Multiscaling Properties of Rainfall: Methods and Interpretation

Abstract

Multiscaling analysis is introduced as a statistical technique for characterising intermittency in stochastic processes and is applied to rainfall data. The analysis method comprises primarily of parameterising power-law (scaling) Fourier power spectra and scaling moments. In most cases it is the rainfall fluctuations which are studied and display scaling moments. These techniques are applied to study relations between the multiscaling properties of rain fields and their physical and meteorological environment. As a particular example, an analysis is performed on rain gauge time series collected in the Southern Alps of New Zealand. As a result of the orographic effects on rainfall processes, the rainfall is characterised as having less intermittence with increasing altitude from the coast to the main divide of the Alps. Following this initial application of multiscaling analysis, the techniques are more critically assessed. Focus is given to 1) the sampling uncertainty of estimated parameters, 2) the effect of joining time series with dissimilar multiscaling statistics into a single series for analysis and 3) the effect of instrumental artefacts on analysis results. The sampling uncertainties are estimated for cascade simulations and are generally found to exceed estimation uncertainties in parameters. The results of analysing extended data sets which are not meteorologically stationary, and thus contain statistically differing processes, are often found to be dominated by the most intermittent process. Multiscaling analysis is sensitive to strong instrumental glitches but are resilient to low levels of instrumental noise and artefacts. In the case of the fluctuations of a random field, as is often studied, even small amounts of noise are detrimental. Finally the theory of breakdown coefficients (BDCs) is applied to rainfall. The properties of BDCs are investigated using cascade simulations. The method of BDCs as applied to statistically self similar fields is modified to accommodate the study of rain fields where this may not necessarily be the case.