3.1 Lidar data acquisition and processing

Full details of data acquisition can be found in Hartmeyer et al. (2020a). In brief, terrestrial lidar acquisition was based on a Riegl LMS-Z620i laser scanner equipped with a calibrated high-resolution digital camera to take referenced colour images.

Rockwalls were scanned in reflectorless mode at least once a year between 2011 and 2017 at the end of the ablation period. A total of 56 rockwall scans were carried out with variable mean object distances (140–650 m) depending on the used scan position. Resulting point cloud resolution typically ranges between 0.1 and 0.3 m (see Table S3 of Hartmeyer et al., 2020a, for a full list of data acquisition parameters).

Iterative-closest-point (ICP) procedures (Chen and Medioni, 1992) were applied for point cloud alignment. Areas that have been subject to surface change between surveys were discarded during the process and therefore do not negatively affect the quality of surface matching (Abellán et al., 2010; Abellán et al., 2011), resulting in alignment errors between 1.5 and 3.7 cm. Surface changes between point clouds were identified using the M3C2 algorithm of Lague et al. (2013) due to its robust performance on irregular surfaces, with missing data and changes in point density. For each distance measurement, the algorithm calculates the local confidence interval (at one sigma level), which was added to the alignment error and propagated into the volume error. Full details on rockfall volume computation and error quantification are provided in Hartmeyer et al. (2020a). In addition to rockfall volume and its associated uncertainty, a suite of morphometric parameters including slope aspect, gradient and elevation above glacier surface was determined for each rockfall source area.

3.2 Rockfall magnitude–frequency calculation

Numerous studies (e.g. Hungr et al., 1999) demonstrate that the relationship between rockfall volume and cumulative rockfall frequency can be defined by a power law following Eq. (1):

where f(V) is the cumulative number of rockfalls, V is the rockfall volume, α is the pre-factor, and b is the power-law exponent. To test the power-law fit of an empirical distribution, earlier studies mainly relied on two regression approaches: cumulative distribution functions (CDFs) and probability density functions (PDFs) (Bennett et al., 2012; Strunden et al., 2015). According to Bennett et al. (2012), the PDF is better suited to visualize rollovers, i.e. a decrease in the frequency density for small events. It requires, however, logarithmic binning of rockfall volumes that is rather subjective and has been demonstrated to introduce bias in the calculation of power-law exponents (Bennett et al., 2012; Clauset et al., 2009). As will be shown in Sect. 4.4, the magnitude–frequency data used here do not show a rollover at low event sizes, and so CDFs were constructed using the R package poweRlaw (Gillespie, 2015).

Following earlier analyses of rockfall magnitude–frequency distributions (Barlow et al., 2012; Strunden et al., 2015), the sensitivity of the power-law exponent was tested using a bootstrapping approach (Monte Carlo simulation), in which 20 % of the rockfalls were randomly removed and the dataset resampled 100 000 times to calculate median and 2.5th and 97.5th percentiles.

3.3 Rockwall retreat rate calculation

First, the total rockfall volume registered was divided by the number of observation years to obtain mean annual volume (m³). Second, the volume was divided by the surface area of the investigated rockwall (m²) to derive the (slope-perpendicular) rockwall retreat rate. Rockwall surface area calculations were carried out in CloudCompare: point clouds of rockwalls were first subsampled (thinned) to a homogenous point spacing of 0.5 m in order to prevent a potential bias due to variable resolution within point clouds. The subsampled point cloud was then used to generate a mesh based on a Delaunay triangulation (maximum edge length 3 m), which served as basis for the surface area calculation.

4.1 Rockfall magnitudes

Over the course of the monitoring programme which investigated the same five cirque walls for 6 consecutive years (2011–2017), scan positions and acquisition resolution had to be altered, resulting in differing data resolution between scans. To enable direct comparison of scans of differing resolution, the impact of scan resolution on the number of events detected was constrained. Using a regression analysis, it is shown that for rockfall volumes larger than 0.1 m³ scan resolution has no statistically significant impact (Hartmeyer et al., 2020a).

Above this threshold, 374 rockfalls were identified, resulting in a total volume of 2551.4±136.7 m³. Magnitude–frequency distributions of rockfalls often follow a power-law function (as is also the case here; see Sect. 4.4). To classify rockfall volumes, the recorded events were grouped into bins of logarithmically increasing size to balance against strongly uneven event volumes (Fig. 3). This follows the volumetric classification introduced by Whalley (1974, 1984) (debris falls < 10 m³; boulder falls 10–10² m³; block falls 10²–10⁴ m³), which is commonly used in science and engineering (e.g. Brunetti et al., 2009; Krautblatter et al., 2012; Sellmeier, 2015).

A dominance of large events is evident as two-thirds (67 %) of the rockfall volume fall into the largest size class (100–1000 m³), while the next smaller class (10–100 m³) accounts for approximately one-fourth (23 %), and the two smallest classes (0.1–10 m³) combined constitute only about 1∕10 (10 %) of the total rockfall volume.

Figure 3(a) Absolute rockfall volume (m³ a⁻¹) and (b) relative rockfall volume (%) for all monitored rockwalls. About two-thirds (67 %) of the total rockfall volume fall into the largest size class (100–1000 m³), reflecting the dominance of large events.

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When analysed individually for each rockwall, the size distribution shows significant differences due to the impact of individual large rockfalls: at all walls, most of the rockfall volume is represented by the largest size classes (at KN rockfalls > 100 m³ contribute 88 %, at MKE and KNW contributions equal 74 % and 50 %, respectively, and no rockfalls > 100 m³ occurred at MKW and MGE). The combined share of the two largest size classes (i.e. rockfalls > 10 m³) ranges between 77 % (MGE) and 95 % (KN), whereas the smallest size class (0.1–1 m³) represents only around 2 % of the total volume at KN and at the Magnetkoepfl (MKE, MKW) and about 10 % at MGE and KNW.

In a companion study, we demonstrate significantly increased rockfall in the immediate surroundings of the glacier resulting from antecedent rockfall preparation inside the randkluft and recent glacial downwasting adjacent to the investigated cirque walls (Hartmeyer et al., 2020a). This is also evident if the volume classification is further differentiated according to distance from the glacier (Fig. 4): at 0–10 m above the glacier surface (“proximal areas”), rockfalls larger than 100 m³ constitute 84 % of the total volume, whereas in rockwall sections located > 10 m above the glacier surface (“distal areas”) the contribution of this class drops to just 41 %. Small rockfalls below 1 m³ on the other hand contribute around 1 % to the total rockfall volume in proximal areas, while in distal areas this part increases to 7 %.

Figure 4(a) Absolute rockfall volume (m³ a⁻¹), (b) relative rockfall volume (%) for rockwall sections 0–10 vertical metres above the glacier surface (“proximal”) and for higher (> 10 m) rockwall sections (“distal”). Large events (100–1000 m³ ) dominate rockfall size distributions in proximal areas, while distal areas show a more balanced distribution.

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4.2 Rockwall retreat rates

Across the full 6-year period of observation and across all rockwalls, the total rockfall volume is 2551.4±136.7 m³, which corresponds to a mean retreat rate of 1.86±0.10 mm a⁻¹. In detail, annual rockwall retreat varies considerably between the rockwalls investigated and is highest along highly fractured weakness zones close to the glacier surface (Hartmeyer et al., 2020a). The maximum rate is found at KN (10.32±0.22 mm a⁻¹), followed by the two rockwalls of the Magnetkoepfl. At MKW, the retreat rate equals 5.94±0.38 mm a⁻¹, and at MKE 4.20±0.29 mm a⁻¹ was recorded. Lowest rates were calculated for KNW (0.68±0.07 mm a⁻¹) and MGE (0.35±0.04 mm a⁻¹) (Fig. 5).

Figure 5Rockwall retreat rates (mm a⁻¹) for the entire rockwall (grey), for proximal areas (0–10 m, dark blue) and for distal areas (> 10 m, light blue). The mean rate over the 6-year observation period is just under 2 mm a⁻¹. Rockwall retreat rates in proximal areas (7.6 mm a⁻¹) were almost an order of magnitude higher than in distal areas (0.9 mm a⁻¹).

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In proximal areas, mean retreat rates of 7.56±0.22 mm a⁻¹ are found, and in distal areas rates are almost an order of magnitude lower (0.88±0.08 mm a⁻¹). By far, the highest retreat rates in proximal areas were registered at KN (57.32±0.67 mm a⁻¹), followed by MKE (16.97±1.16 mm a⁻¹). At KN, several large rockfalls were recorded adjacent to the glacier surface along a prominent joint intersection. Following the cleavage direction at MKE, a ledge of highly fractured mica schists runs diagonally through the rockwall. Here, the highest instability occurs especially in the immediate vicinity of the glacier surface from where a major share of the rockfall volume originates.

The highest distal retreat rate is found at MKW (11.14±0.67 mm a⁻¹). This is also the only site where retreat rates in the first 10 m are exceeded by retreat rates in more distal sections due to continuing mass wasting from a rockfall scarp initiated in the 2000s and located about 15 m above the current glacier surface.

4.3 Rockfall frequencies

To compare rockfall frequency across rockwalls, rockfall numbers were normalized for rockwall size (Fig. 6). Averaged over all five monitored rockwalls and the entire 6-year monitoring period, 2.7 rockfalls per 10 000 m² a⁻¹ were registered. Maximum numbers were recorded at KN (n=7.4) followed by MKW (n=6.0), while the lowest numbers were found at MGE (n=1.5).

Figure 6Normalized rockfall numbers (n per 10 000 m² a⁻¹) for all monitored rockwalls. Rockfall frequency decreases exponentially with increasing rockfall size; 80 % of all rockfalls rank in the smallest size class (0.1–1 m³).

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Rockfall frequency follows a power-law decrease with increasing rockfall size. Almost 80 % of all rockfalls fall in the smallest size class (0.1–1 m³), while the next larger size class (1–10 m³) comprises 14 % and the two largest size classes (10–100 m³, 100–1000 m³) 6 % and 1 %, respectively. The frequency pattern is rather similar for all rockwalls, and only the Magnetkoepfl rockwalls (MKE, MKW) show some minor deviations. Here, the smallest size class represents a relatively low share (65 % and 53 %, respectively), whereas the larger size classes account for a comparatively high proportion (see Table S4 of Hartmeyer et al., 2020a, for full details).

The difference between rockfall frequency in proximal areas (n=3.9) and distal areas (n=2.5) is considerable yet less pronounced than the (8-fold) difference between proximal (7.6 mm a⁻¹) and distal (0.9 mm a⁻¹) rockwall retreat rates. Proximal rockfall frequency exceeds distal rockfall frequency for all size classes. The discrepancy between proximal and distal rockfall frequency grows with rockfall size. Rockfalls > 10 m³ constitute 10 % of all proximal rockfalls, whereas in distal areas only around 5 % of all rockfalls exceed 10 m³. Rockfalls > 100 m³ represent around 4 % of all proximal rockfalls (< 1 % in distal areas) and thus occur 8.6 times more often in proximal areas than in distal areas. Low magnitudes represent a smaller share in proximal areas (73 %) and a larger share in distal areas (82 %).

4.4 Magnitude–frequency distributions

To further characterize spatiotemporal rockfall variations, the magnitude–frequency distributions were fitted using a power law. The resulting distinct negative power-law distribution extends over 4 orders of magnitude and tails off towards high magnitudes. Including all events the power-law exponent is b=0.64 (Fig. 7). Rockfall magnitude–frequency distributions for proximal rockfalls yield an exponent b=0.51 and for distal rockfalls the exponent b=0.69. This significant difference between proximal and distal rockfall magnitude–frequency distributions is primarily caused by an increased frequency of large rockfalls in proximal rockwall sections.

Figure 7Magnitude–frequency distribution for all detected rockfalls, proximal rockfalls and distal rockfalls. The power-law exponent (b) determines the slope of the regression line (straight line in log–log space). Proximal rockfalls (b=0.51) are fitted by a flatter regression line than distal rockfalls (b=0.69), pointing to an increased frequency of large rockfalls in the vicinity of the glacier (i.e. in areas more recently exposed by glacier retreat).

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Accounting for the stochastic nature of rockfall processes, the robustness of the power-law fit was estimated by a bootstrapping simulation. Results demonstrated only minimal variations of the power-law exponent b for the entire (${\mathrm{0.64}}_{-\mathrm{0.03}}^{+\mathrm{0.04}}$), proximal (${\mathrm{0.51}}_{-\mathrm{0.05}}^{+\mathrm{0.07}}$) and distal datasets (${\mathrm{0.69}}_{-\mathrm{0.03}}^{+\mathrm{0.04}}$) at a 95 % confidence interval. To selectively examine the sensitivity of the regression to individual rare events, the power-law fits were recalculated after omitting the five largest events (rockfalls > 100 m³) from the dataset. The results show only minor deviations with slightly increased power-law exponents (+0.03) for the magnitude–frequency distribution using the reduced dataset (+0.08 for proximal rockfalls, +0.02 for distal rockfalls). The large rockfalls recorded (100–1000 m³) do not fundamentally alter the regression underlining the robustness of the magnitude–frequency relationships.

Ignoring lithological and topographic constraints and extrapolating the inferred power law beyond the upper end of the observed magnitude spectrum (∼1000 m³) allows theoretical estimates of recurrence intervals of high-magnitude events. For rockfalls ≥1000 m³, a power-law-predicted return period of around 4 years is indicated while rockfalls ≥10 000 m³ (≥100 000 m³) recur approximately once every 25 years (100 years). With increasing rockfall magnitude, proximal and distal regression lines increasingly diverge. Normalized for rockwall size, rockfalls ≥1000 m³ are around 10 times more likely in proximal rockwall sections than in distal rockwall sections and about 15 times (25 times) more likely for rockfalls ≥10 000 m³ (≥100 000 m³) (Fig. 7).

5.1 Cirque erosion

Erosional processes are both highly discontinuous and unsteady over time (Sadler, 1981), particularly in paraglacial environments (Ballantyne, 2002; McColl, 2012). Erosion rates recorded during short observation periods are therefore unlikely to accurately reflect long-term rockwall retreat over geological timescales (Krautblatter et al., 2012). High-magnitude events occur with lower frequency and are usually undersampled, contributing to a systematic underestimation of long-term rockwall retreat (e.g. Strunden et al., 2015). Observations made during periods of elevated geomorphic activity result in an overestimation of long-term rates (e.g. Ballantyne and Benn, 1994). Interpretation of short-term erosion records in a broader landscape evolution context thus requires careful consideration of the respective geomorphological setting.

To date, only few retreat rate estimates have been reported for cirques (see reviews in Benn and Evans, 2010; Sanders et al., 2013; Barr and Spagnolo, 2015). Investigations carried out in cirques in the Sangre de Cristo range, USA (Grout, 1979), Kråkenes, Norway (Larsen and Mangerud, 1981), the Ben Ohau range, New Zealand (Brook et al., 2006), the Annapurna range, India (Heimsath and McGlynn, 2008), and the Canadian Rockies (Sanders et al., 2013), all report (long-term) rockwall retreat rates around or below 1 mm a⁻¹ (Table 1). Higher rates (> 2 mm a⁻¹) were reported for headward cirque retreat in soft volcanic breccia in Antarctica (5.8 mm a⁻¹) (Andrews and LeMasurier, 1973) for selected sections of a deglaciating rocky ridge in the Swiss Alps (6.5 mm a⁻¹) (Kenner et al., 2011) and for cirque wall sections in the French Alps affected by a single, large rockfall event (8.4 mm a⁻¹) (Rabatel et al., 2008). These results were, however, not derived from cirque-scale monitoring but instead reflect short-term, local erosion rates in selected, highly active rockwalls. Such data are better compared to the range of maximum headward erosion rates established at the Kitzsteinhorn, the maximum of which is 10.3 mm a⁻¹ at KN.

Table 1Comparison of published cirque wall retreat rates (extended from Sanders et al., 2013; Barr and Spagnolo, 2015).

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Direct cross-study comparison across various spatiotemporal scales is difficult due to differing study designs and key environmental factors (Barr and Spagnolo, 2015). Still, the mean retreat rate at the Kitzsteinhorn of just under 2 mm a⁻¹ is one of the highest values published worldwide. Recent extensive compilations of mostly long-term rockwall retreat rates from periglacial environments (not restricted to cirques) yield similar results, with rates generally below 1 mm a⁻¹ (de Haas et al., 2015; Ballantyne, 2018). Taking it beyond Earth, Kitzsteinhorn results still are at the higher end of a range of time-span-corrected terrestrial and extraterrestrial rockwall retreat rates as compiled by de Haas et al. (2015; see their Fig. 12 and Table S1). Higher rates were reported for headwalls above rock glaciers in the Swiss Alps (2.5 mm a⁻¹) (Barsch, 1977), the French Alps (2.5 mm a⁻¹) (Francou, 1988) and West Greenland (5 mm a⁻¹) (Humlum, 2000), and for rock slopes subject to intense chemical weathering (2.5–6 mm a⁻¹) (Åkerman, 1983; Dionne and Michaud, 1986).

Long-term cirque evolution is considered to show highest erosion rates during the transition to ice-free conditions, when cirques are occupied by small glaciers only. Cirque growth is thus considered being far from a steady process but meant to happen in spurts during deglacial and interglacial periods (Delmas et al., 2009; Crest et al., 2017). The data analysed here and in a companion study (Hartmeyer et al., 2020a) confirm such patterns and reveals considerably elevated retreat rates in recently deglaciated glacier-proximal areas (7.6 mm a⁻¹), while more distal rockwall sections show retreat rates of less than 1 mm a⁻¹ (Fig. 5). High rates in proximal areas are directly related to glacier downwasting, which is expected to induce pronounced thermal stress, cause rock fatigue through cyclic freeze–thaw action and lead to the first-time formation of a deep active layer in freshly deglaciated terrain (Hartmeyer et al., 2020a).

Despite the intrinsically difficult comparison of geomorphic evidence from vastly different spatiotemporal scales, our findings indicate enhanced cirque growth during deglaciation. Two subsequent process sets potentially underscore the geomorphic significance of deglaciation-related rockfall and the correlation between glacier retreat and cirque wall dismantling. Firstly, initial thermomechanical stresses due to deglaciation-induced rock mass damage condition instabilities that persist far beyond the actual deglaciation (Grämiger et al., 2018); and secondly, the substantial input of fresh rockfall debris to the randkluft and into the sliding glacier base is likely to cause enhanced subglacial erosion and thus drive cirque erosion also over longer timescales (Sanders et al., 2013).

Rockwall retreat primarily advances along major joint intersections (Sass, 2005; Moore et al., 2009; Hartmeyer et al., 2020a), and therefore rockfall activity varies considerably spatially across cirque walls (Fig. 5). The highest rates overall were recorded at KN, the only of the five monitored rockwalls where inclination follows cleavage dip (∼45^∘ N) and enables significant dip-slope failures of large cubic rock fragments (Fig. 2). High rates were also recorded at the Magnetkoepfl (MKW, MKE) where instability in part results from intense glacial strain during past glaciations due to the Magnetkoepfl's location between two ice flows (Fig. 1) providing intense abrasion.

During the 6-year monitoring period headward cirque erosion at KN (10.3 mm a⁻¹ overall, 57.3 mm a⁻¹ in proximal areas) exceeded lateral cirque erosion at KNW/MKE/MKW/MGE (0.9 mm a⁻¹ overall, 2.3 mm a⁻¹ in proximal areas) by an order of magnitude. At the western cirque (sidewalls MKW, MGE), only small remnants of a backwall exist, exhibiting a similar, cataclinal discontinuity setup as KN. While this specific area was not monitored in the present study, the absence of a significant backwall provides clear evidence for intense headward erosion in the past predisposed by the mica-schist cleavage.

The eastern cirque – confined by backwall KN and sidewalls KNW, MKE – and to a lesser degree the western cirque, display clear north-south elongated shapes with long sidewalls (KNW, MGE) (Fig. 8). Length∕width (L∕W) ratios of both cirques (1.2 for western cirque, 1.5 for eastern cirque) exceed most L∕W ratios given in the literature. In an extensive review of 25 different cirque inventories containing over 10 000 cirques from around the world, Barr and Spagnolo (2015) found a mean L∕W ratio of 1.03 and showed that about 70 % of all cirques investigated range between 0.9 and 1.1. Deviations from circularity have mostly been attributed to glaciation history (Barr and Spagnolo, 2013) but geological structure is considered an important factor too. In the Western Alps and in the uplands of North Wales, cirques that cut along geological strike are more elongated than those cutting across strike (Federici and Spagnolo, 2004; Bennett and Glasser, 2009), in the Carpathians the dipping of bedding planes significantly influences cirque shape (Mindrescu and Evans, 2014), and in the French Pyrenees bedrock characteristics are considered key controls of cirque shape in anisotropic schists (Delmas et al., 2015). Cirque morphology and lithology at the Kitzsteinhorn are in line with these findings and indicate that due to highly effective cleavage-driven sapping the headward cirque erosion (north faces) has outpaced lateral cirque erosion (west and east faces) over extended time periods. The cataclinal backwalls thus not only affect short-term rockfall dynamics but also have a substantial effect on long-term erosion patterns that carved today's elongated cirque, which deviates significantly from ideal circularity.

Figure 8Hillshade of the Kitzsteinhorn and the Schmiedingerkees glacier. Length (L) and width (W) of the two cirques indicated (red dotted lines). Both cirques display a clear north–south elongated shape with high L∕W ratios (1.2 for the western cirque, 1.5 for the eastern cirque) indicating effective cleavage-driven headward cirque erosion (north faces) over extended time periods.

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5.2 Rockfall magnitudes and frequencies

Many earlier studies have deduced magnitude–frequency distributions to statistically describe spatiotemporal rockfall variation in various non-glacial environments (Dussauge-Peisser et al., 2002). Here, we present the first rockfall magnitude–frequency distribution for a deglaciating cirque (Fig. 7) that also shows characteristic negative power functions between rockfall number and rockfall volume (Hungr et al., 1999; Stark and Hovius, 2001).

During the monitoring period, about two-thirds of the rockwall retreat resulted from low-frequency rockfalls > 100 m³, while smaller high-frequency events being of minor relevance only (Fig. 3). At low magnitudes, no rollover (i.e. drop-off in rockfall frequency) was registered. Rollovers are more frequent in landslide inventories (Malamud et al., 2004) but have also been reported for rockfall inventories (Strunden et al., 2015). Their existence has been attributed to physical causes (Bennett et al., 2012), more frequently also as indicative of undersampling small failures due to insufficient spatial resolution (Stark and Hovius, 2001). The absence of a rollover in the inventory presented emphasizes consistent data quality and confirms an unbiased identification of rockfalls down to (at least) the cutoff threshold of 0.1 m³.

The contribution of rockfalls smaller than the specified size threshold of 0.1 m³ remains uncharacterized. Extending the power law established to the unspecified space below the 0.1 m³ cutoff threshold demonstrates that the unexamined small-magnitude rockfalls do not provide a significant contribution to the total mass wasting budget (magnitudes 0.001–0.1 m³ contribute around 10 m³ a⁻¹). Rock slope erosion in the two studied cirques is therefore dominated by the upper end of the investigated magnitude spectrum, which provides a valuable contribution to an ongoing debate on geomorphological effectiveness that dates back to the origins of quantitative research on rockwall retreat (Heim, 1932; Jaeckli, 1957).

Large rockfalls are rare in the observational record, yet they are of significant relevance for the shaping of alpine landscapes (Guthrie and Evans, 2007). How observations made over a few months or years relate to landscape evolution over millennia or longer (Paine, 1985) still remains elusive. The straight mathematical extrapolation (Sect. 4.4) indicates that rockfalls ≥10 000 m³ (≥100 000 m³) recur on multi-decadal (centennial) timescales. Data from short observation periods, however, can only provide a partial explanation of episodic process dynamics (Crozier, 1999). Furthermore, event frequency estimates based on short records assume long-term stationary systems (e.g. Klemeš, 1993) – an assumption that is particularly unrealistic given the severity of recent climate change. Similar to hydrological systems, estimating the event probability for rare, large events outside the observed magnitude–frequency spectrum introduces significant timescale issues (Blöschl and Sivapalan, 1995) and should be considered with caution also in slope systems.

Due to the episodic dynamics of rockfall processes, sensitivity estimations of observed magnitude–frequency distributions such as performed in the present study (Sect. 4.4) are of high relevance. Repeated random removal of one-fifth of the events (bootstrapping simulation) as well as the targeted removal of large events (> 100 m³) did not significantly alter the resulting power-law exponents and thus confirms the validity of the differences observed between proximal and distal areas.

Values of the power-law exponent b reported in the literature correlate negatively with lithological strength, as larger events are getting less frequent as slope strength decreases. Smaller exponents are typically observed in stronger bedrock, whereas high values correspond either to slopes of weaker bedrock or to soil-mantled slopes (Bennett et al., 2012). Exponents for landslide inventories (b∼1–1.5) are therefore significantly higher than exponents for rockfall inventories, which typically range between 0.1 and 1 (Dussauge et al., 2003; Bennett et al., 2012). The power-law exponent calculated here for distal rockwall sections (b=0.69) falls in the upper range observed for rockfall distributions and clearly below the range determined for landslides. The high exponent is caused by (i) the rather high bedrock erodibility of the local calcareous mica schists (Terweh, 2012) and (ii) highly fractured zones with low lithological strength along structural weaknesses that are highly susceptible to rockfall (Sass, 2005; Moore et al., 2009; Hartmeyer et al., 2020a).

Beside lithological strength, differences in power-law exponents between different studies may also be related to the temporal data resolution (given here by the survey interval). Longer return periods between surveys increase the probability of superimposition and coalescence of events and result in decreasing failure numbers and increasing failure volumes, and thus lower power-law exponents (Barlow et al., 2012). Recent near-continuous lidar monitoring of cliff erosion highlights how different return periods between surveys affect magnitude–frequency distributions (Williams et al., 2018). While frequent monitoring provides more realistic magnitude–frequency distributions, longer durations between scans increase data precision and are advantageous for quantifying longer-term erosion rates due to reduced accumulative uncertainties (van Veen et al., 2017; Williams et al., 2018).

The significant differences between magnitude–frequency distributions in proximal areas (b=0.51) and distal areas (b=0.69) cannot be related to variations in lithology, sampling interval or stochastic behaviour but result from the destabilizing effect of recent ice retreat. Following deglaciation, pronounced thermal stress is induced and an active layer penetrates into the exposed bedrock (Draebing and Krautblatter, 2019; Hartmeyer et al., 2020a) contributing to an increased rockfall frequency close to the glacier surface. Variations between rockfall magnitude–frequency distributions in (proximal) areas directly affected by deglaciation and (distal) areas unaffected by recent deglaciation become most apparent at the upper end of the magnitude spectrum investigated: the (normalized) frequency of rockfalls > 100 m³ is almost 10 times higher in proximal areas than in distal areas (Fig. 6). The increased occurrence of large rockfalls in the vicinity of the glacier leads to a flatter regression line and thus to a reduced power-law exponent for proximal areas. In distal areas, large rockfalls are of reduced importance and the rockfall volume distribution here shows a less pronounced rise and peaks at lower magnitudes (Fig. 4b), which could theoretically contribute to an “archway-shaped” pattern proposed for hard metamorphic rocks with a single maximum of mid-magnitude rockfalls (Krautblatter et al., 2012).

Substituting space for time, the results indicate how recent climate warming modifies spatiotemporal rockfall occurrence in glacial environments over decades subsequent to glacier downwasting. The patterns obtained are important for rockfall hazard assessments, as they indicate that in rockwalls affected by glacier retreat historical rockfall patterns may no longer be used as indicators for future events (Sass and Oberlechner, 2012; Krautblatter and Moore, 2014). Recurrence intervals of different events are proposed to change with time since deglaciation, which is helpful information for sediment cascade modelling (e.g. Bennett et al., 2014) and hazard assessment more generally. The latter is particularly critical in cirque environments, where the presence of glacially oversteepened rockwalls and low-friction glacier surfaces promote long rockfall runout distances (Schober et al., 2012). Many high-alpine, glacier tourism areas that are enjoying growing popularity worldwide, may have to adapt risk-reduction measures in the near future (Purdie et al., 2015).