Fractal forecasting

There’s an interesting piece in New Scientist, No 2733 [07 November 2009] outlining some new published research which has used satellite derived rainfall data to explore how atmospheric processes show the same patterns of variation whatever scale they are examined on. Such behaviour is called multi-fractal and basically means that if you look at something on a large scale you see a certain pattern of variation but then when you look in more detail at a smaller scale the same pattern shows up (an oft-quoted example of this are coastlines which show large-scale undulations/headlands/bays but which, when viewed more closely show similar undulations at smaller scale). Fractal behaviour is starting to show up in all kinds of data and processes.

Anyway, the importance of this finding for meteorology is that currently it is verydifficult to build numerical models which accurate forecast larger scale processes because the resolution of the models prevents accurate description of processes on smaller scales (and so these have to be added into the model as special parameterisations). If atmospheric processes are really fractal (an idea that was first suggested at least 80 years ago by Lewis Fry Richardson) then it will be possible to properly (or at least better) describe the smaller scale processes in numerical weather prediction models.

I’m a believer that much of the complexity that we observe in the real world is governed by relative simple underlying principles and behaviour and this research is an example of this occuring in practice.