| Prediction of water temperatures is essential for the management of aquatic resources in our rivers. Researchers strongly believe that changes in temperatures due to climate change in the Atlantic region will involve higher temperatures in the summer, a period already having a negative affect on aquatic resources. The goal of this research was to predict stream water temperatures by using a stochastic model for estimating extreme events. The study region was the Catamaran Brook, a tributary of the Miramichi watershed. Water temperature data were available from 1992 to 2000. Two components can explain water temperature time series: the annual component and the residuals. A Fourier series was used to explain the annual component and the short-term residuals were then calculated. In order to model the occurrence of extreme events, a peak over threshold value model was chosen, and the series of temperature events above this threshold were modelled by a Poisson process. From this series, two analyses were done. First, the durations (days), intensities (°C) and volumes (°C*days) of the events were considered separately as independent and identically distributed sets of random variables. Secondly, a bivariate analysis was carried out with the following combinations: intensity-volume, duration-intensity and duration-volume. Bivariate distributions with exponential marginals, which are presented by Singh and Singh (1991) (model A) and by Nagao and Kadoya (1971) (model B) were modified to yield Pareto distributed marginals, as suggested by Ashkar and El-Jabi (2002) and Ashkar and Bayentin (2001). Khi-square (χ 2) and Kolgomorov-Smirnov (K-S) goodness of fit tests were used to evaluate the distributions. The fits between the theoretical and observed distributions were generally found to be acceptable. However, model B performed better than model A. |
