The Shape of Large Tropospheric Clouds, or “Very Like a Whale”

Abstract

Lovejoy (1982) analyzed radar and satellite images of convective clouds and rainbands extending over an area range from 10 to 106 km2 and found the fractal cloud-perimeter dimension to equal 1.35, indicating the presence of a Richardson, three-dimensional, turbulent-energy cascade in the atmosphere below linear scales of at least 103 km. It is shown here that the upper third of these data points, corresponding to linear scales greater than 300?400 km, have a fractal dimension of 1.77. Comparisons with tropospheric energy spectra and long-range diffusion data suggest that atmospheric eddy motions at these larger scales define an enstrophy-cascade region whose motions rapidly distort diffusing clouds. This rapid distortion leads to a greater increase in cloud perimeter relative to area, and consequently a larger fractal dimension, than the cloud spreading by relative diffusion in the smaller-scale, energy-cascade range. Satellite observations of the increase in area with time of the volcanic clouds from several major eruptions show a similar increase in fractal dimension in the same scale range. This supports observations of atmospheric relative diffusion, which show that rapid, accelerating (horizontal) cloud growth occurs up to cloud or plume ages on the order of 6?12 hours (a few times the outer turbulence scale of ?104 sec) and suggests that clouds are rapidly deformed and convoluted at greater times by larger, horizontal eddy motions.