World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Multifractality, Imperfect Scaling and Hydrological Properties of Rainfall Time Series Simulated by Continuous Universal Multifractal and Discrete Random Cascade Models : Volume 17, Issue 6 (08/12/2010)

By Serinaldi, F.

Click here to view

Book Id: WPLBN0003976173
Format Type: PDF Article :
File Size: Pages 18
Reproduction Date: 2015

Title: Multifractality, Imperfect Scaling and Hydrological Properties of Rainfall Time Series Simulated by Continuous Universal Multifractal and Discrete Random Cascade Models : Volume 17, Issue 6 (08/12/2010)  
Author: Serinaldi, F.
Volume: Vol. 17, Issue 6
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Serinaldi, F. (2010). Multifractality, Imperfect Scaling and Hydrological Properties of Rainfall Time Series Simulated by Continuous Universal Multifractal and Discrete Random Cascade Models : Volume 17, Issue 6 (08/12/2010). Retrieved from

Description: Dipartimento di Geologia e Ingegneria Meccanica, Naturalistica e Idraulica per il Territorio – GEMINI, Università della Tuscia, Via S. Camillo de Lellis snc, 01100 Viterbo, Italy. Discrete multiplicative random cascade (MRC) models were extensively studied and applied to disaggregate rainfall data, thanks to their formal simplicity and the small number of involved parameters. Focusing on temporal disaggregation, the rationale of these models is based on multiplying the value assumed by a physical attribute (e.g., rainfall intensity) at a given time scale L, by a suitable number b of random weights, to obtain b attribute values corresponding to statistically plausible observations at a smaller L/b time resolution. In the original formulation of the MRC models, the random weights were assumed to be independent and identically distributed. However, for several studies this hypothesis did not appear to be realistic for the observed rainfall series as the distribution of the weights was shown to depend on the space-time scale and rainfall intensity. Since these findings contrast with the scale invariance assumption behind the MRC models and impact on the applicability of these models, it is worth studying their nature. This study explores the possible presence of dependence of the parameters of two discrete MRC models on rainfall intensity and time scale, by analyzing point rainfall series with 5-min time resolution. Taking into account a discrete microcanonical (MC) model based on beta distribution and a discrete canonical beta-logstable (BLS), the analysis points out that the relations between the parameters and rainfall intensity across the time scales are detectable and can be modeled by a set of simple functions accounting for the parameter-rainfall intensity relationship, and another set describing the link between the parameters and the time scale. Therefore, MC and BLS models were modified to explicitly account for these relationships and compared with the continuous in scale universal multifractal (CUM) model, which is used as a physically based benchmark model. Monte Carlo simulations point out that the dependence of MC and BLS parameters on rainfall intensity and cascade scales can be recognized also in CUM series, meaning that these relations cannot be considered as a definitive sign of departure from multifractality. Even though the modified MC model is not properly a scaling model (parameters depend on rainfall intensity and scale), it reproduces the empirical traces of the moments and moment exponent function as effective as the CUM model. Moreover, the MC model is able to reproduce some rainfall properties of hydrological interest, such as the distribution of event rainfall amount, wet/dry spell length, and the autocorrelation function, better than its competitors owing to its strong, albeit unrealistic, conservative nature. Therefore, even though the CUM model represents the most parsimonious and the only physically/theoretically consistent model, results provided by MC model motivate, to some extent, the interest recognized in the literature for this type of discrete models.

Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models

Dhanya, C. T. and Nagesh Kumar, D.: Nonlinear ensemble prediction of chaotic daily rainfall, Adv. Water Resour., 33, 327–347, 2010.; de Lima, M. I. P. and de Lima, J. L. M. P.: Investigating the multifractality of point precipitation in the Madeira archipelago, Nonlin. Processes Geophys., 16, 299–311, doi:10.5194/npg-16-299-2009, 2009.; de Lima, M. I. P. and Grasman, J.: Multifractal analysis of 15-min and daily rainfall from a semi-arid region in Portugal, J. Hydrol., 220, 1–11, doi:10.1016/S0022-1694(99)00053-0, 1999.; Deidda, R.: Rainfall downscaling in a space-time multifractal framework, Water Resour. Res., 36, 1779–1794, doi:10.1029/2000WR900038, 2000.; Deidda, R., Benzi, R., and Siccardi, F.: Multifractal modeling of anomalous scaling laws in rainfall, Water Resour. Res., 35, 1853–1867, doi:10.1029/1999WR900036, 1999.; Deidda, R., Badas, M. G., and Piga, E.: Space-time multifractality of remotely sensed rainfall fields, J. Hydrol., 322, 2–13, doi:10.1016/j.jhydrol.2005.02.036, 2006.; Dennis Jr., J. E., Gay, D. M., and Welsch, R. E.: Algorithm 573: {NL2SOL}–An adaptive nonlinear least-squares algorithm [{E4}], ACM Transactions on Mathematical Software, 7, 369–383, 1981.; Gaume, E., Mouhous, N., and Andrieu, H.: Rainfall stochastic disaggregation models: {C}alibration and validation of a multiplicative cascade model, Adv. Water Resour., 30, 1301–1319, 2007.; Grassberger, P. and Procaccia, I.: Characterization of strange attractors, Phys. Rev. Lett., 50, 346–349, 1983.; Güntner, A., Olsson, J., Calver, A., and Gannon, B.: Cascade-based disaggregation of continuous rainfall time series: the influence of climate, Hydrol. Earth Syst. Sci., 5, 145–164, doi:10.5194/hess-5-145-2001, 2001.; Gupta, V. and Waymire, E.: A statistical analysis of mesoscale rainfall as a random cascade, J. Appl. Meteorol., 32, 251–267, 1993.; Harris, D., Seed, A., Menabde, M., and Austin, G.: Factors affecting multiscaling analysis of rainfall time series, Nonlin. Processes Geophys., 4, 137–155, doi:10.5194/npg-4-137-1997, 1997.; Onof, C., Townend, J., and Kee, R.: Comparison of two hourly to 5-min rainfall disaggregators, Atmos. Res., 77, 176–187, 2005.; Kolmogorov, A. N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Proceedings of the USSR Academy of Sciences, 30, 299–303, 1941.; Kolmogorov, A. N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Proceeding of Royal Society of London, Series A, 434, 9–13, 1991.; Koutsoyiannis, D.: On the quest for chaotic attractors in hydrological processes, Hydrolog. Sci. J., 51, 1065–1091, 2006.; Koutsoyiannis, D. and Pachakis, D.: Deterministic chaos versus stochasticity in analysis and modeling of point rainfall series, J. Geophys. Res., 101, 26441–26451, doi:10.1029/96JD01389, 1996.; Koutsoyiannis, D. and Xanthopoulos, T.: A dynamic model for short-scale rainfall disaggregation, Hydrolog. Sci. J., 35, 303–322, 1990.; Koutsoyiannis, D., Onof, C., and Wheater, H. S.: Multivariate rainfall disaggregation at a fine time scale, Water Resour. Res., 39, 1173, doi:10.1029/2002WR001600, 2003.; Lavallée, D., Schertzer, D., and Lovejoy, S.: On the determination of the codimension function, in: Scaling, fractals and non-linear variability in geophysics, edited by: Schertzer, D. and Lovejoy, S., pp. 99–110, Kluwer, 1991.; Lovejoy, S. and Schertzer, D.: Multifractals and Rain, in: New Uncertainty Concepts in Hydrology and Hydrological modelling, e


Click To View

Additional Books

  • A Method to Calculate Finite-time Lyapun... (by )
  • Estimation of Sedimentary Proxy Records ... (by )
  • Assimilation of Hf Radar Surface Current... (by )
  • The Use of Artificial Neural Networks to... (by )
  • The Evolution of a Thermocline Effected ... (by )
  • Extreme Events and Long-range Correlatio... (by )
  • On the Multi-scale Nature of Large Geoma... (by )
  • A Simple Model for the Earthquake Cycle ... (by )
  • Characteristics of Electrostatic Solitar... (by )
  • A Simple Nonlinear Model of Low Frequenc... (by )
  • A Quasi-analytical Ice-sheet Model for C... (by )
  • Ion Acceleration by Parallel Propagating... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.