TOWARD HIGH-RESOLUTION FLOOD FORECASTING FOR LARGE URBAN AREAS - NEW SOLUTIONS FOR 1D ROUTING

Abstract

The ability to forecast flow, depth, and velocity in flooding events is one of the most important needs in highly populated urban areas. Urbanization and climate change highlight the necessity to understand and accurately predict water-related hazards in urban areas due to extreme precipitation. Towards that end, this study initially assesses the impact of changes in precipitation magnitude and imperviousness on urban inundation in a flooding prone urban catchment in the Dallas-Fort Worth Metroplex. Consequently, this study focuses on identifying potential alternatives to the conventional inundation models to improve operational viability of real-time flood forecasting in urban areas by downscaling coarse-resolution model output. Taking advantage of high-resolutions physiographic information, the problem is then transformed into developing efficient methods for routing flow in a network of 1D channels to represent sub-grid variability of hydraulic parameters within coarse 2D cells. Accordingly, two existing methods for such a routing problem are discussed, i.e., the diffusion wave routing and nonlinear routing with power-law storage functions. Each of the aforementioned methods is then solved innovatively to improve their efficiency for real-time routing of flow through many small streams quickly over a large area. In this work, two new methods for solving the 1-dimensional linear diffusion wave equation for finite domain is presented. Referred to as the Continuous Time Discrete Space (CTDS) methods, they yield explicit symbolic expressions for time-continuous solutions at discrete points in space. As such, the methods provide a powerful tool for very easily obtaining accurate diffusive wave solutions in lieu of numerical integration when predictions are desired only at specific locations along the channel. The proposed methods are easy to implement and may be used in a variety of routing applications where accurate explicit symbolic solutions are desired for linear advection-diffusion at specific locations. Also, a new direct solution for nonlinear reservoir routing with a general power-law storage function is presented. The resulting implicit solution is expressed in terms of the incomplete Beta function and is valid for inflow hydrographs that may be approximated by a series of pulses of finite duration. A separate solution for zero inflow representing recession is also presented. The new analytical solution extends the previous results reported in the literature which provide direct solutions only for certain exponents in the power-law storage function. In addition to the wide spectrum of applications that require modeling of nonlinear reservoirs or open channels, the direct solution may also be used for physically-based semi-distributed routing of hillslope flow following simplification of the flow paths as a dendritic network of nonlinear reservoirs. The proposed solutions offer new pathways for simple and efficient modeling of flood waves in real-world applications with minimal computational effort that makes them suitable candidates for flood forecasting in large urban areas.