Artificial viscosity technique for direct runoff calculation

Abstract

In this study, an Artificial Viscosity (AV) technique was developed for direct runoff calculation, instead of using the conventional Synthetic Unit Hydrograph (SUH) methods. We solved the Shallow Water Equations (SWE) with second-order accurate Godunov finite volume model and fourth-order Runge-Kutta explicit scheme. The AV technique was devised with a Laplacian and a biharmonic operator, and employed to solve the convective terms of the SWE. This technique was applied to rainfall-runoff laboratory cases with the measured rainfall and observed direct runoff values. For comparison purpose, several SUH methods commonly used such as SCS, Snyder, GAMA-1, ITB-1, ITB-2, and Nakayasu, were also used to compute the direct runoff values. The results showed that the AV technique could predict three parameters (i.e., peak discharge, time-to-peak, and shape of the direct runoff hydrograph) accurately. Meanwhile, significant discrepancies were shown by the SUH methods in estimating such parameters, thus indicating that the SWE modeling with an AV technique is significantly more accurate than the SUH methods in predicting the direct runoff hydrograph. This study shows an interesting example of how modern numerical computations can improve the runoff prediction and may be included as a standard technique for runoff computation in the future.