Applicability of Kinematic Wave Model for Flood Routing under Unsteady Inflow

This study implemented kinematic wave and dynamic wave approximation of flood routing for a prismatic rectangular channel. The results of the two methods were compared by differences in maximum flow depth, and the applicability of kinematic wave equation was discussed. The influences of hydraulic and geometrical factors on the applicability of kinematic wave equation were considered. It was found that a portion of the numerical results violated existing criteria used to indicate the applicability of kinematic wave equation, particularly when geometrical and hydraulic factors were considered together. This is because the characteristics of upstream inflow were rarely or incompletely considered in these criteria. Therefore, the present study proposed a new criterion. The theoretical influence of all factors was considered using three parameters, namely, KF02, ηts/T0′ and Qbottom/Qpeak (K, F0, ηts, T0′, Qbottom, and Qpeak represent the kinematic wave number, Froude number, the time span of discharge exceeding 90% of maximum discharge in hydrograph, wave travel time in the channel, base flow discharge, and peak discharge, respectively, while the subscript 0 represent the value of reference discharge). The influences of these three parameters were illustrated by the momentum equation of one-dimensional Saint-Venant equation. The numerical results showed that the value of ηts/T0′ (KF02)D could be used to determine the relative error ξh of kinematic wave equation. In addition, for each Qbottom/Qpeak the value of ηts/T0′ (KF02)D used to depict the same relative error ξh was different. This new criterion was validated using two real case studies, and it showed a good performance.

PERFORMANCE OF RADIAL POINT INTERPOLATION METHOD IN SOLVING KINEMATIC WAVE EQUATION FOR HYDROLOGIC MODELLING

This paper presents the solution of the kinematic wave equation using a meshless radial point interpolation method (RPIM). The partial differential equation is discretized using a Galerkin weighted residual method employing RPIM shape functions. A forward difference scheme is used for temporal discretization, while the direct substitution method is employed to solve the nonlinear system at each time step. The formulation is validated against solutions from conventional numerical techniques and physical observation. In all cases, excellent agreements are achieved and hence the validation of the proposed formulation. Optimum values of the multi-quadrics shape parameters were then determined before the assessment of the performance of the method. Based on the convergence rate, it has been shown that the proposed method performs better than the finite difference method and equivalent to the finite element method. This highlights the potential of RPIM as an alternative method for hydrologic modeling.

Solving the erosion transport equation on three dimensional catchments

<p>Modeling the kinematic wave equation and sediment transport equation enables a deterministic approach for predicting surface runoff and resulting sediment transport. Both the kinematic wave equation and the sediment transport equation are first order differential equations. Moreover the kinematic wave equation is a quasilinear problem. In many engineering applications this set of equations is solved on one-dimensional representative cross-sections. However, a proper selection of representative cross-section(s) is  cumbersome. On the other hand integrating this set of equations on real catchment topography  yields difficulties for standard variational methods such as continous Galerkin method. These difficulties are two-fold (1) the nonlinearity of the kinematic wave, and (2) the absence of diffusion term, which acts as a stabilization term for convection-diffusion equation. In a theory, the Peclet number of numerical stability reaches infinity. </p><p>In this contribution we will focus on a stable numerical approximation of this convection-only problem using least square method. With this method we are able to reliably solve both the kinematic wave equation and the sediment transport equation on computational  domains representing real catchment topography. Several examples representing real-world scenarios will be given.</p>

Development of a Flow Routing Model Including Inundation Effect for the Extreme Flood in the Chao Phraya River Basin, Thailand 2011

In the second half of 2011, massive flooding in the lower part of the Yom and Nan River Basins and the Chao Phraya River Basin resulted in tremendous loss and adversely impacted on the livelihood, society, and economy of Thailand. The development of reliable and efficient prediction tools is important for prevent similar occurrences in the future. Consequently, this study thus aimed to develop an applicable distributed flow routing model including the inundation effect. A flow routing model using a kinematic wave equation was modified based on the concept of a diffusive tank model, which included the inundation effect. Overbank flow was estimated by using a broad crested weir equation. The inundation model had ten parameters that provided a good fit for observed and simulated discharge in 2011 at the C.2 Station with a Nash-Sutcliffe efficiency of 0.91.

Analytical solution of a kinematic wave approximation for channel routing

The kinematic wave approach is often used in hydrological models to describe channel and overland flow. The kinematic wave is suitable for situations where the local and convective acceleration, as well as the pressure term in the dynamic wave model is negligible with respect to the friction and body forces. This is the case when describing runoff processes in the upper parts of catchments, where slopes are generally of the order of 10−3. In physical-based hydrological models, the point-scale conservation equations are integrated over model entities, such as grid pixels or control volumes. The integration leads to a set of ordinary differential governing equations, which can be solved numerically by methods such as the Runge–Kutta integrator. Here, we propose an analytical solution of a Taylor-series approximation of the kinematic wave equation, which is presented as non-linear reservoir equation. We show that the analytical solution is numerically robust and third-order accurate. It is compared with the numerical solution and the solution of the complete dynamic wave model. The analytical solution proves to be computationally better performing and more accurate than the numerical solution. The proposed analytical solution can also be generalized to situations of leaking channels.