Nonlinear Prediction in Riverflow - The Paiva River Case

Abstract

We exploit ideas of nonlinear dynamics in a non-deterministic dynamical setting. Our object of study is the observed riverflow time series of the Portuguese Paiva river whose water is used for public supply. The Takens delay embedding of the daily riverflow time series revealed an intermittent dynamical behaviour due to precipitation occurrence. The laminar phase occurs in the absence of rainfall. The nearest neighbour method of prediction revealed good predictability in the laminar regime but we warn that this method is misleading in the presence of rain. The correlation integral curve analysis, Singular Value Decomposition and the Nearest Neighbour Method indicate that the laminar regime of flow is in a small neighbourhood of a one-dimensional affine subspace in the phase space. The Nearest Neighbour method attested also that in the laminar phase and for a data set of 53 years the information of the current runoff is by far the most relevant information to predict future runoff. However the information of the past two runoffs is important to correct non-linear effects of the riverflow as the MSE and MRE criteria results show. The results point out that the Nearest Neighbours method fails when used in the irregular phase because it does not predict precipitation occurrence.