Three Methods for Estimating the Entropy Parameter M Based on a Decreasing Number of Velocity Measurements in a River Cross-Section

Abstract

Abstract:The theoretical development and practical application of three new methods for estimating the entropy parameter M used within the framework of the entropy method proposed by Chiu in the 1980s as a valid alternative to the velocity-area method for measuring the discharge in a river is here illustrated. The first method is based on reproducing the cumulative velocity distribution function associated with a flood event and requires measurements regarding the entire cross-section, whereas, in the second and third method, the estimate of M is based on reproducing the cross-sectional mean velocity U by following two different procedures. Both of them rely on the entropy parameter M alone and look for that value of M that brings two different estimates of U , obtained by using two different M-dependent-approaches, as close as possible. From an operational viewpoint, the acquisition of velocity data becomes increasingly simplified going from the first to the third approach, which uses only one surface velocity measurement. The procedures proposed are applied in a case study based on the Ponte Nuovo hydrometric station on the Tiber River in central Italy.

From Surface Flow Velocity Measurements to Discharge Assessment by the Entropy Theory

“…The entropic parameter M, which is a characteristic of the section [20], can be easily estimated through the pairs (u m , u max ) of the available velocity dataset at a gauge site by using the linear entropic relation [14]:…”

“…The method can be applied for gage sites in which a robust velocity dataset is available and Φ(M obs ) can be easily estimated by the observed pairs (u m , u max ). For ungauged sites, the M parameter can be even estimated by expressing its value in terms of hydraulic and geometric characteristics such as proposed by [21] and/or following [20], who identified a simple way to estimate M from the maximum surface velocity typically located near the middle of the channel [24]. where is a parameter representing the dip at the y-axis and which is updated through an iterative process, wherein at each iteration, p, a constant value (0.1 m) is added to the initial value 1 , assumed to be equal to 0.05 m.…”

A novel permanent gauge-cam station for surface-flow observations on the Tiber River

“…Such methodologies enable the estimation of the surface-flow velocity field over extended regions from the relative motion of naturally occurring debris or floaters dragged by the current (Fujita et al, 1997). Surface-flow velocity measurements are typically related to depth-averaged velocity, and discharge is computed from information on the cross section (Alessandrini et al, 2013;Chiu, 1991;Farina et al, 2014;Jodeau et al, 2008;Moramarco et al, 2004;Tazioli, 2011). Among optical approaches, large-scale particle image velocimetry (LSPIV) is an extension of classical particle image velocimetry (PIV) (Adrian, 1991;Raffel et al, 2007).…”

Conventional Point-Velocity Records and Surface Velocity Observations for Estimating High Flow Discharge

“…These approaches are based on different levels of knowledge of the velocity field consisting of (i) the entire spatial distribution of velocity in the flow area, (ii) the surface velocity distribution and (iii) the sole sampling of umax. In this latter case, the assumption on the surface velocity distribution may influence the accuracy of the M estimate [19].…”

“…Another possibility is to estimate M by using one of the approaches proposed by Farina et al [19]. These approaches are based on different levels of knowledge of the velocity field consisting of (i) the entire spatial distribution of velocity in the flow area, (ii) the surface velocity distribution and (iii) the sole sampling of umax.…”