Modeling the uncertainty of hydrologic processes exhibiting changes
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The Geometric-Normal-Normal (GNN) model was analyzed and tested for the purpose of simulating hydrologic processes that exhibit changes. The general moment equations of the GNN model were derived, particularly the lag-k autocorrelation function. They can be used to estimate the model parameters based on the method of moments. Other estimation methods were also suggested. They include regression analysis, fitting the autocorrelation function (ACF), using the range properties, and using the run properties. The performance of these methods was tested by using simulation experiments. The results showed that in terms of bias and mean square error the regression and range methods are better than the other methods for estimating the model parameters. The GNN model was applied to the White Nile River flows at Malakal and the annual net basin supply (NBS) data for Lake St. Clair of the Great Lakes system. Simulation experiments were conducted to test the ability of the GNN model to preserve a number of observed statistics such as the mean, standard deviation, skewness, rescaled range, Hurst coefficient, longest drought, maximum deficit, and surplus. Results show that the GNN model, in general, performs quite well in preserving these statistics. An extended version of the GNN model was also formulated and analyzed in this study. Different methods of estimation were suggested to estimate the model parameters. However, application of this model to Malakal flows and Lake St.Clair NBS data did not show any advantage over simpler GNN.