Multifractal analysis of hourly precipitation

The multifractal nature of the rainfall field is analysed using the methodology of singular measures. The analysis is applied to a long time series (54 years) of hourly rainfall intensities recorded at Valentia on the South-West Coast of Ireland. The empirical probability distribution function suggests a hyperbolic intermittency with the divergence of the statistical moments being higher than the second order. The latter is in agreement with findings of other authors for similar climatic regions (e.g. Sweden). The Fourier transform statistics of the data are used to obtain the scaling range in which the data obey a power law with a coefficient of similar to 0.5. The scale invariance as identified by the spectral power law, ranges from 2 hours to about 24 hours. This is a narrower range than has been found for similar studies using continental sites where the range was found to be from 2 hours to about 3 days. Studies of Valentia rainfall using conventional statistics suggest that two distinct periods, (1940-1975 and 1976-1993) are clearly present. The second period is characterised by a greater annual rainfall depth than the first, and the increased depth was found to be concentrated primarily in the months of March and October. The intermittency analysis of the rain field of the two periods reveals two different K(q)-functions. The curvature of the K(q) convexity has been found to be larger for the second period suggesting lower intermittency or more frequent rain events. The intermittency function CI for the period 1976-1993 is shown to be quantitatively less than C-1 for the period 1940-1975, for die annual, March and October time series verifying increasing precipitation since 1975. (C) 1999 Elsevier Science Ltd. All rights reserved.