Multifractality and rainfall extremes: A review

Veneziano, Daniele; Langousis, Andreas; Furcolo, Pierluigi

doi:10.1029/2005wr004716

Cited by 126 publications

(105 citation statements)

References 51 publications

(76 reference statements)

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“…The straightening ofK(q) above q + is due to the nonobservability of extreme singularities in a sample. As the resolution level n→∞, the ensemble moments µ q n =E ε q n are dominated by values of ε n on the order of 2 nK (q) , but in a finite number s of realizations, as the level n→∞ these values occur with probability one for q<q + and with probability zero for q>q + Waymire, 2000, 2002;Lashermes et al, 2004;Veneziano et al, 2006). It follows that with probaiblity 1 the sample maximum of ε n , ε n,max , satisfies…”

Section: The Standard Nonparametric Estimatork(q)mentioning

confidence: 99%

Improved moment scaling estimation for multifractal signals

Veneziano

Furcolo

2009

Nonlin. Processes Geophys.

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Abstract.A fundamental problem in the analysis of multifractal processes is to estimate the scaling exponent K(q) of moments of different order q from data. Conventional estimators use the empirical momentsμ q r = |ε r (τ )| q of wavelet coefficients ε r (τ ), where τ is location and r is resolution. For stationary measures one usually considers "wavelets of order 0" (averages), whereas for functions with multifractal increments one must use wavelets of order at least 1. One obtainsK(q) as the slope of log(μ q r ) against log(r) over a range of r. Negative moments are sensitive to measurement noise and quantization. For them, one typically uses only the local maxima of |ε r (τ )| (modulus maxima methods). For the positive moments, we modify the standard estimatorK(q) to significantly reduce its variance at the expense of a modest increase in the bias. This is done by separately estimating K(q) from sub-records and averaging the results. For the negative moments, we show that the standard modulus maxima estimator is biased and, in the case of additive noise or quantization, is not applicable with wavelets of order 1 or higher. For these cases we propose alternative estimators. We also consider the fitting of parametric models of K(q) and show how, by splitting the record into sub-records as indicated above, the accuracy of standard methods can be significantly improved.

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Section: The Standard Nonparametric Estimatork(q)mentioning

confidence: 99%

Improved moment scaling estimation for multifractal signals

Veneziano

Furcolo

2009

Nonlin. Processes Geophys.

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“…A class of methods that is often adopted is statistical downscaling via Stochastic Space Random Cascade approach, henceforth termed SSRC (Tessier et al, 1993;Over andGupta, 1994, 1996;Menabde and Sivapalan, 2000;Veneziano and Langousis, 2005;Veneziano et al, 2006), already used for downscaling of precipitation from GCMs for climate change projections (Kang and Ramírez, 2007) as well as for improvement of water balance estimation (see e.g. Lammering and Dwyer, 2000).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of future hydrological cycle under climate change scenarios in a mesoscale Alpine watershed of Italy

Groppelli

Soncini

Bocchiola

et al. 2011

Nat. Hazards Earth Syst. Sci.

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Abstract. We investigate future (2045)(2046)(2047)(2048)(2049)(2050)(2051)(2052)(2053)(2054) hydrological cycle of the snow fed Oglio (≈1800 km 2 ) Alpine watershed in Northern Italy. A Stochastic Space Random Cascade (SSRC) approach is used to downscale future precipitation from three general circulation models, GCMs (PCM, CCSM3, and HadCM3) available within the IPCC's data base and chosen for this purpose based upon previous studies. We then downscale temperature output from the GCMs to obtain temperature fields for the area. We also consider a projected scenario based upon trends locally observed in former studies, LOC scenario. Then, we feed the downscaled fields to a minimal hydrological model to build future hydrological scenarios. We provide projected flow duration curves and selected flow descriptors, giving indication of expected modified (against control run for 1990-1999) regime of low flows and droughts and flood hazard, and thus evaluate modified peak floods regime through indexed flood. We then assess the degree of uncertainty, or spread, of the projected water resources scenarios by feeding the hydrological model with ensembles projections consistent with our deterministic (GCMs + LOC) scenarios, and we evaluate the significance of the projected flow variables against those observed in the control run. The climate scenarios from the adopted GCMs differ greatly from one another with respect to projected precipitation amount and temperature regimes, and so do the projected hydrological scenarios. A relatively good agreement is found upon prospective shrinkage and shorter duration of the seasonal snow cover due to increased temperature patterns, and upon prospective increase of hydrological losses, i.e. evapotranspiration, for the same reason. However, precipitation patterns are less consistent, because HadCM3 and PCM models project noticeably increased precipitation for 2045-2054, whereas CCSM3 provides decreased precipCorrespondence to: D. Bocchiola (daniele.bocchiola@polimi.it) itation patterns therein. The LOC scenario instead displays unchanged precipitation. The ensemble simulations indicate that several projected flow variables under the considered scenarios are significantly different from their control run counterparts, and also that snow cover seems to significantly decrease in duration and depth. The proposed hydrological scenarios eventually provide a what-if analysis, giving a broad view of the possible expected impacts of climate change within the Italian Alps, necessary to trigger the discussion about future adaptation strategies.

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“…All Rights Reserved. [e.g., Schertzer and Lovejoy, 1987;Schmitt et al, 1992;Tessier et al, 1993Tessier et al, , 1996Olsson and Niemzcynowicz, 1996;Harris et al, 1996;Lovejoy et al, 1996Lovejoy et al, , 2008Deidda, 2000;Lilley et al, 2006;Kantelhardt et al, 2006;Veneziano et al, 2006;Venugopal et al, 2006;Lovejoy and Schertzer, 2006, 2010a, 2010bGarcia-Marin et al, 2008;Serinaldi, 2010;. In particular, Lui [2002] Anh et al [2007Anh et al [ , 2008 and Yu et al [2010Yu et al [ , 2012 used MFA and fractional stochastic differential equations to study the AE and geomagnetic field data.…”

Section: Journal Of Geophysical Research: Space Physicsmentioning

confidence: 99%

“…While D st has been shown to be correlated with solar wind data [e.g., Burton et al, 1975], the response of AE to the solar wind conditions has proved to be harder to determine [Holzer and Slavin, 1982;Bargatze et al, 1985;Vassiliadis, 2006]. Gleisner and Lundstedt [1997] used solar wind density, velocity, and magnetic field as separate inputs into a neural network model to predict AE.…”

Section: Introductionmentioning

confidence: 99%

Underlying scaling relationships between solar activity and geomagnetic activity revealed by multifractal analyses

Anh

Eastes

2014

JGR Space Physics

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This paper identifies some scaling relationships between solar activity and geomagnetic activity. We examine the scaling properties of hourly data for two geomagnetic indices (a p and AE), two solar indices (solar X-rays X l and solar flux F10.7), and two inner heliospheric indices (ion density Ni and flow speed Vs) over the period 1995-2001 by the universal multifractal approach and the traditional multifractal analysis. We found that the universal multifractal model (UMM) provides a good fit to the empirical K(q) and (q) curves of these time series. The estimated values of the Lévy index in the UMM indicate that multifractality exists in the time series for a p , AE, X l , and Ni, while those for F10.7 and Vs are monofractal.The estimated values of the nonconservation parameter H of this model confirm that these time series are conservative which indicate that the mean value of the process is constant for varying resolution. Additionally, the multifractal K(q) and (q) curves, and the estimated values of the sparseness parameter C 1 of the UMM indicate that there are three pairs of indices displaying similar scaling properties, namely a p and X l , AE and Ni, and F10.7 and Vs. The similarity in the scaling properties of pairs (a p , X l ) and (AE, Ni) suggests that a p and X l , AE and Ni are better correlated-in terms of scaling-than previous thought, respectively. But our results still cannot be used to advance forecasting of a p and AE by X l and Ni, respectively, due to some reasons.

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Multifractality and rainfall extremes: A review

Cited by 126 publications

References 51 publications

Improved moment scaling estimation for multifractal signals

Improved moment scaling estimation for multifractal signals

Evaluation of future hydrological cycle under climate change scenarios in a mesoscale Alpine watershed of Italy

Underlying scaling relationships between solar activity and geomagnetic activity revealed by multifractal analyses

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