Climate change projections indicate that extreme snowfall is expected to increase in cold areas, i.e., at high latitudes and/or high elevation, and to decrease in warmer areas, i.e., at mid-latitudes and low elevation.
However, the magnitude of these contrasting patterns of change and their precise relations to elevation at the scale of a given mountain range remain poorly known.
This study analyzes annual maxima of daily snowfall based on the SAFRAN reanalysis spanning the time period 1959–2019 and provided within 23 massifs in the French Alps every 300

Extreme snowfall can generate casualties and economic damage.
For instance, it can cause major natural hazards (avalanche, winter storms) that might be intensified with high winds and freezing rain.
Heavy snowfall can also disrupt transportation (road, rail, and air traffic), tourism, electricity (power lines), and communication systems with a significant impact on economic services

Extreme snowfall stems from extreme precipitation occurring in a range of optimal temperatures slightly below

On a global scale, extreme precipitation is expected to increase with the augmentation of global mean temperature.
Specifically, the most intense precipitation rates are theoretically expected to roughly increase at a rate of

In the European Alps, past observations show both that the warming rate is larger than the global warming rate and that trends in extreme precipitation depend on the season and on the region.
Indeed, past trends in mean annual surface temperature point to a temperature increase in high mountain regions of central Europe, with a warming rate ranging from

In and around the French Alps, studies analyzing extreme snowfall are rare

Temporal trends in extreme snowfall with respect to elevation in and around the French Alps. Elevations are in meters above sea level (m a.s.l.).

This study addresses the gap identified above, by assessing past temporal trends in the 23 massifs of the French Alps, with special emphasis on the 100-

We study annual maxima of daily snowfall in the French Alps, which are located between Lake Geneva to the north and the Mediterranean Sea to the south (Fig.

The SAFRAN reanalysis

The SAFRAN reanalysis focuses on the elevation dependency of meteorological conditions. Indeed, this reanalysis is not produced on a regular grid but provides data for each massif every 300

The SAFRAN reanalysis has been evaluated both directly with in situ temperature and precipitation observations and indirectly with various snow depth observations compared to snow cover simulations of the model Crocus driven by SAFRAN atmospheric data

Following the block maxima approach from extreme value theory

We consider non-stationary models that depend on both elevation and time.
Such models combine a stationary random component (a fixed extreme value distribution, e.g., GEV distribution) with non-stationary deterministic functions that map each covariate to the changing parameters of the distribution

As illustrated in Table

Elevational–temporal models considered rely on the GEV distribution. For the elevational non-stationarity, the location and the scale parameters vary linearly with the elevation

First, models are fitted with the maximum likelihood method.
Let

Then, we select the model with the minimal Akaike information criterion (AIC) for each massif and range of elevations. Indeed, the AIC is the best criterion in a non-stationary context with small sample sizes

The

We study trends in return levels.
For any considered model, the time derivative of the return level

In Sect.

In Sect.

In Sect.

Changes in GEV parameters

Elevation gradients for the GEV parameters

Selected models and shape parameter values for each range of elevations in the 23 massifs of the French Alps.
We write the suffix of the name of each selected model on the map; e.g., we write

Comparison of pointwise distributions with our approach based on piecewise elevational–temporal models for the Vanoise massif.
GEV parameters

Percentages of massifs with significant/non-significant trends in 100-

According to pointwise fits, the location and scale parameters increase linearly with elevation (Fig.

In Fig.

Figure

Furthermore, we observe that the shape parameter values remain between

Figure

Figure

In Fig.

In Fig.

In Fig.

Changes in 100-

The 100-

We discuss the statistical models considered to estimate temporal trends in 100-

For small-size time series of annual maxima,
e.g., a few decades,
return level uncertainty largely depends on the uncertainty in the shape parameter

Then, we fit the models to at least two time series, i.e., from at least two elevations.
As illustrated in Fig.

Afterwards, for different ranges of elevation containing at most three consecutive elevations, we fit the models using all corresponding time series.
For each model, this ensures that the temporal non-stationarity can be assumed to not depend on the elevation.
Indeed, initially we intended for each massif to fit a single model to time series from all elevations.
However, to account for decreasing trends at low elevations and increasing trends at high elevations, this led to complex overparameterized models that often did not fit well.
We decided to consider a piecewise approach, i.e., simpler models fitted to
ranges of consecutive elevations at most separated by 900

Finally, for each range of elevations, we consider models with a temporal non-stationarity only for the location and scale parameter.
Indeed, in the literature, a linear non-stationarity is considered sometimes only for the location parameter

In Fig.

Following the evaluation of the SAFRAN reanalysis cited in Sect.

In Fig.

These changes contradict expectations based on the climatological differences between the north and south of the French Alps.
Indeed, since the north is climatologically colder than the south in both winter and summer (Fig. 5 of

Thus, this spatial pattern of changes cannot be solely explained by the spatial pattern of mean temperature. In particular, we believe that dynamical changes, i.e., heterogeneous changes in extreme precipitation in the French Alps, may have contributed to generate this contrasting pattern.
In Appendix

This contrasting pattern is observed at all elevations for changes in 100-

In practice, this increasing trend in extreme snowfall in the south should be temporary. Indeed, with climate change, temperatures are expected to shift further away from the optimal range of temperatures for extreme snowfall. Thus, in the long run, extreme snowfall is expected to decrease as the increase in extreme precipitation shall not compensate for the decreasing probability of being close to the optimal range of temperatures.

We estimate temporal trends in 100-

Many potential extensions of this work could be considered.
First, reanalyses are increasingly available at the European scale (e.g.,

A quantile–quantile (Q–Q) plot is a standard diagnosis
tool
based on the comparison of empirical quantiles (computed from the empirical distribution) and theoretical quantiles (computed from the expected distribution).
For non-stationary extreme value models, the approach is two-fold

We start by transforming the observations

Q–Q plots of the selected elevational–temporal models for the Vanoise massif for the four ranges of elevations considered (see Fig.

The transformed observations, a.k.a. residuals, are denoted as

In Fig.

In the context of maximum likelihood estimation, uncertainty related to return levels can be evaluated with the delta method, which quickly provides confidence intervals in both the stationary and the non-stationary cases

We generate

In practice, we rely on this set of GEV parameters to obtain

The 100-

Percentages of massifs with significant/non-significant trends in return levels of daily snowfall for each range of elevation and for a return period equal to

We apply the same methodology as in our study (Sect.

Changes in GEV parameters

Changes in 100-

In Fig.

Seasons when the annual maxima of daily snowfall occurred for elevation range 1 (below 1000

The full SAFRAN reanalysis on which this study is grounded is freely available on AERIS

ELR, GE, and NE designed the research. ELR performed the analysis and drafted the first version of the manuscript. All authors discussed the results and edited the manuscript.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We are grateful to Eric Gilleland for his “extRemes” R package and Ali Saeb for his “gnFit” R package. INRAE, CNRM, and IGE are members of Labex OSUG.

Erwan Le Roux holds a PhD grant from INRAE.

This paper was edited by Jürg Schweizer and reviewed by J. Ignacio López-Moreno, Sven Kotlarski, and one anonymous referee.