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.

Stream thermal regimes are critical to the stability of freshwater habitats. There is growing concern that climate change will result in stream warming due to rising air temperatures, decreased shading in forested areas due to wildfires, and changes in streamflow. Groundwater plays an important role in controlling stream temperatures in mountain headwaters, where it makes up a considerable portion of discharge. This study investigated the controls on the thermal regime of a headwater stream, and the surrounding groundwater processes, in a catchment on the eastern slopes of the Canadian Rocky Mountains. Groundwater discharge to the headwater spring is partially sourced by a seasonal lake. Spring, stream and lake temperature, water level, discharge and chemistry data were used to build a conceptual model of the system. Meteorological data was used to set up a stream temperature model. This study presents a unique example of an indirectly lake-headed stream, that is, a lake that only has transient subsurface hydrologic connections to the stream and no surface connections. The interaction of groundwater and lake water, and the subsurface connectivity between the lake and the headwater spring determine the resulting stream temperature. Radiation dominated the non-advective fluxes in the stream energy balance. Sensible and latent heat fluxes play a secondary role, but their effects generally cancel out. During snowfall events, the latent heat associated with melting of direct snowfall onto the water surface was responsible for rapid stream cooling. An increase in advective inputs from groundwater and hillslope pathways did not result in observed cooling of stream water during rainfall events. The results from this study will assist water resource and fisheries managers in adapting to stream temperature changes under a warming climate.