA) dataset (Hersbach, 2020) was used, produced by the European Centre for Medium-Range Weather Forecast (ECMWF); hereafter referred to as ERA-Land (Muñoz-Sabater et al., 2021).The ERA-Land dataset is driven by meteorological fields from ERA and has an enhanced spatial resolution of 0.1 (31 km in ERA).For the needs of this study, we used daily data of total accumulated precipitation in a regular latitude-longitude grid with a spatial resolution of 0.1 x 0.1 for the period 1991-2020 over Greece.
Following the previous work of Kocin and Uccellini (2004) and Squires et al. (2014), which ranked snowstorms in the United States, we rank the storms in Greece through the calculation of the RPI.The first step includes the percentile analysis of the days of the period 1991-2020 with non-zero daily total precipitation.We first compute the spatial distribution of the 95th, 98th, and 99th percentiles of daily accumulated precipitation over all grid points in Greece.In the second step, using these three two-dimensional fields the countrywide 99th percentile of each one of them is computed and three precipitation thresholds, namely 35, 50, and 60 mm are obtained.In contrast to Squires et al. (2014), who used different thresholds for different parts of the United States, in the present study, the same set of thresholds all over Greece is used, taking into account the relatively small geographical extent of the country ($131,000 square kilometers).Then, the rainfall ranking is performed by taking into account the following: • The exceedance of the daily total rainfall at each grid point for three defined thresholds (i.e., 35, 50, and 60 mm).• The total area over which these exceedances occur.
• The population of the affected area.
The RPI calculation is performed using the following equation: where T is the daily precipitation threshold (35, 50, and 60 mm), A T is the area affected by precipitation greater than threshold T, A T is the climatology-based mean area affected by precipitation greater than the threshold T, P T is the population affected by precipitation greater than the threshold T and P ̄T is the climatology-based mean population affected by precipitation greater than the threshold T.
As stated by Squires et al. (2014), scaling the terms of area (A) and population (P) by their mean values transform these two terms in "percent of normal" and, therefore, have similar magnitudes.
Then, by applying the RPI equation on ERA-Land data, all the storms that impacted Greece during 30 years spanning from 1991 up to 2020 are ranked, and a categorization of the storms is proposed based on the percentiles of all the non-zero RPI values.
3 | APPLICATION TO 30-YEAR DATASET-RANKING PRECIPITATION EVENTS

| Distribution and ranking
During the period spanning from 1991 up to 2020, the RPI was greater than 0.01 for 1374 days (out of 10,957 days) and these days are considered as wet days.The daily distribution of RPI is shown in Figure 1.
A percentile analysis of the RPI distribution allows us to construct Table 1, which presents the five categories of RPI (from 1 to 5) that are used for the categorization of the events.
Inspection of Figure 2 reveals that the highest RPI values (equal or greater than 0.45, corresponding to category 3) show a statistically significant increasing trend during the analyzed period.According to the applied Mann-Kendall test this trend is statistically significant.Of interest is to notice 2 years, 1994 and 2003, with very high RPI values, For example, year 2003 was a year with abundant rainfall in January and February while December 2003 was the second wettest December in Athens since 1897.
Analysis of long precipitation time series by Founda et al. (2013) in the Athens area has shown that there is a pronounced increase in the percentage of precipitation amount due to heavy (>30 mm day À1 ) and extreme (>50 mm day À1 ) precipitation during the decade 2000-2010.This fact can also explain the increasing trend of the number of events with RPI > =3 found in the current analysis.
A seasonal analysis of the RPI values revealed that 41% of RPI values over 0.01 occurred during winter, followed by 37% of them during autumn.Focusing only on the top 2% of the RPI values (category 5), 18 days (60%) occurred during autumn, and 5 days (25%) occurred during winter.
F I G U R E 1 Daily variation of RPI over Greece, for the period 1991-2020, based on ERA-Land data.
To evaluate the impact of the ranked storms, namely those that are highly ranked (RPI category 4 or 5), we employed the high impact weather events (HIWE) database, developed by the METEO unit at NOA (Papagiannaki et al., 2013, see also https://www.meteo.gr/weather_cases.cfm, in Greek).This database comprises the events which occurred since the year 2000 and it is continuously updated.For our analysis, the events categorized as RPI categories 4 and 5 (see Table 1) which occurred between 2000 and 2021 have been selected (50 events out of the total number of 69).The comparison between RPI classifications and the reports of the HIWE database has shown that 45 out of the 50 events of RPI categories 4 and 5 were classified in the corresponding HIWE database as having severe impacts on society.These 45 high-RPI events were associated with 52 fatalities, which accounts for 40% of the total number of flood fatalities related to excessive precipitation within the 22 years of the HIWE database.

| The four most extreme RPI days
Between 1991 and 2020, the highest RPI value (30.2) was computed on March 26, 1998.The corresponding map of the 24-h accumulated rainfall provided by the ERA-Land dataset is shown in Figure 3a.This day was characterized by the presence of a deep low-pressure system (central mean sea-level pressure below 996 hPa) originating from the lee side of the Alps that moved slowly eastwards, over the southern parts of Greece.An interaction of warm and moist air masses over the Mediterranean with dry and cold air masses aloft resulted in an extensive warm conveyor belt above Greece, where heavy precipitation was recorded for several hours.The high RPI value is mainly due to the high rainfall accumulation over the Attica/Athens area, the most highly populated city in Greece (with 45% of the country's population living in that area).More information on this specific event is provided by Lagouvardos and Kotroni (1999).
The second highest RPI value in the list is equal to 26.3 and was computed on January 12, 1997.The day before downstream of a long-wave trough with an elongated axis reaching Central Libyan, a mid-tropospheric vorticity maximum was associated with a surface low that was moving slowly from Italy toward the Ionian Sea.On January 12, an anticyclonic wave breaking resulted in a cut-off over Central Mediterranean that was in phase with the surface low offshore southern continental Greece.The most affected area with severe damages was south-eastern continental Greece, where 24-h accumulated rainfall exceeded 300 mm (Kotroni et al., 1999).Indeed, high-resolution numerical weather prediction modeling, as well as sensitivity simulations, revealed that the orientation of the flow was optimal for the advection of moist and thus, unstable air with a maximized fetch over the sea, and at an angle of impact optimum for orographic lifting ahead of the main topographic axes of continental Greece.The corresponding map of the 24-h accumulated rainfall provided by the ERA-Land dataset is shown in Figure 3b.
T A B L E 1 The five RPI categories, the corresponding RPI range, the percent of storms and the total number of days under each category.The third day in the list was the case of February 3, 2011, with an RPI value of 23.5.The synoptic set-up was characterized by a relatively shallow but slow-moving lowpressure system over the southern parts of Greece, below an upper-level cut-off low.Surface analysis revealed an occluded front over southern continental Greece, where more than 125 mm of accumulated precipitation was recorded in the northern parts of Athens.In addition, high 24-h accumulated precipitation amounts were recorded on many other stations in the highly populated Attica area (see Figure 3c), in agreement with the ERA-Land dataset.Fortunately, no human casualties were reported during this event, but the Fire Brigade received more than 300 emergency calls related to flooding in Attica.
The fourth day in the list, with an RPI value of 15.8, was associated with a Medicane that made landfall on the west coast of Greece.Medicane Ianos (Lagouvardos et al., 2022) affected a large part of Greece in 2020 and it was associated with 4 casualties and extensive damages in Western and Central Greece.This Medicane was the strongest ever observed in the Mediterranean and associated with large transport of low-and mid-tropospheric moisture from Central Mediterranean toward Greece.The corresponding map is shown in Figure 3d.In contrast with the previous three cases, Attica/ Athens area was only slightly affected, but the high RPI value is mainly attributed to the large extent of heavy rainfall, covering many medium-sized Greek cities (>50,000 residents).

| POTENTIAL FOR REAL-TIME APPLICATION
When Kocin and Uccellini (2004) first introduced the North East Snowfall Impact Scale, they highlighted that F I G U R E 3 (a) 24-h accumulated precipitation over Greece, as derived from ERA-Land dataset, ending at 0000 March 27, 1998, (b) as in (a) but ending at 0000 UTC January 13, 1997, (c) as in (a) but ending at 0000 UTC February 04, 2011, and (d) as in (a) but ending at 0000 UTC September 19, 2020.such indices are valuable for the assessment of storms that have already occurred.Their recommendation was against the use of such indices in a predictive procedure.Almost 20 years later, precipitation forecast skill (especially the quantitative precipitation forecasts) has considerably improved and therefore, the procedure of categorization of upcoming precipitation events could be part of the operational activities.
For that purpose, the METEO unit at NOA has started an experimental period during which the RPI ranking is applied to expected precipitation events.The RPI categorization calculation is performed based on the forecasts provided by the operational high-resolution numerical weather prediction (NWP) models implemented by the METEO unit at NOA. Verification of the RPI value attributed a priori to an event based on the 24-h accumulated rainfall forecasts is evaluated on an event basis against the RPI value calculated a posteriori by the 24-h accumulated rainfall observed by a network of 510 surface weather stations (NOAAN), operated also by the METEO unit at NOA (Lagouvardos et al., 2017).
An example of the RPI operational application is discussed in the following, and it concerns the October 14, 2021 case of an extreme precipitation event over Central and Southern Greece.This event, named "Ballos" by the Hellenic National Meteorological Service, following a procedure initiated by NOA in 2017 (for details see Kotroni et al., 2021), provoked considerable damages, mainly in Athens.Figure 4a shows the 24-h accumulated precipitation in Greece, as forecasted 1 day earlier, using the operational NWP output from BOLAM and WRF models.According to this forecast, the 24-h accumulated precipitation was expected to exceed 150 mm.The RPI value, calculated using Equation (1) was 15.35 for BOLAM and 14.3 for WRF, thus indicating that the expected precipitation event would be of category 5 following Table 1 (the highest rank).
Verification of the RPI calculation was made a posteriori based on the observations provided by NOAAN.
Indeed, despite the spatial discrepancies, the observed RPI value was 17.54, very close to the model-based forecasted values while both were of category 5.
Preliminary analysis of the RPI calculation during year 2022 revealed promising results.Among the 12 days of the year announced in categories 3 and higher, the verification based on the NOAAN data revealed that two storms categorized as level 3 were finally in category 2, while two other storms that occurred in November and December 2022, categorized as level 4 were finally within category 3, but with RPI values close to the upper limit of the range of category 3 shown in Table 1 (2.95 and 2.57, respectively).
The overall procedure will be further evaluated in the coming years when a robust sample of events will have been collected.

| CONCLUSION
The Regional Precipitation Index, based on a methodology presented earlier in the literature for snowfall events (Squires et al., 2014), was proposed and formulated to categorize and rank the severity of rainfall events that influenced Greece within the period 1991-2020.Our analysis, based on the ERA-Land 24-h accumulated precipitation, permitted us to identify 1374 days with RPI values greater than 0.01 that correspond to all precipitation events that affected Greece during the elapsed 30 years.Then, the RPI values and corresponding events were distributed in five categories (from 1 to 5) Focusing on the number of days identified as category 3 or greater, a statistically significant positive trend was identified during the analyzed 30-year period.
The precipitation accumulations of the top-4 RPI events were briefly presented and discussed, showing that RPI can be (by definition) very high when either the Athens area (the densest populated area in Greece) is affected by high rainfall amounts, or when a large part of the Greek territory is affected by high precipitation amounts.
This categorization helped to identify the major precipitation events in Greece, analyze them in terms of socioeconomic impacts, and set the basis for the application of the index operationally.Indeed, it is believed that the RPI can be used operationally as a component daily operational activities, since it permits the objective categorization of an expected storm and the issue of corresponding warnings for the authorities and the public, mentioning the level of storm potential in threatening life and property.For that purpose, based on the high-resolution rainfall forecasts produced by the METEO unit at NOA, an RPI value is calculated operationally, on a daily basis, and the corresponding category is publicly announced when it is greater or equal to 3. The first results of the operational application of RPI categorization as a forecasting tool showed very promising results, especially during the Ballos event, the most significant rainfall episode that occurred in Greece since fall 2021.Although extensive testing for a longer period is necessary (a work under realization), RPI can provide a good estimation of expected impacts, thus providing an additional tool for increasing awareness and enhancing the readiness of the citizens, and contributing to mitigating the effects of adverse weather on society.
U R E 2 Time evolution and trend of the annual number of days with RPI equal to or greater than 0.45.

F
I G U R E 4 (a) 24-h accumulated precipitation over Greece, as forecasted by the BOLAM model, ending at 0000 October 15, 2021, (b) as in (a) but from WRF model, and (c) as constructed by rain gauge data of NOAAN.