Optimizing river discharge measurements using Monte Carlo Markov Chain

In this work we implement Monte Carlo Markov Chain (MCMC) dynamics in the search of rules that may lead to optimizing river discharge measurements, which should prove useful in situations when resources are scarce. The MCMC dynamics is based on a recently proposed computational interpolation scheme, where the velocity profile for each vertical section is first determined by applying polynomial regression, and then a continuous approximation for the velocity across the entire vertical section is obtained through interpolation. To this end, we use the data obtained experimentally on rivers Exu and Capibaribe, state of Pernambuco, in the northeast of Brazil. By considering the velocity profile obtained through this procedure using all the available measurement points as the “best known profile”, or benchmark, we proceed by randomly choosing a small number of measurement points, repeating the above procedure, and comparing the result with the benchmark. The deviation of the reduced point approximation from the benchmark is then used as an objective function, which is minimized through an iterative MCMC process of moving the individual measurement points in different directions, and accepting or rejecting these movements. MCMC dynamics is applied for different choices of the reduced number of measurements, and finally a “recipe” is proposed for the practical choice of the number of measurement points and their placement, which optimizes the river discharge measurement. More precisely, instead of performing the full set of measurements at k vertical sections using several points for each vertical in order to apply the standard area-velocity method, one may perform just a single measurement close to the surface for every other of the k verticals, and then apply the proposed computational scheme. If the image of the velocity profile keeps changing as new measurements are incorporated, and one is interested in the details of the multiple flow structure, additional measurements should be made between adjacent high velocity observations. The software implementing the numerical procedure is available for free download at the internet page .