A simple model of flood peak attenuation

Abstract

A simple analytical model was developed for evaluating the attenuation of flood wave peak discharge. The physically-based model represents the flood wave along its trajectory, based on the diffusive model. Relative peak discharge decreases along the downstream distance according to a power function. The distance is scaled by the attenuation factor related to river hydrodynamics (flow rating, hydraulic diffusivity, celerity, and floodplain storage) and input hydrograph (initial peak discharge, hydrograph volume, and its relative curvature). It also informs the attenuation length, which is a practical indicator of the river distance in which discharge decreases by a given factor. Sensitivity analyses indicate that initial peak discharge, volume, floodplain storage, and slope are the governing factors of attenuation. Model's validity and accuracy were demonstrated by reproducing data from (a) numerical solutions of the Saint-Venant equations covering a wide range of conditions, (b) 29 observations from 11 historical dam-breaks, (c) 15 observations of natural floods in seven rivers and (d) a detailed hydrodynamic model. The model errors were generally lower than 10% and not larger than the typical uncertainty of flood observations. The accuracy is higher than simplified empirical models and analogous to a detailed hydrodynamic model that is representative of current practice. The proposed flood attenuation model can be easily applied using a few common parameters and a simple equation in a basic spreadsheet. It is suitable for practical applications such as first assessments of natural and dam-break floods, engineering design, and analyses of large river networks supported by remote sensing data.