Climatic changes are expected to strongly affect the build-up and melt of seasonal snow covers in mountain regions. Because snow cover regulates the seasonal rhythm of mountain ecosystems and represents a key component of the hydrological cycle, a detailed knowledge of its past, current and future state is of great significance . In addition to in-situ observations and remote sensing data, snow models are often used to assess the current state of the snow cover and the effects of climatic changes. Such impacts of climatic changes are typically evaluated by forcing the snow-hydrological models with bias adjusted scenario data from ensembles of climate models e.g.. Thereby, empirical snow models using degree day factors (DDFs) are often used in climate change impact studies because they require little input data and are computationally very efficient. These temperature index (T-Index) approaches are typically optimized using seasonally and/or spatially varying DDFs . , for example, use a semi-distributed hydrological model with an improved degree-day method including a seasonally variable DDF to assess runoff changes in Alpine catchments in Austria. In the SNOWGRID-CL model, which was applied to the Ötztal Alps (Austria) presented in the climate change impact study by , an extended degree-day approach that accounts for air temperature and shortwave radiation was used . The degree-day approach is also utilized in the semi-distributed HBV model or in the GR models e.g.. To better describe rain-on-snow events, the mesoscale Hydrological model (mHM), which has been applied to assess changes in low flows and river floods at different warming levels , accounts for energy input from liquid rain; DDFs are thereby increased depending on the amount of liquid precipitation .

In addition to degree-day approaches, energy balance based snow models, which explicitly represent the relevant energy and mass fluxes, are used to simulate the seasonal snow cover. These physically based modelling approaches require more input data and go along with a higher computational effort. Despite the increased complexity and effort, first studies have already employed energy balance based melt process description methods to assess the climate change impact on the seasonal snow cover. , for example, use an energy balance based snowmelt modelling approach to assess cryospheric and hydrological impacts in the Ötztal Alps (Austria). They process an ensemble of climate model data using statistical bias correction methods as well as temporal disaggregation tools to conduct their energy balance based simulations. force the Alpine3D snow pack model with an ensemble of downscaled climate data for three emission scenarios in two Swiss catchments. A semi-distributed approach using representative elementary areas and the Crocus snow model has been used to simulate the snow cover dynamics in French mountain massifs for historical conditions and to assess potential climate change impacts . A multi-physics ensemble approach for Crocus, which supports the representation of modelling errors, is presented in .

When designing a climate change impact study for complex mountain terrain, not only the selection of the snowmelt modelling method needs to be considered, also the need for lateral snow redistribution and snow-canopy processes have to be addressed. The selection of the model configuration should be tailored to the specific research goal. In practice, however, the data availability and computational resources are often limited. Currently, newly available ensembles of kilometer-scale climate data e.g. are paving the way for a new generation of climate change impact studies in mountain areas. However, while the uncertainty in the climate scenario data is typically addressed using an ensemble of model runs, the snow model uncertainty receives only little attention. Further studies that quantify the effect of different snow model configurations are therefore required to support the development of robust modelling approaches for climate change impact studies in seasonally snow covered mountain areas.

In this study, we use the open source, intermediate complexity mountain snow model openAMUNDSEN to simulate the build-up and melt of the seasonal snow cover in the complex mountain terrain of the Berchtesgaden National Park (BGNP) under historical conditions (October 2013–September 2023) and for a 10 year period characterized by a 1 °C warming. The warming period is obtained using a stochastic block bootstrap resampler (climate generator), which is available as external pre-processing routine of openAMUNDSEN. We conduct snow simulations under historic and warming conditions using degree-day as well as energy balance based snow simulation routines, different land cover maps and grid geometries for the modelling with varying spatial resolutions (Fig. ). For the historical period, model runs are evaluated against snow coverage maps derived from Sentinel-2 and MODIS data. For each model run, we calculate snow cover durations (SCDs) and snow disappearance days (SDDs) across the entire elevation range of the BGNP. Our main goal is to assess differences in the snow modelling results induced by different snow model configurations relative to the effect of a 1 °C warming. The results support the need for careful consideration in the choice of snow model type, input data, and spatial resolution. The simulated effects of a climate change signal need to be interpreted having these uncertainties in mind.

We identified the BGNP as an ideal study site for our snow modelling experiment. The BGNP covers an area of 208 km2 and is located in the state of Bavaria (Germany) in the North-East of the European Alps. It is the only German national park in the Alps and is characterized by a complex mountain landscape with an extreme topography covering elevations between 603–2713 m a.s.l. (meter above sea level) (Figs.  and ). The open areas with bare rock and Alpine grassland in the higher elevations transition into coniferous, mixed and deciduous forest toward the lower elevations. Annual precipitation ranges from 1500 mm in the lower elevations to roughly 2600 mm in the peak regions, and the build-up and melt of a seasonal snow cover dominates the hydrology in the area e.g.. In cooperation with the Bavarian Avalanche Warning Service, the administration of the BGNP operates a dense network of automatic weather stations (AWSs) in the area. A detailed description of the station network including station names, locations, measured variables, example time series, and a description of the pre-processing of the AWS data is presented in . The BGNP administration also provides a digital elevation model (DEM) in 10 m resolution, which we resample to resolutions between 20 and 1000 m (Fig. ), and the BGNP habitat map (Fig. a). This habitat map was reclassified to seven classes, the three forest classes being the most important because forest types govern snow-canopy interactions and thus the entire seasonal dynamics of the snow cover in the forested areas. In addition to the BGNP land cover map, we process five other land cover maps for the area, all based on freely available and widely used datasets (Fig. b–f). Our aim is to capture the uncertainty that can be introduced into the distributed snow modelling with the selection of the land cover map. For comparability, we re-classify the data to similar land cover types. With regard to the forest representation, some data sources only have one forest class, whereas others distinguish different forest types and densities (Fig. ). The land cover maps that we processed are based on the following data: (i) CORINE Land Cover 2018 obtained from the European Union's Copernicus Land Monitoring Service (10.2909/960998c1-1870-4e82-8051-6485205ebbac, last access: 8 July 2025), (ii) OpenStreetMap (OSM) (https://www.openstreetmap.org/, last access: 8 July 2025), which we download using the R package “osmdata” (https://github.com/ropensci/osmdata, last access: 8 July 2025) , (iii) WorldCover from the European Space Agency (ESA) (https://esa-worldcover.org/, last access; 8 July 2025) , (iv) Land Use/Cover Map for the European Alps developed by and (v) Land Cover Germany from the German Aerospace Agency (DLR) described in (10.15489/1ccmlap3mn39, last access: 7 July 2025).

The evaluation of the openAMUNDSEN snow simulations in non-forested areas, using the satellite-based snow data, indicates that all model configurations can well capture the build-up and melt of the seasonal snow cover in the study area. A detailed description of the snow model evaluations is provided in the Appendix . The pixel-by-pixel comparison of simulated snow with FSC from Sentinel-2 (Figs.  and ) as well as the comparison with MODIS snow cover extent data (Figs.  and ) confirm the model's ability to capture the seasonal snow cover dynamics in the BGNP.

The stochastic block bootstrap resampler (climate generator) generated a 10 year period characterized by 1 °C warmer temperatures (Fig. a). Due to the stochastic nature of the approach as well as the inherent natural variability of the observational data, not every month exhibits the exact same warming. Temperatures in December, for example, are on average 1.25 °C warmer, whereas March shows a more moderate warming of 0.61 °C. With regard to precipitation amounts, slight increases/decreases show up (Fig. ). Again, theses differences reflect the stochastic nature of the method as well as the inherent variability in the data. We consider this variability in the signal appropriate for 10 year averages. In our experience, similar variabilities in the signal can show up in the comparison of 10 year periods of observations and data from climate models.

With regard to SWE, the snow model spread caused by the usage of different model configurations increases with progressing snow season and reaches its maximum between February and April. The average SWE in the BGNP can differ by more than 100 mm. Although the ensemble mean of the average SWE in warming conditions is below the ensemble mean of the historical simulations, there is a strong overlap of the shaded areas that indicated the spread caused by the usage of different snow model configurations (Fig. c). All model simulations under historical as well as warming conditions suggest that the BGNP is almost fully snow-covered in January and February (Fig. d). Furthermore, our snow simulations hint at an earlier disappearance of snow in the BGNP under a 1 °C warming by approx. one week. However, the strong overlap of the shaded areas indicates that the model spread in the second half of the main snowmelt season (May–June) is large compared to the magnitude of this shift. The model spread in this part of the year is characterized by values of approx. 50 mm for SWE and 12.5 % for the snow cover extent (Fig. c and d).

SCDs reach the highest values of approx. 200 d in elevation zones between 1800 and 2400 m (Fig. e). Our simulations suggest that a 1 °C warming can cause an average decrease in SCD of 20.5 d in the BGNP. For SDD, our modelling experiment suggests that changes due to a 1 °C warming can be small compared to the differences arising from the different model configurations (Fig. f). In general, our model results suggest that for SCD and SDD small differences between model configurations show up in elevations between 1600–2200 m. A larger spread in the snow model results can be detected below 1600 m and above 2200 m (Fig. e and f).

Our analysis of the effect of the spatial resolution suggests that results are largely consistent for resolutions between 20 and 250 m and up to elevations of 2000 m (Fig. ). Simulation results for coarser spatial resolutions (i.e., 500 or 1000 m) can deviate from the ones obtained for higher resolution model runs. The median SCD for the elevation band 2200–2400 m simulated using the T-Index approach (Fig. a), for example, is 229, 218, 207 and 192 d using a spatial resolution of 20, 50, 100 and 250 m, respectively.

The analysis of the model simulations with regard to the usage of different land cover maps indicates that the T-Index approach is largely insensitive to land cover (Fig. a and b). However, when using the enhanced T-index or energy balance based snowmelt approach, differences in SCD and SDD can show up in elevation zones with forest classes (Fig. c–f). The median SCD or SDD for elevations bands can be shifted by up to one week when using different land cover maps. In high elevations with no or only very small forested areas, the selection of the land cover map has no or only a negligible effect on the modelling results.

Our model experiments indicate that a 1 °C warming can cause a reduction in SCD of more than 20 d in the BGNP (Fig. a, c and f). With regard to SDD, the change signal in our model experiment is smaller with values of a few days up to ten days (Fig. b, d and f). The changes induced by higher temperatures and assessed for elevation bands seem consistent for spatial resolutions between 20–250 m. Deviations between model configuration using different spatial resolutions mainly show up at coarser modelling resolutions (i.e., 500 or 1000 m) and for elevations below 800 m and above 2200 m. Our results also indicate that the magnitude of the difference can vary strongly within an elevation band. The length of the boxes, which cover 50 % of the cells within the elevation band, can easily span across a range of 10 d (Fig. ).

Our analyses of the effect of using different land cover maps on a potential climate change signal indicate that when using the T-Index approach, only small differences show up (Fig. a and b). When using the enhanced T-Index or energy balance approach, the usage of different land cover maps characterized by different extents and distributions of forest type classes can be stronger and alter results for elevation bands with forest (Fig. c–f).

Next, we directly compare results for SCDs and SDDs using different snowmelt simulation methods and assess results with respect to differences stemming from different aspect, land cover map and a 1 °C warming (Fig. ). The aspects for the different model resolutions are presented in Appendix  (Fig. ). Our results point out that the selection of the snowmelt modelling method can strongly influence SCD and SDD. Differences between the snowmelt modelling methods are most prominent below approx. 1600 m with simulations using the T-Index approach resulting in considerable shorter SCDs (Fig. a, c and e) and earlier SDDs (Fig. b, d and f). Energy balance based simulations, however, produce longer SCDs and later SDDs for this elevation zone, while results from the enhanced T-Index approach tend to be between those of the other two approaches. This signal reverses at high elevations (>2000m) and the T-Index approach suggests longer SCDs and later SDDs than the other two snowmelt modelling approaches. Our modelling results indicate that at elevations below approx. 1600 m and above approx. 2200 m the differences induced by different snowmelt modelling approaches are stronger than the signal of change induced by a 1 °C warming (Fig. e and f). For elevation bands between 1600 and 2200 m, the results for SCDs and SDDs are more consistent and the change induced by a 1 °C warming exceeds the spread caused by different snowmelt simulation methods. Also the usage of different land cover maps can induce changes in SCDs and SDDs that can be within the same range as the change induced by a 1 °C warming (Fig. c and d), however, differences are less pronounced than differences resulting from the different snowmelt modelling methods, and are limited to elevations with differences in the forest representation in the land cover maps. While the enhanced T-Index and the energy balance approach can capture the differences in SCDs and SDDs depending on the exposition within elevation bands, the T-Index approach cannot account for such variabilities (Fig. a and b). Also the difference between northern and southern slopes is of the same magnitude as the signal induced by a 1 °C warming (Fig. ).

The open source snow model openAMUNDSEN proved to be a versatile snow modelling framework offering a wide range of configuration options including degree-day and physically based snowmelt modelling approaches. The stochastic block bootstrap resampler (climate generator), an external pre-processing routine, is a useful extension of openAMUNDSEN and enables the generation of physically consistent meteorological times series with pre-defined warming trends. The incorporation of the climate generator into the modelling experiment enables us to analyse the snow model uncertainty in the context of a potential climate warming. While using the climate generator for our particular purpose – comparison of the results of different snow model configuration simulations in relation to a potential warming signal – is appropriate, we do not recommend employing a stochastic block bootstrapping procedure to produce climate change scenario data for impact studies, in particular, when the goal is the investigation of snow-hydrological extremes, as no new extreme events can be produced by simple re-organization of observational time slices. Moreover, it needs to be noted that the climate generator cannot adequately produce elevation- and season-dependent features of long-term climatic changes.

In our study, we compare averages of meteorological and snow-related variables for two 10 year periods. The average monthly temperatures and precipitation totals as well as the average seasonal cycles indicate that the inter-annual variability of the data is affecting the averages investigated (Fig. a–d). Our analysis highlights the need for caution when quantifying climate change signals obtained using such short time frames. However, in our study, we deliberately decided to compare 10 year periods, as this is the type of data currently being available from ensemble climate simulations at kilometer-scale resolution. These high resolution climate model runs better capture the topographic forcing of precipitation and allow for an explicit, physical description of deep convection without having to use parameterization schemes . , for example, conduct the first multi-model ensemble climate simulations for the greater Alpine region at the kilometer-scale for the ten year period 2000–2009. Multi-model 10 year kilometer-scale scenarios for the greater Alpine domain are presented in . First case study simulations and results for a hydrological year for the “Third Pole”, using a multi-model and multi-physics ensemble at the kilometer-scale, are presented in and , respectively. On the contrary, high resolution regional climate model runs covering longer time frames (e.g. 30 years or more) often are limited to a single model only e.g.. Furthermore, depending on the complexity of the terrain, resolutions below 1 km are required to adequately represent the processes that cause the spatial variability of the simulated snow cover, such as lateral redistribution of snow by wind or snow-canopy interaction. Consequently, further dynamical or statistical downscaling of kilometer-scale climate model data is required to assess changes in the seasonal snow cover dynamics in complex mountain terrain such as the BGNP. Recent studies have demonstrated that the combination of high resolution weather model output, e.g. from the Weather Research and Forecasting (WRF) model, with physically-based snow energy balance models is feasible and can provide new insights into snow dynamics at the regional scale e.g.. Ongoing improvements of the snow process descriptions in the weather models may eventually make the coupling to an additional snow model unnecessary in the future e.g..

The recent progress in climate and snow modelling research suggests that, step by step, computational hurdles will be overcome, and that future climate change impact studies using models that better capture the topographic forcing of precipitation and explicit treatment of deep convection, and physically based snow models including lateral redistribution and snow canopy processes can adequately describe the snow cover dynamics in complex mountain terrain for potential future warming conditions. In this study, we show that the selection of the snowmelt simulation method is a very important aspect to consider when conceptualizing climate change impact studies in complex mountain areas. Our modelling experiments indicate that the snow model uncertainty can be of the same magnitude or even larger than changes in the snow cover induced by a 1 °C warming (Fig. e and f). A particular focus is required for forested areas, as additional snow-canopy processes need to be taken into account. In contrast to degree-day approaches, which usually only consider temperature and a calibrated degree-day factor and are largely insensitive to different land cover types, energy balance snow cover models do react sensitively to the choice of the land cover map and the forest representation therein (Fig. ), given the meteorological forcing is properly adjusted to inside-canopy conditions. The comparison of model simulations with different spatial resolutions suggests that for a robust quantification of changes in snow patterns in the highest elevations, spatial resolutions considerably below 1 km are required (Fig. ). In our simulations, we use a simple snow redistribution parameterization to account for the lateral snow redistribution processes (Fig. ). More process-oriented approaches incorporating wind fields and explicit representation of gravitational snow redistribution processes exist and need to be considered in future developments of the openAMUNDSEN model e.g..

Our study contributes to the broader research objective of quantifying snow model uncertainty and follows up on the investigations by , , and who assessed uncertainties in snow model results arising from snow model complexity, parameter errors and errors in the forcing data. The effect of process representations on the results are also presented in . Particular consideration of snow in forested area was given in the second phase of the Snow Model Intercomparison Project (SnowMIP2) where output from 33 different models was compared . These studies highlight that the accuracy of the forcing data is more critical than parameter selection, while the type of the model seems of less importance. In addition, human errors are an important aspect affecting snow model performance . Our snow modelling experiments complement existing research by defining a large set of configurations for distributed snow model simulations in complex mountain terrain with open and forested areas, resulting in a large number of openAMUNDSEN model configurations (n=108) with both degree-day and physically based snowmelt simulations, varying land cover maps and different spatial resolutions. The assessment of results under a 1 °C warming allows for a quantification of snow model uncertainty relative to a potential warming signal.

As many seasonally snow covered areas are also forest covered, further research is needed to better understand the effect of the snow-canopy processes in the context of a changing climate. A direct coupling of forest and snow models will thereby be an important next step in this regard, since not only climate will change, but also species composition and hence the snow hydrological processes inside the canopy. The complex mountain research site BGNP seems to be an ideal study site for such a task, given the dense measurement network and the existing expertise in forest processes modelling e.g. as well as snow modelling e.g.. At the same time, however, the evaluation of snow models inside forests remains challenging, particularly, as forest canopies obstruct the satellite-based detection of snow on the ground. An alternative approach, the evaluation of openAMUNDSEN snow modelling results inside the forest using a network of microclimate sensors, is presented in . Further research will support the development of new approaches for the evaluation of distributed snow models applied to forested areas, e.g. with respect to plant physiological simulation of LAI or improved scaling function for the meteorological variables from the location of the measurement to inside-canopy conditions. In our view, such new techniques for snow model evaluation are required to prepare a new generation of distributed and physically-based snow models for the application in the climate change impact context. There is no physical bases for assuming that DDFs used to simulate historical conditions are valid under future climatic conditions, and recent investigations of DDFs based on energy flux components show that DDFs cannot be treated as constant factors. They are changing with progressing melt season and need to be specifically adapted. Also our results suggest that degree-day snowmelt modelling approaches have their limitations, i.e. the DDF needs careful calibration and varies with elevation. We found that in higher elevations the best DDF is larger than in the valley region, where intermittent melting of the shallow snow cover in early winter can be very fast. Accordingly, the most consistent results and only small differences between model configurations show up in elevations between 1600–2200 m (Figs. e, f and e, f). The spatially and seasonally variable snowmelt dynamics from the enhanced T-Index approach seem to improve results by accounting for aspect- and season-dependent variations in radiation. However, the differences in SCDs and SDDs between the enhanced T-Index and the energy balance simulation runs can be substantial (Fig. ). At lower elevations, the different forest representation in each particular land cover map causes additional uncertainties in the results, while SCDs and SDDs in the highest elevations react very sensitively to the selection of the spatial resolution (Figs.  and ). Results are only consistent for spatial resolutions between 20 and 250 m and at elevations up to 2000 m.

openAMUNDSEN is a versatile snow modelling framework that supports distributed snow cover simulations in complex mountain areas, including snow-canopy interaction and lateral snow redistribution, using degree-day as well as energy balance snowmelt methods. In this study, we employ a large number of openAMUNDSEN model configurations (n=108) characterized by different snowmelt modelling methods, land cover maps and spatial resolutions to simulate the seasonal snow cover in the complex mountain terrain of the BGNP for the historical period October 2013–September 2023 and a 10 year period characterized by a 1 °C warming. The data describing the warming period was obtained using a stochastic block bootstrap resampler (climate generator), which is available as external pre-processing routine of openAMUNDSEN. The incorporation of the climate generator into our modelling experiment enabled us to assess snow model uncertainty in relation to the effect of a potential warming signal. The complex and diverse mountain landscape of the BGNP proved to be an ideal study area for snow modelling research and the presented investigation of snow model uncertainty. Our analyses suggest that differences in the resulting SCDs and SDDs, arising from the selected snowmelt simulation method, the used land cover map and the chosen spatial resolution can be comparable to the impact of a 1 °C warming. The uncertainties in the results are pronounced in the forest covered areas and in the high elevations of the study area. Our results emphasize the importance of evaluating the uncertainty of a given snow modelling setup when quantifying the effect of a warmer climate. Sources of uncertainty like the selection of the snowmelt method, land cover map, or the chosen resolution can have effects on the results in the same order of magnitude as the climate change signal. Future snow modelling studies investigating the effect of climatic changes on the seasonal snow cover in complex mountain terrain can build on our findings by carefully selecting snow model configurations and related uncertainties.