[Update Sep 26 2019: Paper was retracted at the journal's request. Check at the end.]
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Excerpts:
On November 1st there was extensive coverage in the mainstream media1 and online2 of a paper just published in the prestigious journal Nature. The article,3 by Laure Resplandy of Princeton University, Ralph Keeling of the Scripps Institute of Oceanography and eight other authors, used a novel method to estimate heat uptake by the ocean over the period 1991–2016 and came up with an atypically high value.4 The press release 5 accompanying the Resplandy et al. paper was entitled "Earth's oceans have absorbed 60 percent more heat per year than previously thought",6 and said that this suggested that Earth is more sensitive to fossil-fuel emissions than previously thought.
I was asked for my thoughts on the Resplandy paper as soon as it obtained media coverage. Most commentators appear to have been content to rely on what was said in the press release. However, being a scientist, I thought it appropriate to read the paper itself, and if possible look at its data, before forming a view.
Trend estimates
The method used by Resplandy et al. was novel, and certainly worthy of publication. The authors start with observed changes in 'atmospheric potential oxygen' (ΔAPOOBS).7 In their model, one component of this change (ΔAPOClimate) is due to warming of the oceans, and they derived an estimate of its value by calculating values for the other components.8 A simple conversion factor then allows them to convert the trend in ΔAPOClimate into an estimate of ocean heat uptake (the trend in ocean heat content).
On page 1 they say:
From equation (1), we thereby find that ΔAPOClimate = 23.20 ± 12.20 per meg, corresponding to a least squares linear trend of +1.16 ± 0.15 per meg per year 9
A quick bit of mental arithmetic indicated that a change of 23.2 between 1991 and 2016 represented an annual rate of approximately 0.9, well below their 1.16 value. As that seemed surprising, I extracted the annual ΔAPO best-estimate values and uncertainties from the paper's Extended Data Table 410 and computed the 1991–2016 least squares linear fit trend in the ΔAPOClimate values. The trend was 0.88, not 1.16, per meg per year, implying an ocean heat uptake estimate of 10.1 ZJ per year,11 well below the estimate in the paper of 13.3 ZJ per year.12
Resplandy et al. derive ΔAPOClimate from estimates of ΔAPOOBS and of its other components, ΔAPOFF, ΔAPOCant, and ΔAPOAtmD, using – rearranging their equation (1):
ΔAPOClimate = ΔAPOOBS − ΔAPOFF − ΔAPOCant − ΔAPOAtmD
I derived the same best estimate trend when I allowed for uncertainty in each of the components of ΔAPOOBS, in the way that Resplandy et al.'s Methods description appears to indicate,13 so my simple initial method of trend estimation does not explain the discrepancy.
[...]
I wanted to make sure that I had not overlooked something in my calculations, so later on November 1st I emailed Laure Resplandy querying the ΔAPOClimate trend figure in her paper and asking for her to look into the difference in our trend estimates as a matter of urgency, explaining that in view of the media coverage of the paper I was contemplating web-publishing a comment on it within a matter of days. To date I have had no substantive response from her, despite subsequently sending a further email containing the key analysis sections from a draft of this article.
[...]
Uncertainty analysis
I now turn to the uncertainty analysis in the paper.16 Strangely, the Resplandy et al. paper has two different values for the uncertainty in the results. On page 1 they give the ΔAPOClimate trend (in per meg per year) as 1.16 ± 0.15. But on page 2 they say it is 1.16 ± 0.18. In the Methods section they go back to 1.16 ± 0.15. Probably the ± 0.18 figure is a typographical error. 17
It is amazing, uncertainty in page 1 is 0.15, then in page two is 0.18.
And 23.20/26 = 1.16 (?!?!?!).
Ten authors and at least two reviewers see nothing... Is there not a single journalist able to read the first page of a paper?
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Notes:
1 Examples are: https://www.bbc.co.uk/news/science-environment-46046067 https://www.nytimes.com/2018/10/31/climate/ocean-temperatures-hotter.html https://www.washingtonpost.com/energy-environment/2018/10/31/startling-new-research-finds-large-buildup-heat-oceans-suggesting-faster-rate-global-warming/ https://www.scientificamerican.com/article/the-oceans-are-heating-up-faster-than-expected/ https://edition.cnn.com/2018/11/01/australia/ocean-warming-report-intl/index.html http://www.latimes.com/science/sciencenow/la-sci-sn-oceans-study-climate-change-20181031-story.html https://www.usatoday.com/story/news/nation-now/2018/11/01/oceans-more-heat-study-global-warming-climate-change-nature/1843074002/ https://www.independent.co.uk/environment/climate-change-global-warming-ocean-temperature-heat-fossil-fuels-science-research-a8612796.html
2 Examples are: http://www.realclimate.org/index.php/archives/2018/11/unforced-variations-nov-2018/ https://wattsupwiththat.com/2018/11/02/friday-funny-at-long-last-kevin-trenberths-missing-heat-may-have-been-found-repeat-may-have-been/ https://bskiesresearch.wordpress.com/2018/11/01/that-new-ocean-heat-content-estimate/ https://andthentheresphysics.wordpress.com/2018/11/03/new-ocean-heat-content-analysis/ https://twitter.com/Knutti_ETH/status/1057960390502608901
3 L. Resplandy, R. F. Keeling, Y. Eddebbar, M. K. Brooks, R. Wang, L. Bopp, M. C. Long, J. P. Dunne, W. Koeve & A. Oschlies, 2018: Quantification of ocean heat uptake from changes in atmospheric O2 and CO2 composition. Nature, 563, 105-108. https://doi.org/10.1038/s41586-018-0651-8 ("Resplandy et al.")
4 A value of 13.3 zetta Joules (ZJ) per year, or 0.83 Watts per square metre of the Earth's surface. ZJ is the symbol for zetta Joules; 1 ZJ = 1021 J. 1 ZJ per year = 0.0621 Watts per square metre (W/m2 or Wm–2) of the Earth's surface.
5 http://web.archive.org/web/20181103021900/https://www.princeton.edu/news/2018/11/01/earths-oceans-have-absorbed-60-percent-more-heat-year-previously-thought
6 However that is in comparison with an IPCC estimate for 1993–2010; estimates for 1991–2016 are higher.
7 ΔAPO is the change in 'atmospheric potential oxygen', the overall level of which has been observationally measured since 1991 (ΔAPOOBS). It is the sum of the atmospheric concentrations of O2 and of CO2 weighted respectively 1⤬ and 1.1⤬.
8 The authors break the observed change in ΔAPOOBS into four components, ΔAPOFF, ΔAPOCant, ΔAPOAtmD and ΔAPOClimate, deriving the last component (which is related to ocean warming) by deducting estimates of the other three components from ΔAPOOBS. ΔAPOFF is the decrease in APO caused by industrial processes (fossil-fuel burning and cement production). ΔAPOCant accounts for the oceanic uptake of excess anthropogenic atmospheric CO2. ΔAPOAtmD accounts for air–sea exchanges driven by ocean fertilization from anthropogenic aerosol deposition.
9 1 per meg literally means 1 part per million (1 ppm), however 'per meg' and 'ppm' are defined differently in relation to atmospheric concentrations and are not identical units.
10 The same data is available in Excel format from a link on Nature's website, as "Source Data Fig. 2".
11 Dividing by their conversion factor of 0.087 ± 0.003 per meg per ZJ. ZJ is the symbol for zetta Joules; 1 ZJ = 1021 Joules.
12 I used ordinary least squares (OLS) regression with an intercept. That is the standard form of least squares regression for estimating a trend. Resplandy et al. show all APO variables as changes from a baseline of zero in 1991, but that is an arbitrary choice and would not justify forcing the regression fit to be zero in 1991 (by not using an intercept term). Doing so would not in any event raise the ΔAPOClimate estimated trend to the level given by Resplandy et al.
13 I took a large number of sets of samples for each of the years 1991 to 2016 from the applicable error distributions of ΔAPOOBS, ΔAPOFF, ΔAPOCant, and ΔAPOAtmD given in Extended Data Table 4, and calculated all the corresponding sample values of ΔAPOClimate using equation (1). I then computed the ordinary least squares linear trend for each set of 1991–2016 sampled values of ΔAPOClimate, and calculated the mean and standard deviation of the trends.
14 Laure Resplandy was responsible for directing the analysis of the datasets and models.
15 This fact was spotted by Frank Bosse, with whom I discussed the apparent error in the Resplandy et al. ΔAPOClimate trend.
16 All uncertainty values in the paper are ± 1 sigma (1 standard deviation). Errors are presumably assumed to be Normally distributed, as no other distributions are specified.
17 The statement in their Methods that "ΔCant′ cannot be derived from observations and was estimated at 0.05 Pg C yr−1, equivalent to a trend of +0.2 per meg−1, using model simulations" is presumably also a typographical error. The correct value appears to be +0.12 per meg yr−1, as stated elsewhere in Methods and in Extended Data Table 3.
18 On that basis , I can replicate the Extended Data Table 4 ΔAPOOBS uncertainty time series values within ±0.1. Note that all the values in that table, although given to two decimal places, appear to be rounded to one decimal place.
19 The overall uncertainties given in Table 3 in Resplandy et al.'s source paper for its errors in ΔAPOOBS support my analysis.
20 When using the Resplandy et al. Extended Data Table 4 ΔAPOClimate total uncertainty time series and assuming that each year's errors are independent, despite the trend and scale systematic errors being their largest component, the estimated ΔAPOClimate uncertainty reduces to between ± 0.20 and ± 0.21 per meg yr−1. That is still slightly higher than the ± 0.15 and ± 0.18 per meg yr−1 values given in the paper. The reason for the small remaining difference is unclear.
21 It seems likely that the same non-independence over time issue largely or wholly applies to errors in ΔAPOCant, ΔAPOAtmD and probably ΔAPOFF. If the errors in ΔAPOCant and ΔAPOAtmD (but not in ΔAPOFF)
were also treated as perfectly correlated between years, the ΔAPOClimate trend uncertainty would be ± 0.60 per meg yr−1.
22 Lewis, N., and Curry, J., 2018: The impact of recent forcing and ocean heat uptake data on estimates of climate sensitivity. J. Climate, 31(15), 6051-6071.
23 Even if the 2007–2016 ocean heat uptake estimate used in Lewis and Curry (2018) were increased by 3 ZJ yr−1 to match Resplandy et al.'s (incorrect) estimate for 1991–2016, the 1.05°C 5% lower bound of its HadCRUT4v5-based estimate of effective/equilibrium climate sensitivity would only increase to 1.15°C. Moreover, Resplandy et al.'s ΔAPOClimate data imply have a lower ocean heat uptake estimate for 2007–2016 than they do for 1991–2016.
24 See the IPCC's 2018 Special Report on Global Warming of 1.5°C
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Update Sep 26 2019: Paper was retracted at the journal's request.
Retraction Note: Quantification of ocean heat uptake from changes in atmospheric O2 and CO2 composition. L. Resplandy et al. Nature 573, 614 (2019). https://www.nature.com/articles/s41586-019-1585-5
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