Shallow landslide disposition in burnt European beech (Fagus sylvatica L.) forests

Tree roots contribute significantly to soil strength on hillslopes. In the case of wildfires, this effect may abruptly vanish and be lacking for a considerable period of time depending on the resistance and resilience of the forest. Despite its importance, quantitative data on the impact and dynamics of wildfires on slope stabilization is still lacking. We use the study case of the Fagus sylvatica L. to quantify the medium-term evolution of root reinforcement and its effect on slope stability in fire-injured forests. In the study, we upscale root reinforcement using field data for the calibration of the Root Bundle Model and detailed information on forest structure in 244 plots, and calculate the spatio-temporal dynamics of forest protective capacity using a three-dimensional probabilistic slope stability model (slideforNET) for different site types. In unburnt and low-burn forests, the protective capacity was found to remain constant over time. Forests hit by moderate burns continue to provide adequate protection for shallow (depth < 0.5 m) and cohesive soils only, whereas in the case of high severity fires, the protective capacity vanishes for 15 years and an increased shallow landslide probability remains for at least 40 years. These conditions call for appropriate sylvicultural post-fire measures.

The protective function of forests against gravitational natural hazards in mountainous regions is one of their most important ecosystem services. These services help to maintain the habitability of mountainous regions 1,2 and represent a highly effective way of implementing ecosystem-based solutions for disaster risk reduction (usually referred as Eco-DRR 3 ). Forest management strategies aiming at ensuring the long-term effectiveness of such ecosystem services should be based on holistic and well-grounded scientific knowledge. For instance, forest stand species composition and structure potentially imply considerable differences in the resistance and resilience of forest systems against disturbances and the related protection against gravitational natural hazards 4 .
In the case of shallow landslides, it is well-known that predisposing factors mainly consist of soil cohesion, friction angle, slope gradient, and shear plane depth 5 . The presence of trees and their root systems, in particular, provide a significant increase in soil strength and slope stability [6][7][8][9][10][11] . Root reinforcement depends on the root distribution in the soil and their mechanical properties (e.g. strength under tension, compression and bending) [12][13][14][15] . However, roots are likely to be affected by the vegetation responses to soil properties 16,17 , climate [18][19][20] , and sudden disturbances such as timber harvesting 9,21-23 or wildfire 24 . For example, tree death occurring after a stand-replacing wildfire also implies a subsequent progressive root decomposition process, which inevitably reduces the related soil stabilizing effect [24][25][26] . Consequently, depending on the disturbance and soil type, the stabilizing effect of a forest against shallow landslides may vary greatly in space and time 20,[27][28][29][30][31] . However, the fire intensity-related medium-term dynamics in terms of root spatial distribution and root reinforcement have been neglected so far in literature. No quantitative information in particular exists on the post-fire evolution of the protection capacity of forest stands against shallow landslide, which should be a prerequisite for a precise and effective Eco-DRR approach.
In this work, we combine newly collected data on the root distribution and mechanical properties of European beech with the post-fire beech stand structure dataset provided by Maringer et al. 32 to calculate the medium-term (i.e., 35 years) post-fire evolution of root reinforcement in mixed-severity (low, medium, and high) forest fires in

Results
Forest characteristics. From the 34 selected fire sites, plots classified as burnt (210 plots − 200 m 2 ) and unburnt (34 plots near the burnt areas) were assessed. Data from the unburnt plots were merged with the low burn category (hereafter referred to as "low burn") because of similarity of results also obtained by Maringer et al. 32 . This lead to 35% of the sampled plots being classified as high severity burn and the remaining two thirds as moderate (33%) and low (unburnt + low) severity (32%) burn. The average occurrence of beech was always higher than 80% in tree species composition. This was true for low and moderate severity burn plots, where coniferous (<=2%) and other broadleaved species (<=17%) rarely occurred. This differed for high severity burn plots, where beech reached barely 60% and broadleaved species reached up to 39% (Table 1).
The average mean stand density (number of living trees per hectare) was highest in the low burn plots (762 ha −1 ) and progressively decreased depending on burn severity up to 193 ha −1 in the high burn plots (Table 1). Specifically, the evolution of tree density by DBH class based on years since fire did not reveal any clear pattern in low and moderate burn plots (Fig. 1). In contrast, for high severity burns, also larger trees (24-36 cm and >36 cm DBH) are reduced in numbers, especially after 10 years post-fire. Contrariwise, the proportion of small-diameter trees (<12 cm) is initially (<16 years post-fire) very low and increases strongly from 16 years post-fire onwards becoming the most represented DBH class by far ( Fig. 1 and Table 1).  Forest protective capacity for different soils and scenarios. The mean forest protective capacity generally decreased with increasing slope and soil depth when considering burn severity classes separately (low-, moderate-, high-burn; Table 2). Comparing the protective capacity of low with moderate-/high-severity burns, significant decreases were found in all soil class and scenarios ( Table 2).
Soil class 1 (non-cohesive soil) was found to consistently have the worst protective capacity conditions (Fig. 3) compared to classes 2 and 3 (cohesive soil; Fig. 4 and Fig. 5), decreasing as soon as the slope becomes steeper than 25° (Table 2). Soil class 3 is generally stable on gentle slopes (<=25°) regardless of forest presence or soil depth (NA in Table 2 and Fig. 5). Soil classes 2 and 3 behave similarly and provide a protective capacity of over 50% in low and moderate burns, as long as the soil is not deeper than one meter and the slope is not steeper than 35°. For steeper slopes (i.e., 45°), their protective capacity remains above 50% for shallow soils (<=0.5 m; Table 2) only. Finally, when burn severity is high, the protective capacity gets very low (<25%), regardless of the soil class or burn scenario.
Temporal trends in forest protective capacity against shallow landslides. Low burn severity. In low burn forests protective capacity is generally constantly higher than 75% for shallow soils (<=0.5 m) and for soil classes 2 and 3, regardless of slope (Figs 4a and 5a). In contrast, for soil class 1 it decreases from high to medium-low as slope becomes steeper (Fig. 3a). For deeper soils (>0.5), it provides medium-high (>50%) protection on gentle slopes (25°) only (Fig. 3b,c). Soil classes 2 and 3 follow similar trends, although always with higher protection compared to class 1, becoming very low (<25%) for deep soils (1.5 m) with slopes of 45° (Figs 4c and 5c).
Moderate burn severity. In the case of moderate burns, all scenarios report lower protective capacity with respect to low burns with a slightly decreasing trend over the years (Figs 3, 4 and 5, moderate burn severity). After 35 years post-fire, protection capacity does not drop below 50% for shallow soils (0.5 m) and classes 2 and 3.
High burn severity. Finally, for high-severity burns, a protective capacity >50% is reached with burns less than six years post-fire and in shallow soils (0.5 m) only. Steeper slopes and deeper soils cause the protective capacity to drop below 50% for all soil classes. From six years post-fire onward, the protective capacity drastically decreases for all scenarios reaching minimum values (ca. <10%) at 15-20 years post-fire (Figs 3, 4 and 5, high burn severity).

Discussion
In this study, we analyzed the medium-term temporal trends of the forest stabilizing effect in beech stands disturbed by forest fires of different severities. According to our simulations, even in unburnt or low severity burn forests the protection level against shallow landslides may be below 50%, especially in the case of deep soils (1.5 m) and steep slopes (45°). www.nature.com/scientificreports www.nature.com/scientificreports/ Beech forests provide a good stabilizing effect for cohesionless soils (class 1) only when the slope is below 25° and/or the soil is not deeper than 0.5 m. As a general rule, as soon as the slope exceeds 35° and the soil is more than 1 m deep, protective capacity strongly decreases regardless of the soil type. Fortunately, these combinations of factors are rare, mainly because on steep slopes surface erosion strongly limits the accumulation of the soil mantle 46 . Low intensity wildfires cause little or no change in forest structure, including the amount and timing of regeneration 44 . This ensures a stable degree of protective capacity over the medium-term at a pre-fire level 32,47 .
In the case of moderate wildfires, delayed post-fire mortality due to secondary pathogens (i.e., fungi) and insects may, over the medium-term, gradually affect the protective capacity of the concerned stands, whereas incoming regeneration is still too young for significantly contribute to soil stability. The mean root reinforcement start to slightly recover after about 25 years, but beech stand dynamics after moderate fire severity are very heterogeneous 45 , so that the overall protective capacity tends to keep low. When high severity wildfires occur, forest structure changes abruptly causing a sudden decrease in protective capacity against shallow landslides, regardless of soil class, slope, or soil depth. According to Maringer et al. 29 , following high-severity burns, most intermediate and large beech trees die within the first ten years post-fire. Subsequently, root systems neither provide a soil-stabilizing function nor protection against shallow landslides. This is in line with other studies showing a total decay of the root system within a decade for beech forest 48 and within 10/15 years for spruce (Picea abies 49,50 ). Moreover, when severe wildfires occur, beech forests lose half of their protective capacity within the first five years post-fire due to the very high root decay rate, which may be as high as 11% per year 48 . In Scots pine (Pinus sylvestris) forests, root reinforcement has been found to decrease by a factor of 3.6 in four years post-fire 24 . Similarly, other studies highlighted a significant loss of strength after logging or clearcuttings that rapidly affected small roots (ca. two years after) and then progressively also larger ones (ca. ten years after) 23,51,52 . It is thus reasonable to assume that this will lead with time to an increased risk of landslide 25,31,49,53,54 .

Conclusions
In the present study, we reconstruct for the first time the quantitative medium-term evolution of the protection effects of European beech forests in terms of shallow landslide reduced probability considering a broad combination of factors such burn intensity, soil types, slope inclination and landslide depth.
Our results show that burnt beech forests that experienced low-severity fires does not show any post-fire decreasing trend for the whole study period (i.e., 37 years). In the case of moderate to high severity fires, the protection function of the forest completely vanishes within 15 years, without any sign of medium-term recovery even though regeneration usually starts soon after the fire event. Related shallow landslide probability likely remains high for 40-50 years post-fire.
In order to implement effective Ecosystem-based solutions for Disaster Risk Reduction (Eco-DRR) it is thus highly important to properly plan sylvicultural and/or technical measures in areas where the risk for humans and/or infrastructures is high. The proposed approach for quantifying the temporal dynamic of the post-fire root reinforcement can be easily extended to other disturbances (e.g. windthrow) and other disturbance-sensitive forest species. Most sensitive and priority areas for applying such approach may be easily identified by combining disturbance severity with local geomorphological (elevation, slope, and micro-topography) and forest (stand composition and structure) parameters. This approach may gain importance in future in view of ongoing climate change and increasing population and infrastructure densities in mountainous regions.  www.nature.com/scientificreports www.nature.com/scientificreports/ Methods Methodological workflow. The quantification of forest protective capacity is calculated by combining different sets of input parameters that describe the distribution and mechanical properties of roots as well as the post-fire stand dynamics of European beech forests. In the first step, the acquired field data on root distribution and root pullout tests 57 are used to calibrate the analytical model for the estimation of maximum root reinforcement as a function of tree dimension (DBH), distance from tree, and soil depth 4 , hereafter referred to as "root reinforcement dataset". Subsequently, the data on post-fire beech stand structure (i.e., number of stems and related DBH, hereafter called "forest dataset") 32 is used to upscale the root reinforcement estimation at the stand scale 58 . Finally, different combinations of soil mechanical conditions, landslide depth, and slope inclination are considered to simulate the post-fire forest protective capacity using the 3-dimensional probabilistic slope stability model SlideforNET 47,58 (see "Slope stability calculations and forest protective capacity" subchapter for details).
Root reinforcement dataset: upscaling approach for root reinforcement. The root reinforcement dataset was collected in four different study sites (Schangnau, Spissibach, Laura, Bremgarten) as described in Table 3.  www.nature.com/scientificreports www.nature.com/scientificreports/ Field root pullout tests and root distribution data were used to quantify the maximum tensile force of root bundles (Root Bundle Model -RBMw 59 ) and for calculating the overall root reinforcement within the whole root system 4 .
The RBMw parameters were calibrated for beech using so far unpublished own data from 22 field pullout tests on coarse roots with diameters of up to 2.5 cm, and data on 191 labor tensile tests with root diameters of up to 6 mm available in literature 60 . Field tests were performed following the method described in Vergani et al. 61 , whereas the procedure for the tensile tests are described in Bischetti et al. 60 . The equations fitted for the RBMw are described in detail in Dazio et al. 4 . The maximum pullout force F max as a function of root diameter, φ[m], is calculated as www.nature.com/scientificreports www.nature.com/scientificreports/ where Δx * is the normalized pullout displacement and ω = 2.24[−].
The calculated values of maximum root reinforcement for each soil trench, where root distribution was measured, were used to calibrate the equation parameters used to estimate the root reinforcement, RR max [Nm −1 ], as a function of tree dimension, DBH[m], and distance from the tree stem, d[m], as follows: ≥ . where z α = 1.284 and z β = 3.688 are the calibrated coefficients of the gamma density function, and z is the soil depth. Equations 3 and 4 are used to calculate the minimum values of basal and lateral root reinforcement at stand scale considering the forest structure dataset, as described in Dazio et al. 4 . In contrast to other studies 33,51,[53][54][55] dealing with the decay-related progressive decrease of the root reinforcement, this study focus on the dynamic of root reinforcement as determined by the fire-surviving trees.

Forest dataset. The forest dataset refers to European beech forest stands in the southwestern European
Alps across Canton Ticino (Switzerland) and Piedmont (Italy), where the species is usually concentrated at an intermediate elevation belt ranging from 600 to 1,700 m a.s.l. and represents 16% in Switzerland and 26% in Italy, respectively of the protection forests 63,64 . The species is a deciduous broadleaf tree with a cordate root system 65 characterized by an intensive development of fine roots in the upper soil layer 66 directly related to various factors such as climate, age, BHD, and stand composition [66][67][68][69] . Study design is described in detail in Maringer et al. 28 , and basically consisted in selecting beech-dominated stands (>95% of the stems) that experienced a single fire event of at least 0.25 ha in size between 1970 and 2012 and did not experience any anthropogenic activity (salvage logging, afforestation, pasture) since the fire event. Spanning the selection over 40 years allowed us to use a space-for-time approach to model the long-term dynamic of the post-fire protection capacity against shallow landslides.
Due to the high relief energy in the study region, which fosters heterogeneous burns, single sample plots where additionally categorized according to the resulting burn severity (low, moderate, and high) using the proportion of tree crown volume and basal area losses with respect to the pre-fire conditions as a fire severity proxy. For a thorough description of field data collection methodology, please refer to Maringer et al. 32 .
Slope stability calculations and forest protective capacity. SlideforNET. The web tool SlideforNET (www.slidefor.net) bases on a probabilistic approach that considers the landslide size probability distribution. It enables the estimation of the contribution of root reinforcement to slope stability and the comparison of the related protective effect based on different forest types and slope. Details on the model calculation are presented in Schwarz et al. 47,58 . In SlideforNET, the slope stability calculation refers to a 3D force balance that assumes shallow landslides to be elliptical in shape, and provides a real-event-based probabilistic estimation of the landslide dimension 46,70 . Root reinforcement is then calculated by taking into account 1) the roots crossing the upper margin of the landslide (lateral root reinforcement along the potential tension crack) and 2) the roots crossing the basal shearing plane (basal root reinforcement, Eq. 4). The number of calculated landslides represents the partial probability that they may occur within a certain area under fully saturated conditions and that they are not influenced by a specific rainfall event magnitude or return period. The input parameter (shearing plane depth) as well as effective soil shear strength parameters (soil friction angle and soil cohesion) are defined based on scenarios covering all plausible conditions where shallow landslides may occur. For each scenario, 10,000 slope stability calculations with different randomly generated landslide dimension 46  www.nature.com/scientificreports www.nature.com/scientificreports/ We in particular considered three classes of soil mechanical properties obtained by grouping soils with similar friction angle (deg) and soil cohesion (kPa) based on the Unified Soil Classification System (USCS) 71 as follow: class 1 (non cohesive soil) = 25 deg and 0 kPa; class 2 (cohesive soil) = 25 deg and 2-5 Kpa, class 3 (cohesive soil) = 35 deg and 0-2 kpa. The three classes retained for landslide depth failure were 0.5, 1, and 1.5 m, whereas the three classes of mean slope inclination were 25°, 35°, and 45°, respectively. Different fire-injured beech forests conditions (unburnt + low-, moderate-, high-burn) were considered in the modeling in order to assess post-fire beech forest protective capacity against shallow landslides. The resulting forest protective capacity expressed as the percentage of landslides frequency reduced due to root reinforcement is then grouped into the following categories: ≥90% -very high protection against shallow landslides, 75-90%high, 50-75% -medium-high, 25-50% -medium-low, and <25% -very low protection.
In order to check the robustness of the slideforNET model, two sets of simulations were run. Results showed that no significant difference in forest protective capacity values were found in any scenario between the two simulation sets, using a nonparametric Wilcoxon signed-rank test with the Holm adjustment for p-values. Overall, maximum differences ranged from −7.8 to 10.8% with only 1.2% (21 cases out of 1,772) greater than 5%.
Statistical analysis. In order to consider the combination of factors that are representative for shallow landslide exposed slopes only, we limited the analysis to scenarios (i.e., combination of soil class, slope, and soil depth failures) with more than 1% probability that such events may occur (i.e., where at least 100 out of the 10,000 potential calculated landslides resulted unstable when excluding the effect of vegetation. Moreover, due to the lack of data on different fire severity scenarios, only sites whose fire event was more recent than 41 years ago were retained for the analysis.
Finally, due to the lack of significant impact of low severity fires on the beech stand composition and density 32 , unburnt and low severity plots were grouped in a single category.
Post-fire temporal trends in forest protective capacity were reconstructed using LOESS regression (locally estimated scatterplot smoothing 72,73 due to the nonlinear response. The LOESS span parameter that determines the proportion of points in the plot which influence the trend at each value, was set to 1 in order to increase smoothness and thus visualize general trends 74 . Possible significant differences in the protective capacity among the different burn classes (unburnt + low, moderate, and high severity) were tested by means of a univariate comparative analysis using a Mann-Whitney U test.
All analyses were performed using the R software (version 3.4.1; R Core Team 2017). The main additional packages used were ggplot2 for producing graphics 75 , dplyr 76 and tidyr 77 .

Data Availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.