Scaling regimes of composite rainfall time series

Abstract

The scaling behaviour of rainfall is analysed both for a range of scales in time and for a given scale in intensity using the statistics of the Fourier transform and the cumulative probability distribution. The analyses are applied to sets of long time series of daily rainfall (26 (8) files of 45 (90) years at 13 European stations) and sets of 5-min totals (13 single station summer seasons) thus covering a wide scaling range. The results of both analyses are interpreted in terms of their asymptotically hyperbolic (i.e. power law) behaviour: The ensemble averaged power spectra exhibit distinct scaling regimes with their associated power law behaviour, P(f) ˜f^-b: a regime of climatic variability (< 3 years: b ˜ 0.7), a spectral plateau (3 years to 1 month: b ˜ 0) of general circulation fluctuations, a transition regime (1 month to 3 days: a dropping power spectrum without scaling), and a range governed by frontal systems (&lt; 3 days: b ˜ 0.5). The transition region is interpreted as being generated by both of its neighbouring regimes whose scaling can therefore be expanded into the transition regime. Finally an apparent break in scaling (at 2.4 h) can possibly be attributed to the instruments inability to measure frequent weak signals. The tail-end of the hyperbolic distribution (characterizing the intermittency regime) is not approached smoothly but shows a break from the rest of the distribution. Finally, an outlook to multifractal scaling is given.