Meteorology triggering factors analysis for rainfall induced hydrogeological events in alpine region

This paper presents an extended back analysis of the major hydrogeological events that occurred in the last 70 years in the alpine area of the Lombardy region, Italy. This work is focused on the description and the interpretation of the major meteorological triggering factors that have caused these mass movements. The triggering factors for each hydrogeological event were analysed into twofold approaches, with the final intent of ranking their magnitude in terms of consequent damages. Firstly, an analysis of precipitation was conducted using local rain-gauge 10 data, comparing them against rainfall-threshold curves proposed by several authors. Moreover, the return time of precipitation and the information about the spatial extension of the triggering factors were considered for the assessment of an empirical magnitude index of the hydrogeological event. Secondly, considering the currently available meteorological reanalysis database, provided globally by National Centres of Environmental Prediction (NCEP), additional information on the dynamics, the nature and intensity of meteorological triggers were taken into account. The two approaches were 15 compared throughout two indexes that tried to assess the strength of rainfall phenomena: the first one is empirical while the second one is physical. The results obtained from the application of the two methodologies have been discussed. The rainfall method permits to highlight which are the critical hydrogeological events, not giving any quantitative information about their magnitude. The second approach analyses better the characteristic and the dynamic of meteorological triggers, suggesting, through a physical 20 index, a quantitative ranking of their intensities that has revealed to be a good predictor for the magnitude of hydrogeological rainfall-induced events.


Introduction
Landslides represent one of the main hydrogeological hazards in Alpine and Apennines regions (Albano et al., 2017;Ballio et al., 2010;Caine, 1980;Gao et al., 2018). Italy is a country historically affected by a diffuse hydrogeological fragility of 25 the environment (Longoni et al., 2016) and mountain slopes are the most vulnerable places where landslides and flash floods can occur (Iverson, 2000;Longoni et al., 2011;Montrasio, 2000;Montrasio and Valentino, 2016). This is the case of Valtellina (Lombardy) in 1987 as well as Piedmont in 1994 and 2000 and Genova city in 2011 and 2013, which were affected by several flash floods and landslides phenomena. All of these catastrophic events have been caused by exceptional https://doi.org/10.5194/nhess-2020-118 Preprint. Discussion started: 20 May 2020 c Author(s) 2020. CC BY 4.0 License. meteorological events that rarely occur and have particular features regards their duration and their intensity (Ceriani et al., 30 1994).
In the context of hydrogeological risk prevention, urban planners and infrastructure engineers have to deal with the analysis of triggering factors and need instruments for its quantification (Ozturk et al., 2015;Papini et al., 2017;Piciullo et al., 2017;Rossi et al., 2019). In this paper, a back analysis of the meteorological triggers of past hydrogeological events is presented.
Indeed, a quantitative study of local precipitation is mandatory to correlate these meteorological events with landslide 35 failures (Corominas et al., 2014;Guzzetti et al., 2007).
A common approach used consists of the analysis of the return period (RP) of the triggering rainfall (Caine, 1980;Iverson, 2000). It is not trivial to evaluate the recurrence of a flood or a landslide unless we make a hypothesis of iso-frequency with the RP of precipitation (De Michele et al., 2005;ISPRA, 2018). For a flood that occurred in a flood plain or in a large valley, this hypothesis is generally acceptable due to the fact that it can happen even though a large amount of water is available, 40 coming from an intense and prolonged meteorological event (Albano et al., 2017;De Michele et al., 2005). For a landslide failure, defining a return period is not a common practice because it is not a periodic event but a sudden collapse (ISPRA, 2018). This is particularly true for complex and deep landslide where the triggering factors are intimately bounded with the local predisposing factors, i.e. the territory morphology, geology, etc. (Ciccarese et al., 2020;Guzzetti et al., 2007;ISPRA, 2014ISPRA, , 2018Longoni et al., 2016;Montrasio, 2000;Ozturk et al., 2015;Papini et al., 2017). Therefore, try to interpret this 45 cause-effect relationship looking only at the rainfall series cannot be used.
However, for shallow landslides and debris flows hazard assessment, are considered the rainfall intensity-duration curves (Ceriani et al., 1994;Ciccarese et al., 2020;Gao et al., 2018;Longoni et al., 2011;Olivares et al., 2014;Rappelli, 2008;Rosi et al., 2016;Rossi et al., 2019). These define a rainfall threshold for a specific region on which, taking into account the duration and the average intensity of the rainfall episode, a landslide could be triggered. This interpretation is acceptable, 50 considering this type of landslide rainfall-induced (Ceriani et al., 1994;Guzzetti et al., 2007;Piciullo et al., 2017;Rosi et al., 2016). These thresholds data are calibrated looking at the past events occurred in the area and directly correlated with the nearest rain gauge measures (Rappelli, 2008). Intrinsically they include the susceptibility of the local territory to landslide failure so their usability generally can't be extended to other regions (Caine, 1980;Guzzetti et al., 2007;ISPRA, 2018;Longoni et al., 2011). On the other hand, this method is widely used for predicting the occurrence of shallow landslide and 55 debris flow events but, due to its empirical nature, it is rather approximate and leads sometimes to "false alarm" detecting (Abbate et al., 2019;Guzzetti et al., 2007;Peres et al., 2018).
Even though the rainfall return period estimation and rainfall thresholds have been widely used in different parts of the world (Gao et al., 2018), some open questions still exist. Are these approaches sufficient for a complete description of triggering factors? Can rainfall analysis be improved considering also other meteorological variables, which could better describe the 60 rainfall events and the linked consequences?
Generally, a local study on the triggering causes is not completely descriptive of the real magnitude of the meteorological triggering event (COPERNICUS, 2020;Rotunno and Houze, 2007;Stull, 2017). This is particularly true in mountain areas https://doi.org/10.5194/nhess-2020-118 Preprint. Discussion started: 20 May 2020 c Author(s) 2020. CC BY 4.0 License.
where the territory enhances the heterogeneity of rainfall field that is not able to exhaustively represented only taking into account the local rain gauge network (Rotunno and Houze, 2007). In particular, the type of rainfall events cannot always be 65 recognized directly from rain gauge time-series so that other meteorological variables should be taken into account for its description. This is crucial because different precipitation type can affect the characteristics of the hydrogeological failures (Corominas et al., 2014;Guzzetti et al., 2007). An intense but rather localized rainfall, such as a thunderstorm, could trigger a certain type of hydrogeological issues, such as shallow landslides and soils slips (Montrasio, 2000). On the other hand, a persistent orographic rainfall, which could affect an entire region for several days, may have completely different effects on 70 the territory, enhancing its hydrogeological fragility (Longoni et al., 2011;Rotunno and Houze, 2007;Tropeano, 1997). Therefore, a more complete description of the type of triggering factor is necessary to better explain the territorial hydrogeological dynamics.
The goal of this paper is to investigate the relationship between hydrogeological issues and their triggering factors in a broader sense, starting from the back analysis of past hydrogeological events, where landslide and flash flood occurred. The 75 alpine region in the northern part of Lombardy, Italy, was considered because of its past critical hydrogeological events (CNR, 2020;ISPRA, 2014;Rappelli, 2008;Tropeano, 1997). Triggering factors were analysed into twofold approaches. The first one uses only local rainfall data applying the threshold curves method as a reference for detecting shallow landslide failure. The second considers also meteorological reanalysis maps provided globally by National Centres of Environmental Prediction (NCEP) (Kalnay et al., 1996;MeteoCiel, 2020;NOAA, 2020) where is possible to gather additional information 80 about the spatial and temporal evolution of the triggering events at larger scale (Andrews, 2010;Grazzini, 2007;Grazzini and Vitart, 2015;Stull, 2017).
The paper will be organized as follows: in section 2 is presented the databases of the historical hydrological events and the materials and methods adopted in our analysis of triggering factors related to these events. In section 3 the results and relative discussion are reported, with some comparisons and comments regarding the two approaches and in section 4 some 85 final remarks and conclusions of the ongoing research work are reported.

Data, Methods and Models
This section presents the methodology followed for the back analysis.

Historical database of hydrogeological events
A group of past hydrogeological events has been considered for the alpine area of Sondrio Province, northern Lombardy, 90 Italy, Figure 1. This area was affected by exceptional hydrogeological events in July 1987 causing extended damages and loss of lives (CNR, 2020). The most important and severe was the Val Pola landslide that occurred in the upper part of Valtellina and happened as a sudden collapse of 40 million cubic meter of old debris, destroying 5 villages and six hamlets with 35 people died of various disaster-related causes (Tropeano, 1997). On the other hand, the entire province was also https://doi.org/10.5194/nhess-2020-118 Preprint. Discussion started: 20 May 2020 c Author(s) 2020. CC BY 4.0 License. affected mainly by diffuse hydrogeological episodes such as shallow landslide and flash floods, that caused people injuries 95 and comparable damages to infrastructure and buildings, estimated in 2 billion of euros. These hydrogeological issues were caused by a rather intense and prolonged rainfall episode (Rappelli, 2008;Tropeano, 1997) and the effects were enhanced by rapid glacier melting increased by high-altitude summer temperatures.

100
The back analysis has considered also other critical hydrogeological episodes like the 1987 that affected the Sondrio Province. Two different data sources have been used to collect data for the analysis of the historical hydrogeological events: the "Aree Vulnerate Italiane" (AVI) database and the "Inventario Fenomeni Franosi Italiano" (IFFI) database (CNR, 2020;ISPRA, 2014). The AVI database is directly available inside a geoportal-web site that is managed by CNR (Centro Nazionale della Ricerca) and the IFFI database, available from the national geoportal website (CNR, 2020;ISPRA, 2014). 105 The data stored collects historical information from past natural disaster starting from the medieval age up to nowadays.
Looking at the available time-series, data are not homogeneous and the lack of information is generally diffused (CNR, 2020;ISPRA, 2018). For the area of Sondrio Province, a quite extensive historical bibliography was found in literature (Ceriani et al., 1994) that considers all the events starting from 1850 up to 2000. In this case, the two databases' consistency was evaluated, and redundant records have been corrected. Then, a merging operation between the AVI and the IFFI 110 database information was needed for the years comprised between 2000 and 2019.
The period chosen for the back analysis is comprised between 1951 and 2019. Indeed, systematic monitoring of the precipitation and temperature started in Italy since 1951 by SIMN (Servizio Idrografico e Mareografico Nazionale) and looking at the antecedent periods these data were missed or characterized by several uncertainties or errors (ISPRA, 2019).
The available rain gauge data series were gathered from local archives of SIMN (ISPRA, 2019) and ARPA Lombardia 115 (Agenzia Nazionale per la Protezione dell'Ambiente) (ARPA Lombardia, 2020). These series have been conventionally recorded on daily bases until the 2000s years so "a daily rain" represents the maximum resolution of our dataset before that period. Starting from 2001, the increased temporal resolution available that moved to a sub-hourly time-step increased the accuracy of the rainfall analysis.
The list of the hydrogeological events analysed in the study and their description retrieved from AVI and IFFI databases is 120 reported in Table 1. The precise location of each hydrogeological event was not directly reported in the dataset, but an indication of the municipalities affected by hydrogeological issues was present. These data were taken into consideration for defining the extension of the triggering phenomena and were corrected looking at the recorded rain gauges series. In particular, rainfall events were distinguished in two types: extremely localized events (EXL), with an influence area lower than 1000 km 2 , or 130 diffuse events (DIF), with significant territorial diffusion greater than 1000 km 2 . This value has been motivated considering the nature of the meteorological triggers: "EXL" were generally associated with convective rainfall phenomena which extension has an order of 10 x 10 km 2 and "DIF" were characterized by diffuse and uniform rainfall with an extension around 100 x100 km 2 (Martin, 2006;Rotunno and Houze, 2007).
The dataset analysis of Table 1 shows a clear seasonal distribution of the events mainly concentrated during summer and 135 autumn. July and November are the months much more prone to hydrogeological events and this strong seasonality highlights that triggers phenomena involved may have a different nature (Martin, 2006;Rotunno and Houze, 2007). In July, https://doi.org/10.5194/nhess-2020-118 Preprint. Discussion started: 20 May 2020 c Author(s) 2020. CC BY 4.0 License. meteorological events are characterized mainly by high intensity and short duration with a typical convective behaviour of precipitation (thunderstorms), and their average duration is generally around 1 or 2 days. In particular, 1951In particular, , 1953In particular, , 1987 2008 events happened during the summer season and rainfall cumulated were comprised between 100-200 mm, apart from 140 1987 and 1997 that were rather exceptional (254 mm and 275 mm in three days). During October and November, rainfall events are characterized by higher persistency (4-5 days) and rainfall cumulated can easily reach amounts around 250-350 mm, such as for the events that happened in 2000, 2002 and 2018. They are usually associated with extratropical cyclone structures that moving eastward from Atlantic Ocean can affect directly the Alpine mountain range (Martin, 2006).
These observations from the dataset have been studied in deep from a quantitative viewpoint considering the two approaches 145 proposed: the traditional rainfall approach and the meteorological reanalysis approach.

Traditional Approach: Rainfall Threshold Curves and Rainfall Return Period analysis
The rainfall data were elaborated considering the spatial extension of the triggering events, i.e. rainfall field characteristics.
For the "EXL" data, the nearest rain gauge or at least the 2 nearest rain gauges were chosen as local rainfall data. For the "DIF" group, all the available daily rain data in the affected territory have been considered and averaged with respect to 150 the number of rain gauges stations " " in order to obtain a representative value for .
Then, the average daily rainfall rate was calculated dividing the cumulative rainfall by the duration . The results were then plotted against the local rainfall intensity-duration threshold curve. For the examined area was considered a group of threshold curves proposed in the literature by several authors.
The "Caine" curve (Caine, 1980) is the general one, valid for shallow hydrogeological processes around the world, Eq. (2.a). 155 The "Ceriani" curve (Ceriani et al., 1994) was proposed in 1994 and was calibrated directly on the recorded data available in Sondrio Province, Eq. (2.b). A more recent study conducted by (Guzzetti et al., 2007)  a location (Corominas et al., 2014;De Michele et al., 2005). Using the Curve of Pluviometric Possibility (CPP) (De Michele et al., 2005) available for the Lombardy region and provided by (ARPA Lombardia, 2020), the RP of precipitation was 165 estimated for each event. Localized events "EXL" were treated separately with respect to the diffuse "DIF" ones. For the localized events, the on-site coefficient of CPPs has been used but for the diffusive ones, a spatially averaged value of the coefficients has been elaborated for the area of interest.

Reanalysis Approach: NCEP Reanalysis Maps
To improve the analysis of triggering factors, the database was studied considering other variables associated with the 170 meteorological event. In particular, the National Centre for Environmental Prediction (NCEP) data (Kalnay et al., 1996; MeteoCiel, 2020) were examined. The NCEP reanalysis maps are a valuable instrument for investigating the past evolution of meteorology around a target area (Faggian, 2015;Grazzini, 2007;Rotunno and Houze, 2007;Stull, 2017). They have a spatial resolution of 2.5° x 2.5° degrees of latitude and longitude, covering the whole planet with a temporal frequency of 12 h. These maps contain information about temperature and pressure distribution at different geopotential heights, i.e. 850 hPa 175 and 500 hPa, to describe air mass advection and front formations. The pressure values reported at sea level are valid indicators of a cyclone or anticyclone structure developments at regional scale (Andrews, 2010;Grazzini and Vitart, 2015;Stull, 2017). Moreover, the wind fluxes velocities are important for establishing the spatial and temporal evolution of a particular rainfall event (Andrews, 2010;Grazzini, 2007;Stull, 2017). A qualitative looking at the reanalysis maps for each considered event highlights some similarities regarding the 185 meteorological configuration of air masses. Not surprisingly, the major hydrogeological events have occurred during strong extratropical cyclone (EC), as described in Figure 2.  (Grazzini and Vitart, 2015;Martin, 2006). These generate at the boundary of the polar vortex strong jet streams that can move air masses in the 190 direction of the southern Alps, as is represented in Figure 2. Across the southern flank of Alps, one of the critical consequences of this configuration is the enhancement of persistent and heavy orographic precipitation (Rotunno and Houze, 2007) thanks to the instauration of a strong southern moist and warm flow, the "Scirocco" wind, as reported by (Grazzini, 2007). Rainfall intensities can reach remarkably high amounts if these conditions are prolonged for several days, leading up to 400 mm in 2/3 days (Grazzini, 2007;Rotunno and Houze, 2007). In addition, the presence of convection especially during 195 the summer season may add another level of complexity, producing a further enhancing of local rainfall rates (De Michele et al., 2005;Rotunno and Houze, 2007). This dynamic is characterized by some peculiarities that are necessary to be understood for interpreting the local scale rainfall effects on the territory. Therefore, using the NCEP maps, a synthetic model proposed by (Godson, 1948;Martin, 2006;Stull, 2017) was chosen for the estimation of a strength index related to the extratropical cyclone intensity. The model 200 calculates indirectly the Sea-Level Pressure Tendency (SLPT), the time-variation ratio of sea-level atmospheric pressure Δpsl/Δt [hPa/h], that represents an indicator of the strength of a cyclone structure (Andrews, 2010;Godson, 1948;Martin, 2006;Stull, 2017;Wallace and Hobbs, 2006). In general, this ratio is higher, in an absolute sense, when the EC is more intense. According to (Stull, 2017), this index is obtained as a sum of three different influencing factors that correspond to the most important processes implicated in the dynamic evolution of extratropical cyclone: 205 ▪ 1 expresses the "upper-level air divergence" due to jet streams, which remove air mass from an ideal atmosphere air column.
[ / ] is the mean air column vertical velocity, evaluated considering the continuity equation in the proximity of the local change of jet stream velocity gradient.
= 0.5 / 3 is the average density of air column and = 9.8 [ / 2 ]. 210 ▪ 2 is the "atmosphere boundary layer pumping", that causes the horizontal wind to spiral inward toward a lowpressure center. The air density of the boundary layer is = 1.112 / 3 , = 9.8 [ / 2 ] and is the vertical velocities at boundary-layer calculated using the approximation proposed by (Stull, 2017) for cyclone structures.

Results and Discussion 230
The first approach, based on the definition of critical events against threshold curves, carried out the analysis only on rainfall parameters, i.e. the rain intensity ( ) and the duration ( ). The second extended the precipitation study considering also other meteorological parameters, reported inside NCEP reanalysis maps, and applying the model proposed in Eq. (4) for EC intensity.

Approach 1: the Rainfall Analysis 235
Considering the average daily rain rate and the duration of the rainfall episodes reported in Table 1, these data were plotted against the rainfall threshold curves listed from Eq. (2.a) to Eq. (2.e) inside Figure 4. A large number of events can be clustered in the right-bottom corner of the graph due to their characteristics of a rather long duration 2-4 days and slightly low intensities. Only the event of 2019, 2008 and 1953 are dispersed on the other side of the graph where the duration is around or less than a day. 240 Considering the thresholds proposed by (Guzzetti et al., 2007), all the events points are correctly settled above lines. In particular, no big differences are seen among the general one (3), the curve valid for mid-latitude climate (4) and the one valid for highlands climate (5). On the other hand, the thresholds proposed by Ceriani (2) and Caine (1) are settled above the previous. The "Ceriani" one seems to fit very well the data, posing only the 1966 event slightly below the curve and the 1953 and 1960 close to the curve. This result was expected because the "Ceriani" threshold has been calibrated using a 245 dataset of local events until 1994. Conversely, the "Caine" threshold seems to work worst rather than the previous. 1953, 1960 and the 1966 events are not identified as critical and appear below the curve. In this case, the threshold curve has been unable to detect these events. Moreover, the 1997 and 2000 are settled borderline on the curve.

250
For each critical event, the related rainfall return period has been also specified in Figure 4. According to (Gao et al., 2018;Iida, 2004;Rosso et al., 2006), a beam of rainfall intensity-duration curves can be elaborated including their dependence from RP. Considering the "Ceriani" threshold, the critical events that exhibit higher RPs are located at higher distances from the curve and, on the other hand, the events with a small return time are settled nearer. Therefore, the vertical distance between the curve and the critical event point could be addressed as a possible indicator of the magnitude of the 255 1951, 100 1953, 2 1960, 5 1966, 5 1983, 100 1987 hydrogeological events, but the empirical correlation founded in these literature analyses suggests that it may be subjected to large uncertainties (Gao et al., 2018).
In conclusion, the threshold curves assess if a rainfall event can trigger hydrogeological issue, but no further detailed information can be retrieved to the effective magnitude of the event occurred. The physical nature description of the rainfall phenomena is generally missed and a relative comparison among the different critical events cannot be properly done. In 260 addition, the wide range of threshold curves available for the area and their empirical evaluation increase the uncertainty around the assessment of the critical events. Moreover, the small database of our study does not permit us to clearly assess a magnitude of the hydrogeological event simply looking at these distances among the threshold and each critical event point.
A further step of the analysis has been carried out considering not only the information about the intensities of the triggering phenomena but also their spatial extension, i.e. "EXL" or "DIF". 265 Looking at Figure 5.A, the Sondrio Province has experienced at least four exceptional rainfall events with a return period equal to 100 years : 1951, 1983, 1987 and 2002. From RP analysis, they were ranked with the same intensity but among them 1987 has been recorded historically as the most catastrophic one, i.e. with the highest magnitude, that affected the area in the 270 second half of the XX century. This apparent contradiction has a possible explanation considering the information about the spatial extension of the affected areas, as reported in Figure 5.B, which is a property strictly related to the nature of the rainfall event (Corominas et al., 2014;Gao et al., 2018). Those were not directly considered in RP evaluation that takes into account only the local amount of precipitation or an averaged value across a region. Therefore, if only the RP is considered, 1983 is intended to be intense as 1987, but, considering the spatial distribution the 1983 event affected only a limited area 275 and the 1987 spread across the entire province. In this light, the RP information leads to a false interpretation of the nature of the two triggering phenomena and it cannot be considered directly for establishing a magnitude of the related hydrogeological consequences on the territory.
According to (Corominas et al., 2014), the hazard intensity of a hydrogeological event can be addressed considering three different contributes. Excluding the territorial susceptibility, the extension of the affected area and the intensity of the 280 triggers are the other two main components. In scientific literature, it does not exist a unique method for the magnitude assessment of a hydrogeological episode because its quantification depends on the type of triggered phenomena involved and on the scope of the hazard study (Corominas et al., 2014;ISPRA, 2018). In the special case of the rainfall-induced shallow landslides, a logarithmic function seems to explain roughly the relationship among the event magnitude and the characteristics of the trigger. According to (Malamud et al., 2004), a magnitude index can be defined as a logarithmic 285 function of the number of triggered landslide and considering the study of (Bovolo and Bathurst, 2011;Frattini et al., 2009;Reid and Page, 2003), a similar frequency-magnitude relation can be found for the intensity of rainfall event. Based on these evidences, two indices 1 and 2 have been considered for defining the magnitude of analysed hydrogeological events, taking into account the fact that both the spatial extension and the intensity of triggering are involved in its definition. and rather spatial diffuse. On the contrary, 1983 shows a low value of 1 and high one for 2 , i.e. a very localized event but also particularly intense. In order to give a unique and quantitative ranking of the event's magnitude, for each events the indices 1 and 2 have been averaged (AVG). The latter was considered as a reference for the comparison with the SLPT 295 physically based index proposed in the meteorological reanalysis approach.

Approach 2: Meteorological Analysis
The second approach consists of the application of the model proposed by (Stull, 2017) and described in Eq.(4). 300 Atmospheric pressure gradients, wind velocities, and air masses advection through the Alpine region were studied for feeding each of the model components illustrated in the Equation (4.a), (4.b), and (4.c). According to (Stull, 2017), the sea- triggering events. This estimation has been done in correspondence to the critical phase of each event, i.e. the "D" phase of the scheme reported in Figure 3. 305

Wind Components
For determining the 1 term ("upper layer divergence" Equation (4.a)), the dynamic of geostrophic wind components was examined considering the NCEP reanalysis maps.
Geostrophic wind is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force and it is a valuable first approximation of the general circulation of the air masses at a regional scale 310 (Andrews, 2010;Martin, 2006;Stull, 2017). Generally, intense geostrophic wind means that the pressure gradient between a low and high pressure is sharp, and it is associated with strong EC structures ( Figure 2). Therefore, geostrophic wind velocity is an indicator of the meteorological event intensity (Stull, 2017).

315
The geostrophic wind velocity, calculated in correspondence of the central phase of the event (stage "D" in Figure 3), exhibit a range comprised between 35 km/h -50 km/h (Figure 7). The results show that the events characterized by higher velocities have been also interested in more intense rainfall, such as the case of 1987, but on average the events have shown similar values. Regarding the wind direction, not reported, it was observed that all the events have been characterized by the presence of sustained southern flows at 850 hPa geopotential height. This evidence is in accordance with the typical air 320 masses configuration that characterizes this type of event where orographic precipitations are enhanced in intensity and they are generally prolonged for several hours or days (Grazzini, 2007;Rotunno and Houze, 2007). The interpretation of geostrophic balance of wind is generally valid at large scale but it does not take into account the secondary effects that can modify consistently the local intensities of rainfall phenomena (Martin, 2006;Stull, 2017

Air Masses Evolution Paths
For determining the 2 term, ("boundary layer pumping" Equation (4.b)), the air masses evolution paths were examined during each event. Respect to the 1 and 3 terms, it acts inhibiting the ECs development and it is rather influenced by ECs latitude evolution. In fact, ECs do not follow the same advection path seasonally and this is a key parameter for distinguishing and interpreting different types of rainfall events. 330 Rossby waves track (Rotunno and Houze, 2007;Stull, 2017). This is the case of 1960, 1966, 2000, 2002 and 2018 events occurred between September and November. Autumnal periods are also characterized by the presence of high-temperature gradient between the Mediterranean Sea (warm) and the North Atlantic region (cold) which leads to the formation of strong EC structures more frequently (Rotunno and Houze, 2007;Stull, 2017). Summer events of 1951Summer events of , 1953Summer events of , 1987Summer events of , 1997 and 2019 exhibit a low-pressure tracking path that did not cross the Alps 340 mountain range (Figure 8.B). This fact can be explained by considering that Rossby waves are in general northern shifted and less meandered during the summer period (Grazzini and Vitart, 2015;Martin, 2006). This reflects on the events that affect the southern side of the alpine region which are more rapid, less persistent, locally intense but not well organized such as the typical autumnal EC. In this framework, 1987 has assumed a character of exceptionality due to its anomaly features regarding, in particular, its temporal persistence on the examined area. 345

Sea-Level Pressure Tendency Index
The 3 term has not explicitly analysed because it is represented as a linear function of the daily rainfall rate RR, which was already considered in the precipitation analysis. In particular, it is an expression of the local effects of the ECs on the territory, i.e. the rainfall intensity, and it is intimately bound with the thermodynamic of the ECs structure (Martin, 2006), acting positively for its development (Stull, 2017).  Looking at Figure 9, the SLPT index shows a range comprised between the -0.28 hPa/h, recorded for the 1953 event and -355 1.76 hPa/h recorded for 1987. The latter and the 2002 (-1.67 hPa/h) are reported to have been the EC structures with the highest intensity that affected the Northern Lombardy area. An important characteristic is that some of these ECs have been characterized by explosive cyclogenesis. Explosive cyclogenesis happens when an extratropical cyclone exhibits in its central part a low pressure deepening of 24 hPa in 24 h, which corresponds to an average rate of 1 hPa/h (Sanders and Gyakum, 1980). They are potentially dangerous for the territory due to their rapid evolution, causing flash floods and diffuse 360 hydrogeological issues that, in our case, have been confirmed by the historical chronicles found in the AVI and IFFI databases.

Magnitude Indexes Comparison
The SLPT index has been able to assess through a physical formulation the intensity of the meteorological triggering factors of the hydrogeological event examined. Considering the rather strong cause-effect relation that was highlighted by historical 365 chronicle among the intensity of the rainfall episodes and the severity of the subsequent hydrogeological issues, the SLPT index was tested as a predictor of the hazard magnitude. In order to address this, the index was normalized among 0 and 1 and then compared with the empirical index (AVG index) proposed within rainfall analysis, that represent in our study the reference for magnitude evaluation.
Looking at Figure 10 it is rather clear how the two indexes, the empirical and the physical based, are in accordance, giving a 370 similar magnitude ranking of the events studied. In particular, both have addressed again the 1987 and 2002 as the two most critical of the entire dataset and have ranked 1953 as the lowest intense. For the other events, the ranking was rather similar showing an overall root mean square error (RMSE) less than 7%.  The result obtained here are representative of the qualitative information found inside the historical database analysed, where an objective criterion for the magnitude quantification was not applicable due to poorly data reported (ISPRA, 2018). In this light, NCEP reanalysis map have represented an important source for the quantitative interpretation of the meteorological triggering factors in correspondence of the critical events analysed, allowing also a more complete examination of the 380 severity of the subsequent rainfall induced hydrogeological events.

Conclusions
This study presented an extended back analysis of the triggering meteorological factors that have caused in the past several hydrogeological issues in the alpine mountain territory of the Sondrio Province, Northern Lombardy, Italy.
Excluding the analysis of the local geomorphological predisposing causes, the attention was pointed out on the 385 characteristics of rainfall that were considered as the primary cause of hydrogeological hazards analysed. The main goal of the study was to develop a quantitative analysis of the meteorological triggering factors that were able to explain the magnitude of the rainfall induced hydrogeological issues that affected the studied area. Two different approaches have been proposed: the first one considered the local information about rainfall amounts, intensities, and durations for characterizing the critical events through the rainfall threshold curves. The second takes into account other meteorological parameters 390 implicated in the physical description of a rainfall phenomenon.
Following the first approach, the rainfall threshold curves have been able to predict the instabilities, but no useful information was gathered for the magnitude assessment of the hydrogeological events. The analysis was improved considering the return period of precipitation. Nevertheless, looking only at the RPs may lead to a misleading and wrong interpretation of the triggering causes because recorded rain-gauges data series represent a local estimation of the rainfall 395 event intensity. The RP values do not take into account explicitly the spatial distribution of the meteorological phenomena that are directly correlated to the consequent hydrogeological issues triggered in the territory. Therefore, a composite magnitude index for assessing a ranking of hydrogeological events considered has been proposed taking into account not only the intensity of the triggers, i.e. return period of rainfalls, established from the analysis of the rainfall series, but also the information about the spatial extension of the affected areas. 400 In the second approach, a meteorological analysis of the triggering has been carried out taking into account the NCEP reanalysis maps. The model in Eq. (4) was implemented for the description of each meteorological event intensities through the physically based index SLPT. This index was chosen because considers not only the local rain-gauges series but also other meteorological variables that are descriptive of the whole dynamic of the triggering event. That physical index was then normalized and compared with the previous empirical one obtained from the analysis of precipitation data. 405 Both two indices have shown good accordance in the assessment of the magnitude of the studied events. In particular, the 1987 and the 2002 events have been correctly ranked as the strongest of the entire dataset, caused by explosive cyclogenesis.
Respect to the 1 and 2 indices that are based on empirical evidence extracted from local data analysis, the SLPT indicator is physically based and can discriminate straightforwardly localized events "EXL" with respect to the more diffused ones "DIF", that is a key information. The hydrogeological issues that affected the alpine territory were proportional to the overall 410 intensity of extratropical cyclone systems and the SLPT index has been able to highlight this fact, also distinguishing the nature of the triggers.
In the view of the future climate change that, with high confidence (Faggian, 2015), will affect the Mediterranean and the Alpine environment, extreme meteorological events are supposed to increase (Ciervo et al., 2017;Gariano and Guzzetti, 2016;Moreiras et al., 2018). Our study moves in this direction, trying to consider integration between the traditional 415 approach (i.e. local rainfall analysis) and the new instruments that meteorological models are starting to provide (i.e. meteorological reanalysis map) in order to give a comprehensive interpretation of the triggering factors of severe hydrogeological events.
Code and data availability: All the data reported in this paper are freely consultable on the Internet websites. In particular, 420 reanalysis weather maps are freely downloadable from Meteociel Website (MeteoCiel, 2020), IFFI and AVI database are freely consultable and downloadable from (CNR, 2020;ISPRA, 2014), and Rain Gauges data are extracted from local Environmental Agency (ARPA Lombardia, 2020). The model applied in this work is also freely consultable and downloadable from (Stull, 2017).

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Author Contribution: Andrea Abbate carried out the formal analysis and prepared the manuscript with contributions from all co-authors. Monica Papini supervised the research and Laura Longoni the review & editing.