IWRA World Water Congress 2008 Montpellier France
1. Water availability, use and management
A. A. Pinto
Nonlinear dynamics, Ruelle-
Takens embedding, BHP distribution, river flow prediction
AbstractWe exploit ideas of
nonlinear dynamics and statistical physics in a complex 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 Ruelle-
Takens delay embedding of the daily riverflow time series revealed an intermittent dynamical behavior due to
precipitation occurrence. The laminar phase occurs in the absence of rainfall. The nearest neighbor method of
prediction revealed good predictability in the laminar regime, but we warn that this method is misleading in the
presence of rain.
We present some new insights between the quality of the prediction in the laminar regime, the
embedding dimension, and the number of nearest neighbors considered. After this careful study of the laminar phase,
we find, unexpectedly, that the BHP distribution is an approximation of the empirical distribution of the relative
decay. Furthermore, the empirical distribution of the relative decay computed using the nearest neighbors predictor is
even closer to the BHP distribution.
Hence, the nearest neighbor method of prediction acts as a filter which does
not eliminate the randomness but exhibits its main character in the laminar regime.