Global-mean surface air temperature change overestimates global warming rate

Banglin Zhang; Jeremy Cheuk-Hin Leung; Qiuying Gan

REVIEW 4 major objections 7 minor 10 references

Global-mean surface air temperature change overestimates global warming rate

T0 review · 4 major / 7 minor · reviewed 2026-07-30 · grok-4.5

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Pith's one-line read Global-mean surface temperature change systematically exceeds the warming experienced over most of Earth's surface because SAT change is positively skewed.

desk verdict Solid multi-dataset quantification that mean exceeds a histogram-shift location statistic under skew, but the title and “regional-scale” residual framing overreach what the statistics can support. read the letter →

arxiv 2607.23541 v1 pith:7KZ7KQIS submitted 2026-07-26 physics.ao-ph physics.data-an

Jeremy Cheuk-Hin Leung , Qiuying Gan , Banglin Zhang This is my paper · ORCID

classification physics.ao-phphysics.data-an

keywords globalmeantemperaturewarmingrateglobal-scaleregional-scaleasymmetryimagehistogramArcticamplification

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Climate policy treats the area-weighted global-mean surface air temperature change, ΔTmean, as the single measure of the global warming rate. This paper shows that surface temperature change is positively skewed, so the arithmetic mean is pulled upward by extreme regional warming and therefore exceeds the temperature shift that actually occurs over the largest share of the planet. Using image histograms of global SAT, the authors define a global-scale change ΔTgs as the horizontal shift that best matches the base-year histogram; in reanalyses ΔTmean already exceeds ΔTgs by roughly 0.2 °C for 2000–2019 relative to 1979, and CMIP6 projections widen the gap to 0.27–0.54 °C by 2080–2099. The excess is interpreted as net regional-scale warming, dominated by Arctic amplification. The result is offered as a warning that relying on ΔTmean alone can misrepresent how much of the planet is warming at the headline rate and can therefore mislead both impact assessments and mitigation targets.

What carries the argument

The image-histogram representation of global SAT and the derived metric ΔTgs: the horizontal temperature shift that maximizes cross-correlation with the 1979 histogram, taken as the warming experienced over the majority of Earth's surface.

What would settle it

Recompute ΔTgs with an alternative similarity measure or after masking the Arctic; if the mean–shift gap collapses or the histogram shape change itself accounts for most of the discrepancy, the overestimate interpretation fails.

Watch

Extended reading notes

Core claim

Because the spatial distribution of surface-air-temperature change is positively skewed, the conventional global-mean change ΔTmean is systematically larger than the global-scale change ΔTgs obtained from the rigid horizontal shift of the SAT image histogram. The difference reaches 0.19–0.23 °C in recent decades and 0.27–0.54 °C by the end of the century under rising emissions, and is attributed mainly to Arctic amplification acting as a net positive regional warming contribution.

Load-bearing premise

The claim that the maximum-cross-correlation horizontal shift of the global SAT histogram is the physically correct definition of “global-scale warming,” so that any excess of the arithmetic mean over that shift counts as an overestimate.

Editorial extensions

If this is right

Headline global-warming figures used in policy already contain a several-tenths-of-a-degree regional contribution that is not experienced over most of the surface.
Under higher-emission pathways the mean–global-scale gap widens, so the same ΔTmean target corresponds to less uniform planetary warming.
Impact metrics tied to polar or regional extremes (ice loss, sea-level rise, local heat) will diverge further from ΔTmean-based projections.
Reporting median, mode or histogram-shift measures alongside the mean would give a more complete picture of how much of the planet is warming at the stated rate.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If negotiators treated ΔTgs rather than ΔTmean as the controlled variable, the allowable emissions path consistent with a 1.5 °C or 2 °C “global-scale” limit would be less stringent than present pathways framed on the mean.
The same histogram-shift logic could be applied to other spatially skewed fields (precipitation intensity, extreme heat days) to separate planetary-scale from regional-scale contributions.
Stabilizing or reducing Arctic amplification would shrink the mean–ΔTgs gap even if global-mean warming continued, offering a distinct regional lever on the headline indicator.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The useful core here is straightforward and well executed: SAT-change fields are positively skewed, so area-weighted ΔTmean sits above median, mode, and a maximum-cross-correlation histogram shift (their ΔTgs) by ~0.19–0.23 °C (2000–2019 vs 1979) across four reanalyses and by 0.27–0.54 °C late-century in a 20-model CMIP6 ensemble, with Arctic latitudes explaining most of the gap. Methods are transparent (0.01 °C bins, correlation shift, t-tested trends), multi-source consistency is real, and the tables/figures make the numbers easy to check. That packaging of their prior histogram work into a systematic mean-vs-shift comparison is the actual increment; inhomogeneous warming and mean≠median under skew are not new.

The soft spot is interpretive, not numerical. ΔTmean − ΔTgs is just mean minus a robust location estimate of the same field—i.e., a skewness residual. It does not perform spatial-scale separation. Arctic amplification, which they correctly flag as the main driver, is a large-scale coupled pattern, not a leftover “regional” term you can percentage-decompose (71.8/28.2, 78.9/21.1) and then hold up against the Paris 2 °C target. The title/abstract claim that ΔTmean “overestimates global warming rate” therefore rests on elevating ΔTgs to the true global-scale rate by definition. If the energy-budget and policy quantity remains the area-weighted mean, the overestimate framing fails even while the inequality holds. Base year, bin width, and Arctic cutoff are free parameters but not load-bearing; the definitional move is.

Who it is for: people who already track multi-metric SAT reporting or communication of polar amplification. A serious referee should see it—after the overestimate language is narrowed to “mean exceeds typical-area/histogram-shift warming.” I would engage the numbers, not the residual story as written.

Referee Report

4 major / 7 minor

Summary. The manuscript argues that the conventional global-mean surface air temperature change (ΔTmean) systematically exceeds a proposed "global-scale" warming measure (ΔTgs), defined as the horizontal shift of the global SAT image histogram that maximizes cross-correlation with the 1979 histogram. Using four reanalyses (ERA5, JRA55, NCEP1, NCEP2) and 20 CMIP6 models under three SSPs, the authors show that the SAT-change distribution is positively skewed, so the arithmetic mean exceeds the median, mode, and histogram shift: by 0.19–0.23°C for 2000–2019 relative to 1979 in reanalyses, and by 0.27–0.54°C for 2080–2099 in projections. Excluding the Arctic (65°N–90°N) collapses the trend differences to 0.01–0.02°C/decade, identifying Arctic amplification as the dominant source of the skew. The residual ΔTmean − ΔTgs is interpreted as a "net regional-scale warming effect" and decomposed into percentage contributions (71.8%/28.2% for the two-decade change; 78.9%/21.1% for trends), with the SSP5-8.5 residual (0.54°C) described as "as high as 27%" of the 2°C Paris target.

Significance. If the numerical results hold — and they appear to, given four independent reanalyses and a 20-model CMIP6 ensemble producing consistent mean-vs-shift gaps (0.19–0.23°C for 2000–2019; 0.27–0.54°C by 2080–2099), plus a clean Arctic-exclusion test (Fig. 2c–d) — the paper documents a robust and underappreciated property of spatial warming distributions: the area-weighted mean SAT change systematically exceeds the warming experienced over the majority of the Earth's surface, by an amount that grows with emissions. The methods are transparent and the numbers are in principle reproducible from public data. However, the paper's headline significance as framed ("ΔTmean overestimates the global warming rate," with implications for the Paris targets) rests on an interpretive claim — that mean minus histogram-shift isolates "regional-scale warming" — that the diagnostics cannot support, and this currently overstates what the analysis delivers.

major comments (4)

[§3.1 (and repeated in §3.2, §4)] The central interpretive move — that ΔTmean − ΔTgs represents "net positive regional-scale warming" — is not supported by the statistics used. Both ΔTmean (area-weighted mean) and ΔTgs (maximum-cross-correlation histogram shift) are scale-blind location statistics of the same global field; their difference measures the skewness of the SAT-change distribution, not warming at any particular spatial scale. A perfectly smooth, hemispheric-scale pattern such as Arctic amplification (which the paper itself identifies as the dominant contributor, Fig. 2c–d, where excluding 65°N–90°N collapses the trend gap to 0.01–0.02°C/decade) will produce mean − shift ≠ 0 exactly as observed. The decomposition of ΔTmean into 71.8% 'global-scale' and 28.2% 'regional-scale' contributions (repeated as 78.9%/21.1% for trends in §3.2) therefore has no physical basis as stated. The numerical finding (mean > ΔTgs >
[§2.2, Abstract, and Title] The definition of ΔTgs as 'global-scale SAT change' — the horizontal shift of the SAT histogram maximizing cross-correlation with the 1979 histogram — is presented as the physically appropriate measure of 'the global warming rate,' against which ΔTmean is an 'overestimate.' This is asserted, not justified. The area-weighted arithmetic mean is not an estimator that 'assumes symmetry' (as the abstract and §1 claim); it is the area integral of the temperature anomaly and is the quantity that enters radiative feedbacks, ocean heat uptake, and the GMST metric used in assessments. The histogram-shift statistic is instead a robust, mode-like location measure: it tracks the warming at the most common SAT values, which is a defensible diagnostic but not obviously 'the' global warming rate. The title and abstract claim ('overestimates global warming rate') is therefore definitional rather than dem
[§4 (Discussion) and §3.3, referencing Table 1] The statement that the SSP5-8.5 ΔTmean − ΔTgs difference (0.54°C) is 'as high as 27% compared to the 2°C target of the Paris Agreement' is a category error with a baseline mismatch. The 2°C target is defined on ΔTmean relative to preindustrial; the 0.54°C is the difference between two location statistics of the same field relative to a 1979 base year. The ratio of a within-field statistical difference to an absolute policy threshold has no decision-relevant meaning as presented, and the 1979 baseline makes the numerical comparison additionally incommensurate. This passage should be removed or recast (e.g., as the residual's size relative to projected twenty-first-century warming within the same baseline).
[§2.2 (Method) and Table 1] ΔTgs is the paper's central constructed quantity, yet no sensitivity analysis is provided for its free choices: the 0.01°C bin width (with the acknowledged empty-bin problem at fine resolution, §2.2 step 3), the 1979 base year, the smoothing applied to histograms, and the effect of genuine shape change over time (Fig. S3–S4 show skewness and variance trends, so the near-rigid-shift assumption is only approximate — under SSP5-8.5 the shape change is large, precisely where the largest residuals are reported). The single sentence that RMS-difference matching 'gives the same result' is reassuring but insufficient. Table 1's headline numbers (0.19–0.23°C; 0.27–0.54°C) should be shown to be stable under reasonable perturbations of bin width, base period, and shift-estimation method.

minor comments (7)

[Author contributions] The Author Contributions section lists Y.G., J.X.L.W., W.Z., and W.Q., but the byline contains only three authors (Leung, Gan, Zhang). Please reconcile.
[§3.2, penultimate paragraph; Author contributions] Typos: 'reigonal-scale' should be 'regional-scale'; 'original draf' should be 'draft'.
[Table 1] The percentages in parentheses in Table 1 use ΔTgs as the denominator (e.g., 0.19/0.33 = 57.6%), whereas the same residual is expressed in §3.1 as 28.2% of ΔTmean. The two conventions should be unified or explicitly labeled to avoid confusion.
[Figure S4 caption] Caption of Fig. S4 reads 'Same as Fig. S4, except for…' — a self-reference; presumably Fig. S3 is intended.
[§2.2 and §3.2] The choice of the single year 1979 as the anomaly base is unconventional (a climatological reference period is standard) and is never justified; please explain and note any sensitivity, particularly for the reanalysis intercomparison in Table 1.
[Figure 2 caption] Fig. 2(b) caption ends mid-word ('...and ΔT75th include.'); also 'include' should be 'included'.
[§3.1, skewness definition] The skewness formula in §3.1 is typeset ambiguously (the exponents and the summation placement are unclear in the rendered equation); please reformat.

Circularity Check

1 steps flagged · score 2.0 of 10

Mild definitional circularity only: ΔTgs is defined as the max-cross-correlation histogram shift, then equated with “global-scale warming,” so mean−ΔTgs is labeled “regional” by construction; the numerical gaps themselves are not fitted or forced.

self definitional [§2.2 (Method) and §3.1 (Results, contribution decomposition)]
"Thus, one could estimate ΔTgs by measuring how far the SAT histogram shifts... we define ΔTgs as the degree... to which the SAT histogram in a given year shifts to the right considering the similarity with the SAT histogram for 1979. ΔTgs estimates the SAT change that likely occurs over the largest proportion of grid points... The comparatively large ΔTmean suggests that... it yields an overestimated rate of global-scale warming and there is a net positive warming effect of regional-scale temperature change.... The contributions of global-scale temperature change and regional-scale temperature"

ΔTgs is defined as the max-cross-correlation histogram shift and immediately identified with “global-scale warming.” The residual ΔTmean−ΔTgs is then labeled the regional-scale contribution and percentage-decomposed. That residual equals mean minus the authors’ chosen robust location statistic of the same SAT-change field; calling it “regional-scale warming” and an “overestimate of the global warming rate” follows by the paper’s definition of global-scale, not from an independent scale separation or external benchmark.

full rationale

The paper’s empirical core is non-circular. ΔTmean, median, mode, and the histogram-shift statistic ΔTgs are all computed from external reanalyses (ERA5, JRA55, NCEP1/2) and CMIP6 output; no free parameter is fitted to a target warming rate and then re-presented as a prediction. The only circular step is interpretive and definitional: §2.2 defines ΔTgs as the horizontal shift that maximizes cross-correlation with the 1979 SAT histogram and states that this shift “could be referred to as global-scale warming”; §3.1 then treats ΔTmean−ΔTgs as the “net positive regional-scale warming effect” and decomposes contributions (71.8%/28.2%, later 78.9%/21.1%) by simple arithmetic on that residual. Once “global-scale” is identified with the authors’ shift statistic, the claim that ΔTmean “overestimates” global-scale warming and that the residual is regional is true by construction—it is mean minus a robust location measure of the same field, not an independent spatial-scale separation. Self-citations (Leung et al. 2022; Gan et al. 2023, 2026a,b; Liu et al. 2025) supply the image-histogram method but are not load-bearing uniqueness theorems. No fitted-input-as-prediction, no uniqueness imported from authors, no ansatz smuggled via citation. Score 2 reflects one minor self-definitional move that frames the central interpretation without forcing the measured numbers.

Assumptions & free parameters 4 free parameters · 5 assumptions · 2 invented entities

The load-bearing move is definitional and statistical, not a deep new physical axiom set: accept image histograms of SAT, define global-scale warming as cross-correlation shift relative to 1979, and treat mean−shift as net regional warming. Standard climate data and skewness facts do the rest. Free choices (bin width, base year, Arctic latitude cut, model list) affect gap size modestly; the invented quantity is ΔTgs itself.

free parameters (4)

histogram bin width = 0.01°C
Set to 0.01°C (§2.2) without sensitivity analysis; affects empty-bin rate and smoothing needs for mode/shift.
base year for ΔTgs and anomalies = 1979
All shifts and reported levels are relative to 1979, chosen as satellite-era start, not preindustrial; gap magnitudes are baseline-dependent.
Arctic exclusion latitude = 65°N
65°N–90°N cut used to attribute the mean−ΔTgs gap to Arctic amplification (Fig. 2c–d); cutoff is conventional but hand-chosen.
CMIP6 ensemble membership = 20 models, equal weight
Twenty named models, equally averaged; no weighting or screening beyond availability—ensemble gap sizes depend on this set.

assumptions (5)

standard math Arithmetic mean is a poor central-tendency measure for asymmetric samples and is unduly influenced by outliers (invoked via Hays 1994; Walpole et al. 2016 in §1).
Standard statistics; used to motivate distrust of ΔTmean for skewed SAT change.
ad hoc to paper If the SAT histogram shape is roughly stable, a rigid horizontal shift equals the warming experienced at most grid points and is therefore “global-scale warming” ΔTgs (§2.2).
Core identification of the paper; shape does change (skewness/variance trends in Figs. S3–S4), so the axiom is approximate by the authors’ own results.
domain assumption Area-weighted global mean SAT change is the quantity climate policy and assessments treat as the global warming rate (§1, abstract).
True as institutional fact (IPCC, Paris); the paper then argues this practice is limited.
domain assumption Reanalysis and CMIP6 surface air temperature fields are adequate to measure multi-decadal spatial distributions of SAT and SAT change.
Standard in the field; polar and sparse-observation biases could still affect tails that drive the mean−shift gap.
ad hoc to paper Mean minus ΔTgs equals the net contribution of regional-scale warming to ΔTmean (results §3.1–3.3).
Definitional decomposition once ΔTgs is fixed; not derived from energy budget or dynamical regionalization.

invented entities (2)

ΔTgs (global-scale SAT change via maximum cross-correlation histogram shift)
purpose: Provide a location measure of warming allegedly representing the majority of Earth’s surface and less sensitive to extremes than ΔTmean.
Operationally new named metric in this paper’s framing (method kin to authors’ prior histogram work). Independent evidence is only internal consistency with median/mode and Arctic exclusion—not a separately measured geophysical observable.
Net positive regional-scale warming effect (mean−ΔTgs residual)
purpose: Interpret the mean−ΔTgs gap as extra warming from regional processes, chiefly Arctic amplification.
Residual after defining ΔTgs; useful label but not a new physical flux or mode with external conservation law.

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Cite this review

Pith. "Pith review of Global-mean surface air temperature change overestimates global warming rate." pith.science (2026). https://pith.science/paper/7KZ7KQIS

@misc{pith2026260723541,
  author       = {Pith},
  title        = {Pith review of: Global-mean surface air temperature change overestimates global warming rate},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7KZ7KQIS}},
  note         = {Machine review of arXiv:2607.23541}
}

read the original abstract

Current climate policies are targeted at slowing down the global warming rate, or the global mean surface air temperature (SAT) change ({\Delta}Tmean), which is measured by the arithmetic mean approach under the assumption that SAT changes are symmetrically distributed. However, in reality, the SAT change is asymmetric in nature and its influence on the {\Delta}Tmean interpretation seldom received attention in previous research about climate change. This study theorizes, based on the image histogram approach, that while {\Delta}Tmean measures the Earth's overall SAT change, it yields a value larger than the global-scale SAT change ({\Delta}Tgs) because of the asymmetrical distribution of SAT change. Results show that {\Delta}Tmean is greater than that based on {\Delta}Tgs by 0.19-0.23{\deg}C from 2000-2019, relative to the global SAT in 1979. In future climate projections, where more significant inhomogeneous warming is expected, the disagreement between {\Delta}Tmean and {\Delta}Tgs reach 0.27-0.54{\deg}C by the end of the 21st century (2080-2099) under different emission scenarios. The large difference between {\Delta}Tmean and {\Delta}Tgs implies that there is a net positive regional-scale warming effect over the globe which is mainly contributed by Arctic Amplification. This paper constitutes a warning that extreme regional warming effects could have large impacts on the interpretation of {\Delta}Tmean, which is often considered in climate assessments and policies making, and illustrates the limitations and cautions inherent in using {\Delta}Tmean as the only indicator of the global warming rate.

Figures

Figures reproduced from arXiv: 2607.23541 by the authors.

**Figure 1.** The asymmetrical distribution of the SAT and SAT change. (a) Two-decadal mean SAT histograms from 1980– 1999 (blue) and 2000–2019 (red) and their difference (2000–2019 minus 1980–1999, green). (b) Same as (a), except that the x-axis ranges from -30°C to 30°C. The shaded region between the red and blue lines in (a) and (b) indicates increases and decreases in the SAT probability (i.e., area), respectively. The values… view at source ↗

**Figure 2.** The influence of a SAT’s asymmetrical nature on the value of global mean SAT change in the past four decades. (a) Time series (unit: °C) of ΔTmean (black line), ΔTmedian (blue line), ΔTmode (red line) and ΔTgs (green line) relative to the SAT in the base year of 1979. Shading indicates the image histogram value (unit: %) of SAT change of each year. (b) Same as (a) except plotted with a larger range of y-axis, and wi… view at source ↗

**Figure 3.** Excessively high Global mean SAT change in the CMIP6 model simulations. (a)–(d) Same as Fig. 2a, except for (a) the historical model run and the (b) SSP1-2.6, (c) SSP2-4.5, and (d) SSP5-8.5 projections based on the CMIP6 simulations. (e)–(h) Same as Fig. 2b, except for (e) the historical model run and the (f) SSP1-2.6, (g) SSP2-4.5, and (h) SSP5-8.5 projections based on the CMIP6 simulations. All panels are based on… view at source ↗

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Reference graph

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Pith tools

Reviewed July 30, 2026 · model on record in the stance chip above.

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24 Figure S3

In (b), shading denotes significant linear trends (90% confidence level), and insignificant trends are not plotted (white). 24 Figure S3. Decreases in the magnitudes of the variance and skewness of the SAT histogram from 1979 to

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