Articles | Volume 27, issue 1
Nonlin. Processes Geophys., 27, 133–145, 2020
Nonlin. Processes Geophys., 27, 133–145, 2020
Research article
19 Mar 2020
Research article | 19 Mar 2020

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

Auguste Gires et al.

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Subject: Scaling, multifractals, turbulence, complex systems, self-organized criticality | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
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Cited articles

Battaglia, A., Rustemeier, E., Tokay, A., Blahak, U., and Simmer, C.: PARSIVEL Snow Observations: A Critical Assessment, J. Atmos. Ocean. Tech., 27, 333–344,, 2010. a
Bertol, I., Schick, J., Bandeira, D. H., Paz-Ferreiro, J., and Vázquez, E. V.: Multifractal and joint multifractal analysis of water and soil losses from erosion plots: A case study under subtropical conditions in Santa Catarina highlands, Brazil, Geoderma, 287, 116–125,, 2017. a, b
Calif, R. and Schmitt, F. G.: Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm, Nonlinear Process. Geophys., 21, 379–392,, 2014. a, b
Douglas, E. M. and Barros, A. P.: Probable maximum precipitation estimation using multifractals: Application in the eastern United States, J. Hydrometeorol., 4, 1012–1024, 2003. a
Gires, A., Tchiguirinskaia, I., and Schertzer, D.: Multifractal comparison of the outputs of two optical disdrometers, Hydrol. Sci. J., 61, 1641–1651,, 2016. a, b
Short summary
This paper aims to analyse and simulate correlations between two fields in a scale-invariant framework. It starts by theoretically assessing and numerically confirming the behaviour of renormalized multiplicative power law combinations of two fields with known scale-invariant properties. Then a new indicator of correlation is suggested and tested on rainfall data to study the correlation between the common rain rate and drop size distribution features.