How big is a cloud?

We have discussed two extreme views of atmospheric variability: the scalebound view, in which every factor of 10 or so involves some new mechanism or law; and the opposing self- similar scaling view, in which zooming gives us something essentially the same— a single mechanism or law that could hold over ranges of thousands or more. By considering time series and spatial transects, we saw that, over various ranges of scale in space and in time, atmospheric scaling seemed to work quite well. We looked at a complication: Interesting geophysical quantities are not simply black or white (geometric sets of points), but have gray shades; they have numerical values everywhere. To deal with the associated extreme variability and intermit­tency, we saw that we had to go beyond fractal sets to multifractal fields (Box 2.2). Understanding multifractals turned out to be important. Failure to appre­ciate their importance led to numerous deleterious consequences.1 In this chapter, I want to consider something quite different: the morphologies of shapes in two or three dimensions. Up until now, we have identified scaling with self- similarity, the property that, following a usual isotropic zoom (one that is the same in all directions), small parts resemble the whole in some way. Yet in Chapter 1 (Fig. 1.8A, B), we saw that zooming into lidar vertical sections uncovered morphologies that changed with scale. As we zoomed into flat, stratified layers, structures became visibly more “roundish” (compare Fig. 1.8A with Fig. 1.8B). Vertical sections are thus not self- similar. Their degree of stratification— anisotropy— changes systematically with scale. But the vertical isn’t the only place where self- similarity is unrealistic. Although it is not as obvious, the same difficulty arises if we zoom into clouds in the hori­zontal. We criticized Orlanski’s powers of ten classification as being arbitrary and in contradiction with the scaling area– perimeter relation, but Orlanski was only trying to update an older phenomenological classification scheme, some of which predated the twentieth century.