Modeling and forecasting river flows by means of filtered Poisson processes

To model and forecast daily river flows, filtered Poisson processes with a response function that generalizes the one commonly used in hydrology are considered. The form of the response function is based on the concept of the instantaneous unit hydrograph and improves the quality of the classical model. A statistical procedure based on the theoretical autocorrelation coefficients is used to estimate the model parameters. Then, the quality of the model is assessed by comparing the theoretical autocorrelation coefficients obtained with both the generalized and the classical models to the corresponding empirical coefficients. Furthermore, an estimator of the flow at time t+1t+1, given the flows at time t-1t-1 and t, is developed in a particular case and the forecasting power of the model is checked, using some indicators of difference, compared to the classical model and to an autoregressive model. An application to the Delaware and the Hudson Rivers, located in the United States, is presented.