More on the statistical dispute between Scafetta and Schmidt

A graph with red and blue lines Description automatically generated

By Andy May

The argument about the proper way to estimate error in the European Centre for Medium-Range Weather Forecast (ECMWF) ERA5 weather reanalysis dataset between Nicola Scafetta and Gavin Schmidt has finally been published by Geophysical Research Letters. Schmidt, Jones, and Kennedy’s comment is here (Schmidt, Jones, & Kennedy, 2023), and Scafetta’s response is here (Scafetta N., 2023a).

I first wrote about this dispute earlier in the year here. Nothing much has changed in the final versions.

Schmidt, Jones, and Kennedy’s assessment of the error in the ERA5 surface temperature dataset average still (incorrectly) assumes that, during such a period, the global surface temperature was constant from 2011-2021 and that its yearly variability is due to random noise. This is clearly a nonphysical interpretation of Earth’s climate, since there are real systematic changes in the climate from year to year, whether one assumes they are due to natural or man-made forces, or both.

By conflating natural and man-made climatic forces with random noise Schmidt, Jones, and Kennedy inflate the real error of the temperature mean by 5–10 times. In fact, a proper analysis of the ensemble of observed global surface temperature members yields a decadal-scale error of about 0.01–0.02°C, as reported in published records. BEST (Berkeley Earth Land/Ocean Temperature record) derives an error of +/- 0.018- 0.020 °C for the 11-year period 2011-2021 (1951-1980 anomalies and the April 2023 version of the BEST dataset). Instead, Schmidt, Jones, and Kennedy assessed the error using the standard deviation of the mean (see Chapter 3 here) from the period 2011-2021. The equation they use is an equation that can only be used when there are multiple measurements of the same quantity, not eleven annual estimates for eleven different years. It cannot be used to properly estimate the error of a quantity, in this case the average surface temperature of the Earth, that changes naturally and possibly due to human emissions, from year to year.

Scafetta’s original paper, the reason for the dispute can be downloaded here. In the paper Scafetta shows that all IPCC/CMIP6 climate models that result in an ECS[1] that is greater than 3°C warming per doubling of CO2 overestimate observed global warming at a statistically significant level. How to determine what is statistically significant is at the heart of the dispute. But statistics or not, Scafetta’s point is apparent in figure 1. When in doubt look at the data.

A graph with red and blue lines

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Figure . IPCC/CMIP6 climate-modeled temperatures (in red) compared to observations (blue, ERA5 2 meter temperatures). Source: (Scafetta N. , 2022a).

In figure 1, the observations are from ECMWF ERA5. Clearly, if CO2 and other greenhouse gases are causing all the recent warming, as the IPCC AR6 report claims (IPCC, 2021, pp. 425 & 961-962), the climate sensitivity we are observing is lower than 3°C. Scafetta’s analysis of ECS is very compelling, but there is still more evidence that the higher AR6 ECS estimates are incorrect. For more on this subject, see my four part series on the mysterious AR6 ECS: Part 1, Part 2, Part 3, and Part 4. There is also a very good summary of observational estimates of ECS, and a critique of the AR6 methods of determining ECS in Chapter 7 of the Clintel volume on AR6, here.

Works Cited

Crok, M., & May, A. (2023). The Frozen Climate Views of the IPCC, An Analysis of AR6.

IPCC. (2021). Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. In V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, . . . B. Zhou (Ed.)., WG1. Retrieved from

Scafetta, N. (2022a). Advanced Testing of Low, Medium, and High ECS CMIP6 GCM Simulations Versus ERA5-T2m. Geophysical Research Letters, 49. doi:10.1029/2022GL097716

Scafetta, N. (2023a). Reply to “Comment on ‘Advanced testing of low, medium, and high ECS CMIP6 GCM simulations versus ERA5-T2m’. Geophysical Research Letters, 50. doi:10.1029/2023GL104960

Schmidt, G. A., Jones, G. S., & Kennedy, J. J. (2023). Comment on “Advanced testing of low, medium, and high ECS CMIP6 GCM simulations versus ERA5-T2m”. Geophysical Research Letters, 50. doi:10.1029/2022GL102530

Taylor, J. (1997). An Introduction to Error Analysis, second edition. University Science Books. Retrieved from

  1. ECS is the equilibrium climate sensitivity, or the ultimate change in global average surface temperature after an instantaneous doubling of CO2. See here for more details.

Published by Andy May

Petrophysicist, details available here:

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