Generalized scale invariance and differential rotation in cloud radiances

Scale invariant symmetries are usually restricted to systems involving extremely special types of scale changes; self-similar and self-affine fractals involving isotropy and differential stratification respectively. In contrast, geophysical and astrophysical systems can be scale invariant but display complex anisotropy including differential rotation. The formalism required to handle such symmetries is generalized scale invariance; using the new Monte Carlo differential rotation technique we test it on satellite cloud radiances over the range 1–1200 km. Our results underscore the limited usefulness of self-similar and self-affine scaling ideas in atmospheric dynamics since we find substancial differential rotation which is, nevertheless, scaling.