Greenhouse-Gas Emission Targets for Limiting Global Warming to 2 °C
Nature, 2009 · paper · Earth science
Supplementary methods for a study of greenhouse-gas emission targets for limiting global warming to 2°C. They describe a simple coupled carbon-cycle climate model with 82 uncertain parameters, constrained by observed temperatures, and used to estimate probabilities of warming outcomes.
Checked: PDF from media.springernature.com, fetched 4 Oct 2026. Page numbers are those of that PDF.
9 findings
Substance "a one million member ensemble of EQW pathways we generated with all permutations of 10 possible reduction or increase rates (-6%, ..., +3%) at each of the 5 chosen branching points (2010, 2015, 2020, 2030, 2050)": 10 rates at 5 points give 100,000 combinations, not one million.
- p. 6 Emission scenarios, second paragraph
a one million member ensemble of EQW pathways
- p. 6 Emission scenarios, second paragraph
at each of the 5 chosen branching points (2010, 2015, 2020,
- p. 6 Emission scenarios, second paragraph
We drew 948 EQW pathways from a one million member ensemble of EQW pathways we
- p. 6 Emission scenarios, second paragraph
all permutations of 10 possible reduction or increase rates
Only the authors can say what is right here.
Judge's note: Page 6 image: ten rates are listed and five branching years are listed, matching the stated '10' and '5'. 10^5 = 100,000; one million needs six branching points. Searched the section and the following sensitivity section for a sixth free parameter: none is described (the sensitivity ensemble separately uses 5 rates at 6 points). Either the ensemble size or the number of branching points is misstated; only the authors can say which. It affects the description of the method, not a result.
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Reference or label Two wrong pointers in the Fossil fuel reserves section: "as shown in Fig 3b and Table S2" and "emissions from proven recoverable fossil fuel reserves (Table S2)"; the reserve emissions are in Table S3, and Table S2 is "Constraints applied in this study".
- p. 7 Fossil fuel reserves, first paragraph
as shown in Fig 3b and Table S2
- p. 18 Table S2 caption
Table S2 | Constraints applied in this study.
- p. 19 Table S3 caption
Table S3 | Median and 80% range estimates of potential CO2 emissions arising from burning
- p. 7
as shown in Fig 3b and Table S2, according to
Judge's note: Opened Table S2 on page 18: it lists only observational constraints (surface temperature, ocean heat uptake, radiative forcing, effective climate sensitivity ratio) and has no reserve or emission rows. Table S3 on page 19 is 'Median and 80% range estimates of potential CO2 emissions arising from burning all proven recoverable reserves of fossil fuels (see text)'. Both pointers on page 7 should read Table S3. The Table S2 pointer on page 3 (radiative forcing constraints) is correct.
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Reference or label Figure S1 legend lists "6 EMF Reference" and "14 EMF Reference"; the dark-blue set of 14 is labelled "14 EMF Mitigation" in Figs S5 and S6, so the second Fig. S1 entry should read "14 EMF Mitigation".
- p. 9 Figure S1c legend
14 EMF Reference
- p. 9 Figure S1c legend
6 EMF Reference
- p. 14 Figure S6a legend
14 EMF Mitigation
Judge's note: Zoomed renders of all three legends. Fig. S1c: orange '6 EMF Reference', dark blue '14 EMF Reference'. Figs S5 and S6: orange '6 EMF Reference', dark blue '14 EMF Mitigation'. Same count and colour, and no second reference set of 14 is described in the text.
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Reference or label Table S1 row 33, RF_SOLAR_SCALE, "Scaling factor for solar forcing", has unit "W/m2"; a scaling factor is dimensionless and the Unit cell should be blank.
- p. 16 Table S1, row 33 RF_SOLAR_SCALE, Unit column
Scaling factor for solar forcing
- p. 11 Figure S3, panel g axis label
Scaling Solar
Judge's note: p16 page image: row 33 shows W/m² with range 0.100 to 2.500, while the other scaling factors (rows 25, 27, 36, 38) have an empty Unit cell. Fig. S3 panel g, 'Scaling Solar Forcing', labels its axis '(Factor)' (zoomed render of p11). The row sits between W/m² rows, which suggests a fill-down slip.
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Reference or label Figure S5 axes for the cumulative Kyoto-GHG panels a and b are labelled "(10³ GtCO₂eq/yr)"; a cumulative quantity should be in GtCO₂eq, without "/yr".
- p. 13 Fig S5 axis labels, panels a/b
(10³ GtCO₂eq/yr)
- p. 13 Fig S5 caption
cumulative Kyoto-GHG emissions between 2000 and 2049
Judge's note: Zoomed renders of the top, bottom and right axes of Fig. S5: panels a and b (cumulative 2000-2049 and 2000-2099) carry '(10³ GtCO2eq/yr)', while the cumulative fossil CO2 panels d and e correctly carry '(GtC)' and the single-year panels c and f carry per-year units. The reviewer's second point, that d-f use GtC where the text uses GtCO2, is a unit choice and not an error.
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Reference or label Table S4 row 11 reads "Knutti et al. (2005)" with Ref. 11, but reference 11 is "Knutti, R., Meehl, G. A., Allen, M. R. & Stainforth, D. A. ... Journal of Climate 19, 4224-4233 (2006)".
- p. 19 Table S4, label 11
Knutti et al. (2005)
- p. 20 reference 11
from the seasonal cycle in surface temperature. Journal of Climate 19, 4224-4233
- p. 20 Reference 11
Journal of Climate 19, 4224-4233 (2006)
- p. 20 Reference 11
Knutti, R., Meehl, G. A., Allen, M. R. & Stainforth, D. A. Constraining climate sensitivity
Judge's note: p19 page image shows row 11 'Knutti et al. (2005)', ref 11, remark Climateprediction.net. The reference-list crop on p20 prints 2006 for entry 11. The years in the other Table S4 rows match their references in the list. Which year is the true one is not needed: the two places in this document disagree, and the table should match its own reference list.
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Wording With Pm defined as "mx628-dimensional" and Tm=PmT, the covariance is printed as "Pm^T Σ Pm"; the conformable m x m form is Pm Σ Pm^T (transpose on the wrong factor).
- p. 3 second paragraph, near the end
We then find the mx628-dimensional matrix Pm
- p. 3 second paragraph, last sentence
estimate the mxm-dimensional covariance matrix Σm from the data set as Pm
- p. 3 second paragraph, near the end
and estimate the mxm-dimensional covariance matrix
Judge's note: On the page image the superscript T sits on the first Pm: 'P_m^T Σ P_m,,'. The same paragraph states Pm is m x 628 and Tm = Pm T, with Σ 628 x 628. (628 x m)(628 x 628) is not conformable, so the printed expression cannot give the stated m x m matrix. Nothing elsewhere redefines Pm as 628 x m. A notation slip; the method itself is not affected.
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Wording The default EQW ensemble has three sizes: "We drew 948 EQW pathways" (text) and "948 EQW" (Fig. S1), "1000 EQW pathways" (Fig. S6 legend), and "3225 sampled EQW pathways" (Fig. S5 legend, whose caption calls it "the default EQW pathway ensemble used in this study").
- p. 14 Figure S6a legend
1000 EQW pathways
- p. 9 Figure S1c legend
948 EQW
- p. 6 Emission scenarios
We drew 948 EQW pathways
- p. 13 Fig S5 legend
3225 sampled EQW pathways
Only the authors can say what is right here.
Judge's note: Read the p6 text crop and the three legends from zoomed renders. The text says 6004 pathways were kept and one in six sampled, which gives about 1001, not 948; the legend of Fig. S6 may be that rounded figure. Nothing in the supplement produces 3225 (the sensitivity ensemble is 1,573 with one in four sampled). Only the authors can say which counts are right.
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Wording "We estimate the 80% uncertainty range in these reserve estimate as being ±10% the WEC estimates or the range of estimates in the literature, whichever is greater": (a) the 80% ranges in Table S3 are narrower than ±10% for natural gas (360; 345 to 379) and conventional oil (497; 465 to 530); (b) "these reserve estimate" should be "these reserve estimates".
- p. 7 Fossil fuel reserves, third paragraph
We estimate the 80% uncertainty range in these reserve estimate as being ±10% the WEC
- p. 19 Table S3, Natural Gas row
345
- p. 19 Table S3, Oil (conventional) row
465
- p. 7
80% uncertainty range in these reserve estimate as being
Only the authors can say what is right here.
Judge's note: Read Table S3 on the page 19 image: Natural Gas 360 / 345 / 379, Oil (conventional) 497 / 465 / 530. The text sets a minimum 80% range of ±10% for reserves and then adds uncertainty in calorific value and carbon content, so the emission ranges should be at least ±10% of the median. Gas is about -4.2%/+5.3% and conventional oil about ±6.5%. The full width for gas is about 9.4% of the median, so '±10%' may have been meant as a total width of 10%; the text does not say so, and no other passage explains it. Only the authors can settle which is intended. The grammatical slip (plural 'these' with singular 'estimate') is visible on the page 7 image and is a plain correction.
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16 minor (typos and the like; most checked by the judge only)
Wording The size of the EQW ensemble is given three ways: "We drew 948 EQW pathways" (text p.6 and Fig. S1c legend), "1000 EQW pathways" (Fig. S6a legend) and "3225 sampled EQW pathways" (Fig. S5 legend, whose caption calls it "the default EQW pathway ensemble used in this study"). The paper does not reconcile them.
- p. 6 Emission scenarios, second paragraph
We drew 948 EQW pathways
- p. 9 Figure S1c legend
948 EQW
- p. 14 Figure S6a legend
1000 EQW pathways
- p. 13 Figure S5 legend
3225 sampled EQW pathways
Only the authors can say what is right here.
Judge's note: I checked the page-6 text: 6004 pathways are kept and one in every six is sampled 'at random'. 6004/6 is about 1001. With random Bernoulli sampling, 948 is within about 2 SD of that, so 948 on its own is plausible and Fig. S6's '1000' could be a round figure. However, the Fig. S5 legend (I read it on the page-13 image) gives 3225, and its caption says it shows the default ensemble. That conflicts with 948, and the paper never explains it. The other scenario counts also differ between legends: Fig. S1 has 35 SRES and 3 Stern/EQW, Fig. S6 has 27 SRES and 5 Stern/EQW, and Fig. S5 has 35 SRES and 5 Stern/EQW. Only the authors can say which sample each figure uses. A separate point: the text says the 'one million member ensemble' comes from all permutations of 10 rates at 5 branching points, but 10^5 is 100,000. The text states no other dimension that would give 10^6, so the authors should also be asked about this.
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Typo The page-1 header reads "doi: 10.1038/nature00817", but pages 2-22 read "doi: 10.1038/nature08017".
- p. 1 page header, top left
doi: 10.1038/nature00817
- p. 2 page header, top left
doi: 10.1038/nature08017
Judge's note: The page-1 crop clearly shows 'nature00817'. The page-2 header and the page-13 full image show 'nature08017'. The digits on page 1 are transposed. It is a publisher-set header, so this is cosmetic, and the fix is evident.
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Typo Duplicated word: "control runs of all AOGCMs runs available at PCMDI" should read "control runs of all AOGCMs available at PCMDI".
- p. 3 first paragraph
runs of all AOGCMs runs available at PCMDI
- p. 3
control runs of all AOGCMs runs available at PCMDI
Judge's note: Visible on the page 3 image, first paragraph.
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Typo There is a doubled comma after the subscript in "from the data set as Pm^T Σ Pm,, where Σ is the previously derived covariance matrix".
- p. 3
from the data set as Pm T Σ Pm,, where Σ is
- p. 3
Σm from the data set as Pm T Σ Pm,, where
Judge's note: The page-3 crop shows the subscript printed as 'm,,', so the doubled comma is real and not an extraction artefact. This is cosmetic punctuation.
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Typo Table S2 gives the ocean heat uptake trend unit as "10E22 J/yr"; the text gives 10^22 J/yr, which in E-notation is 1E22 (10E22 would be 10^23).
- p. 18 Table S2, ocean heat uptake row, Unit column
10E22
- p. 3 third paragraph
+0.3721(1-sigma: ±0.0698) 10
- p. 10 Fig S2 caption
95% uncertainty range for northern hemisphere ocean
Judge's note: p18 page image shows '10E22 J/yr'; the p3 crop shows '+0.3721(1-sigma: ±0.0698) 10²² J/yr' with a superscript. The value is not in doubt, so this is a notation slip. Table S1 uses '1E3' in the standard sense. The third reviewer's remark on the Fig. S2 caption (95% observational range against 90/68/50% model ranges) concerns two different ranges and is not a defect.
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Typo The sentence "...as proportional to the product of the likelihood L(Θ) and the prior π(Θ):" ends in a colon but no displayed equation for g(Θ) follows.
- p. 4 Likelihood estimation, second paragraph
proportional to the product of the likelihood L(Θ) and the prior
- p. 4 Likelihood estimation, second paragraph
as proportional to the product of the likelihood L(Θ) and the prior
Judge's note: Page 4 image: the likelihood equation L(Θ) above is displayed, but after 'π(Θ):' the next line is the new paragraph 'Sensitivity to the chosen prior...', with no equation and no gap. The relation is fully given in words (g(Θ) ∝ L(Θ)π(Θ)), so no content is lost; this is a dropped display equation or a stray colon.
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Typo Text gives the "default 0-20K range of the CS prior" while Table S1 lists the climate sensitivity prior as Min 0.050, Max 20.000 K.
- p. 4 Representing published climate sensitivity distributions
default 0-20K range of the CS prior
- p. 15 Table S1 row 1
0.050
Judge's note: Table S1 row 1 on page 15 shows Min 0.050, Max 20.000. The text's '0-20K' is a rounded description of 0.05-20 K. The difference has no practical effect; either form is defensible.
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Typo Number disagreement: "we chose the climate sensitivity distributions by Frame et al. (2006) as our default, given that this distributions resembles most closely the IPCC AR4 estimate"; should be "distribution" (singular) in both places.
- p. 5 second paragraph
given that this distributions resembles most closely
- p. 5
given that this distributions resembles most closely the IPCC
Judge's note: Visible in the page 5 crop. One distribution (Frame et al. 2006 UniTCR) is meant, as the following sentences state.
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Typo Unidiomatic "That is why – in average – our non-CO2 forcing contributions"; the Figure S6 caption has the correct "on average".
- p. 6 first paragraph
That is why – in average – our non-CO2 forcing contributions
- p. 14 Figure S6 caption
on average
Judge's note: Both wordings are visible on the page 6 and page 14 images. Cosmetic only.
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Typo "We fit 'skewed normal' distributions (cf. section 2 above)" points to a numbered section, but the supplement's sections are unnumbered; the definition is under OBSERVATIONAL CONSTRAINTS.
- p. 7 Fossil fuel reserves
(cf. section 2 above)
Judge's note: Checked p7 and the contents list on p1 and headings on p2. No section carries a number. 'Skewed normal' is defined under Observational Constraints, which is the second heading in the contents, so the pointer is resolvable by counting but imprecise. Minor.
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Typo The same work is listed twice in the reference list: ref. 19 "World Energy Council. Survey of Energy Resources 2007. pp. 600 (World Energy Council, London United Kingdom, 2007)." and ref. 25 "WEC. 2007 Survey of Energy Resources. pp. 600 (World Energy Council, 2007)."; the text then contrasts "±10% the WEC19 estimates or the range of estimates in the literature20,21,23-26", citing the WEC survey on both sides.
- p. 21 reference 19
World Energy Council. Survey of Energy Resources 2007. pp. 600
- p. 21 reference 25
WEC. 2007 Survey of Energy Resources.
- p. 7 Fossil fuel reserves, third paragraph
±10% the WEC19
- p. 21 Additional References, entry 25
WEC. 2007 Survey of Energy Resources. pp. 600 (World Energy Council, 2007).
Judge's note: Read both entries on page 21 and the sentence on page 7. Title, publisher, year and page count (600) match, so this is a duplicate entry and not a different edition, and ref. 25 falls inside the range 23-26 cited as 'the literature'. It is a reference-list duplication with no effect on the numbers.
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Typo Figure S1 caption: "b, 2050 Kyoto-gas emissions: c, 2020 Kyoto-gas emissions" has a colon where the panel list needs a semicolon.
- p. 9 Figure S1 caption
b, 2050 Kyoto-gas emissions: c, 2020 Kyoto-gas emissions
- p. 9 Figure S1 caption
2050 Kyoto-gas emissions: c, 2020
Judge's note: Visible on the p9 page image: panels a and b are separated by a semicolon, b and c by a colon.
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Typo Table S4, label 13, Remarks reads "Combination of those PDFs that including nat. radiative forcing." (should be "that include" or "including"); the Fig. S1 caption has a colon where a semicolon belongs: "a, cumulative Kyoto-gas emissions 2000-2049; b, 2050 Kyoto-gas emissions: c, 2020 Kyoto-gas emissions."
- p. 19 Table S4, label 13, Remarks
Combination of those PDFs that including nat.
- p. 19
Combination of those PDFs that including nat. radiative forcing.
- p. 9 Fig S1 caption
b, 2050 Kyoto-gas emissions: c
Judge's note: Both read on the page images. The Table S4 remark on page 19 is printed as quoted. In the Fig. S1 caption on page 9 the list separator after panel a is a semicolon and after panel b a colon. Both are cosmetic.
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Typo Legends of Figures S3 and S5 read "Histogramm of MCMC parameter sets" and "Histogramm of characteristics of 3225 sampled EQW pathways"; "Histogramm" should be "Histogram".
- p. 11 Figure S3, legend
Histogramm of MCMC parameter sets
- p. 13 Figure S5, legend
Histogramm of characteristics of
Judge's note: Legends are raster text, not in the text layer. Read both from zoomed renders of p11 and p13; the double m is clear in each.
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Typo Table S2: "Direct biomass buring aerosol (BIOMASSAER_RF)"; "buring" should be "burning".
- p. 18 Table S2, radiative forcing constraints
Direct biomass buring aerosol
- p. 18
Direct biomass buring aerosol (BIOMASSAER_RF)
Judge's note: Visible on the p18 page image and in the text layer.
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Typo Reference 23 ends with an unmatched closing parenthesis: "...Coal Reserves Data Base (April 2007), as cited on www.eia.doe.gov/aer/txt/stb1113.xls, 2007)."
- p. 21 reference 23
www.eia.doe.gov/aer/txt/stb1113.xls, 2007).
Judge's note: Read on the page 21 image. The only opening parenthesis in the entry, '(April 2007)', is already closed, so the final ')' after '2007' has no partner. Cosmetic formatting slip.
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