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.

Related authors

Measurements of the water balance components of a large green roof in the greater Paris area
Pierre-Antoine Versini, Filip Stanic, Auguste Gires, Daniel Schertzer, and Ioulia Tchiguirinskaia
Earth Syst. Sci. Data, 12, 1025–1035,,, 2020
Short summary
Disdrometer measurements under Sense-City rainfall simulator
Auguste Gires, Philippe Bruley, Anne Ruas, Daniel Schertzer, and Ioulia Tchiguirinskaia
Earth Syst. Sci. Data, 12, 835–845,,, 2020
Short summary
Two months of disdrometer data in the Paris area
Auguste Gires, Ioulia Tchiguirinskaia, and Daniel Schertzer
Earth Syst. Sci. Data, 10, 941–950,,, 2018
Short summary
Scale effect challenges in urban hydrology highlighted with a distributed hydrological model
Abdellah Ichiba, Auguste Gires, Ioulia Tchiguirinskaia, Daniel Schertzer, Philippe Bompard, and Marie-Claire Ten Veldhuis
Hydrol. Earth Syst. Sci., 22, 331–350,,, 2018
Short summary
Multifractal evaluation of simulated precipitation intensities from the COSMO NWP model
Daniel Wolfensberger, Auguste Gires, Ioulia Tchiguirinskaia, Daniel Schertzer, and Alexis Berne
Atmos. Chem. Phys., 17, 14253–14273,,, 2017
Short summary

Related subject area

Subject: Scaling, multifractals, turbulence, complex systems, self-organized criticality | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
Non-linear hydrologic organization
Allen Hunt, Boris Faybishenko, and Behzad Ghanbarian
Nonlin. Processes Geophys., 28, 599–614,,, 2021
Short summary
The impact of entrained air on ocean waves
Juan M. Restrepo, Alex Ayet, and Luigi Cavaleri
Nonlin. Processes Geophys., 28, 285–293,,, 2021
Short summary
Lewis fry Richardson Medal Lecture – How many modes are neededto predict climate bifurcations?: Lessons from an experiment
Bérengère Dubrulle, François Daviaud, Davide Faranda, Louis Marié, and Brice Saint-Michel
Nonlin. Processes Geophys. Discuss.,,, 2021
Revised manuscript accepted for NPG
Short summary

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.