Numerical Representation of Hydrological Connectivity and Erosion at Hillslope Scale

The pattern of hydrological connectivity between unsealed forest roads and adjacent nearby streams is examined numerically by evaluating the effect of spatial and temporal variability of factors that contribute to runoff and erosion. Significant factors affecting infiltration rate, roughness, sediment detachment and entrainment are identified and represented in the form of algebraic equations. The diffusive equations as simplification to St. Venant equations in hydraulics are applied to create one and two-dimensional models to represent the behaviour of flow dynamics and sediment transport mathematically. The system of nonlinear partial differential equations is solved numerically by choosing the appropriate initial and boundary conditions. The MacCormack finite difference method is used to solve flow variables in the runoff part of the model. The concepts behind sediment detachment due to rainfall and flow dynamics are linked to the equations of mass conservation and continuity to represent erosion. The erosion equations are discretized by applying Forward in Time and Backward in Space finite difference scheme. Since both methods are meant to solve the equations explicitly, care must be taken for stability and convergence of the methods by investigating suitable spatial and temporal increments which satisfies Courant-Friedrichs-Lewy condition. The effect of vegetation and litter on the ground is considered by introducing drag coefficients in the roughness calculation. Validation of the model was accomplished by series of overland flow pumping experiments. Ultimately, the model's simulation outcome for different sets of input parameters will be compared and illustrated in graphs to demonstrate the role of variability in each parameter in the final solution. The numerical representation involves various parameters, many of which are unavailable or difficult to obtain for practical field applications. The final goal of this numerical approach is to develop a more parsimonious model of connectivity between forest roads and streams that will enable better estimates of the impact of forest roads on water quality at catchment scales. Keywords: Two-Dimensional Overland Flow; Sediment Transport Modelling; MacCormack;Finite Difference Scheme;Parsimonious Model