Approximate multifractal correlation and products of universal multifractal fields, with application to rainfall data

Universal multifractals (UMs) have been widely used to simulate and characterize, with the help of only two physically meaningful parameters, geophysical fields that are extremely variable across a wide range of scales. Such a framework relies on the assumption that the underlying field is generated...

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Bibliographic Details
Published in:Nonlinear processes in geophysics 2020-03, Vol.27 (1), p.133-145
Main Authors: Gires, Auguste, Tchiguirinskaia, Ioulia, Schertzer, Daniel
Format: Article
Language:English
Subjects:
Approximation
Atmospheric water
Computer simulation
Correlation
Correlation analysis
Covariance
Disdrometers
Drop size
Drop size distribution
Earth Sciences
Environmental Engineering
Environmental Sciences
Fields
Fractal analysis
Geophysics
Moisture content
Numerical analysis
Numerical simulations
Parameters
Phase transitions
Plankton
Power (Philosophy)
Rain
Rainfall
Rainfall data
Sciences of the Universe
Size distribution
Water
Water content
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Summary:Universal multifractals (UMs) have been widely used to simulate and characterize, with the help of only two physically meaningful parameters, geophysical fields that are extremely variable across a wide range of scales. Such a framework relies on the assumption that the underlying field is generated through a multiplicative cascade process. Derived analysis techniques have been extended to study correlations between two fields not only at a single scale and for a single statistical moment as with the covariance, but across scales and for all moments. Such a framework of joint multifractal analysis is used here as a starting point to develop and test an approach enabling correlations between UM fields to be analysed and approximately simulated.
ISSN:1607-7946
1023-5809
1607-7946
DOI:10.5194/npg-27-133-2020