the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 24 Feb 2026
Correct use of radiative efficiencies in calculating global warming potentials and other emission metrics
Abstract. The calculations of Global Warming Potentials (GWPs) and other related climate emission metrics should use radiative efficiencies that are representative of the mean atmospheric mole fraction, rather than the surface mole fraction as is commonly used. This correction leads to an upward revision of GWP values. Radiative forcing from projected changes in mean atmospheric mole fraction (such as for climate scenario) also need to be corrected. For species with lifetimes greater than a few years, the revision is an increase of a few percent e.g., 8 % for trichlorofluoromethane (CFC-11). For species with lifetimes less than a year this correction can lead to increases in the GWPs (and in some cases radiative forcing) of tens of percent, which could impact on policymaker decisions on the desirability of using such gases.
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Status: final response (author comments only)
- RC1: 'Correction of AR6 GWPs may be neccessary, but explanation needs clarity', Michael Prather, 17 Mar 2026
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RC2: 'Comment on egusphere-2026-674', Chris Smith, 17 Apr 2026
This paper introduces an adjustment for AWGP that takes into account vertical profiles of greenhouse gases which are not uniform and a function of lifetime. It aims to relate radiative efficiency in W m-2 kg-1 surface emission terms to W m-2 ppb-1 atmospheric average terms, where the current treatment is to convert W m-2 kg-1 at the surface to W m-2 ppb-1 at the surface. The adjustment is required because the radiative transfer models used to calculate the W m-2 ppb-1 radiative efficiencies are calculated based on a whole-atmosphere average W m-2 ppb-1 value (possibly a constant vertical profile).
This has knock on effects for ratios of AGWP (i.e. the GWP, where the comparator gas is CO2) and related metrics like AGTP/GTP, with the general conclusion that not taking into account the vertical profile adjustment leads to an underestimation of GWP.
It’s a short paper which I appreciate. I am convinced it is technically correct. However, it provides the potential to cause confusion. The authors suggest reporting both the GWPs based on surface and full-atmosphere concentrations (lines 126-129). I am not sure this would be well-understood by policymakers and has the potential to be misused. The question to ask could be “how significant are these changes in light of the overall uncertainty in certain metrics?” If the answer is not very, then are the current practices, though including this inconsistency, sufficient for policy purposes?
Also, this further highlights the difficulty of attempting to distil multi-faceted climate effects into one number. Though this isn’t the focus of the paper, related to this is why indirect effects are reported for some GHGs and excluded for others (and since the authors report CFC and HCFC values in their table 1, it is in scope). For example, tropospheric ozone formation and stratospheric water vapour formation for CH4 is included, but stratospheric ozone depletion for chlorinated gases isn’t at least in headline figures (WMO2022 reports it in chapter 7 but the headline Annex A values do not). I understand the policy implications of quoting negative GWPs for CFCs, but the inconsistency is rarely mentioned.
Specific comments:
Lines 15-17: are gases with species of less than one year that important anyway? Radiationally active short-lived forcers like SO2, CO and NOx are emitted in much larger quantities than these GHGs but we don’t talk much about their direct GWPs (we rightly focus on their chemistry implications).
Line 39: are these assumed vertical profiles invariant? If emissions are increasing (sources exceed sinks), steady (sources equal sinks) or reducing (sources are less than sinks), does this change the profile and adjustment factor?
Line 49: Hodnebrog et al. (2013) – please write down these equations somewhere.
Line 50: spatial (3D) or vertical (1D)? Spatial brings in new challenges. Where things are emitted matters and this will depend on regional socioeconomic interplays. For the shortest lived GHGs this is probably important.
Line 97: For gases with tropospheric and stratospheric loss pathways, does evidence suggest that using the larger of equation (3) and (4) the most appropriate or is there some combination based on inverse lifetimes? As a general point, as a practitioner who will be calculating GHG metrics for IPCC AR7, I would need the information for every GHG on whether the primary loss is stratospheric or tropospheric.
Figure 1b: This looks like it could very easily be an exponential – Is there a justification for choosing this shape as the curve fit?
Equation 1 and surrounding text – to make the units balance, the 10^9 is strictly [ppb atm-1] and T_M is [kg atm].
Line 102-103: similar question to line 39 on whether the profiles from Myhre and Stordahl, based on a 1997 atmosphere (or earlier), are still valid today. Getting these numbers correct for CH4 and N2O are important. Then the authors report that these numbers are less than expected from equation 3 (should it also be equation 4 for CH4?), so why are these two gases treated as special cases and why do they deviate from the trend? When plugging this into a generalised formula to calculate metrics which are often reported to three significant figures in IPCC, I would want another decimal place in the precision of these ratios (even if not justified by the uncertainty in them). An additional potential complication is that the radiative efficiencies of CH4 and N2O are not constant and are reported in Etminan for a present-day (at the time) concentration. The Etminan radiative forcing relationship was further updated by Meinshausen et al. (2020) that provided a closer fit to the Etminan radiative transfer results. How do I apply all of this?
Line 117: Why is it fine to assume a constant vertical profile for CO2? We know that this isn’t quite true. The CO2 should be adjusted similarly to the other GHGs. The authors extend the use case of adjusting radiative forcing for vertical profiles to reduced complexity climate models. Then we really start to think about how the models were run. Abrupt-4xCO2 is often used as a calibration experiment for simple climate models because it has a constant uniform forcing. Any ESM experiment running concentration driven would typically (with one notable exception I know from CMIP6) specify a uniform atmospheric profile. Running CO2-emissions driven as many simple models would do, and some carbon-cycle enabled ESMs which would typically emit CO2 into the lowest atmospheric layer, would again result in this surface concentration/full atmosphere mismatch.
Minor and stylistic comments:
13: climate scenarios
27: put equation in a new line and update the sentence structure so that this reads better.
Citation: https://doi.org/10.5194/egusphere-2026-674-RC2
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I have high esteem for the authors of this Letter, they are good colleagues and friends, and they have decades of experience in quantifying the impact of different greenhouse gases (GHG). In my personal view, unfortunately, this Letter is mistaken and adds more confusion than elucidation to our understanding of atmospheric trace gases, their distributions, their lifetimes, and how we assess their climate impacts. The letter seems to explain a small mistake or confusion that was made by the authors in calculating the global warming potentials (GWPs) for the assessments. Thus, maybe it should appear as an IPCC erratum on /ipcc.ch rather than as a scientific advance in ACP, although maybe corrections do belong in ACP.
The authors present a corrected methodology for calculating the conversion factor CF relating the increase in atmospheric GHG burden (in Tg) to the mean tropospheric abundance (X, mole fraction with respect to dry air in ppb, parts per billion). This revision results in a set of %-corrections for the recent set of GWPs that the authors calculated in the first place. The authors should be commended for correcting the record.
CF (Tg per ppb) is used with the Radiative Efficiency (e.g., RE in W m-2 per ppb) to calculate the radiative imbalance caused by an increase of 1 Tg in the atmospheric burden of the GHG (W m-2 per Tg). CF values have been published and used extensively throughout the IPCC to convert emissions scenarios (Tg) into tropospheric mean X (ppb). From this Letter, it appears that the GWP calculations have used different, incorrect CF values. The recent IPCC AR6 assessment, Table 7.15 in ref [0], does not list the CFs used in the GWP calculation, and this Letter also fails to list the corrected CFs so that they can be checked by others. The CF is a very simple quantity and can be simply verified from the observed or modeled distribution of the GHG in troposphere and stratosphere.
The central question here is what “ppb” should we be using in CF and RE. For RE it obviously the abundance in the middle to upper troposphere since GHG in the near-surface layer have no thermal infrared radiative effect being indistinguishable from the surface, and GHG in the stratosphere are not so coupled to the troposphere-climate system (as recognized by the stratospheric adjusted RF, SARF). For CF, thus it should relate total burden to the mean tropospheric abundance, since that is a quantity that we typically measure (e.g., NOAA’s marine boundary layer GHG record) or model, and the one that should be used in the RE calculations.
For well-mixed (tropospheric that is) GHG, we must account for the stratospheric fall-off in abundance. I am familiar with this approach since I derived some of the key values, including the CF used in the IPCC SAR & TAR [1]. The 2001 TAR conversion factors, 2.78 Tg-CH4/ppb and 4.81 Tg-N(N2O)/pbb, are used in sections 4.2.1.1 & 4.2.1.2, respectively. I was unhappy with these simplistic TAR numbers and pursued a more careful and quantitative evaluation of the CF (Tg/ppb) values in [2] based on a well-mixed troposphere (from NOAA remote surface sites) and the observed fall-off of stratospheric profiles. These updated 2012 [2] values were published as 2.75 Tg-CH4/ppb ±1% and 4.79 Tg-N(N2O)/ppb ±1% (68% confidence interval), which as expected are notably less than the values 2.84 and 4.96 derived from Equation (1) in the Letter and well outside the expected uncertainty. What is surprising is that based on the references in the Letter (2005 and 2013), one side of IPCC did not apparently know what the other side was publishing. In addition, the 2013 AR5 Annex II GHG Tables [3] use and explicitly reference the ref [2] methodology. These values are used in the scenario calculations by Meineshausen and the MAGICC code to convert Tg to ppb. It appears from the authors of this Letter that the GWP calculations since the TAR have assumed that all GHG are well mixed to the top of the atmosphere and now need to be corrected. It is good to see the GWPs 'corrected' but the Letter could note the problem with a better historical perspective and make sure the AR6 GWPs are updated on /ipcc.ch.
There remain two fundamental disagreements with the approach and derivations presented here: (1) the incorrect use of surface abundance, X_srf; and (2) the derivation of lifetimes for short-lived (<0.2 yr) gases simply as a function of their chemical rates.
(1) The “ppb” used in both CF and RE should be the tropospheric mean, X_trop. The repeated use of X_srf in this Letter is simply wrong. No one seriously uses the mean surface abundance for anything because it is not observed nor modeled correctly. For one, X_sfc globally averaged is impossible to measure. Near source regions (and these GHG do have regions of intense surface emissions) one could never assemble enough observing sites to accurately measure the global mean, and satellite remote sensing cannot really detect surface abundances. That is why NOAA and ALE/GAGE have put together a latitudinal range of remote marine boundary layer sites which are combined to derive a mean tropospheric abundance, X_trop. It is this X_trop that is quoted in the rest of the IPCC as the mean abundance for the GHG, not a mean surface value that would have to include averages over source regions. For two, we really cannot model the global mean X_sfc very well either. In a model like CTM2, this value depends on the model layers and the nighttime boundary layer, including the diurnal cycle of emissions that will control the large build up overnight. While our ability to model X_sfc is very limited, our ability to model and measure X_trop is solid and insensitive to boundary layers, diurnal cycles, etc.
(2) Lifetime is defined correctly as total burden of the entire reservoir divided by source or sink. That definition is critical if we are to use the steady-state lifetime as an integral of the impacts of the emitted gas, see review and derivations in ref [4]. Lifetime depends on the kinetics of the chemical loss throughout the atmosphere, but it also depends on the location and time of the source. For example, in the derivation of the N2O chemical feedback on lifetime [5], it is shown that emissions of N2O at 40 km result in a lifetime of 2.5 years, rather than 120 yr for tropospheric emissions. These facts about lifetime are woefully and incorrectly propagated in this Letter. The authors assume that their corrections and lifetime adjustments for short-lived GHG (<0.2 yr) are meaningful and valid and can be used for GWPs. This assumption is simply wrong and can have very large errors. The burden that accumulates following emission, and the resulting GWP, will vary by large factors depending on where and in what season the gas is emitted. Tropical emissions will have a short lifetime, probably <0.1 yr, and small GWP (lower X_trop), but high latitude winter-time emissions will accumulate and probably have an effective lifetime >0.5 yr and correspondingly greater GWP. Consequently, one cannot scale ERF to emissions with a metric like GWP. For different example, recent studies of tropospheric O3 [6] show a lifetime ranging from 6 to 27 days depending on latitude and season of its production. This result means that the ERF of an O3 “source” has range of a factor of 4 or more, and cannot be simply “corrected” as done here. The idea of an RE (per ppb) is still mostly valid but the CF is now widely variable. To be fair, we should not publish single GWPs for such short-lived GHG unless we deliver a range based on possible emission scenarios.
The current Letter could be revised in its discussion of surface abundances and lifetimes to avoid propagating old science. Then, collectively, we – as authors of the past IPCC chapters on trace gases and radiation – must accept our failure to communicate with one another.
Michael Prather, UC Irvine
[0] see Table 7.15 of Forster, P., T. Storelvmo, K. Armour, W. Collins, J.-L. Dufresne, D. Frame, D.J. Lunt, T. Mauritsen, M.D. Palmer, M. Watanabe, M. Wild, and H. Zhang, 2021: The Earth’s Energy Budget, Climate Feedbacks, and Climate Sensitivity. In Climate Change 2021: The Physical Science Basis. Contribution of WGI to IPCC AR6 [Masson-Delmotte, V., P. Zhai, A. Pirani, et al. (eds.)]. Cambridge University Press, Cambridge, United Kingdom, pp. 923–1054, doi:10.1017/9781009157896.009.
[1] D. Ehhalt, M. Prather, F. Dentener, R. G. Derwent, E. Dlugokencky, E. Holland, I. S. A. Isaksen, J. Katima, V. Kirchhoff, P. Matson, P. M. Midgley, and M. Wang (2001) Chapter 4. Atmospheric Chemistry and Greenhouse Gases, in Climate Change 2001: The Scientific Basis, J.T. Houghton et al., eds., Cambridge U. Press, pp. 239-287.
[2] Prather, M.J., C.D. Holmes, J. Hsu (2012), Reactive greenhouse gas scenarios: Systematic exploration of uncertainties and the role of atmospheric chemistry, Geophys. Res. Lett., 39, L09803, 5 pp., doi:10.1029/2012GL051440.
[3] Prather, M., G. Flato, P. Friedlingstein, C. Jones, J.-F. Lamarque, H. Liao and P. Rasch (section eds.) (2013) Annex II: Climate System Scenario Tables. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, New York, NY, USA, pp. 1395-1445.
[4] Prather, M.J. (2007) Lifetimes and time-scales in atmospheric chemistry, Phil. Trans. R. Soc., A 365: 1705–1726, https://doi.org/10.1098/rsta.2007.2040
[5] Prather, M.J. (1998) Time scales in atmospheric chemistry: coupled perturbations to N2O, NOy, and O3, Science, 279, 1339-1341.
[6] Prather, M.J. and Xin Zhu (2024) Lifetimes and timescales of tropospheric ozone, Elementa: Science of the Anthropocene, 12 (1): 00112, doi: 10.1525/elementa.2023.00112