Typical applications of process- or physically-based models aim to gain a better process understanding or provide the basis for a decision-making process. To adequately represent the physical system, models should include all essential processes. However, model errors can still occur. Other than large systematic observation errors, simplified, misrepresented, inadequately parametrised or missing processes are potential sources of errors. This study presents a set of methods and a proposed workflow for analysing errors of process-based models as a basis for relating them to process representations. The evaluated approach consists of three steps: (1) training a machine-learning (ML) error model using the input data of the process-based model and other available variables, (2) estimation of local explanations (i.e., contributions of each variable to an individual prediction) for each predicted model error using SHapley Additive exPlanations (SHAP) in combination with principal component analysis, (3) clustering of SHAP values of all predicted errors to derive groups with similar error generation characteristics. By analysing these groups of different error-variable association, hypotheses on error generation and corresponding processes can be formulated. That can ultimately lead to improvements in process understanding and prediction. The approach is applied to a process-based stream water temperature model HFLUX in a case study for modelling an alpine stream in the Canadian Rocky Mountains. By using available meteorological and hydrological variables as inputs, the applied ML model is able to predict model residuals. Clustering of SHAP values results in three distinct error groups that are mainly related to shading and vegetation-emitted long wave radiation. Model errors are rarely random and often contain valuable information. Assessing model error associations is ultimately a way of enhancing trust in implemented processes and of providing information on potential areas of improvement to the model.

Abstract. For many ungauged mountain regions, global datasets of different meteorological and land surface parameters are the only data sources available. However, their applicability in modelling high-alpine regions has been insufficiently investigated so far. Therefore, we tested a suite of globally available datasets by applying the physically based Cold Regions Hydrological Model (CRHM) for a 10-year (September 2000–August 2010) period in the gauged high-alpine Research Catchment Zugspitze (RCZ), which is 12 km2 and located in the European Alps. Besides meteorological data, snow depth is measured at two stations. We ran CRHM with a reference run with in situ-measured meteorological data and a 2.5 m high-resolution digital elevation model (DEM) for the parameterization of the surface characteristics. Regarding different meteorological setups, we used 10 different globally available datasets (including versions of ERA, GLDAS, CFSR, CHIRPS) and additionally one transferred dataset from a similar station in the vicinity. Regarding the different DEMs, we used ALOS (Advanced Land Observing Satellite) and SRTM (Shuttle Radar Topography Mission) (both 30 m) as well as GTOPO30 (1 km). The following two main goals were investigated: (a) the reliability of simulations of snow depth, specific snow hydrological parameters and runoff with global meteorological products and (b) the influence of different global DEMs on snow hydrological simulations in such a topographically complex terrain. The range between all setups in mean decadal temperature is high at 3.5 ∘C and for the mean decadal precipitation sum at 1510 mm, which subsequently leads to large offsets in the snow hydrological results. Only three meteorological setups, the reference, the transferred in situ dataset and the CHIRPS dataset, substituting precipitation only, showed agreeable results when comparing modelled to measured snow depth. Nevertheless, those setups showed obvious differences in the catchment's runoff regime and in snow depth, snow cover, ablation period, the date, and quantity of maximum snow water equivalent in the entire catchment and in specific parts. All other globally available meteorological datasets performed worse. In contrast, all globally available DEM setups reproduced snow depth, the snow hydrological parameters and runoff quite well. Differences occurred mainly due to differences in radiation model input due to different spatial realizations. Even though SRTM and ALOS have the same spatial resolution, they showed considerable differences due to their different product origins. Despite the fact that the very coarse GTOPO30 DEM performed relatively well on the catchment mean, we advise against using this product in such heterogeneous high-alpine terrain since small-scale topographic characteristics cannot be captured. While global meteorological data are not suitable for sound snow hydrological modelling in the RCZ, the choice of the DEM with resolutions in the decametre level is less critical. Nevertheless, global meteorological data can be a valuable source to substitute single missing variables. For the future, however, we expect an increasing role of global data in modelling ungauged high-alpine basins due to further product improvements, spatial refinements and further steps regarding assimilation with remote sensing data.

Snow cover dynamics in alpine regions play a crucial role in view of the water balance of head water catchments. The temporal storage of water in form of snow and ice leads to a decoupling of precipitation and runoff. Changes in the volume and the temporal dynamics of the snow storage lead to modified runoff regimes and can influence the frequency of low flow events and floods. For a better estimation of the possible range and direction of future changes, projection runs can be realized by using process-based models. In this study, the Cold Regions Hydrological Modelling platform (CRHM) is used to compile such a model for simulating the snow cover development within research catchment Zugspitze (RCZ; 11.4 km2/Germany). Therefore, the catchment is divided into four hydrological response units (HRUs), able to cover the physiographic characteristics in four elevation zones. The model is evaluated over snow depth measurements. The range of variability within and differences between the HRUs are analyzed, and future projections (2001–2100) are performed on the basis of three different WETTREG realizations. It could be shown that CRHM is able to reproduce the snow cover dynamics very well and that the ongoing climate change does have an identifiable influence on the average extent and size of the snow storage. Furthermore, it could be shown that variations in snow cover dynamics within the RCZ are strongly connected to NAO.