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International Journal of Geo-Information

Article Spatio-Temporal Analysis of Intense Convective Tracks in a Densely Urbanized Italian Basin

Matteo Sangiorgio 1 and Stefano Barindelli 2,* 1 Department of Electronics, Information, and Bioengineering, Politecnico di Milano, 20133 Milan, Italy; [email protected] 2 Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milan, Italy * Correspondence: [email protected]

 Received: 4 February 2020; Accepted: 22 March 2020; Published: 24 March 2020 

Abstract: Intense convective storms usually produce large rainfall volumes in short time periods, increasing the risk of floods and causing damages to population, buildings, and infrastructures. In this paper, we propose a framework to couple visual and statistical analyses of convective at the basin scale, considering both the spatial and temporal dimensions of the process. The dataset analyzed in this paper contains intense convective events that occurred in seven (2012–2018) in the Seveso-Olona-Lambro basin ( of Italy). The data has been acquired by MeteoSwiss using the Radar Tracking (TRT) algorithm. The results show that the most favorable conditions for the formation of convective events occur in the early afternoon and during summertime, confirming the key role of the in . The orography emerged as a driver for convection, which takes place more frequently in mountain areas. The paths analysis shows that the predominant direction is from South-West to North-East. Considering storm duration, long-lasting events reach higher values of radar reflectivity and cover more extended areas than short-lasting ones. The results obtained can be exploited for many practical applications including nowcasting, alert systems, and sensors deployment.

Keywords: data exploration; convective thunderstorms; radar; spatio-temporal statistics

1. Introduction Convective storms are a typical source of rainfall in many regions, especially during periods. The causes behind these phenomena are not completely known due to the complexity of the physical processes behind them, that jointly involves spatial and temporal aspects at different scales [1]. Several research studies tried to improve the understanding of convective storm mechanisms by collecting and analyzing observations of the past few decades. Radar-based climatology has been developed to clarify convective storm behaviors, distributions, and frequencies in different domains and environments [2–6]. Intense convective storms can cause adverse effect such as floods, landslides, , and strong winds. These extreme natural events, that will increase in frequency due to change [7,8], cause not only huge economic damages, but also significant losses. In the period 1994–2013, 6,863 natural disasters occurred worldwide, and more than 70% have been strictly related to severe rainfall events: 2,937 floods, and 1,942 storms. These phenomena affected 3 billion people, causing almost 310,000 deaths (30% of the human losses due to natural disasters), and more than 1,500 billion US$ of economic damages (60% of the total) [9]. It is thus fundamental to gain a better understanding of the physical processes behind convective storms. This is usually done by investigating the causes and the atmospheric mechanisms which originate these phenomena [10–12] and identifying the most critical areas by monitoring past

ISPRS Int. J. Geo-Inf. 2020, 9, 183; doi:10.3390/ijgi9030183 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2020, 9, 183 2 of 14 events [13–15]. Among all the drivers that concur in the formation of such convective events, the temperature has a key role [16,17]. For this reason, global warming caused by climate change [18–24] could potentially strongly affect the behavior of such storms. The convective storms usually interest limited areas, and their duration is almost always less than two hours [25]. Despite that, they often reach higher intensity in less time than orographic and frontal storms, originating fast but intense rainfalls, which are the worst case for the flood protection systems and other hydraulic infrastructures (e.g., sewer and subterranean urban streams) [26,27]. Researchers are trying to enhance the forecasting performances of convective rainfall events, integrating information extracted by the dataset available nowadays which couple traditional and innovative meteorological variables [28,29]. Other authors proposed to adopt a different paradigm, switching from the conventional physically-based meteorological model to more recent machine learning techniques [30–34] to exploit the huge amount of available data. A better understanding of the physical processes and the features characterizing convective events is important, to better define the equation of the physically based models on the one hand, and to properly select inputs and structure of the machine learning tools on the other. The dataset considered in this paper has been acquired using the Thunderstorm Radar Tracking (TRT) algorithm developed by MeteoSwiss [35,36]. This algorithm couples traditional and innovative techniques and allows us to acquire the position of convective cells and follow their evolution through time. The result of the data acquisition process is a sequence of snapshots, one every five minutes, containing the convective cells characterized by a radar reflectivity exceeding a given threshold. Once acquired, the dataset can be used by the meteorologists to perform a visual analysis in order to examine the behavior of the convective cells and the relationships among different weather features [37]. Visualizing the sequence of snapshots is useful but working in this way the spatial and temporal dimensions of the process evolve at the same time. The main goal of our work consists of synthesizing general features of the behavior of the convective cells that occurred in the Lambro, Seveso, and Olona catchments in Northern Italy from 2012 to 2018. To do that, we performed statistical analyses splitting the spatial and the temporal aspects in order to focus on a single dimension. The spatial analysis allows us to visualize the high-risk areas, which could provide useful insights on how to deploy a meteorological monitoring network. It also allows us to obtain the climatology of the area of interest [38,39]. Conversely, the temporal dimension helps to visualize how the events are distributed within the month of the , or within the hour of the day [24]. Coupling a visual and statistical exploration of the big data available can open an innovative perspective in the comprehension of meteorological aspects behind intense events [40]. The rest of this article is organized as follows. In Section2, we briefly present some relevant features of the considered study area, and describe the convective thunderstorm events dataset. Section3 reports the results of the statistical and graphical analysis performed, focusing on the spatial and temporal dimensions, and on the thunderstorm life cycle. In Section4, we discuss the results obtained, and we draw some concluding remarks.

2. Materials and Methods

2.1. Study Area The study area includes the hydrological basins of Seveso, Olona, and Lambro rivers and lies in the Northern part of Italy: latitude spans from 45.37 N to 45.93 N, and longitude from 8.77 E to 9.40 E, with an extension of approximately 1400 km2 (Figure1). ISPRS Int. J. Geo-Inf. 2020, 9, 183 3 of 14 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 3 of 14

Figure 1. A geographical overview of the study area. The black line represents the watershed, and the lightFigure blue 1. linesA geographical represent rivers overview and of streams the study inside area. the The area. black line represents the watershed, and the light blue lines represent rivers and streams inside the area. According to the Koppen classification [41], the study area is characterized by a temperate climate with typicalAccording patterns to the of Koppen the mid-latitude classification regions [41], (Cfa the instudy the Koppenarea is characterized notation). It by is dominateda temperate by theclimate presence with of typical the Italian patterns Prealps of the in mid-latitude the northern regi part,ons Milan(Cfa in municipality the Koppen notation). in the southern It is dominated part, and anby almost the presence flat area of in the the Italian middle Prealps with ain strong the northe connotationrn part, Milan of urban municipality sprawl. It in is the frequently southern aff part,ected byand convective an almost cells, flat especiallyarea in the during middle summer, with a strong due to connotation its peculiar of morphology. urban sprawl. Quite It is often, frequently humid airaffected remains by forconvective long periods cells, especially in the Po’ during Valley summer, and is dragged due to its by peculiar an uplift morphology. mechanism Quite triggered often, by surfacehumid heating air remains by thefor sun.long periods The northern in the Po’ part Valley of the and considered is dragged area by an is windieruplift mechanism (quite often triggered during winterby surface foehn heating rises) thanby the the sun. southern The northern part, which part of is the characterized considered area by frequent is windier foggy (quite days often and during strong thermalwinter inversions.foehn rises) than the southern part, which is characterized by frequent foggy days and strong thermalAll these inversions. local drivers contribute to the vulnerability of the studied area from a hydrological All these local drivers contribute to the vulnerability of the studied area from a hydrological perspective, and the need to understand deeply convective thunderstorms patterns, that quite often perspective, and the need to understand deeply convective thunderstorms patterns, that quite often lead to high economic losses here. lead to high economic losses here. 2.2. Convective Rain Dataset 2.2. Convective Rain Dataset The convective rain dataset analyzed in this paper has been sampled with the MeteoSwiss TRT The convective rain dataset analyzed in this paper has been sampled with the MeteoSwiss TRT algorithm. This algorithm is fed with data recorded by the Swiss radar network. The closest radar algorithm. This algorithm is fed with data recorded by the Swiss radar network. The closest radar to to the region of study is located at Monte Lema (1626 m a.s.l.) in the Canton Ticino. Due to the the region of study is located at Monte Lema (1626 m a.s.l.) in the Canton Ticino. Due to the orography orography of the area of interest and the radar position, there are no limitations in terms of coverage of the area of interest and the radar position, there are no limitations in terms of coverage and and blockage [42,43]. blockage [42,43]. The dataset employed in this study spans the seven years from 2012 to 2018. The time resolution The dataset employed in this study spans the seven years from 2012 to 2018. The time resolution at which data were recorded was five minutes, while the spatial resolution was 2 km. The algorithm at which data were recorded was five minutes, while the spatial resolution was 2 km. The algorithm was designed to identify convective cells, and it is based on an adaptive thresholding scheme which was designed to identify convective cells, and it is based on an adaptive thresholding scheme which allows the detection of convective cells depending on their development phase [34]. Convective cells allows the detection of convective cells depending on their development phase [34]. Convective cells 2 areare considered considered intense intense and and thus thus detected detected if if they they reach reach an an area area of of 16 16 km kmat2 at a a minimum minimum reflectivity reflectivity of of 36 dBZ36 dBZ and and at least at least one one pixel pixel inside inside them them attains attains 42 42 dBZ. dBZ. These These eventsevents areare thus detected at at a a variable variable threshold,threshold, depending depending on on their their development development phase.phase. This allows allows the the detection detection of of thunderstorms thunderstorms at at an an earlyearly stage stage of of their their life life cycles cycles at at thethe lowestlowest possiblepossible reflectivityreflectivity threshold, i.e. i.e. 36 36 dBZ, dBZ, as as well well as as in in the the maturemature phase phase at at a a higher higher threshold threshold [ 34[34].]. AdoptingAdopting this this technique, technique, thunderstorms thunderstorms can can be be tracked tracked very very early early during during their their growing growing phase phase as wellas well as in as the in maturethe mature stage, stage, and and trajectories trajectories are createdare created from from a sequence a sequence of radar of radar images images [34]. [34]. For For each convectiveeach convective cell and cell each and timeeach step,time thestep, dataset the dataset consists consists of a uniqueof a unique identification identification number, number, date date and timeand of time detection, of detection, coordinates coordinates of the of center the center of gravity of gravity of the of cell, the velocity cell, velocity of the of cell, the area cell, coveredarea covered by the cellby asthe a cell polygon as a polygon feature, feature, and mean and and mean maximum and maximum reflectivity reflectivity recorded. recorded. FigureFigure2 shows2 shows an an intuitive intuitive way way to to visualize visualize the the dataset.dataset. TheThe wholewhole sequence of of snapshots, snapshots, in in principle,principle, could could be be plotted plotted one one afterafter thethe otherother with th thee desired temporal temporal step. step. In In this this case, case, 10 10 minutes. minutes. ThisThis methodology methodology could could be be usefuluseful toto interpretinterpret convectiveconvective events belonging belonging to to a a particular particular temporal temporal

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ISPRSISPRS Int. J. Geo-Inf.Int. J. Geo-Inf. 2019, 82019, x FOR, 8, x PEER FOR PEERREVIEW REVIEW 4 of 14 4 of 14 window visually, but it is not appropriate for long period analysis to understand systematic patterns windowduringwindow visually, convection visually, but it phasesbut is not it is appropriate not appropriate for long for longperiod period analysis analysis to understand to understand systematic systematic patterns patterns duringduring convection convection phases phases

FigureFigure 2. An 2.example An example of visualization of visualization of three of threesnapshots snapshots of convective of convective storms storms event event that occurred that occurred on on Figure 2. An example of visualization of three snapshots of convective storms event that occurred 9 August9 August 2018 2018(10:10 (10:10 pm, left;pm, 10:20left; 10:20pm, center;pm, center; 10:30 10:pm,30 right).pm, right). The blackThe blackline representsline represents the the on 9 August 2018 (10:10 pm, left; 10:20 pm, center; 10:30 pm, right). The black line represents the watershed,watershed, the yellow the yellow dots aredots the are centers the centers of gravit of gravity, whiley, while the blue the polygonsblue polygons represent represent convective convective watershed, the yellow dots are the centers of gravity, while the blue polygons represent convective cells. cells. cells. A viable alternative consists in showing all the center of gravity trajectories on the same map A viableA viable alternative alternative consists consists in showing in showing all the all center the center of gravity of gravity trajectories trajectories on the on same the same map map (Figure3). This procedure could be useful in visualizing a limited number of events, but it turns out to (Figure(Figure 3). This 3). Thisprocedure procedure could could be useful be useful in visualizing in visualizing a limited a limited number number of events, of events, but it but turns it turns out out be inappropriate due to the high number of records stored in the dataset. The plot reported in Figure3 to beto inappropriate be inappropriate due todue the to high the highnumber number of reco of rdsreco storedrds stored in the in dataset. the dataset. The plotThe reportedplot reported in in does not help to synthesize any general features of the convective storms paths. FigureFigure 3 does 3 doesnot help not helpto synthesize to synthesize any genera any general featuresl features of the of convective the convective storms storms paths. paths.

FigureFigureFigure 3. Convective 3. 3.Convective Convective events eventsevents born borninsideborn insideinside (pink) (pink) and outsid and outsid outsidee (lighte (light (lightblue) blue)the blue) region the the region regionof interest of of interest interest between between between 20122012 and2012 and2018. and 2018. 2018.Subsequent Subsequent Subsequent centers centers centers of gravity’s of of gravity’s gravity’s position positions positions of the ofs of thesame the same sameevent event event are are linked are linked linked with with awith straight a straight a straight line. line. line. For this reason, a well-designed data visualization approach, able to highlight different aspects ofFor the thisFor ongoing reason,this reason, process, a well-designed a well-designed is the key data to retrieving datavisualization visualization useful approach, information approach, able toable hidden highlight to highlight in thedifferent data. different aspects This aspects task has of thebeenof ongoing the faced ongoing usingprocess, process, Python is the is libraries key the tokey retrieving for to dataretrieving visualization useful useful information information (Matplotlib hidden hidden [44 in], Seabornthe in data. the data. [This45]) andThistask forhastask spatial has been beenfaced faced using using Python Python libraries libraries for data for datavisualization visualization (Matplotlib (Matplotlib [44], Seaborn[44], Seaborn [45]) [45])and forand spatial for spatial

ISPRS Int. J. Geo-Inf. 2020, 9, 183 5 of 14 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 5 of 14 analysisanalysis (GeoPandas(GeoPandas [[46],46], GeoplotGeoplot [[47],47], CartopyCartopy [[48],48], GDALGDAL [[49],49], ShapelyShapely [[50]),50]), togethertogether withwith QGISQGIS softwaresoftware [[51].51].

3.3. ResultsResults TheThe primaryprimary focusfocus ofof thisthis workwork waswas toto visualizevisualize thethe keykey characteristicscharacteristics ofof thethe datadata andand eliminateeliminate misleadingmisleading interpretations.interpretations. WithWith thisthis aim,aim, the temporaltemporal and spatial scales were considered separately. InIn thethe followingfollowing twotwo subsections,subsections, aa couplecouple ofof didifferfferentent setssets ofof figuresfigures areare presented:presented: thethe firstfirst dealsdeals withwith thethe spatialspatial distributiondistribution ofof thethe data,data, andand thethe secondsecond focusesfocuses onon thethe temporaltemporal dimensiondimension ofof thesethese phenomena.phenomena. TheThe lastlast subsectionsubsection providesprovides anan analysisanalysisof of thethe storm’sstorm’s lifelife cyclecycle consideringconsidering thethe durationduration ofof thethe eventsevents andand howhow itit isis relatedrelated toto thethe reflectivityreflectivity and and the the area area of of the the convective convective thunderstorms. thunderstorms.

3.1.3.1. SpatialSpatial FocusFocus TheThe simplestsimplest attemptattempt toto derivingderiving aa spatialspatial visualizationvisualization consistsconsists ofof plottingplotting thethe distributiondistribution ofof allall thethe availableavailable centerscenters ofof gravitygravity insideinside thethe studystudy area,area, producingproducing aa heatmap.heatmap. StartingStarting fromfrom thisthis setset ofof pointpoint features,features, aa probabilityprobability distributiondistribution adoptingadopting thethe standardstandard KernelKernel DensityDensity EstimationEstimation (KDE)(KDE) techniquetechnique providedprovided byby SeabornSeaborn library library was was estimated estimated (Figure (Figure4 ).4).

FigureFigure 4.4. Distribution ofof allall points.points. Light hue indicates high density, darkdark huehue lowlow density.density.

FigureFigure4 4 highlights highlights the the areas areas more more frequently frequently a affffectedected byby thethe considered convective phenomena. AsAs alreadyalready underlinedunderlined inin previousprevious research,research, thethe spatialspatial distributiondistribution followsfollows thethe orographyorography ofof thethe basinbasin [[52].52]. TheThe higherhigher densitiesdensities werewere observedobserved inin thethe NorthNorth partpart ofof thethe basin,basin, nearnear thethe Prealps.Prealps. TheThe lowerlower valuesvalues inin thethe South-WestSouth-West portionportion werewere probablyprobably due due to to drydry windswinds comingcoming fromfrom thethe ApenninesApennines mountains.mountains. TheThe main main drawback drawback of thisof this graph graph is that is it that mixes itall mixes the points, all the hiding points, behind hiding the orographicbehind the eorographicffect some interestingeffect some patterns. interesting Figure patterns.4 could beFigu veryre useful4 could for thebe purposevery useful of deploying for the purpose a network of ofdeploying meteorological a network sensors. of meteorologic Locating themal sensors. where the Locating occurrence them of where intense the rain occurrence events is moreof intense probable rain couldevents give is more useful probable forecast could insights. give useful forecast insights. FigureFigure4 4 reports reports aa staticstatic representation of the the data dataset,set, not not allowing allowing us us to to figure figure out out which which are are the themost most frequent frequent paths paths followed followed by by the the convective convective ce cells.lls. For For this this reason, reason, an an analysis analysis of thethe averageaverage trajectoriestrajectories ofof thethe convectiveconvective cells’cells' centerscenters ofof gravitygravity waswas reportedreported inin FigureFigure5 .5. On On average, average, these these trajectoriestrajectories were were oriented oriented from from South-West South-West to North-Eastto North-East due due to local to local interaction interaction of the of air the masses air masses with orographywith orography and morphology and morphology of the of region. the region. This pattern This pattern has been has extensively been extensiv analyzedely analyzed in [24] in and [24] it wasand confirmedit was confirmed by our analysisby our analysis that the mid-troposphericthat the mid-tropospheric wind, coupled wind, withcoupled the amountwith the of amount moisture, of ismoisture, the main is cause the main for this cause preferential for this direction,preferential while direction, local breeze while systemlocal breeze only asystemffects probably only affects the triggeringprobably the areas. triggering Due to areas. the natural Due to configuration the natural configuration of the region, of South-West the region, South-West winds carry winds air masses carry air masses rich in water vapor originating from the Mediterranean Sea, generating more favorable conditions for convection processes. Conversely, the presence of the Alps is a strong orographic

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ISPRSISPRS Int.Int. J.J. Geo-Inf.Geo-Inf. 20192019,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 6 6 ofof 1414 rich in water vapor originating from the Mediterranean Sea, generating more favorable conditions for convectionobstacleobstacle toto air processes.air massmass fluxflux Conversely, comingcoming fromfrom the North-West presenceNorth-West of the directions.directions. Alps is a ThisThis strong isis anotanot orographicherher reasonreason obstacle whywhy South-WestSouth-West to air mass fluxwindswinds coming areare thethe from mainmain North-West driverdriver ofof convectiveconvective directions. thunderstorms.thunderstorms. This is another reason why South-West winds are the main driver of convective thunderstorms.

Figure 5. Representation of the average vector field of convective events born outside the basin. Figure 5. Representation of the average vector field field of convective events bornborn outside the basin.

3.2.3.2. Temporal Temporal FocusFocus WhileWhile consideringconsideringconsidering meteorological meteorologicalmeteorological phenomena, phenomena,phenomena, it is itit also isis alsoalso important importantimportant to evaluate toto evaluateevaluate the temporal thethe temporaltemporal aspect ofaspectaspect their ofof dynamics. theirtheir dynamics.dynamics. A visual AA analysis visualvisual analysisanalysis would help wouldwould to spot helphelp some toto spotspot temporal somesome tempor structures,temporalal structures,structures, such as daily suchsuch and asas annualdailydaily andand periodicity, annualannual periodicity,periodicity, and possible andand increasing possiblepossible/ decreasing increasing/decreasingincreasing/decreasing trends. Figure trends.trends.6 reports FigureFigure the 66 annual reportsreports distribution thethe annualannual ofdistributiondistribution convective ofof events. convectiveconvective The maximumevenevents.ts. TheThe number maximummaximum of convective numbernumber ofof cells convecconvec (1119)tivetivewas cellscells recorded (1119)(1119) waswas during recordedrecorded 2014, whileduringduring values 2014,2014, forwhilewhile the valuesvalues remaining forfor thethe years remainingremaining span from yearsyears 600 spanspan to 900. fromfrom 600600 toto 900.900.

Figure 6. Distribution of the events per year. FigureFigure 6.6. DistributionDistribution ofof thethe eventsevents perper year.year. As expected, the convective events also exhibit a seasonal periodicity (Figure7). Convective As expected, the convective events also exhibit a seasonal periodicity (Figure 7). Convective eventsAs occur expected, only duringthe convective andevents summer also exhibi (fromt Aprila seasonal to September), periodicity suggesting (Figure 7). that Convective they are events occur only during spring and summer (from April to September), suggesting that they are stronglyevents occur related only to during high-temperature spring and summer values. Of(from course, April it to is duringSeptember), these suggesting two , that especially they are strongly related to high-temperature values. Of course, it is during these two seasons, especially summer,strongly related that solar to radiationhigh-temperature reaches itsvalues. peak. Of The co diurnalurse, it temperatureis during these during two theseseasons, months especially leads summer, that solar radiation reaches its peak. The diurnal temperature during these months leads to tosummer, a strong that increase solar radiation in surface reaches temperature its peak. that The aff diurnalects the temperatur lower atmospherice during these layer months by warming leads upto a strong increase in surface temperature that affects the lower atmospheric layer by warming up atmospherica strong increase masses. in surface This is atemperature typical unstable that situationaffects the favorable lower atmospheric to convection layer processes, by warming where up air atmospheric masses. This is a typical unstable situation favorable to convection processes, where air withatmospheric low temperature masses. This is above is a typical air with unstable high temperature. situation favorable Other researchto convection on convective processes, rain where events air with low temperature is above air with high temperature. Other research on convective rain events showwith low similar temperature results for is other above locations air with [ 53high–56 temper]. ature. Other research on convective rain events showshow similarsimilar resultsresults forfor otherother locationslocations [53–56].[53–56].

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Figure 7. Monthly distributions of average temperature (data provided by ARPA Lombardia) and Figure 7.7. Monthly distributions of average temperatur temperaturee (data provided by ARPA Lombardia)Lombardia) and convective events. convective events.events.

The half-violin plot in Figure8 confirms the seasonality of convective events but shows that the The half-violin plot in Figure 8 confirms the seasonality of convective events but shows that the distribution across years is quite different. It sometimes has a quasi-bimodal shape. The first peak is in distribution across years is quite different. It sometimes has a quasi-bimodal shape. The first peak is late spring/early summer, while the second is at the end of the summer. In other cases, the distribution in late spring/early summer, while the second is atat thethe endend ofof thethe summer.summer. InIn otherother cases,cases, thethe is unimodal, as in 2014 and 2016, with a high number of convective events lumped in a single period in distribution is unimodal, as in 2014 and 2016, with aa highhigh numbernumber ofof convectiveconvective eventsevents lumpedlumped inin aa the middle of summer. The reasons behind these behaviors should be investigated in future research single period in the middle of summer. The reasons behind these behaviors should be investigated making use of a longer time series. in future research making use of a longer time series.

Figure 8. Distribution of the events per day of the year. Figure 8. Distribution of the events per day of the year. The effect of the temperature on the occurrence of convective cells is suggested also at the daily The eeffectffect ofof thethe temperaturetemperature onon thethe occurrenceoccurrence ofof convectiveconvective cells is suggested also at the daily scale, as reported in Figure 9. Most of the convective cells occur in the afternoon, with a peak between scale, as reported inin FigureFigure9 9.. MostMost ofof thethe convectiveconvective cellscells occuroccur inin thethe afternoon,afternoon, withwith aa peakpeak betweenbetween 14:00 and 16:00 local time, where the highest number of convective events was recorded (about 400). 14:0014:00 andand 16:00 local time, where the highest number of convective events wa wass recorded (about 400). Given the fact that, in the considered area, the values of daily surface temperature usually reach its Given the fact that, that, in in the the considered considered area, area, the the va valueslues of of daily daily surface surface temperature temperature usually usually reach reach its maximum from 13:00 to 14:00, the time lag between the peaks of and the number of itsmaximum maximum from from 13:00 13:00 to 14:00, to 14:00, the the time time lag lag between between the the peaks peaks of oftemperatures temperatures and and the the number number of convective events could be related to the thermal inertia of the soil surface. Moreover, once the ofconvective convective events events could could be be related related to to the the thermal thermal inertia inertia of of the the soil soil surface. Moreover, Moreover, once thethe temperature is high enough to allow the breaking of the boundary layer inversion, thermals can reach temperaturetemperature is is high high enough enough to to allo alloww the the breaking breaking of the of theboundary boundary layer layer inversion, inversion, thermals thermals can reach can the lifting condensation level, which represents the limit over which the becomes reachthe lifting the lifting condensation condensation level, level, which which represents represents the the limit limit over over which which the the atmosphere atmosphere becomesbecomes unstable [24]. unstable [[24].24].

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FigureFigure 9. Daytime9. 9. DaytimeDaytime distribution distribution distribution of temperatureof temperature of temperature (data (data provided pr (dataovided by provided byARPA ARPA Lombardia) by Lombardia) ARPA and Lombardia) and convective convective and events.events.convective events.

FigureFigure 10 10shows shows a data a data visualization visualization visualization focusing focusing on onthe the the monthly monthly monthly distribution distribution distribution of theof of the the events events events crossing crossing crossing thethethe watershed watershed watershed boundary. boundary. boundary. The The The convective convective convective cells, cells, cells, and and and the the the related related related centers centers centers of gravity,of of gravity, gravity, have have been been split split split into into into twotwotwo categories: categories: those thosethose belonging belongingbelonging to to toevents events events born born born ou outside tsideoutside and and and heading heading heading inside inside inside the the watershed watershed (IN),(IN), (IN), andand and the thetheother other other ones ones ones belonging belonging belonging to to events eventsto events born born born inside inside inside and and and heading heading heading outside outside outside the the watershedthe watershed watershed (OUT). (OUT). (OUT).

Figure 10. Monthly distribution of the events born inside heading outside (OUT) and born outside FigureFigure 10. 10.MonthlyMonthly distribution distribution of the of theevents events born born inside inside heading heading outside outside (OUT) (OUT) and and born born outside outside heading inside (IN) the basin per month. Orange refers to IN events, blue to OUT ones, while brown headingheading inside inside (IN) (IN) the thebasin basin per per month. month. Orange Orange refers refers to IN to INevents, events, blue blue to OUT to OUT ones, ones, while while brown brown bars represent overlapping areas. The watershed border has been split into six different sectors. barsbars represent represent overlapping overlapping areas. areas. The The watershed watershed border border has has been been split split into into six sixdifferent different sectors. sectors.

ThisThis representation representationrepresentation is is isparticularly particularly particularly interestinginteresting interesting fromfrom from a meteorologicala meteorologicala meteorological point point ofpoint view, of ofview, since view, itsince suggestssince it it suggestssuggeststhe main the the directions main main directions directions of the storm of theof the trajectories storm storm trajectories trajectories for each for month. for each each Mostmonth. month. of Most the Most cells of theof that the cells enter cells that the that enter basin enter the come the basinbasinfrom come thecome from South-West. from the the South-West. South-West. It was interesting It was It was interesting interesting to notice to that noticeto notice the peakthat that the number the peak peak number of number the IN of category theof the IN IN category in category sector 1 in sectorin sector 1 happens 1 happens in August,in August, while while for for sector sector 2 it 2 is it in is June.in June. This This seems seems to suggestto suggest that that the the circulation circulation patternspatterns that that are are causing causing these these events events are are slightly slightly different, different, probably probably due due to ato seasonal a seasonal related related effect. effect.

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ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 9 of 14 happens in August, while for sector 2 it is in June. This seems to suggest that the circulation patterns thatAgain, are according causing these to the events findings are in slightly Figure di5, fftheerent, majority probably of the due events to a belonging seasonal related to the OUT effect. category Again, accordingcrosses sectors to the 3, findings 4, and 5. in In Figure particular,5, the majorityfor sectors of 3, the 4, events5, and belonging6, the OUT to peaks the OUT happen category in June. crosses As a sectorsgeneral 3,consideration, 4, and 5. In particular, the number for sectorsof events 3, 4, born 5, and inside 6, the the OUT watershed peaks happen is slightly in June. less As than a general those consideration,coming from outside. the number In sectors of events 1 and born 2, the inside number the watershed of the IN isevents slightly is higher less than than those the comingOUT events; from outside.in sector In3 and sectors 4, the 1 and number 2, the of number the OUT ofthe events IN events is always is higher higher than than the the OUT IN events;ones; while in sector in sectors 3 and 4,5 theand number 6, the number of the OUTof OUT events events is always are larger higher than than IN theones, IN except ones; whilefor April in sectors and May. 5 and This 6, theis probably number ofdue OUT to eventsthe location are larger of this than sector, IN ones, with except respect for April to the and preferential May. This is direction probably dueof the to theconvective location ofthunderstorms. this sector, with It respectis oriented to the through preferential the Nort directionh-West of thewhere, convective additionally, thunderstorms. there are Itthe is orientedPrealps throughmountains. the When North-West analyzing where, these additionally, mesoscale there phenom are theena, Prealps local factors mountains. and the When interaction analyzing between these mesoscalecells themselves phenomena, plays a localkey role factors in the and dynamics the interaction of cell betweendisplacements cells themselves and triggering. plays a key role in the dynamics of cell displacements and triggering. 3.3. Storm Lifecycle Analysis 3.3. Storm Lifecycle Analysis An additional analysis relative to the convective thunderstorm life cycle has been performed. FigureAn 11 additional reports the analysis distribution relative of the to the events' convective duration. thunderstorm The duration life of cycle the convective has been performed.events has Figurean exponential 11 reports distribution. the distribution Ninety of thepercent events’ of duration.the events The last durationfrom 20 minutes of the convective to two hours. events has an exponential distribution. Ninety percent of the events last from 20 minutes to two hours.

Figure 11. Distribution of the event duration.

Other interesting insights on the convective eventsevents lifecycle can be obtained by looking at how the distributiondistribution ofof the the spatial spatial statistics statistics of of the the thunderstorm thunderstorm (mean (mean and and maximum maximum reflectivity reflectivity and area)and variesarea) varies as a function as a function of the eventof the duration.event duration. Note that Note we that limit we our limit analysis our analysis between between 20 and 150 20 minutesand 150 (95%minutes of the (95% events of the are events within are this within range) this in orderrange) to in guarantee order to guarantee the statistical the significancestatistical significance of the results. of the results.The mean reflectivity (Figure 12, left) has a slightly increasing trend and relatively low variability. This isThe due mean to the reflectivity filtering eff ect(Figure of performing 12, left) thehas meana slightly across increasing the spatial dimension.trend and relatively low variability.The trend This of is thedue maximumto the filtering reflectivity effect of (Figure performing 12, center) the mean is quite across di thefferent. spatial Half dimension. of the data (betweenThe trend the 0.25 of andthe 0.75maximum quantile) reflecti are invity the (Figure range 46–53 12, center) dBZ for is shortquite events different. (20–25 Half minutes). of the data The range(between between the 0.25 the and 0.25 0.75 and quantile) 0.75 quantile are in shiftsthe range to higher 46–53 values dBZ for if weshort consider events (20–25 events minutes). that last for The a longerrange between period. Forthe instance,0.25 and events0.75 quantile lasting forshifts one to hour higher usually values assume if we reflectivityconsider events values that in thelast range for a oflonger 50–56 period. dBZ. TheFor variabilityinstance, events is not lasting affected for by one the ho duration.ur usually assume reflectivity values in the range of 50–56Conversely, dBZ. The the variability area interested is not affected by convective by the cellsduration. (Figure 12, right) is highly dependent on the durationConversely, of the thunderstorm the area interested event. Anotherby convective peculiar cell features (Figure characterizing 12, right) is highly this distribution dependent is on that the it isduration not symmetric. of the thunderstorm The median event. is closer Another to the peculiar 0.25 quantile feature than characterizing to the 0.75 quantile. this distribution The latter is that is a criticalit is not feature, symmetric. because The there median is a is higher closer probability to the 0.25 ofquantile having than an event to the characterized 0.75 quantile. by The an unusuallylatter is a largecritical areal feature, extension, because than there one is witha higher an unusually probability small of having extension. an event characterized by an unusually large areal extension, than one with an unusually small extension.

ISPRS Int. J. Geo-Inf. 2020, 9, 183 10 of 14 ISPRS Int. J. Geo-Inf. 2019, 8, x FOR PEER REVIEW 10 of 14

FigureFigure 12. 12.Distribution Distribution of mean of mean reflectivity reflectivity (left), maximum (left), ma reflectivityximum reflectivity (center), and (center the thunderstorm), and the areathunderstorm (right) as a area function (right of) as the a event function duration. of the event The line duration. represents The the line median represents of the the data. median The shadedof the areadata. covers The shaded the interval area covers between the 0.25 interval and 0.75between quantiles. 0.25 and 0.75 quantile s.

AnAn increase increase in inthe theduration duration ofof convective events events,, leads leads to to an an increase increase in in the the mean mean and and maximum maximum reflectivityreflectivity and and of of the the area area involved involved inin thethe convectionconvection process. The The combination combination of of a asynchronized synchronized growthgrowth of of the the reflectivity, reflectivity, which which is is strictly strictly related related to to the the rainfall rainfall intensity, intensity, and and of of the the areal areal extension extension of theof the convective convective cells, cells, strongly strongly increases increases the the rainfall rainfall volume. volume. Consequently,Consequently, the the probability probability of of facing facing dangerousdangerous situations, situations i.e., i.e. intenseintense rainfall over a large area, area, is is much much higher higher in in long long-lasting-lasting storm stormss than than inin short-lasting short-lasting ones. ones.

4.4. Discussion Discussion InIn this this paper, paper, wewe performedperformed aa comprehensivecomprehensive analysis analysis of of the the convective convective rainfall rainfall events events that that occurredoccurred in in the the seven seven yearsyearsfrom from 20122012 toto 2018 over the Seveso, Seveso, Olona, Olona, and and Lambro Lambro rivers rivers basin. basin. The The convectiveconvective events events composing composing the the considered considered dataset dataset were wer detectede detected and and tracked tracked by by the the MeteoSwiss MeteoSwiss TRT algorithm,TRT algorithm, which which is fed withis fed radar with data radar collected data collected from the from Swiss the radar Swiss network. radar network. The huge The amount huge of informationamount of information sampled had sampled to be visualized had to be in visualized a way that in points a way out that the points relevant out the properties relevant of properties the dataset. Weof the thus dataset. decoupled We thu thes decouple geospatiald the and geospatial temporal and aspects temporal of the aspects convective of the convective phenomena, phenomena, proposing severalproposing visual several and visual statistical and techniquesstatistical techniques in order to in exploreorder to theexplore available the available data extensively. data extensively Further. analysisFurther wasanalysis dedicated was dedicated to the thunderstorm to the thunderstorm life cycle. life cycle. TheThe visualization visualization of of thethe geospatialgeospatial distribution allowed us us to to highlight highlight areas areas where where convective convective thunderstormsthunderstorms were were moremore frequent. This This static static distribution distribution highly highly correlated correlated with with the orography the orography of the region: frequencies were higher near the Prealps and lower in the southern area of the basin, of the region: frequencies were higher near the Prealps and lower in the southern area of the basin, characterized by a flat . Additional analysis of the trajectories, followed by the convective characterized by a flat landscape. Additional analysis of the trajectories, followed by the convective cells' centers of gravity, shows that the preferable direction is oriented from South-West to North- cells’ centers of gravity, shows that the preferable direction is oriented from South-West to North-East. East. This is due to the meteorological phenomena characterizing the region. South-West winds carry This is due to the meteorological phenomena characterizing the region. South-West winds carry air air masses rich in water vapor originating from the Mediterranean Sea, generating favorable masses rich in water vapor originating from the Mediterranean Sea, generating favorable conditions conditions for convection processes. Conversely, the presence of the Alps does not allow a for convection processes. Conversely, the presence of the Alps does not allow a considerable number considerable number of events coming from the North to come across the region. of events coming from the North to come across the region. The analyses of the temporal patterns confirm that the occurrence of convective events is stronglyThe analyses correlated of to the the temporal surfacepatterns temperature. confirm The that latter the can occurrence thus be considered of convective as eventsone of theis strongly main correlateddrivers of tothe the atmospheric surface temperature. mechanism The generating latter can convective thus be considered cells. The fact as one is demonstrated of the main drivers by the of thedistribu atmospheriction of the mechanism occurrences generating in months convective, and by the cells. intraday The fact average is demonstrated pattern. Theby events the distributiontake place ofonly the occurrences from April in to months, September, and bywith the a intraday daily peak average after pattern. midday The in events correspondence take place with only thefrom Apriltemperature to September, peaks. withThe annual a daily distributions peak after midday of the convective in correspondence events arewith different thetemperature year by year, peaks. and Thethere annual is no distributionsevidence of an of increasing the convective trend events in the number are different of events year byoccurring year, and per there year. is In no this evidence regard, of anthe increasing seven year trend dataset in the available number is probably of events too occurring limited perto robustly year. In investigate this regard, the the presence seven yearor absence dataset availableof increasing is probably trends, toowhich limited could to be robustly induced investigate by climate thechange. presence or absence of increasing trends, whichLastly could, bewe induced performed by climatean analysis change. of the main features of the convective cells' life cycle. The durationLastly, of wethe performed storm life follows an analysis an exponential of the main distribution features of. T thehe events convective usually cells’ last life less cycle. than The30 durationminutes, ofand the onl stormy a limited life follows number an of exponentialcells persist on distribution. the basin for The more events than 2 usually hours. Long last less-lasting than 30cells minutes, usually and reach only higher a limited values number of reflectivity of cells persist (the average on the basin reflectivity for more is thanslightly 2 hours. higher, Long-lasting while its cellsmaximum usually exhibits reach higher a more valuessubstantial of reflectivity growth) and (the cover average more reflectivityextended areas. is slightly As a consequence, higher, while the its impact of long-lasting cells is notably greater than that of short-lasting ones, due to the combined

ISPRS Int. J. Geo-Inf. 2020, 9, 183 11 of 14 maximum exhibits a more substantial growth) and cover more extended areas. As a consequence, the impact of long-lasting cells is notably greater than that of short-lasting ones, due to the combined effect of reflectivity (intimately connected with the rainfall intensity) and areal extension of the convective cells on the rainfall volume. The visual and statistical analyses performed in this paper experimentally confirm well-known characteristics of the convective phenomena and provide new findings regarding the mesoscale and local processes behind these events, showing the high potential of radar-sampled thunderstorm data. Several applications can, therefore, benefit from the results presented. For instance, the convective parameterization scheme of physically based models can be improved, and the feature selection process necessary for machine learning applications can be enhanced. Moreover, potentially dangerous patterns could be identified and exploited by the meteorological units of civil protection agencies to try to mitigate the impacts of these events. Early warning systems could gain some benefits, together with the planning and design of hydraulics infrastructures, and also the deployment of meteorological monitoring sensors. This work could also constitute the starting point to improve the knowledge of severe thunderstorms in the region of study. Considering only severe events, it is possible to identify distinctive factors that concur to their severity. A dataset covering a longer time period would provide the opportunity to evaluate more reliably the effects of climate change on the occurrence, intensity, spatial distribution, and duration of convective rain phenomena. The framework proposed in this paper can be applied to any area where a time series of snapshots recorded by a radar storm tracking algorithm is available. The statistical analysis and the visualizations obtained can be used as a general-purpose support tool for both nowcasting and climatological studies at the basin scale.

Author Contributions: Conceptualization, Matteo Sangiorgio and Stefano Barindelli; Methodology, Matteo Sangiorgio and Stefano Barindelli; Software, Matteo Sangiorgio and Stefano Barindelli; Writing-Original Draft Preparation, Matteo Sangiorgio and Stefano Barindelli; Writing-Review & Editing, Matteo Sangiorgio and Stefano Barindelli; Visualization, Matteo Sangiorgio and Stefano Barindelli All authors have read and agreed to the published version of the manuscript. Funding: This research was partially funded by Fondazione Cariplo (2017 - 0725), project: Lombardy-based Advanced Meteorological Predictions and Observations (LAMPO). Acknowledgments: We would like to thank MeteoSwiss, in particular Luca Nisi, for providing the TRT algorithm dataset, and Giorgio Guariso for supervising our work and for his useful hints. Thanks also to Enrico Solazzo and Daniele Loiacono for their suggestions regarding the physics of the convective phenomena and their visualization. Conflicts of Interest: The authors declare no conflict of interest.

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