Otimização do método área-velocidade para estimação de vazão fluvial usando MCMC

Abstract

The velocity-area method is a standard procedure for measurement of river discharge, with wide application in hydrometric studies, standardized at the international level by the norm ISO 748:2007 of the International Standards Organization. This method requires measurement of velocity at several verticals of the river, at different depths for each vertical. In general, a relatively high number of measurements is necessary do determine the discharge. Recently a technique was proposed which results in a robust estimate of river discharge using a reduced number of measurement points, based on elementary properties of fluid dynamics, stemming from the Navier-Stokes equations, and the use of continuous interpolation between the verticals for calculating velocity across the entire river cross section. In the present work the Monte Carlo Markov Chain (MCMC) method is used to search for the optimum positions for velocity measurement, with the objective of reducing the number of measurement points without significant loss of precision, and therefore maximizing the efficiency of the estimate. A dedicated computer algorithm was developed in C programming language and applied to measurements collected on the river Exu, state of Pernambuco, Brazil, in April 2008. It is found that the discharge estimates with three or more measurement points exhibit variations well within uncertainty limits corresponding to the full 27 point estimate using the traditional velocity-area method. Simulation results indicate that the best positions for velocity measurement are close to the surface, and that significant savings in cost and labor may be accomplished by positioning the measurements at strategic points, without precision loss.