Editorial Type:
Article
Article Type:
Research Article

The Role of the Nonlinearity of the Stefan–Boltzmann Law on the Structure of Radiatively Forced Temperature Change

Matthew Henry McGill University, Montreal, Quebec, Canada

Search for other papers by Matthew Henry in
Current site
Google Scholar
PubMed Close
and
Timothy M. Merlis McGill University, Montreal, Quebec, Canada

Search for other papers by Timothy M. Merlis in
Current site
Google Scholar
PubMed Close
Print Publication:
15 Jan 2019
DOI:
https://doi.org/10.1175/JCLI-D-17-0603.1
Page(s):
335–348
Restricted access

Abstract

The Stefan–Boltzmann law governs the temperature dependence of the blackbody emission of radiation: . A consequence of this nonlinearity is that a cold object needs a greater increase in temperature than a hot object in order to reach the same increase in radiation emitted. Therefore, this nonlinearity potentially has an impact on the structure of radiatively forced atmospheric temperature change in both the horizontal and vertical directions. For example, it has previously been argued to be a cause of polar amplification (PA) of surface air warming. Here, the role of this nonlinearity is investigated by 1) assessing the magnitude of its effect on PA compared to spatial variations in CO2’s radiative forcing for Earth’s atmosphere and 2) linearizing in a gray radiation atmospheric general circulation model (GCM) with an interactive hydrological cycle. Estimates for Earth’s atmosphere show that the combination of the Planck feedback and forcing from CO2 would produce a tropically amplified warming if they were the only means of changing the Earth’s energy balance. Contrary to expectations, climate change simulations with linearized radiation do not have reduced polar amplification of surface air warming relative to the standard GCM configuration. However, simulations with linearized radiation consistently show less warming in the upper troposphere and more warming in the lower troposphere across latitudes. The lapse rate feedbacks from pure radiative and radiative–convective configurations of the model are used to show that the “cold-altitudes-warm-more” effect of the nonlinearity carries across this model hierarchy.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Matthew Henry, matthew.henry@mail.mcgill.ca

Abstract

The Stefan–Boltzmann law governs the temperature dependence of the blackbody emission of radiation: . A consequence of this nonlinearity is that a cold object needs a greater increase in temperature than a hot object in order to reach the same increase in radiation emitted. Therefore, this nonlinearity potentially has an impact on the structure of radiatively forced atmospheric temperature change in both the horizontal and vertical directions. For example, it has previously been argued to be a cause of polar amplification (PA) of surface air warming. Here, the role of this nonlinearity is investigated by 1) assessing the magnitude of its effect on PA compared to spatial variations in CO2’s radiative forcing for Earth’s atmosphere and 2) linearizing in a gray radiation atmospheric general circulation model (GCM) with an interactive hydrological cycle. Estimates for Earth’s atmosphere show that the combination of the Planck feedback and forcing from CO2 would produce a tropically amplified warming if they were the only means of changing the Earth’s energy balance. Contrary to expectations, climate change simulations with linearized radiation do not have reduced polar amplification of surface air warming relative to the standard GCM configuration. However, simulations with linearized radiation consistently show less warming in the upper troposphere and more warming in the lower troposphere across latitudes. The lapse rate feedbacks from pure radiative and radiative–convective configurations of the model are used to show that the “cold-altitudes-warm-more” effect of the nonlinearity carries across this model hierarchy.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Matthew Henry, matthew.henry@mail.mcgill.ca
Save
Cover Journal of Climate
Journal of Climate

  • Alexeev, V. A., and C. H. Jackson, 2013: Polar amplification: Is atmospheric heat transport important? Climate Dyn., 41, 533–547, https://doi.org/10.1007/s00382-012-1601-z.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Bloch-Johnson, J., R. T. Pierrehumbert, and D. S. Abbot, 2015: Feedback temperature dependence determines the risk of high warming. Geophys. Res. Lett., 42, 4973–4980, https://doi.org/10.1002/2015GL064240.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Curry, J., 1983: On the formation of continental polar air. J. Atmos. Sci., 40, 2278–2292, https://doi.org/10.1175/1520-0469(1983)040<2278:OTFOCP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Feldl, N., and G. H. Roe, 2013a: Four perspectives on climate feedbacks. Geophys. Res. Lett., 40, 4007–4011, https://doi.org/10.1002/grl.50711.

  • Feldl, N., and G. H. Roe, 2013b: The nonlinear and nonlocal nature of climate feedbacks. J. Climate, 26, 8289–8304, https://doi.org/10.1175/JCLI-D-12-00631.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Feldl, N., and S. Bordoni, 2016: Characterizing the Hadley circulation response through regional climate feedbacks. J. Climate, 29, 613–622, https://doi.org/10.1175/JCLI-D-15-0424.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Frierson, D. M., 2007: The dynamics of idealized convection schemes and their effect on the zonally averaged tropical circulation. J. Atmos. Sci., 64, 1959–1976, https://doi.org/10.1175/JAS3935.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Frierson, D. M., I. M. Held, and P. Zurita-Gotor, 2006: A gray-radiation aquaplanet moist GCM. Part 1: Static stability and eddy scale. J. Atmos. Sci., 63, 2548–2566, https://doi.org/10.1175/JAS3753.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Graversen, R. G., P. L. Langen, and T. Mauritsen, 2014: Polar amplification in CCSM4: Contributions from the lapse rate and the surface albedo feedbacks. J. Climate, 27, 4433–4450, https://doi.org/10.1175/JCLI-D-13-00551.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Hansen, J., and Coauthors, 2005: Efficacy of climate forcings. J. Geophys. Res., 110, D18104, https://doi.org/10.1029/2005JD005776.

  • Huang, Y., and M. Zhang, 2014: The implication of radiative forcing for poleward energy transport. Geophys. Res. Lett., 41, 1665–1672, https://doi.org/10.1002/2013GL059079.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Huang, Y., X. Tan, and Y. Xia, 2016: Inhomogeneous radiative forcing of homogeneous greenhouse gases. J. Geophys. Res. Atmos., 121, 2780–2789, https://doi.org/10.1002/2015JD024569.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • IPCC, 2013: Climate Change 2013: The Physical Science Basis. T. F. Stocker et al., Eds., Cambridge University Press, 1535 pp.

  • Langen, P. L., R. G. Graversen, and T. Mauritsen, 2012: Separation of contributions from radiative feedbacks to polar amplification on an aquaplanet. J. Climate, 25, 3010–3024, https://doi.org/10.1175/JCLI-D-11-00246.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Lee, S., 2014: A theory for polar amplification from a general circulation perspective. Asia-Pac. J. Atmos. Sci., 50, 31–43, https://doi.org/10.1007/s13143-014-0024-7.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Manabe, S., and R. T. Wetherald, 1975: The effects of doubling the CO2 concentration on the climate of a general circulation model. J. Atmos. Sci., 32, 3–15, https://doi.org/10.1175/1520-0469(1975)032<0003:TEODTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Manabe, S., R. Stouffer, M. Spelman, and K. Bryan, 1991: Transient responses of a coupled ocean–atmosphere model to gradual changes of atmospheric CO2. Part I. Annual mean response. J. Climate, 4, 785–818, https://doi.org/10.1175/1520-0442(1991)004<0785:TROACO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Mauritsen, T., R. G. Graversen, D. Klocke, P. L. Langen, B. Stevens, and L. Tomassini, 2013: Climate feedback efficiency and synergy. Climate Dyn., xx, 2539–2554, https://doi.org/10.1007/s00382-013-1808-7.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Merlis, T. M., 2014: Interacting components of the top-of-atmosphere energy balance affect changes in regional surface temperature. Geophys. Res. Lett., 41, 7291–7297, https://doi.org/10.1002/2014GL061700.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Merlis, T. M., 2015: Direct weakening of tropical circulations from masked CO2 radiative forcing. Proc. Natl. Acad. Sci. USA, 112, 13 167–13 171, https://doi.org/10.1073/pnas.1508268112.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Merlis, T. M., and M. Henry, 2018: Simple estimates of polar amplification in moist diffusive energy balance models. J. Climate, 31, 5811–5824, https://doi.org/10.1175/JCLI-D-17-0578.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • O’Gorman, P. A., and T. Schneider, 2008: The hydrological cycle over a wide range of climates simulated with an idealized GCM. J. Climate, 21, 3815–3832, https://doi.org/10.1175/2007JCLI2065.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • O’Gorman, P. A., and M. S. Singh, 2013: Vertical structure of warming consistent with an upward shift in the middle and upper troposphere. Geophys. Res. Lett., 40, 1838–1842, https://doi.org/10.1002/grl.50328.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Payne, A. E., M. F. Jansen, and T. W. Cronin, 2015: Conceptual model analysis of the influence of temperature feedbacks on polar amplification. Geophys. Res. Lett., 42, 9561–9570, https://doi.org/10.1002/2015GL065889.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Pithan, F., and T. Mauritsen, 2014: Arctic amplification dominated by temperature feedbacks in contemporary climate models. Nat. Geosci., 7, 181–184, https://doi.org/10.1038/ngeo2071.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Po-Chedley, S., and Q. Fu, 2012: Discrepancies in tropical upper tropospheric warming between atmospheric circulation models and satellites. Environ. Res. Lett., 7, 044018, https://doi.org/10.1088/1748-9326/7/4/044018.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Roe, G. H., and M. B. Baker, 2007: Why is climate sensitivity so unpredictable? Science, 318, 629–632, https://doi.org/10.1126/science.1144735.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Santer, B. D., and Coauthors, 2005: Amplification of surface temperature trends and variability in the tropical atmosphere. Science, 309, 1551–1556, https://doi.org/10.1126/science.1114867.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Smith, K. L., G. Chiodo, M. Previdi, and L. M. Polvani, 2018: No surface cooling over Antarctica from the negative greenhouse effect associated with instantaneous quadrupling of CO2 concentrations. J. Climate, 31, 317–323, https://doi.org/10.1175/JCLI-D-17-0418.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Soden, B. J., I. M. Held, R. Colman, K. M. Shell, J. T. Kiehl, and C. A. Shields, 2008: Quantifying climate feedbacks using radiative kernels. J. Climate, 21, 3504–3520, https://doi.org/10.1175/2007JCLI2110.1.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Weaver, C., and V. Ramanathan, 1995: Deductions from a simple climate model: Factors governing surface temperature and atmospheric thermal structure. J. Geophys. Res., 100, 11 585–11 591, https://doi.org/10.1029/95JD00770.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Winton, M., 2006: Amplified Arctic climate change: What does surface albedo feedback have to do with it? Geophys. Res. Lett., 33, L03701, https://doi.org/10.1029/2005GL025244.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Zhang, M., and Y. Huang, 2014: Radiative forcing of quadrupling CO2. J. Climate, 27, 2496–2508, https://doi.org/10.1175/JCLI-D-13-00535.1.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 6240 2361 231
PDF Downloads 3160 924 102