A systematic approach to noise reduction in chaotic hydrological time series

Recent studies have shown that the noise limits the performance of many tec hniques used for identification and prediction of deterministic systems. Th e 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 l evel and nature of the noise. Meanwhile, a variety of nonlinear noise reduc tion methods have been developed and applied to hydrological (and other rea l) data. The present study addresses some of the potential problems in appl ying 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 reducti on in chaotic hydrological (or any real) data, by coupling a noise level de termination method and a noise reduction method. The approach is first demo nstrated on noise-added artificial chaotic data (Henon data) and then appli ed on real chaotic hydrological data, the Singapore rainfall data. The appr oach uses the prediction accuracy as the main diagnostic tool to determine the most probable noise level, and the correlation dimension as a supplemen tary tool. The results indicate a noise level between 9 and 11% in the Sing apore rainfall data, providing a possible explanation for the low predictio n accuracy achieved in earlier studies for the (noisy) original rainfall da ta. Significant improvement in the prediction accuracy achieved for the noi se-reduced rainfall data provides additional support for the above. (C) 199 9 Elsevier Science B.V. All rights reserved.