Discharge Estimation Using Tsallis and Shannon Entropy Theory in Natural Channels

Abstract

Streamflow measurements during high floods is a challenge for which the World Meteorological Organization fosters the development of innovative technologies for achieving an accurate estimation of the discharge. The use of non-contact sensors for monitoring surface flow velocities is of interest to turn these observed values into a cross-sectional mean flow velocity, and subsequently, into discharge if bathymetry is given. In this context, several techniques are available for the estimation of mean flow velocity, starting from observed surface velocities. Among them, the entropy-based methodology for river discharge assessment is often applied by leveraging the theoretical entropic principles of Shannon and Tsallis, both of which link the maximum flow velocity measured at a vertical of the flow area, named the y-axis, and the cross-sectional mean flow velocity at a river site. This study investigates the performance of the two different entropic approaches in estimating the mean flow velocity, starting from the maximum surface flow velocity sampled at the y-axis. A velocity dataset consisting of 70 events of measurements collected at two gauged stations with different geometric and hydraulic characteristics on the Po and Tiber Rivers in Italy was used for the analysis. The comparative evaluation of the velocity distribution observed at the y-axis of all 70 events of measurement was closely reproduced using both the Shannon and Tsallis entropy approaches. Accurate values in terms of the cross-sectional mean flow velocity and discharge were obtained with average errors not exceeding 10%, demonstrating that the Shannon and Tsallis entropy concepts were equally efficient for discharge estimation in any flow conditions.