Limits and characteristics of the multifractal behavior of a high-resolution rainfall time series

The multifractal properties of a 2-year time series of 8-min rainfall intensity observations are investigated. The empirical probability distribution function suggests a hyperbolic intermittency with divergence of moments of order greater than 2. The power spectrum E(f) of the series obeys a power law form E(f)=f(-0.66) in the range of scales 8 mm to approximately 3 days. The variation of the average statistical moments with scale shows that the series is characterized by a multifractal behavior between 8 mm and approximately 11 days. The multifractal parameters associated with universality were estimated to be alpha =0.63 and C-1=0.44 by using the Double Trace Moment, DTM, technique. The moment scaling functions obtained from the empirical values and the universal expression are in good agreement in the approximate range 1 <= q <= 3. Outside of this range, however, differences exist which may be related to either limitations of the data or an inexact estimation of the parameters by DTM. The evident multifractal nature of rainfall time series is encouraging since it may lead to new and improved ways of processing rainfall data used in hydrological calculations.