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Dendrogeomorphic assessment of rockfall recurrence intervals at Saint Paul de Varces, Western French Alps

Evaluation dendrogéomorphologique de l’intervalle de récurrence des chutes de pierre à Saint-Paul-de-Varces, Alpes françaises
Adrien Favillier, Robin Mainieri, Jérôme Lopez Saez, Frédéric Berger, Markus Stoffel and Christophe Corona

Abstracts

Determination of spatial and temporal patterns of rockfall events remains a serious challenge in most mountain areas and especially when it comes to quantitative hazard assessments, because of the scarcity and incompleteness of long-term records. This lack of reliable baseline data is particularly problematic in urbanized areas where rockfall risk tend to increase as urbanization is climbing up on slopes. On forested slopes, dendrogeomorphic methods have been applied repeatedly to fill this data gap, as they provide both spatial and temporal reconstructions of past rockfall events with high accuracy. In this study, the systematic mapping of 1,004 broadleaved trees at Saint-Paul-de-Varces (French Alps) was used to document a total of 1,516 rockfall scars visible on the surface of stems. We then coupled the so-called scar counting approach with the conditional impact probability concept, so as to estimate the likelihood of those rockfalls which did not collide with trees. This coupled method allows estimating and mapping of recurrence interval of rockfalls. Our results show a clear reduction of rockfall frequency in the down slope direction as well as a noticeable lateral change in it. This is consistent with the concave profile of the slope and the barrier effect of trees at the study site. These findings also demonstrate, on one hand, the usefulness of broadleaved tree species to reconstruct rockfall frequencies and, on the other hand, the efficiency of our approach to reveal spatio-temporal patterns of rockfall activity. The approach presented here could become a powerful tool for rockfall hazard assessments which, coupled with a 3D-modelling of block trajectories, will further allow computation of frequency - intensity maps on forested slopes.

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Editor's notes

Soumis le 03 février 2017, reçu sous sa forme révisée le 10 mai 2017. Définitivement accepté le 19 mai 2017.

Full text

This research has been supported by the national research project C2ROP (Chutes de blocs, Risques Rocheux, Ouvrages de Protection) supported by the MEDDE, French Ministry of Ecology, Sustainable Development and Energy. The authors are grateful to the entire IRSTEA Mountain Ecosystems team for their scientific and technical supports and helpful comments. The authors also acknowledge the valuable feedbacks of Dr. Daniel Trappmann and an anonymous reviewer. The authors are also grateful to the handling editor for his help in the review process.

1. Introduction

1Rockfall is a common and dangerous natural process occurring on steep slopes; in many instances, their occurrence can lead to important economic loses and even casualties (Hantz et al., 2003). A rockfall is defined as a fragment of rock, generally of small volume, detaching from a cliff face to progress downslope by falling, bouncing and rolling (Varnes, 1984; Berger et al., 2002; Dorren et al., 2005). In principle, rockfall hazard can be defined as the probability that a specific location on a slope is reached by a rockfall of a given magnitude and within a specified period of time (Varnes, 1984). Rockfall magnitude-frequency relationship can be obtained from statistical analysis of inventories of past rockfall events (Hungr et al., 1999; Dussauge-Pessier et al., 2002). Although this approach is well established in the field of natural hazards, and in particular for earthquakes (Main, 1996), its application to rockfall hazards is somewhat more limited because of the generalized lack of historical archives and the spatial and temporal heterogeneity of available inventories (Sass and Oberlechner, 2012). An alternative tool to historical archives is the derivation of onset frequencies from long-term visual observations of rockwalls (Matsuoka, 2008; Hantz et al., 2014) or based on assessments using terrestrial laser scanning (Abellán et al., 2010; D’Amato et al., 2015), but such datasets are rarely available and can only cover short time periods.

2If forest covers the rockfall depositional area, fallen blocks may damage or even destroy trees (Stoffel, 2006; Trappmann et al., 2014). Consequently, analysis of woody vegetation damaged by rockfalls on talus slopes is a valuable method for determining past rockfall activity with high accuracy and over fairly long time periods (Stoffel et al., 2010; Šilhán et al., 2011). Dendrogeomorphic methods aiming at inferring data on past processes from information preserved in tree rings, have been successfully applied in the past to study rockfall hazards (Stoffel et al., 2005a, b; Stoffel and Corona, 2014). Previous tree-ring studies primarily focused on rockfall damage in conifers, so as to reconstruct rockfall frequencies (Stoffel et al., 2005a, b; Perret et al., 2006; Morel et al., 2015), the spatial distribution and magnitude of rockfalls (Stoffel et al., 2005b), the triggering of rockfalls by fluctuations of the climate (Schneuwly and Stoffel, 2008; Šilhán et al., 2011) as well as to compare observed and/or reconstructed rockfall inventories with process activity as predicted by three-dimensional, process-based rockfall models (Stoffel et al., 2006; Corona et al., 2013; Corona et al., 2017). Occasionally, rockfall research has included broadleaved tree species growing on talus slopes to document more recent rockfall activity (Moya et al., 2010a, b; Šilhán et al., 2011; Trappmann and Stoffel, 2013). Broadleaved species are often characterized by relatively thin and smooth bark structures which not only facilitate wounding but also enhance the long-term visibility of scars (Stoffel and Perret, 2006). Accordingly, many broadleaved species are suitable for the counting scars approach (Trappmann and Stoffel, 2013). This method has been demonstrated to be comparably suitable – yet slightly less precise – than classical tree-ring approaches, and to clearly allow a quantification of rockfall activity in space and time with limited efforts and at reasonable cost (Trappmann and Stoffel, 2013; Trappmann et al., 2013).

3This paper aims at proposing a procedure for estimating and mapping of rockfall recurrence intervals based on (i) the counting of visible scars (Trappmann et al., 2013) on broadleaved tree stems and (ii) an estimation of tree ages using a diameter-age linear regression. In addition, (iii) the conditional impact probability (Moya et al., 2010a) has been used to quantify the percentage of rockfalls passing the forest without impacting on tree stems. This procedure has been employed at the “Croupe du Plantin” (French Alps) where frequent rockfalls, detached from Valanginian limestone and marl cliffs, threaten settlements from the municipality of Saint-Paul-de-Varces and impact a mixed protection forest mainly composed of pubescent oaks and Italian maples.

2. Study site

4The study site, a locality known as the “Croupe du Plantin” (45°0502N, 5°3916E, 470‑630 m asl) is located on the eastern slopes of the Vercors massif in the French Alps (fig. 1A), on the territory of the village of Saint-Paul-de-Varces (2,500 inhabitants). Rockfall originates from a ~30-m-high, south-east-facing cliff (fig. 1B) consisting of Valanginian limestones and marls, where narrow jointing, roughly characterized by subhorizontal bedding and subvertical orthogonal joints, favors considerable fragmentation and the release of small rock fragments with volumes ranging from a few dm³ to 1 m³ (fig. 1C). The study site formed a ~240-m long talus slope with a downslope gradient ranging from 39° to 25° (mean ~34°) bordered by two interfluves (Favillier et al., 2015). At the apex of the talus, slope morphology is characterized by a slight depression (depth ~2 m) separating the study area into two ~30-m-wide couloirs which tend to channelize falling blocks (fig. 2A‑B).

Fig. 1 – Overview of the study site.
Fig. 1 – Localisation du site d’étude.

Fig. 1 – Overview of the study site.Fig. 1 – Localisation du site d’étude.

The study site is located in the French Alps (A), on the eastern slopes of the Vercors massif, 20 km south-west of Grenoble. (B) The study site – delimited by a white polygon – is dominated by a ~30-m-high, south-east-facing cliff built of Valanginian limestone. (C) Illustration of injured Acer opalus mill. in the forest stand.
Le site d’étude se trouve dans les Alpes françaises (A), sur le versant Est du massif du Vercors, à 20 km au sud-est de Grenoble. (B) Le site d’étude – délimité par un polygone blanc – est surplombé par un escarpement de calcaire valanginien, haut d’une trentaine de mètres et orienté au sud-est. (C) Illustration d’un Acer opalus mill. blessé, dans le massif forestier.

Fig. 2 – Geomorphic analysis of the study site.
Fig. 2 – Analyse géomorphologique du site d’étude.

Fig. 2 – Geomorphic analysis of the study site.Fig. 2 – Analyse géomorphologique du site d’étude.

A. Hillshade map built from a DEM derived from airborne LiDAR data. B. Longitudinal and lateral profiles of the slope under investigation.
A. Carte d’ombrage construite à partir d’un MNT issu du traitement de données d’un LiDAR aéroporté. B. Profils longitudinal et latéral du versant étudié.

5The tree plot analyzed here has an area of 0.6 ha (120 × 50 m) and is covered by a dense (~2000 trees.ha-¹) forest stand predominantly composed of Acer opalus subsp. opalus (Italian maple) and Quercus pubescens subsp. pubescens (pubescent oak), mixed with Sorbus aria (L.) Crantz (common whitebeam), Acer campestre subsp. Leiocarpum (field maple) and Fraxinus excelsior L. subsp excelsior (common ash). Frequent scars on the stem surface clearly evidence the presence of regular rockfall activity. Mean annual precipitation (1961‑2013) at the nearest meteorological station, Grenoble (45°09′58″N, 5°45′58″E, 220 m asl), located 10 km northeast of the study site, is 934 mm. Mean annual temperature is 12.5°C with 64 days experiencing freezing. Historical and instrumental series of seismic activity are not available at the study site and the possible role of seismic waves in mobilizing the rock mass cannot be evaluated (Dussauge et al., 2003; Dietze et al., 2017). Rockfall is the dominant geomorphic process operating at the site, signs of any other geomorphic processes inducing tree damage are missing.

6The municipality of Saint-Paul-de-Varces is severely exposed to rockfall hazards. Two major collapses have been reported in historical archives, one at the beginning of the seventeenth century and another one in December 2008, with the latter having had a volume estimated to 1,625 m³ (Hantz et al., 2014). Vulnerability of the settlement to rockfall has increased rapidly since the 1950s, owing to the rapid periurban expansion of settlements in the wider Grenoble region (Astrade et al., 2007). As a consequence, rockfall hazard assessments have become a key concern for local stakeholders and policy makers.

3. Material and methods

7The “Croupe du Plantin” tree plot was selected as (i) past rockfalls have left numerous visible impacts on tree stems, (ii) no other geomorphic processes caused injuries to trees, and as (iii) the forest was not exploited over the last century. Rockfall frequency was evaluated with a three-step procedure including (i) the scar-counting approach on all trees located within the sample plot as described by Trappmann and Stoffel (2013), (ii) an estimation of the age of each tree using a diameter-age linear regression (Favillier et al., 2015) and (iii) the assessment of the rockfall frequency using the conditional impact probability to account for possible events that missed tree stems (Moya et al., 2010a; Trappmann et al., 2013).

3.1. Tree plot and scar-counting approach

8At the study site, virtually all trees show visible growth anomalies on the stem surface resulting from past rockfalls, predominantly in the form of injuries. We search for scars on stem on the study site as they represent the most accurate and reliable growth disturbance (GD) to date past rockfalls in tree-ring records (Schneuwly et al., 2009a, b; Stoffel et al., 2013). First step to assess rockfall activity in the site was tree mapping. Trees with a diameter at breast height (DBH) > 5 cm were systematically located in a 50 × 120 m tree plot orientated perpendicular to the line of maximum slope gradient (fig. 3). The position of each tree was determined ( ±  100 cm) using a sonic rangefinder, compass, and inclinometer. All trees were positioned in a geographical information system (GIS) as geo-objects. The study area was clustered into 10 × 10 m cells in order to ease further computations. Mapped trees were then assigned to cells according to their location.

9Trappmann and Stoffel (2013, 2015) have previously demonstrated the reliability of the scar-counting approach to reconstruct spatial patterns of rockfall activity. We therefore employed this method as well, as it requires much less time and effort to estimate rockfall frequency at the level of individual trees from the plot than would conventional dendrogeomorphic approaches. The latter is often time-consuming as it requires an exhaustive sampling (with cross-sections and cores), identification, as well as dating of GD forming after mechanical disturbance by rock impacts; see Trappmann and Stoffel (2013), and Stoffel et al., (2013) for more details. Recent scars were identified according to their appearance, chipped bark, or injured wood; see Trappmann and Stoffel (2015) for details. Wounds which are overgrowing at the time of sampling were identified by the callus pad that seals the injuries from the border toward the center (Stoffel and Perret, 2006). Older, completely healed injuries are more difficult to be detected visually; they were inferred via the occurrence of swelling and blisters on the stem surface. Extremely long, vertical scars or scars with vertical extensions < 3 cm were excluded to avoid misclassification and/or the inclusion of injuries caused by branch breakage or falling neighboring trees (Perret et al., 2006). The DBH distribution of trees is even over the slope (fig. 3), such that one may also expect a comparable distribution of tree ages across the slope and an absence of age-related biases in the results at the slope scale.

Fig. 3 – Spatial distribution and diameters at breast height (DBH, in cm) of trees at the study plot.
Fig. 3 – Distribution spatiale des arbres et de leur diamètre à hauteur de poitrine (DBH, en cm) sur la parcelle étudiée.

Fig. 3 – Spatial distribution and diameters at breast height (DBH, in cm) of trees at the study plot.Fig. 3 – Distribution spatiale des arbres et de leur diamètre à hauteur de poitrine (DBH, en cm) sur la parcelle étudiée.

3.2. Development of age–diameter regression models

10In a second step, linear diameter-age regression models (Rozas, 2003) were built for Ao and Qp, as they are the dominant tree species at the stand scale (fig. 4). A total of 90 undisturbed trees (41 Qp, 49 Ao) with a DBH ≥ 10 cm were cored using a Pressler increment borer. Trees were selected according to five diameter classes, representative at the tree plot scale, and we discriminated between single trees and coppice stands. Samples were analyzed and data processed following standard dendrochronological procedures (Bräker, 2002). In the laboratory, tree rings were counted using a digital LINTAB positioning table connected to a Leica stereomicroscope. Missing rings toward the pith were estimated from ring curvature (Villalba and Veblen, 1997; Bollschweiler et al., 2008). In a final step, we used data from the linear regression models to estimate tree ages of individual trees for which scars were identified and counted on the stem surface and the DBH has been measured. According to the comparability of diameter-age models derived from Ao and Qp, a mixed regression model based on both Acer opalus and Quercus pubescens trees has then been established so as to estimate the age of other tree species.

Fig. 4 – Age–diameter linear models.
Fig. 4 – Modèles linéaires âge–diamètre.

Fig. 4 – Age–diameter linear models.Fig. 4 – Modèles linéaires âge–diamètre.

1. Acer opalus–single tree; 2. Linear regression of Acer opalus–single tree, Age = 1.80*DBH + 14.15, r² = 0.70; 3. Acer opalus–coppice stand; 4. Linear regression of Acer opalus–coppice stand, Age = 2.09*DBH + 15.6, r² = 0.63; 5. Quercus pubescens; 6. Linear regression of Quercus pubescens, Age = 1.59*DBH + 23.9, r² = 0.66; 7. Linear regression for all other species, Age = 1.64*DBH + 20.85, r² = 0.65.
1. Acer opalus–tige unique ; 2. Régression linéaire d’Acer opalus–tige unique, Âge = 1,80 * DBH + 14,15, r² = 0,70 ; 3. Acer opalus–cépée ; 4. Régression linéaire d’Acer opalus–cépée, Âge = 2,09 * DBH + 15,6, r² = 0,63 ; 5. Quercus pubescens ; 6. Régression linéaire de Quercus pubescens Âge = 1,59 * DBH + 23,9, r² = 0,66 ; 7. Régression linéaire pour les autres essences, Âge = 1,64 * DBH + 20,85, r² = 0,65.

3.3. Estimation of recurrence interval of individual rockfall impacts

11Recurrence interval is an old concept that is regularly used in the analysis of all type of hazards, but it was only introduced into dendrogeomorphic studies very lately such as avalanche zoning (Corona et al., 2010; Schläppy et al., 2014) or rockfall studies (Šilhán et al., 2013; Trappmann et al., 2014). Recurrence intervals derived from inventory data consider normally the frequency of actual events, which often contain several rocks that fall simultaneously at a time. In dendrogeomorphic studies, the recurrence intervals are considered in a different way as they represent the average time period between two successive impacts at a specific point. Accordingly, observed recurrence intervals (ObRi) were calculated for each cell C as followed:

          

           [1]

where AC represents the mean age of trees, estimated from age–diameter models, contained in the cell C and ScC represents the sum of the number of scars counted on the stem surface of trees contained in cell C.

3.4. The conditional impact probability

12The conditional impact probability approach (CIP) was first developed by Moya et al. (2010a) and then refined further by Trappmann et al. (2013). It is employed here to estimate likelihood of rockfalls missing tree trunks. The assessment depends both on the characteristics of the forest (i.e. stand density, tree location and DBH) and on the characteristics of the rockfall event (volume of the falling rocks). The CIP is a three-dimensional problem which can be solved in the horizontal plane and reduced to one dimension making some simplifying assumptions (Moya et al., 2010a):

13(i) Falling block is assumed to move through the cell in a downslope direction and is represented as a straight line down the slope. Changes in fall direction due to an impact with the talus surface or trees are assumed to not influence the CIP as it measures the probability of a falling block impacting at least one tree in the cell. Once a block impacts a tree, the value of the CIP does not change if the block subsequently impacts another tree after changing its trajectory.

14(ii) The dendrochronological record of rockfall used to calculate the recurrence intervals is only based on impacts on the tree trunk, but not on its branches. Thus, trees can be represented only by the stem. Trees in the analyzed cell are assumed to have a straight and vertical trunk. These are represented by a circle in the horizontal plane.

15(iii) Any change of the trunk diameter with height and age is small enough – for the period for which rockfall recurrence interval is calculated – to be insignificant for the CIP estimation.

16Based on these assumptions, the CIP concept is based on the idea that each tree is surrounded by a “circle of impact”, i.e. that it covers a range of the slope which determines its probability of being impacted. A falling rock, however, will impact a tree if its trajectory is closer to the stem than half of its diameter (ϕ). This “circle of impact” can be expressed as a circular area around each tree with a diameter defined by the tree’s DBH and the rock diameter (ϕ). The sum of the impact circles of all trees from one cell therefore represents the total length of impact circles (Lic) or the range that is covered by trees (fig. 5A‑B). Accordingly, with a given mean rock diameter and measured DBH of all trees, the CIP, expressed as a fraction of cell length, can be calculated for each analysis cell as:

          

           [2]

where LIC is the cumulative length of the projections of the circles of impact on the downslope side of the cell, and Lplot is the length of the downslope side of the cell (i.e. width of analysis cell; 10 m in this case).

          

           [3]

where Itotal represents the total number of documented rockfall impacts and amean the mean age of trees in the cell. The final return period (Ri) is calculated as the inverse of the frequency F.

Fig. 5 – Geometrical conditions used for the assessment of the conditional impact probability (CIP) adapted from Moya et al. (2010a).
Fig. 5 – Conditions géométriques utilisées pour l’évaluation de la probabilité conditionnelle d’impact (
CIP) adapté de Moya et al. (2010a).

Fig. 5 – Geometrical conditions used for the assessment of the conditional impact probability (CIP) adapted from Moya et al. (2010a).Fig. 5 – Conditions géométriques utilisées pour l’évaluation de la probabilité conditionnelle d’impact (CIP) adapté de Moya et al. (2010a).

A. Computation of the CIP from the geometric analysis of the spatial distribution of trees at the cell scale. B. Computation of the impact circle. 1. Cell boundary; 2. Tree stem; 3. Circle of impact; 4. Projection of the circles of impacts on the downslope boundary of the analysis cell; 5. Rock of a given diameter, noted ϕ; 6. Trajectory of the falling rock; 7. Rockfall impact. L1, L2, Land Lare the width of the projection of the circles of impact on the downslope boundary of the cell analysis. Lplot is the width of the analysis cell.
A. Calcul du CIP à partir d’une analyse géométrique de la distribution spatiale des troncs à l’échelle de la cellule. B. Calcul du cercle d’impact. 1. Limite de la cellule d’analyse ; 2. Tronc ; 3. Cercle d’impact ; 4. Projection des cercles d’impact sur la limite inférieure de la cellule d’analyse ; 5. Pierre d’un diamètre donné, noté ϕ ; 6. Trajectoire de la pierre en chute ; 7. Impact. L1, L2, Let Lcorrespondent à la largeur de la projection des cercles d’impact sur la limite inférieure de la cellule d’analyse. Lplot correspond à la largeur de la cellule d’analyse.

4. Results

4.1. Structure of the forest

17A total of 1004 trees were mapped (mean DBH: 14.6  ±  6.2 cm) at the study plot. A majority belonged to Quercus pubescens Willd. (Qp, n = 441, 43.9%, mean DBH: 17.6 ± 5.1 cm) and Acer opalus Mill. (AO, n = 406, 40.4%, mean DBH: 13.2 ± 6.4 cm) tree species. In addition, eight less abundant species were also mapped, they are summarized in Table 1.

Tab. 1 – Overview on investigated trees: species, diameter at breast height (DBH), age and their scars.
Tab. 1 – Aperçu des arbres étudiés : essences, diamètre à hauteur de poitrine (DBH), âge et de leurs blessures.

Tab. 1 – Overview on investigated trees: species, diameter at breast height (DBH), age and their scars.Tab. 1 – Aperçu des arbres étudiés : essences, diamètre à hauteur de poitrine (DBH), âge et de leurs blessures.

The proportion in percent (%) and the standard deviation are specified between parentheses.
La proportion en pourcentage (%) et l’écart-type sont précisés entre parenthèses.

18The regression models established for Qp and Ao are statistically significant (p < 0.05), with comparable regression slopes (from 1.6 cm.yr-¹ to 2.1 cm.yr-¹), thus enabling derivations of reliable tree ages from tree diameters (fig. 4). According to these models, the mean age of the forest stand, computed from the 1,004 mapped trees, is 45 ± 11.6 years (fig. 6). The oldest tree is 86-year-old whereas the youngest was 23-year-old at the time of field analysis. From a spatial perspective, the mean age of trees did not reveal a clear pattern, with trees aging 44.7 ± 2.7 years in the upper third of the slope (cells A‑D), 47.1 ± 5.2 years in the central third (E‑H) and 46.5 ± 3.5 years in the lower third (I‑L).

19The mean number of trees per cell was 18 ± 6.0 on average (fig. 6), without any clear pattern with regard to stem density (15.6 ± 6.7 trees per cell in the upper part of slope, 19.3 ± 4.9 in the middle part, and 18.6 ± 6.2 in the lower part).

Fig. 6 – Conditional impact probability per cell and spatial distribution of trees.
Fig. 6 – Probabilité conditionnelle d’impact par cellule et distribution spatiale des arbres.

Fig. 6 – Conditional impact probability per cell and spatial distribution of trees.Fig. 6 – Probabilité conditionnelle d’impact par cellule et distribution spatiale des arbres.

4.2. Spatiotemporal patterns of rockfall activity

20Based on the scar-counting approach, 1,516 scars were recorded on the stem surfaces of the 1,004 mapped trees. At the plot scale, the mean number of scars per tree is 1.6 ± 1.8. A total of 331 trees (33%) did not present any visual evidence of past rockfall impacts. From a spatial perspective, the distribution of impacted trees exhibits a strong, decreasing trend as one moves down the slope (fig. 7): the mean number of scars revealed by the scar-counting approach gradually decreases from an average of 2.6 ± 2.5 scars per tree in the top third of the slope to 1.5 ± 1.5 scars per tree in the central segments of the plot to reach values of 1.0 ± 1.0 in the lowest third of the plot. Similarly, the largest absolute number of impacts (> 10 scars) was recorded in the upper half of the plot from A to F (fig. 7), whereas the number of stems without impacts steadily increases from 17% in the top third of the plot to 40% in its lowest third. With respect to lateral spread, Figure 7 shows two preferential rockfall paths from A4 to L4 and from D1 to K1, which is in good agreement with the topographic depressions existing in the field. Several non-wounded trees in cells H3‑L3 and G5‑L5 are located on the interfluves, which are separating the two rockfall couloirs.

21Coupling of the longitudinal gradient of impacts with the random distribution of tree ages results in a clear spatial downward trend of observed recurrence intervals (ObRi) from a mean of 2.0 ± 2.1 years in the top third of the slope (cells A‑D) to 2.1 ± 1.0 years in the central segments of the plot (cells E‑H), before they reach values of 3.5 ± 2.5 years in the lowest third of the plot (cells I‑L).

Fig. 7 – Observed rockfall recurrence interval map and number of scars per tree.
Fig. 7 – Carte des intervalles de récurrence observés des chutes de pierre et nombre de cicatrices par arbre.

Fig. 7 – Observed rockfall recurrence interval map and number of scars per tree.Fig. 7 – Carte des intervalles de récurrence observés des chutes de pierre et nombre de cicatrices par arbre.

22Based on field observations, 30 fallen blocks with non-weathered surfaces and absence of moss or lichen cover have been measured to identify characteristic block sizes involved in rockfall activity (Corona et al., 2017). A median block diameter (ϕ) of 40 cm has been used to calculate the CIP. Based on the diameter (ϕ), DBHs and the spatial disposition of trees, CIPs computed within each cell range between 0.91 in L1 to to 0.28 at A5 (average 0.66). In other words, CIP varies from 28% in A5 to 91% in L1. The spatial pattern of trees in each cell is a key factor that has a greater influence on the CIP value than tree density. Comparison between B5 and C5, (18 and 19 trees and a total DBH of 208 cm and 292 cm, respectively) revealed that trees aligned in parallel to a topographic depression tend to limit the potential interception in B5 (CIP = 0.55) whereas the CIP reaches 0.82 in C5 where trees are distributed along a strip perpendicular to the slope. At the plot scale, CIPs are lower (0.56 ± 0.19) in the upper forest strip, where they are in contact with the cliff, but gradually increase in the middle (0.68 ± 0.12) and lower (0.70 ± 0.11) parts of the plot. This significant downward trend (fig. 6) is susceptible to induce strong variations in the spatial reliability of the reconstruction of recurrence interval based on the scar counting approach.

23The adjustment of the recurrence interval by applying the conditional impact probability concept, introduced to account for rockfalls which are not leaving visible signs of past impacts in tree stems at all, substantially strengthens the spatial downward trend. Major adjustments were made in cells (A5, C2, D1, D2) characterized by low CIPs. At A5 and C2, recurrence intervals decreased from 2‑3 to < 1 year after adjustment. At D1, D2, observed recurrence intervals of 3‑5 and 5‑10 years decreased, after correction, to 1‑1.5 and 2‑3 years, respectively. At the cluster scale, the adjusted recurrence interval markedly increases from 0.9 ± 0.7 yr in the top segments to 1.4 ± 0.7 yr in the central sector, to reach 2.36 ± 1.47 yr in the lower third of the plot (fig. 8). The two preferential rockfall paths coinciding with the topographic depressions described before (A4‑L4, D1‑K1), become more easily recognizable in this approach, especially in the lower third of the slope. Along the path going from cell D1 to cell K1, adjusted recurrence intervals increase from 1.32 yr at D1 to 2.26 yr at K1, with a mean of 1.53 yr. At the path leading from A4 to L4, the adjusted recurrence interval is 5 times higher at L4 (1.5 yr) than at B4 (0.3 yr).

Fig. 8 – Rockfall recurrence interval map, corrected with the conditional impact probability (CIP).
Fig. 8 – Carte des intervalles de récurrence des chutes de pierres, corrigée avec la probabilité conditionnelle d’impact (CIP).

Fig. 8 – Rockfall recurrence interval map, corrected with the conditional impact probability (CIP). Fig. 8 – Carte des intervalles de récurrence des chutes de pierres, corrigée avec la probabilité conditionnelle d’impact (CIP).

5. Discussion

24Based on an exhaustive mapping of 1,004 trees and the systematic counting (Trappmann et al., 2013) of 1,516 visible scars on all tree stems within a 0.6-ha plot, we derived adjusted recurrence intervals from injuries on tree stems using a conditional impact probability approach (Moya et al., 2010a; Trappmann et al., 2014) so as to estimate the number of rocks which occurred unnoticed, without leaving any damage to trees, and which do not therefore appear in our reconstruction. Our study shows a marked downslope decrease in the number of observed scars per stem. This result is consistent with the well-known energy reduction of fallen blocks down the slope (Gsteiger, 1989; Dorren et al., 2005, 2006). The CIP approach also enables assessment of past rockfall activity which did not impact any tree stem along its trajectory. We observed an increase of rockfall recurrence intervals from two impacts per year in the upper part of the slope to less than one impact per decade in the less affected clusters of the lower third of the slope. Using of exhaustively mapped trees for CIP assessment represent a significant improvement with respect the former approaches. Moya et al. (2010a) computed the CIP only for a small (150 m²) plot of the zone studied which was regarded as representative, and did not therefore integrate the spatial variability of CIPs which was revealed by our study (fig. 6). Similarly, in the absence of a precise tree map, Trappmann et al. (2014) quantified CIP at Evolène (Swiss Alps) based on a visual estimation of mean tree DBH in 40 × 40 m clusters, and do not, therefore, account for the spatial distribution of stems, which we demonstrate has a crucial impact on CIP values. Even if the major species at the study site – Acer opalus and Quercus pubescens – have proven to be reliable for rockfall reconstructions (Favillier et al., 2015), and despite the estimation of some uncertainties provided by the improved CIP assessment, the rockfall recurrence intervals computed in this paper still suffer from some limitations, which are related to:

25(i) the scar counting approach used, which has been demonstrated to overestimate rockfall activity due to potential multiple scars left by one single rock on a tree stem (Trappmann et al., 2013, 2014) as well as to rock fragmentation, leading to a higher number but smaller volume of blocks causing multiple impacts on trees (Trappmann et al., 2013).

26(ii) the clustered spatial stem distribution of coppices in clumps, especially in the case of Acer, which in turn might result in an overestimation of frequencies. Indeed, as clumps consist of a dense bundle of stems with relatively small diameters, one single boulder passing through a cluster would likely hit several stems and might thus leave multiple scars (Ciabocco et al., 2009). Yet, this phenomenon clearly also depends on the volume of the block. If the boulder is small, the likelihood for it to pass through the coppice shoots of the same stump will be larger than in the case of a larger stump. This phenomenon is further amplified when boulders bounce higher; so that they cross the coppice shoots at greater height, where the distance between trunks naturally increases (Trappmann et al., 2013; Morel et al., 2015).

27(iii) the species-specific differences in bark structure and thickness, especially for broadleaved species, that weight into the capacity of each tree to be wounded by a rockfall. Indeed, rockfall wounding only occurs if a falling block has sufficient energy to abrade the bark and to mechanically damage the underlying cambium (Stoffel and Bollschweiler, 2008; Schneuwly et al., 2009a, b). At Saint-Paul-de-Varces, Favillier et al. (2015) shown that the bark thickness of Q. pubescens, which grows at twice the rate of A. opalus, acted as a mechanical barrier to damage (Fritts, 1976), thereby buffering low energy rockfalls and avoiding injury of the underlying tissues. Similarly, surfaces exposed to decay as a result of wounding will be most rapidly covered by the centripetal growth of the cambium in species with thicker barks whereas sealing of the wounds can take - depending on scar size, increment rate, tree age, health state of the tree (Bollschweiler et al., 2008; Schneuwly et al., 2009a, b) – up to several decades for thinner-barked species (Fisher, 1981; Sachs, 1991). Stoffel (2005), for instance, could identify 75% of all scars by visual interpretation through the simple inspection of the bark structure of F. sylvatica, whereas only 51% of the injuries remained visible on the stem surface of P. abies. Similarly, in a mixed forest stand in the Austrian Alps, Trappmann and Stoffel (2013) observed that the mean number of scars on the stem surface of F. sylvatica exceeded that of P. abies by a factor of 2.7 and for the same site.

28(iv) Finally, and by contrast to Trappmann et al. (2014) who used particular mean block diameters to account for the lateral variability of rockfalls at Evolène (Swiss Alps), our estimation of the CIP only relies on a unique block diameter. It could thus leads to an (over or) underestimation of conditional impact probabilities (CIPs) along certain fall lines.

6. Conclusions

29On forested slopes, the frequency of recent rockfalls can be determined through the analysis of rockfall wounds which remain visible on the tree surface. Wounding is the most common type of disturbance currently available for the dating of rockfalls at Saint-Paul-de-Varces, where the forest consists of broadleaved species. As such, other types of tree responses to rockfall, such as compression wood formation or traumatic resin ducts, are not present. The scar counting approach provided a spatial pattern of the number of scars per stem, but adjusted recurrence intervals could only be deduced after correction of the frequency of tree injuries by the conditional impact probability, which accounts for the spatial distribution and the diameter of exposed trees. After this correction, a much more pronounced decrease of the rockfall recurrence intervals down the talus slope was obtained, which is consistent with the concave profile of the slope and with the energy absorption of rockfalls through impacts on the soil and on trees. Our results therefore confirm the reliability of broadleaved tree species for the reconstruction rockfall activity. They also reveal the efficiency and effectiveness of our procedure – which can be applied in a relatively quick way and limited financial efforts – for the spatial assessment of rockfall activity on larger surfaces.

30In the future, the uncertainties due to the assumptions made with respect to the scar counting approach, age-diameter linear models and the conditional impact probability should be estimated using accurate wound dating or inventory data. Despite these remaining limitations and possible caveats as outlined above, broadleaved species should be used more widely in future studies, especially on low-altitude slope close to urbanized areas where inventories and historical archives on rockfalls are generally lacking and/or suffering from several shortcomings.

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Annex

Version française abrégée

Dans les massifs montagneux, les chutes de pierre sont un aléa commun. Elles peuvent être à l’origine de pertes économiques et humaines parfois importantes (Hantz et al., 2003). L’aléa chute de blocs est défini comme la probabilité qu’un point sur un versant soit atteint par un bloc, généralement de petit volume, détaché d’une paroi (Varnes, 1984 ; Berger et al., 2002 ; Dorren et al., 2005). La fréquence d’un événement d’une intensité donnée (volume) peut être évaluée par l’analyse statistique d’inventaires de chutes de pierre (Hungr et al., 1999). Cependant, ces inventaires sont rares, souvent lacunaires et hétérogènes tant sur le plan temporel que d’un point de vue spatial (Sass et Oberlechner, 2012). Ceci est particulièrement problématique dans les zones urbaines où le risque lié aux chutes de pierre augmente avec l’urbanisation des versants (Astrade et al., 2007).

Sur les versants forestiers, la dendrogéomorphologie (Stoffel et al., 2005a,b; Stoffel et Corona, 2014) permet de pallier les biais et les lacunes des inventaires. Basée sur l’analyse de la croissance radiale des arbres, de leur morphologie et de leur anatomie, cette méthode a permis de dater les chutes de pierre passées avec une résolution temporelle annuelle à mensuelle (Stoffel et al., 2005a, b) mais également de reconstruire leur fréquence, leur enveloppe spatiale ou leur intensité (Perret et al., 2006). La majorité des études ont été réalisées à haute altitude, sur des résineux, en raison (i) du caractère longévif de ces espèces (ii) à structure anatomique simple permettant (iii) une identification et une datation aisée des perturbations de croissance liées à l’impact (Trappman et Stoffel, 2013 ; Trappmann et al., 2013). Au contraire, les feuillus prédominants à proximité des zones urbanisées, à écorces peu épaisses et à faible pouvoir cicatrisant, donc susceptibles d’enregistrer durablement les impacts passés (Trappman et Stoffel, 2013) n’ont été que très rarement utilisés pour la reconstruction de l’aléa (Moya et al., 2010a, b ; Šilhán et al., 2011 ; Trappmann et Stoffel, 2013).

Dans ce contexte, cet article se propose de tester le potentiel des essences de feuillus pour la reconstruction et la cartographie de la période de retour des chutes de blocs par le couplage (i) d’un dénombrement et d’une cartographie systématique des cicatrices d’impacts, (ii) d’une estimation de l’âge des tiges au moyen d’une courbe allométrique (âge-diamètre) et (iii) d’une probabilité conditionnelle d’impact (Moya et al., 2010a) utilisée pour quantifier le pourcentage de chutes de pierre n’ayant pas laissé de trace visible sur la végétation ligneuse et estimer la qualité de la reconstruction. Cette méthodologie a été employée sur le versant de Saint-Paul-de-Varces dans le Massif du Vercors (Alpes françaises) (fig. 1A) sur une parcelle forestière de 0,6 ha soumise à l’aléa chutes de blocs. Sur cette parcelle, 1 004 feuillus et 1 516 cicatrices d’impacts causées par des chutes de pierre provenant d’un escarpement de calcaire-marneux valanginien (fig. 1B) ont été systématiquement inventoriés et cartographiés. L’analyse de la distribution des cicatrices d’impacts montre une forte décroissance amont-aval du nombre de blessures, avec une moyenne de 2,6 blessures par arbre sur le tiers supérieur du versant et une moyenne de 1,0 blessure par arbre sur le tiers inférieur du versant. Cette observation est confortée par l’augmentation de la part des arbres indemnes, de 17 % sur le tiers supérieur à 40 % sur le tiers inférieur du versant. La récurrence moyenne de l’aléa (ratio entre l’âge de la tige estimé au moyen de la courbe allométrique et le nombre d’impacts, eq. 1) atteint 2 ans dans le tiers supérieur du versant et 3,5 ans dans le tiers inférieur de la parcelle. En prenant en compte la probabilité conditionnelle d’impact (eq. 2) (fig. 5-6, 8), ce gradient est renforcé, les valeurs moyennes de récurrence atteignant 0,9 ans pour le tiers supérieur du versant et de 2,3 ans pour le tiers inférieur. Cette décroissance des chutes de pierre met en évidence l’effet de barrière de la forêt. Elle est également en accord avec le profil longitudinal concave du versant et avec la dissipation importante de l’énergie lors de l’impact du bloc avec le sol ou des tiges (Gsteiger, 1989 ; Dorren et al., 2005, 2006). Sur un plan méthodologique, l’inclusion de la probabilité conditionnelle d’impact, estimée très précisément grâce à la cartographie systématique des arbres sur la parcelle étudiée, améliore la qualité et la fiabilité des analyses dendrogéomorphologiques.

Toutefois, malgré ces précautions, des incertitudes demeurent dans les résultats obtenus. Celles-ci sont d’ordre méthodologique puisqu’il a été démontré qu’en l’absence de prélèvements, le dénombrement visuel des blessures surestime l’activité des chutes de pierre, une pierre en chute pouvant impacter plusieurs arbres, chaque impact étant interprété comme un événement distinct (Trappman et al., 2013). Elles résident également dans la structure du peuplement forestier, plusieurs impacts pouvant être laissés par un même bloc sur des troncs distincts du fait de la proximité des tiges au sein d’une même cépée, par exemple (Ciabocco et al., 2009). Enfin, elles sont liées à la structure anatomique des différents feuillus et notamment à l’épaisseur de leur écorce puisque les essences à écorces fines (érables par exemple) sont plus facilement endommagées et cicatrisent moins vite que les essences à écorces plus épaisse tels que les chênes (Favillier et al., 2015).

En conclusion, cet article démontre la fiabilité de la méthodologie mise en œuvre qui nécessite des investissements humains et techniques limités. Malgré les limites soulignées précédemment, il met en évidence le potentiel des essences de feuillus pour la reconstruction spatio-temporelle de l’activité de l’aléa chute de pierres à proximité des zones périurbaines, où ces essences sont communes, les inventaires rares et/ou lacunaires et le risque important.

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List of illustrations

Title Fig. 1 – Overview of the study site.Fig. 1 – Localisation du site d’étude.
Caption The study site is located in the French Alps (A), on the eastern slopes of the Vercors massif, 20 km south-west of Grenoble. (B) The study site – delimited by a white polygon – is dominated by a ~30-m-high, south-east-facing cliff built of Valanginian limestone. (C) Illustration of injured Acer opalus mill. in the forest stand.Le site d’étude se trouve dans les Alpes françaises (A), sur le versant Est du massif du Vercors, à 20 km au sud-est de Grenoble. (B) Le site d’étude – délimité par un polygone blanc – est surplombé par un escarpement de calcaire valanginien, haut d’une trentaine de mètres et orienté au sud-est. (C) Illustration d’un Acer opalus mill. blessé, dans le massif forestier.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-1.jpg
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Title Fig. 2 – Geomorphic analysis of the study site.Fig. 2 – Analyse géomorphologique du site d’étude.
Caption A. Hillshade map built from a DEM derived from airborne LiDAR data. B. Longitudinal and lateral profiles of the slope under investigation.A. Carte d’ombrage construite à partir d’un MNT issu du traitement de données d’un LiDAR aéroporté. B. Profils longitudinal et latéral du versant étudié.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-2.jpg
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Title Fig. 3 – Spatial distribution and diameters at breast height (DBH, in cm) of trees at the study plot.Fig. 3 – Distribution spatiale des arbres et de leur diamètre à hauteur de poitrine (DBH, en cm) sur la parcelle étudiée.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-3.jpg
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Title Fig. 4 – Age–diameter linear models.Fig. 4 – Modèles linéaires âge–diamètre.
Caption 1. Acer opalus–single tree; 2. Linear regression of Acer opalus–single tree, Age = 1.80*DBH + 14.15, r² = 0.70; 3. Acer opalus–coppice stand; 4. Linear regression of Acer opalus–coppice stand, Age = 2.09*DBH + 15.6, r² = 0.63; 5. Quercus pubescens; 6. Linear regression of Quercus pubescens, Age = 1.59*DBH + 23.9, r² = 0.66; 7. Linear regression for all other species, Age = 1.64*DBH + 20.85, r² = 0.65.1. Acer opalus–tige unique ; 2. Régression linéaire d’Acer opalus–tige unique, Âge = 1,80 * DBH + 14,15, r² = 0,70 ; 3. Acer opalus–cépée ; 4. Régression linéaire d’Acer opalus–cépée, Âge = 2,09 * DBH + 15,6, r² = 0,63 ; 5. Quercus pubescens ; 6. Régression linéaire de Quercus pubescens Âge = 1,59 * DBH + 23,9, r² = 0,66 ; 7. Régression linéaire pour les autres essences, Âge = 1,64 * DBH + 20,85, r² = 0,65.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-4.jpg
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Title Fig. 5 – Geometrical conditions used for the assessment of the conditional impact probability (CIP) adapted from Moya et al. (2010a).Fig. 5 – Conditions géométriques utilisées pour l’évaluation de la probabilité conditionnelle d’impact (CIP) adapté de Moya et al. (2010a).
Caption A. Computation of the CIP from the geometric analysis of the spatial distribution of trees at the cell scale. B. Computation of the impact circle. 1. Cell boundary; 2. Tree stem; 3. Circle of impact; 4. Projection of the circles of impacts on the downslope boundary of the analysis cell; 5. Rock of a given diameter, noted ϕ; 6. Trajectory of the falling rock; 7. Rockfall impact. L1, L2, Land Lare the width of the projection of the circles of impact on the downslope boundary of the cell analysis. Lplot is the width of the analysis cell.A. Calcul du CIP à partir d’une analyse géométrique de la distribution spatiale des troncs à l’échelle de la cellule. B. Calcul du cercle d’impact. 1. Limite de la cellule d’analyse ; 2. Tronc ; 3. Cercle d’impact ; 4. Projection des cercles d’impact sur la limite inférieure de la cellule d’analyse ; 5. Pierre d’un diamètre donné, noté ϕ ; 6. Trajectoire de la pierre en chute ; 7. Impact. L1, L2, Let Lcorrespondent à la largeur de la projection des cercles d’impact sur la limite inférieure de la cellule d’analyse. Lplot correspond à la largeur de la cellule d’analyse.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-8.jpg
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Title Tab. 1 – Overview on investigated trees: species, diameter at breast height (DBH), age and their scars.Tab. 1 – Aperçu des arbres étudiés : essences, diamètre à hauteur de poitrine (DBH), âge et de leurs blessures.
Caption The proportion in percent (%) and the standard deviation are specified between parentheses.La proportion en pourcentage (%) et l’écart-type sont précisés entre parenthèses.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-9.jpg
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Title Fig. 6 – Conditional impact probability per cell and spatial distribution of trees.Fig. 6 – Probabilité conditionnelle d’impact par cellule et distribution spatiale des arbres.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-10.jpg
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Title Fig. 7 – Observed rockfall recurrence interval map and number of scars per tree.Fig. 7 – Carte des intervalles de récurrence observés des chutes de pierre et nombre de cicatrices par arbre.
URL http://geomorphologie.revues.org/docannexe/image/11681/img-11.jpg
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Title Fig. 8 – Rockfall recurrence interval map, corrected with the conditional impact probability (CIP). Fig. 8 – Carte des intervalles de récurrence des chutes de pierres, corrigée avec la probabilité conditionnelle d’impact (CIP).
URL http://geomorphologie.revues.org/docannexe/image/11681/img-12.jpg
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References

Electronic reference

Adrien Favillier, Robin Mainieri, Jérôme Lopez Saez, Frédéric Berger, Markus Stoffel and Christophe Corona, « Dendrogeomorphic assessment of rockfall recurrence intervals at Saint Paul de Varces, Western French Alps », Géomorphologie : relief, processus, environnement [Online], vol. 23 - n° 2 | 2017, Online since 12 June 2017, connection on 21 September 2017. URL : http://geomorphologie.revues.org/11681 ; DOI : 10.4000/geomorphologie.11681

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About the authors

Adrien Favillier

Université Clermont Auvergne, CNRS, GEOLAB – 63000 Clermont-Ferrand, France (adrien.favillier@uca.fr). Tel : +33 4 73 34 68 23.

Robin Mainieri

Université Grenoble Alpes, Irstea, UR EMGR – 2 rue de la Papeterie, BP76, 38402 St‑Martin‑d’Hères, France (robin.mainieri@irstea.fr).

Jérôme Lopez Saez

Université Grenoble Alpes, Irstea, UR EMGR – 2 rue de la Papeterie, BP76, 38402 St‑Martin‑d’Hères, France (jerome.lopez@irstea.fr).

Frédéric Berger

Université Grenoble Alpes, Irstea, UR EMGR – 2 rue de la Papeterie, BP76, 38402 St‑Martin‑d’Hères, France (frederic.berger@irstea.fr).

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Markus Stoffel

Climatic Change and Climate Impacts, Institute for Environmental Sciences, University of Geneva – 66 Boulevard Carl Vogt, 1205 Geneva, Switzerland | Dendrolab.ch, Department of Earth Sciences, University of Geneva – Rue des Maraîchers 13, 1205 Geneva, Switzerland (markus.stoffel@dendrolab.ch).

By this author

Christophe Corona

Université Clermont Auvergne, CNRS, GEOLAB – 63000 Clermont-Ferrand, France (christophe.corona@uca.fr).

By this author

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