Hydrologic processes in snowmelt dominated systems are traditionally measured and understood at the point scale. However, snowmelt, sublimation, and snowfall rates exhibit significant spatial variability across larger landscapes. These variations are influenced by local atmospheric and terrain characteristics, which control the deviations between small-scale measurements and areally averaged responses to spatially heterogeneous mass and energy inputs. Appropriate upscaling relations are needed to translate small-scale descriptions of snow processes into constitutive relationships that are applicable at larger scales. As a proof of concept, this study examines the temporal and spatial variability of sublimation and snowmelt fluxes in a drainage basin in the Canadian Rockies using machine learning methods. Raven, a hydrological model, generates high-resolution fluxes and state variables used to train a random forest algorithm. The random forest (RF) algorithm is then applied to estimate coarse resolution fluxes. This study involves estimating spatially averaged results from discretized fine-scaled models without explicit knowledge of detailed local response, both with and without low-order statistics of state (e.g., the standard deviation of snow water equivalent). A series of experiments are used to verify that the upscaling methodology can successfully represent the impact of heterogeneity within the system. Spatially averaged forcing estimated from the scale-appropriate machine learning model is then incorporated into a mass balance equation at a coarse resolution to demonstrate the efficacy of this upscaling methodology.

Stream temperature is a critical ecosystem indicator and plays an important role in river ice formation and breakup. Typically, stream temperature is simulated either using statistical models or discrete Eulerian energy balance models. These physically-based models often rely upon a grid-based finite difference or finite volume approach for simulating the advection-dominated in-stream energy balance. Such methods are conditionally stable and thus introduce constraints upon time and space step (e.g., Courant and Peclet constraints). They are also not conceptually consistent with commonly applied convolution-based hydrologic routing approaches, which don’t require reach discretization. Here, a novel semi-analytical technique for simulating advection, latent and sensible heat transfer, heat generation from friction, and hyporheic exchange with groundwater is introduced. It assumes a discrete convolution (i.e., transfer function or unit hydrograph) method is used for routing flows through the reach. The energy balance is applied to discrete parcels of water that travel along the reach exchanging energy with their surroundings; the parcel-based energy balance is solved exactly. The method is unconditionally stable, runs at the native time step of the hydrological model, and requires no spatial discretization. It can also easily simulate edge cases that are exceedingly difficult using discrete methods, such as a near-infinite convective exchange coefficient. The only approximation errors are associated with the model time step used to represent the inflow time series, the linearization of the Stefan-Boltzmann equation for longwave radiation flux, and the full mixing assumed at nodes of the stream network. The stream temperature model, as implemented within the Raven hydrological modelling framework, is demonstrated at several test catchments in the North American Rocky Mountains.

Over winter freeze-thaw events are notoriously difficult to represent in hydrologic models and have serious implications for the hydrologic function of intermittently freezing regions. With changing climate leading to higher variability in observed weather patterns, it is anticipated that mid-winter thaw events may become more numerous at locales where intermittent thaw was previously rare. Midwinter thaw events are often the cause of flooding due to the combined impacts of snowmelt, precipitation, and limited soil infiltrability. A numerically efficient, semi-analytical coupled thermal and mass transport model is presented that is capable of representing the ice content of near-surface soil. This model allows for rapid and stable prediction of the ice content of frozen or partially frozen near-surface soil without having to solve a discrete form of the coupled partial differential equations describing the soil water and energy balance. The model tracks pore ice formation and mean soil temperature in terms of enthalpy. It is tested against data collected in Southern Saskatchewan and is shown to capably reproduce field observations. This model is efficient enough to be incorporated as a module into existing regional hydrologic models and is expected to improve predictions of soil ice content, which can later lead to improved estimates of over-winter streamflow and flood potential.

Over winter freeze-thaw events are notoriously difficult to represent in hydrologic models and have serious implications for the hydrologic function of intermittently freezing regions. With changing climate leading to higher variability in observed weather patterns, it is anticipated that mid-winter thaw events may become more numerous, especially in cold regions. Midwinter thaw events are often the cause of flooding due to the coupled impact of rain-on-snow, and limited soil infiltrability. A numerically efficient, semi-analytical coupled thermal and mass transport model is presented that is capable of representing the ice content of near-surface soil. This model allows for rapid and stable prediction of the ice content of frozen or partially frozen soil without having to solve a discrete form of the coupled partial differential equations. The model tracks pore ice formation and soil cold content in terms of enthalpy. It is tested against data collected in Southern Saskatchewan and is shown to reproduce field observations. This model is efficient enough to be incorporated as a module into existing regional hydrologic models and is expected to improve predictions of over-winter streamflow and flooding potential.