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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Laura Schild, Peter Ewald, Chenzhi Li, Raphaël Hébert, Thomas Laepple, and Ulrike Herzschuh
Earth Syst. Sci. Data, 17, 2007–2033, https://doi.org/10.5194/essd-17-2007-2025, https://doi.org/10.5194/essd-17-2007-2025, 2025
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This study reconstructed vegetation and tree cover in the Northern Hemisphere from a harmonized dataset of pollen counts from sediment and peat cores for the past 14 000 years. A model was applied to correct for differences in pollen production between different plants, and modern remote-sensing forest cover was used to validate the reconstructed tree cover. Accurate data on past vegetation are invaluable for the investigation of vegetation–climate dynamics and the validation of vegetation models.
Mara Y. McPartland, Thomas Münch, Andrew M. Dolman, Raphaël Hébert, and Thomas Laepple
Clim. Past Discuss., https://doi.org/10.5194/cp-2024-73, https://doi.org/10.5194/cp-2024-73, 2024
Preprint under review for CP
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Paleoclimate proxy records contain a combination of climate signals and non-climatic noise. This noise can affect year-to-year variations, or introduce uncertainty on medium and long timescales. Proxies contain different types, or "colors" of noise stemming from the diverse physical and biological processes that go into their creation. We show how non-climatic noise affects tree rings, corals and ice cores. We aim to improve representations of noise in paleoclimate research activities.
Nicolás Acuña Reyes, Elwin van't Wout, Shaun Lovejoy, and Fabrice Lambert
Clim. Past, 20, 1579–1594, https://doi.org/10.5194/cp-20-1579-2024, https://doi.org/10.5194/cp-20-1579-2024, 2024
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This study employs Haar fluctuations to analyse global atmospheric variability over the Last Glacial Cycle, revealing a latitudinal dependency in the transition from macroweather to climate regimes. Findings indicate faster synchronisation between poles and lower latitudes, supporting the pivotal role of poles as climate change drivers.
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
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How big is a cloud?and
How long does the weather last?require scaling to answer. We review the advances in scaling that have occurred over the last 4 decades: (a) intermittency (multifractality) and (b) stratified and rotating scaling notions (generalized scale invariance). Although scaling theory and the data are now voluminous, atmospheric phenomena are too often viewed through an outdated scalebound lens, and turbulence remains confined to isotropic theories of little relevance.
Ulrike Herzschuh, Thomas Böhmer, Manuel Chevalier, Raphaël Hébert, Anne Dallmeyer, Chenzhi Li, Xianyong Cao, Odile Peyron, Larisa Nazarova, Elena Y. Novenko, Jungjae Park, Natalia A. Rudaya, Frank Schlütz, Lyudmila S. Shumilovskikh, Pavel E. Tarasov, Yongbo Wang, Ruilin Wen, Qinghai Xu, and Zhuo Zheng
Clim. Past, 19, 1481–1506, https://doi.org/10.5194/cp-19-1481-2023, https://doi.org/10.5194/cp-19-1481-2023, 2023
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A mismatch between model- and proxy-based Holocene climate change may partially originate from the poor spatial coverage of climate reconstructions. Here we investigate quantitative reconstructions of mean annual temperature and annual precipitation from 1908 pollen records in the Northern Hemisphere. Trends show strong latitudinal patterns and differ between (sub-)continents. Our work contributes to a better understanding of the global mean.
Ulrike Herzschuh, Thomas Böhmer, Chenzhi Li, Manuel Chevalier, Raphaël Hébert, Anne Dallmeyer, Xianyong Cao, Nancy H. Bigelow, Larisa Nazarova, Elena Y. Novenko, Jungjae Park, Odile Peyron, Natalia A. Rudaya, Frank Schlütz, Lyudmila S. Shumilovskikh, Pavel E. Tarasov, Yongbo Wang, Ruilin Wen, Qinghai Xu, and Zhuo Zheng
Earth Syst. Sci. Data, 15, 2235–2258, https://doi.org/10.5194/essd-15-2235-2023, https://doi.org/10.5194/essd-15-2235-2023, 2023
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Climate reconstruction from proxy data can help evaluate climate models. We present pollen-based reconstructions of mean July temperature, mean annual temperature, and annual precipitation from 2594 pollen records from the Northern Hemisphere, using three reconstruction methods (WA-PLS, WA-PLS_tailored, and MAT). Since no global or hemispheric synthesis of quantitative precipitation changes are available for the Holocene so far, this dataset will be of great value to the geoscientific community.
Shaun Lovejoy
Nonlin. Processes Geophys., 29, 93–121, https://doi.org/10.5194/npg-29-93-2022, https://doi.org/10.5194/npg-29-93-2022, 2022
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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.
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
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Paleoclimate proxy data are essential for broadening our understanding of climate variability. There remain, however, challenges for traditional methods of variability analysis to be applied to such data, which are usually irregular. We perform a comparative analysis of different methods of scaling analysis, which provide variability estimates as a function of timescales, applied to irregular paleoclimate proxy data.
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
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Monthly scale, seasonal-scale, and decadal-scale modeling of the atmosphere is possible using the principle of energy balance. Yet the scope of classical approaches is limited because they do not adequately deal with energy storage in the Earth system. We show that the introduction of a vertical coordinate implies that the storage has a huge memory. This memory can be used for macroweather (long-range) forecasts and climate projections.
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
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Radiant energy is exchanged between the Earth's surface and outer space. Some of the local imbalances are stored in the subsurface, and some are transported horizontally. In Part 1 I showed how – in a horizontally homogeneous Earth – these classical approaches imply long-memory storage useful for seasonal forecasting and multidecadal projections. In this Part 2, I show how to apply these results to the heterogeneous real Earth.
Cited articles
Annan, J. D. and Hargreaves, J. C.: Reliability of the CMIP3 ensemble,
Geophys. Res. Lett., 37, L02703, https://doi.org/10.1029/2009gl041994, 2010. a
Bellouin, N., Quaas, J., Gryspeerdt, E., Kinne, S., Stier, P., Watson-Parris,
D., Boucher, O., Carslaw, K. S., Christensen, M., Daniau, A.-L., Dufresne,
J.-L., Feingold, G., Fiedler, S., Forster, P., Gettelman, A., Haywood, J. M.,
Lohmann, U., Malavelle, F., Mauritsen, T., McCoy, D. T., Myhre, G.,
Mülmenstädt, J., Neubauer, D., Possner, A., Rugenstein, M., Sato, Y.,
Schulz, M., Schwartz, S. E., Sourdeval, O., Storelvmo, T., Toll, V., Winker,
D., and Stevens, B.: Bounding Global Aerosol Radiative Forcing of Climate
Change, Rev. Geophys., 58, e2019RG000660, https://doi.org/10.1029/2019RG000660, 2020. a, b
Bretherton, S.: A National Strategy for Advancing Climate Modeling, The
National Academies Press, Washington, DC, https://doi.org/10.17226/13430, 2012. a
Chan, D. and Huybers, P.: Correcting Observational Biases in Sea-Surface
Temperature Observations Removes Anomalous Warmth during World War II,
J. Climate, 34, 4585–4602, https://doi.org/10.1175/JCLI-D-20-0907.1, 2021. a
Collins, M., Knutti, R., Arblaster, J., Dufresne, J.-L., Fichefet, T.,
Friedlingstein, P., Gao, X., Gutowski, W. J., Johns, T., Krinner, G.,
Shongwe, M., Tebaldi, C., Weaver, A. J., and Wehner, M.: Long-term climate
change: Projections, commitments and irreversibility, Cambridge University Press, Cambridge, UK, 1029–1136, https://doi.org/10.1017/CBO9781107415324.024, 2013. a
Cowtan, K. and Way, R.: Update to `Coverage bias in the HadCRUT4 temperature
series and its impact on recent temperature trends'. Temperature
reconstruction by domain: version 2.0 temperature series, Quarterly Journal of the Royal Meteorological Society, Q. J. Roy. Meteorol. Soc., 140,
1935–1944, https://doi.org/10.1002/qj.2297, 2014a. a
Cowtan, K. and Way, R. G.: Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends, Q. J. Roy. Meteorol. Soc. 140, 1935–1944, https://doi.org/10.1002/qj.2297, 2014b. a
Cowtan, K., Hausfather, Z., Hawkins, E., Jacobs, P., Mann, M. E., Miller, S. K., Steinman, B. A., Stolpe, M. B., and Way, R. G.: Robust comparison of climate models with observations using blended land air and ocean sea surface
temperatures, Geophys. Res. Lett., 42, 6526–6534, 2015. a
Crowley, T. J., Zielinski, G., Vinther, B., Udisti, R., Kreutz, K., Cole-Dai,
J., and Castellano, E.: Volcanism and the little ice age, PAGES News, 16,
22–23, 2008. a
de Lima, M. I. P. and Lovejoy, S.: Macroweather precipitation variability up to global and centennial scales, Water Resour. Res., 51, 9490–9513,
https://doi.org/10.1002/2015WR017455, 2015. a
Del Rio Amador, L. and Lovejoy, S.: Long-Range Forecasting as a Past Value
Problem: Untangling Correlations and Causality With Scaling, Geophy. Res. Lett., 48, e2020GL092147, https://doi.org/10.1029/2020GL092147, 2021a. a, b, c
Del Rio Amador, L. and Lovejoy, S.: Using regional scaling for temperature
forecasts with the Stochastic Seasonal to Interannual Prediction System (StocSIPS), Clim. Dynam., 57, 727–756, https://doi.org/10.1007/s00382-021-05737-5, 2021b. a, b
ESGF – Earth System Grid Federation: ESGF Node at DOE/LLNL, Earth System Grid Federation (ESGF), available at: https://esgf-node.llnl.gov/projects/esgf-llnl/, last access: 20 December 2019. a
Flynn, C. M. and Mauritsen, T.: On the climate sensitivity and historical warming evolution in recent coupled model ensembles, Atmos. Chem. Phys., 20, 7829–7842, https://doi.org/10.5194/acp-20-7829-2020, 2020. a, b, c, d
Forest, C. E., Stone, P. H., Sokolov, A. P., Allen, M. R., and Webster, M. D.: Quantifying Uncertainties in Climate System Properties with the Use of Recent Climate Observations, Science, 295, 113–117, https://doi.org/10.1126/science.1064419, 2002. a
Forest, C. E., Stone, P. H., and Sokolov, A. P.: Estimated PDFs of climate
system properties including natural and anthropogenic forcings, Geophys. Res. Lett., 33, L01705, https://doi.org/10.1029/2005GL023977, 2006. a
Forster, P. M., Maycock, A. C., McKenna, C. M., and Smith, C. J.: Latest
climate models confirm need for urgent mitigation, Nat. Clim. Change, 10,
7–10, https://doi.org/10.1038/s41558-019-0660-0, 2020. a
Ghil, M. and Lucarini, V.: The physics of climate variability and climate
change, Rev. Mod. Phys., 92, 035002, https://doi.org/10.1103/RevModPhys.92.035002, 2020. a
Gregory, J. M. and Andrews, T.: Variation in climate sensitivity and feedback
parameters during the historical period, Geophys. Res. Lett., 43, 3911–3920, 2016. a
Harries, J. E. and Belotti, C.: On the Variability of the Global Net Radiative Energy Balance of the Nonequilibrium Earth, J. Climate, 23, 1277–1290, https://doi.org/10.1175/2009JCLI2797.1, 2010. a
Harvey, L. D. and Kaufmann, R. K.: Simultaneously constraining climate
sensitivity and aerosol radiative forcing, J. Climate, 15, 2837–2861, 2002. a
Hasselmann, K.: Stochastic climate models Part I. Theory, Tellus, 28, 473–485, https://doi.org/10.3402/tellusa.v28i6.11316, 1976. a, b
Hébert, R. and Lovejoy, S.: Interactive comment on “Global warming
projections derived from an observation-based minimal model” by K. Rypdal,
Earth Syst. Dynam., 7, 51–70, https://doi.org/10.5194/esd-7-51-2016, 2015. a
Hébert, R. and Lovejoy, S.: Regional Climate Sensitivity- and Historical-Based Projections to 2100, Geophys. Res. Lett., 45, 4248–4254, https://doi.org/10.1002/2017GL076649, 2018. a
Held, I., Winton, M., Takahashi, K., Delworth, T., Zeng, F., and Vallis, G. K.: Probing the Fast and Slow Components of Global Warming by Returning Abruptly to Preindustrial Forcing, J. Climate, 23, 2418–2427,
https://doi.org/10.1175/2009JCLI3466.1, 2010. a, b
Huang, B., Menne, M. J., Boyer, T., Freeman, E., Gleason, B. E., Lawrimore, J. H., Liu, C., Rennie, J. J., Schreck, C. J., Sun, F., Vose, R., Williams, C. N., Yin, X., and Zhang, H.-M.: Uncertainty Estimates for Sea Surface Temperature and Land Surface Air Temperature in NOAAGlobalTemp Version 5, J. Climate, 33, 1351–1379, https://doi.org/10.1175/JCLI-D-19-0395.1, 2020. a
Imkeller, P. and Von Storch, J.-S.: Stochastic climate models, in: vol. 49,
Birkhäuser, Birkhäuser, Basel, 2001. a
IPCC: Climate Change 2013: The Physical Science Basis, in: Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, UK and New York, NY, USA, https://doi.org/10.1017/CBO9781107415324, 2013. a, b, c, d
Irrgang, C., Boers, N., Sonnewald, M., Barnes, E. A., Kadow, C., Staneva, J.,
and Saynisch-Wagner, J.: Towards neural Earth system modelling by integrating
artificial intelligence in Earth system science, Nat. Mach. Intell., 3, 667–674, 2021. a
Iseri, Y., Yoshikawa, S., Kiguchi, M., Tawatari, R., Kanae, S., and Oki, T.:
Towards the incorporation of tipping elements in global climate risk
management: probability and potential impacts of passing a threshold, Sustainabil. Sci., 13, 315–328, https://doi.org/10.1007/s11625-018-0536-7, 2018. a
Johansson, D. J., O'Neill, B. C., Tebaldi, C., and Häggström, O.:
Equilibrium climate sensitivity in light of observations over the warming
hiatus, Nat. Clim. Change, 5, 449–453, 2015. a
Kaufmann, R. K., Kauppi, H., Mann, M. L., and Stock, J. H.: Reconciling
anthropogenic climate change with observed temperature 1998–2008, P. Natl. Acad. Sci. USA, 108, 11790–11793, https://doi.org/10.1073/pnas.1102467108, 2011. a
Knutti, R., Furrer, R., Tebaldi, C., Cermak, J., and Meehl, G. A.: Challenges
in Combining Projections from Multiple Climate Models, J. Climate, 23, 2739–2758, https://doi.org/10.1175/2009JCLI3361.1, 2010. a
Lenssen, N., Schmidt, G., Hansen, J., Menne, M., Persin, A., Ruedy, R., and
Zyss, D.: Improvements in the GISTEMP uncertainty model, J. Geophys. Res.-Atmos., 124, 6307–6326, https://doi.org/10.1029/2018JD029522, 2019. a
Lewis, N. and Curry, J. A.: The implications for climate sensitivity of AR5
forcing and heat uptake estimates, Clim. Dynam., 45, 1009–1023,
https://doi.org/10.1007/s00382-014-2342-y, 2015. a, b
Lewis, N. and Curry, J.: The Impact of Recent Forcing and Ocean Heat Uptake
Data on Estimates of Climate Sensitivity, J. Climate, 31, 6051–6071,
https://doi.org/10.1175/JCLI-D-17-0667.1, 2018. a
Lovejoy, S.: What Is Climate?, Eos Trans. Am. Geophys. Union, 94, 1–2, https://doi.org/10.1002/2013EO010001, 2013. a, b
Lovejoy, S.: A voyage through scales, a missing quadrillion and why the climate is not what you expect, Clim. Dynam., 44, 3187–3210,
https://doi.org/10.1007/s00382-014-2324-0, 2015b. a, b, c
Lovejoy, S. and Schertzer, D.: The Weather and Climate: Emergent Laws and
Multifractal Cascades, Cambridge University Press, Cambridge,
https://doi.org/10.1017/CBO9781139093811, 2013. a, b, c, d
Lovejoy, S. and Varotsos, C.: Scaling regimes and linear/nonlinear responses of last millennium climate to volcanic and solar forcings, Earth Syst. Dynam., 7, 133–150, https://doi.org/10.5194/esd-7-133-2016, 2016. a, b
Lovejoy, S., del Rio Amador, L., and Hébert, R.: The ScaLIng Macroweather Model (SLIMM): using scaling to forecast global-scale macroweather from months to decades, Earth Syst. Dynam., 6, 637–658, https://doi.org/10.5194/esd-6-637-2015, 2015. a, b, c, d
Lovejoy, S., Del Rio Amador, L., and Hébert, R.: Harnessing Butterflies:
Theory and Practice of the Stochastic Seasonal to Interannual Prediction
System (StocSIPS), in: Advances in Nonlinear Geosciences, edited by: Tsonis, A., Springer, Cham, 305–355, https://doi.org/10.1007/978-3-319-58895-7_17, 2017. a
Medhaug, I., Stolpe, M., Fischer, E., and Knutti, R.: Reconciling controversies about the `global warming hiatus', Nature, 545, 41–47,
https://doi.org/10.1038/nature22315, 2017. a
Meehl, G., Arblaster, J., Fasullo, J., Hu, A., and Trenberth, K.: Model-based
evidence of deep-ocean heat uptake during surface-temperature hiatus periods,
Nat. Clim. Change, 1, 360–364, https://doi.org/10.1038/nclimate1229, 2011. a
Meinshausen, M., Raper, S. C. B., and Wigley, T. M. L.: Emulating coupled
atmosphere-ocean and carbon cycle models with a simpler model, MAGICC6 –
Part 1: Model description and calibration, Atmos. Chem. Phys., 11, 1417–1456, https://doi.org/10.5194/acp-11-1417-2011, 2011a. a
Meinshausen, M., Smith, S. J., Calvin, K., Daniel, S. J., Kainuma, M. L. T., Lamarque, J. F., Matsumoto, J. F., Montzka, S. A., Raper, S. C. B., Riahi, K., Thomson, A., Velders, G. J. M., and van Vuuren, D. P. P.: The RCP greenhouse gas concentrations and their extensions from 1765 to 2300, Climatic Change, 109, 213–241, https://doi.org/10.1007/s10584-011-0156-z, 2011b. a, b, c
Meinshausen, M., Nicholls, Z. R. J., Lewis, J., Gidden, M. J., Vogel, E.,
Freund, M., Beyerle, U., Gessner, C., Nauels, A., Bauer, N., Canadell, J. G.,
Daniel, J. S., John, A., Krummel, P. B., Luderer, G., Meinshausen, N.,
Montzka, S. A., Rayner, P. J., Reimann, S., Smith, S. J., van den Berg, M.,
Velders, G. J. M., Vollmer, M. K., and Wang, R. H. J.: The shared socio-economic pathway (SSP) greenhouse gas concentrations and their extensions to 2500, Geosci. Model Dev., 13, 3571–3605,
https://doi.org/10.5194/gmd-13-3571-2020, 2020. a
Millar, R. J., Otto, A., Forster, P. M., Lowe, J. A., Ingram, W. J., and Allen, M. R.: Model structure in observational constraints on transient climate response, Climatic Change, 131, 199–211, 2015. a
Morice, C. P., Kennedy, J. J., Rayner, N. A., and Jones, P. D.: Quantifying
uncertainties in global and regional temperature change using an ensemble of
observational estimates: The HadCRUT4 data set, J. Geophys. Res.-Atmos., 117, D08101, https://doi.org/10.1029/2011JD017187, 2012. a
Murphy, D., Solomon, S., Portmann, R., Rosenlof, K., Forster, P., and Wong, T.: An observationally based energy balance for the Earth since 1950, J. Geophys. Res.-Atmos., 114, D17107, 2009. a
Myhre, G., Highwood, E. J., Shine, K. P., and Stordal, F.: New estimates of
radiative forcing due to well mixed greenhouse gases, Geophys. Res. Lett., 25, 2715–2718, 1998. a
Myhre, G., Samset, B. H., Schulz, M., Balkanski, Y., Bauer, S., Berntsen, T. K., Bian, H., Bellouin, N., Chin, M., Diehl, T., Easter, R. C., Feichter, J., Ghan, S. J., Hauglustaine, D., Iversen, T., Kinne, S., Kirkevåg, A.,
Lamarque, J.-F., Lin, G., Liu, X., Lund, M. T., Luo, G., Ma, X., van Noije,
T., Penner, J. E., Rasch, P. J., Ruiz, A., Seland, Ø., Skeie, R. B., Stier, P., Takemura, T., Tsigaridis, K., Wang, P., Wang, Z., Xu, L., Yu, H.,
Yu, F., Yoon, J.-H., Zhang, K., Zhang, H., and Zhou, C.: Radiative forcing of
the direct aerosol effect from AeroCom Phase II simulations, Atmos. Chem. Phys., 13, 1853–1877, https://doi.org/10.5194/acp-13-1853-2013, 2013. a
Myrvoll-Nilsen, E., Sørbye, S. H., Fredriksen, H.-B., Rue, H., and Rypdal,
M.: Statistical estimation of global surface temperature response to forcing
under the assumption of temporal scaling, Earth Syst. Dynam., 11, 329–345, https://doi.org/10.5194/esd-11-329-2020, 2020. a
Nazarenko, L., Rind, D., Tsigaridis, K., Del Genio, A. D., Kelley, M., and
Tausnev, N.: Interactive nature of climate change and aerosol forcing, J. Geophys. Res.-Atmos., 122, 3457–3480, https://doi.org/10.1002/2016JD025809, 2017. a
North, G. R.: Theory of Energy-Balance Climate Models, J. Atmos. Sci., 32, 2033–2043, https://doi.org/10.1175/1520-0469(1975)032<2033:TOEBCM>2.0.CO;2, 1975. a
North, G. R. and Kim, K.-Y.: Energy Balance Climate Models, 1st Edn., Wiley, available at: https://www.perlego.com/book/992583/energy-balance-climate-models-pdf (last access: 17 December 2021), 2017. a
North, G. R., Cahalan, R. F., and Coakley Jr., J. A.: Energy balance climate
models, Rev. Geophys., 19, 91–121, 1981. a
Otto, A., Otto, F. E. L., Boucher, O., Church, J., Hegerl, G., Forster, P. M., Gillett, N. P., Gregory, J., Johnson, G. C., Knutti, R., Lewis, N., Lohmann, U., Marotzke, J., Myhre, G., Shindell, D., Stevens, B., and Allen, M. R.: Energy budget constraints on climate response, Nat. Geosci., 6, 415–416, https://doi.org/10.1038/ngeo1836, 2013. a
Padilla, L. E., Vallis, G. K., and Rowley, C. W.: Probabilistic Estimates of
Transient Climate Sensitivity Subject to Uncertainty in Forcing and Natural
Variability, J. Climate, 24, 5521–5537, https://doi.org/10.1175/2011JCLI3989.1, 2011. a, b
Penner, J., Andreae, M., Annegarn, H., Barrie, L., Feichter, J., Hegg, D.,
Achuthan, J., Leaitch, R., Murphy, D., Nganga, J., and Pitari, G.: Aerosols,
their Direct and Indirect Effects, Climate Change 2001: The Scientific Basis, in: Contribution of Working Group I to the Third Assessment Report of the
Intergovernmental Panel on Climate Change, World Meteorological Organization United Nations Environment Program, 289–348, 2001. a
Procyk, R.: The Fractional Energy Balance Equation: the Unification of
Externally Forced and Internal Variability, MS thesis, McGill University, Montreal, Canada, 2021. a
Proistosescu, C., Donohoe, A., Armour, K. C., Roe, G. H., Stuecker, M. F., and Bitz, C. M.: Radiative feedbacks from stochastic variability in surface
temperature and radiative imbalance, Geophys. Res. Lett., 45, 5082–5094, 2018. a
Richardson, L. F.: Atmospheric diffusion shown on a distance-neighbour graph,
P. Roy. Soc. Lond. A, 110, 709–737, https://doi.org/10.1098/rspa.1926.0043, 1926. a
Ring, M. J., Lindner, D., Cross, E. F., and Schlesinger, M. E.: Causes of the
Global Warming Observed since the 19th Century, Atmos. Clim. Sci., 02, 401–415, https://doi.org/10.4236/acs.2012.24035, 2012. a
Rohde, R. A. and Hausfather, Z.: The Berkeley Earth Land/Ocean Temperature
Record, Earth Syst. Sci. Data, 12, 3469–3479, https://doi.org/10.5194/essd-12-3469-2020, 2020. a
Rypdal, K.: Global temperature response to radiative forcing: Solar cycle
versus volcanic eruptions, J. Geophys. Res.-Atmos., 117, D06115, https://doi.org/10.1029/2011JD017283, 2012. a
Rypdal, M. and Rypdal, K.: Long-Memory Effects in Linear Response Models of
Earth's Temperature and Implications for Future Global Warming, J. Climate, 27, 5240–5258, https://doi.org/10.1175/JCLI-D-13-00296.1, 2014. a
Sato, M., Hansen, J. E., McCormick, M. P., and Pollack, J. B.: Stratospheric aerosol optical depths, 1850–1990, J. Geophys. Res., 98, 22987–22994, 1993. a
Sato, Y., Goto, D., Michibata, T., Suzuki, K., Takemura, T., Tomita, H., and
Nakajima, T.: Aerosol effects on cloud water amounts were successfully
simulated by a global cloud-system resolving model, Nat. Commun., 9, 985, https://doi.org/10.1038/s41467-018-03379-6, 2018. a
Schurer, A. P., Mann, M. E., Hawkins, E., Tett, S. F. B., and Hegerl, G. C.:
Importance of the pre-industrial baseline for likelihood of exceeding Paris
goals, Nat. Clim. Change, 7, 563–567, https://doi.org/10.1038/nclimate3345, 2017. a
Schwartz, S. E.: Uncertainty in climate sensitivity: causes, consequences,
challenges, Energ. Environ. Sci., 1, 430–453, 2008. a
Sherwood, S., Webb, M. J., Annan, J. D., Armour, K., Forster, P. M.,
Hargreaves, J. C., Hegerl, G., Klein, S. A., Marvel, K. D., Rohling, E. J., Watanabe, M., Andrews, T., Braconnot, P., Bretherton, C. S., Foster, G. L., Hausfather, Z., von der Heydt, A. S., Knutti, R., Mauritsen, T., Norris, J. R., Proistosescu, C., Rugenstein, M., Schmidt, G. A., Tokarska, K. B., and Zelinka, M. D.: An assessment of Earth's climate sensitivity using multiple lines of evidence, Rev. Geophys., 58, e2019RG000678, https://doi.org/10.1029/2019RG000678, 2020. a
Skeie, R. B., Berntsen, T., Aldrin, M., Holden, M., and Myhre, G.: A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series, Earth Syst. Dynam., 5, 139–175, https://doi.org/10.5194/esd-5-139-2014, 2014. a
Smith, C. J.: Effective Radiative Forcing from Shared Socioeconomic Pathways (v0.3.1). Zenodo [data set], https://doi.org/10.5281/zenodo.3515339, 2019. a
Smith, C. J., Forster, P. M., Allen, M., Leach, N., Millar, R. J., Passerello, G. A., and Regayre, L. A.: FAIR v1.3: a simple emissions-based impulse response and carbon cycle model, Geosci. Model Dev., 11, 2273–2297, https://doi.org/10.5194/gmd-11-2273-2018, 2018. a, b, c
Smith, D. M., Scaife, A. A., Hawkins, E., Bilbao, R., Boer, G. J., Caian, M.,
Caron, L.-P., Danabasoglu, G., Delworth, T., Doblas-Reyes, F. J., Doescher, R., Dunstone, N. J., Eade, R., Hermanson, L., Ishii, M., Kharin, V., Kimoto,
M., Koenigk, T., Kushnir, Y., Matei, D., Meehl, G. A., Menegoz, M., Merryfield, W. J., Mochizuki, T., Müller, W. A., Pohlmann, H., Power, S., Rixen, M., Sospedra-Alfonso, R., Tuma, M., Wyser, K., Yang, X., and Yeager,
S.: Predicted Chance That Global Warming Will Temporarily Exceed 1.5 ∘C, Geophys. Res. Lett., 45, 11895–11903, https://doi.org/10.1029/2018GL079362, 2018. a
Smith, T. M., Reynolds, R. W., Peterson, T. C., and Lawrimore, J.: Improvements to NOAA’s historical merged land–ocean surface temperature analysis (1880–2006), J. Climate, 21, 2283–2296, 2008. a
Solomon, S.: Climate Change 2007 the physical science basis: contribution of
Working Group I to the Fourth Assessment Report of the IPCC, Cambridge
University Press, Cambridge, 2007. a
Solomon, S., Plattner, G.-K., and Friedlingstein, P.: Irreversible climate
change due to carbon dioxide emissions, P. Natl. Acad. Sci. USA, 106, 1704–1709, https://doi.org/10.1073/pnas.0812721106, 2009. a
Stainforth, D., Allen, M., Tredger, E., and Smith, L.: Confidence, uncertainty and decision-support relevance in climate predictions, Philos. T. Roy. Soc. A, 365, 2145–2161, https://doi.org/10.1098/rsta.2007.2074, 2007. a
Stevens, B.: Rethinking the Lower Bound on Aerosol Radiative Forcing, J. Climate, 28, 4794–4819, https://doi.org/10.1175/JCLI-D-14-00656.1, 2015. a, b, c, d
Stouffer, R. J.: Time scales of climate response, J. Climate, 17, 209–217, https://doi.org/10.1175/1520-0442(2004)017<0209:TSOCR>2.0.CO;2, 2004. a
Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An overview of CMIP5 and the experiment design, B. Am. Meteorol. Soc., 93, 485–498, 2012. a
Tebaldi, C. and Knutti, R.: The use of the multi-model ensemble in
probabilistic climate projections, Philos. T. Roy. Soc. A, 365, 2053–2075,
https://doi.org/10.1098/rsta.2007.2076, 2007. a
Tokarska, K. B., Stolpe, M. B., Sippel, S., Fischer, E. M., Smith, C. J.,
Lehner, F., and Knutti, R.: Past warming trend constrains future warming in
CMIP6 models, Sci. Adv., 6, eaaz9549, https://doi.org/10.1126/sciadv.aaz9549, 2020. a, b
Tomassini, L., Reichert, P., Knutti, R., Stocker, T. F., and Borsuk, M. E.:
Robust Bayesian Uncertainty Analysis of Climate System Properties Using
Markov Chain Monte Carlo Methods, J. Climate, 20, 1239–1254,
https://doi.org/10.1175/JCLI4064.1, 2007. a
Trenberth, K. E., Fasullo, J. T., and Kiehl, J.: Earth's Global Energy Budget, B. Am. Meteorol. Soc., 90, 311–324, https://doi.org/10.1175/2008BAMS2634.1, 2009. a
Trenberth, K. E., Fasullo, J. T., and Balmaseda, M. A.: Earth’s energy imbalance, J. Climate, 27, 3129–3144, 2014. a
Wang, Y.-M., Lean, J., and Sheeley Jr., N.: Modeling the Sun's magnetic field
and irradiance since 1713, Astrophys. J., 625, 522, https://doi.org/10.1086/429689, 2005. a
Weisheimer, A. and Palmer, T. N.: On the reliability of seasonal climate
forecasts, J. Roy. Soc. Interface, 11, 20131162, https://doi.org/10.1098/rsif.2013.1162, 2014. a
Wolfram Research, Inc.: Mathematica, Version 12.2, Champaign, IL, available at: https://www.wolfram.com/mathematica (last access: 15 December 2021), 2020. a
Zelinka, M. D., Myers, T. A., McCoy, D. T., Po-Chedley, S., Caldwell, P. M.,
Ceppi, P., Klein, S. A., and Taylor, K. E.: Causes of Higher Climate
Sensitivity in CMIP6 Models, Geophys. Res. Lett., 47, e2019GL085782, https://doi.org/10.1029/2019GL085782, 2020. a, b, c, d
Zhang, H., Huang, B., Lawrimore, J., Menne, M., and Smith, T. M.: Global
Surface Temperature Dataset (NOAAGlobalTemp), Version 4.0, [NOAA Global
Surface Temperature Data], https://doi.org/10.7289/V5FN144H, 2019. a
Zhou, C. and Penner, J. E.: Why do general circulation models overestimate the aerosol cloud lifetime effect? A case study comparing CAM5 and a CRM,
Atmos. Chem. Phys., 17, 21–29, https://doi.org/10.5194/acp-17-21-2017, 2017.
a
Ziegler, E. and Rehfeld, K.: TransEBM v. 1.0: description, tuning, and validation of a transient model of the Earth's energy balance in two dimensions, Geosci. Model Dev., 14, 2843–2866, https://doi.org/10.5194/gmd-14-2843-2021, 2021. a
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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