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Usage of a deterministic fractal-multifractal (FM) procedure to model high-resolution rainfall time series, as derived distributions of multifractal measures via fractal interpolating functions, is reported. Four rainfall storm events having distinct geometries, one gathered in Boston and three others observed in Iowa City, are analyzed. Results show that the FM approach captures the main characteristics of these events, as the fitted storms preserve the records' general trends, their autocorrelations and spectra, and their multifractal character.

Rainfall is a highly intermittent field over a wide range of time and space scales. We study a high resolution rainfall time series exhibiting large intensity fluctuations and localized events. We consider the return times of a given intensity, and show that the time series composed of these return times is itself also very intermittent, obeying to a hyperbolic probability density, entailing that the mean return time diverges. This is an unexpected property since mean return times are often introduced in meteorology, especially for the study of risk associated to extreme events. It suggests that the intermittency of first return times of extreme events should be taken into account when making statistical predictions.

The time series data of the monthly rainfall records (for the time period 1871–2002) in All India and different regions of India are analyzed. It is found that the distributions of the rainfall intensity exhibit perfect power law behavior. The scaling analysis revealed two distinct scaling regions in the rainfall time series.

Natural data sets, such as precipitation records, often contain geometries that are too complex to model in their totality with classical stochastic methods. In the past years, we have developed a promising deterministic geometric procedure, the fractal-multifractal (FM) method, capable of generating patterns as projections that share textures and other fine details of individual data sets, in addition to the usual statistics of interest. In this paper, we formulate an extension of the FM method around the concept of "closing the loop" by linking ends of two fractal interpolating functions and then test it on four geometrically distinct rainfall data sets to show that this generalization can provide excellent results.