Multi-components ensembles of future meteorological and natural snow conditions in the Northern French Alps

This article introduces climate variations of annual-scale indicators for seasonal snow and its meteorological drivers, at 1500 m altitude in the Chartreuse mountain range in the Northern French Alps. Past and future variations were computed based on reanalysis and observations from 1958 to 2016, and using CMIP5/EURO-CORDEX GCM/RCM pairs spanning historical (1950-2005) and RCP2.6 (4), RCP4.5 and RCP8.5 (13 each) future scenarios (2006-2100). The adjusted climate 5 model runs were used to drive the multiphysics ensemble configuration of the detailed snowpack model Crocus. Uncertainty arising from physical modeling of snow accounts for 20 % typically, although the multiphysics is likely to have a much smaller impact on trends. Ensembles of climate projections are rather similar until the middle of the 21 century, and all show a continuation of the ongoing reduction in mean interannual snow conditions, and maintained interannual variability. The impact of the RCP becomes significant for the second half of the 21 century, with overall stable conditions with RCP2.6, and 10 continued degradation of snow conditions for RCP4.5 and 8.5, the latter leading to more frequent ephemeral snow conditions. Variations of local meteorological and snow conditions show significant correlation with global temperature variations. Global temperature levels on the order of 1.5◦C above pre-industrial levels correspond to a 25 % reduction of winter mean snow depth (reference 1986-2005). Even larger reduction is expected for global temperature levels exceeding 2◦C. The method can address other sectorial indicators, in the field of hydropower, mountain tourism or natural hazards. 15 Copyright statement. TEXT


Introduction
Snow on the ground is one of the most climate-sensitive components of the mountain environment.Indeed, temperature changes drive shifts of the partitioning between rain and snow precipitation, and are strongly linked with the magnitude of ablation This study uses the EURO-CORDEX dataset (Jacob et al., 2014;Kotlarski et al., 2014) available in April 2017, consisting of 6 regional climate models (RCMs) forced by 5 different global climate models (GCMs) from the CMIP5 ensemble (Taylor et al., 2012) over Europe, for the historical, RCP 2.6, RCP 4.5 and RCP 8.5 scenarios (Moss et al., 2010).Only the GCM/RCM pairs for which the geopotential data for the CMIP5 GCMs were available were used.Historical runs generally cover the period 1950-2005 and RCPs cover the period 2006-2100, with some exceptions due either to the availability of the RCM or of the GCM.Table 1 provides the different GCM/RCM combinations used in this study.In total, 43 different 0.11 • resolution (EUR 11, ≈ 12.5 km) time series of daily minimum and maximum temperature, total precipitation, longwave and shortwave incoming radiation, zonal and meridian near-surface wind speed and specific humidity were used.In order to analyze continuous longterm series (generally from 1950 to 2100 with a few exceptions), historical (HIST) and each RCP time series were concatenated (named RCP2.6,RCP4.5 and RCP8.5 in the following).The spread of this ensemble for a given RCP is due to three distinct factors: the different responses among the GCMs to a given RCP, the different responses among RCMs to a given GCM forcing, and the internal variability of climate at different time scales affecting the response of one specific model run.As in most impact studies based on EURO-CORDEX scenarios, we assume here that the 13 GCM/RCM pairs reasonably sample the overall uncertainty resulting from these 3 sources, even though not all GCM/RCM combinations are available.
The EURO-CORDEX raw surface fields were adjusted using the ADAMONT method, which is a quantile mapping and disaggregation method taking into account weather regimes to provide multi-variable hourly adjusted climate projections (Verfaillie et al., 2017).The method uses a meteorological observational dataset at hourly time resolution (here the SAFRAN meteorological reanalysis from 1980 to 2011), and regional climate model outputs covering the geographical domain of interest (here the EURO-CORDEX dataset).Raw RCM outputs for the grid point closest to the middle of the Chartreuse massif were used (see Verfaillie et al., 2017 for details).The altitude values of the RCM grid points used range from 612 to 1085 m, with a mean value across all RCMs of 880 m.Note that Verfaillie et al. (2017) have demonstrated that the ADAMONT method provides adequate results under this setting with several hundreds of meters difference between RCM and the target altitude, and that selecting RCM grid points with a larger geographical distance but lower altitude difference does not necessarily improve the outcome of the adjustment procedure.

Snowpack model
We used the Crocus (Vionnet et al., 2012) unidimensional multilayer snowpack model to predict snow conditions based on meteorological input data (both reanalysis and adjusted climate projections).Crocus computes the exchanges of energy and mass between the snow surface and the atmosphere and between the snowpack and the ground underneath.It requires sub-diurnal (ideally hourly) meteorological forcing data and is able to simulate the evolution of the snowpack over time, by accounting for several processes occurring in the snowpack, such as thermal diffusion, phase changes, metamorphism, etc.In this study, we used the ESCROC (Ensemble System CROCus) multiphysics approach described in Lafaysse et al. (2017), which consists in using multiple combinations of different physical options of the model to build an ensemble of model configurations.We Table 1.EURO-CORDEX GCM/RCM combinations used in this study (rows: RCMs, columns: GCMs), with the time period available for the HIST and RCP 4.5 and 8.5 scenarios (RCPs) specifically use ensemble E 2 as defined in Lafaysse et al. (2017) which includes a subset of 35 configurations selected to be equiprobable at CDP.The spread of this ensemble has been optimized at CDP and is able to explain about 2/3 of total error in simulations driven by meteorological measurements at CDP, which is a realistic contribution of snowpack model error to the total simulation error (Raleigh et al., 2015;Lafaysse et al., 2017).An additional configuration corresponding to the default Crocus configuration run was also used, totalling 36 model configurations.Based on meteorological and snow-related variables at daily time resolution, we computed and analyzed different indicators defined at the annual time scale, using an indicator-oriented approach described in Strasser et al. (2014).Defining "winter" as the period from December to April inclusive (5 months long), the following snow condition indicators were computed: mean 10 winter snow depth (SD), exceedance duration over a snow depth threshold for thresholds values of 5 cm, 50 cm and 1 m (ST ED 5 , ST ED 50 , ST ED 100 , expressed in days).In terms of meteorological indicators, given the focus of the present study on wintertime processes and snow conditions, we considered mean winter temperature (T ), cumulated winter total (rain and snow) precipitation (P ) and mean winter ratio between snow and total precipitation (R).Relaxing the focus on the winter time period, we also computed the maximum annual snow water equivalent ( SW E) as well as the snowpack onset and melt-out dates (SOD and SM OD), which correspond to the earliest/latest time bounds of the longest period of time with snow depth values exceeding 5 cm, which can be interpreted as the longest period of time with continuous snow cover.These indicators are meant to represent the most significant features of natural snow on the ground at the annual scale (Schmucki et al., 2014), although they are not immediately relevant for snow conditions in ski resorts (Spandre et al., 2016a;Steiger et al., 2017) and should not be the sole source of information to be used in this context.Figure 1 provides an overview of the snow-related indicators introduced above.

Statistical post-processing of indicators
The entire model chain provides estimates of a series of annual indicators spanning continuously the historical period from 1950 to 2005, typically, to the end of the 21 st century.A total of 13 GCM/RCM pairs were considered in the case of RCP4.5 and RCP8.5, out of which 4 are also available for RCP2.6.We generally used a 15-year window to assess the statistical distribution of the indicators considered.For a given GCM/RCM pair and a given RCP, statistics corresponding to a given year can be computed using indicator values for the 15 years surrounding it (7 before, the central year, and 7 after).In what follows, we assume that all GCM/RCM pairs bear equal probability (Knutti et al., 2010).We post-processed the distribution of annual indicator values in two ways.
1. Quantiles of annual values: In this case, for a given RCP, all annual values of the indicators spanning the 15 year time window for all the corresponding GCM/RCM pairs were pooled together (195 in the case of RCP4.5 and RCP8.5, 60 in the case of RCP2.6).The quantiles of the distribution of the annual values were determined using a kernel smoothing approach.We computed the 5%, 17%, 50%, 83% and 95% values (Q5, Q17, Q50, Q83, Q95), consistent with IPCC (2013).This approach provides statistical estimates for annual values of the indicator, although it mixes together the effects of interannual variability and inter-model variability.
2. Moments of multi-year averages: A running average of annual indicator values was computed using the 15 year sample window, for a given RCP and for each GCM/RCM pair.For a given RCP, mean (µ) and standard deviation (σ) values were computed for the ensemble of multi-annual averages of all GCM/RCM pairs.This approach provides information on the statistical distribution of each indicator for a given RCP on a multi-annual average perspective.In practice, we compute σ = 0.95 σ, corresponding to the 17% and 83% quantiles in the case of a normal distribution, so that this approach becomes more comparable to the annual quantiles approach described earlier.In the case of the multiphysics Crocus model implementation, we mostly used the multi-year averages approach, and applied it to all Crocus members.
The spread of the distributions of these two approaches can be assessed in rather similar ways.In the multi-year average approach, the coefficient of variation CV can be determined as CV= 2 × σ /µ.In the annual quantiles approach, the spread can be assessed by dividing Q83-Q17 by Q50 to form a formal equivalent to the coefficient of variation, defined using quantile values instead of mean and standard deviation (referred to as quantile-based coefficient of variation -QCV-hereafter).for a given r and a given t were determined.These calculations were performed for each RCP using all available GCM/RCM pairs.For the reference period 1986-2005 and future time periods, the multi-model calculations were performed using either all the GCM/RCM pairs providing RCP2.6,RCP4.5 and RCP8.5 model runs ( 4), or all the GCM/RCM providing RCP4.5 and RCP8.5 model runs (13).

Relationships between local indicators and global air temperature between reference and future time periods
For the reference period 1986-2005 and for three 30 year periods during the 21 st century (beginning of century (BOC), 2011-2040, middle of century (MOD) 2041-2070 and end of century (EOC), 2071-2100), we computed interannual mean values corresponding to a given GCM/RCM pair for the meteorological and snow indicators introduced above, for all RCPs available for a given GCM/RCM pair (either RCP4.5 and RCP8.5 only, or all three RCP2.6,RCP4.5 and RCP8.5 scenarios).For each GCM/RCM model run under each available RCP configuration, the global temperature difference between future time periods (BOC, MOC and EOC, respectively) and the pre-industrial period (1851-1880), referred to as ∆T g,BOC−P I , ∆T g,M OC−P I and ∆T g,EOC−P I , respectively, for the corresponding GCM and RCP was calculated (Taylor et al., 2012).In addition, the global temperature difference was also computed between future periods (BOC, MOC and EOC) and the reference (Ref) given bin were computed.

Comparison between results of numerical simulations and observations
On the basis of the annual values of the indicators SD, T and P for the time period from 1986 to 2005, statistics of the differences between reanalysis data and Col de Porte observations were computed, in terms of mean bias, root mean square deviation (RMSD) and correlation (only T , P ).This is not meant to represent an evaluation of the SAFRAN-Crocus reanalysis, because the SAFRAN dataset used in this study was not optimized to correspond exactly to the geographical setting of the Col de Porte observation site (appropriate altitude, specific terrain masks impacting solar radiation time distribution).However, the geographical setting of the observations and simulations are sufficiently close to each other that the two can be analyzed concurrently and provide reasonable information pertaining to the ability of the model chain to represent meteorological conditions in such a mountainous area.A better statistical match between observation and reanalysis would however be expected using meteorological data more applicable to the observation configuration, which is not the purpose of this article and was addressed in previous publications (Durand et al., 2009b;Lafaysse et al., 2013).

Results
This study introduces multi-component ensembles of past and future simulations of meteorological and snow conditions in the Chartreuse mountain range in the Northern French Alps at 1500 m altitude.As described previously, simulations encompass multiple RCPs, multiple GCM/RCM pairs from the EURO-CORDEX database adjusted using the ADAMONT method, and multiple Crocus snowpack model runs using the ESCROC ensemble system.This section describes the wealth of information generated through this process, focussing on meteorological and snow indicators described previously and addressing various components of the uncertainty and variability sources affecting the simulations.

Full ensemble configuration and uncertainty apportionment
Figures 2-3 provide an overview of all sources of uncertainty and variability accounted for in this study, in terms of snow conditions (using the SD indicator as an example) for the period from 1950 to 2100, for RCP4.5 and RCP8.5 climate projection data respectively.
Figures 2a and 3a show continuous time series of annual values of mean winter snow depth data (SD), either observed or generated by the default snowpack model configuration fed by meteorological data from a reanalysis or an adjusted RCM for RCP4.5 and 8.5.They highlight the significant interannual variability in observed, reanalyzed and climate model datasets.
For the time period 1986-2005, the mean observed SD value is 0.64 m.Using the default Crocus configuration fed by the SAFRAN reanalysis at 1500 m altitude yields bias and RMSD values of annual SD values of 0.10 m and 0.18 m, respectively, against the Col de Porte observational record, which falls within the commonly accepted range of snowpack modeling errors at observing stations when models are driven by meteorological observations (Essery et al., 2013;Lafaysse et al., 2017).The mean observed T value over the same period is 0.9   adjustment method.This could partly explain why the uncertainty of GCM/RCM appears lower than the multiphysics uncertainty during the historical period, in combination with the deeper snowpack in the historical period.The relative proportion of these two components was estimated as the simple ratio of the corresponding variance values to the total variance value.
The variance is used in this comparison because the variances of both factors would be additive if they were independent (the interaction term is neglected here).It shows that the ESCROC component plays in the future period a smaller role than the GCM/RCM component, decreasing over time.This shows that the uncertainty arising from snowpack modeling errors plays a significant (always more than 15% of variance), although secondary role, for future climate projections.Furthermore, we anticipate that the impact of snowpack modeling uncertainties plays an even smaller role when focusing on relative changes of simulated snow conditions because for one given GCM/RCM the different ESCROC members are usually ranked in a similar order all along the simulation period.For these reasons, we focus below on modeling results solely using the default Crocus model configuration and not the multiphysics ensemble.This is further discussed in the Discussion section.

Projections of multi-RCP annual quantile values
Fifteen-year sliding quantiles for annual indicators of snow and meteorological conditions are displayed in Fig. 4. Figures for each RCP taken separately are available in the Supporting Information (Figs.S1-S3).Values for specific time periods (highlighted in Fig. 4) are provided in Table 2 and in Table S1 of the Supporting Information.For the reference period 1986-2005, the median of annual values of SD, snow onset date (SOD) and snow melt-out date (SM OD) is consistent between observations, reanalysis and simulations driven by adjusted historical climate model simulations (HIST using 13 GCM/RCM pairs), with some differences.For example, as can be observed in Table 2, while the SOD median value is similar between observations and simulations (within 1 day), the SM OD median value occurs approximately 10 days later in the reanalysis than in observations, consistent with the 3 cm deviation between the median value of reanalysis-driven and observed SD.Simulations driven by adjusted historical climate model runs indicate slightly less snow than observations and reanalysis.Similar features can be identified in terms of ST ED values in Table S1 of the Supporting Information.
In the case where a smaller number of GCM/RCM pairs are considered for the same time period HIST, i.e. when only the 4 GCM/RCM pairs for which RCP2.6 model runs are available and not the 13 GCM/RCM pairs for which RCP4.5 and RCP8.5     2 and S1) show very small deviation to the values obtained with 13 GCM/RCM pairs.Quantile values differ by up to 3 cm for SD (≈10%), 14 kg m −2 for SW E (≈6%) and 3 days for SOD and SM OD.For ST ED quantile values, the largest difference is 5 days (≈15%).This shows that in terms of statistical distributions of annual values of the indicators, the sub-ensemble of four GCM/RCM pairs for which RCP2.6 are available exhibits similar statistical features than the full ensemble of 13 GCM/RCM pairs, in terms of mean trends and spread.
At the scale of 20-year spaced future intervals provided in Tables 2 and S1 decrease.However the interquantile Q83-Q17 value remains rather constant throughout the century, in comparison with the reference period, except in the late 21 st century under RCP8.5 where snow conditions become increasingly ephemeral.For example, in the case of SD, the Q83-Q17 value of 0.72 m for the reference period varies for future conditions between 0.62 m and 0.67 m for RCP2.6, 0.50 m and 0.66 m for RCP4.5 and 0.16 m and 0.64 m for RCP8.5 (lowest value at the end of the century).The variability of snow conditions is therefore projected to remain significant, as large as currently encountered as long as snow conditions remain comparable.
The SD quantile-based coefficient of variation (QCV=(Q83-Q17)/Q50) for the reference period is equal to 1.14, which means that the spread between the Q17 and Q83 quantile values, which comprise 2/3 of the values potentially obtained for a given winter, exceeds the median value itself, highlighting quantitatively how variable snow conditions can be from one winter to the next.For future conditions, QCV values are never found to be lower than the reference value, and vary between 1.46 and 1.81 for RCP2.6, 1.43 and 2.08 for RCP4.5, and 1.42 and 2.67 for RCP8.5.This indicates that, with the gradual decrease of median and other quantile values for SD, the interannual/intermodel variability is projected to remain significant and even increase in relative terms (compared to the median value).Very similar results can be obtained when considering SW E. In the case of ST ED values, however, the situation is different especially for ST ED 50 and ST ED 100 because the number of snow-scarce winter increase will directly lower the Q83 quantile value while the Q17 quantile value is bounded by 0 and already equal to this value in the early 21 st century for all RCPs for ST ED 100 and approaching it by the middle of the 21 st century for all RCPs (including RCP2.6) in the case of ST ED 50 .In contrast to Fig. 4, by design Fig. 5 suppresses most of the effects of the interannual variability, focussing on long-term trends and highlighting the uncertainty components originating from global and regional climate models.As illustrated in Tables 3 and S2, the uncertainty pertaining to multi-annual / multi-model averages is computed based on the standard deviation of the mean of the multi-model multi-annual averages over sliding time periods, as described above.Values for σ ( = 0.95 σ)

Projections of multi-RCP multi-annual mean values
are generally lower for the HIST 1986-2005 period than for the future periods centered on 2030, 2050, 2070 and 2090.For example, σ for SD over the HIST 1986-2005 period is equal to 0.06 m, while for all future periods, it is rather on the order of 0.06-0.12m, except for RCP8.5 towards the end of the century, with σ values 0.06 m, but associated to significantly lower µ values on the order of 0.09-0.17m.A similar observation can be made for SW E, SOD, SM OD and ST ED values.
In terms of absolute values, as illustrated in Fig. 5, and indicated in Tables 3 and S2  reanalysis data.This is consistent with the only slight deviation observed between median values in the previous section.
As shown in Fig. 5a, the decadal dynamics however differs, with snow conditions (observed and reanalyzed) showing rather stable conditions in the 1970s followed by abrupt change in the mid-1980s, followed by another period of relative stability.
Simulations driven by climate model data show a different pattern of SD changes, with an earlier reduction in the 1970s, followed by a relative increase in the 1980s followed by another reduction in the 1990s onwards.The length of the observation, reanalysis and historical climate records is too small to generalize, but all three sources of information point towards low frequency fluctuations at the decadal time scale, superimposing on a long-term trend of general snow reduction.
At the scale of 20-year spaced future intervals provided in Tables 3 and S2, similarly to the results of the annual quantiles approach, all snow-related indicators exhibit a trend towards gradually increased snow scarcity.Also similarly, in most cases, climate projections for the 15-year periods centered around 2030 and 2050 depend only slightly if at all on the RCP, the 10 periods centered around 2070 and 2090 show significant deviations between RCPs, with reinforced downwards trends for RCP8.5-basedindicators, pursued decrease under RCP4.5 and stabilization or reduced decreasing trend for RCP2.6.Similarly to the previous section, the values of the indicators are calculated for the reference period either taking into account the 4 model pairs available in RCP2.6 (HIST** ) or the 13 pairs for which RCP4.5 and RCP8.5 are available, see in Tables 3-4 and S2.Mean values are only slightly impacted for some indicators (e.g., for SW E or P ).This shows that at the interannual time scales, the sub-ensemble of four GCM/RCM pairs for which RCP2.6 are available exhibits similar statistical features than the full ensemble of 13 GCM/RCM pairs, in terms of mean trends and spread.

5
The SD coefficient of variation (CV=2×σ /µ) for the reference period is equal to 0.18, which illustrates well the suppression of the interannual variability effect.This corresponds to only 16% of the QCV (see above), which indicates that for the reference period and for this case, the interannual variability of annual indicator values plays a stronger role than the inter-model spread for a given year.For future conditions, CV tends to increase, but this is more due to a decrease of µ in all cases than to σ differences, as shown above.CV remains always smaller than QCV, which indicates that, regardless of the scenario and the 10 time period in the future, the variability/uncertainty related to the inter-model spread (for a given RCP and time period) remains always lower than the inter-annual fluctuations.
Table 4 provides a summary of the meteorological conditions associated to the past and future snow conditions addressed in this study, in terms of multi-annual means.While the mean winter temperature value for the reference period 1986-2005 is on the order of 0.4 -0.9 • C in the Chartreuse mountain range at 1500 m depending on whether the SAFRAN reanalysis or the historical climate runs are considered, the 15-year period centered on 2030 already exhibits a mean increase of +1.0 ± 0.3 • C regardless of the RCP.The results for the three RCPs already differentiate for the 2050 lead time, and the difference continues to widen until the end of the century with +1.4 ± 0.4 • C for RCP2.6, +2.3 ± 0.6 • C for RCP4.5 and +4.6 ± 0.7 • C for RCP8.5.
While the temperature trends are unequivocal, there is no significant trend for total winter precipitation, as shown in Table 4.
The snow/rain precipitation ratio is projected to evolve markedly along with the temperature rise, with a maximum reduction by 37.3 ± 5.1% of the snow precipitation share over the total winter precipitation.With the notable exception of the cumulated winter precipitation P , all indicators show consistent relationship with ∆T g .The slope of the regression curve is very similar for all three future time periods BOC, MOC and EOC, as well as when all future time periods are pooled together.The maximum correlation is found for the snow precipitation ratio with a coefficient of determination of 0.90, followed by local air temperature with a coefficient of determination of 0.86.The worst correlation is found for ST ED 100 (R 2 =0.48 for all time periods).All snow-related indicators R 2 values range between 0.76 and 0.83 (for all future time periods together), with a trend to lower values for BOC only time period, and higher values for EOC and all time periods together.The slope of the regression curve, in terms of % change per global Relating to specific target values of global surface air temperature changes since the pre-industrial period, Figure 6 and the data provided in Table 6 show for example that for a global temperature increase of 1.5 • C compared to the pre-industrial period, the mean change of mean snow depth at 1500 m altitude in the Chartreuse mountain range is in the order of -25%, and this value increases very rapidly with increasing global temperature changes, reaching reductions of 65% for 3 • C global temperature values and local impacts is not unequivocal.This is materialized by the standard deviation provided in Table 6.

Relationship between global temperature trends and local snow and meteorological conditions
The same applies in terms of trends to all local meteorological and snow indicators (except total precipitation, as noted before).

Discussion
This study is based on a multi-component ensemble framework in order to provide future values of meteorological and snow conditions at a typical mid-altitude (1500 m) mountain range in the Northern French Alps, accounting for these uncertainty and variability sources in the most consistent and rigorous possible manner.To this end, a multi-component ensemble framework was designed and built, addressing various sources of uncertainty and variability, i.e. several RCPs (RCP 2.6, RCP 4.5 and RCP8.5), feeding several GCM model runs from the CMIP5 intercomparison exercise, which themselves feed various RCM model runs as part of the EURO-CORDEX downscaling exercise, which are adjusted using the ADAMONT method against the meteorological reanalysis product SAFRAN, making it possible to drive a multi-physical version of the energy balance multi-layer snowpack model Crocus.Here we discuss the results obtained for the period from 1950 to 2100, in comparison to reanalysis and comparable observation data for the past period, and with other existing scientific studies for future conditions.

On the comparability between adjusted historical climate model runs and observations and reanalyses
As shown in section 3.1, SAFRAN and Crocus (either multiphysics or default configuration) results show acceptable performance metrics compared to in-situ observations of meteorological conditions and snow conditions, respectively.By definition no performance metrics pertaining to annual fluctuations can be computed between the adjusted climate output and either observations or reanalysis data, because the two are not designed to exhibit synchronous fluctuations.Only multi-annual statistics may be compared, under certain assumptions, which is done in sections 3.2 and 3.3, for the snow indicators defined in this study.Indeed, even over a time scale of 20 years, it is likely and even expected that low frequency variability in the climate, in nature and as it is represented in GCMs, leads to deviations at this time scale, which the statistical adjustment method can only partially mitigate.For the reference period 1986-2005, the match between observation and reanalysis data, and historical GCM/RCM runs is nevertheless satisfying.However, it is also clear from Fig. 4 and Fig. 5 that the match is not as good for a period extending back into the past, with a tendency for adjusted climate model data to provide reduced snow conditions compared to observed and reanalyzed data for the period before 1985.While the reasons for such a behaviour are likely multiple, it is certainly influenced by the fact that this period is almost independent from the time period for calibration of the ADAMONT adjustment method , and during which major climate shifts occurred (Reid et al., 2015).This could also be due to the fact that Crocus model outputs result from the interaction between various meteorological variables, both in terms of mean values but also their day to day fluctuations, especially precipitation and temperature conditions which together yield either to rain or snow precipitation.By design, the ADAMONT method adjusts the variables independently from each other (Verfaillie et al., 2017).Even if special care is taken to minimize the disadvantages of this approach, such as the use of weather regimes for the quantile mapping statistical adjustment method, or applying the final quantile mapping separately to rain and snow precipitation in order to mitigate detrimental interactions between temperature and precipitation (Verfaillie et al., 2017), some interaction terms probably remain uncorrected.The adjustment method also probably exerts an influence on the variability during the historical period, which may be responsible for the overall lower spread (either expressed in terms of quantile-based coefficient of variation of annual values or the coefficient of variation of the interannual means) compared to future projections.Indeed, by design the adjustment method attempts to bring reanalysis meteorological data and historical model runs to the same ground in terms of quantile distributions, which inevitably reduces the spread between different GCM/RCM pairs.This is visible in the analyzed results, because the reference time period used 1986-2005 is included in the period used for the statistical adjustment method.In addition, the lower spread, compared to future periods of 15 years, could also be due to the fact that the reference period is longer than the future time periods considered, so that a wider range of climate conditions are sampled in the multi-annual mean, thereby bringing closer the values originating from the various RCMs.

Uncertainty and variability sources
The study uses multi-component ensembles to address uncertainty and variability sources, which are analyzed through indicators computed using various sub-ensembles.Based on the results shown above, it clearly appears that snowpack modeling errors, due to uncertain physical knowledge of processes at play and their imperfect implementation in the model, can be responsible for a significant fraction of the uncertainty pertaining to future climate projections, consistent with previous results obtained based on observations at instrumented sites (Essery et al., 2013;Lafaysse et al., 2017).While this must be taken into account for a fully comprehensive assessment, evidence from this study suggests that, under the conditions of the Northern French Alps and after the middle of the 21 st century, the uncertainty component attributed to the snowpack modeling errors alone is on the order of 20%, which is significant but of second order compared to the spread originating from multiple climate models.
Because the number of GCM/RCM model pairs was different for RCP2.6 (4) and RCP4.5 and RCP8.5 (13), we compared the statistics for indicators during the historical period based on the 4 RCP2.6 pairs alone, as well as the full ensemble of 13 GCM/RCM pairs.Both in terms of statistics distributions of annual values for a period of 20 years (1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005) or in terms of multi-model spread of multi-annual average values, results were extremely close for the full and sub-ensemble.While it remains desirable, when possible, to use the largest possible number of different GCM/RCM pairs in order to mitigate the impact of multi-model variability and climate internal variability, this tends to show that, in this case, robust results can be obtained using a subset of a few models dealt with appropriately.However, as shown in Figure 6, individual GCM/RCM pairs only sample imperfectly the range of possible future climate conditions, so that choosing, randomly or not, a too small number of GCM/RCM pairs, would inevitably lead to biased results.This is consistent with the fact that the variability of snow conditions is primarily dominated by interannual variability, over which inter-model spread superimposes an additional uncertainty component.It is very likely that the 4 GCM/RCM pairs used in this study, which feature RCP2.6,RCP4.5 and RCP8.5 model results, possess appropriate interannual variability properties and overall no major deviation from the average behaviour of the full ensemble of 13 GCM/RCM pairs, which leads to the fact that similar statistics are found for these 4 model pairs as for the full ensemble of thirteen.It is not certain that a similar result would be obtained by picking randomly 4 GCM/RCM pairs within the full ensemble available (see Figure 6 for contrasted individual model behaviour).

General trends and added value of the approach developed
That natural snow conditions at 1500 m in the Northern French Alps are projected to decrease under ongoing climate change is an expected result, which deserves however to be put in perspective with other existing studies on the matter.Figures 4-5 and Tables 2 and 3 indicate a general decreasing trend in SD towards the end of the century (≈ −0.8 cm per decade for RCP2.6, −3.2 cm per decade for RCP4.5 and −6.5 cm per decade for RCP8.5 over the period 2030-2090), accompanied by a shortening of the snow season (later SOD and earlier SM OD).This is consistent with previous results from Steger et al. (2013) for the 1000 -1500 m a.s.l.range in the European Alps.The magnitude of the SD decrease is similar to the one found by Marty et al. (2017a) for the Aare and Grisons regions in Switzerland, although their GCM/RCM models and future scenarios differ from ours.This trend is visible for all scenarios, but stronger for RCP8.5.At the end of the century, simulations carried out under this scenario predict an increasingly ephemeral snow cover (multi-annual mean value of 9 ± 6 cm for the 2090 time slot, see Table 3) and more frequent seasons with barely any snow on the ground (Figs.4-5 and Tables 2 and 3).The shortening of the snow season is projected to become asymetric towards the end of the century, with a stronger reduction in spring than in autumn (Tables 2 and 3), similar to findings from Steger et al. (2013) and Marty et al. (2017a).The decreasing SD trend is also combined with a decreasing SW E trend (≈ -6 kg m −2 per decade for RCP2.6, -18 kg m −2 per decade for RCP4.5 and -35 kg m −2 per decade for RCP8.5 over the period 2030-2090, Table 3) and decreasing trends of ST ED 5 (as in Marty et al. (2017a)), ST ED 50 and ST ED 100 (Table S2).4).Values for the change in T and P are comparable to Steger et al. (2013) and Marty et al. (2017a), even though their GCM/RCM models and future scenarios differ from ours.The insignificant trend in P and its variable sign depending on the projections is fully consistent with previous studies identifying the internal variability of climate as the main uncertainty component for precipitation in the Alpine region all along the 21 st century (Lafaysse et al., 2014;Fatichi et al., 2014).Table 4 further shows a strong decrease in R (by 2090, -12.0 ± 2.3% for RCP2.6, -17.7 ± 5.6% for RCP4.5 and-37.3 ± 5.1% for RCP8.5, compared to 1986-2005), with values very similar to Frei et al. (2018).
The comparison of trends of meteorological indicators (temperature, total precipitation and ratio of snow to total precipitation) and indicators characterizing the state of snow on the ground provides insights into the physical mechanisms responsible for changes in snow conditions.The snowpack is progressively initiated and complemented by precipitation events during the wintertime, and it is thus unsurprising and consistent with previous evidence that the decline in snow precipitation is one of the main responsible for the decline in snow conditions, even if total precipitation does not exhibit any significant trend (Steger et al., 2013;Gobiet et al., 2014;Castebrunet et al., 2014;Lafaysse et al., 2014;Schmucki et al., 2014;Beniston et al., 2018).
That the reduction of the snow season is asymmetrical with a stronger reduction in the spring than in autumn is consistent with the fact that not only snow precipitation amounts drive the response of the snowpack to climate change, but also the intensity of the melt rate, which also depends on atmospheric conditions and is enhanced under warmer conditions (e.g., Steger et al., 2013;Pierce and Cayan, 2013).The data sets underpinning the present study could be used to address in a more quantitative manner the physical processes responsible for the results of the simulations, however this falls beyond the scope of this study (e.g., Pierce and Cayan, 2013).
Beyond the general trends, which provide an unsurprising -yet required-update of previous assessments based on older climate scenarios applied to the French Alps (e.g., Rousselot et al., 2012;Castebrunet et al., 2014;Piazza et al., 2014), the main added value of the approach developed here lies in its ability to capture high-order moments of possible snow futures.For example, that the year-to-year variability of snow conditions on the ground remains as large as currently, and even increases in relative terms (until the middle of the century for all RCPs, and towards the end of the century for all RCPs except RCP8.5), may be of equal, if not higher significance, to stakeholders operating in the alpine environment, than the long term trends.
Such results can only be attained making use of a sufficiently large number of independent global and regional climate models, the EURO-CORDEX database corresponding to a significant achievement of the climate modeling community enabling such impact studies to take place.
Many of the results discussed above indicate a strong consistency between our results and results obtained using deltachange methods, in French mountain regions as well as in Switzerland (e.g., Castebrunet et al., 2014;Schmucki et al., 2014).
This consistency is shown for multi-annual multi-model trends on snow depth or snow water equivalent mean values, but cannot be assessed regarding the interannual variability because this is generally not addressed in these studies.The model chain implemented here, explicitly making use of the intra-seasonal and inter-seasonal RCM chronology, inherently captures more appropriately potential changes in timing of meteorological conditions, in particular precipitation.Differences between the current study and studies based on delta-change approaches would be expected under a situation where the chronology of precipitation would differ significantly in the future, because the delta-change approach would only modify the air temperature and rain/snow partitioning, but not the timing of the events.These changes in the multivariate chronology of meteorological events in the Alpine region have not been investigated in details until now to the best of our knowledge, although their stationarity is a requirement for the validity of the delta-change method.Furthermore, although our results do not exhibit significant changes in the interannual variability of the snow indicators, this is a result of our projections whereas it is only an assumption when applying a delta-change method.More in-depth comparisons between outputs of delta-change approaches and direct adjustments to RCM output could be carried out in the future, but are beyond the scope of this article.

Link with global temperature increase
The international framework for climate negotiations, culminating at the yearly Conferences Of Parties (COP), and basing the technical part of its decision process on IPCC assessments, shows a strong tendency to focus on global temperature changes.
In recent years, there has been increasing societal demand for quantifying the local impacts of global warming levels since the pre-industrial time period of 1.5 • C, 2 • C and beyond.While for a number of reason this approach is limited and only partially represents climate change (Rogelj et al., 2015;Millar et al., 2017;James et al., 2017), its infusion in the public debate at all levels, from the international, national and even local level, makes it relevant to discuss and illustrate local impacts of global climate change.With Figure 6 and Tables 5 and 6 we provide such a link, thereby highlighting the specific sensitivity of the mountain meteorological and snow conditions to global climate conditions.Such figures allow stakeholders interested in snow and meteorological conditions at the local scale to directly infer the consequences of climate policies in their socio-economic domain (James et al., 2017;Marty et al., 2017a).However, using only such an approach with a focus on the end of the 21 st century, may lower the impact of the results and the motivation of stakeholders, if the consequences appear too distant in time.The power of the approach shown in this article, is that, not only it makes it possible to infer EOC impacts of climate change, but also provides a continuous vision of past and current climate context, and its most likely evolution according to state-of-the-art GCM/RCM pairs driven by RCPs.Furthermore, our results indicate that the response of local meteorological and snow conditions is essentially the same regardless whether data from the beginning or end of the century are sampled.This indicates that the seasonal snowpack at this location and altitude level responds in a linear and reversible way to global-scale climate change, and the near-term and mid-term responses can be used, in addition to the end of century information, to infer the relationship between local and global conditions using a larger dataset thereby providing more robust assessments of the influence of the global air temperature on local snow and meteorological data.This is all the more relevant in that none of the GCMs used for this study predict EOC warming below 1.5 • C compared to pre-industrial levels, so that using less distant future time periods makes it possible to assess the response of the local snow conditions to 1.5 • C and 2 • C difference in a more robust way than EOC only (see Table 6) (James et al., 2017).Even for the lowest level of global warming, none of the model results predict that local snow conditions will be unaffected by climate change, the minimum level of decrease of mean winter snow depth being on the order of 25% for 1.5 • C global increase since pre-industrial period.
In more details, these results highlight several discussion points.First of all, it is remarkable that the regression line of the local mean winter temperature with global temperature increase shows a slope of 1.1 • C • C −1 , which represents a low additional warming of the mountain environment in contrast to previous studies (Durand et al., 2009a;Pepin et al., 2015).This result may stem in part from the fact that although elevation dependent warming is generally maximal in the fall and springtime, our target period covers mostly wintertime.Alternatively, this low enhancement factor could be due to the fact that the RCM grid points used for our analysis are at lower altitudes, from 612 to 1085 m, with a mean value across all RCMs of 880 m.Snow conditions at such altitude levels are generally limited already at present time, so that the local snow albedo feedback which drives much the elevation warming (Pepin et al., 2015) may be limited at such a low elevation.Addressing this issue in more detail is left open for future research, as it may imply that the temperature trends identified in this study are underestimated for this reason.Second, it is interesting to note that the relationship between snow conditions and global air temperature is different for winter mean snow depth and peak SWE.The latter shows a lower sensitivity (-20% • C −1 ) than mean snow depth (-25% • C −1 ), see Table 5.While this is first due to the different nature of the indicators (peak SWE value vs. mean winter snow depth value), this may also be due to the fact that rain on snow events (whose frequency is projected to increase) can positively contribute to SWE, through refreezing of the precipitation water in the snowpack, while not contributing to increasing snow depth.This shows that the difference of response of the snow-related indicators must be carefully assessed depending on the target environmental or socio-economic domain of interest, because specific snow-related variables may provide distinct messages regarding their impact (Pierce and Cayan, 2013).While global temperature is well correlated to the snow indicators, the slope of the regression curve is not the same for all indicators, illustrating the usefulness of using a detailed snowpack model to predict the impact of climate change of snow conditions, accounting for a maximum amount of processes operating at the boundaries and within the snowpack.Nevertheless, the significant correlation between 30-years average global temperature difference to pre-industrial levels of the GCMs, and the local effects on air temperature and snow conditions simulated using the same driving GCMs processed by means of a cascade of physically-based (RCM) and statistical (ADAMONT) downscaling and adjustment methods, followed by the use a multi-layer energy and mass balance snowpack model (Crocus), is consistent with the fact that (i) 30-years average regional and local temperature in the European Alps are strongly and directly influenced by the global climate and (ii) the multi-annual mean response of the snowpack at 1500 m altitude is substantially governed by and responds to multi-annual mean local air temperature..

Conclusions
This study introduced a multi-component ensemble framework in order to provide future values of meteorological and snow conditions in mountainous regions, exemplified for a typical mid-altitude (1500 m) mountain range in the Northern French Alps.The multi-component ensemble framework makes it possible to account for the various sources of uncertainty and variability that affect future climate projections, some of which are neglected in both previous and ongoing climate change impact studies.The multi-ensemble framework developed here draws on several RCPs (RCP 2.6, RCP 4.5 and RCP8.5), feeding several GCM model runs from the CMIP5 intercomparison exercise, which themselves feed various RCP model runs from the EURO-CORDEX downscaling exercise.Those are adjusted using the refined quantile mapping method ADAMONT against the meteorological reanalysis SAFRAN, making it possible to drive a multi-physical version of the energy balance multi-layer snowpack model Crocus.The method defines a series of annual snow and meteorological indicators that represent various aspects of the winter season (mean annual snow depth, peak Snow Water Equivalent, date of inception and melt out of the snowpack, mean air temperature, cumulated winter precipitation etc.), which are computed from daily values of the variables representing meteorological and snow conditions (here temperature, precipitation, snow depth and SWE).
Based on an analysis of various sub-ensembles of past, current and future observations and simulations, spanning the period from 1950 to 2100, and focussing on this particular yet representative geographical setting, the main conclusions of this study are that: -Uncertainty arising from physical modeling of snow after the middle of the century can account to 20% typically of the simulation results, although the multiphysics is likely to have a much smaller impact on trends, because of the systematic nature of a large fraction of the error sources considered.
-The ADAMONT method appropriately adjusts the output of the EURO-CORDEX GCM/RCM model runs, making it possible to drive an energy balance land surface model such as Crocus based on the chronology of the driving climate model, thereby leveraging the caveats of using delta-change methods applied to past observations, which do not make it possible to take into account differences in seasonality or climatically-variable weather patterns (blocking, extreme precipitation events, etc.).The method can be readily applied to the next generation of climate model runs, generated using refined greenhouse gas emission scenarios and/or improved model components (Rogelj et al., 2015;Millar et al., 2017).This should make it possible to update climate change impact assessments more quickly than previously, thereby reducing the phase lag between the production of assessments of global, regional and local climate change and of its impacts.
-The four GCM/RCM models within the EURO-CORDEX ensemble, which provided not only RCP4.5 and RCP8.5, but also RCP2.6 model runs, exhibit similar statistics at the interannual and multi-annual scale as the full 13-member ensemble, making results obtained for RCP2.6 comparable with results obtained for RCP4.5 and RCP8.5 even though they are not based on the same number of models.This result may not generalize to any sub-ensemble of the available GCM/RCM runs of EURO-CORDEX, therefore we consider it preferable to use as many as possible GCM/RCM model runs in ensemble-based assessments.
-Projections of meteorological and snow conditions corresponding to RCP2.6, RCP4.5 and RCP8.5 show similar behaviour until the middle of the 21 st century.They all exhibit significant interannual variability, and a long term trend of increasing snow scarcity.Our study shows that, for this location, the interannual variability is larger than inter-model spread for a given RCP.
-The impact of the RCP becomes significant for the second half of the 21 st century, with overall stable conditions under the RCP2.6 scenario, and continued degradation of snow conditions along with increased air temperature for RCP4.5 and 8.5, the latter leading to frequent occurrence of ephemeral or nearly snow-free conditions at the end of the century.
-Changes of local meteorological and snow conditions show significant correlations with global temperature levels (using 30 year means), with respect to pre-industrial levels.For example, the change in mean snow depth at 1500 m altitude in the Chartreuse mountain range is in the order of -25% and -32% for a 1.5 • C and 2 • C global temperature rise, respectively, with respect to pre-industrial levels, and the magnitude of the impact consistently increases along with global mean temperature reaching reductions of 80% for 4 • C of global warming.
While this work provides scientific results directly exploitable for snow and meteorological conditions at 1500 m altitude in the Chartreuse mountain range, our results do not directly allow extrapolation of the conclusions in other mountain regions in France or other elevations.It is, however, expected that the response of neighbouring mountain ranges may be comparable at the same altitude level, because their behaviour in the past (Durand et al., 2009b, a) and in previous studies addressing future changes (Rousselot et al., 2012;Castebrunet et al., 2014) was generally rather similar.This remains to be explored more quantitatively and will be the topic of upcoming studies, based on the methodological framework introduced here and the data available in the SAFRAN reanalysis for the French Alps and Pyrenees (Durand et al., 2009b, a;Maris et al., 2009).The method can obviously be applied beyond French borders, provided that an adequate long-term observational dataset can be used as a basis for RCM output adjustment using the ADAMONT method (Verfaillie et al., 2017).
Beyond the geographical scope, which can be extended to address a wider diversity of territorial climate-related challenges, sector-specific further applications can now be considered.For example, the adjusted climate scenarios can be projected on sloping surfaces, making it possible to address the impact of climate change on avalanche hazard using Crocus model runs, thereby upgrading and consolidating the results of Castebrunet et al. (2014).Also, the adjusted climate scenarios could be employed to simulate snow conditions on ski slopes in French ski resorts, drawing on the method developed by François et al. (2014) to be applied using the version of Crocus accounting explicitly for snowmaking and grooming (Spandre et al., 2016b).This method has shown significant potential to account simultaneously for the impact of natural snow precipitation and temperature conditions (driving the capability to produce snow) on the operating capabilities of alpine ski resorts over the past decades (Spandre et al., Under Review).It is now ready to be applied for future conditions, drawing on the framework developed in this study.It must be emphasized that while the projected changes in meteorological and natural snow conditions shown in this work are likely to affect operating conditions of ski resorts, no quantitative conclusions can be drawn on this topic.Indeed, snow management practices, especially snowmaking, play an essential role in their operations, and they should be accounted for in studies specifically addressing the impact of climate change on this socio-economic sector (Hanzer et al., 2014;Spandre et al., 2016b;Steiger et al., 2017).Beyond these applications to seasonal snow, the method is ready to use for a wide range of environmental impact studies addressing various mountain features potentially affected by climate change, such as natural hazards, cryospheric components (glaciers and permafrost), water resources including hydropower, ecosystems functioning and the impact of their changes on human societies.
ONERC, in the framework of the ADAMONT project, from the Interreg project POCTEFA/Clim'Py and from the IDEX Univ.Grenoble Alpes Cross Disciplinary Project "Trajectories".CNRM/CEN and Irstea are part of LabEX OSUG@2020 (ANR10 LABX56).We thank the two anonymous reviewers and the Editor Ross Brown for useful and constructive comments.

Figure 1 .
Figure 1.Overview of the snow-related indicators introduced in section 2.5, using an arbitrary SWE and snow depth time series over the course of a given year.Top : SWE time series, displaying the maximum value SW E. Bottom : snow depth time series, displaying graphically the related indicators.See text for details.
period 1986-2005 ∆T g,BOC−Ref , ∆T g,M OC−Ref and ∆T g,EOC−Ref , respectively.Based on these datasets, we computed linear regressions curves (intercept forced to 0) between interannual means of the local meteorological and snow indicators during BOC, MOC and EOC, and the corresponding global annual temperature difference between the corresponding time period and the Ref period.Linear regressions were also computed using all future time periods together (ALL).In addition, the future values of the local meteorological and snow indicators of all future time periods were binned according to the corresponding global temperature by steps of 0.5 • C (± 0.25 • C), and the mean and standard deviation of all values within a respectively.This corresponds to the second statistical post-processing described in Section 2.5.2 which removes the interannual variability and allows an easier quantification of each source of uncertainty.

Figures
Figures 2e and 3e aim to apportion the uncertainty in the time series of Figures 2d and 3d respectively, between the uncertainty arising from GCM/RCM inter-model variability (including model uncertainty and internal variability of climate at different time scales) and the uncertainty arising from the multiphysics snowpack model.For that purpose, the standard deviations of the 455 values of Figures 2d and 3d were computed for each 15-year window, and correspond to the total standard deviations of the SD.This is shown in black solid line in Figures 2e and 3e. Figure 2e displays values on the order of 0.08 to 0.11 m with decadal variability but no temporal trend from 1950 to 2100. Figure 3e, on the other hand, shows a decline of standard deviation with time, as SD becomes smaller.This standard deviation can be viewed as the total quantified uncertainty level for a given RCP affecting individual values of 15-year averages of SD.The snowpack multiphysics (referred to as ES-CROC) and GCM/RCM uncertainty components were computed based on a further post-processing of the 455 SD 15-year averages for each 15-year window.The ESCROC component was quantified as the mean value of the 13 values (one for each GCM/RCM pair) of the standard deviation of the 35 multiphysics configurations.Similarly, the GCM/RCM component was quantified as the mean value of the 35 values (one for each multiphysics configuration) of the standard deviation of the 13 GCM/RCM pairs.Time series of these individual values are displayed in Figures 2e and 3e.The ESCROC component shows values ranging from 0.02 m to 0.07 m depending on the RCP scenario considered, exhibiting rather smooth fluctuations from 1950 to 2100 and a general decreasing trend, along with the general decreasing trend of SD over the considered time period (see below).In contrast, the GCM/RCM component shows significant spread, with values from 0.02 m to 0.11 m.Note that

Fig. 4
Fig.4shows the significant interannual variability in snow and meteorologically related indicators in the observations and SAFRAN reanalysis.The observation and reanalysis indicators for snow and meteorological conditions exhibit fluctuations which span the entire range covered by climate projections, under both historical and early-21 st century RCPs (the transition between historical and RCP occurs in 2005, which current observations and reanalysis overcross).This indicates that the historical and early-21 st century RCPs are consistent with the observed range and interannual variability at the considered location, which corroborates the use of the EURO-CORDEX regional climate simulations together with the ADAMONT method and the Crocus snowpack model to address past and future changes of snow conditions in this mountainous area.

Figure 2 .
Figure 2. Observed and simulated time series of SD. a) Continuous time series of annual values of mean winter snow depth data (SD), either observed or generated by the default snowpack model configuration fed by meteorological data from a reanalysis or an adjusted RCM.b) SD values obtained using the ensemble of Crocus model configurations ESCROC.c) Ensemble of Crocus model configurations driven by the 13 RCP 4.5 GCM/RCM pairs; each GCM/RCM pair is displayed with a different color.d) 15-year running average values of all simulation members presented in c. e) Estimate of absolute and relative contribution of uncertainty components arising from GCM/RCM inter-model variability and multiphysics snowpack model uncertainty (ESCROC).
, all snow-related indicators exhibit a trend towards gradually increased snow scarcity.SD, SW E quantile values sampled every 20 years generally decrease, SOD increases (later snow onset) and SM OD decreases (earlier snow melt-out date), and ST ED values decrease.In most cases, climate projections for the 15-year periods centered around 2030 and 2050 depend only slightly if at all on the RCP.The periods centered around 10 2070 and 2090 show significant deviations between RCPs, with reinforced downwards trends for RCP8.5-basedindicators, pursued decrease under RCP4.5 and stabilization or reduced decreasing trend for RCP2.6.In comparison to the historical model runs during the reference period 1986-2005, not only the median but also the individual quantile Q17 and Q83 values

Figure 5
Figure 5 represents the mean ± σ for the same indicators as Fig. 4. Figures for each RCP taken separately are available in the Supporting Information (Figs.S4-S6).Table3and TableS2of the Supporting Information also contain values for specific

Figure 6
Figure 6 shows the relationships between computed changes of the snow and meteorological indicators between 1986-2005 (reference period for this study) and three future time periods (beginning of century (BOC), 2011-2040, middle of century (MOD) 2041-2070 and end of century (EOC), 2071-2100), and the corresponding global temperature changes simulated by the driving GCM.This figure uses ∆T g,EOC−P I as a reference (lower axis).The corresponding relationship to ∆T g,EOC−Ref is also shown (upper axis), which consists in a shift of 0.62 • C (∆T g,Ref −P I ) although individual ∆T g,Ref −P I values range from 0.19 to 0.84 • C depending on the GCM.Regressions were however computed using the values of ∆T g,BOC−Ref , ∆T g,M OC−Ref and ∆T g,EOC−Ref for each GCM, as well as all three future periods taken together.Table 5 shows the slope (per global • C difference with the Ref value) of the change of the local indicator, as well as the coefficient of determination.

Figure 6 .
Figure 6.Response of local meteorological and snow indicators to global warming level.Indicator response is computed as the difference of multi-annual means between end of century (EOC, 2071-2100), middle of century (MOC, 2041-2070), or beginning of century (BOC, 2011-2040) and the reference period (Ref, 1986-2005).Global warming level is computed as the difference in global mean surface air temperature between EOC, MOC or BOC and either the reference period (top axes) or the pre-industrial period (P-I, 1851-1880)(lower axes).Each point corresponds to a snow or meteorological indicator computed using a given RCP and one GCM/RCM pair, for which the global surface air temperature change is inferred from the corresponding GCM run: a) SD (%), b) SW E (%), c) SOD and SM OD (days), d) ST ED5 (days), e) ST ED50 (days), f) ST ED100 (days), g) T ( • C), h) P (%), i) R (%).Warming levels of 1.5 • C and 2 • C compared to pre-industrial are shown with the vertical dashed lines.Regression lines are shown for the response at EOC, MOC, BOC or all three periods (ALL) (except for P ).Mean values and standard deviations among ALL changes of each indicator for 0.5 • C ∆Tg,EOC−P I intervals (± 0.25 • C) are displayed as error bars.
• C, with bias and RMSD values of -0.1 • C and 0.6 • C, respectively, when comparing SAFRAN with the Col de Porte observational record.The coefficient of determination between SAFRAN and the observations is equal to 0.85.For P , the mean observed value is 777 kg m −2 , with a bias value of 7 kg m −2 and a RMSD value of 149 kg m −2 .The coefficient of determination is equal to 0.74.The interannual fluctuations among GCM/RCM are only correlated between RCMs forced by the same GCM but decorrelated between the different GCMs, as expected.
are available, the indicators calculated for the reference period only taking into account the 4 model pairs available in RCP2.6 (HIST** in Tables Table3and TableS2of the Supporting Information also contain values for specific time slots and for additional indicators.Table4lists the relative change in T , P and R for the same time slots compared to the reference period1986-2005.
) than the date of snowpack melt out (17 days per global • C difference with the Ref value).Taking the sum of absolute values of SOD and SM OD as a measure of the changes of total snow season length, it is found that the total snow season length is decreased by 29 days, i.e. about one month, per global • C difference with the Ref value.The slope of the local temperature regression curve is 1.1 • C • C −1 , which indicates that the local rate of warming only slightly exceeds the global warming rate during the 21 st century, using this method.
• C difference with the Ref value, is larger for SD (about -25% • C −1 ) than for SW E (-20% • C −1 ).Similarly to previous sections, the SOD and SM OD changes are not symmetrical, i.e. the date of snowpack onset exhibits a lower relative reduction (12 days per global • C difference with the Ref value
• C temperature rise.However, for a given ∆T g,EOC−P I value, model runs spanning several tens of % reduction rate can be sampled (e.g., around 2 • C), showing that the relationship between global