Two-dimensional Approaches For Simulating Overland Flow

One-dimensional overland flow has been successfully simulated with kinematic and diffusion wave models. Previous work has been directed toward extending the one-dimensional kinematic and diffusion wave models directly to two-dimensional form. The validity of this approach, however, has not been discussed yet. Using both theoretical and numerical analyses, we evaluated possible errors of the direct generalization approach. The results show that direct generalization can bring errors in both flow magnitude and direction. The direct generalization approach manifests internal inconsistencies such that results vary with the coordinate directions, which is not a numerical effect, though we found that errors are not very sensitive to slope gradient. A simple example shows that on a five-degree slope, when flow direction is 45 degrees away from the x coordinate, the calculated flow rate will be 19% larger than actual flow rate. Numerical analysis shows that the magnitude of the error increases with the angle between flow direction and one coordinate axis, and reaches maximum at 45 degree. The error also increases with the slope gradient, though the slope itself was not found to be a major factor causing the error. Our analysis also shows that the calculated flow direction can be skewed up to 16 degrees away from the real flow direction. The underlying root cause of these errors is that the flow-depth relationship (i.e., the Manning's equation) is essentially a one-dimensional equation, and is not valid for all directions. A new approach is presented that avoids the above drawbacks. We apply the kinematic or diffusion wave approximation to the flow direction and decompose it in two coordinate directions. The results show that this approach overcomes the aforementioned problems and is theoretically independent of coordinates.