| Abstract: | ABSTRACT: The dynamic relationship between stage and discharge which is unique to a particular flood for a selected station along the river can be determined via a mathematical model based on the complete one-dimensional equations of unsteady flow, i.e., the equations for the conservation of mass and momentum of the flood wave, and the Manning equation which accounts for energy losses. By assuming the bulk of the flood wave moves as a kinematic wave, the need for spatial resolution of the flood can be eliminated, and only the time variation of either the discharge or stage at the selected station is necessary for the computation of the other. The mathematical model can be used in river forecasting to convert the forecast discharge hydrograph into a stage hydrograph which properly reflects the unique dynamic stage-discharge relationship produced by the variable energy slope of the flood discharge. The model can be used also in stream gaging to convert a recorded stage hydrograph into a discharge hydrograph which properly accounts for the effects of unsteady flow. The model is applied to several observed floods at selected stations along the Lower Mississippi, Red, and Atchafalaya Rivers. The root mean square errors between observed and computed discharges are in the range of 3 to 7 percent, values well within the accuracy of the observations. A simple, easily-applied graphical procedure is also provided for estimating the magnitude of the effect of the unsteady flow on stage-discharge ratings. As a general rule, the dynamic effect may be significant if the channel bottom slope is less than 0.001 ft/ft (about 5 ft/mi) when the rate of change of stage is greater than about 0.10 ft/hr. |
