Assessment of Hydrologic Controls on Applicability of Routing Methods

Abstract

Various applicability criteria have been developed to determine the appropriateness of different hydraulic routing methods (e.g., kinematic, diffusive, or dynamic) a priori (i.e., before any routing is done). However, little has been done to account for hydrologic variability and basin size in these criteria. To account for hydrologic variability and basin size in this paper, an existing applicability criteria for routing methods is linked analytically to a model of peak flow, a simple stochastic representation of rainfall, and relationships of river basin geomorphology. This linkage provides a novel way for understanding and quantifying the interrelationship between basin-scale hydrologic phenomena and routing methods. Using this linkage, the aim of this paper is to explore and assess the applicability of routing methods in strongly coupled systems or headwater basins. To illustrate and assess the linkage, the Illinois River basin is used. From this assessment, the diffusive and dynamic contributions are both found to increase for the general condition of an increasing peak flow and decreasing time to peak at a given basin size. After accounting for scale dependencies, the mean diffusive and dynamic contributions are found to increase with the basin size. The rate of increase seems controlled by the interplay between the slope-area relationship and the scaling of the time to peak, which in turn depends on both the mean rainfall duration and the time of concentration in this paper. In terms of the annual maximum flood series, the dynamic and diffusive contributions show decreasing and increasing trends, respectively, as a function of the basin size for a fixed return period. The latter is found to depend on the scaling of peak floods and the slope-area relationship. For a fixed basin size, both the diffusive and dynamic contributions are found to increase with the return period. The developed framework is able to provide insight at the basin scale into the influence of hydrologic controls arising from climate, runoff, and geomorphology on the applicability of routing methods.