We developed a machine learning model that predicts the daily number of avalanches per aspect sector from simulated weather and snowpack conditions, after training on a human-based avalanche inventory. Similar to , we relate daily meteorological and snow conditions to daily avalanche activity. We split the area under study into four aspect sectors: North, East, South, and West-oriented sectors, as snow-related variables depend heavily on incoming solar radiation and sometimes on wind direction.

In this section, we first present the target variable (i.e., the variable we want to predict): the daily number of avalanches in the Haute-Maurienne valley, as reported by the EPA inventory. Next, we describe the model input features (i.e., predictors of the target variable). These features are either derived from reanalysed weather and snow data or from snow-climate simulations. Then, we detail the machine learning model itself. In particular, we describe how we account for uncertainties and biases in the avalanche observations. Finally, we define three indicators derived from the daily prediction that we use to evaluate the model and quantify avalanche activity.

The Enquête Permanente sur les Avalanches (EPA) is a French survey that reports all avalanches that meet a specified threshold on designated avalanche paths . Approximately 3900 avalanche paths are monitored in France, mainly by operators of the forestry service . Each path has an associated flow threshold, and any avalanche that exceeds this threshold is expected to be included in the inventory. Each reported avalanche is at least described by the associated path and the time window during which it occurred. Each path is characterized by the average aspect and altitude of the typical release zone. One of the main advantages of this dataset is its presumed temporal homogeneity, as the flow thresholds have remained unchanged over the years. However, the EPA has been rigorously revised after the Montroc avalanche in 1999 and, in 2006, the observation protocol was revised, including the addition of new descriptors of the avalanches . A second advantage of the EPA is that avalanches are reported almost daily. The occurrence of an avalanche is controlled by the snow conditions at the time it occurred, and is only very weakly controlled, for instance, by the snow conditions averaged over the winter season . To learn the relationship between snow conditions and avalanche occurrence, it is thus important to rely on data of high temporal resolution of the order one day. However, the EPA is not perfect in this aspect: for each avalanche event recorded, the observer identifies a time window defined by 2 d [d1,d2] during which the avalanche probably occurred. This period may correspond either to the interval between two successive observations or to a narrower time frame based on the observer's evaluation of meteorological and snow conditions. The length of this interval is rarely 1 d but generally spans 1 to 5 d due to avalanche danger, visibility conditions, holidays, etc. Lastly, it should be noted that the EPA dataset does not inventory all avalanches but only those in pre-designated paths. This survey was primarily developed for risk management in areas near the valley floor, so avalanches in unpopulated areas or those threatening snow recreationists are far from all included.

This study focuses on the Haute-Maurienne valley, located in the French Alps. This valley has long been a critical area for avalanche observation due to its geography, with relatively high mountains and steep avalanche paths e.g.. We focus on the upper valley, which is characterized by more active avalanche paths. The study area comprises the three district municipalities of Bessans, Bonneval-sur-Arc and Lanslevillard (Fig. ). It is characterized by about a hundred monitored EPA avalanche paths and thousands of avalanches have been recorded between 2006 and 2023. The typical flow threshold is at an elevation around 1800 m (slightly above the valley bottom) while the avalanche paths extend to maximum elevations of up to 3300 m, with an average upper limit of about 2700 m. In this subset, the observations show very few avalanches in the 1950s and significantly higher avalanche counts in recent decades (Fig. ), which is inconsistent with larger-scale trends . This behavior may be specific to the considered domain. The number of days of uncertainty associated with each avalanche release date is variable: the exact day a given avalanche occurred is known only in about 18 % of the cases and 96 % of the avalanche occurrence days are known with less than five days of uncertainty (Fig. ).

In practice, we filtered the raw avalanche events recorded in the EPA to overcome its limitations. First, we excluded the data prior to the last renovation of the observation protocol in 2006 to evaluate the machine learning model, considering only the period spanning from winter seasons 2006/2007 to 2022/2023. Second, we assumed that an event reported in the time window [d1, d2] occurred between 18:00 UTC on day d1-1 and d2 at 18:00 UTC. We also chose to exclude events with more than 5 d of uncertainty from this analysis, which correspond to 3.6 % of the listed events. In other words, we arbitrarily assumed that these very uncertain but sporadic events never happened. Third, we considered only the paths that have been monitored during the entire period 2006–2023. This final filtered dataset consists of n = 89 EPA avalanche paths and m = 2080 recorded avalanches between the winter seasons 2006/2007 and 2022/2023. Winter seasons will subsequently be denoted by the year in which they end; for example, winter 2020/2021 will be denoted as 2021.

The input features for the machine learning model are generated from a series of models. An atmospheric model provides input data to a snowpack model, which simulates the evolution of snowpack stratigraphy. From this, various predictors related to avalanche formation are calculated.

We first evaluate the four versions of the model between winter seasons spanning from 2007 to 2023 (Table ). Accounting for both observation uncertainties and potential observation bias before the 2007 winter season reduces prediction errors. The annual MAE is reduced by half (from about 50 avalanches to 28 avalanches per year), the seasonal MAE by a factor of 2.5 (from about 5.5 avalanches to 2.3 per month) and the worst week MAE by half to one fourth (from 10–19 avalanches to 5 avalanches per week). Thus, the relevance of the modeling choices is confirmed, as they substantially improve the methodology and lead to the best scores on the three metrics.

The predictions of the model Md1-d22007-2023 are detailed in Fig. . We recall that these predictions are generated with the leave-one-year-out method (see Sect. ). The inter-annual variability of the number of avalanches per year (between about 40 and 500) is well predicted by the machine learning model (Fig. a, b). The model correctly identifies specific years, such as winter season 2018 with a record-breaking number of avalanches, and 2011 with very low avalanche activity. The mean absolute annual error is 32.5 avalanches per year (26.5 % of the mean number of avalanches per winter season). The bias is small: 8.5 avalanches (7 % of the mean number of avalanches per winter), showing that the error is almost centered on zero. The model is also capable of reproducing the average number of avalanches per winter month (Fig. c, d). There are almost no avalanches predicted or reported before November. Then the number of avalanches progressively rises until the peak activity in March. Avalanche activity almost disappears in May. The mean absolute monthly error is approximately 2.3 avalanches (17 % of the mean number of avalanches per month during the winter season), with a small bias of 0.9 avalanches. Focusing on the maximum number of avalanches during 1 rolling week per season (Fig. e, f), the mean absolute error is approximately 4.5 avalanches, representing 12.5 % of the mean value. The model correctly predicts the inter-annual variability, but slightly underestimates the maximum number of avalanches per week, by around 10 % over the entire period, as shown by a negative bias of around -4.0 avalanches for the most active week of the year. All in all, the results show that the model performs well at annual and monthly and at the most active week scales. This demonstrates that the model is suitable for investigating climate-driven trends in these avalanche activity indicators.

A single XGBoost model is trained using all the winter seasons from 2007 to 2023. The model is then applied using the S2M reanalysis dataset from winter seasons 1959 to 2006 as input data. To obtain a continuous time series spanning winter seasons 1959 to 2023, these reconstructed values were combined with the predictions for the winter seasons between 2007 and 2023 obtained using the leave-one-year-out method described above. The predicted daily number of avalanches is used to derive the three previously defined indicators of avalanche activity (Fig. ). In addition, we compute the temporal linear trends of these indicators using a Bayesian framework . The linear trends are systematically expressed in % per decade relative to the 1975–2005 climatology, with its median value and the 10th–90th percentile posterior credible interval.

The predicted number of avalanches per winter season shows large inter-annual variability but an average decreasing trend (Fig. a). For instance, years with more than 200 avalanches are rather frequent (approximately every three years on average) before the late 1980s and become rare thereafter. As expected, the trends from the raw observations are completely off from these assessments, which highlights that raw observations over a long period may be affected by sampling biases. Quantitatively, our model predicts a median decreasing linear trend of -4.8 % per decade in the annual number of avalanches over the period 1958–2023, with a 10th–90th percentile credible interval ranging from −10.0 % to +0.4 % (Appendix Fig. ).

The decrease of the annual number of avalanches is not uniform during the winter season as shown by contrasting 30-year periods at the beginning and at the end of the dataset: 1958–1988 and 1993–2023 (Fig. b). For instance, the resulting trends indicate a median slope of -1.6 % (with a credible interval ranging from -7.7 % to +4.6 %) per decade in the avalanche activity in December, January, and February (DJF) and of -8.3 % (between -13.4 % and -3.5 %) per decade in March, April and May, with a peak at -14.3 % for the April avalanche activity (Appendix Fig. ). Therefore, the decrease in avalanche activity in the past has been greater in spring than in winter.

The weekly maximum number of avalanches for each winter season is shown in Fig. c. As we use a Bayesian framework to fit the GEV distribution on the data, the slope distribution of the return levels is directly provided within the inference procedure. The results show a decreasing slope of the 30-year return level by -1.4 % (between -7.3 % and +4.3 %) per decade relative to the mean return level between 1975 and 2005. This downward trend is less significant than the one observed in the total number of avalanches, suggesting that the magnitude of large cycles has decreased at a lower rate than the total number of avalanches.

The same machine learning model is applied to all members of the climate simulations (18 per scenario), and the avalanche activity is quantified by the three previously defined indicators. In contrast to the single reanalysis, the linear trends derived from climate simulations for a given scenario are not only made uncertain by the inter-annual variability but also by the inter-model variability. To compute the probability distribution function of the trend slope, we arbitrarily assumed that all GCM/RCM pairs are equiprobable and evaluated the overall credibility interval by pooling posterior samples derived from individual projections (see Appendix Fig. ).

The annual number of avalanches clearly shows a decreasing trend under advanced climate change and its consequences for snowpack characteristics (Fig. a). The mean number of avalanches in the historical simulations is around 25 % higher than that in the reanalysis. However, the trends are similar with a historical decrease at a median rate of -5.9 % per decade, but with large uncertainties (10th–90th percentile posterior credible interval ranging from −17.1 % to 7.6 %). The projections for the 21st century show a decrease in the annual number of avalanches at median rates of -4.6 % per decade for the RCP4.5 scenario and -8.8 % for the RCP8.5 scenario with respect to the period spanning from the winter seasons 1975 to 2005. The associated uncertainties are shown in Table . In other words, the results indicate a reduction of approximately 37 % (respectively 65 %) in the mean number of avalanches over the 2070–2100 period compared with the 1975–2005 baseline in the RCP4.5 scenario (resp. RCP8.5).

The expected decline of avalanche activity is heterogeneous between seasons (Fig. b). First, the higher number of avalanches predicted by historical climate simulations compared to the reanalysis mainly arises from stronger activity in March and April, while DJF avalanche activity is broadly consistent between the two datasets. Then, the projected DJF avalanche activity appears almost unaffected by climate change, except for the RCP8.5 at the end of the century. Conversely, a marked decline in avalanche activity is expected in March, April, and May (MAM) for all scenarios. The projected decrease in the annual number of avalanches is thus primarily driven by the strong reduction in spring avalanche activity. For instance, the number of avalanches in DJF is expected to decrease only by 3.1 % per decade under RCP4.5 and by 6.9 % per decade under RCP8.5, while in MAM, the expected decreases correspond to 5.4 % per decade under RCP4.5 and 10 % per decade under RCP8.5, relative to the 1975–2005 reference period (Table ). April was historically one of the most active months for avalanches; however, under the RCP8.5 scenario, by the end of the century, avalanche activity in April is projected to be very limited. Similarly, in May, avalanche activity is expected to be nearly absent under both scenarios, indicating a substantial shortening of the avalanche season.

It is projected that there will be a decrease in the amplitude of large avalanche cycles by the end of the century, with a lower rate for RCP4.5 and a higher rate for RCP8.5 (Fig. c). Yet, considering the credible intervals, for the near future (2020–2050) or under the RCP4.5 scenario at all temporal horizons, large avalanche events with intensities comparable to those observed during the 1975–2005 reference period remain possible with a similar probability. Indeed, the 30-year return levels show respective trends of -2.2 % per decade and -5.5 % per decade for the RCP4.5 and RCP8.5 scenarios relative to the mean return levels computed from the historical runs between winters from 1975 to 2005. In other words, the 30-year avalanche cycle is expected to be composed of approximately 15 % (resp. 35 %) fewer avalanches in 2100 compared to the 1975–2005 reference period in the RCP4.5 scenario (resp. RCP8.5).

This work uses a new methodology compared to previous studies to investigate future changes in avalanche activity by using a regressor and considering two key aspects of the training dataset: the heterogeneity of observations over time and uncertainties associated with triggering dates.

First, using a machine learning regressor algorithm enables us to progress beyond studies that used binary classifiers. To our knowledge, all studies that predict daily avalanche activity from snow stratigraphy using machine learning methods rely on classification algorithms to predict whether a day is avalanche-prone , or to categorize daily avalanche activity into three classes: null, moderate, or high . These models do not provide quantified information about the magnitude of avalanche activity during the avalanche days, and are mainly used for short-term avalanche hazard forecasting and for pre-detecting situations that may require specific attention by the forecaster. Their predictions generally show high recall but low precision: most observed avalanche days are well predicted, but the predictions may contain many false alarms. Using a regressor thus allows us to predict the daily number of avalanches and to quantify climate trends in avalanche activity using different indicators, without treating all avalanche days equally. However, the number of avalanches gives no information on the size of avalanches and the potential damage: many small avalanches may have no impact at all, while a small number of large ones could cause significant damage. Future research could investigate additional target variables, such as deposit volume , to enhance the scope of potential applications. In addition, we may improve our regressor algorithm. Indeed, the observed daily avalanche counts follow a zero-inflated count distribution, characterized by integer-valued observations with an excess of zeros . We did not use a specific model to handle this distribution. More complex models adapted to zero-inflated count data , such as a two-stage model that combines a classifier and a Poisson regressor, might improve the methodology e.g.. In such a framework, the GEV component would need to be formulated using a discrete extreme value distribution, as proposed by . In the present study, it relies on a continuous GEV formulation as the model predicts continuous daily numbers of avalanches. Moreover, the model tends to underestimate the most active week of the year (Fig. e), indicating limitations in its ability to predict extreme avalanche activity. These underestimations likely result from the combined effects of the rarity of extreme avalanche cycles in the training dataset, the smoothing introduced by the loss function that distributes avalanche occurrences across potential release days, and the spatial averaging of meteorological and snowpack conditions over the SAFRAN geometry, which can attenuate the predictor signals associated with the most intense events. Combining a similar machine learning framework with an extreme value approach could help better represent the tail behavior of the distribution and improve the credibility of predicted extremes .

Secondly, to address heterogeneity in past observations, we trained a machine learning model using the EPA dataset between the winter seasons 2006/2007 and 2022/2023. We have shown that training the model on a larger time period (Table ), as done in previous studies e.g., leads to lower scores. Besides, the predicted number of avalanches based on the reanalysis significantly deviates from the observations in the distant past (Fig. ). These results suggest that avalanche reporting was not consistent throughout the 1958–2023 period in the Haute-Maurienne valley, with possible under-reporting during the earlier decades. While this result is specific to the studied area, it confirms that the EPA dataset, as with most avalanche records stemming from human observations or archives, should be used with caution when considering the distant past . However, training the model on a smaller dataset also has its drawbacks. In particular, the approach implicitly assumes that the range of snow conditions encountered during the model application period (1950–2100) is represented within the training dataset (2006–2023). This assumption becomes more plausible as the length and diversity of the training period increase. When the model is applied to conditions outside the range of its training data, its predictions are likely to be unreliable. In other words, the model cannot handle new, unknown avalanche situations and only predicts the future probability of situations that have already occurred. This limitation is particularly critical when analyzing extreme avalanche cycles. In this regard, including the 2017/2018 winter season – characterized by exceptionally unusual snow conditions – within the training dataset is especially valuable. To overcome this limitation, physics-based avalanche models may help this machine learning approach handle new conditions not encountered during training.

Thirdly, we showed that accounting for the uncertainties in the release dates in the training step significantly improves the prediction scores (Table ). This was achieved through the use of a custom loss function in the XGBoost algorithm. This approach enabled us to accurately associate daily snow conditions with the corresponding avalanche activity without making any assumptions about the exact triggering dates. Standard random forests widely used in the literature e.g. do not allow for the integration of uncertainties through a loss function.

The results are strongly influenced by the quality of the input data, specifically the avalanche observations and associated predictors. Enhancing the quality of these data sources may lead to improved outcomes. Furthermore, as this study is limited to a single location and utilizes high-quality data, additional research is necessary to determine whether these findings can be generalized to other regions.

The avalanche activity described in this paper corresponds to the one reported by the EPA, which is not representative of all the avalanches that can occur, particularly those at higher altitudes that do not reach the EPA thresholds (Fig. ). Nevertheless, these avalanches can still pose a threat to snow recreationists. In addition, the EPA thresholds of the studied area are located within a relatively narrow elevation range, and we assumed that avalanche activity is driven by snow conditions aggregated over all the elevation bands between 1800 and 2700 m. As a result, the influence of elevation on temporal trends in avalanche activity cannot be explicitly isolated in the present analysis. This limitation is noteworthy, as elevation has been shown to play a major role in governing snowpack evolution and long-term changes in avalanche activity, particularly in the context of climate change . Moreover, this study is specific to the Haute-Maurienne valley, characterized by numerous recorded avalanches. The exact same methodology is not applicable in other areas where the too small number of recorded avalanches does not yield a sufficient training data set. Working on model transferability or by reasoning at alternative spatial scales (e.g. considering individual avalanche paths and accounting for their topographical specificity by adding topographic properties in the features) could further strengthen the methodology and facilitate its application to other locations.

The model is trained on weather and snow predictors derived from the S2M reanalysis at the massif scale. In the Haute-Maurienne valley, snowfall is highly influenced by specific meteorological events (easterly return flows) that can produce substantial localized accumulation near the Italian border while nearby areas receive minimal snowfall, as exemplified by the large 2008 avalanche cycle in Southeast France . Consequently, the snowpack simulations cannot fully capture this heterogeneity and may yield locally unrepresentative conditions. Nevertheless, as these issues are present in both the training and application datasets, there should still be a predictive relationship between simulated meteorological and snowpack conditions and avalanche activity. Besides, the S2M reanalysis is also subjected to biases that can vary with time, which affects reanalysed climatic trends : the number of assimilated observations varies over time and the meteorological conditions are simulated by the ERA40 model before 2002 and by the operational forecasts of the French global NWP model ARPEGE thereafter. In addition, we assumed here that avalanche hazard evolution is solely controlled by changes in snow cover. However, avalanche activity can also be impacted by changes in land use, such as land abandonment and reforestation . The projected reduction of avalanches may also initiate a positive feedback loop: fewer avalanches may increase the density of small-diameter trees in avalanche starting zones, reducing future avalanche magnitudes even more . The choice of predictors could also be further refined. For example, we only used the strength-to-stress ratio to characterize persistent weak-layer avalanche problems. It provides a very simplified description of snowpack stability. More physically based metrics, such as the critical crack length , could potentially offer a more realistic representation of avalanche release processes and improve predictive skill. However, the identification, evaluation, and optimization of relevant predictors constitute a substantial research topic in their own right and are beyond the scope of the present study. The objective here was not to determine the optimal predictor set, but rather to assess the ability of a physically informed machine-learning framework to reproduce and project avalanche activity.

The climate trends computed in this study are based on the ADAMONT framework, which relies on a projection onto a massif-elevation grid of RCM simulations and on an advanced quantile mapping with the reanalysis on the historical period . The EURO-CORDEX Regional Climate Model Ensemble simulations are generally too cold and too wet . The ADAMONT method is designed to reduce systematic discrepancies between climate model outputs and the reference reanalysis. However, in high-mountain environments, the correspondence between regional climate model grid points and the associated reanalysis points is challenging due to strong elevation gradients and complex topography. Furthermore, the ADAMONT bias-correction procedure is applied independently to each elevation band, without explicitly enforcing vertical coherence among corrected variables. This approach may therefore disrupt altitude-dependent physical relationships and introduce inconsistencies across elevations. These limitations are further amplified near the rain–snow transition zone, where strong non-linear responses to small temperature biases can generate significant biases in snow-related variables. Indeed, in the Haute-Maurienne valley at 2700 m, the mean winter snow depth is still around 30 % higher in ADAMONT climate simulations than in the reanalysis (not shown), which may explain why the avalanche activity computed from historical ADAMONT simulations is significantly higher compared to one computed from the reanalysis (Fig. ). A strong assumption of quantile mapping is also the temporal stationarity of the bias, which remains questionable under pronounced climate change . As a result, we based our analysis on climatic trends (in % per decade) rather than absolute values, which are more prone to systematic biases. Moreover, analyzed the impact of bias correction via quantile mapping on extreme precipitation and concluded that quantile mapping can inflate the magnitude of relative trends in precipitation extremes with respect to the raw dataset. A specific treatment of extreme values is used in ADAMONT: for RCM values greater than the 99.5 % quantile, the quantile mapping method is not applied and a constant adjustment is applied to allow for new extremes . This treatment of the extreme values might be better than a simple quantile mapping method, but may be insufficient to capture the correct trends in the extreme values. Future work should therefore focus on more advanced extreme-value frameworks to better constrain the upper tail and assess the robustness of the projected changes in the extreme events.

The past trend in avalanche activity based on the S2M reanalysis (1958–2023) shows a decrease in the mean annual number of avalanches between 1958 and 2023, at a rate of approximately 5 % per decade. Based on the S2M reanalysis and the raw EPA dataset without any prior statistical pre-processing, found no significant trend in avalanche occurrences at the scale of the Northern French Alps between 1958 and 2009. Using a more advanced statistical treatment of the EPA dataset, found a decrease of 19 % in the mean number of avalanches per winter between 1980 and 2009 in the entire French Alps, which corresponds to approximately 6 % per decade, in line with our result. We also showed that the decrease in avalanche activity is more pronounced during spring, which is consistent with who reported an advancement of about 3 weeks of the onset date of wet-snow activity from 1958 to 2020. Moreover, we found that the magnitude of large avalanche cycles, quantified by the maximum number of avalanches during 1 week, decreased by around 1.4 % per decade, at a lower rate compared to the annual number of avalanches. used dendrochronology analysis in the Rocky Mountains and demonstrated that the probability of large avalanche occurrence decreased by approximately 2 % per decade from 1950 to 2017. Although this metric is not directly comparable to our results, since we analyze avalanche counts during one week rather than the occurrence of large avalanches, both metrics address changes in the frequency of large avalanche cycles over time.

Regarding future climate simulations, our results are in agreement with the small number of existing studies that provide quantitative assessments, which consistently report a marked decrease in the mean annual avalanche occurrence. reported a decrease in the number of avalanche days between the periods 1990–2020 and 2069–2099, with the magnitude of the decrease depending on station elevation. At the station with the lowest elevation (1824 m, similar to the Haute-Maurienne valley floor), the number of avalanche days declined by approximately 30 % under the RCP4.5 scenario and by about 60 % under the RCP8.5 scenario. At higher altitudes, between 2300 and 2800 m, this decline is less pronounced, reaching around 10 % in the RCP4.5 scenario and 20 % to 30 % in the RCP8.5 scenario. also showed that seasonality in dry-snow avalanche activity (characterized by peaks in January and February) remains mostly unchanged while the wet snow avalanches are expected to appear earlier in the season and decrease in number in April and May. Taking into account all avalanche problems, it leads to a significant reduction in spring avalanches. Similarly, in the Rocky Mountains, the wet avalanches are expected to start earlier than historical averages (around 40 to 45 d earlier in the high emission scenario) . This is consistent with our findings which indicate a drop in the number of avalanches in April and May, especially in the RCP8.5 scenario. More generally, the observed decrease in the annual number of avalanches appears to be largely associated with the shortening of the avalanche season, as discussed in . We also found that the return levels of large avalanche cycles are expected to decrease, but at a slower rate than the mean avalanche activity. This is consistent with the results of , which show that despite climate change, some locations continue to be at high risk of avalanches. Furthermore, demonstrated that the mean daily snowfall in the Pyrenees at 2500–3000 m will decline significantly and emphasize that extreme snowfall events will change only slightly. Similarly, demonstrated that the expected decrease in the 100-year return level of daily snowfall is slower than the expected decrease in the mean annual maximum value. This illustrates that a decrease in mean conditions does not necessarily imply a proportional decrease in extreme values.

The snowpack conditions in the Haute-Maurienne valley are rather specific: a relatively high valley floor compared to typical alpine valleys and substantial precipitation associated with eastern flows. Therefore, the spatial generalization of these results should be addressed in future work. In particular, future analyses should explicitly account for the influence of elevation on avalanche activity, given its major role in modulating the impacts of climate change on snowpack conditions and extreme snowfall events . Based on documented changes at low elevations and high elevations , a conceptual framework describing elevation-dependent avalanche activity has been proposed by . However, further investigations are required to provide quantitative assessments of these elevation-dependent effects.