On the Existence of Spatially Uniform Scaling Laws in the Climate System

Scale invariance (scaling) in a time series of an observable quantity is a symmetry law which when it exists can provide unique insights about the process in question. It describes variability and transitions at all scales and is often a result of nonlinear dynamics. It is well known that the spectra of atmospheric and climatic variables possess considerable power at low frequencies. Since "red" spectra often associate with scaling processes, it is reasonable to suppose that a search for scaling laws in climatic data might be fruitful. Consequently, the search for scaling in such data over the past decade has produced some exciting ways to describe climate variability. In the past and lately, there has been a growing interest in the existence of uniform in space temporal scaling laws for observable properties of the climate system, since such a property would provide a common rule describing temporal variability everywhere on the globe. Here we show that in spatially extended systems, uniform in space scaling demands that global averages be time invariant. A corollary to this is that where global averages do exhibit temporal variability, as in our climate system, spatial variation in scaling properties is required.
Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences