Encoding hydrologic information via a fractal geometric approach and its extensions

Cortis, A.; Puente, Carlos E.; Sivakumar, Bellie

doi:10.1007/s00477-009-0349-4

Cited by 9 publications

(9 citation statements)

References 23 publications

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“…Since the last reason, the glance of rainfall modelling has changed fairly. Nowadays, there exists important efforts in the applications of derived multifractal models [1,7,14,19,21,23,24,26] and even more in multifractal random cascades models [ 5,6,8,9,15,16,17,30].…”

Section: Looking For a Model Of Rainfallmentioning

confidence: 99%

Multifractal Space-Time Dynamic of Mesoscale Tropical Rainfall

Monroy¹,

Peñaranda²,

Rousta³

2019

IJET

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For several years, hydrology has required a holistic theory of space-time evolution of mesoscale tropical rainfall which would allow us to take advantage from it to its application in water resources engineering. Nevertheless, various efforts have covered many techniques from the deterministic to stochastic models but not one gives a complete and satisfactory answer to how rainfall behaves in all its space-time scales and even more how its emerging patterns change. This article reviews some facts that show multifractality is an intrinsic property of rainfall and a coupled theory between multifractal theory and stochastic processes could lead us to a better understanding of tropical rainfall and its forecast.

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Section: Looking For a Model Of Rainfallmentioning

confidence: 99%

Multifractal Space-Time Dynamic of Mesoscale Tropical Rainfall

Monroy¹,

Peñaranda²,

Rousta³

2019

IJET

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“…These measures are useful for describing the experimental observations, as reported by Frisch and Parisi (1985), Meneveau and Sreenivasan (1987), and Puthenveettil et al (2005). Multifractal is also used to characterize the wetland topography (Tchiguirinskaia et al 2000), airborne geophysical data (Tennekoon et al 2005), and to generate complex hydrologic spatiotemporal datasets (Cortis et al 2009(Cortis et al , 2010. For river networks, Seo et al (2014) examined the peak flow distribution on stochastic network models.…”

Section: Introductionmentioning

confidence: 97%

Multifractal characteristics of the jet turbulent intensity depending on the outfall nozzle geometry

Seo

Lyu

2015

Stoch Environ Res Risk Assess

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The multifractal measure enables an examination of the characteristics of a quantity distributed over a domain. This study examined the multifractal properties of turbulent intensities obtained from jet discharge experiments, where three types of nozzle geometries were examined in terms of the velocity fields and turbulent characteristics using particle image velocimetry. Depending on the nozzle geometry, the experimental results showed that the distribution of turbulent intensities and resulting dilution exhibited different behaviors. The experiment also showed that the transversal velocity profiles are similar to each other regardless of the outfall nozzle shapes and demonstrates the traditional similarity assumption at the same time. The multifractal exponents of the turbulent intensities were obtained with Box Count Method in a two-dimensional space. The results showed that the turbulent intensities obtained in two-dimensional space have a common multifractal spectrum, which was not the case for the velocity or shear stress observed in the same space. Although the transversal velocity profiles are similar, the multifractal exponent clearly shows a difference depending on the outfall geometries. In particular, the minimum value of the Lipschitz-Hölder exponent (a min ) and the entropy dimension (a 1 ) tends to increase as turbulent intensity and dilution increase. These results suggest that the multifractal properties can be utilized potentially to categorize and evaluate the discharge outfall capabilities in terms of the resulting dilution.

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“…Inspired by the advent of chaos theory (e.g., Lorenz 1963) and by its usage to model precipitation (e.g., Rodriguez-Iturbe et al 1989), Puente and Obregón (1996), Puente et al (2001a, b), and Puente and Sivakumar (2007) showed that the FM method was able to capture hidden order in the dynamics of geophysical sets and demonstrated fruitful applications of such methodology for different rainfall sets gathered every few seconds (e.g., Puente and Obregón 1996;Cortis et al 2009Cortis et al , 2010Cortis et al , 2013Huang et al 2012). Indeed, the deterministic FM methodology may generate complex-looking sets with a relatively small number of parameters, and this happens despite the fact that the associated parameter-space is rather intricate, hence requiring a suitable optimization approach for a given set (Huang et al 2012.…”

Section: Introductionmentioning

confidence: 98%

Encoding daily rainfall records via adaptations of the fractal multifractal method

Maskey

Puente

Sivakumar

et al. 2015

Stoch Environ Res Risk Assess

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A deterministic geometric approach, the fractal-multifractal (FM) method, already found useful in modeling storm events, is adapted here in order to encode, for the first time, highly intermittent daily rainfall records gathered over a water year and containing many days of zero rain. Through application to data sets gathered at Laikakota in Bolivia and Tinkham in Washington, USA, it is demonstrated that the modified FM approach can represent erratic rainfall records faithfully, while using only a few FM parameters. It is shown that the modified FM approach, by capturing the rain accumulated over the season, ends up preserving other statistical attributes as well as the overall ''texture'' of the records, leading to FM sets that are indistinguishable from observed sets and certainly within the limits of accuracy of measured rainfall. This fact is further corroborated comparing 20 consecutive years at Laikakota and a modified FM representation, via common statistical qualifiers, such as histogram, entropy function, and inter-arrival times.

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Encoding hydrologic information via a fractal geometric approach and its extensions

Cited by 9 publications

References 23 publications

Multifractal Space-Time Dynamic of Mesoscale Tropical Rainfall

Multifractal Space-Time Dynamic of Mesoscale Tropical Rainfall

Multifractal characteristics of the jet turbulent intensity depending on the outfall nozzle geometry

Encoding daily rainfall records via adaptations of the fractal multifractal method

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