A group of past geo-hydrological events has been considered from the alpine area of Sondrio Province, northern Lombardy, Italy (Fig. 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 exceptional geo-hydrological events triggered by a rather intense and prolonged rainfall episode (Rappelli, 2008; Tropeano, 1997). The effects on the territory were severe: shallow landslides, debris flows, and flash floods were recorded causing human injuries; 35 fatalities; and extensive damage to infrastructure and buildings, estimated at EUR 2 billion (Sistema Informativo sulle Catastrofi idrogeologiche, 2020).

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, 2020). The data collect historical information from past natural disasters from the medieval age up to nowadays; the AVI database is directly available via a geoportal website (http://sici.irpi.cnr.it/; last access: July 2021) that is managed by CNR (Consiglio Nazionale delle Ricerche), and the IFFI database is available from a national geoportal website (Sistema Informativo sulle Catastrofi idrogeologiche, 2020). Available event time series were not homogeneous, so the consistency of the database was evaluated, redundant records have been dropped, and final integration between the AVI and the IFFI database information was carried out.

The period chosen for the reanalysis is between 1951 and 2019. Systematic monitoring of the precipitation and temperature was 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, 2020). The available rain gauge data series were gathered from local archives of SIMN (SCIA, 2020) and ARPA Lombardia (ARPA Lombardia, 2020). These series were conventionally recorded on a daily basis until the 2000s, so “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 the AVI and IFFI databases, the precise location of geo-hydrological episodes was not available even for the most recent events that happened after the 2000s. Therefore, some indications about locations were retrieved from the AVI database considering the municipalities affected by disasters. The spatial extent of affected areas (AAs) describes those locations that have experienced some damage due to geo-hydrological events that have 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 reconstruct for each rainfall event its spatial distribution. Selected events have been classified in terms of the AA parameter: extremely localized events (EXLs), with an influence area lower than 1000 km2, or diffuse events (DIFs), with significant territorial diffusion greater than 1000 km2. This threshold has been motivated referring to the nature of the meteorological triggers: EXLs were generally associated with convective rainfall phenomena whose extent is of the order of 10×10 km2, and DIFs were characterized by diffuse and uniform rainfall with an extent of around 100×100 km2 (Martin, 2006; Rotunno and Houze, 2007). In Table 1 a list of geo-hydrological events analysed in our study is reported.

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; MeteoCiel, 2020; NOAA, 2021). The latter has a spatial resolution of 2.5∘×2.5∘ latitude by 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 mass dynamics in the 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 develop in the Atlantic Ocean near the British Isles. ECs are responsible for a large part of the precipitation recorded over the Alps mountain range (Rotunno and Houze, 2007) because they are generally advected eastward through the Mediterranean area by Rossby waves (RWs) (Grazzini and Vitart, 2015; Martin, 2006). At the boundary of the polar vortex, RWs can generate strong jet streams that can move air masses in the direction of the Southern Alps, enhancing vertical air motions. Across the southern flank of the Alps, this mechanism may trigger persistent and heavy precipitation (Rotunno and Houze, 2007) that can intensify if an orographic uplift of the incoming southerly flow is also triggered (Abbate et al., 2021; Grazzini, 2007). Rainfall can reach remarkably high amounts if these conditions are prolonged for several days, leading to up to 400 mm in 2 to 3 d (Grazzini, 2007; Rotunno and Houze, 2007). For each event listed in Table 1, we have examined correspondent NCEP maps to investigate the mechanism responsible for generating such intense precipitation over the target area.

The daily rainfall rate has been determined from the total amounts and the duration listed in Table 1. Rainfall amount (RA) was estimated keeping the distinction between EXLs and DIFs (Fig. 2a). For EXLs the nearest rain gauge or the two nearest rain gauges were chosen as reference. For DIFs, all the available daily rain data RAi in the territory have been summed and averaged considering the number of rain gauge stations n to obtain a representative value for RAavg (Eq. 1a). We have assumed a uniform spatial distribution of the rain gauge stations, Fig. 2b, neglecting any influence of elevation on rainfall data (Abbate et al., 2021). Then, the rainfall rate (RR) was computed as the ratio of the cumulative rainfall RAavg to the duration D (Eq. 1b). 1aRAavg=∑i=1nRAininmm1bRR=RAavgDinmmh-1

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 (Eq. 2a) (Caine, 1980) is the most general one, valid worldwide for shallow landslides and debris flow phenomena. At a regional scale, a more recent study conducted by Guzzetti et al. (2007) proposed a new set of curves valid for central and southern Europe, considering a distinction among different climate types. In our study, three of them were selected: the general one (“Guzzetti” curve; Eq. 2b), the curve valid for mid-latitude climate (“mid-latitude climate” curve; Eq. 2c), and the one suitable for highlands and mountain environments (“highland climate” curve; Eq. 2d). Another study from Peruccacci et al. (2017) further extended the previous study by Guzzetti et al. (2007), addressing a new I–D threshold (“Peruccacci” curve) valid for the Italian country. At the local scale, the “Cancelli Nova” (Eq. 2e) (Rappelli, 2008), the “Ceriani” (Eq. 2f) (Ceriani et al., 1994), and the “Crosta Frattini” curves (Eq. 2h) (Crosta and Frattini, 2001) were proposed in 1985, 1994, and 1998 respectively. All of them were calibrated directly on the recorded data available in Sondrio Province.

For each event, the coupled points RR–D were plotted against the I–D threshold curves, and their return period (RP) was evaluated. The latter was determined following the methodology based on the IDF (intensity–duration–frequency) curves (De Michele et al., 2005) available for the Lombardy region and provided by ARPA Lombardia (2020). 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, 2020) gathered from 1960 up to 1990 across the whole territory of the region. Bearing in mind that our localized events (EXLs) have been distinguished from the diffuse events (DIFs), including 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, while for the diffusive ones, a spatially averaged value has been computed.

A further step in the precipitation analysis consists of the hazard and magnitude assessment for each event. According to Guzzetti et al. (2005) the general landslide hazard could be defined as a probabilistic function of three terms (Eq. 2a): the size Al, the temporal occurrence Tl, and the spatial susceptibility S. The “size” term stores the information about the volume, the area, or the density of landslides that have occurred over a particular area. The temporal occurrence considers the periodical reactivation of a single landslide (deep-seated) or the recurrence of shallow landslides inside a catchment. The spatial susceptibility represents the quantification of the territory predisposition to a landslide phenomenon. 2aHlandslide=PAl≥al⋅PTl≥tl⋅S2bS=12clog⁡PAl≥al=a-bAA,whereaandbarethecoefficients2dlog⁡PTl≥tl=c-dRP,wherecanddarethecoefficients Starting from the definition of Eq. (2a), 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 geo-hydrological events considering the temporal and spatial probability of occurrence of the triggering rainfall. According to Malamud et al. (2004) a scale for the magnitude is necessary to interpret quantitatively the episodes and to highlight the most severe ones. For landslides and rainfall-induced geo-hydrological events, a unique method that describes the “energy” does not exist because several variables may play an important role in its definition (Bovolo and Bathurst, 2011; Frattini et al., 2009; Gao et al., 2018; Iida, 2004; Reid and Page, 2003). Therefore, making some assumptions, 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 S=1 to shallow landslides and debris flow triggering. This choice was motivated by geological and morphological features and also by looking at recent susceptibility maps proposed by ISPRA (2018b). Then we moved to other terms trying to determine the spatial and temporal probability of exceedance from AA and RP parameters, recalling the theory of the frequency–magnitude relationship.

The 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 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 greater than or equal to 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 to determine its hazard as described in Eq. (2a). The temporal occurrence term requires the estimation P(Tl≥tl) from the RP's frequency–magnitude relationship. This represents the probability of occurrence of an event Tl with RP ≥tl. According to Guzzetti et al. (2005), the other hazard component is addressed by the landslide size (Eq. 2d). In this regard, in our database it was not possible to retrieve enough 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 for the “trigger's size” and was treated similarly to the RP term. The probability of spatial occurrence P(Al≥al) of an event Al with AA ≥ al was retrieved from the FMC (Eq. 2c). Then, the hazard was estimated using Eq. (3a). Due to the modification of the first term P(Al≥al), it does not properly represent the landslide hazard, but Htrigger is an indicator of the hazard as a function of the trigger's temporal frequency and spatial extent.

In most natural cases, the frequency of low-magnitude geo-hydrological events is rather high and vice versa. Therefore, we tried to estimate the trigger magnitude as an inverse function of the hazard. The latter is a combination of two probabilities of occurrence (Eq. 3b); therefore it can be transformed into a magnitude recalling again the FMC in Eq. (3c). Working out some algebra with Eq. (3a–c) we have obtained a representation of the magnitude expressed by the MI (Eq. 3d). The MI is a sum of two contributions: the first describes its spatial extent through the parameter AA, and the second describes its temporal occurrence through the RP. In this light, the MI was intended to be more complete rather than the single RP because through the AA term it is possible to consider the “integral effects” related to the trigger's extent. The MI was taken as a reference for testing the SLPT index presented in the next section. 3aHtrigger=PAl≥al⋅PTl≥tl3bHtrigger=exp⁡(a-bAA)⋅exp⁡(c-dRP)Mtrigger=-log⁡Htrigger=-log⁡(exp⁡(a-bAA)3c⋅exp⁡(c-dRP))3dMI=Mtrigger=-((a-bAA)+(c-dRP))

The extratropical cyclone dynamic influences the rainfall intensities: if the EC is stronger, more precipitation is expected over an area, but, depending on EC spatial and temporal evolution, rainfall could exhibit different total amounts and durations. Therefore, using the NCEP maps, the Norwegian cyclone model (NCM) (Godson, 1948; Martin, 2006; Stull, 2017) was chosen for estimating a strength index of ECs. The NCM was formulated in the early 20th century. It describes an 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 Δpsl/Δt (hPa h-1) that represents an indicator of the strength of a cyclone structure (Andrews, 2010; Godson, 1948; Martin, 2006; Stull, 2017; Wallace and Hobbs, 2006). When the EC is more intense, the absolute value of the SLPT ratio is higher, and, consequently, the EC can cause more rainfall. According to Stull (2017), this index is obtained as a sum of four different influencing factors that correspond to the processes implicated in the dynamic evolution of extratropical cyclones: 4ΔpslΔt=T1+T2+T3+T4=SLPT.

T1 expresses the “upper-layer divergence mechanism” due to jet streams, which removes air mass from the air column. In Eq. (5b), ρMID=0.5 kg m-3 is the average density of air column and g is 9.8 m s-2. WMID (m s-1) is the mean air column vertical velocity that is evaluated considering Eq. (5a) in the proximity of the local change in the jet stream velocity gradient ΔWjs (m s-1), where Δz is approximately equal to 5000 m and Δs1 (m) is jet streak elongation. According to Stull (2017), Eq. (5a) is a strong approximation because it supposes air density to be constant over the air column, so we have considered a revised version (Stull, 2017) that expresses the WMID in terms of other parameters such as the geostrophic wind velocity G (m s-1), the curvature radius R (km) of Rossby waves, and the Coriolis parameter fc (s-1); 5aWMID=ΔWjsΔz/Δs1,5bT1=-gρMIDWMID.

The dataset of Table 1 shows a clear seasonal distribution of the events mainly concentrated during the summer and autumn seasons. July and November are the months more prone to geo-hydrological events, and this strong seasonality highlights that the trigger phenomena involved may have different origins (Martin, 2006; Rotunno and Houze, 2007). 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 d. In particular, 1951, 1953, 1987, 1997, 2008, and 2019 events happened during the summer season, and cumulated rainfall comprised between 100–200 mm, apart from in 1987 and 1997 which were rather exceptional (254 and 275 mm in 3 d). During October and November, rainfall events are characterized by higher persistency (4–5 d) and cumulated rainfall can easily reach amounts around 250–350 mm, such as for the events that happened in 2000, 2002, and 2018.

Through the analysis of NCEP maps, we have observed that all the events reported in Table 1 have been triggered in connection with EC structures that moved eastward from the Atlantic Ocean in the direction of the Alpine mountain range. In Fig. 4 three examples of reanalysis maps are reported that show the pressure distribution at a 500 hPa reference height across Europe during the 1966, 2002, and 2018 events. A qualitative comparison among the three maps 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 Isles. This recurrent configuration has been responsible for the torrential rainfall recorded in the Southern Alps across Sondrio Province. Consequently, the geo-hydrological effects could be directly attributed to the intensification of these EC structures. Starting from this qualitative evidence we have moved to a quantitative analysis following the two approaches proposed.

In Fig. 5, the average daily rain rate I and the duration D of the rainfall episodes in Table 1 were plotted against the rainfall threshold curves listed from Eq. (2a–f). Most events can be clustered in the bottom right corner of the graph due to their characteristics of a rather long duration of 2–4 d and slightly low intensities. Only the events of 2019, 2008, and 1953 are dispersed on the other side of the graph where the duration is around or less than 1 d.

Considering the thresholds proposed by Guzzetti et al. (2007), all the events are correctly identified above these curves (Fig. 5). No significant differences are seen between the general one (b), the curve valid for mid-latitude climate (c), and the one valid for highland climate (d). Peruccacci (e) and Crosta Frattini (h) are positioned intermediately between the regional threshold of Guzzetti and the local ones of 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 events.

The thresholds of Caine (a), Cancelli Nova (f), and Ceriani (g) are placed above the previous ones. The Ceriani curve seems to fit the data very well, positioning only the 1966 event slightly below the curve and the 1953 and 1960 close to the curve. Also, Cancelli Nova works rather well positioning only 1953 below the threshold. These results were expected because both the (g) and the (f) thresholds were calibrated using a local dataset up to 1985 and 1994 respectively. Conversely, the Caine threshold seems to work the worst, leading to underprediction: the 1953, 1960, and 1966 events are not identified as critical and appear below the curve. Moreover, the 1997 and 2000 events are situated borderline on the curve.

The threshold curves analysed have divided our events into critical and non-critical ones, but no further information on their magnitude has been retrieved yet. Some authors have shown that a measure of magnitude may be established considering the relative distances between the I–D points and the threshold curve. According to Crosta and Frattini (2001), Gao et al. (2018), Iida (2004), and Rosso et al. (2006), a beam of rainfall I–D curves can be elaborated including their dependence on the RP. For the same area, rainfall events with a higher RP should be statistically located much more distantly from the threshold lines, but this fact strongly depends on the reference curve considered the lower bound. In our study, local thresholds of Ceriani and Cancelli Nova have been demonstrated to best fit the dataset, avoiding under- and overpredictions. Moreover, they are delimited by the 1953, 1960, 1966, and 2008 events which exhibit the lowest RPs comprising between 2–5 years. Taking these curves as a reference we can appreciate that other critical events showing higher RPs are also located at more distance from these curves. This represents a confirmation of what has been 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 the GEV that take into account the spatial variability in local precipitation statistics (De Michele et al., 2005). In those cases where rainfall intensity and duration are fixed, changing the GEV parameters means the RP may also vary even though the relative distance from the curve is the same. In our dataset, we have encountered this fact two times comparing 1983 and 1987 events and 1997 and 2018 events that 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 for the magnitude only for rainfall analysis carried out at the same location as where the GEV parameters remain constant, confirming what has been suggested by other authors. In our case study, this condition was not satisfied because the GEV parameters were not constant in space.

Looking at Fig. 6a, Sondrio Province has experienced at least four exceptional rainfall events with a return period equal to or higher than 100 years: in 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 second half of the 20th century. This apparent contradiction has a possible explanation if we also include the information about the spatial extent of the triggers, as reported in Fig. 6b, which is a property strictly related to the nature of the rainfall event (Corominas et al., 2014; Gao et al., 2018). 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, the 1983 intensity is equal to that of 1987, but considering the spatial distribution, the 1983 event affected only a limited area, while the 1987 event spread across the entire province. For this reason, if we are interested in determining the magnitude of meteorological triggers, the 1987 event should be seen as more critical than the 1983 one. In this regard, the RP information could be misleading.

According to Corominas et al. (2014) and Guzzetti et al. (2005) and following the methodology proposed in Eqs. (2) and (3), we have moved further in considering both the RP and AA for determining the trigger hazard and magnitude. First of all, the FMCs have been established, allowing us to define the probability of spatial and time occurrence as a function of the parameters AA in Fig. 7a and RP in Fig. 7b. Secondly, AA has been plotted against the RP in Fig. 8a, and their low statistical correlation was observed. Then, considering Eq. (3a), the trigger hazard has been defined and reported in Fig. 8b. We can see that the trigger hazard is higher when the probabilities of spatial and temporal occurrence are higher. In particular, 1953, 2018, and 2019 represent the most hazardous events with lower RPs and AA. On the other hand, 1987 and 2002 represent the least hazardous events because, from a probabilistic viewpoint, they exhibit both the highest return period and the largest extent. Applying Eq. (3c) the trigger hazard has been translated into the magnitude index (MI), normalized in respect of its maximum and shown in Fig. 8b. We can see that the MI has highlighted 1987 and 2002 as the most severe events. On the other hand, 1953 and 2008 are depicted with the lowest magnitudes. An intermediate magnitude ranking was assessed for the 1951, 1983, 1997, 2000, and 2018 events, confirming historical evidence.

In the second approach, we applied the NCM described in Eq. (4). Using the NCEP data, atmospheric pressure gradients, wind velocities, and air masses advection through the Alpine region, the model components in Eqs. (5b)–(7b) and (8c) were studied.

For determining the T1 term (Eq. 5b, upper-layer divergence), the geostrophic wind velocities were estimated. Geostrophic 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. Intense geostrophic velocities are generally associated with strong EC structures (Andrews, 2010; Martin, 2006; Stull, 2017). As reported in Fig. 9a, geostrophic velocities were higher for 1983, 1987, 2000, and 2002, a sub-group of the most intense events of our dataset. Upwind velocities in Fig. 9b are also correlated with the presence of sustained geostrophic winds. Again 1987, 2002, and now 2018 have shown the highest values of the entire dataset.

For determining the T2 and T3 terms (Eq. 6b, boundary layer pumping, and Eq. 7b, advection), the air masses' evolutionary paths were examined. Figure 9c shows the short distance Δs2 between the low pressure (L) and Sondrio Province. We can see that the relative position of ECs does not vary too much, 1183 km on average. This represents a characteristic of the EC structures that tends to evolve across the Mediterranean and the Alpine area similarly. Nevertheless, 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 (North Sea) to the southern part, entering the Mediterranean Sea and moving eastward following the Rossby wave track (Rotunno and Houze, 2007; Stull, 2017). This is the case for the 1960, 1966, 2000, 2002, and 2018 events that occurred between September and November. Summer events of 1951, 1953, 1987, 1997, and 2019 exhibit a low-pressure tracking path that did not cross the Alps mountain range. This fact can be explained by considering that Rossby waves are in general shifted northward during the summer period (Grazzini and Vitart, 2015; Martin, 2006). This is reflected in the events that affect the southern side of the alpine region which are more rapid, less persistent, and locally intense but not well organized, such as the typical autumnal EC.

The T4 term (Eq. 8c) is represented by a linear function of the daily rainfall rates (RRs) considered in the precipitation analysis. In the formulation adopted we made strong assumptions to make the problem more tractable. This is the only component that depends on the accurate estimation of the ground-based rainfall data.

After calculating the intermediate components T1, T2, T3, and T4, the sea level pressure tendency (SLPT) index of Eq. (4) was determined (Fig. 9d). Firstly, we can see 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 (Sanders and Gyakum, 1980). Looking at Fig. 9d, the SLPT index shows a range between -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 at around -3.67±0.63 kPa h-1 which is compatible with the EC structures shown by NCEP maps.

The two methodologies proposed for the trigger magnitude assessment are now compared. The two indexes MI and SLPT have been normalized in respect of their maximum and are shown in Fig. 10a. We can observe that it is rather clear how the two indexes give a similar magnitude rank for the events examined in our dataset. Looking at bias errors, the mean absolute error (MAE) is computed at around 7 % and the root mean square error (RMSE) is about 10.3 %. The highest absolute error values were addressed by the 2008 and 2019 events. Moreover, we can show that two indexes are in accordance, identifying 1987 as the episode with the highest magnitude, followed by 2002 and 1951. The lowest-ranking scores are established for the 1953 and 2008 events which were already identified by I–D analysis as borderline for the Cancelli Nova and Ceriani thresholds. In the middle, we found 1960, 1966, 1983, 1997, 2000, 2018, and 2019, which were also depicted by historical chronicles as rather intense but not catastrophic for Sondrio Province. In Fig. 10b the MI and the SLPT index have been plotted against each other. From Fig. 10b it can be appreciated that the points lie on the diagonal and the correlation index R2 is about 0.88, which is rather high and near to 1.