Reproduction of Hysteresis in Rating Curves

摘要

The well-known Jones formula has long been used to convert a stage hydrograph to a discharge hydrograph under many unsteady flow situations. The logic behind the formula can be explained with the use of the approximate convection-diffusion equation in its development. However, its applicability criterion has not yet been quantified. Assessment of the applicability of the Jones formula is studied herein. In addition, two variations of the Jones formula have been developed: one, incorporating the inertial forces of the one-dimensional momentum equation and the other, incorporating a refined estimate of partial deriv y/ partial deriv x, the longitudinal gradient of the water depth, accounting approximately for the parabolic variation of the water surface. The suitability of these three formulas in converting a given hypothetical stage hydrograph to a discharge hydrograph is assessed under varying channel conditions. The study shows, that the Jones formula and its variants developed in this study, indicate a limit of |(1/S_0) partial deriv y/ partial deriv x|<0.5, where, S_0 is the bed slope, for their successful application. Further, it is found that the formula developed considering a refined estimate of the longitudinal gradient of the water depth performs better than the other two formulas.