Entropy Based River Discharge Estimation Using One‐Point Velocity Measurement at 0.6D

Abstract

Entropy theory applied to hydrometric measurements enables establishing a relationship between the maximum and the mean velocities of flow passing a river section. In many developing countries, river discharge is still estimated by the velocity‐area method following the procedure established based on the point‐velocities measured at 0.6D depth from the water surface of many verticals of flow section. This study explores the establishment of a relationship between the maximum point‐velocity estimated at 0.6D depth of the vertical located at or nearer to the deepest flow depth, and the maximum point‐velocity occurring somewhere along the same vertical which in turn can be linked to the sectional mean flow velocity based on the established entropy theory. The appropriateness of the proposed two‐steps based approach of discharge estimation is first verified on the Tiber River and the Po River of Italy. The study finds that the values of the maximum point‐velocity estimated using the proposed approach closely matches with the recorded maximum flow velocity values along the same flow‐depths. After this verification, the proposed method was applied for discharge estimation at two Indian river gauging stations, where only the point‐velocity measurements at 0.6D depth locations of the verticals are recorded. The study finds that the discharges estimated by both the proposed approach and the velocity‐area method closely match with each other with the estimated Nash‐Sutcliffe Efficiency (NSE) values greater than 0.99. Thus the proposed two‐steps approach involving the entropy concept based relationship for discharge estimation enables to replace the tedious and time‐consuming velocity‐area approach.

Estimating the Average River Cross‐Section Velocity by Observing Only One Surface Velocity Value and Calibrating the Entropic Parameter

“…Therefore, M is fundamental to addressing velocity measurements during high floods when measurements can be conducted out only in the upper region of flow area where the maximum velocity U max occurs (Moramarco & Singh, 2010). The magnitudes of Φ(M) for the present study were in agreement with the data reported for small rivers for example, 0.66 < Φ(M) < 0.80 for natural channels in the United States (Chiu et al, 2000), 0.6 < Φ(M) < 0.68 for Tiber River in Italy (Moramarco et al, 2019), 0.63 < Φ(M) < 0.69 for Godavari and Ulhas Rivers in India (Vyas et al, 2021), and for large rivers for example, 0.4 < Φ(M) < 0.61 for Amazon River in Brazil (Bahmanpouri et al, 2022). Also, Φ(M) = 0.88 (Hii River data of Shinohara and Tsubaki (1959)) and Φ(M) = 0.91 (Leo-River data of Leopold (1969)) were reported by Choo et al (2011).…”

“…Further, the transverse location of the maximum surface velocity was assumed to change very little during high flow conditions (Vyas et al., 2021). Confirming this, Table 6 presents the effect of changing the transverse location of the maximum surface velocity on the estimation of the discharge and mean velocity.…”