Non-contact discharge estimation at a river site by using only the maximum surface flow velocity

Abstract

The study proposes a novel method of computing river discharge based on the maximum surface velocity recorded using a non-contact-based measurement at a singular water surface point. This location, generally, coincides with the maximum flow depth of the cross-section and accounts for the dip phenomena, where the maximum instream velocity occurs below the water surface. The method is based on information entropy theory developed by Shannon (1948) and applied to river hydraulics. In this study an alternate form of entropy is used to compute discharge as a function of the cross-sectional mean velocity, maximum velocity and shear velocity (Keulegan,1938) by minimizing the error of the state equilibrium constant, $\Phi \left(M\right)$, which is the ratio between the mean and maximum flow velocity, and that estimated using the Keulegan-based relationship. To test the accuracy of the proposed method, the maximum surface flow velocities measured at two gauging stations, each located on two different Italian rivers were studied. The estimated discharges by the proposed method were found to be comparable with the existing non-contact discharge method advocated by Moramarco et al. (2017) and, the traditional velocity-area method, using, e.g., the mean-section approach, based on the following metrics: the Nash-sutcliffe Efficiency (NSE), the coefficient of correlation and the percent bias (PBIAS). The mean velocity error emulates a Gaussian distribution for both the gauging stations and was within 95% and 5% confidance levels. Further, the entropy-based velocity profiles generated by the proposed method at the y-axis are consistent with those of the depth-based velocity profiles observed by the mechanical-current meter, thus, proving the appropriateness of the proposed discharge estimation method.