Simulating the influence of snow surface processes on soil moisture dynamics and streamflow generation in an alpine catchment

The assessment of flood risks in alpine, snow-covered catchments requires an understanding of the linkage between the snow cover, soil and discharge in the stream network. Here, we apply the comprehensive, distributed model Alpine3D to investigate the role of soil moisture in the predisposition of the Dischma catchment in Switzerland to high flows from rainfall and snowmelt. The recently updated soil module of the physics-based multilayer snow cover model SNOWPACK, which solves the surface energy and mass balance in Alpine3D, is verified against soil moisture measurements at seven sites and various depths inside and in close proximity to the Dischma catchment. Measurements and simulations in such terrain are difficult and consequently, soil moisture was simulated with varying degrees of success. Differences between simulated and measured soil moisture mainly arise from an overestimation of soil freezing and an absence of a groundwater description in the Alpine3D model. Both were found to have an influence in the soil moisture measurements. Using the Alpine3D simulation as the surface scheme for a spatially explicit hydrologic response model using a travel time distribution approach for interflow and baseflow, streamflow simulations were performed for the discharge from the catchment. The streamflow simulations provided a closer agreement with observed streamflow when driving the hydrologic response model with soil water fluxes at 30 cm depth in the Alpine3D model. Performance decreased when using the 2 cm soil water flux, thereby mostly ignoring soil processes. This illustrates that the role of soil moisture is important to take into account when understanding the relationship between both snowpack runoff and rainfall and catchment discharge in high alpine terrain. However, using the soil water flux at 60 cm depth to drive the hydrologic response model also decreased its performance, indicating that an optimal soil depth to include in surface simulations exists and that the runoff dynamics are controlled by only a shallow soil layer. Runoff coefficients (i.e. ratio of rainfall over discharge) based on measurements for high rainfall and snowmelt events were found to be dependent on the simulated initial soil moisture state at the onset of an event, further illustrating the important role of soil moisture for the hydrological processes in the catchment. The runoff coefficients using simulated discharge were found to reproduce this dependency, which shows that the Alpine3D model framework can be successfully applied to assess the predisposition of the catchment to flood risks from both snowmelt and rainfall events.

Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time

In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical directions are considered to be different, resulting in multi-fractional multi-dimensional soil space within which the flow takes place. Toward the development of the fractional governing equations, first a dimensionally consistent continuity equation for soil water flow in multi-dimensional fractional soil space and fractional time is developed. It is shown that the fractional soil water flow continuity equation approaches the conventional integer form of the continuity equation as the fractional derivative powers approach integer values. For the motion equation of soil water flow, or the equation of water flux within the soil matrix in multi-dimensional fractional soil space and fractional time, a dimensionally consistent equation is also developed. Again, it is shown that this fractional water flux equation approaches the conventional Darcy equation as the fractional derivative powers approach integer values. From the combination of the fractional continuity and motion equations, the governing equation of transient soil water flow in multi-dimensional fractional soil space and fractional time is obtained. It is shown that this equation approaches the conventional Richards equation as the fractional derivative powers approach integer values. Then by the introduction of the Brooks–Corey constitutive relationships for soil water into the fractional transient soil water flow equation, an explicit form of the equation is obtained in multi-dimensional fractional soil space and fractional time. The governing fractional equation is then specialized to the case of only vertical soil water flow and of only horizontal soil water flow in fractional time–space. It is shown that the developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations concerning the diffusive behavior of soil water flow.