Modelagem Estocástica de Séries de Vazões, Apresentando Longa Dependência, em Diferentes Escalas Temporais

Abstract

Many studies related with stochastic modeling of periodic river flows series have been developed since the 1960s. Historical statistical parameters reproduction for series presenting long autocorrelation dependence by the most commonly applied models is very difficult. Periodic models and parametric and non-parametric disaggregation models area among those applied in seasonal series stochastic modeling. In this research, it was tested the hypothesis that models that better preserve the historic series statistical characteristics present better performances in disaggregation modeling for flows regularization reservoirs volumes estimation. ARMA(p,q), PAR (p) and PMIX(p,q,P,Q) models were utilized for annual synthetic series generation and evaluation of performances in long dependence historical flow rates series statistical parameters reproduction. The PMIX(p,q,P,Q) models parameters were estimated by two different methods: i) Powell’s optimization algorithm and ii) NSGA-II genetic algorithm. The models were adjusted to series of river flows measured in Brazil, USA and Africa. Models presenting different orders were selected and those that corresponded to the best MAPE performances in the reproduction of annual autocorrelations and Hurst coefficients were chosen. The results corresponding to PARMA(p,q) and PMIX/NSGA-II models were better than those corresponding to PAR (p) and PMIX / Powell models. The annual synthetic series were disaggregated by using parametric and non-parametric methods and the monthly synthetic series MAPE were evaluated considering historical series values. Reservoir volumes and maximum run lengths were estimated for the monthly series. The results were evaluated using the metrics MAPE and RMSE. The results related with PARMA(p,q) and PMIX/NSGA-II models were superior to those related with the other models, corroborating the evaluated hypothesis. All simulations were performed by using the computational tool MAEvaz, developed in this study.