These authors contributed equally to this work.

Predicting the timing and size of natural snow avalanches is crucial for local and regional decision makers but remains one of the major challenges in avalanche forecasting. So far, forecasts are generally made by human experts interpreting a variety of data and drawing on their knowledge and experience. Using avalanche data from the Swiss Alps and one-dimensional physics-based snowpack simulations for virtual slopes, we developed a model predicting the probability of dry-snow avalanches occurring in the region surrounding automated weather stations based on the output of a recently developed instability model. This new avalanche day predictor was compared with benchmark models related to the amount of new snow. Evaluation on an independent data set demonstrated the importance of snow stratigraphy for natural avalanche release, as the avalanche day predictor outperformed the benchmark model based on the 3 d sum of new snow height (F1 scores: 0.71 and 0.65, respectively). The averaged predictions of both models resulted in the best performance (F1 score: 0.75). In a second step, we derived functions describing the probability for certain avalanche size classes. Using the 24 h new snow height as proxy of avalanche failure depth yielded the best estimator of typical (median) observed avalanche size, while the depth of the deepest weak layer, detected using the instability model, provided the better indicator regarding the largest observed avalanche size. Validation of the avalanche size estimator on an independent data set of avalanche observations confirmed these findings. Furthermore, comparing the predictions of the avalanche day predictors and avalanche size estimators with a 21-year data set of re-analysed regional avalanche danger levels showed increasing probabilities for natural avalanches and increasing avalanche size with increasing danger level. We conclude that these models may be valuable tools to support forecasting the occurrence of natural dry-snow avalanches.

Forecasting natural snow avalanches is highly relevant in areas where avalanches may threaten people or infrastructure. Erroneous forecasts may cause costs as missed alarms may result in damage to people or infrastructure, and as false alarms may lead to economic loss due to unnecessary closures or evacuations. Therefore, accurately predicting the occurrence of natural avalanches is crucial, though it is still a major challenge in avalanche forecasting. Currently, forecasts are made by human experts drawing on their knowledge and experience. To forecast natural dry-snow avalanches, the (expected) amount of new snow is one of the main parameters. Accumulated sums of precipitation were found to be among the most important explanatory variables in several studies relating observed avalanche activity to meteorological drivers and observed snowpack parameters

While physical snowpack models, such as CROCUS

An alternative approach to develop snow instability models is to use a target variable based on surrogate data that implicitly contain information on avalanche activity, e.g. avalanche danger levels or stability test results from field observations. According to the definitions of the European avalanche danger levels

The objective of this study was to investigate whether the instability model developed by

We used different data sets to train and validate the avalanche day predictor and the avalanche size estimator (Fig.

Several data sets were used to develop and validate the functions describing the probability of natural avalanche occurrence and avalanche size. The data are described in the sections indicated.

To develop the avalanche day predictor and test the avalanche size estimator, we used avalanche observations collected for the purpose of avalanche forecasting in Switzerland. During the winter season, generally from early December until late April, about 80 observers report avalanches in their region on a daily basis. These observations are highly relevant for the day-to-day verification of the avalanche forecast, particularly at the higher danger levels. Reported avalanche properties include the approximate location and the date of the avalanche release, the elevation and the slope aspect of the release area, the release type (i.e. natural or human-triggered), whether it was a dry- or a wet-snow avalanche

Avalanche size classification

For this study, we only considered natural dry-snow avalanches that were recorded between 1 December and 30 April in the three winter seasons 2019/2020, 2020/2021 and 2021/2022 in the Swiss Alps. In total, 12 940 avalanches were reported. Even though the operational avalanche database also contains avalanche observations prior to 2019, the recording standards were different and did not allow us to unambiguously identify natural dry-snow avalanches.

The data set described in Sect.

Map of Switzerland showing the location of the automated weather stations (dots). The colouring indicates the number of avalanche days (AvDs) per station, summed up over all aspects and over the three winter seasons 2019/2020 to 2021/2022. Stations in the Davos–Zuoz area, which had

For validation, we used avalanches mapped in the region of Davos in the eastern Swiss Alps

We applied the operational setup of the SNOWPACK model

In addition to the simulations on flat terrain, forced with measured snow depths, simulations were also performed for four “virtual” slope orientations (north, east, south and west) with a slope angle of 38

To assess snow instability from simulated snow stratigraphy, we applied the instability model to the simulated snow profile at 12:00 LT on the day of interest, as described in

Example of a simulated snow profile showing the hand hardness profile, the grain type of the simulated layers (colouring of the layers) and the probability of instability

The rate of snowfall and the amount of new snow are known to be important indicators of natural dry-snow avalanche activity, also called direct-action avalanches

Conventionally, the height of new snow is measured in the flat field. Consistent with this definition, the new snow amounts provided by SNOWPACK are therefore for the flat field as well, regardless of whether it is a simulation in the flat or on a virtual slope. However, we also considered the thickness of precipitation particle layers,

Lastly, we also extracted the minimum of the natural stability index sn38, which is implemented in SNOWPACK. Sn38 describes for each snow layer the ratio of the shear strength of the layer to the shear stress exerted by the overlying slab

To validate model predictions, we used a data set of re-analysed regional danger levels. This data set is a subset of the forecast regional avalanche danger levels published by the national avalanche warning service in Switzerland. The data set only contains cases for which the forecast danger level was either validated or corrected (about 5 % of the cases) after considering multiple pieces of evidence, as described by

In a first step, we developed an

To differentiate days with natural dry-snow avalanche activity (avalanche days, AvDs) from days without any avalanche activity (non-avalanche days, nAvDs), we relied on data set AV1 (Sect.

We define the aspect-specific avalanche day index (

This definition separates days with widespread avalanche activity (AvD;

By applying Eq. (

To develop the avalanche day model, we tested a set of predictor variables, including HN1d, HN3d,

In a first step, we investigated the performance of each predictor variable in discriminating between AvDs and nAvDs from the training data set (i.e. data set AV1 and the corresponding SNOWPACK simulations) using a simple threshold-based binary classification model. To find the best threshold, “thr”, for each classification model, we optimized the F1 score, defined as the harmonic mean of the precision, also termed positive predictive value (PPV), and the true-positive rate (TPR; see Table

Confusion matrix defining the possible combinations of observed and predicted labels (upper part) and definition of resulting performance measures true-positive rate (TPR), positive predictive value (PPV), true-negative rate (TNR) and F1 score (F1; lower part).

To examine the robustness of the threshold values and the resulting classification performance, we split the training data into the following subsets, each of which was tested with the complementary data not used for deriving “thr”:

Hydrological year: each hydrological year had its own pattern of snowpack evolution and avalanche hazard characteristics.

Grain type characteristics of the critical weak layer: we distinguished between layers composed of persistent grain types and precipitation particles. There were only a few AvD cases for other grain types; therefore, we did not train on this subset.

Region: the AvDs are not equally distributed over the Swiss Alps (see Fig.

In a second step, we derived avalanche day predictors

To estimate avalanche size for a given failure layer depth, we used data set AV2 (Sect.

The

To evaluate the performance of the avalanche day predictors (

We used the observations of natural dry-snow avalanches in the region of Davos (data set AV3; Sect.

We compared the re-analysed forecast regional avalanche danger levels (DL, Sect.

Avalanche days were generally associated with new snow (

Overview of avalanche data and properties of the simulated most critical weak layer as selected by the instability model and thickness of the overlying slab consisting of precipitation particles (recent slab). Subsets are shown by hydrological year (2020, 2021 and 2022), by region (Davos–Zuoz area and elsewhere; see also Fig.

At least one potentially unstable layer was detected in 84 % of the AvDs, and in only 2 % of the nAvDs. Moreover, in 7 % of the profiles, there was at least one other potentially unstable layer below the critical weak layer. These cases were rare on nAvDs (1 % of the profiles), but quite frequent on AvDs (66 %). The median difference in the depth between the critical and the deepest potentially unstable layer (

All explored variables (HN1d, HN3d,

The optimal thresholds (“thr”) to distinguish between nAvD and AvD for the seven subsets varied when cross-validating the model. For instance, threshold values ranged from 9 to 17 cm for the 24 h amount of new snow HN1d (median 12 cm) or from 22 to 47 cm for

Performance statistics for avalanche day predictors (binary classification). Shown are the cross-validated TPR and PPV values for the seven subsets numbered in Table

Analysing differences between the subsets in more detail also provided interesting insights. For instance, the optimal balanced

Probability that a day is an avalanche day (

Panel

The coefficients for the best-fitting sigmoidal functions

Finally, we explored the performance when averaging the

Brier scores for predicting the median or the largest avalanche for all avalanche days (AvD) with

In data set AV3, containing 5912 observed avalanches (Sect.

Comparing

While the predictive power of the continuous models

Performance statistics of different avalanche day predictors

Estimated probabilities

To evaluate the performance of the avalanche size estimators, we compared

Brier scores for predicting the median or the largest avalanche size for all avalanche days with

We compared individual model predictions with the quality-checked regional avalanche danger level for 21 winter seasons (data set DL; Sect.

Comparison between quality-checked regional danger levels for 21 years (data set DL,

Comparison of quality-checked regional danger levels for 21 years (data set DL,

First, we consider snowpack stability, for which we consider

Avalanche sizes, estimated using the 24 h new snow height HN1d, were mostly size 1 (proportions 0.34–0.42) and size 2 (proportions 0.4–0.44) for danger levels 1 (low) to 3 (considerable) (Fig.

The second proxy of failure depth given by the depth of the simulated deepest weak layer,

Lastly, we explore predictions expected to describe the frequency distribution of snowpack stability. Applying the instability model and the avalanche day predictor to spatially distributed snowpack simulations may yield frequency distributions of snowpack stability with respect to human triggering and natural release, respectively. Spatially distributed simulations of snow stratigraphy can be obtained either with high-resolution output of numerical weather prediction models

Proportion of predictions with

We developed an avalanche day predictor

To develop the avalanche day predictor, we created a robust binary target variable (AvD versus nAvD) imposing restrictions on the observed avalanche activity in the vicinity of the AWS (Eq.

As the exact timing of avalanche release was not included in the data sets of observed avalanches, the explanatory variables were extracted from the snowpack and instability model simulations at fixed time steps (12:00 LT). This introduced uncertainty in the explanatory variables of both the training and validation data sets. With avalanche data sets from remote detection systems, providing the exact release time, this uncertainty would be removed. However, so far such data sets only cover short time periods and are very local in scope

In a first step, we analysed the predictive power of the explanatory variables to distinguish between AvDs and nAvDs using different subsets of the training data set (AV1). An optimized threshold-based classification resulted in a reasonably high performance (cross-validated F1 score: 0.80) of

Evaluating continuous one-dimensional sigmoidal

Most of the recently developed snow instability models

For a model to be considered useful, it has to provide more information than can be obtained from basic prior information

Avalanche size is classified according to the destructive potential of the avalanche

Comparison of modelled instability with recent studies analysing observed or forecast indicators of instability with respect to the five danger levels. Panel

We estimated avalanche size as a function of various proxies of failure depth (HN1d, HN3d,

The three key factors that characterize the avalanche danger levels are snowpack stability, the frequency distribution of snowpack stability and avalanche size

Comparing the model-driven predictions of instability related to human-triggered avalanches with other studies exploring the relationship between the indicators of instability characterizing regional avalanche danger and the danger levels showed similar patterns (Fig.

We relied on simulated snowpack stratigraphy for virtual slopes with a 38

Overall, we conclude that fully data- and model-driven aspect-specific predictions describing the probability of human-triggered avalanches and the occurrence of natural avalanches are clearly related to observational data and may therefore be suitable for estimating snowpack stability at the regional scale.

To investigate whether the instability model based on one-dimensional SNOWPACK simulations recently developed by

We also explored whether indicators of avalanche size can be obtained from one-dimensional SNOWPACK simulations. Our avalanche size estimator, developed using observations of avalanche size and failure depth, produced the best results in predicting the largest avalanche size when the depth of the deepest simulated weak layer (

Lastly, as part of the model validation, we showed that model predictions (avalanche day and size) were related to the danger levels. The results were in line with current definitions of the avalanche danger levels and with previous data-driven studies, highlighting the models' potential to support decision making in regional avalanche forecasting.

The models developed in this study allow for the estimation of two determinants of regional avalanche danger, snow instability and avalanche size. Applied to one-dimensional snowpack simulations driven with data from AWSs or numerical weather prediction models, these models can thus provide valuable support in operational avalanche forecasting.

The data are available at the Envidat data repository

SM and FT contributed equally to this study (concept, data curation and analysis, and preparation of manuscript; joint first authorship). JS and AvH provided feedback during the analysis. All authors discussed the findings and contributed to the writing of the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

We thank Lukas Graz (ETH Zurich) and Marc Ruesch (WSL Institute for Snow and Avalanche Research SLF, Davos) for valuable advice on the development of the regression models.

This work was partly funded by the WSL research programme Climate Change Impacts on Alpine Mass Movements – CCAMM (

This paper was edited by Pascal Haegeli and reviewed by Christoph Mitterer and two anonymous referees.