Regional climate models from the EURO-CORDEX archive (Jacob et al., 2014) were used to obtain the CH2018 climate scenarios (CH2018 Project Team, 2018), which was used in this study to calculate factor of change (FC) (Anandhi et al., 2011) needed to re-parameterize the weather generator AWE-GEN-2d in order to generate downscaled ensembles of future-climate variables (see Sect. 2.2.2). The 10 EURO-CORDEX model chains with the highest spatial resolution of 11 km were used (Table S1 in the Supplement). Factors of change were calculated following Peleg et al. (2019) for mean temperature, mean and variance of precipitation intensity based on seasonal projections (3-month average of the climate models) and for precipitation occurrence based on annual projections (see Appendix). The FC consists of gridded values for precipitation (cf. Fig. 3b in Peleg et al., 2019) and a single value for the entire model region for temperature. They were calculated for two emission scenarios (i.e. RCP 4.5 and RCP 8.5) and two time horizons (i.e. a mid-century period from 2030 to 2059 and an end-of-century period from 2070 to 2099). A control period of 30 years (1981–2010) was used to compute the FC. Finally, the FC was linearly interpolated to our 100 m resolution.

The AWE-GEN-2d model (Peleg et al., 2017) was used to stochastically generate gridded climate variables for the study area at 100 m spatial and hourly temporal resolution. The model was developed to simulate climate variables in complex terrain by combining physical and stochastic-statistical methods that enable the preservation of physical and observed dependencies between climate variables. The weather generator is capable of reproducing both principal climate statistics and the natural climate variability for the climate variables needed for subsequent energy balance snow modelling. A short description of the model structure is given here; the readers are referred to the paper by Peleg et al. (2017), where the model and its equations are described in detail. The model first simulates a time series of dry and wet periods based on a simple renewal process, then simulates the cloud cover and precipitation (together) for each wet time step and the cloud cover during dry periods based on the time passes from/to the closest wet period. Wind speed and direction are then simulated independently and enable the two-dimensional advection of the precipitation fields. The near-surface air temperature is simulated next, conditioned on the cloud cover of each time step. Shortwave radiation is also directly dependent on cloud cover and on the relative humidity and dew-point temperature, which are simulated as an iterative procedure with the near-surface air temperature and vapour pressure at each time step. The longwave radiation is last computed for each time step, based on the cloud cover and near-surface air temperature.

The weather generator requires observational data for calibration, which are summarized in Table 1. Different sets of parameters are assigned for each month to consider the seasonality. The spatial structure of precipitation fields, the areal intensity and the wet fraction of precipitation are calibrated using the radar data at fine space-time scales. The storm renewal process is calibrated based on precipitation data from the Grimsel station, also at fine temporal scale. Correction to the precipitation intensities, to reduce errors due to high uncertainties in the radar estimation, are conducted at the grid cell scale using the MeteoSwiss RhiresD product. In general the calibration procedure follows the procedure presented in Peleg et al. (2017); two important adjustments were made to ensure a realistic input for the energy balance modelling: first, the filter used in AWE-GEN-2d to account for orographic precipitation effects was adjusted to overcome the typical problem of undercatch by rain gauges in mountainous terrain. For this purpose, the methods described by Magnusson et al. (2014) were used to assimilate daily snow depth sensor data into the Swiss gridded precipitation product RhiresD (Schwarb, 2000; MeteoSwiss, 2019). With optimal interpolation, a precipitation partitioning method and a daily gridded temperature field (see Magnusson et al., 2014, for details), the solid precipitation fraction was adjusted. The final product consists of fields of total precipitation in a 1 km resolution for more than 20 years for the whole of Switzerland. This final product also benefits from the much denser station network of snow depth sensors at high elevations in Switzerland compared to the rain gauge network used for RhiresD. The weather generator used these gridded fields to model the spatial distribution of total precipitation on an annual basis. Second, the wind speed was spatially adjusted to match the de-biased wind speeds of a numerical weather prediction model in this region (Winstral et al., 2017).

The weather generator is used in two ways: first in the trained set-up with the above-mentioned data as input to generate current-climate conditions and second in a re-parameterized set-up using an FC approach (see Sect. 2.2.1) to generate future-climate conditions (Peleg et al., 2019). FC directly affects air temperature, precipitation occurrence and intensity. Moreover, when these climate variables are re-parameterized, they indirectly influence other variables based on the interdependencies between the variables implemented in the model (Peleg et al., 2017). Note that for generating current-climate conditions, no information of the regional climate models was used (Fig. 2; Peleg et al., 2017). For both set-ups, a spatial resolution of 100 m was chosen to account for small-scale processes that are imperative for capturing the spatial variability in snowmelt dynamics in small mountain catchments (e.g. terrain shading of direct radiation). A resolution of 1 km was chosen for precipitation, but simulations were subsequently linearly resampled to 100 m. The model domain consists of 120×120 grid points. A total of 50 realizations of 30 years each, representing the same climatic period, were used to explore the natural climate variability. This is consistent with the set-up presented by Peleg et al. (2017, 2019), while for future-climate conditions, the weather generator was re-parameterized using factors of change (see Sect. 2.2; Peleg et al., 2019).

In summary, the weather generator was used to (1) provide hourly data for the full set of required inputs for the energy balance snow model (see next section), (2) generate climate variables with intervariable consistency, (3) downscale and de-bias regional climate model output, and (4) generate multiple realizations of current- and future-climate periods.

The snow model used in this study is an energy balance snow model, an evolution of the Jules Investigation Model (JIM; Essery et al., 2013). Only a single model configuration from this multi-model framework was used, determined by comparison against comprehensive data sets including snow lysimeter data (Magnusson et al., 2015). This model was advanced by integrating a seasonal algorithm for the fraction of snow-covered area (Helbig et al., 2015, 2021), a local adjustment of the albedo routine that better reflects the observed elevation dependency of the albedo decrease rate in Switzerland, and a subgrid precipitation adjustment that takes into account the influence of topography on the distribution and redistribution of snow in mountainous terrain. Correction functions depending on aspect and slope were trained with a set of high-resolution snow depth maps from airborne lidar images in the European Alps as described in Grünewald and Lehning (2015). This method provides an accurate derivation of mean snow depths from snow and precipitation measurements at flat sites. This model set-up is used for the Operational Snow Hydrological Service in Switzerland to predict snowmelt runoff and has been thoroughly developed through several studies (Griessinger et al., 2019; Winstral et al., 2019; Helbig et al., 2021). The snow model requires total precipitation (Precip), air temperature (TA), incoming shortwave radiation (ISWR), incoming longwave radiation (ILWR), wind, air pressure and relative humidity in an hourly resolution which was provided by the weather generator (see Sect. 2.2.2). Precipitation was split into solid and liquid phases using an adaptation of the method presented in Magnusson et al. (2014) originally developed for daily data. The snow model was run on the same resolution as the weather generator (i.e. 120×120 grid points with a 100 m spatial resolution).

Peleg et al. (2017) showed for a nearby mountainous region that the weather generator can reproduce principle statistics of climate variables. A similar verification to Peleg et al. (2017) was conducted. Annual precipitation achieved a comparable quality as the calibration that was done to a nearby Alpine catchment (Peleg et al., 2017), as is expected since annual mean values are used for calibration (not shown). A comparison of daily precipitation intensities with a focus on extremes are shown in Fig. S2, which indicates that extremes are better captured than other intensities, which is considered important for a ROS study. Figure 3 shows a comparison for air temperature (TA), incoming shortwave radiation (ISWR) and incoming longwave radiation (ILWR) with measured data at two stations in the study area. Note that for Grimsel Hospiz (GRH), ISWR was indirectly used for calibration of the weather generator. Specifically, the data were used to calibrate the vapour pressure, but not for the variable itself. It should also be noted that the data availability for the stations spans only a few years and may not represent the long-term distribution well. Apart from these limitations, it can be seen that TA is slightly colder at the lower station OBW2 in AWE-GEN-2d (bias of -0.8 ∘C), while it is quite well represented at the higher station OBW1. ISWR is underestimated in winter months, while ILWR is overestimated in spring. However, it is our understanding that the quality of the output is sufficient to analyse deviations of simulated future-climate conditions from current ones; i.e. no climate-related changes are compared between the model and observed data. Note that the range plotted is inter-year variability, in contrast to Sect. 3.2 and the following, where inter-climate period variability is discussed.

Recent publications demonstrate the quality of point-based snow depth modelling (Winstral et al., 2019), of spatial modelling results as inputs to a hydrologic runoff model (Griessinger et al., 2019), or in comparison to lidar-derived snow depth (HS) data and satellite-derived snowpack fraction data (Helbig et al., 2021). Using only measured station data as meteorological forcing, Magnusson et al. (2015) have already quantified the quality of the original JIM models with lysimeter data. In addition to these results, it is shown here that the improved model can accurately reproduce snow depth at the GUE station near the study area (Fig. 4). A good agreement was achieved in the 2 years studied, with an RMSE of 20 cm and a positive bias of 13 cm, calculated for days when either the model or the observations show positive snow depth (Fig. 4).

Figure 5 shows mean values and a spread of 1500 years simulated by the model chain and (pseudo) observations of HS and SWE of 20 years. The good agreement indicates that the model chain is capable of reproducing both the interannual variability and mean properties. The comparison shows, however, a slight underrepresentation of years with early intense snowfall. Note that the range in the case of the observations is determined by minimum and maximum, compared to the 5th–95th percentiles of the generated data. In addition, the model typically simulates an earlier onset of melting, and subsequent slower melting is typically modelled, which compensates and finally results in a mean meltout that is consistent with observations. These small inconsistencies notwithstanding, the results show a level of performance that does not compromise the use of the model combination to study the effects of climate change based on simulated current and future climate periods.

Figure 6 shows the annual and spatial means of TA, precipitation and SWE on 1 April for the current- and future-climate conditions. Natural climate variability is shown with error bars, while climate model uncertainty can be interpreted with the differences between climate model chains. For TA, climate model uncertainty dominates, while for precipitation, natural climate variability dominates. This result is consistent with those presented in other studies (Hawkins and Sutton, 2009, 2011; Fatichi et al., 2016; Peleg et al., 2019). The total uncertainty range of SWE on 1 April is mainly generated by natural climate variability for the mid-century, while at the end of the century both sources of uncertainty contribute similarly. A more quantitative analysis of the specific uncertainty contributions can be found in Sect. 3.2.7. Note that all of the following figures show uncertainty ranges of climate period averages to illustrate how different equally likely realizations of a future-climate period are. The interannual uncertainty range is much larger (not shown) and is not the subject of this paper.

Figure 7 shows the seasonal evolution of areal mean SWE for different emission scenarios and periods. The uncertainty range for current climate (blue) is, by definition, only determined by natural variability, while for future climate (red) it is influenced by a composite of natural variability and climate model uncertainty. From May on, the changes in SWE for all emission scenarios and time horizons are larger than the uncertainty range (i.e. no overlap of uncertainty ranges). During the accumulation period, only the extreme emission scenario RCP 8.5 at the end of the century shows no overlap, while overlaps of up to 50 % are achieved for the other cases. At the time of the SWE maximum in this region (1 May), the overlap is already close to zero due to the onset of melting in the future scenarios. Similar to Verfaillie et al. (2018), the uncertainty in the emission scenarios is only relevant at the end of the century, as discussed in detail in Sect. 3.2.7.

For all scenarios, the altitude effects are similar. At the lowest altitudes (1400–1950 m a.s.l.), the climate signal is large enough to emerge clearly from the uncertainty ranges, while the largest overlap is achieved at the highest altitudes (3050–3600 m a.s.l.) (Fig. S1 in the Supplement). Only for the most extreme scenario, RCP 8.5 at the end of the century, is no overlap achieved even at the highest altitude range. This is generally consistent with the results of Marty et al. (2017), who also found a weakening of the climate change signal at higher elevations. Furthermore, the results are mostly consistent with Willibald et al. (2020), who found a similar elevation effect in how natural climate variability can mask trends in mean and maximum snow depth, although the role of natural climate variability seems to be larger in their study than in our results. While at a low-altitude site only 15 % of 50 realizations of future-climate conditions under RCP 8.5 showed insignificant trends for time horizons until the middle of the century, at a high-altitude site (Weissfluhjoch, 2540 m) it was still 80 %. For the latter station, they still found 20 % of all realizations with insignificant trends until the end of the century. For our data for RCP 8.5 at the end of the century, no overlap is found for SWE for no time of the year and also not for the highest altitude range. Also, for low elevations at the middle of the century, hardly any overlap is exhibited (Fig. S1a).

In summary, these results suggest that the climate change signal for the area-averaged SWE is generally larger than the associated uncertainty. Only for elevations above 2000 m and for the months between January and April are there likely realizations of future climate with an equal amount of SWE as today. These exceptions can be characterized as situations where precipitation variability can strongly influence SWE amounts, i.e. when most of the precipitation falls as snow, and melt is negligible. However, the later onset of SWE accumulation in future climate prevents natural variability from being able to fully mask the climate change signal in the accumulation season, as is the case with precipitation (Peleg et al., 2019) or runoff (Fatichi et al., 2014; Moraga et al., 2021).

Figure 8 presents the exceedance probability of contributing area sizes of ROS events for all different pixel-based criteria (see Table 2) for RCP 8.5 at the end of the century. For example, in Fig. 8a, using criterion 1, approximately nine ROS events per year (exceedance probability of 0.0247) are simulated with a contributing area greater than 20 % of the total area for current- and future-climate conditions. For this most extreme scenario, there is a climate change signal toward more frequent events for most of the contributing area size thresholds. However, whether or not the climate signal emerges from uncertainty ranges depends on the pixel-based criterion to define a ROS event. For criterion 4 and partially for criterion 2 (see Table 2) the signal of change is apparent, while this is not the case for criteria that also require 20 % of the SWI contribution from snowmelt (criteria 1 and 3). Increasing the rainfall threshold results in a clearer climate change signal, likely because rainfall in higher precipitation intensities is more frequent at the end of the century (Fig. S3) due to more total precipitation (Fig. 6) and due to warmer air temperatures, which increase the liquid fraction. The reason why the increase in ROS frequency is masked when the additional melt demand is used to define a ROS event can be found in the change in seasonality of ROS events and is discussed in Sect. 3.2.4. For other emission scenarios and ROS definitions, the overlap is even more pronounced (Fig. S4).

It is also worth noting the altitude dependence of this analysis for RCP 8.5 at the end of the century. At high elevations typically above 2500 m a.s.l., the increase in ROS events is pronounced for criteria 2 (not shown) and 4 (Fig. S5). For all other criteria defining ROS events and all other emission scenarios and periods, an increase at high altitudes above 2500 m a.s.l. is also observed, but this is masked by the sources of uncertainty (e.g. Fig. S6 for criterion 1). In summary, natural climate variability and climate model uncertainty question the claim that ROS events will become more frequent in a future climate in this high-elevation study area, except for the most extreme scenario RCP 8.5 at the end of the century at high elevations above 2500 m if the ROS definition does not include a snowmelt contribution. If a ROS event is defined such that there must be a substantial snowmelt contribution (> 20 %), then a future increase in ROS frequency is masked by the sources of uncertainty included in this study without any exceptions.

Thus, our results confirm our initial hypothesis that ROS events are strongly influenced by natural climate variability because they are more driven by precipitation than by seasonal SWE curves. However, some studies do find an increase in ROS frequency at higher elevations (e.g. Beniston and Stoffel, 2016; Musselman et al., 2018), and a discussion on this can be found in Sect. 3.2.6.

In this section, we discuss why the climate change signal is more pronounced for frequencies of ROS events with only minor snowmelt contribution versus substantial contribution. Following the definition of criterion 2, each ROS event can spatially consist of pixels that will also satisfy criterion 1, i.e. with snowmelt contribution > 20 % to SWI (see Fig. S7 for a spatial example). Figure 9 shows in a histogram the number of ROS events per month and their spatial characteristic computed as the ratio φ of pixels obeying criterion 1 over pixels obeying criterion 2. During current-climate conditions (Fig. 9a), most ROS events occur from May to July, typically with large φ, i.e. a large spatial proportion of pixels with substantial snowmelt contribution. In January, for example, only a small number of ROS events occur, and most are characterized by a low φ, i.e. a small spatial proportion of pixels with substantial snowmelt contribution. This is consistent with the results of Würzer et al. (2016), who found that ROS events with a substantial snowmelt contribution typically occur in late spring and early summer, when the snowpack is wet and warm at the onset of the event. Conversely, a low snowmelt contribution is expected when the initial snowpack is drier and colder (Würzer et al., 2016). Similar to Würzer et al. (2016), conditions for a substantial contribution from snowmelt are typically found under initially wet and warm snowpack conditions (Fig. S8a and b). This is indicated by the red arrow in Fig. 9, which points to large φ, which is associated with typically wet and warm initial snowpack conditions.

For RCP 8.5 at the end of the century (Fig. 9), the peak of ROS events shifts to earlier in the season, with typically large φ. There is also a higher number of early and midwinter events, with typically small spatial ratios, and almost no ROS events from July through September due to nonexistent snowpack.

The increase in ROS events in March and April with large φ values contrasts with a large decrease in June and July (Fig. 9c). This means that the ROS events with spatially a large number of pixels with substantial snowmelt are not largely changing in the future with regards to their frequency but rather shifted to earlier in the season. Only the frequency of events with small φ will increase in the future. This may be seen as counterintuitive at first because warm and wet conditions are expected to occur more frequently in a future-climate state. Indeed, this is generally the case at the onset of ROS events (Fig. S8c and d). However, rain in early and midwinter will fall on snow that will – even in this extreme warming scenario – be typically too cold and too dry to allow a significant contribution from snowmelt. This result implies that warmer air temperatures due to a changing climate can change the phase of precipitation more often than they can change the state of the snowpack to substantially contribute to runoff. This fact explains the limited increase in early and midwinter ROS events frequency with a large spatial proportion of substantial snowmelt contribution. Towards summer, the drastically reduced snow cover summer in a future climate explains the much faster decrease in the number of ROS events in this time, when ROS events have typically large φ, compared to the current climate.

In summary, the occurrence of rain falling on an initially warm and wet snowpack will likely not increase in the future. This explains that the climate change signal of ROS frequency shown in Fig. 8a and c are masked by uncertainty sources when a ROS event is defined by a substantial snowmelt contribution. However, a significant climate signal with varying signs is expected within individual months, e.g. March and June. These findings imply the need for a process-based snow model that can adequately model snowpack retention, as shown in this study.

Since rain intensity is expected to increase significantly in a future climate for all scenarios studied, also during ROS conditions (Fig. S3), one can expect SWI to increase for rain-on-snow events as well. However, the conclusions are very similar to those for ROS frequency. An increase in high SWI intensities is observable but is masked by the sources of uncertainty quantified in this study for all emission scenarios and time horizons (see Fig. S9 for RCP 4.5 at the end of the century), except for the most extreme scenario (Fig. 10), i.e. RCP 8.5 at the end of the century, still depending, however, on the ROS definition criteria. If the ROS criterion implies a substantial contribution of snowmelt to SWI, again, the increase is masked by uncertainty, whereas without this condition this is not the case. The elevation dependence is also very similar to the ROS frequency (not shown): at higher elevations, the increase is pronounced for criteria 2 and 4 for elevations above 3000 and 2500 m, respectively. For all other definitions of ROS events and all other emission scenarios and time horizons, this increase is also observed but is masked by sources of uncertainty.

Since snow cover decreases massively at the end of the century in the most extreme climate scenario RCP 8.5 (see Fig. 7d), it can be expected that the contribution of snowmelt to SWI also decreases, and the observed increase in ROS events is mainly driven by an increase in rain intensity. However, this depends on the pixel-based definition of whether a positive or negative climate signal can be observed. When substantial snowmelt contributions are required, the signal is largely masked by sources of uncertainty (Fig. S10). These results show that despite a dramatic decrease in snowpack by the end of the century in an RCP 8.5 scenario, the role of snow in contributing to runoff does not largely change for ROS events.

The results obtained here are based on a more complex approach than those of existing studies on this topic (e.g. Beniston and Stoffel, 2016; Morán-Tejeda et al., 2016; Musselman et al., 2018; Ohba and Kawese, 2020; Sezen et al., 2020), as we have added two new dimensions, i.e. internal climate variability and the ROS definition. Beniston and Stoffel (2016) reported that in the Swiss Alps, an increase of nearly 50 % in the number of ROS events occurred with 2–4 ∘C warmer temperatures than today at elevations of 2000 and 2500 m. For altitudes of 1500 m and below, a decrease in the number of ROS events was obtained. Except for two climate models, this temperature increase corresponds to the most extreme scenario RCP 8.5 at the end of the century (see Fig. 6a). Morán-Tejeda et al. (2016) came to very similar conclusions. Beniston and Stoffel (2016) and Morán-Tejeda et al. (2016) did use, however, empirical snow models without the capability that water retention can depend on the state of the snowpack. Ohba and Kawase (2020) did not use snowmelt in their definition of ROS events, and Sezen et al. (2020) defined ROS events with a very small amount of snowmelt (0.1 mm d-1). Thus, reporting more ROS events at high elevations is consistent with our results using a criterion that does not imply a substantial snowmelt contribution. We claim, however, that the ROS definition must account for the runoff perspective and should not be based only on the occurrence of liquid precipitation on snowpack because of the pronounced risk in flood potential due to excess runoff from snowmelt (Würzer et al., 2016). Thus, it is important to note that our results using ROS definitions, which require a substantial snowmelt contribution, differ from existing studies, suggesting that more frequent rain on snow in the future does not result in a more frequent combination of rain and snowmelt, as highlighted in Sect. 3.2.4.

Musselman et al. (2018) defined ROS events identically to the criterion 1 chosen here (i.e. > 10 mm of rain per day, > 10 mm SWE and > 20 % snowmelt contribution to SWI). They analysed spatial energy balance model runs on a 4 km grid in western North America. Similar to the studies in Switzerland, they achieved a decrease in the number of ROS events at lower elevations and an increase at higher elevations for an RCP 8.5 emissions scenario by the end of the century as well as an increase in ROS intensity and a decrease in the contribution of snowmelt. These results can also be found in our study case, but they are largely obscured by sources of uncertainty (Figs. 10a and S10a). When natural climate variability is artificially suppressed in our analysis by plotting only the first realization of a climate period (Fig. S11; note that the first realizations of the current and future climates are initialized with the same parameters in the weather generator), one can more clearly follow the conclusions of Musselman et al. (2018) of an increase in intensity and a decrease in snowmelt contribution.

The following two studies found a decrease in ROS events also in highly elevated catchments: Chegwidden et al. (2020) found that ROS events as a cause of annual runoff maxima will disappear at lower elevations and slightly decrease at higher elevations by the end of the century. They discussed their differences to Musselman et al. (2018), who modelled a similar domain, with having climate model differences and, mainly, analysing only annual runoff maxima, while Musselman et al. (2018) analysed all event magnitudes. In our study, we see an increase in ROS frequency independent of the event size for all except one ROS criterion (Fig. 8b–d). Cheggwidden et al. (2020) used energy-balance-based hydrological models to investigate ROS events, thus encompassing as well the role of soil in changing high flows.

Sikorska-Senoner and Seibert (2020) analysed historic observations and found a decreasing number of ROS events also in highly elevated catchments in Switzerland using a degree-day snow model with a fixed degree-day factor and threshold temperature. The difference in findings can also be found in the ROS definitions. Sikorska-Senoner and Seibert (2020) used for example a quite small snowmelt threshold of 1 mm d-1, which classifies alongside other criteria a flood as a ROS event. Chegwidden et al. (2020), however, used the same ROS definition as Musselman et al. (2018), which is identical to criterion 1 in our study.

In summary, similar conclusions compared to the cited literature would be drawn if our approach were simplified; i.e. (i) one does not distinguish between substantial and non-substantial snowmelt contribution based on snowpack conditions, and/or (ii) natural climate variability was not accounted for. This study shows that the inclusion of both natural climate variability and a snow model capable of modelling liquid water retention based on physical process representations provides new insights, particularly that only ROS events with no significant snowmelt contribution will occur more frequently in the future, while ROS events with significant snowmelt contribution will mainly shift towards earlier in the year.

Figure 11 shows the seasonal SWE (ΔSWE) climate change signal and the partitioning of uncertainty into the individual sources for the middle and end of the century. Note that the individual sources in Fig. 11a and b are shown symmetrically around the mean climate change signal for illustrative purposes only and that the ratio is equal to the square root of the fractions shown in Fig. 11c and d. The climate change signal and also total uncertainty are the largest around 1 May, which corresponds to the date when snow accumulation regularly ends under current-climate conditions (cf. Fig. 7). In absolute terms (Fig. 11a and b), natural climate variability remains roughly the same between mid-century and the end of the century, which has also been noted by others (e.g. for air temperature projections by Yip et al., 2011).

The relative contributions can be assessed with Fig. 11c and d. At mid-century, natural climate variability is the dominant source of uncertainty, accounting for more than 50 % during the main winter season. Climate model uncertainty is the second-largest source, while scenario uncertainty and model–scenario interaction account for only a few percentage points. This picture changes for the end of the century, where emissions scenario uncertainty is the main source, accounting for 40 % to 60 % during the main winter season. Climate model uncertainty is the second-largest source, with a contribution of about 30 %, followed by natural climate variability, whose contribution steadily decreases to just over 10 % in May. At the beginning and end of the snow season, natural climate variability has a larger relative contribution than is normally observed during the season, which means that natural climate variability is particularly important for studies focusing on the duration of the snowpack. The increasing role of emissions scenario uncertainty in SWE projections towards the end of the century means that efforts to reduce uncertainties in snow projections should focus on limiting uncertainties associated with emissions scenarios, similar to efforts to improve climate models.

The larger role of scenario uncertainty at the end of the century was already visible in Fig. 7 and is mentioned by Verfaillie et al. (2018). Verfaillie et al. (2018) also quantified snow model uncertainty and concluded that physical snow modelling has a contribution of up to 20 % of the simulated results after mid-century, which they considered secondary to climate model spread. It was mentioned that its influence on trends (or climate change signals) is likely much smaller but was not quantified more precisely. In this study, we were not able to quantify this additional source of uncertainty, but comparing these two studies, we can assume that natural climate variability and snow model uncertainty may be similar at the end of the century. This assumption needs to be proven by future studies that include all four types of uncertainty sources.

Figure 12 shows the fractional contribution of uncertainty sources for the variables “contributing area” and SWI determined with pixel-based criterion 3. Natural climate variability is the most dominant uncertainty source, with increasing contributions for larger event sizes and larger runoff intensities with values larger than 70 % of the total uncertainty range for event sizes larger than a third of the total area (Fig. 12b) or total area-averaged intensities larger than 20 mm d-1 (Fig. 12d) or with snowmelt contributions larger than 30 % (Fig. S12), even at the end of the century. These ratios depend on the pixel-based criterion, with the smallest contributions from natural climate variability obtained when using criterion 4, although still above 50 % (Fig. S13). The larger contribution from the other sources of uncertainty may be explained by a clearer climate change signal for this criterion (see Fig. 8).

For the climate change signal of the ROS metrics studied here, natural climate variability is more important compared to ΔSWE, in agreement with our initial hypothesis, because the frequency of future ROS events depends more on precipitation and less on air temperature. Precipitation is more influenced by natural climate variability compared to air temperature at this spatial scale (Fatichi et al., 2016; Peleg et al., 2019). In fact, the relative contribution of the uncertainty sources of the ROS metrics studied here compares quite well on a local scale with the purely precipitation-based metrics in Fatichi et al. (2016). This is in contrast to the continental scale studied in Hawkins and Sutton (2011), where the role of natural climate variability in decadal mean precipitation diminishes, and climate model uncertainty dominates toward the end of the century.

In summary, the total uncertainty in projections of the studied variables is composed of natural climate variability, climate model uncertainty and emission scenario uncertainty, in this order for SWE projections only up to mid-century and for all other variables up to the end of the century. The large contribution of natural climate variability demonstrates the need to quantify this source of uncertainty to prevent avoidable biases by end-users and decision-makers.