Fractal rain distributions and chaotic advection

Abstract

Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by treating raindrops as passive tracers advected by the velocity field of a two-dimensional system of point vortices [R. Dickman, PRL 90, 108701 (2003)]. Here I review observational and theoretical aspects of fractal rain distributions and chaotic advection, and present new results on tracer distributions in the vortex model.

Scaling properties of rainfall and desert dust in the Canary Islands

“…However, it has been shown that many complex processes occurring in Earth's atmosphere exhibit fractal or power law scaling (e.g. Dickman, 2004), particularly rainfall occurrences (Mazzarella and Diodato, 2002). That is, statistical properties of a given process are similarly related to each other over a wide range of scales.…”

Anomalous transport in Charney-Hasegawa-Mima flows

“…And second, since we are using chaotic jets to track this origin, we are at the same time testing the existence of these jets in a more complex setting than the system of point vortices used in [9]. Once the presence of jets is confirmed we may be able to speculate that the different anomalous transport behavior portrayed in the nonexhaustive following references [2,16,17,18,19,20] may all find their origin in the presence of long lived chaotic jets in the considered systems.…”

A non arbitrary definition of rain event: the case of stratiform rain

“…Recently, an alternative definition of rain event [7,8,9] has gained some recognition in hydrological literature [10,11,12,13,14,15,16]. According to this new proposal a rain event is identified by the occurrences of consecutive adjacent wet time intervals (the time intervals being equal in duration to the instrument time resolution).…”