Refinement of the Fread Method for Improved Tracking of Stream Discharges during Unsteady Flows

Abstract

There are a plethora of analytical methods that can account for the effect of unsteady flow (i.e., hysteretic behavior) on steady-state stage-discharge rating curves (hQRCs) used to continuously estimate discharge in open-channel flow. One of the most complete and accurate methods for wide rectangular channels is the Fread method. This paper presents an extension of the method that can be applicable to arbitrary geometry of the channel cross section by replacing the hydraulic depth with the hydraulic radius and adjusting formulations associated with wave celerity coefficient and kinematic wave equation in the original Fread method. The modified Fread method improves the accuracy associated with the estimation of conveyance factor and energy slope. It is particularly useful for low-aspect-ratio (i.e., the width-to-depth ratio) channels where the original method’s assumption does not properly hold. These improvements are tested at two sites, each representative of small streams and midsize rivers, to quantitatively illustrate the significance and performance of the refined method.