Analysis of streamflow measurements through the entropy approach

The accuracy of the linear relationship between the mean and maximum flow velocity derived by Chiu [1] through the entropy model is investigated by using data collected during 20 years in three gauged river sections along the Tiber river in Central Italy. The percentage error in estimating the cross-sectional mean velocity from the maximum velocity observed is found distributed according to a normal distribution. The mean value of the error is very close to zero and it does not exceed 0.032, while the maximum value of the standard deviation is about 0.09. As the coefficient of the linear relationship is found similar for the three gauged sections, the same relationship between the mean and the maximum velocity can be surmised in whichever river section within the river reach investigated. Besides for the sites where there are few velocity data, a practical method for estimating the cross-sectional mean velocity starting from the maximum velocity observed is also proposed. The method assumes that the behavior of the mean velocities sampled along the verticals in the different portions of the flow area has a parabolic shape and can be determined through three simple constraints. The method has been applied to different velocity data set. Starting from the maximum velocity observed, the method is able to reconstruct adequately the behavior of the mean velocity in the sampled verticals, allowing to estimate with a fair accuracy the cross-sectional mean velocity.