Enhanced rockwall retreat and modified rockfall magnitudes/frequencies in deglaciating cirques from a 6-year LiDAR monitoring

Cirque erosion contributes significantly to mountain denudation and is a key element of glaciated mountain topography. Despite long-standing efforts, rates of rockwall retreat and the proportional contributions of low-, midand high magnitude rockfalls have remained poorly constrained. Here, a unique, terrestrial LiDAR-derived rockfall inventory (20112017) of two glaciated cirques in the Hohe Tauern Range, Central European Alps, Austria is analysed. The mean cirque wall retreat rate of 1.9 mm a ranks in the top range of reported values and is mainly driven by enhanced rockfall from the 15 lowermost, freshly deglaciated rockwall sections. Retreat rates are significantly elevated over decades subsequent to glacier downwasting. Elongated cirque morphology and recorded cirque wall retreat rates indicate headward erosion is clearly outpacing lateral erosion, most likely due to the cataclinal backwalls, which are prone to large dip-slope failures. The rockfall magnitude-frequency distribution – the first such distribution derived for deglaciating cirques – follows a distinct negative power law over four orders of magnitude. Magnitude-frequency distributions in glacier-proximal and glacier-distal rockwall 20 sections differ significantly due to an increased occurrence of large rockfalls in recently deglaciated areas. In this paper we show how recent climate warming shapes glacial landforms, controls spatiotemporal rockfall variation in glacial environments and indicates a transient signal with decadal scale exhaustion of rockfall activity immediately following deglaciation crucial for future hazard assessments.

represents a prominent entry point to the high-alpine sediment cascade and is, therefore, key to understanding of high-alpine sediment flux (Hales and Roering, 2005;Krautblatter et al., 2012).
Cirque wall retreat is governed by rock slope failure, which can be statistically characterized by their magnitude-frequency distribution (Dussauge et al., 2003;Bennett et al., 2012). Magnitude-frequency distributions are widely used to derive probabilistic recurrence rates of an event of a given size (Dussauge-Peisser et al., 2002) and are key to understanding process 35 efficiency. Mass movement size-distributions can usually be described by a power law (Hovius et al., 1997). Magnitudefrequency distributions of rockfall reflect rock mass properties and triggering mechanisms, and therefore change over time (Krautblatter and Moore, 2014). They constitute an important tool for understanding headwall geomorphology (Densmore et al., 1997), slope response to climatic and environmental change (Schloegel et al., 2011), sediment transport rates (Korup, 2005) and hazard potential (Krautblatter and Moser, 2009). Elevated rockfall activity from freshly excavated rockwalls, such as 40 investigated here, is of major concern in all high-mountain regions, particularly where human pressure increases (Fischer et al., 2011;Purdie, 2013). Due to continuing climate warming its importance is expected to increase throughout the foreseeable future, making accurate knowledge of magnitude-frequency distributions essential for effective risk assessment throughout mountain regions and safeguarding high-alpine infrastructure (Arenson et al., 2009;Bommer et al., 2010).
High-alpine cirques were first studied in the early 20th century when cirque walls were considered to wear back through 45 sapping at the base of the headwall and inside the Randkluft (gap between glacier and headwall) through intense frost weathering (Richter, 1900;Martone, 1901;Johnson, 1904). Subsequently, determining ground thermal conditions at the headwall base underlined the importance of periglacial weathering for cirque wall retreat (Gardner, 1987;. Additional process like rotational ice-flow (Lewis, 1949;Waldrop, 1964), enhanced quarrying due to subglacial meltwater drainage (Hooke, 1991;Iverson, 1991), strong abrasion under thick ice (Strøm, 1945), and slope collapse (Evans, 1997) are 50 also considered key agents of cirque expansion. Numerous allometric studies have focused on cirque morphometry and found remarkably similar cirque length and width across a number of mountain ranges (see review in Barr and Spagnolo, 2015).
Deviations from the typical circular cirque-planform were mainly encountered where isometric cirque growth is modified by bedrock lithology (Bennett and Glasser, 2009;Evans, 2006). Despite an extensive research focussing on cirques, cirque erosion is still poorly constrained and the number of published erosion rates has remained limited (e.g. Larsen and Mangerud, 1981;55 Brook et al., 2006;Sanders et al., 2013).
Inventories of rockfall and rock slope failures in high-alpine environments cover a wide range of spatial and temporal scales.
Studies typically focus on catchment scale (Cossart et al., 2008;Krautblatter et al., 2012) or orogen scale (Noetzli et al., 2003;Allen et al., 2011) and mid-to high-magnitude events. Methods used to compile inventories are divers and include field mapping and aerial photograph interpretation (Holm et al., 2004;Fischer et al., 2012), information from observer networks 60 , comparisons of historical and recent photographs  and direct observations (Fischer et al., 2006).
Comprehensive quantitative studies that also consider low-magnitude events and thus comprise the entire rockfall spectrum are rare. First approaches date back to the middle 20th century (Rapp, 1960). Over the last two decades, the emergence of https://doi.org/10.5194/esurf-2020-9 Preprint. Discussion started: 9 March 2020 c Author(s) 2020. CC BY 4.0 License. new insights on rockfall magnitude-frequency distributions (Abellán et al., 2011). However, due to limited resolution LiDAR systematically undersamples the smallest magnitudes (rockfall particles < 10 cm) (Lim et al., 2010), which in some geological settings contribute significantly to rock slope mass wasting (Krautblatter et al., 2012).
For glaciated cirques, no rockfall magnitude-frequency distributions have been reported so far. Other steep bedrock 75 environments that have been targeted are coastal cliffs (Williams et al., 2018), small river basins (Bennett et al., 2012), gorge systems (Dussauge-Peisser et al., 2002) and valley flanks (Guzzetti et al., 2003). Rockfall studies in cirque environments either focused on large singular events (Rabatel et al., 2008), on rockfall around infrastructures (Ravanel et al., 2013), or on spatially limited sections of (deglaciating) cirques (Kenner et al., 2011). Spatiotemporal rockfall patterns and rockwall retreat rates for entire cirques over several years have not yet been reported. Despite research efforts reaching back more than 100 years, 80 contemporary cirque wall retreat rates and the efficiency of specific magnitudes have remained unconstrained representing a significant problem for landscape evolution studies and a challenge for rockfall risk management (Brocklehurst and Whipple, 2002;Benn and Evans, 2010;Scherler, 2014).
Here we address this research gap by analysing data from a comprehensive, high-alpine terrestrial LiDAR monitoring campaign (2011)(2012)(2013)(2014)(2015)(2016)(2017), carried out in the rockwalls of two neighbouring, glacierized cirques in the Hohe Tauern Range,  85 Central Alps, Austria (Hartmeyer et al., submitted). We (i) identify significantly increased cirque wall dismantling in the vicinity of the current glacier surface, (ii) observe mean cirque wall retreat rates that rank among the highest values reported yet, (iii) reveal that headward erosion outpaces lateral erosion consistent with present cirque shape, (iv) quantify the first ever magnitude-frequency distribution from a deglaciating cirque, and (v) demonstrate how a wave of instability follows current glacier downwasting. Results are framed in the existing knowledge on magnitude-frequency relationships and considering 90 effects of continuing climatic changes.

Study Area
Two neighbouring glacial cirques at the Kitzsteinhorn, Central European Alps, Austria ( Fig. 1) were chosen as study site. The two north-facing cirques (~ 0.3 km²), referred to as eastern cirque and western cirque, constitute the root zone of the Schmiedingerkees glacier (~ 0.8 km²), which has retreated considerably in recent years. Currently, the receding ice masses are 95 constraint within the cirques, a state that is characteristic for many glaciers in the Eastern European Alps (Fischer et al., 2018). https://doi.org/10.5194/esurf-2020-9 Preprint. Discussion started: 9 March 2020 c Author(s) 2020. CC BY 4.0 License.
Adjacent to the investigated rockwalls, warming-related glacial thinning has led to downwasting rates around 0.5 m per year over the last decade leading to the exposure of fresh cirque wall sections (Hartmeyer et al., submitted). Mean annual air temperature and annual precipitation, both measured at a local weather station situated on the upper part of the Schmiedingerkees glacier (2,940 m a.s.l.), vary around -2 °C and 2,500 mm, respectively. Local borehole temperature 100 monitoring demonstrates the existence of permafrost with temperatures of -1.8 °C (north-facing) and -1.3 °C (west-facing) at zero annual amplitude depth. The Schmiedingerkees glacier and the immediately adjacent summit pyramid of the Kitzsteinhorn constitute one of Austria's 110 most frequented high-alpine tourist destinations with close to one million visitors per year. The Kitzsteinhorn hosts an extensive research site to investigate the consequences of climate change on high-alpine infrastructure and rock stability ('Open-Air-Lab Kitzsteinhorn'). Measurements performed at the Kitzsteinhorn focus on rockfall activity (Keuschnig et al., 2015), subsurface temperature changes (Hartmeyer et al., 2012), geophysical monitoring with ERT (Supper et al., 2014;Keuschnig et al., 2016), rock mass pressure using anchor load plates (Plaesken et al., 2017) and fracture dynamics monitoring 115 with crackmeters (Ewald et al., 2019). All cirque walls developed in rocks of the Bündner schist formation within the Glockner Nappe and belong to the Glockner Facies consisting of calcareous micaschist, prasinite, amphibolite, phyllite, marble and serpentinite (Cornelius and Clar, 1935;Hoeck et al., 1994). Within the monitored rockwalls, NNE-dipping (~ 45 °) calcareous micaschists dominate, and isolated marble and serpentinite belts exist at Magnetkoepfl. Two distinct joint sets (J1 dipping steep to W, J2 medium-steep to SW) 125 oriented approximately orthogonal to the cleavage precondition disintegration into cubic rock fragments (Fig. 2). Numerous open fractures infilled with fine-grained material enable water infiltration and affect near-surface rock slope kinematics and thermal dynamics (Keuschnig et al., 2016;Ewald et al., 2019). Rock at the surface is highly fractured due to a pronounced frost weathering susceptibility. Strong tectonic forcing resulted in highly fractured weakness zones along major faults in all rockwalls. Rock mass classifications according to Romana, 1985 andBieniawski, 1993 suggest highly variable lithological 130 strength ranging from low stability values in weakened zones (r = 34) and highly stable conditions in steep, unweathered sections (r = 98) (Terweh, 2012). https://doi.org/10.5194/esurf-2020-9 Preprint. Discussion started: 9 March 2020 c Author(s) 2020. CC BY 4.0 License.

LiDAR Data Acquisition and Processing
Full details of data acquisition can be found in Hartmeyer et al., submitted. In brief, terrestrial LiDAR acquisition was based 140 on a Riegl LMS-Z620i laserscanner equipped with a calibrated high-resolution digital camera to take referenced colour images.  (Table S2) for a full list of data acquisition parameters). 145 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 1-2 cm. Surface change between point clouds were identified using the M3C2 algorithm of Lague et al., 2013 due to is robust performance on irregular surfaces, with missing data and changes in point density. Rockfall volumes were estimated for each individual rockfall 150 source area as well as morphometric parameters like slope aspect, gradient and elevation above glacier surface.

Rockfall Magnitude-Frequency Calculation
Numerous studies (e.g. Hungr et al., 1999) demonstrated 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, and α and b are constants. To test the power-lawfit of an empirical distribution, earlier studies mainly relied on two regression approaches: cumulative distribution functions (CDF) and probability density functions (PDF) (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 160 of power law exponents (Clauset et al., 2009;Bennett et al., 2009). As will be shown in Sect. 4.4, the magnitude-frequency data used here does not show a rollover at low event sizes and so CDFs were constructed using the R package poweRlaw (Gillespie, 2015).

Rockfall Magnitudes 165
Over the course of the monitoring program, 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 events larger than 0.1 m³ scan resolution has no statistically significant impact (Hartmeyer et al., submitted).
Above this threshold, 374 rockfalls were identified resulting in a total volume of 2,551.4 ± 85.3 m³. To classify rockfall 170 volumes, the recorded rockfalls were grouped into bins of logarithmically increasing size to balance against strongly uneven event volumes (Fig. 3). A dominance of large events is evident as two thirds (67 %) of the rockfall volume fall into the largest size class (100-1,000 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 one tenth (10 %) of the total rockfall volume. 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 180 MKW and MGE). The combined share of the two largest size classes (i.e. rockfalls > 10 m³) ranges between 77 % (MGE) and https://doi.org/10.5194/esurf-2020-9 Preprint. Discussion started: 9 March 2020 c Author(s) 2020. CC BY 4.0 License.
In a companion study, we demonstrated 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 185 walls (Hartmeyer et al., submitted). This is also evident if the volume classification is further differentiated according to distance from glacier ( Fig. 4): At 0-10 vertical meters 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 %. 190

Rockwall Retreat Rates 195
Across the full period of observation and across all rockwalls the mean retreat rate is 1.9 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., submitted). The maximum rate is found at KN (10.4 mm a -1 ), followed by the two rockwalls of the Magnetkoepfl. At MKW retreat rates equal 5.9 mm a -1 , and at MKE 4.2 mm a -1 was recorded. Lowest rates were calculated for KNW (0.7 mm a -1 ) and MGE (0.3 mm a -1 ) (Fig. 5). 200 In proximal areas, mean retreat rates of 7.6 mm a -1 are found and in distal areas rates are almost an order of magnitude lower (0.9 mm a -1 ). By far the highest retreat rates in proximal areas were registered at KN (57.3 mm a -1 ), followed by MKE (17.0 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 micaschists 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 205 volume originates.

210
The highest distal retreat rates are found at MKW (11.1 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.

Rockfall Frequencies
To compare rockfall frequency across rockwalls, rockfall numbers were normalized for rockwall size (Fig. 6). Averaged over 215 all five monitored rockwalls, 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).
The difference between rockfall frequency in proximal areas (n = 3.9) and distal areas (n = 2.5) is considerable yet less pronounced than the (eightfold) 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, where as in distal 230 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 %). https://doi.org/10.5194/esurf-2020-9 Preprint. Discussion started: 9 March 2020 c Author(s) 2020. CC BY 4.0 License.

Magnitude-Frequency Distributions
To further characterize spatiotemporal rockfall variations, the magnitude-frequency distributions were fitted using a power-240 law. The resulting distinct negative power law distribution extends over four 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. 245

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 time scales (Krautblatter et al., 2012). High-magnitude events 250 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 erosion rate estimates have been reported for cirques (Benn and Evans, 2010;Barr and Spagnolo, 2015). 255 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) and the Rocky Mountains, Canada (Sanders et al., 2013) all report (long-term) erosion rates around or below 1 mm a -1 . Recent extensive compilations of rockwall retreat rates from periglacial environments (not restricted to cirques) yield similar results, with rates mostly below 1 mm a -1 (de Haas et al., 2015;Ballantyne, 2018). 260 Direct cross-study comparison 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.
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. Higher erosion rates (> 2 mm a -1 ) were reported for headward cirque erosion in Antarctica (5.8 mm a-1) (Andrews and 265 LeMasurier, 1973), 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), for a footwall location at Mt. Eiger in the Swiss Alps (Mair et al., 2019), for a very humid and tectonically active glaciated basin in the Southern Alps of New Zealand (5.6 mm a -1 ) (Hicks et al., 1990), for selected sections of a deglaciating rocky ridge in the Swiss Alps (6.4 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 270 results were, however, not derived from cirque-scale monitoring but instead reflect short-term, local erosion rates in selected, https://doi.org/10.5194/esurf-2020-9 Preprint. Discussion started: 9 March 2020 c Author(s) 2020. CC BY 4.0 License. highly active rockwalls. Such data is better compared to the range of maximum headward erosion rates established at the Kitzsteinhorn, the maximum of which is 10.4 mm a -1 at KN.
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 275 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., submitted) confirms 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). 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 280 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 (Graemiger 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 time scales (Sanders et al., 2013). 285 Rockwall retreat primarily advances along major joint intersections (Sass, 2005;Moore et al., 2009;Hartmeyer et al., submitted) 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 290 between two ice flows ( Fig. 1) providing intense abrasion.
During the six-year monitoring period headward cirque erosion at KN (10.4 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 295 significant backwall provides clear evidence for intense headward erosion in the past predisposed by the mica-schist cleavage.
The eastern cirqueconfined by backwall KN and sidewalls KNW, MKEand to a lesser degree the western cirque, display clear north-south elongated shapes (Fig. 1). These morphologies 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.

Rockfall Magnitudes and Frequencies
Many earlier studies have deduced magnitude-frequency distributions to statistically describe spatiotemporal rockfall variation 305 in various non-glacial environments (Dussauge-Peisser et al., 2002;Malamud et al., 2004). 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 (Hovius et al., 1997;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 310 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. 315 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. 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 that dates back to the origins of quantitative research on rockwall retreat (Heim, 1932;Jaeckli, 1957). 320 To test the robustness of the analyses and 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 data set. 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 (100-1,000 m³) do not fundamentally alter the regression underlining the robustness of the magnitude-frequency relationship. 325 Ignoring lithological and topographic constraints and extrapolating the power law beyond the upper end of the observed magnitude spectrum (~ 1,000 m³) allows rough estimates of recurrence intervals of high-magnitude events. For rockfalls ≥ 10,000 m³ a return period of around 20 years is indicated while rockfalls ≥ 100,000 m³ recur once in a century. With increasing rockfall magnitude proximal and distal regression lines increasingly diverge. Normalized for rockwall size, rockfalls ≥ 10,000 m³ are almost 20 times more likely in proximal rockwall sections than in distal rockwall sections (40 times more likely for 330 rockfalls > 100,000 m³) (Fig. 7).
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 335 range between 0.1-1 (Dussauge et al., 2003;Bennett et al., 2012). The power law exponent calculated here for distal rockwall https://doi.org/10.5194/esurf-2020-9 Preprint. Discussion started: 9 March 2020 c Author(s) 2020. CC BY 4.0 License. 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 micaschists (Terweh, 2012), and (ii) highly fractured zones with low lithological strength along structural weaknesses that are highly susceptible to rockfall (Hartmeyer et al., submitted;Sass, 2005;Moore et al., 2009). 340 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 345 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 or sampling interval but result from the destabilizing effect of recent ice retreat. 350 Following deglaciation, pronounced thermal stress is induced and an active layer penetrates into the exposed bedrock (Hartmeyer et al., submitted;Draebing and Krautblatter, 2019) 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 ten times higher in proximal areas than in 355 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 peaks at lower magnitudes, potentially contributing to a pattern that has been described as "archway-shaped" distribution in earlier studies (Krautblatter et al., 2012).
The results clearly show how recent climate warming modifies spatiotemporal rockfall occurrence in glacial environments 360 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). Implications for risk assessment are 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 365 popularity worldwide, may have to adapt risk-reduction measures in the near future (Purdie et al., 2015).

Conclusions
A unique six-year rockfall inventory (2011-2017) from the lateral and back-walls of two elongated glaciated cirques in the Hohe Tauern Range, Central European Alps, Austria provides unique insights into rockfall dynamics in deglaciating terrain.
The inventory was derived from detailed terrestrial LiDAR data and represents the most extensive high-resolution compilation 370 of rockfall in cirque walls. Besides significantly increased rockfall occurrence close to the glacier surface due to rockfall preconditioning inside the Randkluft and ice surface lowering (Hartmeyer et al., submitted), the analysis of cirque wall retreat and rockfall magnitude-frequency distributions clearly indicates: -High mean cirque wall retreat of 1.9 mm a -1 ranking in the top of reported values worldwide; -Rockfall activity is boosted in the freshly exposed rock surfaces above the glacier; 375 -Pre-existing structural weaknesses modify spatial patterns of rockfall activity; -For glacier-proximal (0-10 m above glacier surface) areas mean retreat rates are an order of magnitude higher than, and RD developed the idea and designed the study. IH and RD conducted the data acquisition and the data analysis. All authors contributed to the discussion and interpretation of the data. IH drafted the manuscript with significant contributions from MKR 395 and AL.
Competing interests. The authors declare that they have no conflict of interest.