The Hierarchy and Self-Affinity of the Time Variability within the Tropical Atmosphere Inferred from the NOAA OLR Data

Abstract

The variability of the tropical atmosphere consists of a hierarchy of time-scales. In order to seethe extent to which there exists clear scale-separation among different levels of the hierarchy, several analyses based on fracta geometry theory are performed for the NOAA OLR data.
The power spectra conform quite roughly to the inverse-power form, which implies no scaleseparation or "scaling" . This tendency is further examined by a fractal analysis of the time series, which measures the change of the magnitude of variability as a period of averaging is changed. Remarkably, the extent of "scaling" changes locally along the equator, due to the locality of the region with a particular dominant time-scale: the intraseasonal variability, the annual cycle, and the El Nino/Southern Oscillation. This locality is quantified by the self-affinity scale, which measures the extent of "scaling". In particular, the self-affinity scale can be identified as the characteristic time-scale of the super clusters in the region where the intraseasonal variability is conspicuous.
The probability that a convectively active period continues longer than a certain time decays exponentially with a characteristic decay time-scale of 3-5 days, which can be identified as the time-scale of cloud clusters.