DAILY PRECIPITATION AND STREAMFLOW MODELING BY DISCRETE AUTOREGRESSIVE MOVING-AVERAGE PROCESSES
Abstract
This thesis constructs two newly defined stochastic processes: the Binary Discrete Autoregressive Moving Average modeling the wet-dry precipitation sequence mixed with an Exponential distribution to express the magnitude of the precipitation (B-DARMA-E) and the Multi-state Discrete Autoregressive Moving Average process (M-DARMA). Both processes are used to model the daily precipitation time series in Indiana. A three-step procedure of Identification, Estimation, and Diagnostic Checking, is formulated for the modeling by the B-DARMA-E and the M-DARMA processes. The identification by means of the autocorrelation function is convenient from an engineering point of view, while the estimation through the preservation of the autocorrelations is quite suitable for a stochastic process. The diagnostic checking by means of the run length distributions is shown to be statistically efficient. The binary run length distribution is defined and derived for the former, while the multi-state run length distributions are constructed for the latter. A criterion for the selection of the best model is discussed separately and makes use of the run length property. These schemes of diagnostic checking and of best model selection are shown very effective in the illustrative example which uses Indiana data. Finally the Transfer Discrete Autocoregressive Moving Average model (T-DARMA) is conceptually constructed for the daily precipitation-streamflow transfer process based on the known properties of the B-DARMA-E or the M-DARMA precipitation model. The statistical relationships between the input and the output series are formulated and used to estimate the model parameters so that the T-DARMA model preserves the first and the second order statistical properties as well as the conceptual water balance. The residual series are investigated and show that the model is very satisfactory.
Degree
Ph.D.
Subject Area
Hydrology
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