Analysis of meteorological parameters triggering rainfall induced landslide: a review of 70 years in Valtellina

This paper presents an extended reanalysis of the rainfall-induced hydrogeologicalgeo-hydrological events that occurred in the last 70 years in the alpine area of the Lombardy region, Italy. The work is focused on the description of the major meteorological triggering factors that have caused diffuse episodes of shallow landslide and debris flow. The aim of this reanalysis was to try to evaluate their magnitude quantitatively. 10 The triggering factors were studied following two approaches. The first one started from the conventional analysis of the rainfall intensity (I) and duration (D) considering local rain-gauge data and applying the I-D threshold methodology, integrated with an estimation of the events’ return period. We then extended this analysis and proposed a new index for the magnitude assessment (MI) based on frequency-magnitude theory. The MI index was defined considering both the return period and the spatial extension of each rainfall episode. 15 The second approach is based on a regional scale analysis of meteorological trigger. In particular, the strength of the extratropical cyclone structure (EC) associated with the precipitation events was assessed through the Sea Level Pressure Tendency (SLPT) meteorological index. The former has been estimated from the Norwegian Cyclone Model (NCM) theory. Both indexes have shown an agreement in ranking the event’s magnitude (R = 0.88) giving a similar interpretation of the severity that was found also in accordance with the information reported in historical databases. 20 This back analysis of 70 years in Valtellina identifies the MI and the SLPT as good magnitude indicators of the event, confirming that a strong cause-effect relationship exists among the EC intensity and the local rainfalls recordedeffects on the ground. In respect to the conventional I-D threshold methodology, which is limited to a binary estimate of likelihood of landslide occurrence, the evaluation of the MI and the SLPT indexes allowpermit to quantify the magnitude of a rainfall episode capable to generate severe hydrogeologicalgeo-hydrological hazards. 25

that places where the natural landscape has been dramatically modified by uncontrolled urbanization in order to avoid human 30 injures and material damages (Albano et al., 2017b;Bronstert et al., 2018). Italy is a country historically affected by a diffuse hydrogeologicalgeo-hydrological fragility (Albano et al., 2017a;  . Alpine and Apennines mountain slopes represent the most vulnerable places of the country where shallow landslides and debris flow can occur more frequently Montrasio and Valentino, 2016;Vessia et al., 2014Vessia et al., , 2016 . 35 We can cite several examples of past events such as the case of Valtellina (Lombardy) in 1987 as well as Piedmont in 1994and Genova city in 2011and 2013ISPRA, 2018). All of these catastrophic events have been caused by rather exceptional rainfall episodes that rarely occur and have particular features regards their durations and their intensities Corominas et al., 2014;. Here, the scientific literature has proposed some analytical methods for relating the triggering event to the occurrence of rainfall-induced 40 landslides.
A first methodology consists of the analysis of the rainfall return period (RP) for establishing the intensity of the meteorological trigger . The RP has a statistical meaning and represents the average recurrence time of a rainfall episode characterized by a certain intensity (I) and duration (D), that happened at a specified location (Bovolo and Bathurst, 2012;. This information can potentially be linked to the recurrence of 45 the eventually triggered hydrogeologicalgeo-hydrological phenomena in case we make the hypothesis of iso-frequency with the RP of precipitation ISPRA, 2018). For a flood or a flash flood, that approximation is generally acceptable because a inundation represents the direct consequence of a heavy precipitation (Albano et al., 2017a;. Instead, defining a RP for a landslide is not a common practice because the failure is not a periodic event but is a sudden collapse (ISPRA, 2018). For complex and deep-seated landslides the meteorological triggering factors are also 50 intimately bounded with the local predisposing factors, i.e. the territory morphology, geology, etc. Inventario Fenomeni Franosi;ISPRA, 2018;. The rupture surface position of the surface rupture and the seasonal groundwater circulation can have a crucial interplay role influencing the overall stability of the landslide (Longoni et al., 2014;Ronchetti et al., 2009;Xiao et al., 2020). Therefore, it is not always clear how to identify the real cause of the collapse and, the correlation with rainfall 55 triggers is sometimes weak (Ibsen and Casagli, 2004).
A certain degree of reciprocity with precipitation triggers is maintained mainly for rainfall-induced events such as shallow landslides, soil slips, and debris flows. Therefore, a common methodology consists of the investigation of rainfall intensityduration (I-D) curves Crosta and Frattini, 2001;Guzzetti et al., 2008;Olivares et al., 2014;Peruccacci et al., 2017;Vessia et al., 60 ▪ In the first approach, we put the events in the context of the classical I-D approach, integrated with the estimation of RP, as mentioned earlier. We then propose an alternative for the classification of the events' magnitude through the introduction of a magnitude index (MI). The index incorporates the return period of an event with the spatial extent of its impact in terms of landslide occurrence. The MI is defined in substitution of the classical magnitude 100 quantification adopted for hydrogeologicalgeo-hydrological events (Corominas et al., 2014;. ▪ A second approach is based on a meteorological analysis of the triggers, considering their interpretation coming from the Norwegian Cyclone Model (NCM) Martin, 2006;. Here, the trigger's magnitude is expressed through a physically physically-based meteorological index called the "Sea Level Pressure Tendency" (SLPT) which is a function of some atmospheric parameters evaluated at the synoptic scale and 105 associated with the rainfall event.
To carry out our study two data sources are considered: ▪ Ground-based meteorological series of rainfalls (Rete Monitoraggio Idro-nivo-meteorologico; SCIA: Sistema Nazionale per l'elaborazione e diffusione di dati climatici), adopted for I-D methodology and for the RP evaluation. 110 ▪ Meteorological maps provided by the National Centres of Environmental Prediction (NCEP) (Kalnay et al., 1996; Observations, Prévisions, Modèles en temps réel; National Center for Environmental Information) for the NCM intensity assessment.
The paper will be organized as follows: in section 2 is presented a brief description of the historical databases and the 115 meteorological reanalysis maps; in section 3 are described the two methodologies behind the definition of the MI, through the extended rain-series analysis, and the SLPT, through the NCM model theory; in section 4 the outcomes from the two presented approaches are reported and the two indexes are then compared. A discussion is developed in section 5 with some comments about the obtained results, with a focus on the SLPT index performances; in the last section are reported some final remarks and conclusions of the ongoing research work. 120 2 Data and Materials

Historical database of hydrogeologicalgeo-hydrological events and rainfall Time Series
A group of past hydrogeologicalgeo-hydrological events has been considered from the alpine area of Sondrio Province, northern Lombardy, Italy, Figure 1Figure 1 . In our study, we have investigated historical databases to identify events that in the recent past exhibited similar cause-effect behaviour, like the 1987 event. In July 1987 this area was affected by 125 exceptional hydrogeologicalgeo-hydrological events triggered by a rather intense and prolonged rainfall episode . The effects on the territory were severe: shallow landslides, debris flows, and flash floods were Two different data sources were investigated to collect historical data: the "Aree Vulnerate Italiane" (AVI) database and the "Inventario Fenomeni Franosi Italiano" (IFFI) database (Sistema Informativo sulle Catastrofi idrogeologiche; Inventario Fenomeni Franosi). The data collect historical information from past natural disaster starting from the medieval age up to nowadays: the AVI database is directly available inside a geoportal-web site that is managed by CNR (Centro Nazionale 135 della Ricerca) and the IFFI database, available from the national geoportal website (Sistema Informativo sulle Catastrofi idrogeologiche; Inventario Fenomeni Franosi). Available events time-series were not homogeneous so that the consistency of the database was evaluated, redundant records have been dropped and a final integration between the AVI and the IFFI database information was carried out.
The period chosen for the reanalysis is comprised between 1951 and 2019. Systematic monitoring of the precipitation and 140 temperature started in Italy in 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 (SCIA: Sistema Nazionale per l'elaborazione e diffusione di dati climatici). The available rain gauge data series were gathered from local archives of SIMN (SCIA: Sistema Nazionale per l'elaborazione e diffusione di dati climatici) and ARPA Lombardia (Agenzia Regionale per la Protezione dell'Ambiente) (Rete Monitoraggio Idro-nivo-meteorologico). These series were conventionally recorded on 145 daily basis until the 2000s years so "a daily rain" represents the maximum resolution of our dataset before that period.
Starting from 2001, the available temporal resolution has moved to a sub-hourly time-step increasing the accuracy of the rainfall analysis.
In AVI and IFFI database, the precise localization location of hydrogeologicalgeo-hydrological episodes waswere not available even for the most recent events that happened after the 2000s. Therefore, some indications about locations were 150 retrieved from the AVI database considering the municipalities affected by disasters. The spatial extension of affected areas (AA) describe those locations that have experimented with some damages due to hydrogeologicalgeo-hydrological events that occurred. This information is indicative of the area where the rainfall event has been supposed to be more intense. In fact, AA was then compared with ground-based rain gauge series from the entire Sondrio Province with the aim to reconstruction for each rainfall event its spatial distribution. Selected events have been classified in function of AA 155 parameter: extremely localized events (EXL), with an influence area lower than 1000 km 2 , or diffuse events (DIF), with significant territorial diffusion greater than 1000 km 2 . This threshold has been motivated referring to 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 x 100 km 2 (Martin, 2006;. In Table 1Table 1 is reported the list of hydrogeologicalgeo-hydrological events analysed 160 in our study.

NCEP reanalysis maps
To improve the description of rainfall triggering factors, the meteorological reanalysis maps were examined considering the National Centre for Environmental Prediction (NCEP) data (Kalnay et al., 1996; Observations, Prévisions, Modèles en temps réel). The former has 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. All the data stored in NCEP maps are useful for the interpretation of air masses dynamic in the 170 middle latitudes such as the Extratropical Cyclones (ECs) that are responsible for the spatial and temporal evolution of intense precipitation phenomena. For the European region, ECs develops in the Atlantic Ocean near the British Islands. ECs are deputed for the large part of precipitation recorded over the Alps mountain range  because they are generally advected eastward through the Mediterranean area by Rossby waves (RW) Martin, 2006). At the boundary of the polar vortex, RW can generate strong jet streams that can move air masses in the 175 direction of the southern Alps, enhancing vertical air motions. Across the southern flank of the Alps, this mechanism may lead to trigger persistent and heavy precipitation  that can intensify if an orographic uplift of the incoming southerly flow is also triggered (Abbate et al., 2021;. Rainfall can reach remarkably high amounts if these conditions are prolonged for several days, leading up to 400 mm in 2/3 days . For each event listed in Table 1 Table 1, we have examined correspondent NCEP maps to investigate the mechanism 180 responsible for generating those intense precipitations over the target area.

Model and Methods
The triggers analysis is here presented considering the I-D thresholds approach, its extension through the MI index definition and the NCM model with SLPT index evaluation.

Rainfall I-D thresholds and Return Period analysis 185
The daily rainfall rate has been determined from the total amounts and the duration listed in Table 1. Rainfall amounts (RA) were estimated keeping the distinction between EXL and DIF events, Figure 2.A. For EXLs the nearest rain gauge or at least the 2 nearest rain gauges were chosen as reference. For DIFs, all the available daily rain data in the territory have been summed and averaged considering the number of rain gauges stations " " to obtain a representative value for , Eq.
(1.a). We have assumed the hypothesis of a uniform spatial distribution of the rain gauge stations, Figure 2.B, neglecting any 190 influence of elevation on rainfall data (Abbate et al., 2021). Then, RR was computed as the ratio of the cumulative rainfall on the duration D, Eq. (1.b). For the studied area, a set of thresholds proposed in the literature was considered, reported in Table 2. All the rainfall thresholds have a monomial expression where D is the duration of the rainfall (hours), and I is the average rainfall intensity (mm h -1 ). The "Caine" curve (2.a)  is the most general one, valid worldwide for shallow landslides and debris flow phenomena. At a regional scale, a more recent study conducted by  proposed a new set of curves 200 valid for central and southern Europe, considering a distinction among different climate types. In our study, three of them were selected: the general one (2.b), the curve valid for mid-climate (2.c), and the one suitable for highlands and mountain environments (2.d). Another study from  further extended the previous study by Guzzetti addressing a new I-D threshold valid for the Italian country. At the local scale, the "Cancelli Nova" (2.e) , the "Ceriani" (2.f) , and the "Crosta Frattini" curves (2.h) (Crosta and Frattini, 2001) were proposed 205 respectively in 1985and 1998. All of them were calibrated directly on the recorded data available in Sondrio Province. For each event, the couple points RR-D were plotted against the I-D threshold curves, and their return period RP was 210 evaluated. The former was determined following the methodology based on the IDF curves (Intensity Duration Frequency)  available for the Lombardy region and provided by (Rete Monitoraggio Idro-nivo-meteorologico).
The coefficients of IDF curves are estimated through the analysis of rainfall extremes addressing the GEV (Generalized Extreme Value) distribution. The dataset considered for the GEV was the SIMN time series (SCIA: Sistema Nazionale per l'elaborazione e diffusione di dati climatici) gathered from 1960 up to 1990 across the whole territory of the region. Bearing 215 in mind that our localized events EXL has been distinguished separately in respect to the diffuse DIF, also for the RP calculation, we have considered the same assumptions as for RR evaluation. For the localized events, the on -site coefficient of IDFs has been taken directly, whilebut for the diffusive ones, a spatially averaged value has been computed.

Trigger's hazard estimation and the MI magnitude index
A further step in the precipitation analysis consists of the hazard and magnitude assessment for each event. According to 220 (Guzzetti et al., 2005) the general landslide hazard could be defined as a probabilistic function of three terms Eq. (2.a): the size Al, the temporal occurrence Tl and the spatial susceptibility S. In Tthe "size" term hasve stored the information about the volume, the area or the density of landslides occurred over a particular area. The temporal occurrence considers the periodical reactivation of a single landslide (deep-seated) or the recurrence of shallow landslides episode inside a catchment.
The spatial susceptibility represents the quantification of the territory predisposition to a landslide phenomenon. 225 Starting from the definition of Eq.2.a. we have extended this concept and adapted it to interpret the events in our reanalysis study. The aim was to define a proper hazard and then a magnitude indicator for the hydrogeologicalgeo-hydrological events considering the temporal and spatial probability of occurrence of the triggering rainfalls. According to  a scale for the magnitude is necessary to interpret quantitatively the episodes and to highlight the most severe ones. 230 For landslides and rainfall-induced hydrogeologicalgeo-hydrological events, a unique method that describe the "energy" does not exist because several variables may play an important role in its definition . Therefore, under some hypothesis, we have proposed a new magnitude index (MI) as a quantitative parameter for assessing a proper magnitude ranking. Firstly, we have assumed that the investigated area had a homogeneous susceptibility = 1 to shallow landslide and debris flow triggering. This choice 235 was motivated by geologicaly and morphologicaly features, also looking at recent susceptibility maps proposed by (ISPRA, 2018). Then we moved on other terms trying to determine the spatial and temporal probability of exceedance from AA and RP parameters, recalling the theory of frequency-magnitude relationship.
FrequencyThe frequency-magnitude curve (FMC) was proposed by (Gutenberg and Richter, 1944) for earthquake studies and then was also extended for interpreting different types of natural phenomena (Gao et al., 2019). The MCF curve is 240 obtained by plotting incremental frequency Fi against the magnitude Mi on a logarithmic scale. Fi represents the frequency of the event that has a magnitude ≥ of a certain value Mi. In our study, the MFCs were considered to evaluate the probability of occurrence of a certain event in time and space and then combined in to determine its hazard as described in Eq. (2.a). The temporal occurrence term requires the estimation ( ≥ ) from RP's frequency-magnitude relationship. This represents the probability of occurrence of an event with a RP ≥ . According to (Guzzetti et al., 2005), the other hazard component 245 is addressed by the landslide size, Eq. (2.d). In this regard, inside our database was not possible to retrieve enough sufficient information about event features, such as the volumes and areas involved or the numbers of landslide failures. Therefore, the AA parameter was used as a proxy of the "trigger's size" and was treated similarly to the RP term. The probability of spatial occurrence ( ≥ ) of an event with a AA ≥ , was retrieved from FMC, Eq. (2.c). Then, the hazard has been estimated using the Eq. (3.a). Due to the modification of the first term ( ≥ ) it not properly represents the landslide 250 hazard, but Htrigger is an indicator of the hazard as a function the trigger's temporal frequency and spatial extension.
In most of the natural cases, the frequency of low magnitude hydrogeologicalgeo-hydrological events is rather high and viceversa. Therefore, we tried to estimate the trigger magnitude as an inverse function of the hazard. The former is a combinatio n of two probabilities of occurrence Eq. (3.b), therefore it can be transformed into a magnitude rec alling again the FMC in Eq.
(3.c). Working out some algebra with Eq. (3.a, 3.b and 3.c) we have obtained a representation of the magnitude expressed by 255 the index MI, Eq. (3.d). The MI is a sum of two contributes: the first describes its spatial extension through the parameter AA and the second its temporal occurrence through the RP. In this light, the MI calculated was intended to be more complete rather than the single RP because through AA term it is possible to considers the "integral effects" related to the trigger's extension. The MI was taken as a reference for testing the SLPT index presented in the next section.

NCM model and SLPT index
The extratropical cyclone dynamic influences the rainfall intensities recorded: if the EC is stronger, more precipitation is expected over an area but, depending on EC spatial and temporal evolution, rainfalls could exhibit different total amounts and duration. Therefore, using the NCEP maps, the Norwegian Cyclone Model (NCM) Martin, 2006; was chosen for estimating a strength index of ECs. NCM was formulated in the early 20th century. It describes an 265 extratropical cyclone that develops as a disturbance along the boundary (front) between the polar and mid-latitude air masses. The model calculates indirectly the Sea-Level Pressure Tendency (SLPT), the time-variation ratio of sea-level atmospheric pressure / (hPa h -1 ) that represents an indicator of the strength of a cyclone structure Martin, 2006;. When the EC is more intense, the absolute value of the SLPT ratio is higher and, consequently, the EC can cause more rainfalls. According to , this index is obtained as 270 a sum of four different influencing factors that correspond to the processes implicated in the dynamic evolution of extratropical cyclone: • 1 expresses the "upper layer divergence mechanism" due to jet streams, which removes air mass from the air column. In the Eq (4.a2), = 0.5 kg m −3 is the average density of air column and = 9.8 −2 . 275 ( −1 ) is the mean air column vertical velocity that is evaluated considering the Eq. (4.a1) in the proximity of the local change of jet stream velocity gradient ∆ ( −1 ), where ∆ ≅ 5000 m and ∆ 1 (m) jet streak elongation. According to , Eq. (4.a1) is a strong approximation because supposes air density constant over air column, so that we have considered a revised version  that expresses the in function of other parameters such as the geostrophic wind velocity ( −1 ), the curvature radius ( ) of Rossby waves 280 and Coriolis parameter ( −1 ); • 2 is the "atmosphere boundary layer pumping", which causes the horizontal wind to spiral inward toward a lowpressure centre. In Eq. (4.b2), the air density of the boundary layer is = 1.112 −3 . ( −1 ) is the vertical velocities at boundary-layer calculated through Eq. (4.b1) following the approach proposed by (Stull, 2017) 285 for cyclone structures: the factor is a function of boundary layer thickness, that can be assumed equal to 1000 m on average, and drag coefficient ≈ 0.005 is defined for flow over land; = 2 2 (4.b1) 2 = (4.b2) • T3 expresses the horizontal air mass advection that moves a low-pressure centre in the direction of the target region, Eq. (4.c2). The advection velocity ( −1 ) is a function of the celerity of Rossby waves ( −1 ) and the 290 geostrophic wind , Eq. (4.c1). The spatial pressure gradient at sea level is evaluated considering the distance ∆ 2 ( ) between the low-pressure centre and the target region; • 4 is the "latent heating" due to water vapour condensation in rainfall. It comes from the theory of thermodynamic transformations of water vapour in the atmosphere where all the parameters for rain condensation processes are 295 stored in the term . The precipitation that does reach the ground is related to the net amount of condensational in Eq (4.d3) that is considered for the description of the net column-average effect.
When the balance in Eq. (4) is negative the cyclogenesis occurs. T1, T3, and T4 bring a negative contribution to the balance strengthening the EC cyclogenesis and lowering the SLPT index. Instead, T2 has a positive contribution and tends to weaken 305 the ECs structure increasing SLPT value. In Figure 3Figure 3.Aa and Figure 3Figure 3.Bb have depicted the mechanisms described by four terms Ti. Figure 3Figure 3.Cc reports how the model works considering the contribution of each four components across the timeline (A to G) that represents the sages of EC: EC's formation phase (i.e. cyclogenesis) is fr om A to D stages and EC's dissipation phase (i.e. cyclolysis) is from D to G. The critical phase of the EC is in the proximity of point D where negative terms overcome the positive one. The SLPT index has been evaluated in correspondence of with C / 310 D stages. Figure 3: A) scheme of the mechanism represented by T1, T2, and T3 terms, B) scheme of the mechanism represented by T4 term, and C) qualitative temporal evolution of each of four terms T1, T2, T3, and T4 during cyclone phases (A to G) and their contribution to cyclone formation (cyclogenesis) and cyclone dissolution (cyclolysis), proposed in , modified after ,.

4 Results
In this section the results are presented the results in four steps. Firstly, is reported the qualitative analysis coming from the direct interpretation of database and NCEP maps is reported. Secondly is carried out the I-D rainfall analysis is carried out and the MI index evaluation is described. Thirdly is estimated the SLPT for each considered event the SLPT is estimated and then compared with MI index. 320

Database interpretation and NCEP maps
The dataset of Table 1Table 1 shows a clear seasonal distribution of the events mainly concentrated during summer and autumn seasons. July and November are the months more prone to hydrogeologicalgeo-hydrological events and this strong seasonality highlights that the triggers phenomena involved may have a different originsnature (Martin, 2006;. In July, meteorological events are characterized mainly by high intensity and short duration with a typical 325 convective behaviour of precipitation (thunderstorms), and their average duration is generally around 1 or 2 days. In particular, 1951, 1953, 1987, 1997, 2008 and 2019 events happened during the summer season and rainfall cumulated were comprised between 100-200 mm, apart from 1987 and 1997 that were rather exceptional (254 mm and 275 mm in three days on average). 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. 330  Through the analysis of NCEP maps, we have observed that all the events reported in Table 1Table 1  highlights that three events have been characterized by the evolution of a rather intense EC that is recognizable from the deep low pressure (L) located near the British Islands. This recurrent configuration has been responsible for the torrential 340 rainfall recorded in the southern Southern Alps across the Sondrio Province. Consequently, the hydrogeologicalgeohydrological effects triggered could be directly imputed to the intensification of these EC structures. Starting from this qualitative evidence we have moved to a quantitative analysis following the two approaches proposed.

Approach 1: I-D threshold rainfall analysis and MI index extension
The average daily rain rate and the duration of the rainfall episodes in Table 1Table 1  Considering the thresholds proposed by Guzzetti, all the events points are correctly settled above. No significative significant differences are seen among the general one (b), the curve valid for mid-latitude climate (c) and the one valid for highlands 350 climate (d). Peruccacci (e) and Crosta-Frattini (h) poses intermediately between the regional threshold of Guzzetti and the local ones proposed by Cancelli-Nova (f) and Ceriani (g). It seems that Guzzetti, Peruccacci and Crosta-Frattini may overpredict critical events because they are positioned rather low, especially for short duration ones.
The thresholds proposed by Caine (a), Cancelli-Nova (f) and Ceriani (g) are placed above the previous ones. The Ceriani curve one seems to fit very well the data, positioning only the 1966 event slightly below the curve and the 1953 and 1960 355 close to the curve. Also, Cancelli Nova works rather well posing only 1953 below the threshold. These results were expected because both (g) and (f) threshold were calibrated using a local dataset, respectively up to 1985 and 1994. Conversely, the Caine threshold seems to work worst rather than the previous leading to underprediction : 1953, 1960   The threshold curves analysed have divided our events into critical and non-critical ones but no further information on their magnitude were was retrieved yet. Some authors have shown that a measure of that magnitude may be established considering the relative distances between the I-D points and the threshold curve. According to (Crosta and Frattini, 2001;, a beam of rainfall I-D curves can be elaborated including their dependence 365 from on RP. For a the same area, rainfall events with higher RP should be statistically located much more distant from the threshold lines, but this fact strongly depends on the reference curve considered as the lower bound. In our study, local thresholds of Ceriani and Cancelli-Nova have demonstrated to best fitting the dataset avoiding under-and over predictions.
Moreover, they are delimited by 1953,1960,1966 and 2008 events which exhibit the lowest RPs comprised between 2-5 years. Taking these curves as a reference we can appreciate that other critical events showing higher RPs are also located at 370 more distance from these curves. This represents a confirmation of what found in the literature, but, in our opinion, the magnitude assessment looking simply at relative threshold distance seems rather approximate. In fact, the RP estimation depends not only on rainfall I-D values but also on parameters of GEV that takes into account the spatial variability of local precipitation statistics . In those cases where rainfall intensity and duration are fixed, changing the GEV parameters also the RP may vary even though the relative distance from the curve is maintained the same. In our 375 dataset, we have encountered this fact two times comparing 1983 and 1987 events, and 1997 and 2018 events that respectively exhibit the same RP with the same duration but a different relative distance from the curves. As a result, these distances could be used as a proxy of the magnitude only for rainfall analysis carried out at the same location where the GEV parameters remain constant, confirming what suggested by other authors. In our case study, this condition was not satisfied because the GEV parameters were not constant in space. 380 Looking at Figure 6Figure 6.A, the Sondrio Province has experienced at least four exceptional rainfall events with a return period equal to, or higher than 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 that affected the area in the 385 second half of the XX century. This apparent contradiction has a possible explanation if we also include the information about the spatial extension of the triggers, as reported in Figure 6Figure 6.B, which is a property strictly related to the nature of the rainfall event (Corominas et al., 2014;. This parameter is not explicitly considered in RP evaluation.
As an example, we can compare the 1983 and 1987 events. If only the RP is considered, 1983 intensity is equal to 1987, but considering the spatial distribution, the 1983 event affected only a limited area while 1987 spread across the entire province. 390 For this reason, if we are interested in determining the magnitude of meteorological triggers, 1987 should be intended worse more critical rather than in 1983. In this regard, the RP information could be misleading., According to (Corominas et al., 2014;Guzzetti et al., 2005)
For determining the 1 term (Eq. 4.a2, upper layer divergence), the geostrophic wind velocities were estimated. Geostrophic 415 wind is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force. It represents a first approximation of the general circulation of the air masses at a regional scale. and Iintense geostrophic velocities are generally associated with strong EC structures Martin, 2006;. As reported in Figure  For determining the 2 and 3 terms (Eq. (4.b2) boundary layer pumping and Eq. (4.c2) advection), the air masses evolution paths were examined. Figure 9Figure 8.C shows the short distance ∆ 2 between the low pressure (L) and the Sondrio Province. We can notice that the relative position of ECs does not vary too much, 1183 km on average. This represents a characteristic of the ECs structures that tends to evolve across the Mediterranean and the Alpine area similarly. Nevertheless, 425 some seasonal changes can be appreciated by looking at the advection path followed by the low-pressure centre (L). The larger part of the autumnal events exhibits a meridian motion of the low pressure from the northern part of Europe (Northern Sea) to the southern part, entering the Mediterranean Sea and moving eastward following Rossby waves track . This is the case of 1960, 1966, 2002events that occurred between September and November. Summer events of 1951, 1953, 1987 and 2019 exhibit a low-pressure tracking path that did not cross the 430 Alps mountain range. This fact can be explained by considering that Rossby waves are in general shifted northward during the summer period 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.
The 4 term is represented by a linear function of the daily rainfall rates RR considered in the precipitation analysis. In the formulation adopted we made strong assumptions to yield the problem more tractable. This is the only component that 435 depends on the accurate estimation of the ground-based rainfall data.
After calculating the intermediate components 1 , 2 , 3 and T4 terms, the Sea-Level Pressure Tendency index (SLPT) of Eq.
(4) has been determined, Figure 9.DFigure 9. Firstly, we can notice that all these ECs have been characterized by explosive cyclogenesis. This definition applies when an extratropical cyclone exhibits a low pressure deepening of 24 hPa in 24 h, which corresponds to an average rate of 1 hPa h -1 . Looking at Figure 9.DFigure 9,, the SLPT 440 index shows a range comprised between the -2.64 hPa h -1 , recorded for the 1953 event and -4.89 hPa h -1 recorded for 1987.
The latter and 2002 (-4.67 hPa -1 ) are reported to have been the EC structures with the highest intensity that affected the Northern Lombardy area. An average value of the SLPT index is reported around -3.67 ± 0.63 kPa h -1 that is compatible with the ECs structures shown by NCEP maps. 445 Figure 9: A) Upwind velocity and B) geostrophic wind velocity calculated for T1 term and C) ∆ considered for T2 and T3 terms. D) The Sea-Level Pressure Tendency Index (SLPT) for the event analysed is compute. Orange lines represent the averages across the dataset while the red line indicates the threshold of explosive cyclogenesis (1 hPa h -1 ).

Comparison between MI and SLPT indexes 450
The two methodologies proposed for the trigger's magnitude assessment are now compared. The two indexes MI and SLPT have been firstly normalized in respect to their maximum and then shown in Figure 10Figure 1960,1966,1983,1997,2000,2018 and 2019, that which were depicted also by historical chronicles as rather intense but not catastrophic for the Sondrio Province. On In Figure 10Figure 10.B the MI index and the SLPT index have been plotted against each other. From the figure can be appreciated that the points lay on the 460 diagonal and the correlation index R 2 is about 0.88, that which is rather high and near to 1.

Discussion
Considering the results obtained, we discuss here the questions that aimed at our study. The first was: "Are the I-D thresholds and the RP evaluation enoughsufficient for a complete description of meteorological triggering factors?" The I-D thresholds are typically used for hydrogeologicalgeo-hydrological risk assessment but some uncertainties about their reliability have risen around two aspects: the choice of the best best-fitted threshold and the threshold's dependency on the 470 RP parameter.
Regarding the first aspect, the thresholds are able tocan distinguish critical or non-critical events giving only a binary outcome of the event classification. Shifting updown the curve or changing the curve, the same event can be detected respectively as a false negative or a false positive and this fact that may lead to a prediction error. In the specific case of our dataset, Guzzetti, Perrucacci and Crosta-Frattini curves seem to overpredict theseat eventsoccurrence while Caine was found 475 to underpredict themit. On the other hand, Cancelli-Nova and Ceriani have demonstrated more suitable for interpreting our dataset. In this regard, the local thresholds seem to be more accurate rather than the regional ones, but uncertainties remain about their correct application and interpretation. In fact, some recent studies have suggested that further investigation around their parameter's definition are required in order to improve detection performances. According to several authors Kim et al., 2020;Lazzari et al., 2018) the threshold may exhibit a dynamic behaviour, shifting 480 up-down in function ofconsidering the soil moisture and the antecedent cumulated rainfall especially for short duration events. This important condition has been normally neglected in the past definition of the thresholds, treating all the triggering events as uniform from the statistical point of view. Therefore, a wise disaggregation of these events in the function of antecedent conditions should be applied for creating a new threshold set that highlight the sensibility to those variables. In our opinion, this may help to improve further the performance of I-D methodology especially for locally based 485 thresholds under the reasonable hypothesis of a uniform spatial susceptibility of the territory. On the other hand, for the regional ones, we think that the improvements would be less effective because also other factors related to the more heterogeneous area, such as morphological or geological predisposing causes, may play a more important role . Including the RP in the threshold analysis can be useful to determine a preliminary magnitude ranking. Even though higher RPs are generally founded at a higher distance from the curve, the relative distance among I-D point and the 490 reference threshold cannot be always considered as a proxy of the event magnitude. According to  this assumptionrelation has been reported not so strong, and this was confirmed also in our reanalysis study. A possible explanation can be found in the way of the RPs are estimated. In principle, this interpretation of the trigger's magnitude is still valid only at a very local scale but cannot be adopted in our study since the GEV parameters used in RPs have changed in each rainfall episodes. Our results have highlighted this fact two times showing different point-threshold distances in with 495 respect to the same RP values. In this perspective, the climate change will pose some challenges about the GEV updating for the future, considering that no stationary processes could affect the statistical distribution of critical precipitation (Albano et al., 2017b;. This may add further uncertainties to this interpretation that considers only I-D thresholds and RPs for event magnitude estimation. These two important observations represent a critical point in the I-D threshold methodology that has driven us to ask: "Is 500 RP a good predictor of the magnitude?" Typically, the magnitude of a rainfall episode is described by the RP value, but this information is evaluated only in from time perspective. Taking inspiration from the landslide hazard definition proposed by (Guzzetti et al., 2005) we defined a new magnitude index, MI, that was also representative of the "triggers energy". In the definition of MI, we have included the information about the trigger's spatial distribution AA. This choice was aimed by at the lack of precise data about the landslide volumes, extensions, or numbers, that which are quantities considered for 505 assessing an event magnitude scale . The AA parameter can be interpreted as another proxy of the trigger's magnitude because indirectly it can describe the nature of the rainfall phenomena, distinguishing between a heavy thunderstorm, localized, in respect to a persistent a rain, more diffused. As shown by our results, RP and AA were uncorrelated so both were considered for the assessment of the magnitude index MI. The MI index was estimated in our study with post-event information but theoretically the index can be evaluated using weather forecasting, looking at expected 510 rainfall rates and amounts across different areas. In this regard, Local Area Meteorological Models (LAMs) can be used to estimate the MI index some hours in advance of the event starting. In our opinion, this represents one of the main advantages of using MI because, in respect to the other magnitude indexes that requires precise information about the "post-failure" effects (number of triggered landslides or peak discharge), the MI can be established using again only meteorological information, much like the SLPT index that we propose further. 515 As a matter of fact, we have implicitly answered to the third question proposed: "Can rainfall analysis be improved considering also other meteorological variables that are related to the trigger's magnitude?" The assessment of the MI index has highlighted that the very local information about precipitation is not exhaustive, and a spatial distribution of the rainfall is also needed for to better comprehend the differences among the events. Moreover, if we are interested in the accurate trigger's description, looking only at the "final product" of a more complex meteorological process may be not enough 520 (Monitoring European climate using surface observations; . This is particularly true in mountain areas where the territory enhances the heterogeneity of the rainfall field (Abbate et al., 2021). For these reasons, other meteorological variables should be taken into account and included in the analysis. In our study, to pursue this goal we moved from a local perspective to a more regional one. This is crucial because it permits to better describe the different precipitation type that may influence the occurrence of hydrogeologicalgeo-hydrological failures (Corominas et al., 2014;525 Guzzetti et al., 2007). As an example, an intense thunderstorm during summertime could trigger few shallow landslides or debris over a limited area (Abbate et al., 2021; in respect to a persistent orographic rainfall that could affect an entire region, trigger diffuse terrain instabilities and reactivate also deep-seated landslides . In this regard, the local rain gauges series have been integrated with the NCEP reanalysis maps data and the SLPT index was evaluated applying the theory of the Norwegian Cyclone Model. The 530 implementation of this methodology has represented an innovative way to gain a comprehensive meteorological description of the rainfall triggers. In fact, in the NCM model, the ground-based rainfall series represent only one term (T4) that is involved in the EC intensification. The former depends also on other processes: the upper layer divergence (T1), boundary layer pumping (T2) and low-pressure advection (T3). This additional information has been addressed to play an important role in EC evolution and helped us on better differentiate critical events characteristics. 535 The SLPT index formulation requires several data about triggers. These can be retrieved easily by looking at a reanalysis database such as the NCEP reanalysis maps. However, NCEP maps interpretation is rather useful only for past events.
Nowadays LAMs are much more suitable for interpreting the mechanism of EC through a complex orographically area like the Alps (Ralph et al., 2004;. In this regard, the NCM model is still valid but the processes involved can be interpreted at a higher detail level with LAMs, avoiding some of the hypothesis required by NCM. The 540 evaluation of the SLPT index should be intended as propaedeutic to further analysis and it cannot be adopted in every situation. As we have foreseen from results, concerning I-D thresholds methodology, the SLPT estimation requires to movemoving from a very local perspective to a regional scale. This operation makes sense if the investigated area is rather extended for excluding very site-specific chain effects that can be triggered by isolated rainfall episodes, such as thunderstorm cells. Another important limitation on the applicability of the SLPT index regards the presence of a 545 recognizable EC's structure from meteorological maps. In fact, for weak EC's, the estimation of the trigger's magnitude may bring larger errors. In our study, this fact was experienced for the cases of 1953, 2008 and 2019 and was confirmed through visual inspection of NCEP maps. In these situations, the rainfall analysis should be restricted to a more local domain trying to include also LAMs outputs, radiosonde, and satellite data (Abbate et al., 2021) and the application of MI index could be much more appropriated for the magnitude estimation. 550 As a result of our study, we have compared the two MI and SLPT indexes to assess the magnitude of critical events. Even if they come from different theories, MI is based on frequency-magnitude theory and SLPT is has a physical meaning in the meteorology field, appears clear how they are in accordance depicting the same critical events with the highest magnitudes. This outcome has found a confirmation in the qualitative information we retrieved in the historical database. These results have demonstrated that exists a strong cause-effect relationship among the strength of EC developed at a regional scale in 555 respect to the effects recorded on a local scale, especially for strong events. For the dataset examined, the SLPT comparison with the MI index was rather encouraging, R 2 = 0.88, and the additional information retrieved from NECP maps has sharply improved the rainfall reanalysis completeness. In our opinion, both proposed indexes are useful instruments for describing the magnitude of the rainfall-induced events, overcoming the uncertainties of the I-D threshold methodology.

Conclusions 560
This study presents an extended reanalysis of the meteorological triggering factors that have caused in the past several hydrogeologicalgeo-hydrological issues in the alpine mountain territory of the Sondrio Province, Northern Lombardy, Italy.
Excluding the geomorphological predisposing causes of the area, the attention was pointed out to the characteristics of the rainfall. The main goal of our study was to assign a quantitative magnitude ranking to the meteorological trigger, following two approaches. 565 In the first one, the I-D threshold curve analysis was considered to identify critical rainfall events. We have demonstrated that the events fit some I-D thresholds, in particular the local thresholds of Cancelli-Nova and Ceriani, and that the distance from the curve does not necessarily mean that an event has a higher RP. For this reason, in order to assign a magnitude to each of the events, we proposed the MI index, which integrates the return period and the spatial extent of the event. The MI index was determined analytically starting from the frequency-magnitude theory, under the hypothesis that the event's 570 magnitude was also a function of the spatial distribution of the trigger, described by the parameter AA. In the second approach, the trigger's analysis was conducted from a simply meteorological viewpoint evaluating the strength of extratropical cyclone structure through the NCM model. Using the information of NCEP reanalysis maps the SLPT index was determined and interpreted as another trigger's magnitude index, much like the MI.
The two indexes have been compared showing good accordance in the assessment of a magnitude ranking for the studied 575 events. The SLPT index has confirmed the important relationship among between the EC's intensity at a regional scale and the correspondent trigger's magnitude recorded locally, described by the MI. The two indexes are based on meteorological data therefore, therefore, may found an application in the now-casting meteorology field. This could represent an important advancement, especially for the early warning systems adopted by municipalities for hydrogeologicalgeo-hydrological risks mitigation. 580 In view of the future climate change that, with high confidence , will affect the Mediterranean and the Alpine environment, extreme meteorological events are supposed to increase Moreiras et al., 2018) and also hydrogeologicalgeo-hydrological hazards may rise in frequency. Our study moves in this direction, trying to extend the interpretation of rainfall triggering factors through a more meteorological perspective.

585
Code and data availability: All the data reported in this paper are freely consultable on Internet websites. In particular, reanalysis weather maps are freely downloadable from Meteociel Website (MeteoCiel, 2020), IFFI and AVI database are freely consultable and downloadable from (Sistema Informativo sulle Catastrofi idrogeologiche; Inventario Fenomeni Franosi), and rain gauges data are extracted from local Environmental Agency (ARPA Lombardia, 2020). The model applied 590 in this work is also freely consultable and downloadable from . Abstract. This paper presents an extended back analysis of the major hydrogeologicalgeo-hydrological events that occurred 805 in the last 70 years in the alpine area of the Lombardy region, Italy. This work is focused on the d escription and the interpretation of the major meteorological triggering factors that have caused these mass movements.
The triggering factors for each hydrogeologicalgeo-hydrological 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 data, comparing them against rainfall-threshold curves proposed by several authors. Moreover, the return 810 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 hydrogeologicalgeo-hydrological 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 compared throughout two indexes that tried to assess the strength of rainfall phenomena: the first 815 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 hydrogeologicalgeo-hydrological 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 index, a quantitative ranking of their intensities that has revealed to be a good predictor for the magnitude 820 of hydrogeologicalgeo-hydrological rainfall-induced events.

Introduction
Landslides represent one of the main hydrogeologicalgeo-hydrological hazards in Alpine and Apennines regions (Albano et al., 2017;. Italy is a country historically affected by a diffuse hydrogeologicalgeo-hydrological fragility of the environment  and mountain slopes are the most 825 vulnerable places where landslides and flash floods can occur 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 meteorological events that rarely occur and have particular features regards their duration and their intensity . 830 In the context of hydrogeologicalgeo-hydrological risk prevention, urban planners and infrastructure engineers have to deal with the analysis of triggering factors and need instruments for its quantification . In this paper, a back analysis of the meteorological triggers of past hydrogeologicalgeo-hydrological events is presented. Indeed, a quantitative study of local precipitation is mandatory to correlate these meteorological events with landslide failures (Corominas et al., 2014;. 835 A common approach used consists of the analysis of the return period (RP) of the triggering rainfall . 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 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,

Codice campo modificato
Codice campo modificato coming from an intense and prolonged meteorological event (Albano et al., 2017;. For a landslide 840 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. ISPRA, 2014ISPRA, , 2018. Therefore, try to interpret this cause-effect relationship looking only at the rainfall series cannot be used. 845 However, for shallow landslides and debris flows hazard assessment, are considered the rainfall intensity-duration curves Olivares et al., 2014;. 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, considering this type of landslide rainfall-induced Rosi et al., 850 2016). These thresholds data are calibrated looking at the past events occurred in the area and directly correlated with the nearest rain gauge measures . Intrinsically they include the susceptibility of the local territory to landslide failure so their usability generally can't be extended to other regions ISPRA, 2018;. On the other hand, this method is widely used for predicting the occurrence of shallow landslide and debris flow events but, due to its empirical nature, it is rather approximate and leads sometimes to "false alarm" detecting 855 .
Even though the rainfall return period estimation and rainfall thresholds have been widely used in different parts of the wor ld , 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 rainfall events and the linked consequences? 860 Generally, a local study on the triggering causes is not completely descriptive of the real magnitude of the meteorological triggering event (COPERNICUS, 2020;. This is particularly true in mountain areas 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 . In particular, the type of rainfall events cannot always be recognized directly from rain gauge time-series so that other meteorological variables should be taken into account for its 865 description. This is crucial because different precipitation type can affect the characteristics of the hydrogeologicalgeohydrological failures (Corominas et al., 2014;. An intense but rather localized rainfall, such as a thunderstorm, could trigger a certain type of hydrogeologicalgeo-hydrological issues, such as shallow landslides and soils slips . On the other hand, a persistent orographic rainfall, which could affect an entire region for several days, may have completely different effects on the territory, enhancing its hydrogeologicalgeo-hydrological fragility 870 . Therefore, a more complete description of the type of triggering factor is necessary to better explain the territorial hydrogeologicalgeo-hydrological dynamics.

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The goal of this paper is to investigate the relationship between hydrogeologicalgeo-hydrological issues and their triggering factors in a broader sense, starting from the back analysis of past hydrogeologicalgeo-hydrological events, where landslide and flash flood occurred. The alpine region in the northern part of Lombardy, Italy, was considered because of its past 875 critical hydrogeologicalgeo-hydrological events (CNR, 2020;ISPRA, 2014;. 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 about the spatial and temporal evolution of the triggering events at 880 larger scale .
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 final remarks and conclusions of the ongoing research work are reported. 885

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

Historical database of hydrogeologicalgeo-hydrological events
A group of past hydrogeologicalgeo-hydrological events has been considered for the alpine area of Sondrio Province, northern Lombardy, Italy, Figure 1. This area was affected by exceptional hydrogeologicalgeo-hydrological events in July 890 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 . On the other hand, the entire province was also affected mainly by diffuse hydrogeologicalgeo-hydrological episodes such as shallow landslide and flash floods, that caused people injuries and comparable damages to infrastructure and buildings, estimated in 895 2 billion of euros. These hydrogeologicalgeo-hydrological issues were caused by a rather intense and prolonged rainfall episode  and the effects were enhanced by rapid glacier melting increased by high-altitude summer temperatures.

900
The back analysis has considered also other critical hydrogeologicalgeo-hydrological 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 hydrogeologicalgeo-hydrological 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 905 website (CNR, 2020;ISPRA, 2014). 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  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 910 between the AVI and the IFFI 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 915 (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 hydrogeologicalgeo-hydrological events analysed in the study and their description retrieved from AVI and 920 IFFI databases is reported in Table 1.

Valtellina Valley
Como Lake SWITZERLAND Codice campo modificato The precise location of each hydrogeologicalgeo-hydrological event was not directly reported in the dataset, but an indication of the municipalities affected by hydrogeologicalgeo-hydrological 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 930 series. In particular, rainfall events were distinguished in two types: extremely localized events (EXL), with an influence area lower than 1000 km 2 , or 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;. 935 The dataset analysis of Table 1 shows a clear seasonal distribution of the events mainly concentrated during summer and autumn. July and November are the months much more prone to hydrogeologicalgeo-hydrological events and this strong seasonality highlights that triggers phenomena involved may have a different nature (Martin, 2006;. In July, 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, , 940 1953In particular, , 1987 and 2008 events happened during the summer season and rainfall cumulated were comprised between 100-200 mm, apart from 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 945 (Martin, 2006). These observations from the dataset have been studied in deep from a quantitative viewpoint considering the two approaches 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. 950 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 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 955 threshold curves proposed in the literature by several authors.
The "Caine" curve  is the general one, valid for shallow hydrogeologicalgeo-hydrological processes around the world, Eq. (2.a). The "Ceriani" curve  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  has proposed a new set of rainfall threshold curves valid for central and southern Europe, considering a distinction among different climate typ es. 960 In our study, three of them have been selected: the general one Eq. (2.c), the curve valid for mid-climate Eq. (2.d) and the one suitable for highlands Eq. (2.e). All the rainfall threshold curves have a monomial expression where the is the duration of the rainfall [hours], and the is the average rainfall intensity [mm/h]. A further step on rainfall analysis dealt with the evaluation of the correspondent return period (RP). The RP is directly associated with the intensity of the rainfall because it expresses the probability of recurrence of a particular rainfall eve nt on 965 a location (Corominas et al., 2014;. Using the Curve of Pluviometric Possibility (CPP)  available for the Lombardy region and provided by (ARPA Lombardia, 2020), the RP of precipitation was 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. 970

Reanalysis Approach: NCEP Reanalysis Maps
To improve the analysis of triggering factors, the database was studied considering other variables associated with the 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 . They have a 975 spatial resolution of 2.5° x 2.5° degrees of latitude and longitude, covering the whole planet with a temporal frequency of 1 2 h. These maps contain information about temperature and pressure distribution at different geopotential heights, i.e. 850 h Pa 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 . Moreover, the wind fluxes velocities are important for establishing the spatial and temporal evolution of a 980 particular rainfall event . A qualitative looking at the reanalysis maps for each considered event highlights some similarities regarding the meteorological configuration of air masses. Not surprisingly, the major hydrogeologicalgeo-hydrological events have occurred during strong extratropical cyclone (EC), as described in Figure 2.
ECs are important meteorological phenomena that develop in the Atlantic Ocean near the British Islands and are moved 990 eastward through the Mediterranean area thanks to the dynamic of the Rossby waves at planetary scale Martin, 2006). These generate at the boundary of the polar vortex strong jet streams that can move air masses in the 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  thanks to the instauration of a strong southern moist and warm flow, the "Scirocco" wind, as reported by (Grazzini, 995 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 . In addition, the presence of convection especially during the summer season may add another level of complexity, producing a further enhancing of local rainfall rates . This dynamic is characterized by some peculiarities that are necessary to be understood for interpreting the local scale 1000 rainfall effects on the territory. Therefore, using the NCEP maps, a synthetic model proposed by Martin, 2006; was chosen for the estimation of a strength index related to the extratropical cyclone intensity. The model 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 Martin, 2006;. In general, this ratio is higher, in an absolute sense, when the EC is more 1005 intense. According to , 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: ▪ 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 1010 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 ]. 1 = − (4.a) ▪ 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  for cyclone 1015 structures.

= (4.b)
▪ 3 is the "latent heating" due to water vapor condensation in rainfall. It comes from the theory of thermodynamic transformations of water vapor in the atmosphere where all the parameters for rain condensation processes are stored in the term = 0.082 [ / ] and [ /ℎ] is the average hourly rainfall rate. In the model proposed, the information related to the local rainfall intensity is considered only in 1020 this term while the other is in the function of the meteorological parameters retrieved from NCEP reanalysis maps [27].
formation (i.e. cyclogenesis, from A to D) and EC dissolution (i.e. cyclolysis, form D to G). When the balance in Eq. (4) is negative the cyclogenesis occurs so that the critical phase of the EC is in the proximity of point D where negative terms overcome the positive one.

Results and Discussion
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 1035 intensity.

Approach 1: the Rainfall Analysis
Considering the average daily rain rate and the duration of the rainfall episodes reported in Table 1 Considering the thresholds proposed by , 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 1045 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 dataset of local events until 1994. Conversely, the "Caine" threshold seems to work worst rather than the previous. 1953, unable to detect these events. Moreover, the 1997 and 2000 are settled borderline on the curve. 1050 For each critical event, the related rainfall return period has been also specified in Figure 4. According to , 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 fro m 1055 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 hydrogeologicalgeo-hydrological events, but the empirical correlation founded in these literature analyses suggests that it may be subjected to large uncertainties .
In conclusion, the threshold curves assess if a rainfall event can trigger hydrogeologicalgeo-hydrological issue, but no further 1060 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 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 hydrogeologicalgeo-hydrological event simply looking at these distances among the 1065 threshold and each critical event point.

1070
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 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 1075 rainfall event (Corominas et al., 2014;. 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 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 1080 hydrogeologicalgeo-hydrological consequences on the territory. According to (Corominas et al., 2014), the hazard intensity of a hydrogeologicalgeo-hydrological event can be addressed considering three different contributes. Excluding the territorial susceptibility, the extension of the affected area and the intensity of the triggers are the other two main components. In scientific literature, it does not exist a unique method for the magnitude assessment of a hydrogeologicalgeo-hydrological episode because its quantification depends on the type of 1085 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 , a magnitude index can be defined as a logarithmic function of the number of triggered landslide and considering the study of , a similar frequency-magnitude relation can be found for the intensity of 1090 rainfall event. Based on these evidences, two indices 1 and 2 have been considered for defining the magnitude of analysed hydrogeologicalgeo-hydrological events, taking into account the fact that both the spatial extension and the intensity of triggering are involved in its definition. experienced higher values of the index 1 and 2 that are in accordance with the previous observations, i.e. intense event 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 physically based index proposed in the meteorological reanalysis approach. 1100

Approach 2: Meteorological Analysis
The second approach consists of the application of the model proposed by  and described in Eq.(4).
Atmospheric pressure gradients, wind velocities, and air masses advection through the Alpine region were studied for 1105 feeding each of the model components illustrated in the Equation (4.a), (4.b), and (4.c). According to , the sealevel pressure tendency index (SLPT) Δpsl/Δt [hPa/h] was calculated for assessing the intensity of the meteorological 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.

Wind Components 1110
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 Martin, 2006; 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 . The geostrophic wind velocity, calculated in correspondence of the central phase of the event (stage "D" in Figure 3), exhibit 1120 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 masses configuration that characterizes this type of event where orographic precipitations are enhanced in intensity and they 1125 are generally prolonged for several hours or days . 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;. Therefore, other terms of Eq. (4) are further discussed.

Air Masses Evolution Paths 1130
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.  Looking at Figure 8.A the larger part of the autumnal events exhibits a meridian motion of the low pressure from the northern part of Europe (Northern Sea) to the southern part, entering the Mediterranean Sea and moving eastward following Rossby waves track . This is the case of 1960, 1966, 2000, 2002 and 2018 events 1140 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 . 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 mountain range (Figure 8.B). This fact can be explained by considering that Rossby waves are in general northern shifted 1145 and less meandered during the summer period 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.

Sea-Level Pressure Tendency Index 1150
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 . Looking at Figure 9, the SLPT index shows a range comprised between the -0.28 hPa/h, recorded for the 1953 event and -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 1160 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 . They are potentially dangerous for the territory due to their rapid evolution, causing flash floods and diffuse hydrogeologicalgeo-hydrological issues that, in our case, have been confirmed by the historical chronicles found in the AVI 1165 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 hydrogeologicalgeo-hydrological event examined. Considering the rather strong cause-effect relation that was highlighted by historical chronicle among the intensity of the rainfall episodes and the severity of the subsequent 1170 hydrogeologicalgeo-hydrological 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 similar magnitude ranking of the events studied. In particular, both have addressed again the 1987 and 2002 as the two most 1175 critical of the entire dataset and have ranked 1953 as the lowest intense. For the other events, the ranking was rather simil ar showing an overall root mean square error (RMSE) less than 7%.

1180
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 severity of the subsequent rainfall induced hydrogeologicalgeo-hydrological events. 1185

Conclusions
This study presented an extended back analysis of the triggering meteorological factors that have caused in the past several hydrogeologicalgeo-hydrological 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 characteristics of rainfall that were considered as the primary cause of hydrogeologicalgeo-hydrological hazards analysed. 1190 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 hydrogeologicalgeo-hydrological 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 implicated in the physical description of a rainfall phenomenon. 1195 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 hydrogeologicalgeo-hydrological 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 event intensity. The RP values do not take into account explicitly the spatial distribu tion of the meteorological 1200 phenomena that are directly correlated to the consequent hydrogeologicalgeo-hydrological issues triggered in the territory. Therefore, a composite magnitude index for assessing a ranking of hydrogeologicalgeo-hydrological events considered has been proposed taking into account not only the intensity of the triggers, i.e. return period of rainfalls, established from t he analysis of the rainfall series, but also the information about the spatial extension of the affected areas.
In the second approach, a meteorological analysis of the triggering has been carried out taking into account the NCEP 1205 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.
Both two indices have shown good accordance in the assessment of the magnitude of the studied events. In particular, the 1210 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 hydrogeologicalgeo-hydrological issues that affected the alpine territory were proportional to the overall intensity of extratropical cyclone systems and the SLPT index has been able to highlight this fact, 1215 also distinguishing the nature of the triggers.
In the view of the future climate change that, with high confidence , will affect the Mediterranean and the Alpine environment, extreme meteorological events are supposed to increase Moreiras et al., 2018). Our study moves in this direction, trying to consider integration between the traditional approach (i.e. local rainfall analysis) and the new instruments that meteorological models are starting to provide (i.e. 1220 meteorological reanalysis map) in order to give a comprehensive interpretation of the triggering factors of severe hydrogeologicalgeo-hydrological events.
Code and data availability: All the data reported in this paper are freely consultable on the Internet websites. In particular, reanalysis weather maps are freely downloadable from Meteociel Website (MeteoCiel, 2020), IFFI and AVI database are 1225 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 .
Author Contribution: Andrea Abbate carried out the formal analysis and prepared the manuscript with contributions from 1230 all co-authors. Monica Papini supervised the research and Laura Longoni the review & editing.