Data from networks of high time resolution (15 second) rain gauges forming a transect from the base to the divide of a mountain range are used to study the multifractal characteristics of precipitation at different locations along the transect. In particular, scaling power spectra, multiscaling moments and power law exceedence probability tails are analyzed from rain gauge time series of ∼35–70 hours in length. The parameters discussed are specifically the spectral scaling exponent, β, the intermittency parameter, C1 (a fundamental parameter of the moment scaling function, K(q)) and qcr, the power law probability tail exponent. Results show a systematic trend in the exponents, indicating a decrease in intermittency, the frequency of extreme values and smoothness of the time series with increasing altitude along the transect. K(q) and qcr are briefly discussed and derived as natural properties of multifractal cascades. It is concluded that the parameters of multifractal cascade models of rainfall are related to the physical processes which are qualitatively discussed in the context of the observed changes in the statistics.

Abstract. The connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed, and a new phenomenological model for rainfall time series simulation is proposed. The bounded random cascade model presented here is a generalization of the well-known a model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales. This allows one to directly simulate a multiscaling random field with an energy spectrum exponent, •3 > 1, which is typical for rainfall time series data but which cannot be produced by a standard a model. A procedure is proposed for estimating the cascade parameters of this new bounded a model from observed data. Parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents. The bounded a model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts. We expect that the occurrence of rainfall and turbulence have something in common since rain is a tracer of turbulence at small scales and the larger eddies may be involved in the processes which produce rainfall. This suggests the two phenomena might be described by the same models. However, we believe it is clear that the physical processes which produce large areas of uniform rain and small convective showers, for example, are radically different and are extremely unlikely to be described as different realizations of a random multiplicative cascade with the same parameters. In our view the best justification for the use of the multiplicative cascade models in rainfall pattern analysis is the remarkable ability of the technique to reproduce the observed structure of rainfall patterns and its statistical properties. We therefore believe that the careful analysis of the goodness of fit of the statistical properties of the simulated pattern with the observed one is actually crucial, especially taking into account the phenomenological character of the cascade models. As already mentioned, /3 is an important exponent in classifying whether an observed field can be modeled by a bounded or unbounded cascade depending on whether/3 > 1 or/3 < 1, respectively. This condition on/3 has often been related to the stationarity of a field. However, we show that this is not the only possible interpretation and illustrate the point with a counterexample of a stationary random process with scaling energy spectrum with /3 > 1. Another important result that follows from this counterexample is that the condition/3 > 1 implies that the moments of the raw field do not scale, and thus K(q) function is not defined. When using discrete cascades to model rainfall (and many other geophysical fields) one runs into the familiar problemSection 3 presents a new type of bounded cascade along with a parameter estimation method for the model from real data.As an applicatioh, the bounded a model parameters are...

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Abstract. The Southern Alps field experiment was designed to identify the dominant rainfall processes in intense orographic events in the South Island of New Zealand and included the deployment of a rain gauge network and meteorological radar. Multiscaling statistics, used to characterize the rainfall from a single extreme event, revealed both orographic and temporal changes in the rainfall nature, with significantly more incessant rainfall observed in the higher-altitude regions. Central to this work was physical interpretation of the statistical parameters, which contributes toward forming links between multiscaling analysis and meteorological processes necessary for practical applications of multiscaling statistics. A further step was taken by combining the statistical results with other meteorological data to infer details of the physical processes, hence providing an example of the utility of multiscaling characterization of rainfall for improving our understanding of physical rainfall processes. Evidence is presented of lateral broadening of precipitating elements as the alpine divide is approached and is used, in conjunction with the wind profile, to explain the quasiincessant rainfall observed near the divide.

Abstract. The theory of self-similar random fields is applied to the statistical description and simulation of rainfall. Fluctuations in rainfields measured by a high resolution weather radar covering a 15 km square are shown to satisfy the condition of self-similarity. The probability density function of the'logarithm of the breakdown coefficients (defined as the ratio of two field means, each computed at different resolutions) of the rainfall fluctuation field generally belongs to the class of infinitely divisible distributions. The theoretical framework for scaling self-similar fields is presented and related to results from alternate frameworks, presented in the literature. A simple procedure for the parameterization and modeling of the experimentally measured probability density function is presented. The obtained generator is then used for rainfall simulation by multiplicative cascades. Simulated results exhibit a good statistical and visual agreement with the measured data.