Detection of rockfall events was performed with the same approach and parameter settings as in a previous study of the same processes in this study area for a justification and discussion of parameters. The vertical component signal of the central station, “Gate of China”, was screened for seismic events using a short-term average / long-term average (STA / LTA) ratio picker . This algorithm is sensitive to instantaneous rises in the recorded seismic signals, which affect the long-term running average only marginally, while raising the short-term running average severely and thus increasing the ratio of the two at the onset of seismic activity. The STA / LTA picker can be used to define the start (on-threshold STA / LTA ratio) and the end of an event (off-threshold STA / LTA ratio), i.e., to extract discrete events from the continuous stream of seismic data. For this, the hourly raw signal files from both monitoring campaigns were collated into daily traces with a 1 h overlap. These time series were filtered between 10 and 30 Hz, the typical frequency band of rockfalls and rock avalanches , and their signal envelopes (i.e., the square root of the squared Hilbert transform of the signal) were calculated. The STA / LTA picker was run with a short-term window of 0.5 s and a long-term window of 90 s to be sensitive to short pulses in the signals . The on-threshold was set to 5 and the off-threshold was set to 2, a combination that yielded the optimal compromise between valid detection of small events and false alarms. The long-term average value was set constant after the start of an event . Following , events that were longer than 20 s (typically earthquakes) or were shorter than 0.5 s (typically local raindrop impacts) were removed. The 20 s constraint was only applied for the STA / LTA picking step. This means that rockfalls would only by rejected if all of their subsequent impact signals lasted more than 20 s each. Likewise, events with a signal-to-noise ratio (SNR, defined as the ratio of the maximum to mean signal amplitude of a picked event) below 6 were removed as they could not be safely interpreted as target events (see below) and appropriately locating them would have been problematic. Further events were excluded when the time delay with which their signal arrived at the seismic stations was higher than the time a seismic wave would need to travel through the array, which was 1.4 s for the average apparent velocity in this area . The location of rockfalls is only meaningful when the same seismic source (e.g., detachment process or impact) is recorded by the stations. Allowing for larger time windows would indeed cause triggering of different event phases by different stations and consequently at least a smearing of the location estimate. Thus, the STA / LTA results of all other stations for the picked event with a two-sided buffer of 1.4 s were checked for coincidence. Only when an event was detected by at least three seismic stations was the result kept. When two or more events were identified within less than 12 s (the maximum free fall duration from the top of the cliff), only the first one was kept and the others were treated as potentially successive impacts of the rock mass at lower cliff sections. The goal of this restrictive signal processing approach is to effectively remove false alarms in a seismically noisy environment while detecting weak signals caused by small rockfalls. The goal is not to automatically detect the correct event onset and end timing. This information is gathered by manually inspecting the remaining valid signals.

Ten rockfall events in the Lauterbrunnen Valley that were detected by laser scanning and seismic methods had seismic characteristics that are different from those of previously published rockfalls or rock avalanches in less steep terrain, which usually show emergent waveforms with slow rising and falling seismic signal time series . In the Lauterbrunnen Valley, the released rock mass typically experiences a significant free fall phase, followed by a powerful impact either somewhere on the cliff or directly on the talus slope. The impact may result in fragmentation of the initial rock mass and/or mobilisation of detritus on the talus slope. Thus, rockfalls in the study area have a distinct seismic signature in comparison to earthquakes and other mass-wasting processes, such as debris flows or landslides e.g.,. All remaining potential rockfall events were manually checked for distinctiveness from the signals of these other mass-wasting and tectonic events as well as potential anthropogenic signals.

In addition to the waveforms of potential events, their spectral evolution with time was investigated using power spectral density estimates (PSDs, or spectrograms). These were calculated for the event duration plus a two-sided buffer of 30 s using multi-taper correction of the spectra and the method of . The spectra were calculated from the deconvolved and filtered vertical component of the signal (1–90 Hz) at the central station along the cliff base (“Funny Rain”) with time windows of 1.1 and 1.5 s and overlaps of 90 %. Rockfall impacts appear as sharp pulses of seismic energy over a wide frequency band, usually between 5 and 60 Hz . Rock avalanches show an emergent onset dominated by low frequencies and progressively increasing higher-frequency content until the event ends with the prevalence of low frequencies . Earthquakes show the dominance of frequencies below 5 Hz and either two distinct wave-train arrival times followed by an exponentially decreasing tail (coda) or a very low-frequency waveform (teleseismic events). Anthropogenic signals can take a range of forms in this area .

For all manually confirmed rockfall signals the source location was estimated by using the signal migration method . This approach is based on finding the location with the highest joined cross-correlation of signal envelopes from all station pairs with time offsets. These time offsets correspond to the finite travel time of the signal from a potential source along the surface or through bedrock to each seismic station. For this, the average seismic wave velocity was set to 2700 m s-1, which provided the best location accuracy in this study area . The input signals were clipped to their STA / LTA-based start and duration plus a two-sided buffer of 2 s unless manual modification was necessary, e.g., when obviously unrelated seismic signals like raindrop impacts at one station had biased the process or when two consecutive impacts had been included. The clipped signals were filtered with four different initial cut-off frequencies, and the location result with the highest joined cross-correlation value was kept. These initial frequency windows were 5–15, 10–20, 10–30 and 20–40 Hz. When an event could not be located in the area of interest (Fig. ) but showed all characteristics of a valid rockfall event, the frequency windows were adjusted according to the dominant frequency range. The migration operations resulted in grids with joined cross-correlation values for each pixel, which may be interpreted as a probability estimate of the most likely location of the impact that causes the seismic signal. In accordance with the findings of only pixels with cross-correlation values above the quantile 0.97 were kept, as this threshold resulted in the smallest possible location estimate area that still included all 10 control events. The resulting data sets were normalised between 0 and 1 to have a common basis for further analyses.

The setting of the Lauterbrunnen Valley allows for the elimination of some of the trigger mechanisms summarised in Sect. . Volcanic tremors and eruptive activities are very unlikely to influence this region of the Alps, as the nearest active volcano is Vesuvius. Snowmelt-generated water input into the cliff face is regarded as irrelevant because the cliff face is snow free in winter due to the steep gradient. Only the small ledges may support accumulations of snow that could supply a local input of meltwater. Snowmelt may be a significant source of water input in the upper parts of the catchment above the cliff face, but this run-off would already be channelised in the hanging valleys by the time it reaches the cliff. It can thus be neglected as a mechanism significantly affecting material properties outside the hanging valleys. Likewise, snow avalanches are unlikely to influence rockfall activity along the cliff face. Root penetration of trees is considered to be of minimum relevance given the steepness of the cliff; trees only grow on the flat parts of the large ledges in the central upper section and at the southern margin of the instrumented cliff section. Thus, these trigger mechanisms are not considered further in the article, which reduces the analysis to the following mechanisms.

Earthquakes were picked from the signals recorded by the seismic sensors with the STA / LTA approach using a 1 s short-term window, a 90 s long-term window and on- and off-ratios of 4 and 2, respectively. These parameters successfully picked all earthquakes from a 10-day control period at the beginning of the monitoring data set. The protocol was applied to data from the station Gate of China, filtered between 1 and 5 Hz, with a minimum event duration of 3 s. All picked events were checked manually for plausibility. Furthermore, the online portal of the Swiss Seismological Service was queried for any earthquake above Mw1 that occurred within a radius of 20 km around the study area. These values were chosen conservatively based on critical magnitude estimates for landslides and rockfalls in road cuts . The online catalogue contains several of the earthquakes picked by the stations used in this study but may miss local earthquakes that could act as rockfall triggers.

Lag times for precipitation were defined as the time span between the end of a precipitation event with > 0.1 mm h-1 (the smallest increment of the meteorological data set) and the next rockfall. For each of these precipitation events the cumulative precipitation amount was calculated by backward summation in time until the beginning of the precipitation event.

Wind was investigated as a trigger using the meteorological time series data. Wind speed values were selected for the hour during which a rockfall occurred. Since there is no meaningful way to objectively determine a threshold of minimum wind speed that could serve as a trigger, a different approach was chosen. The effectiveness of wind was tested by comparing the wind speed distribution function from hours during which rockfalls occurred with 1001 randomly generated distribution functions for the entire monitoring period. If the wind speed regime during a rockfall is different from random regimes, this would be visible from this comparison. Since wind is assumed to be a regional phenomenon, a point measurement of wind speed at the station in Mürren is assumed to be representative, with an awareness of the drawback that we rely on only one station and that the elevation gradient of several hundred metres may result in a spatially non-consistent action of wind. However, this effect would only be relevant for particularly strong wind episodes.

For the effect of lightning there is no independent record. However, thunder also generates a seismic signal. The frequency spectrum of such a thunder signal is similar to quarry blasts and is very broad (above 5 Hz) with peak frequencies between 6 and 13 Hz. Seismic records can be inverted to determine the location, length and orientation of a lightning channel . In the case of the Lauterbrunnen Valley, 1 h of the seismic record preceding a detected rockfall event was screened for all stations. Lightning was interpreted when the signals showed a sharp blast-like pulse, time offsets between stations corresponding to the speed of sound (about 340 m s-1), a wide frequency spectrum peaking between 5 and 15 Hz and a coincidence with precipitation (assuming there were no dry weather lightning events).

Freeze–thaw and thaw–freeze transitions were defined as switches from negative to positive (and vice versa) air temperatures between two consecutive hours. Constraining the thermal effect within rock is not a straightforward task. Direct measurements require intense instrumentation . Geophysical tomography monitoring from the rock surface is an alternative but also requires extensive work. Heat diffusion models e.g., can deliver temperature estimates at different levels of spatial and temporal resolution and complexity; however, at first order, air or surface temperature is a valuable proxy for describing the freeze–thaw actions close to the surface of rock masses. Temperature cannot be treated as a regionally constant parameter as air temperature drops by 0.6 ∘C for every 100 m rise in elevation, and mountain wind systems and topographic shading effects contribute to further modifications of spatial temperature patterns. To relate air temperature as a first-order proxy to freeze–thaw action, lag times were calculated for both uncorrected temperature data from the Mürren meteorological station and elevation-corrected values based on the DEM and the seismically located rockfall events.

Constraining thermal stress is similarly demanding as evaluating freeze–thaw action. One needs to link the heat influx (through sunlight exposure and/or ambient temperature) to the thermodynamic properties of the rock medium e.g.,. However, by excluding the material properties which mainly control the speed and effectiveness of heat propagation, first-order proxies for thermal stress can be provided by the ambient air temperature time series and its first derivative (temperature change rates) as well as spatially resolved sun exposure models, although more complex models are available e.g.,. To investigate thermal stress, the temperature history of rockfall events was described with linear regression slopes of normalised air temperature (Mürren station data) in time windows of 12, 6 and 3 h before each event occurred. Thermal stress is also linked to the exposure duration of a given section of the cliff to direct sunlight on the diurnal and seasonal timescale. The Lauterbrunnen Valley, with its almost north–south-oriented cliff, may exhibit great spatial and temporal variability in exposure time to direct sunlight. The topography-corrected potential exposure time to direct sunlight of the cliff face was modelled with the regional DEM (extending about 30km × 30 km around the instrumented area) and the model insol . Calculations were performed for 1 and 31 March and 2016, yielding the cumulative daily exposure time for each pixel of the DEM and the lowest sunlit elevation along the cliff for a set of hours (8:00, 8:30, 9:00, 10:00, 00:00, 13:00, 14:00) through the entire month. March was chosen because it yielded the largest variability in sun exposure of all instrumented months according to exploratory model runs with lower spatial and temporal resolutions.

Anthropogenic activity in the valley, such as construction work, helicopter flights and rail and road traffic, was observed throughout the deployment and maintenance campaigns and can easily be detected in the seismic records . Due to the broad range of possible signals generated by anthropogenic activity it is not straightforward to develop automatic routines to analyse the lag times with rockfalls. Thus, the history of each potential rockfall event was investigated manually up to 1 h back in time. Ground vibrations caused by other Earth surface processes were also checked manually by screening 1 h of seismic data before the onset of a rockfall event to identify any signals that could be interpreted as geomorphic activity for examples.

All analyses were performed in the R environment for statistical computing (version 3.3.1) using the packages eseis , sp version 1.2-3, raster , fields , insol and rgl . The dates and times of all events are given with respect to the local time, i.e., UTC minus 2 h. For the 2015 period, this includes 12 days without daylight saving time (the switch was on 29 March), which was ignored here.

Records from 6 April 2015 between 15:19:00 and 15:25:00 show two distinct seismic events (Fig. ). Both events are recorded at all four functioning stations. The first one shows the arrival of two pulses with sharp onsets and a more than 1 min coda. All stations record this pattern in almost the same shape and intensity; amplitudes at station Funny Rain are twice as high as at the other stations. The second event is clearly different: the seismogram from Funny Rain shows a sharp amplitude excursion for less than 2 s, followed by an emergent onset of activity for 30 s. The other seismograms only show the first pulse. When filtered between 1 and 3 Hz (Fig. a insets), it becomes clear that the 1.5 s long signal exhibits arrival time offsets between 70 and 450 ms among the stations. Power spectral density estimates of the vertical component of the Funny Rain record (Fig. b) show that the first event is dominated by frequencies between < 1 and up to 60 Hz, with lower frequencies arriving earlier and lasting longer than higher frequencies (triangular pattern). The second event shows a sharp pulse over the entire frequency range above 5 Hz that drops rapidly to a triangular shape of frequencies below 40 Hz. This second signal was a combination of types A and B, with no pause between the two types.

We interpret the recorded events as two fundamentally different seismic sources. The first one shows all characteristics of an earthquake: separated arrival of P and S waves, minimum time offset among the seismic signals, overall marginal signal amplitude differences, a triangular shape of the PSD and a long-lasting coda. In contrast, the second event is a common example of a rockfall because the initial short pulse, visible at all stations, covers a wide frequency spectrum except for frequencies below about 5 Hz. It is followed by signals of subsequent slope activity only at the station at the base of the cliff, which argues for a very local, weak source.

The rockfall is independent of the preceding earthquake, given the more than 3 min time gap and low intensity of ground movement. The first evidence of the rockfall was a faint signal 1.5 s before the most powerful signal part, which is hard to see in the waveform but clear in the power spectral density estimate (zoomed part of Fig. b). Whether this faint signal represents the detachment of the rock mass or the release of some smaller rocks prior to the large detachment cannot be resolved. The strongest signal, visible at all stations, is interpreted as the actual impact of the rock mass on the cliff face, which leads directly to avalanche-like slope activity for more than 30 s. This last part of the sequence did not give any clear location estimate. The first impact could be located at the northern shoulder of a hanging valley (event 12 in Fig. c). Apparently, downslope topography was not steep enough to support an immediate free fall phase. A likely scenario is that upon the first impact the rock mass became fragmented and tumbled down the valley shoulder where it might have become further fragmented, then experienced a free fall phase and started hitting the talus slope as a rain of small rock fragments lasting for more than 30 s. Thus, the seismic data of this rockfall provide insight into all relevant stages: initiation and detachment, free fall, impact and fragmentation, and continuous slope activity caused by impacting and entrained debris.

A rockfall of type A with subsequent emergence of type B (Fig. ) occurred on 26 October 2014 at 22:08:41 and lasted about 45 s in total. Four phases can be distinguished. The first phase was characterised by two short seismic pulses each lasting less than a second. Phase 2 starts 3.52 s after the first one, with a similar double pulse. The pulses are visible at all stations, although the largest amplitudes occur at station Funny Rain. Predominant frequencies are between 5 and 50 Hz. Phase 3 starts with a sudden onset of seismic activity 3.38 s later and lasts about 5 s. It was also visible at all stations, but amplitudes at Funny Rain are 500 times higher than, for example, at “Basejumper's Mess”. Arising from phase 3, phase 4 exhibits an almost rhythmic appearance of more than 16 pulses in the waveform of station Funny Rain and was not visible at any other seismic station. The pulses are 0.15 to 0.25 s long and separated by pauses of 0.5 to 0.8 s. The amplitudes of the individual pulses rise slowly until they peak at 20:09:03.5 and then fall back into seismic background levels after about 5 s.

Interpreting this case (Fig. ) illustrates the potential of environmental seismology to resolve multiple collisions of detached rock masses and the high degree of detail to describe the individual process kinetics of single rocks moving through the landscape. The described rockfall, event 8 of the data set of , is of type A (during phases 1 and 2) followed by a special case of type B (during phases 3 and 4). Phases 1 and 2 are interpreted as two rock mass impacts along the cliff face at subsequently lower positions (Fig. ). Phase 3 represents the impact on the talus slope mobilising a series of rock fragments. Finally (phase 4), one larger rock fragment starts rolling and jumping down the talus slope towards and past the station Funny Rain. The described event has released 0.258 ± 0.014 m3 from a spot at about 994 m a.s.l., the only detachment area in this section of the cliff visible in the TLS data. The detachment area was just above the seismic station at 888 m a.s.l. and some 20 to 30 m to the north. This implies a TLS-based free fall distance of not more than 106 m (Fig. d). The seismic estimate of the impact was 919 m a.s.l., with the most likely impact coordinates only 52 m away from the seismic station. Converting the time between the first and second impacts of phase 1 (3.52 s) into fall distance yields 61 m. The time offset between the second impact and the onset of phase 2 (3.38 s) represents a similar fall distance of 56 m. Thus, in this case, it was possible to show that the two impacts resulted from one rather than two discrete detachment events. The data also give insight into the mechanism through which impacting rock fragments continue to move downslope (short seismic pulses in Fig. d).

Case event III (Fig. ) is a complex sequence of five discrete pulses, which can be interpreted as a type A event (pulses 1–3), followed by a type B (pulse 4) and another subsequent type A event (pulse 5). All pulses last for less than 2 s except for pulse 4, which emerges 6–7 s after pulse 3 and lasts more than 30 s until it is no longer discernible from the background noise. Pulse 5 intersects with pulse 4. Signal amplitudes for pulses 1, 2, 3 and 5 are high compared to pulse 4 at station Basejumper's Mess, whereas this pattern is exactly reversed at station Funny Rain where pulse 4 dominates. Likewise, with increasing distance to Basejumper's Mess, all signals decline in amplitude and become more conjoined for the stations on top of the cliff. Only at Basejumper's Mess (±0.6 µm s-1) and very faintly at Gate of China (±0.03 µm s-1) is there a signal visible that precedes the entire sequence (pulse 0). The same short-duration pulses are also visible in the power spectral density estimates (Fig. b). Pulse 0 ranges between 50 and 80 Hz at station Basejumper's Mess; all other pulses cover the full frequency range. In contrast, station Funny Rain predominantly exhibits lower frequencies, up to 60 Hz for the short-duration pulses and up to 40 Hz for the longer pulse 4, which shows an evolution similar to that of the event described in case I (Fig. ). Location estimates of the seismic sources were possible for all pulses when adjusting the frequency windows prior to the migration of the signal envelopes to the dominant frequency content of the signals (Fig. c and d) manually based on the spectra of the clipped signals. While estimates for pulses 1–3 overlap, there is a clear distinction to pulses 4 and 5. Pulses 1–3 are located at the central cliff part below the large ledge (1148–1124 m a.s.l.), pulse 4 focuses at the base (922 m a.s.l.) and pulse 5 is just below the rim of the ledge (1275 m a.s.l.). The frequency spectra and signal envelopes used for locating the individual impact pulses are contained in the Supplement.

This last case event (Fig. ) illustrates how seismic methods can shed light on the complexity and interaction of processes. The described rockfall is of type A (multiple impacts). Like the first example it exhibits a faint seismic signal (pulse 0 in Fig. ) about 1 s prior to the first strong impact of rocks recorded by all stations. By combining the information from signal waveforms and power spectral density estimates, a detailed evolutionary scenario can be interpreted.

11:16:24.0 – a weak signal dominated by high-frequency content was caused by the impact below the large ledge in the central part of the monitored cliff area at about 1145 m a.s.l.

The location estimates of all events are vague when focusing on the seismic estimates (Fig. c). In fact, the steep part of the cliff is poorly resolved in the vertical direction by only a few DEM pixels, which leads to considerable shifts in the maximum location probabilities. Hence, this case shows the lower limit of location possibilities for such extreme topography. However, when calculating the free fall distances based on the time offsets between the individual impact times, the agreement is remarkable. Based on the seismic location estimate, the second rock mass impact was located 24 m below the first one compared to a distance of 4.9 m calculated based on gravitational acceleration for 1.0 s. Seismic estimates determine the impact at the base 202 m below the former impact, while gravitational acceleration calculation yields a downslope distance of 220 m after 6.7 s of free fall time.

The three examples show the diversity of how rockfalls may evolve and how environmental seismology can provide detailed insights into this geomorphic process, which is difficult to achieve with other methods in such a holistic way. A posterior mapping approach would have misinterpreted the two potentially linked events from case III (Fig. ) as two discrete rockfalls. Likewise, the seismic approach could resolve multiple releases of rock masses from the same detachment area at different times, which would be amalgamated to one larger rockfall event by other methods. Video imagery would have allowed for event detection, location and possibly also insights into event anatomy given that weather (clouds and fog, rain, snow cover) and daylight conditions were suitable. Rocks did not move into tree-covered areas, and the events were large enough to be resolved, which in turn limits the area that can be surveyed.

The seasonal scale is resolved in this study only with two distinct time periods, late summer to autumn (grading from the highest towards moderate temperatures and from the moistest to the driest conditions) and late winter to spring (grading from the lowest to moderate temperatures and from frozen to liquid water dynamics). The last four rockfalls in 2014 occurred after a temperature excursion below 0 ∘C. The first two periods of enhanced rockfall activity in 2015 were associated with freeze–thaw cycles and rainfall. Accordingly, freeze–thaw-related rockfalls occur only in the late autumn and early spring period. The time lags for both freeze–thaw and thaw–freeze transitions are in agreement with the < 20 h rockfall response times identified by . However, four out of the five rockfalls with a freeze–thaw transition time lag below about half a day have precipitation lag times of less than 1 h, which makes it difficult to argue for temperature as the predominant trigger on this seasonal scale. Thus, even though our approach allows for event and trigger timing at hourly resolution it is not possible in these cases to separate the two triggers.

The meteorologically dominated scale is expressed by the three activity periods in 2015 that coincide with strong shifts in temperature (sometimes below zero degrees) but mostly with precipitation events (Fig. ). Accordingly, the precipitation-related lag times, peaking around 1–2 h (Fig. b), suggest a strong link between rain and rockfall occurrence. Other studies found similarly strong links between rockfall and other mass-wasting process e.g., activity and precipitation. However, the small lag time implies that a temporal resolution of several hours is still insufficient to constrain precipitation as a trigger. Perhaps even the hourly aggregated meteorological data used in this study are not detailed enough.

The meteorological time series contains 108 rainfall events with at least 0.1 mm h-1 of cumulative precipitation (0.2 was the minimum cumulative amount recorded preceding a rockfall in this study). However, this does not mean that every second rainfall event caused a rockfall. In September 2014 and June–July 2015 there were multiple rainfall events without any rockfall. Conversely, the two prominent rockfall episodes in late May and late April were not associated with any rainfall or with an exceptionally strong rainfall event (Fig. ).

Wind speeds during rockfall events do not differ from random distributions. The overall calm conditions (35 % of the events occurred during zero wind speed; speed among all rockfall events is about 4 m s-1) do not render wind a plausible trigger for rockfalls in this study area.

Nested into this meteorological framework, bulk rockfall activity shows a somewhat bimodal diurnal pattern, peaking at 08:00 and 20:00 (Fig. a, grey lines). Arguably, the density estimates of the event distribution come close to sampling a random event distribution in time (i.e., a Poisson process). Thus, one explanation for the diurnal pattern of rockfall occurrence is that it is a completely random process. However, the time lag analysis from above and the discussion of triggers in Sect.  point at a series of underlying mechanisms that influence the likelihood that a rockfall will occur.

Accordingly, when grouping the events based on their lag times to meteorological phenomena, the bulk pattern of the density estimate curve changes (Fig. d). The 16 strongly precipitation-related rockfalls (i.e., events with lag times smaller than 4 h coinciding with the significant drop of the KDE; cf. Fig. ) form a bimodal distribution with modes at 03:00–08:00 and 18:00–22:00, which evidently reflects the overall rainfall pattern on diurnal scales regardless of the season. Subtracting precipitation-related and freeze–thaw-related events from the global data set yields only those events that are not related to weather phenomena, keeping in mind that wind speed during rockfalls is not different from random wind speed and that there were no signals of lightning strikes visible in the seismic data. These 26 weather-insensitive rockfalls can be tentatively assigned to four groups (grey polygons in Fig. d) that in turn correspond to the diurnal temperature cycle (Fig. b). Namely, the group from 00:00–06:00 corresponds to the coldest hours of the day just before daylight when thermal contraction of the rock is highest and causes the highest stresses. The group from 08:00–11:00 lags the strongest positive temperature change rates by 1–3 h. This correspondence reflects the strongest stress increase due to thermal input. In analogy, the group from 13:00–17:00 represents the opposite to the former case, with a negative temperature change rate. The last group from 19:00–23:00 appears to be independent from thermal forcing. Arguably, the number of observations designated to be weather independent is too small to statistically support testing whether the combined diurnal forcing (temperature and temperature change rate adding to an almost flat probability density distribution with four modes in 24 h) is a proper model. However, from a mechanistic point of view it would be misleading to assume that rockfalls are randomly distributed across the day when they show obvious lag time bounds to environmental conditions or first-order physics can explain the stress patterns . Thus, we consider the above interpretation as one of perhaps many further solutions, though it is a plausible one based on the two first-order effects of diurnal thermal forcing.

Hence, from this detailed insight into the relations of individual events to potential meteorological and solar drivers, there appear to be three relevant and independent causes of rockfall in the Lauterbrunnen Valley: (i) insolation and heat diffusion that drive thermal expansion and contraction of the rock (17 of 49 rockfalls), (ii) precipitation (19 of 49 rockfalls) and (iii) freeze–thaw transitions, perhaps combined with precipitation (5 of 49 rockfalls), leaving 8 rockfalls triggered by other mechanisms or with longer lag times to the above triggers.

Earthquakes appear to be irrelevant for rockfall activity in the Lauterbrunnen Valley. Although the lag time of a rockfall to an earthquake is between 1 and 2 h and can be as short as a few minutes, this relationship is spurious and reflects the recurrence time distribution of earthquakes rather than the link to rockfalls (Fig. a). The strongest recorded nearby earthquake (Mw 0.9, < 4×10-3 m s-2 at Gate of China) is hardly able to cause any major ground motion in the study area , as is also reflected by almost 3 days until a rockfall occurred. Interestingly, 9 of the 49 events showed the seismic signature of a helicopter passing 10 to 5 min before a rockfall occurred. However, helicopters cause only small ground accelerations of < 10-3 m s-2, making a direct influence unlikely. The other identified anthropogenic signals prior to rockfall activity (see the Supplement), such as train signals, blasts and further signals that cannot be clearly assigned to a process, also always happened several minutes before a rockfall.