Articles | Volume 13, issue 1
https://doi.org/10.5194/esd-13-81-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-13-81-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The fractional energy balance equation for climate projections through 2100
Physics Department, McGill University, 3600 rue University, Montreal, Quebec, H3A 2T8, Canada
Physics Department, McGill University, 3600 rue University, Montreal, Quebec, H3A 2T8, Canada
Raphael Hébert
Alfred-Wegener Institute Helmholtz Centre for Polar and Marine Research, Telegrafenberg A45, 14473 Potsdam, Germany
Institute of Geosciences, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
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Cited
14 citations as recorded by crossref.
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- Exploring behavioral strategies for third-party market cooperation in renewable energy projects: a perspective on addressing climate change Y. Zhao & B. Peng 10.1016/j.renene.2025.124572
- Fractional relaxation noises, motions and the fractional energy balance equation S. Lovejoy 10.5194/npg-29-93-2022
- Climate modelling without irrelevant weather details: The Half-order Energy Balance Equation S. Lovejoy et al. 10.1051/matecconf/202541309001
- Addressing Complexity in Global Aerosol Climate Model Cloud Microphysics U. Proske et al. 10.1029/2022MS003571
- CanStoc: A Hybrid Stochastic–GCM System for Monthly, Seasonal and Interannual Predictions S. Lovejoy & L. Del Rio Amador 10.3390/meteorology2040029
- The Future of Climate Modelling: Weather Details, Macroweather Stochastics—Or Both? S. Lovejoy 10.3390/meteorology1040027
- The impact of long-term memory on the climate response to greenhouse gas emissions N. Yuan et al. 10.1038/s41612-022-00298-8
- The Fractional MacroEvolution Model: a simple quantitative scaling macroevolution model S. Lovejoy & A. Spiridonov 10.1017/pab.2023.38
- The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories S. Lovejoy 10.5194/esd-12-469-2021
- Using regional scaling for temperature forecasts with the Stochastic Seasonal to Interannual Prediction System (StocSIPS) L. Del Rio Amador & S. Lovejoy 10.1007/s00382-021-05737-5
- An observation-based scaling model for climate sensitivity estimates and global projections to 2100 R. Hébert et al. 10.1007/s00382-020-05521-x
- The half-order energy balance equation – Part 2: The inhomogeneous HEBE and 2D energy balance models S. Lovejoy 10.5194/esd-12-489-2021
10 citations as recorded by crossref.
- Review article: Scaling, dynamical regimes, and stratification. How long does weather last? How big is a cloud? S. Lovejoy 10.5194/npg-30-311-2023
- Climatologically invariant scale invariance seen in distributions of cloud horizontal sizes T. DeWitt et al. 10.5194/acp-24-109-2024
- Exploring behavioral strategies for third-party market cooperation in renewable energy projects: a perspective on addressing climate change Y. Zhao & B. Peng 10.1016/j.renene.2025.124572
- Fractional relaxation noises, motions and the fractional energy balance equation S. Lovejoy 10.5194/npg-29-93-2022
- Climate modelling without irrelevant weather details: The Half-order Energy Balance Equation S. Lovejoy et al. 10.1051/matecconf/202541309001
- Addressing Complexity in Global Aerosol Climate Model Cloud Microphysics U. Proske et al. 10.1029/2022MS003571
- CanStoc: A Hybrid Stochastic–GCM System for Monthly, Seasonal and Interannual Predictions S. Lovejoy & L. Del Rio Amador 10.3390/meteorology2040029
- The Future of Climate Modelling: Weather Details, Macroweather Stochastics—Or Both? S. Lovejoy 10.3390/meteorology1040027
- The impact of long-term memory on the climate response to greenhouse gas emissions N. Yuan et al. 10.1038/s41612-022-00298-8
- The Fractional MacroEvolution Model: a simple quantitative scaling macroevolution model S. Lovejoy & A. Spiridonov 10.1017/pab.2023.38
4 citations as recorded by crossref.
- The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories S. Lovejoy 10.5194/esd-12-469-2021
- Using regional scaling for temperature forecasts with the Stochastic Seasonal to Interannual Prediction System (StocSIPS) L. Del Rio Amador & S. Lovejoy 10.1007/s00382-021-05737-5
- An observation-based scaling model for climate sensitivity estimates and global projections to 2100 R. Hébert et al. 10.1007/s00382-020-05521-x
- The half-order energy balance equation – Part 2: The inhomogeneous HEBE and 2D energy balance models S. Lovejoy 10.5194/esd-12-489-2021
Latest update: 23 Oct 2025
Short summary
This paper presents a new class of energy balance model that accounts for the long memory within the Earth's energy storage. The model is calibrated on instrumental temperature records and the historical energy budget of the Earth using an error model predicted by the model itself. Our equilibrium climate sensitivity and future temperature projection estimates are consistent with those estimated by complex climate models.
This paper presents a new class of energy balance model that accounts for the long memory within...
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