Snow avalanches represent a natural hazard to infrastructure and backcountry recreationists. Risk assessment of avalanche hazard is difficult due to the sparse nature of available observations informing on snowpack mechanical and geophysical properties and overall stability. The spatial variability of these properties also adds complexity to decision-making and route finding in avalanche terrain for mountain users. Snow cover models can simulate snow mechanical properties with good accuracy at fairly good spatial resolution (around 100 m). However, monitoring small-scale variability at the slope scale (5–50 m) remains critical, since slope stability and the possible size of an avalanche are governed by that scale. To better understand and estimate the spatial variability at the slope scale, this work explores links between snow mechanical properties and microtopographic indicators. Six spatial snow surveys were conducted in two study areas across Canada. Snow mechanical properties, such as snow density, elastic modulus and shear strength, were estimated from high-resolution snow penetrometer (SMP) profiles at multiple locations over several studied slopes, in Rogers Pass, British Columbia, and Mt. Albert, Québec. Point snow stability metrics, such as the skier crack length, critical propagation crack length and a skier stability index, were derived using the snow mechanical properties from SMP measurements. Microtopographic indicators, such as the topographic position index (TPI), vegetation height and proximity, wind-exposed slope index, and potential radiation index, were derived from unoccupied aerial vehicle (UAV) surveys with sub-metre resolution. We computed the variogram and the fractal dimension of the snow mechanical properties and stability metrics and compared them. The comparison showed some similarities in the correlation distances and fractal dimensions between the slab thickness and the slab snow density and also between the weak layer strength and the stability metrics. We then spatially modelled snow mechanical properties, including point snow stability, using spatial generalized additive models (GAMs) with microtopographic indicators as covariates. The use of covariates in GAMs suggested that microtopographic indicators can be used to adequately estimate the variation in the snow mechanical properties but not the stability metrics. We observed a difference in the spatial pattern between the slab and the weak layer that should be considered in snow mechanical modelling.

Snow avalanches represent a natural hazard to infrastructure and backcountry recreationists in mountainous areas all over the world

The spatial variability of snow properties is well documented in climate studies

There are more effective indicators, such as snow stability tests, to estimate the conditions for snow avalanches. These tests are widely used in the avalanche industry to assess snow stability and, ultimately, snow avalanche hazard. These tests provide a qualitative evaluation of the mechanical interaction between the cohesive slab and the weak layer. Some studies have investigated the variability of several snow stability tests on an avalanche-prone slope

The SMP was used in snow spatial studies because it can rapidly and accurately measure the mechanical properties of the snow relevant to snow stability on a slope prone to avalanche

Based on these findings, several studies have simulated artificial spatial patterns of the weak layer in mechanical models to understand the effect of the spatial variability of the weak layer on the slope stability, given the likelihood of an avalanche

Spatial patterns of snow properties can be explained and estimated by statistical models with exploratory spatial variables. In the past, environmental variables were mapped using a linear regression model and kriging with external drift. Several studies have used kriging to map point snow stability, such as snow stability test results, SMP-derived mechanical properties, and stability metrics

In studies focused on the slope scale, researchers successfully explained and estimated the spatial variability of snow depth, even in cases where slope angle, aspect and elevation remained relatively constant

The snow mechanical variability can also affect the overall slope stability with the so-called knockdown effect

It is necessary to spatially explain and estimate the mechanical properties of snow and snow stability with microtopography indicators at the slope scale. This study is based on the limitations and suggestions of

In order to spatially estimate the spatial variability of snow using microtopography indicators, we selected four study sites based on their specific microtopography and microclimate context. The first study site is located on Mount Albert in Gaspésie National Park, Québec, Canada (Fig.

Two study sites are in Glacier National Park, located in Rogers Pass, British Columbia, Canada (Fig.

Map of the study area of

For the spatial analysis, this study presents four snow spatial surveys collected during the winter of 2021–2022 (Fig.

To ensure an accurate interpretation of the SMP signal, the weak layer needed to be identified and characterized from a snow profile. Full characterization of the snow stratigraphy was not needed for our analysis, so a shorter version of snow profile was used to optimize the time in the field. Two or three snow profiles were conducted per snow spatial survey, spaced at least 20 m apart and positioned next to SMP measurements (Fig.

This section describes the workflow used to process every SMP profile, extracting several snow mechanical properties needed for stability assessment. Three stability metrics were derived from these snow mechanical properties. Figure

Each SMP signal was visually interpreted to identify distinct layers. First, the weak layer was identified on the SMP signal next to the snow profile, based on the failure depth in the corresponding compression test. Then homogeneous layers above the weak layer were classified into slab layers (S

The skier propagation index (SPI) proposed by

The critical crack length is computed using the formulation from

Schematic representation of the workflow used to process the SMP signal to obtain the snow mechanical properties and the stability metrics. The variables and the dashed square in red are the snow mechanical properties and the three stability metrics that are analyzed and spatially estimated in this work. The parameters of the weak layer are denoted by the subscript

The first objective of this paper is to compare the scaling effect on snow mechanical properties and stability metrics for slopes prone to avalanches with different characteristics. We choose three mechanical properties: the slab thickness

The second objective of this study is to explore the link between microtopographic indicators and snow mechanical properties and stability metrics in order to estimate snow spatial variability. The scale of these microtopographic indicators is defined by the size of the moving window used to derive them. Different sizes of moving windows were used to allow for a multiscale approach describing the spatial process

All covariates were raster data with an original spatial resolution below 0.1 m and were upscaled to a spatial resolution of 0.5 m. The final resolution of the spatial model was the same as the covariates. The choice of covariates was based on multiple studies that focus on spatial variation in snow depth and is described below. Three groups of covariates, terrain shape, vegetation and microclimate, are presented in Table

Covariates used for the spatial models with the source (DTM/DSM) and additional parameters.

n/a: not applicable.

General additive models (GAMs) can represent non-linear relationships between the covariates and the response variable. GAMs have been used in the past for spatial estimation of environmental variables

The performance of our models was evaluated with the root mean square error (RMSE) and the mean absolute error (MAE) using a 10-fold cross-validation approach. This involves randomly splitting the sample into 10 subsets, fitting the model to the 9 subsets, comparing it to the remaining subset and repeating this procedure 10 times. The percentage of deviance explained (sum of squared errors) was computed to demonstrate the amount of total variance accounted for by the model. This metric is more suited to non-linear models compared to

Summary for the snow measurements of all spatial surveys. The results of the compression test (CT) results and the propagation saw test (PST) are shown according to the standards of the

The first spatial snow survey was conducted at the AR site. A weak layer of precipitation particles with an observed grain size of 0.5–1 mm was investigated on 25 February 2022 (AR22-PP), with 45 SMP measurements and a spatial extent of 71 m. The average slab thickness was 0.28 m and the mean slab density was relatively high: 252 kg m

At the RH site (RH22-PP), a weak layer of precipitation particles with an observed grain size of 0.5 to 1 mm was found beneath a relatively soft snow slab. The mean slab thickness was 0.19 m, and the mean density was 171 kg m

We conducted two spatial snow surveys at the JBC site in two different areas of the site. The first survey at this site took place on 19 January 2022 (JBC22-SH) when there was a persistent weak layer of buried surface hoar of 1–2 mm. The slab was composed of multiple layers with a mean slab thickness of 0.39 m and a mean density of 188 kg m

The last two surveys presented in Table

Figure

SMP-derived

Experimental variograms (circles) and fitted variogram models (line) for the snow mechanical properties. Note that the square root of the variance gives the absolute variation. The vertical dashed line in each variogram is the range of the fitted variogram model to the experimental variogram.

Experimental variograms (circles) and fitted variogram models (line) for the stability metrics. Note that the square root of the variance gives the absolute variation. The vertical dashed line in each variogram is the range fitted for the theoretical variogram (line) to the empirical variogram (circles).

For all spatial snow surveys, the empirical variogram showed smaller correlation lengths for the slab thickness compared to other properties, ranging from 5 to 10 m (Fig.

Boxplot of fractal dimension for snow mechanical properties and stability metrics with the four surveys in each boxplot.

At first glance, all the correlation lengths of the stability metrics were longer than those of the slab properties. Surveys at the Jim Bay Corner (JBC22-SH and JBC22-PP) showed correlation lengths around 20 m (Fig.

The fractal dimensions for the snow properties indicated a difference in surface complexity between the slab properties, the weak layer properties and the stability metrics (Fig.

The spatial models created by the GAMs explained the variance of the response variable but not entirely. The

Summary of the spatial models, model selections and performance metrics for the snow properties. The performance metrics are the following:

Summary of the spatial models, model selection and performance metrics for the stability metrics. The performance metrics are the following:

The spatial surfaces estimated by the GAMs in JBC22-SH for the snow mechanical properties are presented in Fig.

Spatial estimation of the following snow mechanical properties:

Spatial estimation of the following stability metrics:

There are no clear covariates selected by the model for every site, snow properties or stability metrics. However, some covariates were selected more frequently by the spatial models than others. The covariates most frequently used by the models, for both snow properties and stability metrics, were multiscale TPI and VRM, but their usage varied depending on the scale (Fig.

The frequency usage of covariates in the spatial GAMs. The frequency is weighted with the significance levels of the

Our study aligns with the well-known relationship between slab thickness and slab density, attributed to snow settlement. The comparison of spatial patterns between surveys indicated that these two properties exhibited similar trends in their variogram, the fractal dimension and their covariates used for spatial modelling. For further research, the empirical power law fit

Weak layer variations exhibited longer correlation lengths (smoother spatial pattern) than slab variations, and the increase in shear strength did not necessarily match the increase in the slab thickness. In general, shear strength should increase with slab thickness due to the slab load, but some variation was still present in our dataset (Fig.

This study gathers a unique dataset characterizing the spatial variation in snow mechanical properties and stability metrics at four different study sites. The comparison of variograms and fractal dimensions highlights differences in scale between slab properties and, on the other hand, weak layer properties and stability metrics (smoother patterns). Spatial GAMs were used to estimate with fair accuracy the snow mechanical properties using microtopography. However, the spatial modelling of the stability metrics was poor and not reliable. Additionally, a portion of spatial variances remained unexplained by the models, potentially due to non-spatial variances, such as instrument error or our processing data strategy. This strategy included a visual interpretation of the layer in the SMP resistance profile, as misclassification or misidentification of the weak layer boundaries can impact the result. Nevertheless, the modification of using the parametrization

The cross-validation procedure was performed by randomly selecting 10 subsets. Future work should consider the correlation length during the random selection of subsets in cross-validation procedures to ensure complete independence between subsets. This could improve the reliability of RMSE and MAE estimations. However, our 10-fold cross-validation (repeated 10 times) still provides a reliable estimation of the performance of our models.

This study aimed to use microtopographic covariates for spatial estimations of snow spatial variability and stability. Our spatial generalized additive modelling did not reveal a universal covariate that could spatially estimate both snow mechanical properties and stability metrics. The study of

Unfortunately, no link could be made between our only persistent weak layer survey consisting of surface hoar crystals (JBC22-SH) and the remaining non-persistent weak layer surveys. A bigger dataset is needed to demonstrate clear differences between persistent vs. non-persistent weak layers, as well as between alpine vs. forested areas. The covariates TPI and VRM emerged as the most significant covariates for estimating snow properties; this was also observed by previous studies using spatial models (random forest) for snow depth estimation

The transferability of our results to different sites is not feasible. The selection of covariates by the model was specific to each site, snow properties and stability metrics. As demonstrated by

The study provides insights into the spatial variability of snow mechanical properties and stability metrics. First, we show that in our dataset, the slab properties exhibit spatial patterns that were different from the weak layer spatial patterns. In fact, the slab properties, both the slab thickness and the density, had smaller correlation lengths in their variograms than the weak layer strength. The slab properties had higher fractal dimensions than the weak layer strength, which demonstrates a more “rough” spatial surface. Secondly, spatial modelling using microtopography variables allows for the estimation of snow mechanical properties with reasonable accuracy, although the reliability of stability metric estimations was poor and not reliable. We also show the usefulness of using microtopography to estimate snow spatial variability, but the selection of the indicators was specific to each study site and the snow properties. The spatial models did not predominantly select a microtopographic indicator, indicating that there is no possible extrapolation to other sites or advice to backcountry recreationists. Future research could explore the capability of multiscale microtopographic indicators, like the topographic position index (TPI) and vector ruggedness measure (VRM), to estimate spatial patterns of snow mechanical properties with 3D snow cover modelling. This may contribute to the development of predictive methods for operational avalanche forecasting services, potentially estimating avalanche release sizes through snow cover modelling and mechanical models. Additional work is needed to gather a robust dataset regarding the spatial pattern of snow mechanical properties in order to elucidate trends between different types of weak layers and terrain features.

The code and the data are available upon request.

FM conceptualized and led the research, wrote the code for the processing and analysis of the data, and drafted the paper. FG and AL conceptualized the research and reviewed the paper. AL provided the major part of the funds for the project.

At least one of the (co-)authors is a member of the editorial board of

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.

The authors would like to thank Jeff Goodrich and the Mount Revelstoke Park and Glacier National Park staff for their support. This research was also possible with the help of Claude Isabel and the Gaspésie National Park (SEPAQ) as well as Dominic Boucher and Avalanche Québec staff. The authors would also like to thank Jean-Benoît Madore, Julien Meloche, Antoine Rolland, Alex Blanchette, Jacob Laliberté and William Durand for their help in the field. We want to thank the two anonymous reviewers for their helpful and constructive comments, which significantly improved the quality of our paper. Lastly, we want to thank Jürg Schweizer for his useful comments that improved the presentation of this paper.

This project was funded by the Search and Rescue New Initiatives Fund (SAR NIF) from Public Safety Canada, the Natural Sciences and Engineering Research Council of Canada (NSERC), and the Quebec Research Funds – Nature and Technologies (FRQNT), and the Canada Foundation for Innovation (CFI) provided funding for the Station d’études montagnardes des Chic-Chocs (SEM).

This paper was edited by Jürg Schweizer and reviewed by two anonymous referees.