Radiative kernels from climate models

The radiative kernel technique is a method used to quantify radiative feedbacks in response to global warming.  Radiative kernels are commonly calculated for the water vapor, lapse rate, temperature and albedo feedbacks.  Radiative kernels are used to deconstruct the various contributions of feedbacks and forcings to the total change in top-of-atmosphere (TOA) radiative fluxes in climate.  To calculate a feedback, a kernel is multiplied by the change in the variable of interest, typically normalized by the change in global mean surface temperature.  See 'Expert Guidance' for more information.  Under 'External Data', links to published radiative kernels for a few of the major global climate models are provided.


Expert User Guidance

The following was contributed by Angeline Pendergrass (U of Colorado/ CIRES), February, 2016:


The radiative kernel technique is a method to quantify radiative feedbacks in response to global warming.  It was originally proposed as a way to quantify the water vapor feedback in climate models in Held and Soden (2000), and was later also applied to temperature, lapse rate, and albedo feedbacks in Soden and Held (2006).  It has been applied widely to climate model projections of global warming, over the 21st Century and response to increasing carbon dioxide, in order to calculate the magnitude of climate feedbacks and deconstruct the various contributions of feedbacks and forcings to the total change in top-of-atmosphere (TOA) radiative fluxes.

A radiative feedback kernel is essentially the partial derivative of the radiative flux with respect to a variable that changes with Earth’s temperature, such as temperature itself, moisture, or surface albedo.  To calculate a climate feedback, a kernel is multiplied by the change in the variable of interest in a climate model simulation, typically normalized by the change in global mean surface temperature in the simulation.

To calculate kernel, a climate model’s radiation code is run off-line with small perturbations in temperature (1 K at each level), moisture (moistening that would occur from warming of 1 K at constant relative humidity), a change in surface albedo of one percent, and an increase in surface temperature of 1 K. This is repeated separately for each level at high frequency, typically either every time step or every 3 hours, for each month of a one-year simulation.  The changes in total-sky and clear-sky longwave and shortwave radiation that result from each perturbation are averaged over each month to create the kernel.

The method for calculating cloud feedbacks with the kernel technique is less straightforward than for other variables, and as a result has evolved over time.  Soden and Held (2006) calculated the cloud feedback as the residual between the total radiative change in climate models, a forcing calculation and the sum of the temperature, water vapor, albedo, and lapse rate kernels.  Soden et al (2008) calculated the cloud feedback from the sum of the change in cloud radiative forcing and the difference between all-sky and clear-sky feedbacks temperature, water vapor, lapse rate and albedo feedbacks.  Zelinka et al (2012) extended the technique by calculating cloud feedback kernels as a function of cloud top pressure and cloud optical depth.

Adaptations and extensions

The kernel technique assumes linearity of the radiative responses to changes in climate, which the trail of literature has evidently found useful for the projections of climate change over the 21st century to which it is often applied. A number of adaptations, extensions, and improvements have been developed, some of which are listed below; many more could be devised. 

-    Kernels from different base states to accommodate large forcings with responses that challenge linearity (eg 8x carbon dioxide; Jonko et al 2012)

-    Improve accuracy by calculating kernels with constant-relative-humidity warming and changes in RH, instead of separate temperature and moisture (Held and Shell 2012)

-    Model specific kernels (Sanderson and Shell 2012)

-    Include changing surface fluxes to study the changing atmospheric energy budget in a feedback framework (Previdi 2010, O’Gorman et al 2012)

-    Separate local and non-local by using local, rather than global, surface temperature change to normalize (Feldl and Roe 2013) 

-    Spectral kernels that quantify the effects at different wavelengths (Huang et al 2014)


Prior to the kernel technique, the Partial Radiative Perturbation (PRP, see e.g. Colman 2003) method was used for calculating climate feedbacks.  In this method, radiative calculations are made for states at the beginning and end of a simulation, switching values from each variable of interest one at a time between the beginning and end of the simulation. 

Feedbacks can also be calculated by a regression method (see, eg, Dessler 2013 or Dalton and Shell 2013).  The TOA radiative flux is regressed against each variable of interest to recover a kernel or climate feedback. 

An alternative framework to the kernel technique for feedback analysis is presented in Roe (2009).  It uses the concepts of amplifying and damping feedbacks and gain developed in engineering, which is algebraically related to the kernel technique, to understand the influence of varying climate feedbacks in response to a forcing.##

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Ocean or Land


Vertical Levels

  1. Block, K., and T. Mauritsen, 2013: Forcing and feedback in the MPI-ESM-LR coupled model under abruptly quadrupled CO2, J. Adv. Model. Earth Syst., 5, 676–691, doi:10.1002/jame.20041
  2. Colman, R. (2003). A comparison of climate feedbacks in general circulation models. Climate Dynamics, 20(7-8), 865-873. doi:10.1007/s00382-003-0310-z
  3. Conley, A. J., Lamarque, J. F., Vitt, F., Collins, W. D., & Kiehl, J. (2012). PORT, a CESM tool for the diagnosis of radiative forcing. Geosci. Model Dev. Discuss, 5, 2687-2704
  4. Dalton, M. M., & Shell, K. M. (2013). Comparison of short-term and long-term radiative feedbacks and variability in twentieth-century global climate model simulations. Journal of Climate, 26(24), 10051-10070. doi:10.1175/JCLI-D-12-00564.1
  5. Dessler, A. E. (2013). Observations of Climate Feedbacks over 2000-10 and Comparisons to Climate Models. Journal of Climate, 26(1), 333-342. doi:10.1175/JCLI-D-11-00640.1
  6. Feldl, N. and Roe, G.H., 2013. Four perspectives on climate feedbacks. Geophysical Research Letters, 40(15), pp.4007-4011
  7. Held, I. M., & Soden, B. J. (2000). Water vapor feedback and global warming. Annual Review of Energy and the Environment, 25(1), 441-475.
  8. Huang, X., Chen, X., Soden, B. J., & Liu, X. (2014). The spectral dimension of longwave feedback in the CMIP3 and CMIP5 experiments. Geophysical Research Letters, 41(22), 7830-7837
  9. Jonko, A. K., Shell, K. M., Sanderson, B. M., & Danabasoglu, G. (2012). Climate feedbacks in CCSM3 under changing CO2 forcing. Part I: Adapting the linear radiative kernel technique to feedback calculations for a broad range of forcings. Journal of Climat
  10. Kay, J. E., Deser, C., Phillips, A., Mai, A., Hannay, C., Strand, G., ... & Holland, M. (2014). The Community Earth System Model (CESM) large ensemble project: A community resource for studying climate change in the presence of internal climate variabilit
  11. Roe, G. (2009). Feedbacks, timescales, and seeing red. Annual Review of Earth and Planetary Sciences, 37, 93-115.
  12. Sanderson, B. M., & Shell, K. M. (2012). Model-specific radiative kernels for calculating cloud and noncloud climate feedbacks. Journal of Climate, 25(21), 7607-7624. doi:10.1175/JCLI-D-11-00726.1
  13. Shell, K. M., Kiehl, J. T., & Shields, C. A. (2008). Using the radiative kernel technique to calculate climate feedbacks in NCAR's Community Atmospheric Model. Journal of Climate, 21(10), 2269-2282. doi:10.1175/2007JCLI2044.1
  14. Smith, C. J. et al. (2018), Understanding Rapid Adjustments to Diverse Forcing Agents, Geophys. Res. Lett., doi:10.1029/2018GL079826.": https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018GL079826
  15. Soden, B. J., & Held, I. M. (2006). An assessment of climate feedbacks in coupled ocean-atmosphere models. Journal of Climate, 19(14), 3354-3360. doi:10.1175/JCLI3799.1.
  16. Soden, B. J., Held, I. M., Colman, R., Shell, K. M., Kiehl, J. T., & Shields, C. A. (2008). Quantifying climate feedbacks using radiative kernels. Journal of Climate, 21(14), 3504-3520. doi:10.1175/2007JCLI2110.1.
  17. Zelinka, M. D., Klein, S. A., & Hartmann, D. L. (2012). Computing and partitioning cloud feedbacks using cloud property histograms. Part I: Cloud radiative kernels. Journal of Climate, 25(11), 3715-3735. doi: 10.1175/JCLI-D-11-00248.1

Key Figures

Click the thumbnails to view larger sizes



(contributed by A. Pendergrass) Average TOA feedback kernels, calculated with CESM version 1.1.2 using PORT (Conley et al 2012). Compare with Soden et al (2008) or Block and Mauritsen (2013). Note that the temperature and water vapor kernels here are on sigma rather than pressure levels, which affects the units. (contributed by A. Pendergrass)
Radiative feedbacks in the CESM large ensemble  (contributed by A. Pendergrass) Radiative feedbacks in the CESM large ensemble (Kay et al 2014) calculated with the feedback kernels shown in Figure 1. (contributed by A. Pendergrass)

Cite this page

Pendergrass, Angeline & National Center for Atmospheric Research Staff (Eds). Last modified 24 Oct 2018. "The Climate Data Guide: Radiative kernels from climate models." Retrieved from https://climatedataguide.ucar.edu/climate-data/radiative-kernels-climate-models.

Acknowledgement of any material taken from this page is appreciated. On behalf of experts who have contributed data, advice, and/or figures, please cite their work as well.