Comparison of 1-D and 2-D modeling approaches for simulating runoff and sediment transport in overload areas
One-dimensional and two-dimensional modeling approaches were compared for their abilities in predicting overland runoff and sediment transport. Both the I-D and 2-D models were developed to test the hypothesis that the 2-0 modeling approach could improve the model predictions over the 1-0 approach, based on the same mathematical representations of physical processes for runoff and sediment transport.
Runoff processes were described based on the St. Venant equations and the sediment transport was based on the continuity relationship. The finite element method was employed to solve the governing equations. The nonlinear, time-dependent system of equations obtained by the finite element formulation was solved by the substitution method and the implicit method.
The models were verified by comparing the analytical solutions presented by Singh and Regl (1983) and the solution by the Izzard method (Chow, 1959). The comparison showed that both the 1-0 and 2-D models provided reasonable estimations of runoff and sediment loadings. Evaluation of the models was based on four different hypothetical case studies and two experimental studies. The hypothetical case studies investigated the effects of the discretization level, cross slopes, and the size of the field area on the model predictions. The two experimental studies provided a comparison of model predictions with observed data.
The results of the hypothetical case studies indicated that the maximum differences in the model predictions at the outlet were about 30% between the two modeling approaches. When the discretization level was sufficient to reasonably describe the shape of the surface, the 1-0 model prediction were almost the same as the 2-D model predictions. Even though cross slopes existed in the field, the differences in the model predictions at the outlet were not significant between the 1-0 and 2-0 models. The differences in the model predictions of runoff and sediment loading were not affected by the changes in the size of the field. Since the 2-D model resulted in 10 to 20% differences in model predictions when different boundary conditions were used and the 1-D model predictions were also affected by the choice of element length, the differences in model predictions at the outlet, shown in model application results, which were less than 30% in most cases, could not be considered significant.
The model applications to the experimental studies also showed that no substantial differences existed in the model predictions between the I-D and 2-D models. Even though the spatial distributions of the flow depth and sediment concentration were significantly different, runoff volumes and sediment yields at the outlet showed less than 10% differences.
Compared with the I-D model, the 2-D model required much more computational time and effort to simulate the same problems. In addition, convergence problems due to negative flow depths limited the 2-D model applications. The 2-D simulations required more than twice the computational time needed for the I-D simulations. As long as the model predictions at the outlet are concerned, the much greater computational costs and efforts could not justify the use of the 2-D approach.
Based on the simulation results from the selected hypothetical case and experimental studies, the 2-D model provided better representations of spatial distribution of flow depths and sediment concentrations than the I-D model. However, no substantial differences in predictions of total runoff volume and sediment yield at the outlet area were found between the I-D and 2-D models.