Introduction

Rockfalls, a form of mass movement, can cause major economic risk and endanger human lives worldwide, including in Slovenia and Europe (Petje et al. 2005; Hilker et al. 2009; Jemec Auflič et al. 2017; Vulić et al. 2018; Mikoš 2021). Compared to other types of mass movements, such as deep-seated landslides, rockfalls have not been given the same research priority (Briones-Bitar et al. 2020). This highlights the need for further research in this area to expand our knowledge of this type of mass movement, including analyses of the triggering mechanisms. Such studies can be beneficial for the design of mitigation systems or forecasting systems (Sättele et al. 2016; Carlà et al. 2019). The studies that address rockfall triggering mechanisms range from very detailed studies at the local scale, for which numerous experimental measurements are available (Arosio et al. 2009; Krautblatter and Moser 2009; Abellán et al. 2010; Corona et al. 2017; Williams et al. 2019; Melzner et al. 2020; Jaboyedoff et al. 2021; Auflič et al. 2022), to studies at the regional level, where more general approaches are used to investigate the triggering mechanisms (Melillo et al. 2020; Bajni et al. 2021).

Rockfalls are a type of landslide that varies in size, ranging from individual stones and rocks to catastrophic falls of several million cubic meters (also called bergsturz from its German origin). Small rockfalls usually involve a single stone or a small group of stones that breaks away from the rock face (i.e., falling stones). Rockfall research includes both extreme and large rockfalls with a volume of more than several thousand cubic meters3 (Mikoš et al. 2006; Vulić et al. 2018) as well as small rockfalls with a volume of less than 10–50 m3 (Hungr et al. 1999; Petje et al. 2005; Delonca et al. 2014). According to the Varnes classification, various types of movement can be associated with the phenomenon commonly referred to as rockfall, including rockslides, rock avalanches, boulder slides, rock spreading, or, in some cases, even rock creep (Varnes 1978; Hungr et al. 2014). Rockfall-triggering mechanisms are multifaceted and involve geological, weather-related, dynamic, and hydrological factors (Apostolou et al. 2015; Collins and Stock 2016). Understanding these mechanisms is crucial for risk assessment and the implementation of prevention measures in low mountainous regions and along roads, motorways, and railroads (Budetta 2004; Macciotta et al. 2015). While these processes can occur individually or in clusters, there is generally little dynamic interaction between the moving fragments, which mainly interact with the substrate (Hungr et al. 2014). The detachment of rock fragments can occur due to a variety of triggering mechanisms (Hungr et al. 2014), ranging from weather-related (Delonca et al. 2014; Yu et al. 2022) to earthquake-related (Alvioli et al. 2023; Servou et al. 2023) and even human- or animal-induced (Siddique et al. 2019) mechanisms. In the literature, extreme precipitation events or freeze‒thaw cycles are often cited as important triggers for the occurrence of rockfalls (Hungr et al. 1999; Matsuoka and Sakai 1999; Delonca et al. 2014; D’Amato et al. 2016; Draebing and Krautblatter 2019; Bajni et al. 2021; Birien and Gauthier 2023).

The main objective of this study is to investigate the conditions and mechanisms that trigger small rockfalls under different climatic conditions typical for Slovenia, Europe. More specifically, we focus on (i) exploring the spatial and temporal triggering characteristics of small rockfalls in Slovenia; (ii) analyzing the triggering conditions for small rockfalls considering different meteorological, geological, and morphological factors; and (iii) investigating the triggering mechanisms for small rockfalls, where different triggering scenarios are evaluated. Notably, the collected database mainly includes rockfalls with a volume of less than 10 m3. In summary, this study answers the questions of where and how these small rockfalls usually occur in Slovenia and what the main triggering factors are at the national level. The main novelty of this study is that we combine data mining methods with a scenario-based analysis of triggering conditions and locations for small rockfalls at a regional scale in an area with complex topographic, geological, and climatological features. Therefore, the results of this investigation contribute to a better understanding of the triggering mechanisms for small rockfalls.

Data

Rockfall data

The database used in this study contains 2179 small rockfall events that occurred between December 8, 2020, and December 7, 2021 (Fig. 1). The rockfall database was created by the Slovenian Infrastructure Agency and is the result of regular maintenance of the national road network. Therefore, the database contains information regarding road ID and road section, a short description of the event, including the date, and an indication of the rockfall sizes. In some cases, the short description of the event is very detailed (e.g., removal of 10 stones with diameters of approximately 10 cm), while the majority are more generalized (e.g., removal of stones from the road network). Therefore, the latter description was not used in further steps of the study. Additionally, the database includes the differentiation of rockfalls based on two size categories (above and below 20 cm). The database was linked to the Geographic Information System (GIS) road network database (provided by the Slovenian Infrastructure Agency) using the road section ID to create a spatial dataset that was used in this study. Eighty-eight percent of the entries corresponded to the specific locations where the rockfalls occurred, and 12% indicated the road sections where multiple (unnumbered) rockfalls occurred on the same day. The latter database entries were considered to be one event, which was in the middle of the road section. Preliminary analysis was conducted to investigate whether traffic conditions impact the frequency of rockfalls. Data regarding traffic conditions in 2021 (DRSC 2024) were obtained and compared to the rockfall frequency. We found that there was no significant correlation (p < 0.01) between traffic conditions (i.e., total number of vehicles, number of vehicles above 7 tons, and average annual daily traffic) and rockfall frequency per road section. Hence, we focused only on natural conditions and excluded anthropogenic factors from further consideration.

Fig. 1
figure 1

Location of 2179 rockfalls along a 51,000 km road network and the positions of 283 national meteorological stations

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Meteorological data

Various data sources were combined to investigate the triggering mechanisms and conditions of rockfalls. All meteorological data were taken from the public database of the Slovenian Environmental Agency (ARSO). To characterize the conditions for the occurrence of small rockfalls, the gridded (maps), interpolated average values based on long-term weather observations were integrated for the following meteorological variables: mean annual precipitation (1961–1990, 1 km spatial resolution), 5-min precipitation amount with a 100-year return period (determined based on the statistical analysis of past precipitation events using the Gumbel distribution, 1 km resolution), mean annual number of freeze‒thaw cycles (FTC) (Mikoš et al. (2022), 100 m resolution), average sunshine duration (1991–2020 for summer, autumn, winter, and spring, 1 km resolution), average annual number of days with snow cover (1991–2020, 1 km resolution), average air temperature (1981–2010, 1 km resolution), average wind speed at 10 m above the floor (1995–2001, 1 km resolution), and climatological regions (Kozjek et al. 2017). Notably, these datasets were compiled based on data from inconsistent historical periods, as the availability of some products was limited. However, we argue that most of the datasets used represent long-term average conditions and that the different data periods used have little impact on the results of this study.

For the investigation of the trigger factors, in which several trigger scenarios were evaluated, the following meteorological parameters were taken into account, namely, the maximal daily air temperature at 2 m above the floor ground (°C), minimal daily air temperature at 2 m above the ground (°C), daily amount of precipitation (mm), and daily snow height (cm), from the meteorological station located closest to the location of the small rockfall event (Fig. 1).

Other data sources

When investigating the conditions required for the occurrence of small rockfalls, we also considered several morphological elements, such as the elevation (20 m resolution), the maximum slope gradient within 100 m of the event (calculated based on the 20 m elevation data), the terrain ruggedness index (TRI) calculated with Saga GIS based on the elevation data (Conrad et al. 2015), and the slope aspect (calculated based on the 20 m elevation data). In addition, an engineering geology map was used, which was converted into a rockfall susceptibility map by Mikoš et al. (2022) (100 m resolution). The seismic hazard map of Slovenia (Šket Motnikar et al. 2022) was used as a rough approximation of the earthquake frequency at each location.

Methods

Investigation of the triggering conditions of rockfalls

Two different methods were employed to determine the locations where small rockfalls usually occur in Slovenia. First, 2179 points of the entire Slovenian road network (51,000 km) were randomly selected; this network is referred to as the “non-rockfall” database. The procedure was repeated 10 times. These 2179 points were merged (10 times) with the actual locations of small rockfalls in Slovenia (Fig. 1). In total, we obtained 10 datasets with 4358 points (locations), where half of the locations represent actual events and the other half are random locations where no rockfall was detected in the observed period. For all locations (points), we extracted the meteorological, geological, and morphological characteristics of the datasets described in the “Meteorological data” and “Other data sources” sections. The procedure was repeated 10 times to reduce possible bias in the random generation of the “non-rockfall” locations. Using more random samples (e.g., 100 or 1000) would probably reduce the bias even further. However, as the entire road network is 51,000 km long and 2179 points on the road network were selected each time (i.e., one location every ~ 23 km), a large number of generations means that the same or nearby sections of the road network would be selected multiple times. Therefore, we argue that 10 samples are sufficient to investigate whether the selected data mining methods are able to predict the locations where rockfalls have and have not occurred.

The first approach used to investigate the relative importance of meteorological, geological, and morphological features was based on the generalized boosted regression tree (BRT) model (Elith et al. 2008; Greenwell et al. 2019; Ridgeway 2019). This particular model can be utilized to calculate the relative effects of different parameters on the target variables (by calculating the number of uses of the variables for splitting trees and accounting for model improvements), in our case, whether or not a rockfall has occurred at a particular location. The model has been applied in different research areas for similar purposes (Maček et al. 2018; Zabret et al. 2018; Veronesi and Schillaci 2019; Bezak et al. 2021). The R package “gbm” was employed for the calculations (Greenwell et al. 2019; Ridgeway 2019). The minimum number of trees used was 1500, the minimum number of sets in the terminal node was 10, the number of cross-validation folds was 5, the normal distribution was used as a loss function, and the learning rate was set to 0.05. For all 10 samples with 4358 points, the relative impact of the parameters described in the “Meteorological data” and “Other data sources” sections was assessed.

Orange Data Mining software was used as part of the second approach (Demšar et al. 2013). The 10 compiled datasets (with 4358 points each) were used to test and evaluate the performance of different data mining models in predicting the location of small rockfalls in Slovenia. The models tested included the decision tree, random forest, neural network, and K-nearest neighbors (KNN) models (Demšar et al. 2013). In all cases, the default model settings were used (Demšar et al. 2013), as the main idea of this step was not to adapt and select an optimal data mining model but rather to roughly evaluate whether selected meteorological, geological and morphological input parameters (described in the “Meteorological data” and “Other data sources” sections) can describe the triggering conditions for rockfalls and, in turn, represent important predictors for the locations of small rockfalls. All models were evaluated using a fivefold cross-validation procedure. To evaluate the performance of the tested data mining models, the precision (proportion of true-positive values) and classification accuracy (proportion of correctly classified examples) (Demšar et al. 2013) were applied.

Investigation of the triggering mechanisms of rockfalls

For a detailed understanding of the complex weather-related triggering mechanisms, we focused our analysis on days with an extremely high number of events, which are considered optimal conditions for the occurrence of small rockfalls. The events were spatially clustered, and 1 month of meteorological data, including minimum daily temperature, maximum daily temperature, daily precipitation, and snowpack height, were extracted from the most representative meteorological stations (based on the location of the station and rockfall) for the respective group of events. Nine days with an extreme number of small rockfall events were extracted from the dataset, referring to 7 meteorological phenomena (Table 1). Based on the analysis of weather conditions, weather scenarios associated with the occurrence of multiple small rockfall events were extracted. Finally, to assess the impact of specific weather scenarios on the triggering of small rockfalls in Slovenia, the expected temporal and spatial extents of specific weather conditions were determined based on the analysis of meteorological data from 283 meteorological stations between 2016 and 2020.

Table 1 Weather scenarios triggering the occurrence of small rockfalls in Slovenia
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Results and discussion

Occurrence of rockfalls under local conditions

In 1 year (2021), 2179 small rockfalls were reported along the national roads of Slovenia. Rockfalls with fragments < 20 cm in diameter slightly predominate (56%) over slightly larger rockfalls (> 20 cm in diameter) (44%). In general, the highest density of small rockfalls was observed in the northwestern, alpine part of the country (Fig. 2A). This applies in particular to rockfalls with a diameter of greater than 20 cm (Fig. 2A, red), while small rockfalls were concentrated in the prealpine region (Fig. 2A, blue). Observing the climate zones, most of the small rockfalls during the study period were located in the alpine, subalpine, and continental climate zones (Kozjek et al. 2017). Most rockfalls were recorded in February 2021 (435 database entries), followed by April (285), March (212), January (211), and May (207). In June, July, August, September, and December, there were between 100 and 200 small rockfalls, while in October and November, there were fewer than 100 events (Fig. 2B). In addition, the largest absolute number of small rockfalls was recorded on February 4 (78 database entries), followed by February 18 and 19, with 62 and 48 small rockfalls, respectively. The peaks in February and April are due to small rockfalls, while larger rockfalls occur evenly throughout the year (Fig. 2B, red, blue). We calculated the Pearson correlation coefficient between the number of rockfalls and monthly precipitation for several meteorological stations in different parts of the country. In most cases, the calculated Pearson correlation coefficient was less than 0.1, which can be described as a negligible correlation (Schober and Schwarte 2018). For example, the highest monthly precipitation was measured in May, and the lowest was measured in March, while approximately the same number of small rockfall events was recorded in the database in both months.

Fig. 2
figure 2

Spatial and temporal characteristics of small rockfalls. A Spatial distribution of small rockfalls according to the size of the deposited material. B Temporal distribution of small rockfalls by the size of the deposited material. Blue, < 20 cm rockfall size; red, > 20 cm rockfall size; gray, total monthly number of small rockfalls

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Most of the small rockfalls recorded in the database occurred between 200 and 600 m above sea level (Fig. 3A). Notably, the average altitude of Slovenia is 560 m a.s.l. with a standard deviation of 370 m, and the average altitude of the national road network is 470 m a.s.l. with a standard deviation of 270 m. This shows that only a limited number of rockfalls were detected at high elevations (Fig. 3A). The majority of rockfalls occurred on slopes facing southwest (Fig. 3B). For most rockfalls, the maximum slope inclination within a radius of 100 m was approximately 25–35° (Fig. 3C). The average slope inclination in Slovenia is approximately 17° with a standard deviation of approximately 14°, which means that most of the small rockfalls in the database occurred on above-average slopes (Fig. 3C). The engineering geological units most prone to the occurrence of small rockfalls, particularly small fragments, include limestones and dolomites, limestones with other rocks, dolomites and flysch, and other rock EG units. For larger fragments, the most prone EG units are limestones and dolomites, flysch with other rocks, and dolomites (considering the extent of the particular EG unit in Slovenia) (Fig. 3D).

Fig. 3
figure 3

Geological and geomorphological features of 2179 small rockfalls. A Relationship between the number of small rockfalls and elevation. B Relationship between the number of small rockfalls and slope aspect. C Relationship between the number of small rockfalls and the slope. D Number of small rockfalls by geological engineering unit (for the legend, see supplementary material, Table S1). Blue, rock fragments smaller than 20 cm; red, rock fragments larger than 20 cm; gray, all

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We analyzed the weather conditions on the day of each event at the nearest meteorological station to the location of documented rockfall occurrences. A total of 78% of all events occurred on dry days (0 mm/day) or days with low precipitation (0.1–10 mm/day) (51% and 27%, respectively) (Fig. 4A). Additionally, 69% of all events were related to low antecedent cumulative precipitation (0.1–20 mm) or no antecedent cumulative precipitation (40% and 29%, respectively) (Fig. 4B).

Fig. 4
figure 4

Climatological features of small rockfalls. A Daily precipitation on the day of events. B Three-day cumulative antecedent precipitation. C Minimal daily temperature on the day of the event. D Daily temperature difference on the day of the event

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A total of 21% of all events occurred in snow, while 4% of those occurred on days of melting snow. Three percent of all events occurred when the minimal daily temperature was < 0 °C (freezing days). Twenty-two percent of all events occurred when the daily temperature oscillated around 0 °C and 24% of the events occurred on freezing days (Fig. 4C). On average, the daily temperature difference was 8 °C (Fig. 4D). Six percent of all events occurred on days when the daily precipitation was > 0 and the minimum daily temperature was < 0 °C (rainy and freezing days, respectively). Twelve percent of all events were related to a 3-day cumulative precipitation > 0 and a minimum daily temperature < 0 °C (3-day antecedent cumulative precipitation and freezing days, respectively).

We also investigated the possible connection between rockfalls and earthquake locations. During the period studied, the Slovenian Environment Agency reported 26 earthquakes with magnitudes greater than 2 on the Richter scale (i.e., M > 2), with the strongest earthquake occurring at 2.9 (Fig. 5). There is no indication that earthquakes would increase the number of reported rockfalls on the day of an earthquake or on the three following days (Fig. 5C). The average distance of 80 km between rockfalls and epicenters and the large spatial dispersion of rockfalls do not indicate that the epicenters of earthquakes are hotspots for small rockfalls (Fig. 5A). Furthermore, there is no correlation between earthquake magnitude and the total number of rockfalls reported in the 3 days following an earthquake (Fig. 5D). This can be attributed to the relatively low magnitudes of earthquakes in Slovenia in 2021, which did not reach the minimum magnitude of M = 4.0 suggested by Keefer (1984) to trigger landslides.

Fig. 5
figure 5

Relationships between small rockfalls and earthquakes. A and B Relationships between small rockfalls and earthquakes. C Considers the conditions several days after the earthquake. D Relationship between earthquake magnitude and the number of small rockfalls

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In addition, we evaluated the trigger conditions for rockfalls using the methodology described in the “Investigation of the triggering conditions of rockfalls” section. For the 10 samples of 4358 sites considered (i.e., 2179 rockfalls and 2179 non-rockfalls), the relative importance of the following variables, i.e., the mean annual precipitation, terrain ruggedness index (TRI), freeze‒thaw cycle (FTC) map, maximum slope at a radius of 100 m, sun duration in winter, mean annual air temperature, and seismic hazard map, was found to exceed 3% in at least one of the 10 cases. The BRT model showed that in all 10 cases, the mean annual precipitation (with a relative importance between 37 and 48%) was the most influential parameter, followed by the TRI (between 16 and 23%), FTC (between 10 and 16%), and maximum slope (between 7 and 12%). The other parameters mentioned had a lower relative influence on the rockfall locations. In addition, the other studied parameters described in the “Meteorological data” and “Other data sources” sections (i.e., aspect; sunshine duration in spring, summer, and autumn; windspeed; rockfall susceptibility map determined based on the engineering geological map; elevation; extreme rain; and annual number of days with snow) had a relative importance of less than 3%. These results show that in Slovenia, small rockfalls generally occur in places with higher annual precipitation and steep slopes. However, the triggering factors are complex mechanisms responsible for the occurrence of small rockfalls (“Triggering factors of rockfall occurrence” section).

Using the methodology described in the “Investigation of the triggering conditions of rockfalls” section, we also tested how well the selected data mining models can predict the locations of small rockfalls in Slovenia considering different meteorological, geological, and morphological input parameters. Both the precision and classification accuracy were above 80% in all 10 cases tested. Among the tested data mining techniques, the best performance (in terms of precision and classification accuracy) was generally observed when using the random forest method; the performance criteria exceeded 90% for both selected models. This means that the combined percentage of true-positive (the actual location of a small rockfall was correctly predicted) and true-negative (the actual location without rockfall was correctly predicted) locations was greater than 90%. Via random forest, this was the case for all 10 samples tested. On the other hand, less than 10% of the locations were indicated as either false positives (the actual location of the rockfall was not correctly predicted) or false negatives (the model predicted rockfall at the location of the non-rockfall). The proportions of false positives and false negatives were approximately equal. This means that the selected meteorological, geological, and morphological parameters can relatively successfully predict the locations of small rockfalls in Slovenia after the analysis is performed.

The main triggering mechanisms identified by the BRT model, such as rainfall or freeze‒thaw cycles, are relatively similar to those identified in other studies (Hungr et al. 1999; Matsuoka and Sakai 1999; D’Amato et al. 2016; Birien and Gauthier 2023). This suggests that more rockfalls generally occur in locations with greater rainfall or larger variations in the air temperature (i.e., freeze‒thaw cycles). However, the exact triggering conditions responsible for the initiation of specific rockfalls cannot be determined based solely on the analysis conducted within the scope of this section. Therefore, additional investigations were carried out in the “Triggering factors of rockfall occurrence” section according to the methodology described in the “Investigation of the triggering mechanisms of rockfalls” section to further analyze the triggering mechanisms for small rockfalls in Slovenia.

Triggering factors of rockfall occurrence

A preliminary analysis of the meteorological parameters (see “Meteorological data”) revealed no direct, statistically significant correlations with the occurrence of small rockfalls on the day of the event. This indicates the complexity of the relationship between small rockfalls and weather conditions. Peaks in the number of small rockfalls indicate optimal environmental conditions for their occurrence. Therefore, when analyzing weather conditions, we focused on days with an extreme daily number of small rockfalls, taking into account 1 month of previous weather conditions. Nine days with an extreme daily number of small rockfalls associated with seven weather conditions were extracted from the dataset.

On January 22, 2021, a total of 21 events occurred in northwestern Slovenia due to moderate precipitation 15 days earlier, followed by a freeze‒thaw cycle. On February 4, 2021, a total of 69 events were recorded across Slovenia, with the hotspot occurring in the western part of the country. There, we observed a thick, gradually melting snow cover and abundant precipitation 12 days before the event, followed by a decrease in the daily minimum temperature below 0 °C. An extreme number of rockfall events occurred on the day when the minimum temperature was above 0 °C. Between February 18 and 20, 2021, a total of 125 rockfall events were recorded throughout Slovenia. There was no snow cover in the east at that time; moderate precipitation occurred approximately 8 days before the small rockfall events. After precipitation, the minimum daily temperature decreased to less than 0 °C. An extreme number of rockfall events occurred on the day when the minimum temperature was above 0 °C. In all winter cases, an extreme number of small rockfalls were due to previous precipitation events, followed by at least one freeze‒thaw cycle.

On April 12, 2021, 40 rockfalls occurred across the country, with the main focus on the western part of Slovenia. Five days before the event, moderate precipitation and fairly intense snowmelt were recorded. A particularly high number of rockfall events occurred on the day when the minimum temperature was above 0 °C, followed by the day when the maximum daily temperature was below 0 °C. On April 30, 2021, 25 events were recorded in northwestern Slovenia. Seventeen days prior to this event, a series of daily heavy rainfall events were recorded, followed by rapid snowmelt and a gradual increase in the daily minimum temperature above 0 °C. Moderate precipitation was recorded on the day that the extreme number of rockfall events was triggered. Both extreme events in April 2021 were related to previous precipitation and snowmelt, followed by a freeze‒thaw cycle. In addition, moderate daily precipitation on the day of the events appears to have triggered the extreme number of small rockfalls in early spring.

On both May 7, 2021, and September 17, 2021, small rockfall occurrences were scattered throughout Slovenia due to heavy and intense rainfall on the day of the events. In the warm season, the peaks in the formation of small rockfalls were associated with daily intense and heavy rainfall, generally exceeding 50 mm/day.

A detailed analysis of the weather conditions on days with extreme rockfall events highlights the importance of accounting for prolonged previous weather conditions and shows the specific sequences of weather conditions that trigger small rockfalls. The seasonal dependence of weather scenarios is highly important. Under Slovenian conditions, three seasonal weather scenarios could be distinguished (Table 1, Fig. 6).

Fig. 6
figure 6

Examples of weather sequences triggering small rockfalls in Slovenia. A Winter weather scenario (04/02/2021). B Spring weather scenario (12/04/2021). C Summer weather scenario (05/07/2021). The different meteorological data are shown on the y-axis depending on the weather scenario

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The triggering weather scenarios for winter, spring, and summer were validated using the entire dataset of 2179 small rockfalls. The fit was determined for several time windows from 1 to 30 days before the event. For a better overview, only the values for 20, 10, and 5 days before the event are given. The fits without consideration of the antecedent cumulative precipitation for the winter and spring scenarios were also tested. The fit of the summer scenario was tested for different daily precipitation thresholds between 50 mm and 0.1 mm (Table 2).

Table 2 Validation of the selected triggering weather scenarios (Table 1) on a complete dataset of 2179 small rockfalls that occurred in 2021
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An insignificant increase in the fit of the data in the case of disregarding antecedent cumulative precipitation in the triggering winter scenario (from 72 to 82%) shows that antecedent cumulative winter precipitation is a key triggering factor of a rockfall. A good fit indicates considerable reliability of the extracted scenario for the winter period.

In contrast, the influence of antecedent cumulative precipitation in spring is less pronounced since we achieved a significantly better fit (from 26 to 45%) without considering antecedent cumulative precipitation. However, in general, the relatively poor fit indicates that days with an increased number of events in the spring do not typically describe the triggering weather conditions during this part of the year.

A poor fit of events is also observed for the triggering summer scenario (4% of events in the summertime occurred on a day with more than 50 mm of precipitation). By lowering the criterion, we achieved up to a 63% fit when at least minimal rainfall was present. The reason for the poor fit may be the local nature of the summer storms, where the closest meteorological station was probably too far away to successfully record local precipitation.

For the triggering winter scenario, the fit is best when considering 4 to 18 days of prior weather conditions. In most cases, the weather scenario was successfully captured when considering 7 prior days. For the triggering spring scenario, it is not possible to clearly distinguish the optimal number of preceding days that would successfully capture the entire spring sequence.

To assess the potential for triggering small rockfalls under climatic conditions in Slovenia, we analyzed how often the triggering spring, winter, and summer scenarios (Table 1) were reached between 2016 and 2020 (1826 days in total) (Fig. 6). During this period, the triggering spring scenario was reported for all 116 stations that measured both parameters included in the scenario (air temperature and precipitation). In addition, the triggering summer scenario occurred at almost all meteorological stations measuring precipitation (278 out of 283 stations). The triggering spring scenario occurred in up to 8% of all monitored days at the particular station and was spatially more common in the NW and central-southern parts of the country. The triggering winter scenarios occurred at a much greater frequency, namely, in up to 21% of the days at the specific meteorological station. This triggering scenario is common across the entire country except for the SW and NE regions. The lowest frequency was reported for the triggering summer scenario, occurring up to 6% of the monitored days at the specific meteorological station. Spatially, it is very clearly pronounced in the NW (alpine) part of the country (Fig. 7). Moreover, some of the rockfalls were probably triggered by anthropogenic factors such as the impact of vibrations due to traffic or by animal impact. However, these impacts are very difficult to quantify at the regional scale since there are no detailed data available (e.g., hourly traffic conditions). However, for studies focusing on the local scale, these factors should be taken into consideration.

Fig. 7
figure 7

Fitting of the meteorological data at all meteorological stations in Slovenia for identified weather scenarios (%) for the period between 2016 and 2020. A Spring season. B Winter season. C Summer season. D Comparison of the three scenarios

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The results of this study can be compared with studies carried out under analogous morphological and meteorological conditions. Such comparative analyses enhance our understanding of the underlying processes and contribute to more comprehensive scientific knowledge. For example, Nissen et al. (2022, 2023) analyzed the impact of meteorological parameters over the last 6 decades on data from 642 rockfalls. These researchers found that an increase in daily precipitation approximately doubles the probability of a rockfall event under porewater conditions in German low mountain regions. For the influence of freeze–thaw cycles, Nissen et al. (2022) showed a greater influence, while the present study found only one significant freeze–thaw cycle. However, studies of meteorological parameters in both countries (Slovenia and Germany) indicate that the most critical combination for rockfall is to be expected in winter and early spring after a freeze–thaw transition, followed by a day with high precipitation. A comparison could also be made with the study by Sass and Oberlechner (2012), in which a total of 252 rockfalls were documented in nonpermafrost areas in Austria. These scholars found that the peak of rockfall activity occurs in spring and the second peak occurs in summer, while the correlation with temperature is very weak due to a lack of meteorological data. Delonca et al. (2014) analyzed three French rockfall databases with meteorological parameters as triggering factors (rain, freezing periods, and strong temperature variations). They confirmed the positive correlation between rainfall and rockfalls in the Réunion database and between cumulative rainfall and rockfalls in Burgundy and detected a correlation between the daily minimum temperature and rockfalls in the Auvergne database. However, notably, the climate conditions in their study were significantly different for the Alpine, continental, and Mediterranean areas included in this study.

Using machine learning, Gauthier et al. (2022) conducted a similar study over an extended period of time on a 25 km stretch of road in Canada. These coworkers defined two scenarios, namely, the summer and winter-spring scenarios, with the key parameters of the summer scenario being precipitation intensity and the winter scenario being 24- to 120-h average daily temperature above 0 °C and days with melting. A correlation between the increased occurrence of rockfalls and intense precipitation and freeze‒thaw cycles was also found in the Canadian Cordillera (Macciotta et al. 2015). Seasonal changes in triggering factors were also found in the Japanese Alps, namely, heavy precipitation in summer and fall, a combination of preceding precipitation, freezing and thawing in late fall and late spring, and preceding snowfall, freezing and thawing in winter and early spring (Matsuoka 2019). Interestingly, the most important weather-related triggering factors for rockfalls in mountain climates, where we also expect most of these phenomena, are relatively similar globally, which makes the results spatially transferable.

In addition to the number of events, rockfall size is also decisive, about which much less research has been (Matsuoka 2019; Birien and Gauthier 2023) conducted on this topic; we do not have precise data in Slovenia either. Smaller rockfall events are associated with winter freeze‒thaw cycles with moderate precipitation, while larger events are the result of intense precipitation and thaw in spring (Birien and Gauthier 2023). Therefore, when preparing measures related to the occurrence of a rockfall, particular attention should be paid to spring and summer. However, notably, some of the studies listed above were not focused on the same climate regions investigated in this study.

Study limitations

In the context of this study, there are possible limitations that should be mentioned. First, the calculations are based only on 1 year of rockfall data, and the results cannot reflect the actual seasonal rockfall characteristics in Slovenia. Thus, more studies using longer time series are needed. Second, in some sections of the road network, engineered slopes may have already undergone mitigation measures to prevent more frequent rockfalls, or the slopes could have been weakened during the road construction process, resulting in a greater probability of rockfall incidents. Third, the spatial resolution of the raster data was not uniform, and possibly, some coarse data inputs (1 km grid) were not the optimal solution for the analysis performed. Furthermore, some input data, such as susceptibility maps, are not optimal for investigating small rockfalls, but at present, no map with a more detailed resolution is available. Moreover, there could be some uncertainty in the determination of the rockfall size (above or below 20 cm), but no detailed information regarding the granulometric characteristics was available. Finally, some of the smaller rockfalls could not be detected by the maintenance staff, or detection occurred several days after the actual rockfall event. For these reasons, we attempted to keep our analysis as robust as possible and to draw general conclusions about the triggering mechanisms of rockfalls.

Conclusions

For the results presented, based on rockfalls in 2021, the following conclusions can be drawn:

  • More than 2100 small rockfalls occurred in Slovenia in 2021 (1 small rockfall per 10 km2). Most small rockfalls in 2021 were recorded in winter and spring (January–May). There was no significant correlation between the mean monthly precipitation amount and the mean monthly number of rockfalls. There was no clear correlation with weak earthquakes. Most rockfalls occurred in the western and southwestern parts of the country.

  • Meteorological, geological, and morphological features and other features indicated that many smaller rockfalls were triggered in areas with higher mean annual precipitation and in hilly areas. According to the BRT model, in addition to the mean annual precipitation and maximum slope, the terrain ruggedness index and annual number of freeze‒thaw cycles also had a notable impact on the rockfall locations. Moreover, tested data mining techniques indicated that selected meteorological, geological, and morphological parameters can relatively successfully predict small rockfall locations where the percentage of true-positive and true-negative locations in the case of the random forest model exceeded 90%.

  • The scenario-based analysis (“Triggering factors of rockfall occurrence” section), where scenarios are defined based on expert knowledge, can (in some cases) provide better predictions than some data mining tools, where defining such specific scenarios and combinations is more complicated.

  • The scenario-based analysis (“Triggering factors of rockfall occurrence” section) identifies three seasonal triggering weather conditions for small rockfalls in Slovenia: a winter sequence of precipitation and a freezing–thawing cycle; a spring sequence of precipitation, a freezing–thawing cycle and moderate precipitation; and summer storms (daily precipitation exceeding 50 mm). However, it should be noted that these three scenarios cannot fully explain the triggering of rockfalls included in the database used in this study. Hence, there could be other anthropogenic factors such as construction along roads that locally increase the slope angle or the impact of vibrations due to vehicles that could be important in some cases.

  • The assessment of the actual impact of the extracted triggering weather conditions reveals the high potential of the winter scenario, which occurs far more frequently than all the extracted scenarios (i.e., four times more frequently than the summer scenario and two and a half times more frequently than the spring scenario). It is also spatially distributed throughout most of the country. In contrast, summer storms are the least frequent weather conditions triggering small rockfalls in Slovenia and are the most spatially limited. However, most likely, the actual importance of these weather conditions is masked by the local character of the phenomena and the complex topography of Slovenia.

  • The presented analysis does not cover the complete set of potential influencing factors for small rockfall occurrences, but the high compliance of events that occurred in 2021 with established weather scenarios indicates that weather conditions present at least one important, if not decisive, factor for the occurrence of small rockfall events (in particular, freeze and thaw cycles and precipitations).