Multi-Scale Modelling of Cold Regions Hydrology

Numerical computer simulations are increasingly important tools required to address both research and operational water resource issues related to the hydrological cycle. Cold region hydrological models have requirements to calculate phase change in water via consideration of the energy balance which has high spatial variability. This motivates the inclusion of explicit spatial heterogeneity and field-testable process representations in such models. However, standard techniques for spatial representation such as raster discretization can lead to prohibitively large computational costs and increased uncertainty due to increased degrees of freedom. As well, semi-distributed approaches may not sufficiently represent all the spatial variability. Further, there is uncertainty regarding which process conceptualizations are used and the degree of required complexity, motivating modelling approaches that allow testing multiple working hypotheses. This thesis considers two themes. In the first, the development of improved modelling techniques to efficiently include spatial heterogeneity, investigate warranted model complexity, and appropriate process representation in cold region models is addressed. In the second, the issues of non-linear process cascades, emergence, and compensatory behaviours in cold regions hydrological process representations is addressed. To address these themes, a new modelling framework, the Canadian Hydrological Model (CHM), is presented. Key design goals for CHM include the ability to: capture spatial heterogeneity in an efficient manner, include multiple process representations, be able to change, remove, and decouple hydrological process algorithms, work both at point and spatially distributed scales, reduce computational overhead to facilitate uncertainty analysis, scale over multiple spatial extents, and utilize a variety of boundary and initial conditions. To enable multi-scale modelling in CHM, a novel multi-objective unstructured mesh generation software *mesher* is presented. Mesher represents the landscape using a multi-scale, variable resolution surface mesh. It was found that this explicitly captured the spatial heterogeneity important for emergent behaviours and cold regions processes, and reduced the total number of computational elements by 50\% to 90\% from that of a uniform mesh. Four energy balance snowpack models of varying complexity and degree of coupling of the energy and mass budget were used to simulate SWE in a forest clearing in the Canadian Rocky Mountains. It was found that 1) a compensatory response was present in the fully coupled models’ energy and mass balance that reduced their sensitivity to errors in meteorology and albedo and 2) the weakly coupled models produced less accurate simulations and were more sensitive to errors in forcing meteorology and albedo. The results suggest that the inclusion of a fully coupled mass and energy budget improves prediction of snow accumulation and ablation, but there was little advantage by introducing a multi-layered snowpack scheme. This helps define warranted complexity model decisions for this region. Lastly, a 3-D advection-diffusion blowing snow transport and sublimation model using a finite volume method discretization via a variable resolution unstructured mesh was developed. This found that the blowing snow calculation was able to represent the spatial redistribution of SWE over a sub-arctic mountain basin when compared to detailed snow surveys and the use of the unstructured mesh provided a 62\% reduction in computational elements. Without the inclusion of blowing snow, unrealistic homogeneous snow covers were simulated which would lead to incorrect melt rates and runoff contributions. This thesis shows that there is a need to: use fully coupled energy and mass balance models in mountains terrain, capture snow-drift resolving scales in next-generation hydrological models, employ variable resolution unstructured meshes as a way to reduce computational time, and consider cascading process interactions