STOCHASTIC ANALYSIS AND MODELING OF RIVERFLOW TIME SERIES

LIANG-TSI MAO, Purdue University

Abstract

Three aspects of the stochastic analysis and modeling of hydrological time series are investigated in this study. They are the following: (1) The Bayesian decision rule for optimum choice of type and order of the "best" model among different ARIMA models, (2) the recursive IV-AML method for daily rainfall-runoff modeling, and (3) the Fractional ARIMA to characterize simultaneously the short and long term persistence in hydrological data. The Bayesian decision rule is transitive, consistent and gives posterior probabilities of different candidate models. The best models among AR, MA and ARMA models for eleven sets of annual flows is found by this decision rule and the importance of considering different families of models is illustrated. For monthly flows, models of observed and transformed data are compared. The optimal model for the log transformed data is found to be considerably superior to the best model from the original data. The performance of the recursive IV-AML method in parameter estimation and one-day ahead flow forecasting is studied for Eagle Creek watershed. A soil moisture accounting type of rainfall filter is shown to yield substantial improvement in parameter estimation and flow forecast stages. Models in which parameters are updated do not give better flow forecasts compared to constant coefficient models whose parameters are estimated from a long period of data. The performance of Fractional ARIMA models for modeling annual river flows is examined. A grid-search method and the criterion of minimum residual variance can be used for parameter estimation of Fractional ARIMA models. The Fractional difference models alone perform similarly to that of the Fractional Gausian Noise model. For annual flows of the St. Lawrence and three other rivers, the d(,f) values found in the Fractional ARIMA model are small. Consequently, for the limited data considered in the present study the performance of the Fractional ARIMA models in characterizing the correlation structure and rescaled range characteristics are similar to that of the ARMA models.

Degree

Ph.D.

Subject Area

Mechanical engineering

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