Detecting chaos in heavy-noise environments.

Detecting chaos and estimating the limit of prediction time in heavy-noise environments is an important and challenging task in many areas of science and engineering. An important first step toward this goal is to reduce noise in the signals. Two major types of methods for reducing noise in chaotic signals are chaos-based approaches and wavelet shrinkage. When noise is strong, chaos-based approaches are not very effective, due to failure to accurately approximate the local chaotic dynamics. Here, we propose a nonlinear adaptive algorithm to recover continuous-time chaotic signals in heavy-noise environments. We show that it is more effective than both chaos-based approaches and wavelet shrinkage. Furthermore, we apply our algorithm to study two important issues in geophysics. One is whether chaos exists in river flow dynamics. The other is the limit of prediction time for the Madden-Julian oscillation (MJO), which is one of the most dominant modes of low-frequency variability in the tropical troposphere and affects a wide range of weather and climate systems. Using the adaptive filter, we show that river flow dynamics can indeed be chaotic. We also show that the MJO is weakly chaotic with the prediction time around 50 days, which is considerably longer than the prediction times determined by other approaches.