Small-scale analysis to rank municipalities requiring slow-moving landslide risk mitigation measures: the case study of the Calabria region (southern Italy)

This paper proposes a three-phase method that combines multi-source (i.e. topographic, thematic, monitoring) input data in a GIS environment to rank—at small (1:250,000) scale—administrative units (e.g. municipalities) based on their exposure to slow-moving landslide risk within a selected area (e.g. a region) and, accordingly, detect those primarily requiring mitigation measures. The method is applied in the Calabria region (southern Italy) where several municipalities are widely affected by slow-moving landslides that systematically cause damage to buildings and infrastructure networks resulting in significant economic losses. The results obtained are validated based on the information gathered from previous studies carried out at large (municipal) scale. The work undertaken represents a first, fundamental step of a wider circular approach that can profitably facilitate the decision makers in addressing the issue of the slow-moving landslide risk mitigation in a sustainable way.


Introduction
Slow-moving landslides (SMLs) are slope instabilities with existing (buried) slip zones where the materials are predominately fine-grained with a visco-plastic behaviour (Bertini et al. 1984;Borrelli and Gullà 2017;Di Maio et al. 2013;Ferlisi 2004;Fernández-Merodo et al. 2014;Grana and Tommasi 2014;Gullà 2014;Leroueil 2001;Picarelli et al. 2004). Owing to their particular kinematic features, associated with a permanent or episodic activity, these landslides mainly cause direct damages to exposed buildings and/or infrastructure networks the severity of which progressively increases over time (Antronico et al. 2015;Ferlisi et al. 2021;Peduto et al. 2017). Consequently, also the SML-induced risk increases with detrimental effects on the abovementioned exposed elements that are expected to be higher as displaced masses experience sudden accelerations due to rainfall or earthquakes (Donnini et al. 2017;Gullà 2014;Mavrouli et al. 2019;Negulescu et al. 2014;Uzielli et al. 2015).
To address this issue, which is of particular concern for central and local authorities in charge of SML risk management, top-down multi-scale methodological approaches (Cascini 2015) may help in: prioritizing (at small scale) the municipalities-within a regionwhose SML-affected urban areas require risk mitigation measures; planning (at medium scale) well-defined categories of risk mitigation measures (e.g. slope stabilization works) in the urban area of a municipality selected among the most exposed ones to SML risk based on the outcomes of small-scale analysis; scheduling (at large scale) the implementation, with a proper allocation of economic resources, of the most suitable structural/nonstructural interventions among the categories planned at medium scale; designing (at detailed scale) the interventions selected at large scale .
Focusing on the analysis at small scale (Fell et al. 2008), related activities have to be carried out by using basic methods that involve-as input data to be managed in a GIS environment-topographic and thematic (i.e. geolithological, SML inventory, and built-up area) maps as well as monitoring information such as that gathered from conventional or innovative remote sensing techniques (Corominas et al. 2014;Fell et al. 2008). Among the latter, the differential interferometric processing of synthetic aperture radar images (DInSAR) was successfully tested in the last few decades on several case studies involving SMLs (Catani et al. 2005;Noviello et al. 2020;Peduto et al. 2017Peduto et al. , 2019bWasowski and Bovenga 2014). In particular, DInSAR data proved to be of value and both complementary and supplementary to the conventional geotechnical monitoring Morelli et al. 2020;Peduto et al. 2021b, c;Refice et al. 2019) providing useful information on both the identification of new SMLs boundaries (Herrera et al 2013;Peduto et al. 2016;Wasowski 2006) and the updating of their state of activity Cigna et al 2013) as well as in the analysis of past landslide evidences and in creating and updating, at small and medium scales, inventory maps in specific periods Solari et al. 2019).
Following this line of thought, this paper proposes a method that allows ranking administrative units (e.g. municipalities) exposed to SML risk within a selected area (e.g. a region) and detecting those primarily requiring mitigation measures. The applicability of the proposed method at small scale (i.e. 1:250,000 according to Fell et al. 2008) is tested with reference to the Calabria region (southern Italy) where several municipalities are widely affected by SMLs.

Method and materials
The proposed method is synthesized in Fig. 1.
In the first phase an operative grid ( Fig. 1)-whose geometrical size must be defined according to the spatial resolution of available materials (Fig. 1)-is set (Calvello et al. 2013;Gullà et al. 2008) and the Terrain Computational Units (TCUs) are overlaid on the study area map (Fig. 2a) according to Calvello et al. (2013Calvello et al. ( , 2017. Then, starting from the available materials-geological map, digital terrain model (DTM), built-up urban area map, landslide inventory map, DInSAR data ( Fig. 1)-each TCU (Fig. 2a) is associated with the pertaining information (input data) including: (i) the Lithological Units (LUs), namely groups of lithotypes with a mechanical behaviour that can be assumed as homogeneous at the scale of analysis (i.e. small scale); (ii) the Slope angle (S), as retrieved from the DTM; (iii) the presence/absence of an Urban Area (UA), as resulting from the built-up area map; (iv) the presence/absence of a SML, based on the landslide inventory map; (v) the DInSAR-derived velocity, computed by averaging the velocity values pertaining to the coherent pixels-if any-within the TCU perimeter ).
The second phase (Fig. 1) of the method is comprised of two steps.
In the first step, the information assigned to the TCUs is preliminarily associated with the so-called Vulnerable Areas (VAs) which correspond to the portions of the UA affected by SMLs (Fig. 2b). Then, qualitative indicators (Very Low-VL, Low-L, Medium-M and High-H) are assigned to the VAs according to the SML-induced damage severity level expected to the built-up environment owing to LU or S, in turn assessed at both local (l) (i.e. referred to a given VA) and global (g) (referred to the whole SML affecting the same VA) levels. Each of these levels is grouped in four classes. The latter are distinguished in: (i) LUi (i = 1, …, 4) for LUs, considering the LU prevailing in a given VA or in the SML affecting the same VA; (ii) Si (i = 1, …, 4) for S, considering the average value of S pertaining to a given VA or to the SML affecting the same VA.
To assign the qualitative indicators to the VAs, two matrices (Lithological consistency matrix in Fig. 3a and Slope consistency matrix in Fig. 3b) are introduced to crosscheck the information associated with the TCUs covering a given VA or the SML affecting the same VA. In particular, the prevailing LU and the average value of S-referred to one of the considered LUi/Si (i = 1, …, 4) classes and based on the information previously associated with the TCUs-are preliminarily assigned to either the VAs (at local level) or the SMLs interacting with the VAs (at global level). The retrieved data are used as input in the above mentioned Lithological consistency (Fig. 3a) and Slope consistency (Fig. 3b) matrices that are applied to each VA and provide as output, for both LU and S, the VL LU-l/g , L LU-l/g , M LU-l/g , H LU-l/g (see Fig. 3a), and VL S-l/g , L S-l/g , M S-l/g , H S-l/g (see Fig. 3b) qualitative indicators with l/g standing for local/global. In particular, the very low (VL) category is assigned if local (l) and global (g) indicators-related to the considered (LU or S) thematic variable-are both ranked with very low classes; low (L) category, if the highest value of one of the two (local or global) indicators is at most medium and the lowest is at least very low; medium (M) category, if the highest value of one of the two (local or global) indicators is at most high and the lowest value is at least very low or if the highest value of one of the two (local or global) indicators is at most medium and the lowest value is at least low; high (H) category, if the highest value of one of the two (local or global) indicators is high and the lowest value is at least medium.
In the second step, the state of activity of a given SMLi.e. active or dormant (Cruden and Varnes 1996)-and the DInSAR-based condition of movement of the TCUs covering the affected VA are associated with the same VA ( Fig. 1). In particular, the former information is directly provided by the landslide inventory map; accordingly, the VA is differentiated into "active" (VA_A) or "dormant" (VA_D) based on the state of activity of the affecting SML Fig. 1 Flowchart of the proposed method to rank zoning units exposed to slow-moving landslide (SML) risk at small scale (by the way, built-up areas not affected by SMLs were considered as stable or without vulnerable areas, SA). The latter information derives from the preliminary comparison of the average annual velocity values pertaining to the coherent pixels within each TCU covering the VA with a fixed velocity threshold accounting for the precision of DInSAR data, thus allowing the identification of "moving" TCUs. It is worth observing that the two mentioned sources of information are not expected to provide straightforwardly the same indication. Indeed, the state of activity pertains to the whole SML body and is assigned according to movements recorded in the last cycle of seasons (Cruden and Varnes 1996), in relation to the date in which the inventory map was drawn-up. On the other hand, the DInSAR-based displacements are measured on the VA (which is in a specific portion of the SML body that might not reflect the overall kinematics of the entire SML body) in a certain period, namely the one for which synthetic aperture radar images are available. From the perspective of the proposed methodology, merging both sources of information has a two-fold objective: overcoming the qualitative information that is typically associated with the definition of the state of activity of a SML and confirming that the DInSAR-based where (TCU cm ) i is the number of moving DInSAR-covered TCUs within the i-th VA and (TCU ct ) i their total number. Accordingly, the VA is conservatively assumed as ( Fig. 2c): (i) "potentially moving" if the TCUs pertaining to the VA are not covered by DInSAR data; (ii) "moving" if the I DM value equals or exceeds 0.5 (at least the 50% of the DInSAR-covered TCUs within the i-th VA are moving); (iii) "not moving" if the computed I DM is lower than 0.5 (more than 50% of the DInSAR-covered TCUs within the i-th VA are not moving).
In the third phase ( Fig. 1), the results obtained in the second phase are used for computing an Index of Exposure (IE) referred to the municipal area that is assumed as zoning unit (Calvello et al. 2013) (Fig. 2a). To this aim, the results of the Lithological consistency and Slope consistency matrices are combined into the Litho-Slope combination matrix (Fig. 3c). The latter allows quantifying the high/low proneness associated with the two thematic categories (LU and S) to induce joint effects (in terms of expected consequences) on the urban area through the introduction of the Litho-Slope Correction Coefficients (CC LU-S ) whose values range from 0 (i.e. null effect) to 1 (i.e. maximum effect).
On the other hand, the information related to the landslide state of activity (LSA) and the DInSAR-based movement of the VAs is combined within a LSA-DIn-SAR combination matrix (Fig. 3d). The latter aims to crosscheck these two different sources of information on the status of VA movement-as factor concurring to the severity of expected SML-induced consequences on the UA-through the introduction of a LSA-DIn-SAR Correction Coefficient (CC LSA-D ) whose values may range from 0 (i.e., null effect) to 1 (i.e., maximum effect). For each VA, the application of the two defined correction coefficients (CC LU-S and CC LSA-D ) allows obtaining an Equivalent Vulnerable Area (EVA) (in m 2 ) defined as: Obviously, EVA will be equal to VA if both correction coefficients (CC LU-S and CC L-D ) are unitary in value (i.e. the involved factors can induce a maximum effect in terms of expected consequences to the VA). Otherwise, (1) the EVA will be a subset of the VA should one or both correction coefficients (CC LU-S and CC L-D ) be lower than 1. Finally, considering the total urban area (UA T ) j of the j-th municipality in the study area, the Index of Exposure (IE) j of the j-th municipality (zoning unit) is computed as: In the Eq. (3) (EVA) j is the equivalent vulnerable area of the j-th municipality, obtained by summing the EVAs associated with the same municipality; whereas (EVA) tot and (UA) tot are, respectively, the total equivalent vulnerable area and the total urban area of all the municipalities in the study area.
At small scale and with reference to the materials used, the estimated Index of Exposure (IE) allows ranking the expected detrimental effects of SMLs in VAs and, accordingly, the municipalities requiring mitigation measures.

The study area
The Calabria region, located in the southernmost part of Italy, covers about 15,075 km 2 and includes five Provinces ( Fig. 4a) globally counting 404 municipalities. The elevation ranges from sea level to 2263 m (Fig. 4b), with an average value of 523 m.
The Calabrian climate is generally Mediterranean (Köppen 1936). The coastal zones are characterized by mild winters and hot summers (Brunetti et al. 2012;Caloiero et al. 2015). In particular, the eastern Ionian coast is drier and more arid than the western Tyrrhenian coast, which has a milder climate . On the contrary, along the inland areas of the Calabrian mountain chains, from Pollino, Sila to Aspromonte, the climate is cold in winter (with snow) and fresh in summer (Caloiero et al. 2011). The average annual precipitation ranges from 600 mm to more than 2000 mm moving from the coastal zone to internal and mountainous areas, with a mean regional value of about of 1150 mm (Versace et al. 1989;Terranova and Iaquinta 2011). Yearly rainfall distribution exhibits a peak from October to March when more than 70% of total annual precipitation occurs, with negligible monthly values from June to September (Terranova and Iaquinta 2011) when, however, thunderstorms can occur. (3) The geological setting of Calabria ( Fig. 4c) consists of Palaeozoic crystalline-metamorphic units, composed of low-to-high-grade metamorphic and plutonic rocks, overthrusted during Late Cretaceous-Oligocene on the Mesozoic Apennine derived carbonate units (e.g. Amodio- Morelli et al. 1976;Tortorici 1982;Van Dijk et al. 2000), which include carbonate platform sequences of passive continental margin (Bonardi et al. 1982). Starting from the Miocene, the Calabria margins were covered by terrigenous sedimentary successions and affected, since the Tortonian, by strike-slip and extensional tectonics (Van Dijk et al. 2000). Particularly, during the Late Pliocene-Early Quaternary, several high-angle faults, both longitudinally and transversally, dissected the Calabrian Arc, developing axial intermontane and transversal basins (Ghisetti 1979;Monaco and Tortorici 2000;Sorriso-Valvo and Tansi 1996;Van Dijk et al. 2000). As a result, it was fragmented into structural highs (i.e. Pollino Massif, Coastal Range, Sila Massif, Capo Vaticano Promontory, Serre Massif-Aspromonte)-consisting of crystalline-metamorphic rocks, including phillites, schists, gneiss and granitoids (these latter manly ranging in composition from granite to tonalite)-and structural depressions (i.e. Crati basin, Catanzaro basin, Mesima, Gioia Tauro and Crotone basins) where continental and marine, coarse-grained to fine grained, depositional systems found (Fig. 4c). Furthermore, since the Middle Pleistocene, a strong regional extension, together with an intense regional uplifting, affected the whole Calabrian Arc. The Quaternary tectonic uplift-that is still ongoing, as testified by intense seismic activity (Tortorici et al. 1995)-accounts for most of the relief of the region, and the highest-relief landforms are of tectonic origin (Sorriso-Valvo 1993;Westaway 1993).
Owing to the complex geodynamic history of Calabria, linked to several tectonic phases (Tortorici et al. 1995;Tripodi et al. 2018;Van Dijk et al. 2000), the outcropping lithological units generally show physical and chemical weathering as well as high levels of fragmentation and deformation, which play an important role in the evolution of hillslopes (Biondino et al. 2018;Borrelli et al. 2015;Scarciglia et al. 2005Scarciglia et al. , 2016. Furthermore, the distribution and mechanical behaviour of the lithological units influence the slope dynamics and the nature of geomorphic processes (Sorriso-Valvo 1993).
The mountains ridges-developed on Palaeozoic metamorphic and plutonic rocks, except for the northernmost portion of the region composed by carbonate rocks-are characterized by relicts of summit planation landforms (paleosurfaces), deeply dissected and bordered by steep slopes and cut by deep and narrow valleys (e.g. V-shaped valley). The hilly areas are mainly developed on sedimentary rocks-ranging in age from Palaeogene Period to Pleistocene Epoch-of different composition and erodibility, where selective erosion has given alternatively way to steep slopes cut on hard rocks (e.g. conglomerate, sandstones and limestones) in contrast with typically rounded and gentler landscape (i.e. low-gradient slopes) characterized by pelitic, and more erodible lithologies. Finally, coastal and fluvial plains (i.e. lowland areas) are mainly constituted by loose, coarse-grained to fine grained, Holocene deposits (i.e. sands and gravel, silts, clays). Because of its specific geological framework, tectonic history, and geomorphic landscape features, the Calabria region is very prone and widely affected by slope instability phenomena (Antronico et al. 2015;Borrelli et al. 2014Borrelli et al. , 2015Borrelli et al. , 2018aBorrelli and Gullà 2017;Calcaterra and Parise 2010;Conforti et al. 2021;Gullà et al. 2008Gullà et al. , 2009Gullà et al. , 2014Gullà et al. , 2018aSorriso-Valvo 1993;Sorriso-Valvo et al. 2004), mainly including SMLs that often affect both historic and newly developed built-up areas (Antronico et al. 2015;Cigna et al. 2013;Ferlisi et al. 2015;Nappo et al. 2019;Nicodemo et al. 2017bNicodemo et al. , 2020aPeduto et al. 2017Peduto et al. , 2018Peduto et al. , 2021a. Detailed information, ancillary data and results of previous studies, carried out by the authors at large/detailed scale (Antronico et al. 2015, Borrelli et al. 2007, 2014Ferlisi et al. 2015Ferlisi et al. , 2019Gullà et al. 2014Gullà et al. , 2017Gullà et al. , 2018bNicodemo et al. 2018Nicodemo et al. , 2020aNappo et al. 2019;Peduto et al. 2016Peduto et al. , 2017Peduto et al. , 2018Peduto et al. , 2021c are available. These data allowed taking operative assumptions for this study and a cross-validation of the outcomes achieved by applying the proposed method (Fig. 1).

First phase
The first phase of the method (Fig. 1) involved associating the information pertaining to the materials with the TCUs. The latter strictly correspond to squared cells (20 m × 20 m) composing an operative grid overlaid to the Calabria region (Fig. 5a). The obtained input data consisted of: (i) the SML inventory map-where landslides are mapped according to their location, type and state of activity assigned by way of geomorphological criteria (Fig. 5b)-generated by filtering out fast- moving landslides from the official landslide inventory map at 1.10,000 scale provided by the former Regional Basin Authority of Calabria (PAI 2016); (ii) the Lithological Unit (LU) map obtained from the Geological Map of Calabria at 1:25,000 scale (Casmez 1969) by grouping different lithologies into four classes based on their mechanical behaviour, regardless of their age (Fig. 5c): LU1 (coarsegrained soils, i.e. sands, sandstones, gravels, conglomerates), LU2 (carbonate rocks, i.e. limestone and dolomites), LU3 (crystalline-metamorphic rocks, i.e. phyllite, schist, gneiss, and granitoids), LU4 (fine-grained soils, i.e. silts, clays, marls), being the prevailing LU associated with each TCU; (iii) the slope (S) angle map (Fig. 5d) that shows the spatial distribution of the average slope angles pertaining to the TCUs, as retrieved from the DTM with 20 m spatial resolution and ranked in four classes: S1 ≤ 5°; 5° < S2 ≤ 15°; 15° < S3 ≤ 25°; S4 > 25°, according to a statistical quantile analysis; (iv) the presence/absence of an urban area (UA) on the TCU based on the map of built-up areas (Fig. 5e) (Open data/Geoportal Calabria region 2016).
DInSAR-derived ground displacement measurements integrated the above input data. In particular, DInSAR data were gathered from the processing of ENVISAT radar sensor images, acquired in C-band on both ascending and descending orbits, which offered the advantage of covering the whole study area (Fig. 6). The interferometric database, provided by the Italian Ministry of the Environment of the Environment and Protection of Land and Sea within the "Piano Straordinario di Telerilevamento Ambientale-PST-A" (MATTM 2010) and covering the 2003-2010 period, resulted from processing 417 ENVISAT images via the Persistent Scatterers Interferometry (PSI) technique (Ferretti et al. 2001). Starting from velocity recorded along the Line of Sight (LOS) by coherent pixels (i.e. Permanent Scatterers-PSs) over the study area (Figs. 6a and 6b) and considering only the PSs whose coherence exceeds 0.5 (MATTM 2010), the average velocity value (PS_av) was computed within each TCU .

Second phase
In the second phase (Fig. 1), a condition of movement (distinguished in "moving" and "not moving") was assigned to the TCUs covered by DInSAR data. To this aim, as suggested by several authors (e.g. Cascini et al. 2013;Nappo et al. 2019) according to the accuracy of DInSAR data and   Gullà et al. Geoenvironmental Disasters (2021) 8:31 taking into account the results of quantitative validation tests carried out on DInSAR data based on conventional ground measurements (Nicodemo et al. 2017a;Peduto et al., 2018), a threshold value on the average annual velocity recorded along the LOS equal to 1.5 mm/year was fixed. Then, a given TCU was considered as: "moving" if the average DInSAR velocity of the PSs within it exceeded the fixed threshold of 1.5 mm/year ; "not moving" if the threshold of 1.5 mm/year was not exceeded; "not covered" if no DInSAR information on the TCU was recorded. Then, the SML inventory map (Fig. 5b) was overlaid to the UA map (Fig. 5e) to identify the VAs of the study area. Each VA, in turn, was categorised as "active" (VA_A) or "dormant" (VA_D) according to the state of activity of the pertaining SML (Fig. 7a); whereas the built-up areas not affected by SMLs were considered as stable or without vulnerable areas (SA). An example of some built-up areas included within the administrative boundaries of the five Provinces in Calabria region is shown in Fig. 8.
On the other hand, based on the values of the I DM (Fig. 7b) computed using Eq. (1) the identified VAs were classified as "potentially moving", "moving" or "not moving". In this regard, an example is shown in Fig. 9.
The results obtained by applying the first step of the second phase of the proposed method for each of the five Provinces of Calabria region are summarised in Fig. 10. In particular, the VAs (expressed as a percentage of the total UA pertaining to each Province) are distinguished according to either the state of activity of SMLs they are affected by (Fig. 10a) or the I DM values (Fig. 10b).
The second step of the second phase of the proposed method is aimed at associating each VA with qualitative indicators of the consequences expected to the built-up environment due to LUs and Ss (Very Low-VL, Low-L, Medium-M, and High-H). To this aim, based on the experience (i.e. phenomenological observation and monitoring data) gained on the study area (Antronico et al. 2013;Borrelli et al. 2014Borrelli et al. , 2018bBorrelli and Gullà 2017;Gullà 2014;Gullà et al. 2010Gullà et al. , 2012Gullà et al. , 2017Gullà et al. , 2018aPeduto et al. 2016Peduto et al. , 2021b, the LU classes were ranked as LU1:VL, LU2:L, LU3:M, LU4:H (see Fig. 3a and Fig. 5c) and the S classes as S1:VL, S2:L, S3:M, S4:H (see Fig. 3b and Fig. 5d). Then, the "Lithological consistency matrix" (for LU) and the "Slope consistency matrix" (for S) were used to assign to each VA the proneness category (Fig. 3a, b) also considering both the local (referred to the VA) and global (referred to the whole SML interacting with the VA) effects. Two examples of the achieved results are shown in Figs. 11 and 12 that refer to the application of the "Lithological consistency matrix" and the "Slope consistency matrix", respectively.
The results of this part allowed computing the extent of VAs within the five Provinces of Calabria region according to the qualitative indicators separately associated with LU (Fig. 13a) and S (Fig. 13b) classes.

Third phase
The third phase of the proposed method focused on: (i) heuristically assigning the values pertaining to the Correction Coefficients (CC LU-S and CC LSA-D ) composing either the Litho-Slope combination matrix (Fig. 3c) or the LSA-DInSAR combination matrix (Fig. 3d); (ii) calculating the Equivalent Vulnerable Area (EVA); (iii) evaluating the Index of Exposure (IE).
In this regard, Table 1 shows the values attributed to the Correction Coefficients for the Litho-Slope combination matrix and the LSA-DInSAR combination matrix, respectively. On the other hand, EVA pertaining to each VA was estimated according to the Eq. (2).  Finally, the IE for the j-th municipality was computed using the Eq. (3), provided that Total Urban Areas (UA T ) pertaining to each municipality had been preliminarily estimated. Figure 14 shows the municipalities of Calabria region distinguished according to IE values with the percentage of VA and EVA for the Provinces of: Cosenza (Fig. 14a), Crotone (Fig. 14b), Vibo Valentia (Fig. 14c), Catanzaro (Fig. 14d) and Reggio Calabria (Fig. 14e). Table 2 summarises the municipalities of Calabria region with IE > 3 along with the values of the resulting VA and EVA (in m 2 ).

Validation tests
The results obtained were validated by way of a comparison with the results-including damage to buildings in VAs-gathered from previous studies in four municipalities of Calabria region where LU3 prevails, namely: Lungro and Verbicaro in Cosenza Province (Antronico et al. 2015;Borrelli et al. 2018b;Ferlisi et al. 2015;Gullà et al. 2017;Nicodemo et al. 2017bNicodemo et al. , 2018Nicodemo et al. , 2020aPeduto et al. 2017Peduto et al. , 2018Peduto et al. , 2021a, Gimigliano  and San Mango d' Aquino  in Catanzaro Province. The application of the proposed method ( Fig. 1) provided IE values larger than 8 for three out of the four selected municipalities (Table 2 and Fig. 14): Verbicaro (IE = 19.88), Gimigliano (IE = 12.68) and Lungro (IE = 8.38). On the other hand, an IE value lower than 1 (Fig. 14) was recorded for San Mango D' Aquino (IE = 0.22).
As for the damage to buildings, the data collected for the four municipalities under consideration resulted from surveys carried out in October 2015 in Lungro , in April-May 2014 in Verbicaro Nicodemo et al. 2017b), and in August 2017 in Gimigliano and San Mango D'Aquino (Vitale 2017). To this aim, ad-hoc predisposed factsheets were filled in Nicodemo et al. 2017b) also specifying the damage severity level recorded to the surveyed building according to a classification system adapted from Burland et al. (1977). Particularly, this classification system distinguishes six damage severity levels (D0 = negligible, D1 = very slight, D2 = slight; D3 = moderate; D4 = severe; D5 = very severe) according to the width of cracks and their distribution on building façades as well as to the easy of repair. Generally, the attainment of: (i) the D0-D1-D2 severity levels implies effects on the building aesthetics; (ii) the D3-D4 severity levels may determine a loss of functionality; (iii) the D5 severity level may compromise the building stability.
Figures 15a-c respectively show the spatial distribution of the recorded damage severity levels in Lungro, Verbicaro and Gimigliano, with some examples of the crack patterns recorded in the buildings surveyed within the identified VAs, the latter distinguished in dormant (VA_D) and active (VA_A) (Fig. 8).
The pie charts of the damage severity levels in the three municipalities (Fig. 15d) show that Verbicaro is the municipality with the highest percentage of buildings with a recorded damage exceeding the D0 severity level (40.3% out of the total, Fig. 15d), followed by Lungro (39.4% out of the total, Fig. 15d) and Gimigliano (18.8% out of the total, Fig. 15d).
In Gimigliano the 10.7% of surveyed buildings is within VA_D and the remaining 89.3% is in VA_A (Fig. 15e1), being the 18.8% out of the total with the following damage severity levels: D1 = 13.1%; D2 = 3.5%; D3 = 0.7%; D4 = 0.8%; D5 = 0.7%. Figure 15e2 provides the distribution of the damage severity levels exceeding D0 considering separately the VA_D and VA_A for each municipality. The data confirm that Verbicaro is the municipality mostly affected by SMLs.
Based on the gathered damage data, it is possible to estimate a value representative of the damage severity level averagely recorded at the municipality scale (D av ). To this aim, a numerical index was associated with the macro-classes of damage severity related to a given loss (i.e. aesthetic, functionality, stability); in this regard, the adopted numerical indices equalled 1, 2 and 3 for the macro-classes D0-D1-D2, D3-D4 and D5, respectively. Then, D av was estimated as the average of the above indices weighted on the number of buildings whose recorded damage severity levels belong to a given macro-class. Finally, the obtained D av value was multiplied by the dimensionless ratio of the VA with the UA T to take into account the extent of the areal exposure of a given municipality. The obtained results are synthesised in Table 3. It is worth observing that they are ranked according to the IE values retrieved at small scale, so confirming the reliability of the proposed method.
A similar analysis was carried out for San Mango d' Aquino municipality (Fig. 16a) whose territory is affected by several SMLs (Fig. 16b), being the urban area mainly resting on a deep-seated gravitational slope deformation (DGSD). Figure 16c shows the results in terms of spatial distribution of recorded damages within the areas identified as VAs in Fig. 8.
The outcomes achieved for San Mango D' Aquino confirms the reliability of the proposed method in ranking the zoning units based on the expected detrimental effects of the SMLs on VAs. Indeed, from the pie chart (Fig. 16d) and the damage distribution concerning either the whole UA T (divided in VA_D and VA_A, Fig. 16e1) or, separately, the VA_D and VA_A (see Fig. 16e2), it is evident that most of the surveyed buildings exhibit a negligible damage (D0) or show damage severity levels between D1 and D2 classes. Furthermore, the pertaining product D av × VA/UA T equals 0.018, namely the lowest value obtained for the four tested municipalities (Table 3).

Discussion and conclusions
This paper presented the results of a study aimed at ranking-at small scale-the municipalities of the Calabria region (southern Italy) based on their exposure to SML risk. To this aim, a three-phase method was applied on the basis of the available base materials (i.e. topographic and thematic maps, DInSAR data) the quality of which strongly affects the reliability of the outcomes. As for the SML inventory map, the regular updating is required to guarantee its completeness over time (van Westen et al. 2006). In this regard, the use of DInSAR data may profitably help the involved scientists/technicians, even at small scale (Boni et al. 2020;Raspini et al. 2019). On the other hand, with the general intent to setup an operative tool for central and local authorities in charge of SML risk management based on the proposed three-phase method, using updated base materials is a prerequisite. Currently, this aspect represents one of the limits to the straightforward applicability of the three-phase method in Calabria region (and in other regions of Italy affected by SMLs as well). As for DInSAR data, for instance, they were gathered from the processing of ENVISAT radar sensor images, acquired on both ascending and descending orbits. This interferometric database, provided by MATTM (2010), offered the advantage of covering the DInSAR data may also assist in activities aimed at monitoring SMLs and the built environment at large/detailed scale (Fell et al. 2008), especially when very high-resolution images are available (Bianchini et al. 2015;Nicodemo et al. 2020a, b;Peduto et al. 2017Peduto et al. , 2018Peduto et al. , 2019a. If detected "moving buildings" are outside the boundaries of SMLs mapped in an official inventory, before appointing them as VAs the presence of not-mapped SMLs should be ascertained (and the inventory map updated) as the cause of the recorded DInSAR-based displacements to avoid including in the analysis buildings that are suffering, for instance, from structural problems. Accordingly, the possibility of including DInSAR moving areas out of mapped SMLs in the sample of VA should bring along considerations on the reliability of the available official inventory that, however, is out of the scope of this paper.
As for the validation of the results obtained, which focused on four municipalities of the Calabria region, interestingly, a wider and longer-lasting test could be carried out by way of the use of innovative tools such as Google Street View (Ferlisi et al. 2021;Nappo et al. 2019). This would allow a multi-temporal check of crack patterns of building façades in the analysed VAs in a rapid, easy, and cost-effective way. Moreover, coeval updated overlapped to the identified stable (or without vulnerable) areas (SAs) and vulnerable (VAs)-distinguished in "active" (VA_A) or "dormant" (VA_D) areas-with buildings classified according to the recorded damage severity level and some photos of buildings taken during in-situ surveys. The percentages of the recorded buildings damage severity levels located over the identified VA are shown in d) jointly with their distribution based on e1) the total UA (divided in SA, VA_D and VA_A) and e2) the single (SA, VA_D and VA_A) area SML inventory map/DInSAR data and damage information may be available and, accordingly, SML displacements and related effects on exposed buildings would be properly used for validation purposes. Conversely, the current coverage limitations of Google Street View could limit its application in those countries (e.g. in Eastern Europe, most of the Middle East, Africa) where related images are not fully available yet.
Once validated, the results obtained at small scale can facilitate central/local authorities in selecting the areas, with homogeneous geo-lithological assets and urban fabrics, where in-depth activities (including geotechnical investigations and modelling) must be carried out at larger scales to identify SMLs having typified features ) and, accordingly, choose the intervention categories that prove to be more effective in mitigating the risk. In this regard, inventorying the interventions already put in place might provide useful information in decision making processes, provided that their effectiveness has been checked by way of monitoring activities corroborated by field surveys (Infante et al. 2020;Maino et al. 2021;Nicodemo et al. 2020a). Anyway, implementing the interventions may be difficult considering that it depends upon several issues among which the earmarked economic resources (often limited) must be mentioned.
Owing to the complexity of the issue, circular approaches-of which the proposed method could be a part-can represent the solution . As a rule, circular approaches should involve: (i) at each scale, periodically updating methods and results (and, accordingly, decisions) as quality and quantity of input data increase thanks to information gathered from monitoring and field surveys/ investigations; (ii) from small to detailed scales and vice-versa, using knowledge acquired at a given scale to improve the knowledge at another scale, so making decisions (on how, where and when to intervene) more effective.
From this point of view, this study stands as a first, fundamental step of a wider SML-risk management framework which looks at the same SML-risk as an opportunity to be seized to improve the quality of human life.