Stochastic Modeling of Streamflow Series, with Long Dependence, in Different
Time Scales

Name: Mônica de Souza Mendes
Type: PhD thesis
Publication date: 24/02/2021
Advisor:

Name	Role
Antonio Sérgio Ferreira Mendonça	Advisor *

Examining board:

Name	Role
Antonio Sérgio Ferreira Mendonça	Advisor *
Diogo Costa Buarque	Internal Examiner *
Jorge Machado Damazio	External Examiner *
José Antônio Tosta dos Reis	Internal Examiner *
Wilson dos Santos Fernandes	External Examiner *

Summary: 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.

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