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Modeling of Sequences of Wet and Dry Days by Binary Discrete Autoregressive Moving Average Processes

Tiao J. ChangDepartment of Civil Engineering, Ohio University, Athens, OH 45701

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M. L. KavvasDepartment of Civil Engineering, University of Kentucky, Lexington, KY 40506

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J. W. DelleurSchool of Civil Engineering, Purdue University, West Lafayette, IN 47907

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Abstract

The Binary Discrete Autoregressive Moving Average (B-DARMA) process, which includes the Markov chain as a particular case, is used to describe the wet-dry day sequences that are obtained from daily precipitation time series.

A three-step procedure, consisting of identification, estimation and model selection is developed and shown to be effective in model building. The identification step is based on the plot of the autocorrelation function, while the estimation of the parameters is done by fitting the autocorrelation function by a nonlinear least-squares method. The model selection uses the probability distributions of run lengths, which are defined and discussed in this paper. The persistences of wet and dry spells, which are important properties in the study of floods and droughts, are well reproduced through the preservation of the run length properties. The best model is chosen as the one with the run length distribution that has the minimum sum-of-squares error in estimating the actual run length distribution.

Abstract

The Binary Discrete Autoregressive Moving Average (B-DARMA) process, which includes the Markov chain as a particular case, is used to describe the wet-dry day sequences that are obtained from daily precipitation time series.

A three-step procedure, consisting of identification, estimation and model selection is developed and shown to be effective in model building. The identification step is based on the plot of the autocorrelation function, while the estimation of the parameters is done by fitting the autocorrelation function by a nonlinear least-squares method. The model selection uses the probability distributions of run lengths, which are defined and discussed in this paper. The persistences of wet and dry spells, which are important properties in the study of floods and droughts, are well reproduced through the preservation of the run length properties. The best model is chosen as the one with the run length distribution that has the minimum sum-of-squares error in estimating the actual run length distribution.

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