A one- and two-dimensional generalized Pareto model for a river flow

The main objective of this paper is to find a two-dimensional model for the flow of the Romaine River in Québec, Canada, which could be used to forecast the flow one day after the currently observed flow. The 2D density function proposed must be such that the correlation coefficient between the two variables can be chosen close to 1, since the river flows on two consecutive days are very highly correlated. We find that a generalized Pareto distribution provides a good fit to the data. We then propose 2D versions of this distribution. Finally, a linear combination of two such 2D distributions is used to obtain the required model. In the case of the Romaine River, the model considered works very well. It could be used with or modified for other rivers.