Gauging Rivers during All Seasons Using the Q2D Velocity Index Method

Abstract

This paper presents a new model (Q2D) for the velocity distribution in a channel cross section for use in estimating discharge. It describes the model and its theoretical basis and presents the results of a case study. The distribution is determined by combining the principle of maximum entropy with a probability distribution obtained by the solution of the Poisson equation over the cross section. The model uses observed depth and velocity in the water column, where an acoustic Doppler current profiler is installed to determine three key flow parameters to obtain velocity and discharge. In addition, if supporting field discharge measurements are available, the model can be further calibrated to account for any asymmetry in the flow. If velocity distribution data exist for the entire cross section, the model can be adjusted to stretch the predicted velocity pattern to better conform to experimental observations. When applied to the Châteauguay River, Quebec, for both ice covered and open water, Q2D predicted 12 gauged discharges with a −4% bias and an average absolute error of 7% prior to calibration. After removing the bias through calibration, the average absolute error was reduced to 5%.