A systematic approach to noise reduction in chaotic hydrological time series

Recent studies have shown that the noise limits the performance of many techniques used for identification and prediction of deterministic systems. The extent of the influence of noise on the analysis of hydrological (or any real) data is difficult to understand due to the lack of knowledge on the level and nature of the noise. Meanwhile, a variety of nonlinear noise reduction methods have been developed and applied to hydrological (and other real) data. The present study addresses some of the potential problems in applying such methods to chaotic hydrological (or any real) data, and discusses the usefulness of estimating the noise level prior to noise reduction. The study proposes a systematic approach to additive measurement noise reduction in chaotic hydrological (or any real) data, by coupling a noise level determination method and a noise reduction method. The approach is first demonstrated on noise-added artificial chaotic data (Henon data) and then applied on real chaotic hydrological data, the Singapore rainfall data. The approach uses the prediction accuracy as the main diagnostic tool to determine the most probable noise level, and the correlation dimension as a supplementary tool. The results indicate a noise level between 9 and 11% in the Singapore rainfall data, providing a possible explanation for the low prediction accuracy achieved in earlier studies for the (noisy) original rainfall data. Significant improvement in the prediction accuracy achieved for the noise-reduced rainfall data provides additional support for the above. (C) 1999 Elsevier Science B.V. All rights reserved.