Multifractal analysis of 15-min and daily rainfall from a semi-arid region in Portugal

Recent climatic records from the Greenland ice-core project (GRIP) ice core show that the climate proxy temperatures δ18O (18O/16O ratios) display sharp gradients and large fluctuations over all observed scales. We show that these variations are scale invariant over the range ≈400 yr to ≈40 kyr. The fluctuations corresponding to these scales are studied using multifractal analysis techniques. We estimate universal multifractal indices which characterize all the fluctuations for all the scales in this range and which are close to those obtained for turbulent temperatures at much shorter time scales. We speculate briefly on the origin of these common features intervening all over the observed range from seconds to kyr.

Multifractal analysis of the Greenland Ice‐Core Project climate data

The presence of scaling statistical properties in temporal rainfall has been well established in many empirical investigations during the latest decade. These properties have more and more come to be regarded as a fundamental feature of the rainfall process. How to best use the scaling properties for applied modelling remains to be assessed, however, particularly in the case of continuous rainfall time-series. One therefore is forced to use conventional time-series modelling, e.g. based on point process theory, which does not explicitly take scaling into account. In light of this, there is a need to investigate the degree to which point-process models are able to ‘unintentionally’ reproduce the empirical scaling properties. In the present study, four 25-year series of 20-min rainfall intensities observed in Arno River basin, Italy, were investigated. A Neyman–Scott rectangular pulses (NSRP) model was fitted to these series, so enabling the generation of synthetic time-series suitable for investigation. A multifractal scaling behaviour was found to characterize the raw data within a range of time-scales between approximately 20 min and 1 week. The main features of this behaviour were surprisingly well reproduced in the simulated data, although some differences were observed, particularly at small scales below the typical duration of a rain cell. This suggests the possibility of a combined use of the NSRP model and a scaling approach, in order to extend the NSRP range of applicability for simulation purposes. Copyright © 2002 John Wiley & Sons, Ltd.

Reproduction of temporal scaling by a rectangular pulses rainfall model

. The purpose of this work is to contribute to a better understanding of the variability of precipitation in the Madeira archipelago. This archipelago is located in the Atlantic subtropical belt under the direct influence of the Azores high pressure system. It is formed by Madeira Island (728 km2) and Porto Santo Island (42 km2) and by two other groups of very small inhabited islands. The complex topography of the islands in the Madeira archipelago and their small size play a crucial role in the local precipitation regime, which is marked by high spatial variability. This paper explores the invariance of properties manifested across scales and determines the fractal and multifractal behaviour observed in the temporal structure of precipitation using daily and 10-min time series from several locations scattered over the main islands. The period covered by the precipitation records is 34 years for the daily data and almost 4 months for the 10-min data. The results show that the temporal structure of precipitation in the Madeira Archipelago exhibits scale-invariant and multifractal properties. The empirical exponent functions describing the scaling statistical properties of the precipitation intensity were characterized using multifractal parameters; these parameters are increasing our awareness of the dynamics of this process in these islands.

/pdf/investigating-the-multifractality-of-point-precipitation-in-1lr5hlbv7x.pdf

Investigating the multifractality of point precipitation in the Madeira archipelago

[1] A number of studies have shown that rainfall processes may be described by stochastic scaling models in the time domain. However, most of the data sets have a resolution that is too limited to perceive the internal structure and variability of rain events. In this study, we analyze high-resolution (15 s) disdrometer time series, of total duration 2 years, obtained in Palaiseau, France. Monofractal and multifractal analysis tools are applied to the data set in order to investigate the scaling properties of the process, especially within the framework of universal multifractals (UMs). From spectral analysis and first-order structure function, it is shown that rainfall should be modeled by nonconservative (integrated) processes at small scales (hourly or finer) but not at larger scales. Multifractal analysis shows that two multiscaling regimes should be distinguished, i.e., ∼3 days to 30 min and 15 min to 15 s, with different UM parameters. The former is likely to represent the interevent variability, and the latter is likely to represent the event internal variability. Moreover, most data points contain zero values, which are susceptible to bias multifractal analysis results. In order to assess the effect of the zeros on multifractal analysis results, the UM parameters are also estimated from two variants: from uninterrupted rain events (with almost no zeros) and from a modified (weighted) version of analysis procedure that overweights nonzero values. The parameters are shown to depend noticeably on the proportion of zeros. We propose an approach based on a scaling support of the time series and derive semitheoretical formulas for the bias in the parameters, which are applied in our case study. Finally, we discuss the advantages and drawbacks of some models for numerical simulation of multifractal fields containing a lot of zeros.

https://hal.archives-ouvertes.fr/hal-00635865/document

Multiscaling properties of rain in the time domain, taking into account rain support biases

The atmosphere displays linked spatial/temporal variability over wide ranges in scale. In this paper we study the scaling behaviour of the fluctuations. These properties are characterized by spectral exponents, and the extreme fluctuations by exponents of the corresponding probability distributions. Using both temperature and rain rate data from climatologically representative locations, we find very similar behaviour including relatively small dispersions in the estimated exponents. We also show that the effect of spatial averaging is primarily to reduce the amplitudes of both the fluctuations and their spectra by constant factors, a behaviour which is consistent with global space/time scaling. Finally we argue that these non-standard statistical procedures may be indispensable in taming extremely variable climatic and meteorological data.

Extreme Variability of Climatological Data: Scaling and Intermittency

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Extreme Variability of Climatological Data: Scaling and Intermittency