Detecting low-dimensional chaos in geophysical time series

Driven by the great appeal of the potential capability to reduce very complex and highly erratic phenomenologies to simple deterministic and predictable processes, much effort has been devoted to studying chaotic systems. Unfortunately, such studies have been essentially theoretical, and the problem of detecting chaos in real time series has so far received little attention. As a consequence, the available techniques are fairly inefficient and are often misused. Furthermore, if detecting chaos in real-time data would, in any case, be important from a philosophical stand point, only low-dimensional chaos is of practical interest, since it allows an effective short range predictability and could possibly also be modeled. A critical review of the available methods to detect chaos in a real series is presented together with a procedure which is efficient in the presence of experimental errors and with relatively small sets of data. An application to the series of geomagnetic inversions and to the eruptive activity of the Piton de la Fournaise volcano, for which a chaotic dynamics appeared best documented, does not lead to detection of any low-dimensional chaos. Copyright 1997 by the American Geophysical Union