Updating the Lewis & Curry Estimate for ECS

One of the most common studies cited in favor of a low equilibrium climate sensitivity (ECS) was published by Lewis and Curry in 2018 (LC18).[1] Their paper used the standard energy balance equation I've used in previous blogposts to estimate both ECS and TCR. They arrived at median estimates with 95% uncertainties of 1.66 C for ECS (1.15–2.7 C) and 1.33 C for TCR (1.0–1.9 C). These values are significantly below the range estimated by the more recent IPCC assessment reports. Since the publication of this paper, Sherwood et al 2020[2], published what may be the most comprehensive assessment of ECS and found a 95% range of 2.3–4.7 C.

Argument of LC18

So I thought it might be interesting to do a back-of-the-envelope style update to LC18. I think there are several reasons why this can be valuable. Since the publication of this paper, a number of new insights have been published:

  1. The publication of HadCRUT5 had significant improvements over HadCRUT4, even the dataset with kriging to limit the coverage bias that affected HadCRUT4.
  2. Much more work has been done assessing the size of the Earth's energy imbalance (EEI), with a large amount of agreement between in situ and satellite estimates.
  3. The IPCC updated their estimate for the ERF for 2xCO2 from 3.8 W/m^2 to 3.93 ± 0.47 W/m^2 (high confidence).
  4. LC18 chose date ranges to limit the effect of volcanism and the Atlantic Multidecadal Oscillation (AMO) on their assessment, but newer research suggests that the AMO is likely just an artifact of volcanic forcings and not a real feature of the climate system.[3]
  5. The publication of the IPCC's AR6 contains updated values for ozone, aerosol forcings and other forcings affecting albedo.  

Here are the ERF forcing values that LC18 used to calculate ECS and TCR, together with the values estimated by AR5. LC18's estimate of total anthropogenic forcings was about 0.3 W/m^2 higher than that estimated by AR5, which would have the effect of lowering ECS compared to using values from AR5. 


Using the values they determined for ΔT, ΔF, and ΔN (EEI) and ΔF2xCO2, ECS and TCR can be calculated with the following equations:

ECS = ΔF2xCO2*ΔT/(ΔF-ΔN)
TCR = ΔF2xCO2*ΔT/ΔF 

LC18 produced the following estimates for ECS from various base periods and final periods. Their calculated values for ECS range from 1.50 C to 1.69 C. These calculations used a variety of base periods and final periods. Of the base periods LC18 chose, I'm only interested in using the ones in the 19th century, more specifically 1869-1882 and 1850-1900.
I'm going to use final periods that are a little different from the ones LC18 used so I can use more recent data consistent with values reported in AR6. I'll use 2006-2018 in place of 2007-2016 and 1993-2018 in place of 1995-2016.

Updating LC18 with AR6

With the publication of AR6, we have a new set of estimate for ERF values from 1750 to 2019. The IPCC estimates that the total anthropogenic ERF is about 2.72 W/m^2 (1.96 - 3.48) and solar forcings are -0.02 W/m^2 (-0.08 - 0.06)

Earth's Energy Imbalance (EEI)

In order to update LC18, though, it's not helpful to use ERF values through 2019. We need to use the average values for final periods that can update LC18. To do this, I decided to use the estimates from the IPCC for average energy gain (EEI) in AR6. The IPCC estimates EEI to be 0.72 W/m^2 for 1993-2018 and 0.79 W/m^2 from 2006-2018.

Radiative Forcing Values (ERF)

NOAA's website has a table of well-mixed GHGs in the troposphere. The average ERF for these GHGs are 2.654 W/m^2 for 1993-2018 and 2.873 W/m^2 for 2006-2018. I decided to use the AR6 values for Ozone at 0.47 W/m^2 an stratospheric water vapor at 0.05 W/m^2 for a total of 0.52 W/m^2 for Ozone + WV. 

Anthropogenic aerosols are a bit more complicated. Total aerosol forcings from 1750 to 2014 are estimated to be –1.3 W/m^2 (–2.0 to –0.6) with medium confidence. The IPCC's reconstruction shows aerosols to be roughly flat since the latter part of the 20th century, but from 2014 to 2019, aerosol ERF increased by about +0.2 W/m^2:
Consistent with Figure 2.10, the change in aerosol ERF from about 2014 to 2019 is assessed to be +0.2 W m–2, but with low confidence due to limited evidence. Aerosols are therefore assessed to have contributed an ERF of –1.1 [–1.7 to –0.4] W m–2 over 1750–2019 (medium confidence).
So for 1993-2018 I decided to use -1.3 W/m^2 for aerosol ERF and for 2006-2018 I decided to use -1.1 W/m^2. The IPCC estimated the magnitude of smaller forcings related to albedo (land use, light absorbing particles on snow and ice) and aviation-induced forcings to be -0.06 W/m^2. Solar forcings are predictably negligible at -0.02 W/m^2



Temperature (GMST)

For GMST, LC18 use both 1850-1900 and 1869-1882 for 19th century base periods. So I set the three major datasets that go back to 1850 (NOAA, BEST, and HadCRUT5) to a 1850-1900 baseline and used the average anomalies for all three datasets.

Updated Calculations for ECS and TCR

Combining all of these values, I assembled the temperature and forcing data and calculated both ECS and TCR. The average value for ECS is 2.92 C and the average value for TCR was 1.81 C, pretty much right in line with the central estimates of the IPCC.

I've tried to preserve the 95% confidence intervals in the main text for the above data. Obviously uncertainties are significant, especially for aerosols. But this update produces ECS values that are about 75% higher than those calculated by LC18 and are virtually indistinguishable from the IPCC's central estimates for ECS and TCR. So the question then becomes, why are my calculations ~75% higher than those calculated by LC18? To investigate this, I decided to compare the date range in LC18 that is most similar to one used by me.  Here is how my update compares to LC18.


I calculated the ECS and TCR values for LC18 based on the values published in their study. What I report above is slightly higher than LC18 (at the third decimal place) probably because they used more significant figures in their calculations than they published in their paper - but they are basically the same. I set my columns to three decimal places so that the columns will align nicely. For each of the above values, the decisions by LC18 favor a smaller ECS than my update using mostly AR6 values. For their ΔT and ΔF2xCO2 values, this is very understandable; LC18 used the best data available to them. But for ΔF and ΔN (EEI) values, the differences are significant. As best I can tell, more recent treatments of EEI arrive at better constrained an higher values for ΔN. The ΔF difference is mostly due to their assessment of aerosols, and the AR6 accounting of aerosols shows significant uncertainties that probably dominate the uncertainty of calculations of ECS from energy balance equations.

But I sometimes hear people say that many of the high ECS estimates come from an overdependence on models, while those that rely largely on empirical data and the energy balance equation arrive at low estimates of ECS. I think the above shows that this is not necessarily the case. Using the energy balance equation with the largely consensus values for ΔF and ΔN produces ECS estimates very consistent with the central estimate for ECS that has been common in climate science since the 1970s. The empirical data is very consistent with an ECS value of ~ 3 C.


References:

[1] Lewis, N., & Curry, J. (2018, April 23). The impact of recent forcing and ocean heat uptake data on estimates of climate sensitivity. Journal of Climate. Retrieved from https://journals.ametsoc.org/doi/10.1175/JCLI-D-17-0667.1

[2] Sherwood, S. C., Webb, M. J., Annan, J. D., Armour, K. C., Forster, P. M., Hargreaves, J. C., et al. (2020). An assessment of Earth's climate sensitivity using multiple lines of evidence. Reviews of Geophysics, 58, e2019RG000678. https://doi.org/10.1029/2019RG000678

[3] Michael E. Mann, Byron A. Steinman, Daniel J. Brouillette, Sonya K. Miller. Multidecadal climate oscillations during the past millennium driven by volcanic forcing. Science, 2021 DOI: 10.1126/science.abc5810

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