Keywords

1 Introduction

Climate change is having far-reaching effects ranging from unprecedented forest fires, heatwaves, droughts and extreme rainfall events (IPCC 2014a, b). Natural disturbances are thought to experience a further increase in frequency and severity, progressively affecting areas not endangered in the past also due to land use change (Maringer et al. 2016; Mantero et al. 2020). They can occur alone or in combination with each other and cause and/or be followed by secondary hazards, constituting a complex chain of multi-hazards processes also called cascading effect. As an example, forest fires lead to new avalanche-prone slopes, and to a higher risk of rockfall, debris-flow, mudslides, soil erosion and water quality problems. Recent estimates for the Alpine region, forecasting an increased impact of the climate change effects, suggest wildfires and post-wildfire geological hazards to represent a looming issue in the near future (Zumbrunnen et al. 2009; Moreira et al. 2011; Wastl et al. 2012; Arndt et al. 2013, Dupire et al. 2019, Barbero et al. 2019).

Amongst other hydrological hazards, debris-flow and flood-type events represent the most serious concern, as can be seen in the reports and the scientific literature of the regions (USA, Australia) which are facing the problem nowadays (De Graff 2014). The modification of the hydrological properties, due to litter and vegetation removal, ash deposition, alteration of the physical properties of soil and rocks results in an increase of the availability of easily erodible materials on hillslopes and of runoff rates (Moody and Martin 2001; Parise and Cannon 2008, 2012; Staley et al 2017). In fact, rainsplash, sheetflow and rill erosion increases due to the diminished capacity of rainfall interception by the tree canopies, shrubs and grass. Very soon the surface runoff may concentrate in hollows and low order channels carrying the eroded sediment and entraining the materials deposited in the waterways, eventually exerting a strong erosive action at the expense of the riverbed sediments and causing their “in mass” failure. All of these processes can lead to sediment concentration to levels associated with debris flows (Tang et al. 2019).

Currently, very few models are available for the estimate of the hazard and risk of these phenomena. The USGS preliminary hazard assessment relies on empirical models to assess the likelihood, volume and combined hazard of debris flows for selected watersheds in response to a design storm. These models rely on historical debris–flow occurrence and magnitude data, rainfall storm conditions, terrain and soils information, and burn–severity maps (Staley et al. 2016, 2017). In Australia, the Victorian Department of Sustainability and Environment (DSE) developed an empirical rapid risk assessment procedure for post-fire hydrologic risks, namely debris flows risk, water quality risk and flooding risk. The model, in the early stages of development, is based on available datasets and combines information for terrain, vegetation, rainfall erosivity, burn severity maps and stream network (Sheridan et al. 2009). In other countries, such as the Mediterranean ones, despite an increasing number of hazardous events (Parise and Cannon 2008; Tiranti et al. 2006; Carabella et al. 2019; Esposito et al. 2013, 2017, 2019), no model for the hydro-geomorphic events susceptibility assessment has been implemented or validated extensively. Very few examples of model application can be found in Italy, Greece, Portugal and Spain (Terranova et al. 2009; Fernandez et al. 2010, 2018; Coschignano et al. 2019; Esteves et al. 2013 Rulli et al. 2013; Lanorte et al. 2019; Depountis 2020, Efthimiou 2020). The need to quantify the influence of fires on the propensity for hazardous processes clashes with the fact that, in many regions outside the United States, the scientific community has faced the problem in a consistent way only in recent years and thus the available post-fire event statistics does not allow for a data driven approach. In this study, we focused on the application and validation of a modified version of the RUSLE model (Revised Universal Soil Loss Equation—Wischmeier and Smith 1978) to quantify the post-fire erosive phenomena for a case study in the north-western Italian Alps. In this area, during October 2017, ten wildfires occurred, burning a total area of 10,000 hectares of which 7000 were forests; this value far exceeds the average regional forest burned area (600 ha/year between 2005 and 2013) (Morresi et al. 2022). Season fires in 2017 were favored by the exceptionally dry conditions, high temperatures and the occurrence of several days with hot and dry winds (Arpa Piemonte 2017; Bo et al. 2020). The largest and most severe fire—almost 4000 ha—occurred in the Susa Valley, where fourteen catchments on the left of the Dora Riparia River were involved. Starting from late April 2018 until the early June, several flow events originated from the burned catchments. The larger damages were recorded at the outlet of the Comba delle Foglie, a small drainage basin overhanging the Bussoleno municipality (Vacha et al. 2021). Ground evidence highlighted a remarkable increase in erosion rates exerted by the surface runoff in many sectors within the fire perimeter, in agreement with literature findings (Moody and Martin 2001; Parise and Cannon 2008, 2012; Staley et al. 2017). Based on the assumption that these processes represent the key aspect governing the availability of sediments to be entrained during rainfalls, and taking into account the available spatial data, the structure of the RUSLE model proved to be the most suitable framework to be adopted. In fact, the approach used is deliberately simple, replicable, improvable and easy to implement in a GIS environment. It is also possible to automate it in order to make it available for the rapid production of thematic maps to support authorities and for civil protection purposes. Moreover, it relies mostly on the available open source spatialized data provided by regional authorities and other public bodies, which makes it easy to replicate the conceptual scheme in other areas. The model has been applied and validated on the Comba delle Foglie catchment, for which a detailed temporal reconstruction of the processes and quantification of the volume of mobilized material has been carried out in a previous work (Vacha et al. 2021).

2 Study Area

The study area is located in the Susa Valley, an east–west Alpine valley, located in the western part of Piedmont (starting ~ 20 km West of Turin). It was affected by the largest and more severe of the ten wildfires that occurred in the region in 2017 (The Bussoleno and Mompantero Wildfire) which burned 4000 ha on the left of the Dora Riparia River, going up the valley from east to west and affecting the slope almost to the divide (Fig. 1). The fire started on October 22, 2017 and lasted until November 1, 2017. It interested an area dominated by European Beech (Fagus sylvatica L.) and Scots Pine (Pinus sylvestris L.), the forest cover being the 37.1% and the 26.7% for the Broadleaved and the Coniferous species, respectively, with 36.2% of the wildfire surface being represented by non-forested areas (Morresi et al. 2022). Comba delle Foglie is one of the catchments affected by this exceptional wildfire. It is located towards the eastern side of the wildfire area and is a steep, elongated watershed ranging between 480 and 1747 m a.s.l., characterized by an average slope of 35° and an area of approximatively 1.37 km2 (Vacha et al. 2021). The bedrock of the catchment is represented by polimethamorphic rocks and in particular by Micaschists and gneiss belonging to the Dora Maira pre-triassic basement (DMb), by calcschists, marbles and dolomitic marbles belonging to the Dora Maira Mesozoic cover (DMc) and by calcschists, serpentinites, serpentinoschists and chloritoschist belonging to the Lower Piedmont Zone (PZ) (Carraro et al. 2002; Gasco et al. 2011). The geomorphological setting of the study is both influenced by its geologic history and by quaternary geomorphic events. The main valley is dominated by erosional and depositional landforms of glacial origin, mainly glacial terraces, suspended-tributary valleys and lodgement and ablation till. The post-glacial remodeling action exerted by gravitative and fluvial processes strongly influenced the landscape. In particular, the left side of the Susa Valley hosts a series of ravine and canyon-like features in correspondence of morphological steps at the outlet of suspended valleys into the main valley. As a result, the quaternary deposits mantle the study area heterogeneously: the main valley floor is filled by alluvial deposits, while the slope are patched by glacial, fluvial and gravity related deposits, often reworked (Cadoppi et al. 2007).

Fig. 1
figure 1

Perimeter of the Susa valley wildfire and location of the Comba delle Foglie watershed. The base map is the regional DTM

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The vegetative cover of the catchment before the fire was low with respect to other sectors of the burned area due to previous wildfires (Ascoli et al. 2011), and it was mostly dominated by young trees of Populus tremula and Salix caprea. The most relevant parameters describing the watershed are given in Table 1, in which the major morphometric descriptors can be found.

Table 1 Morphometrical and hydrological descriptors of the Comba delle Foglie watershed; area Aw [km2], perimeter P [km], watershed length Lb [km], minimum elevation Emin [m s.l.m.], maximum elevation Emax [m s.l.m.], mean elevation Emea [m s.l.m.], minimum slope Smin [°], maximum slope Smax [°], mean slope Smea [°], main channel length Lp [km], average main channel slope LpS [°], total streams length L [km], Fan to watershed area ratio Af_Aw [−], Form factor Ff [−] (Horton 1932), Circularity ratio Rc [−] (Miller 1953; Strahler 1964), Elongation ratio Re [−] (Schumm 1956), Melton Index Me [−] (Melton 1965), Drainage density Dd [km/km2] (Strahler 1964), Time of concentration Tc [h] (Kirpich 1940)
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3 Materials and Methods

3.1 Burn Severity

The burn severity map of the Bussoleno and Mompantero Wildfire (Morresi et al. 2022) was adopted in this work. This map was produced through satellite imagery and field surveys, following a methodology based on US FIREMON framework (Key and Benson 2006). The analysis of spectral changes caused by the 2017 wildfires was carried out using multispectral images acquired by the MultiSpectral Instrument (MSI) onboard Sentinel-2 A/B satellites (European Space Agency). In particular, the burn severity obtained by using the uncalibrated RdNBR bi-temporal index (Miller and Thode 2007, Eq. 1) calculated from reflectance composites was adopted here. It was generated using all the clear observations available in the period spanning from 20 May to 10 September for both 2017 and 2018; the validation of the map and the classification in severity categories followed Miller et al. (2009), Miller and Thode (2007) and Parks et al. (2014). This product was chosen because among all the other indices calculated by the authors, it was the one with the best overall accuracy.

$$ RdNBR = { }\frac{dNBR}{{\sqrt {\left| {NBR_{prefire} } \right|} }} $$
(1)

RdNBR is based on the definition of the Normalized Burn Ratio (NBR) (Eq. 2) which is calculated by contrasting the reflectance in the near infrared (NIR) and in the shortwave infrared (SWIR); the delta Normalized Burn Ratio (Key and Benson 2006) is calculated through Eq. (3).

$$ NBR = \left[ {\left( {NIR - SWIR} \right)/\left( {NIR + SWIR} \right)} \right]{ } $$
(2)
$$ dNBR = \left( {NBR_{prefire} - NBR_{postfire} } \right) \times 1000 $$
(3)

RUSLE—Monthly erosion calculation

Sediment erosion has been assessed implementing the RUSLE model at a monthly scale through the following equation:

$$ A_{month} = R_{month} {*} K {*} L {*} S {*} C {*} P $$
(4)

where A = mean soil loss per month [Mg ha−1 m−1], R = rainfall erosivity factor [MJ mm h−1 ha−1 m−1], K = soil erodibility factor [Mg MJ−1 mm−1 h], LS = topographic factor or slope length factor [dimensionless], C = soil coverage [dimensionless], and P = erosion control practices factor [dimensionless]. The value of the sediment loss (SL) is obtained by multiplying the value of A for the drainage surface. The R factor quantifies the mechanical impact energy exerted by a given precipitation and depends on duration and intensity of the rainfall. Remaining parameters in the equation give a measure of the environmental resistance to erosive phenomena. The K, LS and C factors are assumed to change in areas affected by wildfires as a result of fire effect on soil erodibility, vegetative cover and shift in rill to interrill soil erodibility ratio (Terranova et al. 2009). RUSLE model is intended to quantify soil losses in the long term, so that processes such as gully and channel erosion and sediment transport cannot be modelled. Prediction accuracy for individual storm is very low, as controversial is the application on large spatial scale. Despite this, the model can be used as a solid framework to quantify high-risk erodible areas (Efthimiou et al. 2020). With this regard, the product of K, LS and C factor is used to compare post-fire to pre-fire condition; thus, EI [Mg MJ−1 mm−1 h] is introduced to describe the erosion susceptibility:

$$ EI = C {*} K {*} Ls $$
(5)

P factor has been considered equal to 1, because there are no support practices for the erosion reduction in the study area.

Rainfall erosivity factor—R

The rainfall erosivity factor (R) factor has been estimated at a monthly scale by calculating the summation of the parameter EI30 of every single erosive event (k) for each considered month.

$$ R_{month} = \mathop \sum \limits_{k = 1}^{n} EI_{30 k} $$
(6)

Following Brown and Foster (1987), EI30 for a single rainstorm event is defined as the product of the kinetic energy of rainfall events (E) and its maximum 30-min intensity (I30):

$$ EI_{30} = \left( {\mathop \sum \limits_{r = 1}^{m} e_{r} v_{r} } \right)I_{30} $$
(7)

where er = unit rainfall energy [MJ ha−1 mm−1], vr = rainfall volume [mm] during the r-th period of a storm which divided into m parts and I30 is the maximum 30-min rainfall intensity [mm h−1]. The unit rainfall energy er is calculated for each time interval using Eq. (8) (Brown and Foster, 1987):

$$ e_{r} = 0.29\left[ {1 - 0.72e^{{\left( { - 0.05i_{r} } \right)}} } \right] $$
(8)

where ir is the rainfall intensity during the time interval [mm h−1]. High resolution rainfall data (10 min time resolution) were downloaded from Arpa Piemonte database for three rain gauges located in the surrounding of the watershed, namely Prarotto, Borgone and Malciaussia (Table 2 and Fig. 2). Rainfall series covers a period of time ranging from September 1, 2017 to August 3, 2018. The identification of the erosive rainfall (n) events for each station record followed three criteria given by Renard et al. (1997): the cumulative rainfall of an event is greater than 12.7 mm, or the event has at least one peak that is greater than 6.35 mm during a period of 15 min. Individual storms are separated if a rainfall accumulation is less than 1.27 mm during a period of 6 h. Those criteria have been developed for the USA countries, but are also widely accepted in other areas (Panagos et al. 2015a). The Rainfall Intensity Summarisation Tool (RIST) software (USDA 2014) was used to calculate the R-factor based on the single station annual series. After that, the single monthly R factors related to each rain gauge were averaged to get the final value representative of the watershed. The obtained results were compared with the average monthly rainfall erosivity calculated by Ballabio et al. (2017) at European scale analyzing > 17 years of rainfall data and downloaded from ESDAC repository (European Soil Data Centre, European Commission, Joint Research Centre).

Table 2 Location of the three rain gauges of Prarotto, Borgone and Malciaussia
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Fig. 2
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Location of the three rain gauges of Prarotto, Borgone and Malciaussia with respect to the Comba delle Foglie watershed position

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Soil erodibility factor—K

The soil erodibility (K) factor has been determined based on soil textural data. Homogeneous lithological units have been individuated by grouping the geological units derived from 1:50,000 geological map (Carraro et al. 2002). Soil samples have been then collected and processed in laboratory for determining grain size distribution following standard ASTM procedures. Afterwards, the K factor for each unit has been then calculated based on the following formulae (Renard et al. 1997):

$$ K = 0.0034 + 0.0405*\exp \left[ { - 0.5\left( {\frac{{logD_{g} + 1.659}}{0.7101}} \right)^{2} } \right] $$
(9)
$$ D_{g} = \exp \left[ {\sum f_{i} \ln \left( {\frac{{d_{i} + d_{i - 1} }}{2}} \right)} \right] $$
(10)

where Dg = geometric mean particle size for each particle size class (clay, silt, sand), di = maximum diameter (mm), di−1 = minimum diameter and fi is the corresponding mass fraction.

Cover factor—C

The C factor has been assessed based on Forestry/Land Cover Map and by assigning C values according to Panagos et al. (2015b). Tabulated values for each land cover class are given in Table 3, whilst land cover classes areal distribution is given in Table 4.

Table 3 RUSLE cover factor proposed for each land cover class (after Panagos et al. 2015b)
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Table 4 Land cover classes areal distribution over the Comba delle Foglie watershed
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Length/Slope Factor LS

The LS factor in the original RUSLE model describes the interaction between standard parcel length (L) and slope (S). In this study, it is substituted by the unit contributing area Ls, which takes into account the flow convergence (Mitasova et al. 1996; Terranova et al. 2009). Ls is computed for each 5 m wide DTM cell as follows:

$$ Ls = \left( {\mu + 1} \right)\left( {a/a_{0} } \right)^{\mu } \left( {\sin b/b_{0} } \right)^{\eta } $$
(11)

where a [m] = the upslope contributing area for each cell (result of the ArcGIS “flowacc” and “resolution” functions), b [%] = slope, a0 [m] = 21.1 m (the standard USLE plot length), and bo [%] = 9% (the standard USLE plot slope). The parameter μ is calculated as a function of β, which is the ratio of rill to interrill erosion (Miller et al. 2003; Foster et al. 2003):

$$ \mu = \beta / \left( {\left( {1 + \beta } \right)} \right) $$
(12)

Based on literature, β can be set equal to 0.5 for unburned areas and equal to 1 for burned areas with high severity. The parameter η is considered equal to 1.2 following Terranova et al. (2009) and Coschignano et al. (2020). The cell values in a buffer of 10 m around the stream network has been excluded from the calculation since the RUSLE model does not provide estimates for streamflow erosion. For them, a default value of 0 has been assigned.

Model implementation

Pre-fire monthly mean soil loss (Apre) and erodibility index (EIpre) were calculated based on the previous equations on a 5 m resolution raster grid based on DTM cells position. Then the spatially weighted average of Aw_pre was calculated over the entire watershed surface.

Finally, the value of the monthly sediment loss (SLpre) [Mg y−1] for the watershed was calculated multiplying the value of Aw_pre times the watershed area. Post-fire condition was modeled by calculating mean soil loss per month (Apost) and erodibility index (EIpost) following Eqs. (3) and (4). The single factors of the RUSLE model were adjusted as a function of fire severity (unburned, low, moderate or high) following with some modifications the procedures described in Terranova et al. (2009) and Lanorte et al. (2019). The metrics used in this work are given in Table 5. For both scenarios (pre- vs post-fire), A and EI raster cell values have been subsequently averaged for each watershed giving Aw-post and SLpost value.

Table 5 Adjusted cover factors (C), erodibility factors (K) and β value (used for LS factor calculation) (β) for different fire severity classes
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4 Results

The fire severity class distribution over the watershed (Fig. 3) highlight a predominancy (77.10%) of moderate fire severity, while unburned/low and high severity cover the 21.98%, and 0.92% of the watershed area, respectively. Given the fact that the area experienced another fire in 2003, the burn severity map may underestimate the 2017 situation, even if a relativized index such as RdNBR has been used.

Fig. 3
figure 3

Fire severity classes distribution for the Comba delle Foglie catchment

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Monthly R factors for each rain gauge from September 2017 to August 2018 have been quantified by calculating the summation of the parameter EI30 of every single erosive event for each considered month. The R factor obtained for each station has been then averaged for assessing the representative rainfall erosive power at the watershed scale. For the Prarotto, Borgone and Malciaussia rain gauges 22, 24 and 22 erosive events, respectively, have been identified. For the Prarotto rain gauge, the selected storms are characterized by a mean precipitation value of 30.94 mm, duration of 23.23 h and EI30 of 95.99 MJ mm ha−1 h−1. For the Borgone rain gauge mean precipitation, duration and EI30 values are 27.67 mm, 20.19 h and 73.06 MJ mm ha−1 h−1. At the Malciaussia station, mean value recorded are 29.20 mm, 16.02 h and 55.40 MJ mm ha−1 h−1, for precipitation, duration and EI30. The maximum values of R factor are reached in May, April and March 2018, and are, on the contrary, equal to zero for September and October 2017.

R factor distribution over time is consistent with Piedmont meteorological data (Arpa Piemonte 2018a, b, 2019), reporting an extremely dry end of 2017 and very wet month of January, April and May 2018. In fact, erosive events registered in these months represents approximatively the 75% of the entire annual R factor, and in particular the month of May reaching almost the 40%. Erodibility K factor representative of the pre-fire condition has been determined based on soil textural data collected during the field surveys.

The pre-fire K values have been calculated following Eqs. (9) and (10). The post-fire adjusted K values have been then calculated by applying the correction procedure described in Table 5. Pre-fire and post-fire K values are reported in Fig. 4 (a, b). Pre-fire c factor (Fig. 4c) has been calculated following the procedure described above, by using the values reported in Table 3; post-fire c factor (Fig. 4d) has been then calculated as given in Table 5. Pre-fire LS factor has been calculated through Eqs. (11) and (12), while post-fire LS values have been calculated through Eq. 12 and Table 5. Results are reported in Fig. 4e, f. P value has been set equal to 1.

Fig. 4
figure 4

RUSLE factors distribution over the catchment: pre-fire erodibility factor a, post-fire erodibility b, pre-fire cover factor c, post-fire cover factor d, pre-fire LS factor e and post-fire LS factor f

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Erodibility index values for the pre-fire and post-fire situation (Table 6) has been calculated following Eq. (5), and finally monthly mean soil loss A [Mg ha−1 m−1] and averaged monthly sediment loss SL [Mg m−1] for the entire watershed have been computed for both the burned and unburned condition. The post-fire mean erodibility index is more than one order of magnitude higher than the pre-fire one, having a pre-fire value of 4.63E-04 Mg MJ−1 mm−1 h and a post fire value of 1.21E-02 Mg MJ−1 mm−1 h. Also, the maximum values show a rise of about the same order.

Table 6 Post-fire versus pre-fire erodibility index values over the Comba delle Foglie watershed
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Monthly mean soil loss A [Mg ha−1 m−1] and averaged monthly sediment loss SL [Mg m−1] comparison for the pre- and post-fire conditions (Fig. 5, Table 7) results in a post-fire increase of both the indicators of more than 20 times with respect to pre-fire. Maximum pre-fire values occur in May, being 0.307 Mg ha−1 m−1 and 39.86 Mg m−1 for monthly mean soil loss and monthly sediment loss, respectively; for the post-fire, these parameters reach values of 8.066 Mg ha−1 m-1 and 1050.400 Mg m−1, respectively.

Fig. 5
figure 5

Monthly mean soil loss

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Table 7 Spatially averaged mean soil loss (A) and averaged monthly sediment loss (SL) comparison for the burned and unburned situation
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5 Discussion

The sediment erosion has been assessed for the Comba delle Foglie watershed by implementing the RUSLE model at a monthly scale, including model inputs of a detailed erodibility map, the forestry/land cover map, the LS factor map derived from GIS elaboration and a R factor value calculated by retrieving the erosive power of every significant rainfall event. Monthly mean soil loss [Mg ha−1 m−1] and averaged monthly sediment loss [Mg m−1] are the result of the remarkably R values recorded in the months of January, April and May; these three months in fact contribute for about 75% to the annual erosion recorded in the watershed.

Comparing the calculated R factors to average monthly R factor by Ballabio et al (2017) (Fig. 6) is evident a concentration of the erosive events in the post-fire time window, while the precipitations remained well below the average values from September to December 2017, barely reaching the 6% of the cumulated average value. The months of January, April and May show values eleven, eight and four times greater, respectively, than the long time series data. The RUSLE model estimates a SL of approximatively 2430 Mg from the extinction of the fire to June (included), when the most significant event occurred. To validate this result, the only available information is related to the characterization of the 7 June event: in that case, the maximum deposit thickness of the debris-flow reconstructed via photogrammetric modelling was approximatively 2 m and the invasion area covered about 26,000 m2. The total mobilized volume for only the coarser fraction of the deposit, was about 4300 m3, of which about 1500 m3 consisting of materials entrained just at the fan apex. The volume of the coarser sediments coming from the watershed was estimated to be 1300 m3. By applying a simple rule of thumb, considering a bulk density of 1500 kg/m3, the 7 June flow mass can be estimated in 1950 Mg. Considering the fact that other four minor events (one debris/mud flow in April and three floods in May) happened before the 7 June, it is reasonable to presume that the remnant part of the total sediment loss estimated by the model could be related to those events. Some non-negligible aspects undermine the model robustness and accuracy: in fact, the 7 June event volume estimated via photogrammetrical modeling contrast with the one suggested by Arpa Piemonte (2018b) , which after expeditive surveys estimates the total event volume to be about 20,000 m3. Another aspect which should be taken into account when dealing with the model validation is the remarkable erosion exerted by the debris-flows along all their paths, which may have increased their volumes considerably. The results of the model are not suitable to predict streamflow erosion, so when the estimated value is compared to the available surveyed data, this aspect may also increase the uncertainty. Finally, the current model does not take into account the ash and combustion residues which, for sure, contribute to the overall sediment availability to be entrained. Ash and combustion residues are expected to constitute a large part of the removable material especially immediately after the fire, and that they will then be gradually washed away by the runoff as the rainy events occur. Despite all the model limitations and the uncertainties related to its validation, the presented procedure can be considered a reasonable estimator of the amount of material ready to be eroded during the rainstorm events and conveyed in the riverbeds. In fact, it is backed up by ground evidence, the assumption that the considerable amount of sediment mobilized from the date of the fire have been progressively delivered towards the bottom of the slopes and inside the stream network on the repeated rainfalls. In occasion of some smaller mud-flows and hyper-concentrated flows have originated. Then, when the progressive increase of sediments reached a critical threshold in conjunction with a rainy event of a sustained intensity, the most destructive debris-flow on 7 June occurred. During the field inspections prior to 7 June a considerable amount of sediments and combustion residues had been observed inside the channels, especially in the terminal part of the watershed and at the apex of the fan. The investigations carried out following the event revealed evident traces of areal and channeled erosion, starting from the upper part of the slopes and into the lower-order channels. It is clear how all this mass of sediments, both coming from open slopes and being deposited in the drainage network, has constituted the load of the debris-flow during its transit, simultaneously increasing its energy.

Fig. 6
figure 6

Comparison between calculated and long term inter annual R-factor (Ballabio et al. 2017)

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6 Conclusions

The Piedmont region, and in particular the western Italian Alps, experienced an unusually severe wildfire season in 2017. The fires occurred in the late autumn and, after a snowy winter, were followed by spring rains. In particular, some of the catchments burned in the Susa Valley wildfire were interested in May and June 2018 by debris/mud-flows and flood type events. The major debris-flow happened at the outlet of Comba delle Foglie and struck the Bussoleno municipality. Based on field evidence, it was found that the flows mobilized materials and sediments, which were eroded from the burned hillslopes and subsequently deposited in the channels. This is consistent with the literature which reported the main cause of the post-fire debris-flows to be the generation of increased erosion due to excess runoff rather than a discrete landslide failure. On the back of these findings, a modified version of the RUSLE model was applied in the area of Comba delle Foglie to quantify the erosive processes on a monthly scale. The results of its application, incorporating high resolution rainfall series and data deriving from field surveys, made it possible to reproduce and highlight the marked increase in erosion rates, quantified by expressing both the EI (erodibility index), the A (monthly soil loss) and the SL (monthly sediment loss) rise. In particular, overall A and SL increased more than twenty times in the post-fire scenario, the months of April, May and June representing the larger share of the total quantities. This is a consequence of the noticeable increase of t EI, which for the post-fire scenario is more than one order of magnitude higher than the pre-fire one. The intrinsic uncertainties of the model are related to the fact that it does not consider the stream-flow erosion in the channels, it does not account for the material eroded by the debris-flow during its passage and it does not incorporate the eroded volume of ash and combustion residues. Some uncertainties are then linked to the fact that the estimates regarding the actual volumes of the flows are limited to a single case (the major one, 7th June) and also do not agree with each other. Despite these uncertainties, the proposed procedure can be considered a reasonable estimator of the amount of material ready to be eroded, especially if it is used to compare different catchments in a relative way; in this case, it can provide useful guidance to rank the post-fire debris-flow susceptibility and to establish intervention priorities. It can be applied everywhere on the regional territory because the model make use on open-source spatialized data and thanks to its structure, it can be easily implemented into a GIS for thematic map production.