Impact of Different Cumulus Schemes on Weather Forecasting on Complex Orographic Areas

atmosphere

Article The Role of Physical Parameterizations on the Numerical Weather Prediction: Impact of Different Cumulus Schemes on Weather Forecasting on Complex Orographic Areas

Giuseppe Castorina 1,2 , Maria Teresa Caccamo 1,2 , Franco Colombo 2,3 and Salvatore Magazù 1,2,*

1 Department of Mathematical and Informatics Sciences, Physical Sciences and Earth Sciences (MIFT), University of Messina, Viale F. Stagno D’Alcontres 31, 98166 Messina, Italy; [email protected] (G.C.); [email protected] (M.T.C.) 2 CISFA—Interuniversity Consortium of Applied Physical Sciences, 98123 Messina, Italy; [email protected] 3 Italian Air Force Meteorological Service—Comando Aeroporto, 95030 Sigonella, Italy * Correspondence: [email protected]

Abstract: Numerical weather predictions (NWP) play a fundamental role in air quality management. The transport and deposition of all the pollutants (natural and/or anthropogenic) present in the

atmosphere are strongly inﬂuenced by meteorological conditions such as, for example, precipitation and winds. Furthermore, the presence of particulate matter in the atmosphere favors the physical

Citation: Castorina, G.; Caccamo, processes of nucleation of the hydrometeors, thus increasing the risk of even extreme weather M.T.; Colombo, F.; Magazù, S. events. In this framework of reference, the present work aimed to improve the quality of weather The Role of Physical forecasts related to extreme events through the optimization of the weather research and forecasting Parameterizations on the Numerical (WRF) model. For this purpose, the simulation results obtained using the WRF model, where Weather Prediction: Impact of physical parametrizations of the cumulus scheme can be optimized, are reported. As a case study, Different Cumulus Schemes on we considered the extreme meteorological event recorded on 25 November 2016, which affected the Weather Forecasting on Complex whole territory of Sicily and, in particular, the area of Sciacca (Agrigento). In order, to evaluate the Orographic Areas. Atmosphere 2021, performance of the proposed approach, we compared the WRF model outputs with data obtained 12, 616. https://doi.org/10.3390/ by a network of radar and weather stations. The comparison was performed through statistical atmos12050616 methods on the basis of a “contingency table”, which allowed for ascertaining the best suited physical parametrizations able to reproduce this event. Academic Editors: Yun Zhu, Jim Kelly, Jun Zhao, Jia Xing and Keywords: WRF model; air quality; extreme weather conditions; physical parametrizations; convec- Yuqiang Zhang tive phenomena; contingency table

Received: 7 April 2021 Accepted: 6 May 2021 Published: 11 May 2021 1. Introduction Publisher’s Note: MDPI stays neutral The optimization of meteorological models is very important in the prediction of the with regard to jurisdictional claims in genesis of extreme weather events. In the limited area models (LAM) and particularly published maps and institutional affil- in the weather research and forecasting (WRF) model, the physical parameterization of iations. convective phenomena plays a fundamental role in a good simulation of the dynamics of the atmosphere. The physical processes associated with the condensation of water vapor are essentially non-linear, and therefore their overall effect can directly influence large-scale circulation. Copyright: © 2021 by the authors. In this framework, the Sicilian territory is characterized by extreme weather events Licensee MDPI, Basel, Switzerland. that frequently cause flash floods [1]. During these episodes, the precipitations occurring This article is an open access article in few hours often exceed the rain accumulations that normally occur in several months. distributed under the terms and These extreme precipitations are usually connected with intense and quasi-stationary conditions of the Creative Commons mesoscale convective phenomena that insist on the same area for several hours. However, Attribution (CC BY) license (https:// they occur at a local scale (microscale) and hence a fruitful approach requires a deep creativecommons.org/licenses/by/ convection parameterization. Their intensity is often determined by local factors such as 4.0/).

Atmosphere 2021, 12, 616. https://doi.org/10.3390/atmos12050616 https://www.mdpi.com/journal/atmosphere Atmosphere 2021, 12, 616 2 of 13

the presence of orographic reliefs close to the coastline. The upward movement of the air on the windward side of a mountain range (known as the Stau effect) facilitates the formation of clouds and rain. Adiabatic expansions and compressions are well-known examples of thermodynamic processes and have recently been investigated also through the Rüchardt experiment [2] and the frequency analysis procedure [3]. Sicily, due to its geographical position and its complex orographic morphology, is often interested in extreme weather events. Being at the center of the Mediterranean Sea, Sicily is in the transition zone between the arid and dry climate of North Africa and the more temperate and moist climate of central Europe, and hence it is often affected by those phenomena that are triggered by the interactions between processes typical of middle latitudes and tropics [4–6]. In the early autumn months, the seas surrounding Sicily are normally affected by Mediterranean cyclones [7,8] that originate from the contrast between air masses with very different temperatures and moisture [9], which interact with the high-temperature marine water (sea surface temperature, SST). These conditions can cause extreme weather events characterized by sudden and heavy rainfalls and dangerous flash floods. In the summertime, between May and September, the thermo-convective thunderstorm affects the inland areas of Sicily, where temperature can reach very high values [10,11]. One of the most important challenges of meteorological modeling is to develop models that can predict with high rates of success, both the time and the place where a convective cell start to develop as well as their evolution in time and space [12,13]. In recent years, several advances have been made on this purpose, and the limited area models, nowadays used in the major computing centers, are often able to provide an answer with adequate accuracy [14,15]. The weather research forecast (WRF) model is a numerical weather prediction system designed for research needs and operational forecasting of weather phenomena. This model is the result of a collaborative effort between the National Center for Atmospheric Research (NCAR), the National Centers for Environmental Prediction (NCEP), and the Earth System Research Laboratory (ESRL) of the National Oceanic and Atmospheric Administration (NOAA). The WRF is designed both for scientific purposes (for example for the numerical simulations of the atmospheric dynamics) and for applicative purposes, such as numerical weather predictions. Furthermore, it is possible to implement the model through the optimization of an inte- grated system based on the WRF model coupled with the chemistry module (WRF–Chem). It consists of a type of “online” model as it allows for the emission, transport, dispersion, transformation, and sedimentation of all anthropogenic and natural pollutants [16,17]. In the latter case, for example, it is possible to consider both physical processes and chemical transformations of aerosol particles released during volcanic eruptions. Indeed, it is worth noting that, although weather conditions are the main factor that determines the air quality, they depend on the direct and indirect effects that chemical compounds have on solar radiation and cloud microphysics [18]. The results of these simulations were obtained using the weather research and forecasting (WRF) model, version 3.7.1. [19], specifically optimized for Sicily, which is a territory with a complex orography [20–22]. For the sake of the improvement of the model performance, some progress has been made in the understanding of the mechanisms governing the formation and the localization of convective systems capable of producing large quantities of precipitation [23,24]. In particular, the physical parameterizations concerning the convective phenomena have been improved [25]. The parameterization of convective phenomena plays a fundamental role in a good simulation of the dynamics of the atmosphere. The physical processes associated with the condensation of water vapor are essentially non-linear, and therefore their overall effect can directly affect large-scale circulation. [26,27]. In this framework, the study has been addressed to seek the best model configurations capable of giving the best weather forecasting [28]. Atmosphere 2021, 12, x FOR PEER REVIEW 3 of 15

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In this framework, the study has been addressed to seek the best model configurations capable of giving the best weather forecasting [28]. The casecase studystudy treated treated in in the the work work concerns concerns the the extreme extreme meteorological meteorological event event that tookthat placetook place on 25 on November 25 November 2016, which 2016, haswhich interested has interested the entire the territory entire ofterritory Sicily(see of SicilyFigure (see1 ), inFigure particular 1), in particular the area ofthe Sciacca area of (Agrigento). Sciacca (Agrigento). In this event,In this theevent, observed the observed precipitation precip- wasitation purely was purely convective, convective, and therefore and therefore it is advisable it is advisable to compare to compare the numerical the numerical forecasts fore- ascasts the as convective the convective schemes schemes vary. vary. To evaluate To evaluate the performance the performance of the of model the model simulations, simula- wetions, performed we performed statistical statistical analyses analyses using theusing pluviometric the pluviometric data provided data provided for by thefor modelby the andmodel the and daily the precipitation daily precipitation observed observed by 13 weather by 13 stationsweather provided stations byprovided the network by the of net- the Regionalwork of the Department Regional D ofepartment Civil Protection of Civil (DRPC) Protection of Sicily. (DRPC) of Sicily.

Figure 1. Top panel: map showing the location of Sicily in Europe. Bottom panel: Detail of Sicily Figure 1. Top panel: map showing the location of Sicily in Europe. Bottom panel: Detail of Sicily showing the the geographical geographical position position of of the the cities cities of ofMessina, Messina, Catania Catania,, and and Sciacca Sciacca;; the seas the; seas;and and Mount Etna. 2. Description of the Case Study 2.1. Synoptic Analysis November 2016 was characterized by a long and prolonged phase of bad weather that affected the whole of Sicily. Due to its intensity, the event that occurred on the 25th of November was one of the most signiﬁcant, causing spread ﬂoods both on the southern

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2. Description of the Case Study 2.1. Synoptic Analysis Atmosphere 2021, 12, 616 November 2016 was characterized by a long and prolonged phase of bad weather4 of 13 that affected the whole of Sicily. Due to its intensity, the event that occurred on the 25th of November was one of the most significant, causing spread floods both on the southern coast and on the Ionian coast between the towns of Catania and Messina. Large-scale ver- ticalcoast movements and on the were Ionian favored coast by between the presence the towns of a 500 of hPa Catania vortex and located Messina. above Large-scale Spain (seevertical Figure movements 2). were favored by the presence of a 500 hPa vortex located above Spain (see Figure2).

Figure 2. 2. GeopotentialGeopotential at at500 500 hPa. hPa. The The synoptic synoptic analysis analysis shows shows a depression a depression vortex vortex located located on the on the IberianIberian Peninsula. Peninsula.

ThisThis baric baric configuration configuration attracted attracted intense intense flows flows of southern of southern currents currents towards towards Sicily. Sicily. These southern southern flows flows carried carried large large quantities quantities of ofmoisture moisture released released by the by Libyanthe Libyan Sea, Sea, which have have been been interested interested in in high high surf surfaceace temperatures temperatures (close (close to 20 to ° 20C, see◦C, Figure see Figure 3). 3). However, on on the the west west of of Sicily, Sicily, the the air air flows flows were were oriented oriented from from the thewestern western quadrants quadrants,, and the the post post-frontal-frontal air air masses masses were were colder. colder. Therefore, Therefore, there there were were simultaneously simultaneously the the presence of of three three compone componentsnts able able to togenerate generate the the initial initial development development of a ofconvective a convective system:system: the the presence presence of of a ahigh high level level of ofmoisture moisture in the in the lower lower atmosphere atmosphere;; the sea the surface sea surface Atmosphere 2021, 12, x FOR PEER REVIEW 5 of 15 temperaturetemperature still still relatively relatively high, high, capable capable of ofproviding providing latent latent heat heat during during condensation condensation processesprocesses;; and, and, finally, finally, instability instability of of the the troposphere troposphere [29,30 [29,].30 ].

FigureFigure 3. 3. AnalysisAnalysis of ofSST SST and and surface surface wind wind currents. currents. The The figure ﬁgure shows shows the high the high temperatures temperatures of of the thesea sea surface surface that that favors favor thes the increase increase of of the the moisture moisture ofof thethe airair masses that that fly ﬂy over over them. them.

In the hours immediately following 00:00, the first cold air impulses reached the western coasts of Sicily, initially causing thunderstorms to spread in the Trapani area. The frontal lifting operated by the arrival of the cold air mass found an environment already favorable to the trigger of a strong convective storm. The storm line gave rise to a huge V- shaped storm that developed just to the north of the island of Pantelleria, affecting all of the western parts of Sicily with intense rainfall, particularly the southern coast between the towns of Ribera and Sciacca (see Figure 4).

Figure 4. MSG enhanced nephoanalysis of 25.11.2016 at 01:00 UTC.

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Atmosphere 2021, 12, 616 5 of 13 Figure 3. Analysis of SST and surface wind currents. The figure shows the high temperatures of the sea surface that favors the increase of the moisture of the air masses that fly over them.

InIn the hours hours immediately immediately following following 00:00, 00:00, the the first ﬁrst cold cold air impulses air impulses reach reacheded the west- the westernern coasts coasts of Sicily, of Sicily, initially initially causing causing thunderstorms thunderstorms to spread to spread in the in Trapani the Trapani area. area. The Thefrontal frontal lifting lifting operated operated by the by arrival the arrival of the ofcold the air cold mass air found mass an found environment an environment already alreadyfavorable favorable to the trigger to the of trigger a strong of convective a strong convective storm. The storm. storm line The gave storm rise line to gavea huge rise V- toshape a huged storm V-shaped that developed storm that just developed to the north just of to the the island north of of Pantelleria, the island ofaffecting Pantelleria, all of affectingthe western all ofparts the westernof Sicily partswith intense of Sicily rainfall with intense, particularly rainfall, the particularly southern coast the southern between coastthe towns between of Ribera the towns and ofSciacca Ribera (see and Figure Sciacca 4). (see Figure4).

FigureFigure 4.4. MSGMSG enhancedenhanced nephoanalysisnephoanalysis ofof 25.11.201625.11.2016 atat 01:0001:00 UTC.UTC.

These so-called V-shaped thunderstorms were mesoscale storm systems with the characteristic of producing intense precipitations in the southern portion of the V point where super cellular elements could be active [31,32]. About 200 mm of rainfall was recorded by the weather station of Bivona between 05:30 and 11:00 UTC, with maxima values of 51.4 mm in 30 min. The weather station of Giuliana, a few kilometers west of Bivona, recorded 163.2 mm. In the same hours, severe precipitations affected also the eastern coast, producing a ﬂood in the town of Giardini Naxos.

2.2. WRF Model The numerical simulation of this case study was carried out using the weather research and forecasting (WRF) model. The advanced research WRF (ARW) modeling system was adopted. Figure5 shows the numerical domain adopted in the present work. Figure6 shows the orography of the domain under examination. The horizontal space of the grid was 5 km in both directions with 65 vertical levels up to 50 hPa. The initial and boundary conditions were acquired by the global model global forecast system (GFS) at 0.25 degrees with a time interval resolution of 1 h processed starting from the 00Z run relative to 24 November 2016. The real-time global sea surface temperature analysis (RTG-SST) with a resolution of 0.083 degrees was used. For long-wave and short-wave radiations, the rapid radiative transfer model for GCM (RRTMG) scheme was used. In addition, the above models were also used the schemes of Mellor–Yamada–Janjic for the boundary layer and the Noah land surface model. The microphysical scheme utilized was the Thompson, a well- known double-moment scheme widely tested especially for high-resolution simulations. Atmosphere 2021, 12, x FOR PEER REVIEW 6 of 15

These so-called V-shaped thunderstorms were mesoscale storm systems with the characteristic of producing intense precipitations in the southern portion of the V point where super cellular elements could be active [31,32]. About 200 mm of rainfall was recorded by the weather station of Bivona between 05:30 and 11:00 UTC, with maxima values of 51.4 mm in 30 min. The weather station of Giuliana, a few kilometers west of Bivona, recorded 163.2 mm. In the same hours, severe precipitations affected also the eastern coast, producing a flood in the town of Giardini Naxos.

2.2. WRF Model The numerical simulation of this case study was carried out using the weather research and forecasting (WRF) model. The advanced research WRF (ARW) modeling system was adopted. Figure 5 shows the numerical domain adopted in the present work. Figure 6 shows the orography of the domain under examination. The horizontal space of the grid was 5 km in both directions with 65 vertical levels up to 50 hPa. The initial and boundary conditions were acquired by the global model global forecast system (GFS) at 0.25 degrees with a time interval resolution of 1 h processed starting from the 00Z run relative to 24 November 2016. The real-time global sea surface temperature analysis (RTG- SST) with a resolution of 0.083 degrees was used. For long-wave and short-wave radiations, the rapid radiative transfer model for GCM (RRTMG) scheme was used. In addition, the above models were also used the schemes of Mellor–Yamada–Janjic for the boundary Atmosphere 2021, 12, 616 layer and the Noah land surface model. The microphysical scheme utilized was the 6 of 13 Thompson, a well-known double-moment scheme widely tested especially for high-resolution simulations.

Atmosphere 2021, 12, x FOR PEER REVIEWFigure 5. Map of the spatial domain used by the WRF model. The domain7 of is 15 centered in Sicily. The Figure 5. Map of the spatial domain used by the WRF model. The domain is centered in Sicily. modelThe model is configured is conﬁgured with a horizontal with a horizontal grid spacing grid of spacing 5 km and of a 5time km interval and a time resolution interval of resolution1 h. of 1 h.

FigureFigure 6. Topographical 6. Topographical height (expressed height in (expressedmeters above sea in level) meters of the above domain sea under level) exami- of the domain under examination. nation.

3.3. Results Results and Discussion and Discussion TheThe study studycarried out carried in this work out concerns in this the work evaluation concerns of the performance the evaluation of the of the performance of WRFthe model WRF when model different when cumulus different parameterizations cumulus are applied parameterizations [33]. In particular, the are applied [33]. In particular, forecasts of the spatial distribution of rain during the extreme event were compared. The parameterizationsthe forecasts compared of the spatialare the follows: distribution CU0 represents of the rain explicit during convection the; extremeCU1 event were compared. isThe the Kain parameterizations–Fritsch scheme [34,35 compared], which is a deep are the and shallow follows: convection CU0 represents sub-grid the explicit convection; scheme, using a mass flux approach with downdrafts and convective available potential energyCU1 (CAPE) is the removal Kain–Fritsch time scale; CU2 scheme is the B [etts34,–35Miller], which–Janjic scheme is a deepand it is and an op- shallow convection sub-grid erationalscheme, Eta scheme using [36,37 a mass] and fluxa column approach moist adjustment with downdraftsscheme relaxing andtowards convective a available potential wellenergy-mixed profile (CAPE); CU3 removalis the Grell–Devenyi time scale; (GD) scheme CU2, an is ensemble the Betts–Miller–Janjic scheme involv- scheme and it is an ing a multi-closure, multi-parameter, ensemble method with typically 144 sub-grid mem- bersoperational; CU5 is the Grell Eta 3D scheme scheme, [which36,37 is] an and improved a column version moistof the GD adjustment scheme that scheme relaxing towards a maywell-mixed also be used profile; on high resolution CU3 is the(in addition Grell–Devenyi to coarser resolutions) (GD) scheme, if subsidence an ensemble scheme involving spreading (option cugd_avedx) is turned on [38]; CU6 is the Tiedtke scheme, which is a massa multi-closure,-flux type scheme with multi-parameter, CAPE removal time ensemblescale, shallow methodcomponent,with and momen- typically 144 sub-grid members; tumCU5 transport is the; finally, Grell CU14 3D is scheme,the new simplified which Arakawa is an–Schubert improved scheme version [39], a new of the GD scheme that may massalso-flux be scheme used with on deep high and resolution shallow compon (inents addition and momentum to coarser transport. resolutions) if subsidence spreading Figure 7 shows the total rainfall accumulations (accumulate + convective) obtained from(option the WRF cugd_avedx) model simulations is turnedwhen the onphysical [38]; parameterizations CU6 is the Tiedtke of the convective scheme, which is a mass-flux type schemesscheme vary with (Figure CAPE 7a–g). The removal results obtained time scale,were compa shallowred with component, the map of data and momentum transport; observed by the network of meteorological stations by the Regional Department of Civil Protectionfinally, (DRPC) CU14 of is Sicily the (Figure new simplified 7h). Arakawa–Schubert scheme [39], a new mass-flux scheme with deep and shallow components and momentum transport.

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Figure7 shows the total rainfall accumulations (accumulate + convective) obtained from the WRF model simulations when the physical parameterizations of the convective schemes vary (Figure7a–g). The results obtained were compared with the map of data Atmosphere 2021, 12, x FOR PEER REVIEW 8 of 15 observed by the network of meteorological stations by the Regional Department of Civil Protection (DRPC) of Sicily (Figure7h).

Figure 7. Total rainfall maps (accumulate + convective) obtained through the WRF model using differentFigure 7. physicalTotal rainfall parametrizations maps (accumulate of convective + convective schemes) obtained and mapthrough of data the observedWRF by the DRPC weathermodel using stations differen network.t physical (a) Theparametrizations CUO convective of convective parameterization; schemes and (b) map the CU1 of data convective parameterization;observed by the (DRPCc) the CU2weather convective stations parameterization;network. (a) The CUO (d) the convective CU3 convective parameteriza- parameterization; (tion;e) the (b CU5) the convectiveCU1 convective parameterization; parameterization; (f) the (c CU6) the convectiveCU2 convective parameterization; parameterization; (g) the CU14 convective(d) the CU3 parameterization; convective parameterization; (h) the map of a(e pluviometric) the CU5 convective data observation parameterization; provided (f by) the Regional Department of Civil Protection (DRPC) of Sicily.

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Atmosphere 2021, 12, 616 the CU6 convective parameterization; (g) the CU14 convective parameterization; (h) 8the of 13 map of a pluviometric data observation provided by the Regional Department of Civil Protection (DRPC) of Sicily.

However,However, visualvisual analysisanalysis (called “Eyeball”“Eyeball” verification) veriﬁcation) fails fails to to show show which which physical physical parameterizationparameterization of of convective convective schemes schemes provided provided the the best best performance. performance. Furthermore, Furthermore, vis- visualual analysis analysis is only is only a preliminary a preliminary way wayto compare to compare maps; maps; it cannot it cannot be cons beidered considered as a sci- as aentific scientiﬁc approach approach for any for comparison. any comparison. Therefore, Therefore, in order in for order us to for evaluate us to evaluate which param- which parameterizationeterization has provided has provided the most the reliable most reliable performance performance in predicting in predicting the spatial the spatial distribu- dis- tributiontion of rain of rainduring during the extreme the extreme event, event, the use the of use a statistical of a statistical approach approach is fundamental. is fundamental. For Forthis this purpose, purpose, it is it necessary is necessary to toselect select a collection a collection of ofweather weather stations stations in in the the area area affected affected byby thethe extremeextreme event,event, asas shown in Figure8 8.. TheThe datadata of these stations are provided by by the the networknetwork ofof thethe RegionalRegional DepartmentDepartment of Civil Protection (DRPC) (DRPC) of of Sicily. Sicily.

FigureFigure 8.8.Map Map ofof weather weather stations stations used used in in this this case case study: study: 5 stations5 stations in in the the north north of of Sicily Sicily (Castelbuono, (Castel- Lascari,buono, Lascari, Pettineo, Pettineo, Polizzi, Polizzi and Cefal, andù), Cefalù), 4 in the 4 northeast in the northeast sector (Antillo,sector (Antillo, Fiumedinisi, Fiumedinisi, Linguaglossa, Lin- guaglossa, and San Pier Niceto), and 4 in the southwest (Bivona, Giuliana, Ribera, and Sciacca). and San Pier Niceto), and 4 in the southwest (Bivona, Giuliana, Ribera, and Sciacca).

ToTo perform perform the the analysis analysis using the contingency table table and and calculate calculate the the indices indices re- re- portedported inin thethe nextnext section,section, we needed to compare the data data of of the the total total rainfall rainfall observed observed (extrapolated(extrapolated fromfrom thethe DRPC-SicilyDRPC-Sicily meteorological stations) stations) with with those those predicted predicted by by the the WRFWRF model.model. Therefore,Therefore, thethe extrapolation of the rainfall rainfall accumulations accumulations recorded recorded by by the the 13 13 weatherweather stationsstations examinedexamined waswas carried out. The The choice choice of of weather weather stations stations was was performed, performed, accountingaccounting forfor the the spatial spatial localization localization of of the the extreme extreme recorded recorded meteorological meteorological event. event. The The fol- lowingfollowing stations stations were were chosen chosen as reference: as reference: ﬁve five stations stations in the in norththe north of Sicily of Sicily (Castelbuono, (Castel- Lascari,buono, Pettineo,Lascari, Pettineo, Polizzi, and Polizzi, Cefal andù), four Cefalù), in the four northeast in the sector northeast (Antillo, sector Fiumedinisi, (Antillo, Linguaglossa,Fiumedinisi, Linguaglossa, and San Pier and Niceto), San Pier and Niceto), four in theand southwest four in the (Bivona, southwest Giuliana, (Bivona, Ribera, Giu- andliana, Sciacca). Ribera, Subsequently, and Sciacca). Subsequently, the rainfall data the were rainfall extrapolated data were for extrapolated each simulation for each in which sim- theulation physical in which parametrizations the physical ofparametrizations the convective phenomenaof the convective were phenome modiﬁed.na The were forecasted modi- rainfallfied. The data forecasted and observed rainfall data data by and the observed 13 weather data stations by the 13 are weather shown instations Tables are1–3 shown. in TablesThe hour-by-hour 1–3. time series of the pluviometric data forecast and observed for the weather stations of Bivona, Sciacca, Pettineo, and Fiumedinisi are shown as an example in the following graphs (Figure9). The results show that the runs carried out with the WRF model underestimated the expected precipitation compared to that observed by the meteorological stations examined. This may have been due to the resolution of the model’s spatial grid; in fact, these meteorological events usually develop on smaller dimensions than the selected spatial grid. This could explain the underestimation of the total expected rainfall [20]. However, the spatial distribution and location of the meteorological event under consideration are well approximated by the simulations performed.

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Table 1. The forecasted rainfall data and observed data provided by the 5 stations in the north of Sicily.

Stations in the 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain North of Sicily mm mm CU0 mm CU1 mm CU2 mm CU3 mm CU5 mm CU6 mm CU14 Castelbuono 74.1 2.3 12.2 3 1.7 8.5 18.5 7.6 Lascari 53.6 15.7 14.5 3.6 11.1 12.6 7.5 5.3 Pettineo 46.2 10.5 17.9 2.5 3.7 2.8 8.8 7.2 Polizzi 89.4 8.2 7.5 1.1 7.1 7.3 8.2 0.8 Cefalù 34.1 8.1 19.1 3 23.6 25.7 16.3 6.2

Table 2. The forecasted rainfall data and observed data provided by the 5 stations in the northeast of Sicily.

Stations in the 24 H 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain Northeast of Sicily Rain mm mm CU0 mm CU1 mm CU2 mm CU3 mm CU5 mm CU6 mm CU14 Antillo 159.5 40.1 10.8 5.2 22.1 19.8 9.6 1.5 Fiumedinisi 153.8 71.3 26.5 10.8 40 15.3 18.1 2.1 Linguaglossa 92.1 50.1 1.4 0 2.1 0.5 0.4 1.2 San Pier 98.6 22 18.6 2.9 9.4 10.6 4.5 6.6 Niceto

Table 3. The forecasted rainfall data and observed data provided by the 4 stations in the southwest of Sicily.

Stations in the 24 H 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain 24 H Rain Soutwest of Sicily Rain mm mm CU0 mm CU1 mm CU2 mm CU3 mm CU5 mm CU6 mm CU14 Bivona 64.3 29.1 52.5 6.6 53 39.3 102.6 53 AtmosphereGiuliana 2021, 12, x FOR PEER 163.2 REVIEW 33.3 39.0 9.8 41.3 29.3 53.611 of 53.6 15 Ribera 198.4 7.5 52.4 5 28.5 29.2 74.5 12.9 Sciacca 132.3 13.2 50.8 9.9 37.8 46.2 46.6 21

FigureFigure 9. The 9. hour-by-hourThe hour-by-hour time time series series of of the the pluviometric pluviometric datadata forecast and and observed observed for for the the weather weather station. station. (a) The (a) time The time seriesseries of the of Bivona the Bivona weather weather station; station; (b )(b the) the time time series series ofof thethe SciaccaSciacca weather weather station; station; (c) (thec) the time time series series of Fiumedinisi of Fiumedinisi weatherweather station; station (d); the (d) timethe time series series of theof the Pettineo Pettineo weather weather station.station. In In the the graphs, graphs, the the blue blue line line represents represents the data the dataobserved observed by theby weather the weathe station;r station; the the red red line line represents represents the the simulation simulation with the the CU0 CU0 scheme; scheme; the the green green line line represents represents the simulation the simulation with the CU1 scheme; the violet line represents the simulation with the CU2 scheme; the light blue line represents the with the CU1 scheme; the violet line represents the simulation with the CU2 scheme; the light blue line represents the simulation with the CU3 scheme; the orange line represents the simulation of the CU5 scheme; the dark blue line repre- simulationsents the with simulation the CU3 of scheme; the CU6 the scheme; orange the line burgundy represents linethe represents simulation the simulation of the CU5 of scheme; the CU14 the scheme. dark blue line represents the simulation of the CU6 scheme; the burgundy line represents the simulation of the CU14 scheme. 4. Performance Testing of WRF Model Simulations To establish which of the simulations provided the best performance, we needed to use statistical methods. The performance of a forecast model can be evaluated using one or more scalar verification indexes. A possible solution is provided by the dichotomic indexes, yes/no. To obtain them, we needed to place the data in a table of I × J elements, the so-called “contingency table”, which contains the absolute frequencies of all possible com- binations of the observed and predicted data pairs. Considering the case I = J = 2, as shown in Figure 10, “a” indicates the number of cases in which the event was expected to occur and it is happening, “b” is the number of cases in which the event was expected to happens but it did not occur, “c” represents the number of cases in which the event occurred but was not expected, and finally “d” represents the number of cases in which the absence of the event was properly scheduled.

Figure 10. Contingency table schedule. The term a + b represents the forecasted meteorological events by the model. The term c + d represents the not forecasted meteorological events by the

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Figure 9. The hour-by-hour time series of the pluviometric data forecast and observed for the weather station. (a) The time series of the Bivona weather station; (b) the time series of the Sciacca weather station; (c) the time series of Fiumedinisi weather station; (d) the time series of the Pettineo weather station. In the graphs, the blue line represents the data observed by the weather station; the red line represents the simulation with the CU0 scheme; the green line represents the simulation with the CU1 scheme; the violet line represents the simulation with the CU2 scheme; the light blue line represents the Atmospheresimulation2021, 12with, 616 the CU3 scheme; the orange line represents the simulation of the CU5 scheme; the dark blue line repre-10 of 13 sents the simulation of the CU6 scheme; the burgundy line represents the simulation of the CU14 scheme.

4. Performance Testing of WRF Model Simulations 4. PerformanceTo establish Testingwhich of of the WRF simulations Model Simulations provided the best performance, we needed to use statisticalTo establish methods. which The of theperformance simulations of provideda forecast themodel best can performance, be evaluated we using needed one to oruse more statistical scalar verification methods. The indexes. performance A possible of a solution forecast is model provided can beby evaluated the dichotomic using in- one dexes,or more yes/no. scalar To veriﬁcation obtain them, indexes. we needed A possible to place solutionthe data isin provideda table of I by × J the elements, dichotomic the soindexes,-called “ yes/no.contingency To obtain table” them,, which we contains needed the to placeabsolute the frequencies data in a table of all of possible I × J elements, com- binationsthe so-called of the “contingency observed and table”, predicted which data contains pairs. Considering the absolute the frequencies case I = J = of 2, all as possibleshown incombinations Figure 10, “a” of indicates the observed the number and predicted of cases datain which pairs. the Considering event was expected the case to I =occur J = 2, andas shownit is happening, in Figure 10“b”, “a” is the indicates number the of number cases in of which cases the in which event thewas event expected was expectedto hap- pensto occur but it and did it not is happening,occur, “c” represents “b” is the the number number of cases of ca inses which in which the the event event was occurred expected butto was happens not expected but it did, and not finally occur, “d” “c” represents represents the the number number of ofcases cases in which in which the theabsence event ofoccurred the event but was was properly not expected, scheduled. and ﬁnally “d” represents the number of cases in which the absence of the event was properly scheduled.

Figure 10. Contingency table schedule. The term a + b represents the forecasted meteorological Figure 10. Contingency table schedule. The term a + b represents the forecasted meteorological eventsevents by by the the model. model. The The term term c c + + d d represents represents the the not forecast forecasteded meteorological eventsevents by by the the model. The term a + c represents the observed rainy weather events. The term a + d represents the non- observed rainy weather events.

Dividing by N = a + b + c + d, we obtained the combined distribution of prediction relative frequencies and the observed data; a perfect forecast has non-zero values only for the elements on the diagonal of the table. From the contingency table, we were able to define the categorical indexes used to quantify the yield of the simulations performed with this model, in particular: • Accuracy (Hit rate): defined as the ratio between the number of cases in which the event was correctly predicted and the total number of cases considered (n). The value 0 indicates a bad forecast, the value 1 indicates a perfect forecast. • Threat score (TS): an alternative to the hit rate, useful when the event considered has a substantially lower occurrence frequency than non-occurrence. If the threat score assumes the value 0, the forecast will be bad; otherwise, if it assumes the value 1, the forecast will be perfect. • Bias: represents the ratio between the predicted and observed data average. B = 1→ the event was predicted the same number of times that it was observed. B > 1→ over forecasting, the model predicts events with greater frequency than reality. B < 1→ under forecasting, the model predicts events with a lower frequency than reality. • False alarms ratio (FAR): illustrates that the model has made a forecast of rainfall for the valid period but it did not occur during the valid period. It is especially useful to verify the prediction ability of extreme events. If it assumes the value 0, the forecast will be perfect; if it assumes value 1, there will be the prediction of events that will not happen. • Equitable threat score (ETS): based on TS; by definition ranging from −1/3 to 1 (perfect prediction). • Hanssen–Kuipers discriminant: given by the ratio between the events correctly predicted and those actually occurred less the probability of having a false alarm. By definition ranging from −1 to 1 (perfect prediction). • Probability of detection (POD): sensitive to hits, but ignores false alarms. Very sensitive to the climatological frequency of the event. Good for rare events. Should be used Atmosphere 2021, 12, 616 11 of 13

in conjunction with the FAR. Its range is between 0 and 1; if it assumes the value 1, the forecast will be perfect. Table4 and Figure 11 show the numerical values obtained from the statistical analysis carried out to evaluate which simulation provided the best performance in locating the meteorological event under consideration. It should be noted that the contingency table shows the frequency of “yes” and “no” forecasts and occurrences. No comparison or evaluation is made on the expected and observed quantities of pluviometric data.

Table 4. Numeric values of indexes were calculated for each simulation performed by modifying the physical parameterization of the convective processes of the WRF model. For the analysis, all the selected meteorological stations and the respective points of the WRF model were taken into consideration. The ideal values are: accuracy (hit rate) = 1; threat score (TS) = 1; bias = 1; equitable threat score (ETS) = 1; probability of detection (POD) = 1; false alarms ratio (FAR) = 0.

CU0 CU1 CU2 CU3 CU5 CU6 CU14 Accuracy 0.68 0.53 0.45 0.54 0.53 0.51 0.52 TS 0.49 0.43 0.12 0.38 0.35 0.30 0.26 Bias 0.95 1.47 0.49 1.13 1.07 0.91 0.73 ETS 0.22 0.04 -0.06 0.05 0.03 0.01 0.01 Atmosphere 2021, 12, x FOR PEER REVIEWPOD 0.64 0.74 0.16 0.58 0.54 0.44 0.3613 of 15 FAR 0.33 0.50 0.67 0.48 0.50 0.51 0.51

Figure 11. Graphic of indexes calculated for each simulation performed by modifying the physical Figure 11. Graphic of indexes calculated for each simulation performed by modifying parameterization of the convective processes of the WRF model. It shows that the CU0 (blue line) the physical parameterization of the convective processes of the WRF model. It shows was the most reliable and accurate solution. The CU2 (green line) was the worst. CU1 (red line), CU3 that the CU0 (blue line) was the most reliable and accurate solution. The CU2 (green (violet line), and CU5 (light blue line) were the only schemes that tended to overestimate the rain. Theline) CU14 was andthe theworst. CU6 CU1 (orange (red line) line), schemes CU3 (violet were only line), slightly and betterCU5 (light than the blue CU2. line) The were CU14 the and theonly CU6 schemes (orange that line) tend schemesed to were overestimate only slightly the better rain. than The theCU14 CU2. and the CU6 (orange line) schemes were only slightly better than the CU2. The CU14 and the CU6 (orange line) schemesThe analysiswere only shows slightly that better the explicit than the resolution CU2. of convective processes (CU0) was the most reliable and accurate solution with the highest accuracy in terms of threat score and The analysis shows that the explicit resolution of convective processes (CU0) was the equitable threat score. most reliable and accurate solution with the highest accuracy in terms of threat score and The Betts–Miller–Janic scheme (CU2) was the worst and was the one that also gener- equitable threat score. ated the highest number of false alarms (FARs). The new simpliﬁed Arakawa–Schubert The Betts–Miller–Janic scheme (CU2) was the worst and was the one that also gener- (CU14) and Tiedtke (CU 6) schemes were only slightly better than the BMJ (CU2). The new ated the highest number of false alarms (FARs). The new simplified Arakawa–Schubert Kain–Fritsch (CU1), the Grell–Devenyi (CU3), and the Grell 3D (CU 5) schemes were the (CU14) and Tiedtke (CU 6) schemes were only slightly better than the BMJ (CU2). The only schemes that tended to overestimate the rain. The new Kain–Fritsch scheme (CU1), new Kain–Fritsch (CU1), the Grell–Devenyi (CU3), and the Grell 3D (CU 5) schemes were the only schemes that tended to overestimate the rain. The new Kain–Fritsch scheme (CU1), except for an excessive BIAS overlapping, was found to have good overall behavior and was the one that showed the maximum POD (probability of detection).

5. Conclusions The physical parameterization of the convective schemes plays a fundamental role in optimizing the performance of limited area meteorological models, especially in cases of extreme meteorological events. In the case study investigated, the goal was to evaluate which simulation provided the best performance in spatially locating an extreme event as a function of the physical parameterization of the convective patterns. For this purpose, we considered the extreme event recorded in Sicily on 25 November 2016 as a case study. It was shown that the only evaluation by visual analysis (called “Eyeball” verification) was not sufficient to establish which simulation was the best performing. Therefore, a statistical study through the use of the contingency table was found to be fundamental. The study highlighted that the explicit resolution of the convective schemes (CU0) provided the best simulation for the spatial forecast of the extreme meteorological event. This result was expected from the literature, because most convective clouds have horizontal dimensions ranging from 0.1 to 10 km, generally smaller than those of the spatial grid of the limited area model (5 km) used in this case study (typical sub-grid phenomenon).

Atmosphere 2021, 12, 616 12 of 13

except for an excessive BIAS overlapping, was found to have good overall behavior and was the one that showed the maximum POD (probability of detection).

5. Conclusions The physical parameterization of the convective schemes plays a fundamental role in optimizing the performance of limited area meteorological models, especially in cases of extreme meteorological events. In the case study investigated, the goal was to evaluate which simulation provided the best performance in spatially locating an extreme event as a function of the physical parameterization of the convective patterns. For this purpose, we considered the extreme event recorded in Sicily on 25 November 2016 as a case study. It was shown that the only evaluation by visual analysis (called “Eyeball” veriﬁcation) was not sufﬁcient to establish which simulation was the best performing. Therefore, a statistical study through the use of the contingency table was found to be fundamental. The study highlighted that the explicit resolution of the convective schemes (CU0) provided the best simulation for the spatial forecast of the extreme meteorological event. This result was expected from the literature, because most convective clouds have horizontal dimensions ranging from 0.1 to 10 km, generally smaller than those of the spatial grid of the limited area model (5 km) used in this case study (typical sub-grid phenomenon).

Author Contributions: All authors contributed to conceptualization, methodology, investigation, writing, reviewing, and editing of the present work. Writing—review & editing, G.C., M.T.C., F.C. and S.M. All authors have read and agreed to the published version of the manuscript. Funding: This work is to be framed within the Progetto di Ricerca e Sviluppo “Impiego di tec- nologie, materiali e modelli innovativi in ambito aeronautico (AEROMAT)”, Asse II “Sostegno all’innovazione”, Area di Specializzazione “Aerospazio” Avviso n. 1735/Ric del 13 luglio 2017— Codice CUP J66C18000490005, codice identificativo Progetto ARS01_01147 nell’ambito del Pro- gramma Operativo Nazionale “Ricerca e Innovazione” 2014–2020 (PON R&I 2014–2020). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors wish to acknowledge the Regional Department of Civil Protection (DRPC) of Sicily and the Italian Air Force Meteorological Service for the observed rainfall data and maps provided. Conflicts of Interest: The authors declare no conflict of interest.

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