DIMENSION OF WEATHER AND CLIMATE ATTRACTORS

A PROCEDURE for estimating the correlation dimension of the attractor of a dynamical system 1 has been applied to a number of data sets that are representative of weather or climate variations. Reported values of the attractor dimension have typically fallen between 3.0 and 8.0 (refs 2-9). Because the atmosphere is so complex, these values have seemed surprisingly low, and doubts as to their appropriateness have been expressed even by the originators of the method 8,10,11. Here I apply the procedure to 'data' generated by a mathematical system whose dimension can be evaluated by other means, and identify conditions, apparently satisfied by the studies that use real data, in which the procedure will yield systematic underestimates. It therefore seems unlikely that global weather or climate systems possess low-dimensional attractors.