Articles | Volume 29, issue 1
Nonlin. Processes Geophys., 29, 93–121, 2022
https://doi.org/10.5194/npg-29-93-2022

Special issue: Centennial issue on nonlinear geophysics: accomplishments...

Nonlin. Processes Geophys., 29, 93–121, 2022
https://doi.org/10.5194/npg-29-93-2022

Research article 25 Feb 2022

Research article | 25 Feb 2022

Fractional relaxation noises, motions and the fractional energy balance equation

Shaun Lovejoy

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Manuscript not accepted for further review
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Subject: Scaling, multifractals, turbulence, complex systems, self-organized criticality | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Simulation
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Cited articles

Atanackovic, M., Pilipovic, S., Stankovic, B., and Zorica, D.: Fractional Calculus with applications in mechanics: variations and diffusion processes, Wiley, 313 pp., 2014. 
Babenko, Y. I.: Heat and Mass Transfer, Khimiya, Leningrad, 1986 (in Russian). 
Bender, C. M. and Orszag, S. A.: Advanced mathematical methods for scientists and engineers, Mc Graw Hill, 1978. 
Biagini, F., Hu, Y., Øksendal, B., and Zhang, T.: Stochastic Calculus for Fractional Brownian Motion and Applications, Springer-Verlag, https://doi.org/10.1007/978-1-84628-797-8, 2008. 
Budyko, M. I.: The effect of solar radiation variations on the climate of the earth, Tellus, 21, 611–619, 1969. 
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Short summary
The difference between the energy that the Earth receives from the Sun and the energy it emits as black-body radiation is stored in a scaling hierarchy of structures in the ocean, soil and hydrosphere. The simplest scaling storage model leads to the fractional energy balance equation (FEBE). We examine the statistical properties of FEBE when it is driven by random fluctuations. In this paper, we explore the statistical properties of this mathematically simple yet neglected equation.