Articles | Volume 29, issue 1
https://doi.org/10.5194/npg-29-93-2022
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

Related authors

Geographic variability of dust and temperature in climate scaling regimes over the Last Glacial Cycle
Nicolás Acuña Reyes, Elwin van ’t Wout, Fabrice Lambert, and Shaun Lovejoy
EGUsphere, https://doi.org/10.5194/egusphere-2023-1858,https://doi.org/10.5194/egusphere-2023-1858, 2023
Short summary
Review article: Scaling, dynamical regimes, and stratification. How long does weather last? How big is a cloud?
Shaun Lovejoy
Nonlin. Processes Geophys., 30, 311–374, https://doi.org/10.5194/npg-30-311-2023,https://doi.org/10.5194/npg-30-311-2023, 2023
Short summary
The fractional energy balance equation for climate projections through 2100
Roman Procyk, Shaun Lovejoy, and Raphael Hébert
Earth Syst. Dynam., 13, 81–107, https://doi.org/10.5194/esd-13-81-2022,https://doi.org/10.5194/esd-13-81-2022, 2022
Short summary
The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories
Shaun Lovejoy
Earth Syst. Dynam., 12, 469–487, https://doi.org/10.5194/esd-12-469-2021,https://doi.org/10.5194/esd-12-469-2021, 2021
Short summary
The half-order energy balance equation – Part 2: The inhomogeneous HEBE and 2D energy balance models
Shaun Lovejoy
Earth Syst. Dynam., 12, 489–511, https://doi.org/10.5194/esd-12-489-2021,https://doi.org/10.5194/esd-12-489-2021, 2021
Short summary

Related subject area

Subject: Scaling, multifractals, turbulence, complex systems, self-organized criticality | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Simulation
Phytoplankton retention mechanisms in estuaries: a case study of the Elbe estuary
Laurin Steidle and Ross Vennell
Nonlin. Processes Geophys., 31, 151–164, https://doi.org/10.5194/npg-31-151-2024,https://doi.org/10.5194/npg-31-151-2024, 2024
Short summary
Clustering of settling microswimmers in turbulence
Jingran Qiu, Zhiwen Cui, Eric Climent, and Lihao Zhao
EGUsphere, https://doi.org/10.5194/egusphere-2023-911,https://doi.org/10.5194/egusphere-2023-911, 2023
Short summary
Comparing estimation techniques for temporal scaling in palaeoclimate time series
Raphaël Hébert, Kira Rehfeld, and Thomas Laepple
Nonlin. Processes Geophys., 28, 311–328, https://doi.org/10.5194/npg-28-311-2021,https://doi.org/10.5194/npg-28-311-2021, 2021
Short summary

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. 
Download
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.