https://doi.org/10.1130/G47092.1

Manuscript received 10 October 2019 Revised manuscript received 7 January 2020 Manuscript accepted 19 February 2020

© 2020 The Authors. Gold Open Access: This paper is published under the terms of the CC-BY license. Published online 27 March 2020

Temporal variations in rockfall and rock-wall retreat rates in a deglaciated valley over the past 11 k.y. Solmaz Mohadjer, Todd A. Ehlers, Matthias Nettesheim, Marco B. Ott, Christoph Glotzbach and Reinhard Drews Department of Geosciences, University of Tübingen, 72074 Tübingen, Germany

ABSTRACT uniform lithology (e.g., Guzzetti et al., 2003). This study addresses the temporal variations in rockfall activity in the 5.2 km2 ­calcareous Many studies compare rock-wall retreat rates for cliffs of the deglaciated Lauterbrunnen Valley, Switzerland. We did this using 19 campaigns localities in different environments (Siewert et al., of repeated terrestrial laser scans (TLS) over 5.2 yr, power-law predicted behavior from 2012; Curry and Morris, 2004; Hinchliffe and extrapolation of the TLS-derived frequency-magnitude relationship, and estimates of long- Ballantyne, 1999). This comparison may identify time-scale (∼11 k.y.) activity based on the volume of preserved postglacial rockfall talus. factors for differing rates, but it provides limited Results from the short-time-scale observations indicate no statistically significant difference information on the long-term behavior of a given between TLS observations averaging over 1.5 versus 5.2 yr. Rock-wall retreat rates in both rock mass in one location. This study comple- cases are 0.03–0.08 mm/yr. In contrast, the power-law predicted rock-wall retreat rates are ments previous work by calculating rock-wall 0.14–0.22 mm/yr, and long-term rates from talus volumes are 0.27–0.38 mm/yr. These results retreat rates over time scales from years to tens suggest (1) short (1.5 yr) TLS inventories of rockfalls provide (within uncertainties) similar of thousands of years for the 5.2 km2 limestone frequency-magnitude relationships as longer (5.2 yr) inventories, thereby suggesting short rock walls of a deglaciated valley. observation periods may be sufficient for hazard characterization from TLS, and (2) higher rock-wall retreat rates over long time scales (Holocene averaged) may reflect debuttressing STUDY AREA and stress relaxation effects after glacial retreat, and/or enhanced rockfall activity under The Lauterbrunnen Valley is a deglaciated periglacial (climatic) conditions. valley with near-vertical walls consisting of Hel- vetic limestone (Fig. 1; Fig. DR4 in the GSA INTRODUCTION to centennial time scales (Dussauge et al., 2003; Data Repository1). Data on historic rockfalls Rockfalls are efficient agents of erosion, con- Rosser et al., 2005; Barlow et al., 2012; Santana show large slope failures since 1750 CE, includ- trolling the development of rock slopes, and they et al., 2012). In contrast, indirect measurements ing the 1889 landslide that released >104 m3 of can pose a threat to settlements and infrastruc- based on volumetric calculation of talus deposits debris (Michel, 1979). Using TLS data, Strun- ture. Rockfalls occur frequently in deglaciated have been used to estimate rock-wall retreat rates den et al. (2015) detected 122 rockfalls in the alpine valleys where rock walls are oversteep- over millennial time scales (Curry and Morris, valley over an 18 month period. These events ened, exposed, and more susceptible to failure 2004; Sass and Krautblatter, 2007; Siewert et al., ranged in volume from 0.06 m3 to 119.34 m3, after glacial retreat. Rock-wall retreat rates under 2012). Alpine rock-wall retreat rates vary be- with those less than 1 m3 being most common present-day conditions and their temporal change tween both methods. Present-day retreat rates and associated with freeze-thaw cycles. Using since deglaciation remain less understood. Here, for alpine environments range from 0.01 mm/yr seismic signals, Dietze et al. (2017) detected 49 we investigated rock-wall retreat rates over dif- to 0.84 mm/yr, while the Holocene retreat rates rockfalls over a 6 month period, 10% of which ferent time scales (∼5 yr to ∼11 k.y.) in the de- range from 0.2 mm/yr to 2.5 mm/yr (Curry and were influenced by freeze-thaw cycles. They glaciated Lauterbrunnen Valley of the Bernese Morris, 2004, and references within). Various inferred a systematic lowering of a rock mass Alps, Switzerland (Fig. 1). An improved under- factors contribute to this discrepancy, including release zone driven by a lowering of the water standing of these rates is motivated by the need joint spacing and orientation, and rockfall trig- table in the rock wall. Other potential triggers, to understand postglacial erosion and the role of gering processes such as paraglacial unloading such as earthquakes and anthropogenic activity rockfalls in the evolution of alpine landscapes. after deglaciation (Hinchcliffe and Ballantyne, (as shown in Mackey and Quigley, 2014), are Rockfall data sets derived from direct mea- 1999; Arsenault and Meigs, 2005) and peri- unlikely to influence rockfalls in this study area. surements (e.g., terrestrial laser scans [TLS] glacial conditions (e.g., enhanced freeze-thaw and photogrammetry) cover time scales from ­activity and permafrost degradation). METHODS hours to years and are often used in model- Although previous studies have reported rock- TLS Data Collection and Processing ing rock-wall retreat rates based on rockfall wall retreat rates, few have provided a complete A long-range terrestrial light detection ­frequency-magnitude distributions over decadal and continuous coverage of large rock walls with and ranging scanner was used to acquire

1GSA Data Repository item 2020174, additional details on methods and results, including rock-wall retreat rate calculations and return period for large rockfall events, Figures DR1–DR4, and Tables DR1–DR3, is available online at http://www.geosociety.org/datarepository/2020/, or on request from [email protected].

CITATION: Mohadjer, S., et al., 2020, Temporal variations in rockfall and rock-wall retreat rates in a deglaciated valley over the past 11 k.y.: Geology, v. 48, p. 594–598, https://doi.org/10.1130/G47092.1

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Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/594/5051223/594.pdf by guest on 01 October 2021 3 A dividing the total rockfall volume (1610.87 m ) 7°55’ E WT1 from the west wall in the 5.2 yr period by its area (3.7 km2). Similarly, the retreat rate for the east Figure 1. Shaded relief 3 N A wall was obtained using 229.65 m of rockfall vol- ’ digital elevation model 2 of Lauterbrunnen Valley, ume and a wall area of 1.5 km . The short-term N Switzerland (digital ele- wall retreat rates for the west (0.08 mm/yr) and E vation model courtesy east walls (0.03 mm/yr) agree with those obtained

46°35 B B WT2 of Swisstopo, https:// over an 18 month period by Strunden et al. (2015). www.swisstopo.admin. N ch/). Black circle marks west location of Lauterbrun- Power-Law Predicted Wall Retreat Rates wall C WT3 nen Village, and the The empirical log-frequency and log-mag- east wall river Weisse Lütschine nitude distributions for the 5.2 yr rockfall data is shown in blue. Boxes set show a rollover and power-law tail (Fig. 3). C represent location of investigated talus cones. A nonlinear least-squares regression and MLE N 0 Talus surfaces are shown were used to determine the frequency-magni- D WT4 in yellow, with boundaries tude relationship. The inferred rollover volumes, marked with dashed lines. based on optimization of the R2 value and the D Red dashed line marks the scarp of the 1889 Kolmogorov-Smirnov statistic, differed for N CE mass-wasting event. the two methods (Fig. DR1). We observed de-

46°N Switzerland E ET1 WT1–4 and ET1 are talus viations from pure power-law behavior and a names. systematic trend in fit parameters for rollover 3 0 0.5 km volumes of 0.29–0.92 m . For these values, the 0 100 MLE of the scaling exponent b ranged from 0.61 N m to 0.72. The power-law fit parameters agree with previous values obtained for a shorter observa- ­three-dimensional (3-D) point clouds from 22 rates over the last 11 k.y. were inferred from tion duration (1.5 yr; Table DR2, Fig. DR2C). scan positions during each campaign. Nineteen the talus volumes using TLS and a digital el- However, the frequency of rockfalls in the 5.2 yr (19) campaigns were conducted over 5.2 yr (Feb- evation model on a 2 m grid (swissALTI3D; data set is lower compared to the 1.5 yr data set ruary 2012 to April 2017). Scans collected from Fig. DR3 and Section DR2). To compensate (Fig. 3). This is particularly evident for rockfalls similar positions at different times were aligned for the density difference between talus bulk smaller than 2 m3. using an iterative closest point algorithm. To pro- and intact bedrock, we used a density correction Using the above parameters, the pow- duce a continuous surface, triangle meshes of factor of 0.77 for limestone (from Krautblat- er-law predicted eroded volume per year is reference scans were computed. Surface mesh- ter et al., 2012; Sass and Wollny, 2001). The (0.70–1.13) × 103 m3, and wall retreat rates es were compared with point clouds to identify density-corrected volume was divided by the are 0.14–0.22 mm/yr. Using observations from rockfalls between successive campaigns. Rock- rock-wall surface area above each talus fan and Strunden et al. (2015), we recalculated the to- fall volumes were obtained from cut-and-fill cal- the talus production time (i.e., time span elapsed tal eroded volume and power-law predicted culations and validated using photos. The details since deglaciation, which was estimated to be wall retreat rates (i.e., 0.62 ± 0.13 × 103 m3 and of our TLS data collection, processing, and error 11 k.y.). This talus production time is based on 0.12 ± 0.03 mm/yr, respectively; Table DR2). evaluation are given in Strunden et al. (2015). radiocarbon (10.39 ± 0.15 ka) and 10Be surface exposure (12.2–10.8 ka) ages of moraines and Long-Time-Scale (11 k.y.) Wall Rock-Wall Retreat Rate Calculations bedrock samples located in the study area and Retreat Rates We used three different approaches to de- the neighboring Hasli valley (Wipf [2001] and The measured talus volumes ranged from termine retreat rates over different time scales. Wirsig et al. [2016], respectively). The long- 2.1 × 106 m3 to 4.3 × 106 m3 (Fig. 1). These are First, the averaged short-term retreat rates were term rates represent minimum estimated rates considered minimum estimates due to possible calculated from the total volume of all rockfalls over the last ∼11 k.y. Uncertainties in this esti- loss of material or incomplete exposure due based on TLS observations collected over 5.2 yr. mate stem from potential incomplete exposure to alluvial infilling in the valley. However, no Second, power-law predicted retreat rates were of talus, and the timing of deglaciation (see the field evidence supports transport of talus out of derived from TLS measurements under the as- Data Repository for an extended discussion). the valley. The long-term averaged wall retreat sumption of a power-law distribution of rock- rate of >0.33 mm/yr was calculated by dividing fall sizes (for justification, see Strunden et al., RESULTS the talus volume estimated for each talus sec- 2015). This was done by calculating nonlin- Rockfall Activity tion by the surface area of the rock wall above ear least-squares regression fits and maximum In total, 316 rockfalls were detected in the 5.2 yr that section (Table DR3). Due to their complex likelihood estimates (MLE). This approach period, 122 of which were identified by Strun- morphology, talus sections WT1 and WT4 were provides long-term extrapolated results, but it den et al. (2015) in the first 18 months Fig. 2( ). excluded from retreat rate calculations. assumes a power-law distribution of rockfalls Rockfall volumes ranged from 0.030 ± 0.004 m3 that remains constant over time and requires to 267.27 ± 4.39 m3 (Table DR1). Small rockfalls DISCUSSION a maximum event size for exponents ≤1, as is (<1 m3) were most common (63%), 21% had vol- Frequency-Magnitude Analysis the case here. We set this limit to the largest umes of 1–3 m3, and 2% were >50 m3. Power-law relationships can be used to esti- historic event (104 m3), which occurred 130 yr mate the return time of large rockfall events and ago (Fig. DR1, Fig. DR2, and Section 1 in the Short-Time-Scale (<5.2 yr) Wall Retreat long-term erosion. For a sample size of >300 Data Repository). For a thorough discussion on Rates rockfalls (this study), many of the issues asso- the cutoff limit, we refer readers to Hergarten Spatially averaged short-term (5.2 yr) wall ciated with producing robust power-law fits are (2012). Third, the minimum rock-wall retreat retreat rates were calculated for the west wall by negligible (Clauset et al., 2009; Strunden et al.,

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0 East Wall B N S Schwarzmönch

1km E6 E5 E7

E8 E11 E10 E9

0 0 1km

Figure 2. Composite terrestrial laser scanning (TLS) point cloud data for (A) west and (B) east valley walls (Lauterbrunnen Valley, Switzerland). Yellow and red circles mark locations of rockfalls from Strunden et al. (2015) and this study, respectively. Boxes represent scan area for each scan position, with scan name shown above them. The rock surface of Schwarzmönch (dashed box) was not analyzed for rockfalls due to the large mean distance to wall from scan position, and steep inclination angle from scanner.

2015). We found that power-law predicted cal- evaluate the effect of observation time on the can reflect sensitivity to observation time scales culations were sensitive to the choice of rollover frequency-magnitude relationships. Power-law and/or different erosional processes at work. For values. Larger rollover values yielded larger val- exponents and extrapolated wall retreat rates example, in glaciated landscapes, glaciers not ues of exponent b and a longer return time for from both data sets agree within error (Fig. 3; only increase erosion rates during glaciation, a 1000 m3 rockfall and smaller values of long- Table DR2C, Fig. DR2D). However, there was a but they can result in a postglacial increase in term erosion (Fig. DR2), demonstrating that a systematic decrease in the frequency of smaller rates that decays over time scales of 101–104 yr rockfall frequency-magnitude relationship does events for the 5.2 yr data set (Fig. 3). Additional- (Stoffel and Huggel, 2017). Below, we discuss not follow a pure power law, and caution must ly, the number of larger events was higher in the potential sources of this observed difference in be exercised when calculating power-law fit pa- 5.2 yr data set (three events over 250 m3), which short- and long-term retreat rates. rameters. To account for this, ranges of values are permitted extrapolation to larger volumes. The First, we found that over the short-term reported here to encompass the variability in the differences may be explained by the stochastic (5.2 yr), small rockfalls (<1 m3) were the most data and range of possible solutions (Table DR2). nature of rockfalls. frequent in the Lauterbrunnen Valley, and those over 100 m3 (total of 4) were uncommon. How- Comparison of 1.5 yr and 5.2 yr Rockfall Comparison of Wall Retreat Rates ever, several large rockfall episodes (e.g., several Data Sets The long-term wall retreat rates were an or- 103 to 105 m3 rockfalls between 1750 and 1947 TLS measurements from two different time der of magnitude higher than the short-term rates CE) have occurred in the past and released large intervals (1.5 yr and 5.2 yr) were compared to (>0.33 vs. 0.03–0.08 mm/yr). This difference volumes of debris, forming talus slopes and de- positing boulders beyond the base of talus cones.

r The short-term wall retreat rates calculated over a 100 5.2 yr exclude such large events, whereas re- ye treat rates calculated over longer time intervals er Figure 3. Cumulative prob- ability plot for negative (11 k.y.) include these events. Second, previous -(0.67 ± 0.07) work has documented that long-term rates are nt sp N(V) =(31.9 ± 0.9) V power-law scaling param-

ve 10 eters obtained in this sensitive to temporal changes in the stability of study (shaded in blue) and fe rock walls. For example, following deglaciation, by Strunden et al. (2015; ro a debuttressing of rock walls occurs from ice re- shaded in green). In this study, shaded areas repre- moval and releases of confining stresses, which N(V)=[20.1–22.3] V -[0.61–0.72] umbe sent the range of possible can lead to increased rockfalls (André, 1997; Bal- 1 fits (within 1σ standard en lantyne, 2002; Curry and Morris, 2004; Sass and ( ) 1.5yeardataset (below rollover) iv deviation) to the data Krautblatter, 2007; Korup et al., 2012; Messen-

at using the maximum likeli- ( ) 5.2yeardataset (below rollover) hood estimates approach zehl et al., 2017). Similarly, recent studies in other and rollover volumes of areas of the Bernese Alps have documented that 3 Cumul 0.1 0.29–0.92 m . paraglacial slope adjustment by rockfalls has oc- 0.1 110100 1000 curred in response to the reduction of ice volume 3 Rockfallvolume(m ) in recent decades (Keusen et al., 2007; Zumbühl

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Downloaded from http://pubs.geoscienceworld.org/gsa/geology/article-pdf/48/6/594/5051223/594.pdf by guest on 01 October 2021 et al., 2008). Since these effects diminish through the German Science Foundation grant EH329/18–1 to Ivy-Ochs, S., Martin, S., Campedel, P., Hippe, K., time, lower short-term compared to long-term Ehlers. The point cloud data and MATLAB codes used Alfimov, V., Vockenhuber, C., Andreotti, E., Ca- rates may reflect progressive relaxation of post- in this study are available upon request. rugati, G., Pasqual, D., Rigo, M., and Viganò, A., 2017, Geomorphology and age of the Marocche glacial stresses release and an increase in rock- REFERENCES CITED di Dro rock avalanches (Trentino, Italy): Quater- wall stability (Hinchliffe and Ballantyne, 1999). 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Hales, T.C., and Roering, J.J., 2007, Climatic con- for monitoring the process of hard rock coastal trols on frost cracking and implications for the cliff erosion: Quarterly Journal of Engineering evolution of bedrock landscapes: Journal of Geo- Geology and Hydrogeology, v. 38, p. 363–375, ACKNOWLEDGMENTS physical Research–Earth Surface, v. 112, no. F2, https://doi​.org/10.1144/1470-9236/05-008. We thank Josy Burke (née Strunden), Sarah Falkowski, F02033, https://doi​.org/10.1029/2006JF000616. Santana, D., Corominas, J., Mavrouli, O., and Garcia- Lorenz Michel, and Michael Kloos for terrestrial laser Hergarten, S., 2012, Topography-based modeling Sellés, D., 2012, Magnitude-frequency relation scan field assistance. We are grateful to Nick Rosser, of large rockfalls and application to hazard as- for rockfall scars using a terrestrial laser scanner: Alex Densmore, and Michael Krautblatter for valuable sessment: Geophysical Research Letters, v. 39, Engineering Geology, v. 145, p. 50–64, https:// discussions in the early phases of this research, and to L13402, https://doi.org/10.1029/2012GL052090​ . doi​.org/10.1016/​j.enggeo.2012.07.001. the residents of Lauterbrunnen Valley for their support. Hinchcliffe, S., and Ballantyne, C.K., 1999, Ta- Sass, O., and Krautblatter, M., 2007, Debris flow– The manuscript benefited from constructive comments lus accumulation and rockwall retreat, Trot- dominated and rockfall-dominated talus slopes: by Stefan Hergarten, Fritz Schlunegger, and one anon- ternish, Isle of Skye, Scotland: Scottish Geo- Genetic models derived from GPR measure- ymous reviewer. We thank Mark Quigley for editorial graphical Journal, v. 115, p. 53–70, https://doi​ ments: Geomorphology, v. 86, p. 176–192, handling. The funding for this study was provided by .org/10.1080/00369229918737057. https://doi.org/10.1016/​ j.geomorph.2006.08.012​ .

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