Estimates of cyclone track predictability. II: Fractal analysis of mid-latitude cyclones

Abstract

A nonlinear systems analysis is applied to cyclone tracks over the North Pacific area (based on surface pressure analyses and twelve-hourly sampling time) and over the Australian region (based on 500mb heights and daily sampling) for the respective winter seasons. First estimates are obtained of the degree of their chaotic or irregular behaviour in phase space and of the self-affinity of the planar tracks. This information is deduced from distance distributions (correlation integrals) between independent pairs of cyclone trajectories and from the structure function of individual cyclone paths. The correlation integrals reveal average structures of the substitute phase space (such as the dimension of the attractor, a measure of predictability) after stratifying the North Pacific tracks into a western domain of growing and an eastern domain of large amplitude cyclones. A further subdivision into large-scale flow anomalies (the positive and negative Pacific/North America pattern in the eastern North Pacific) provides flowdependent estimates which indicate two subsystems differing in dimension and predictability. the time scaling analysis of the planar cyclone paths characterizes systems of no scale preference: the associated variance spectra decrease by a 2 to 3 power law with increasing frequency.