Undular bores and shocks generated by dam-break flows or tsunamis are examined considering nonhydrostatic pressure and dispersive effects in one- and two-horizontal-dimensional space. The fully nonlinear Boussinesq-type equations based on a weakly nonhydrostatic pressure assumption are chosen as the governing equations. The equation set is solved by a fourth-order accurate finite-volume method with an approximate Riemann solver. Several typical benchmark problems such as dam-break flows and tsunami wave fission are tested in one- and two-horizontal-dimensional space. The computed results by the Boussinesq-type model are at least as accurate as the results by the hydrostatic shallow water equations. This is particularly evident near the steep front of the wave, where frequency dispersion can play an important role. The magnitude of this nonhydrostatic pressure and dispersive effect near the front is quantified, and the engineering implications of neglecting these physics, as would be done through the use o...

[1] The effects of storm movement on rainfall-runoff processes through a V-shaped watershed are investigated using a dynamic wave model based on shallow water equations. The governing equations are solved by a fourth-order accurate finite volume method to obtain accurate computational results. Once the numerical model is verified, a series of rainfall-runoff events on a V-shaped watershed are simulated. To investigate the contribution of each term in the depth-averaged momentum equation, a scale analysis, and quantitative assessment are conducted on the basis of the computational results. As a result, it is found that the speed and the direction of storm movement can play an important role in determining peak discharge and peak arrival time. In addition, the storm movement can generate loop in the stage-discharge relationship curve. Finally, it is revealed that the rating curve depends on the watershed characteristics rather than the rainfall conditions, at least in the idealized V-shaped watershed.

We developed a GPU-accelerated 2D physically based distributed rainfall runoff model for a PC environment. The governing equations were derived from the diffusive wave model for surface flow and the Horton infiltration model for rainfall loss. A numerical method for the diffusive wave equations was implemented based on a Godunov-type finite volume scheme. The flux at the computational cell interface was reconstructed using the piecewise linear monotonic upwind scheme for conservation laws with a van Leer slope total variation diminishing limiter. Parallelization was implemented using CUDA-Fortran with an NVIDIA GeForce GTX 1060 GPU. The proposed model was tested and verified against several 1D and 2D rainfall runoff processes with various topographies containing depressions. Simulated hydrographs, water depth, and velocity were compared to analytical solutions, dynamic wave modeling results, and measurement data. The diffusive wave model reproduced the runoff processes of impermeable basins with results similar to those of analytical solutions and the numerical results of a dynamic wave model. For ideal permeable basins containing depressions such as furrows and ponds, physically reasonable rainfall runoff processes were observed. From tests on a real basin with complex terrain, reasonable agreement with the measured data was observed. The performance of parallel computing was very efficient as the number of grids increased, achieving a maximum speedup of approximately 150 times compared to a CPU version using an Intel i7 4.7-GHz CPU in a PC environment.

We studied how rainfall spatial distribution affects the relationship between rainfall spatiotemporal resolution and runoff prediction accuracy under real field conditions. We gathered radar rainfall and discharge data for three rainfall events. These rainfall-runoff events were then reproduced using a kinematic wave model. Modeling accuracy was estimated quantitatively using the Nash–Sutcliffe model efficiency coefficient and peak discharge ratio. Normalized root-mean-square error ( $\mathrm{nRMSE}$ ), skewness ( $S_k$ ), and second scaled spatial moment of catchment rainfall ( ${\delta }_2$ ) were employed to quantify rainfall spatial distribution characteristics. By relating the accuracy of modeling results to the rainfall spatial characteristics using various rainfall spatiotemporal resolutions, we found that the modeling results converged to a value as the $\mathrm{nRMSE}$ , $\left|S_k\right|$ and $|1-{\delta }_2|$ decreased. That is, rainfall spatial distributions affect the relationship between lower limit of rainfall spatiotemporal resolution for runoff models and runoff prediction accuracy.