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Statistical Noise and Missing Forcing Limit Estimates of Earth's Feedback from Prescribed Sea-Surface Temperature Simulations

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Pith's one-line read This paper shows that prescribing observed sea-surface temperatures to an atmospheric model cannot recover the evolution of Earth's climate feedback, and that feedback trends on timescales shorter than about a century are statistically…

desk verdict A careful controlled experiment showing that amip-piForcing feedback trends are part missing-forcing bias and part moving-window noise; the ~100-year noise floor is estimator-specific, but the case against the method survives. read the letter →

arxiv 2608.13219 v1 pith:X4GLLPJT submitted 2026-08-13 physics.ao-ph

Gergana Gyuleva , Reto Knutti , Robin Noyelle , Urs Beyerle , Erich Fischer , Sebastian Sippel This is my paper · ORCID
classification physics.ao-ph
keywords climatefeedbackparameterpatterneffectamip-piForcingmoving-windowregressionYule-Slutzkysea-surfacetemperaturepatternssensitivityCESM2
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

This paper tests the standard 'amip-piForcing' method for estimating how Earth's climate feedback parameter has changed over the observational record, a method that prescribes observed sea-surface temperatures to an atmospheric model with fixed pre-industrial forcing. By prescribing SSTs from fully coupled historical simulations back into the same atmospheric model, the authors show the method fails to reproduce the coupled model's feedback evolution even when the SSTs are identical. They identify two causes: omitting time-varying atmospheric forcing, especially aerosols, biases the feedback, and the 30-year moving-window regression used to estimate the feedback time series injects statistical noise via the Yule-Slutzky effect. Any feedback trends on timescales shorter than about 100 years are indistinguishable from that noise, and a 4000-year control run shows no significant link between evolving SST patterns and feedback changes. If right, recent claims that observed SST patterns caused a stabilizing trend in Earth's feedback over recent decades are not robust.

What carries the argument

The working object is the feedback parameter $\lambda(t)$, computed by 30-year moving-window regression of the radiative response $R = N - F$ onto temperature change $\Delta T$. The method's second assumption is that variations in this slope are driven by the evolving SST pattern. The paper's key mechanistic finding is the Yule-Slutzky effect: applying a moving-window regression to even pure white-noise time series of $N$ and $T$ generates low-frequency variability in the slope, with a decorrelation timescale of 60 to 100 years. This statistical machinery, rather than any physical memory, explains much of the apparent multi-decadal structure in $\lambda(t)$, as demonstrated by million-year Monte-Carlo simulations fitted to the piClim-control and piControl data. The composite trend analysis on the 4000-year control run then tests whether the SST pattern is nonetheless detectable behind that noise.

What would settle it

A reader could compute feedback time series from the 4000-year piControl using a 50-year or 100-year moving window, or a state-space estimator; if trends shorter than 100 years then emerge as distinguishable from the noise floor, the paper's central bound fails for that estimator.

Watch

Extended reading notes

Core claim

The central discovery is that the amip-piForcing setup, an atmosphere-only model forced with observed SSTs and sea ice while atmospheric forcing stays at pre-industrial levels, cannot recover the time evolution of Earth's feedback parameter even in a perfect-model setting. Forced with SSTs and sea ice from eleven fully coupled historical simulations, the atmosphere-only runs produce a feedback time series with an ensemble-mean correlation of only 0.23 against the coupled feedback, and a systematic negative bias amplifies around 1940 to 2000, the period of strongest aerosol forcing. When historical atmospheric forcing is also prescribed, agreement improves to a correlation of 0.64, but individual members still diverge substantially, showing that SSTs alone do not determine the feedback. In a 4000-year pre-industrial control, periods of feedback strengthening or weakening show no significant or spatially consistent SST trend pattern, and Monte-Carlo experiments show that 30-year moving-window regressions of two white-noise series generate multi-decadal feedback variability peaking at 60 to 100 years. The conclusion is that trends in the feedback parameter on timescales shorter than roughly a century cannot be robustly attributed to evolving SST patterns.

Load-bearing premise

The entire noise-floor and detection argument rests on defining 'detected feedback trend' as the slope from a 30-year moving-window regression; if a different window length or estimation method is used, the noise characteristics and the roughly 100-year bound could change, and the paper does not test that robustness.

Editorial extensions

If this is right

  • Recent amip-piForcing-based conclusions that observed SST patterns drove a stabilizing feedback trend in recent decades are not supported once the coupled feedback is used as reference.
  • Any feedback trend detected over periods shorter than about 100 years could be a statistical artifact of the moving-window regression, independent of any physical SST-pattern effect.
  • amip-piForcing-style experiments should be replaced by amip-histForcing-style runs with time-varying historical atmospheric forcing to reduce the bias.
  • Even with correctly prescribed SSTs, sea ice, and forcing, atmosphere-only runs do not fully reproduce the coupled feedback, so prescribing observations adds an extra, unquantified bias.
  • Estimates of Earth's feedback trend from prescribed-SST simulations carry little evidential weight for constraining changes in climate sensitivity over the observational period.

Reading between the lines

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

  • The 60-to-100-year noise floor is a property of the 30-year moving-window estimator; a longer window or a state-space estimator would shift the floor, so the paper's 'less than ~100 years' bound should be read as estimator-specific rather than as a fixed property of the climate system.
  • The same Yule-Slutzky logic applies to any moving-window regression of ratio variables in climate science, such as carbon-cycle sensitivities or transient climate response estimates, where short windows can generate spurious low-frequency structure.
  • A direct testable extension is to rerun the identical-SST protocol in several other coupled models with and without prescribed forcing; if some models recover the coupled feedback under amip-piForcing, the failure is model-specific rather than intrinsic to the method.
  • The bootstrap composite procedure could be applied to observed SST and feedback data: if observed periods of feedback change show SST pattern agreement stronger than the 4000-year control null, that would be evidence that the observed pattern effect is exceptional rather than absent.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper presents a controlled set of CESM2/CAM6 experiments to test two assumptions underlying the widely used amip-piForcing method for estimating the time evolution of Earth's climate feedback parameter: (i) that prescribing observed SSTs and sea ice with preindustrial atmospheric forcing captures all relevant forcing effects, and (ii) that 30-year moving-window regressions of radiative response on temperature yield a feedback time series whose variations are physically interpretable and SST-driven. The authors find that amip-piForcing-style runs forced with SSTs from coupled historical simulations fail to reproduce the coupled feedback evolution (ensemble-mean Pearson correlation 0.23, MSE 0.90 W² m⁻⁴ K⁻²), and that prescribing historical forcing as well (amip-histForcing) substantially improves agreement (correlation 0.64) but leaves unexplained residual differences. Using piControl and piClim-control simulations together with Monte-Carlo VAR(5) and bivariate-normal surrogates, they then show that the moving-window feedback estimator itself generates low-frequency variability via the Yule-Slutzky effect, with spectral power increasing toward periods of 60–100 years.

Significance. If the results hold, this is an important contribution to the pattern-effect and climate-feedback literature. The strengths include a clean 'perfect model' experimental design that isolates the effect of missing atmospheric forcing from SST-pattern effects, an 11-member ensemble for the historical and GHG-only cases, three independent forcing estimates with largely consistent results, and a Monte-Carlo framework that convincingly reproduces the feedback spectrum from statistical surrogates. The paper also explicitly enumerates its limitations (single GCM, possible effects of severed atmosphere-ocean coupling, and the signal-to-noise problem), which is commendable. The demonstration that amip-piForcing feedback estimates are biased and partly statistically generated is significant for interpreting published claims of a stabilizing SST-driven feedback trend in recent decades. However, the central quantitative claim about a ~100-year noise floor rests on a specific estimator and lacks a robustness test, and the null result on SST-pattern effects is weaker than the wording suggests; these issues need to be resolved before the conclusions can be accepted in their current general form.

major comments (2)
  1. [Sec. 3.2.1, Fig. 7; Abstract; Sec. 5] The ~100-year noise floor is computed using the 30-year moving-window regression of Eq. (6), and because the windows overlap by 29 out of 30 years, the estimated feedback series has autocorrelation imposed by the window length itself. The 60–100 year spectral turnover in Fig. 7b,d is therefore plausibly a property of this estimator rather than of the underlying N and T processes. The paper does not vary the window length, nor does it compare with a non-overlapping or state-space estimator, so the generalized statement in the Abstract and Conclusions that 'any trends in the feedback parameter detected on timescales shorter than ~100 years are indistinguishable from statistical noise' is not established as a property of the climate system. Please add a sensitivity analysis in which the Monte-Carlo spectra are recomputed with, e.g., 15-year and 60-year windows (or with a non-overlapping-window or state-space estimator), and revise the abstract and conclusions to state the noise floor is specific to the 30-year moving-window estimator used here.
  2. [Sec. 3.2.2, Fig. 8] The conclusion that there is no evidence of an unforced SST pattern effect rests on selecting periods of feedback strengthening and weakening from the moving-window feedback series. If, as the authors themselves argue, a large part of the variance in that series is statistical noise from the Yule-Slutzky effect, then the selected periods may not correspond to genuine feedback changes, which would make the composite SST-trend test insensitive by construction. The authors partly acknowledge this in Sec. 4.2, but the stronger statement in Sec. 5 ('we find no evidence of an unforced SST pattern effect in the CESM2 piControl simulation') goes beyond what the test can support. Please either soften the claim to reflect the test's limited power under a noisy feedback estimator, or add a test that explicitly accounts for the noise floor (for example, by comparing the observed composite trend distribution against the Monte-Carlo noise distribution from Sec. 3.2.1).
minor comments (4)
  1. [Code and Data] The 'Code and data availability' section currently contains only the placeholder text 'TEXT.' A complete statement describing where the simulation outputs and analysis code can be obtained is required for reproducibility.
  2. [Eqs. (6)-(7), Sec. 2.2] Please clarify whether the moving-window regression includes an intercept. In the Gregory framework N = F + λT, the slope of a regression with intercept is the standard estimate, but the notation ∂N/∂T and 'regression of N onto ΔT' is ambiguous; this detail affects the numerical values of λ(t).
  3. [Abstract] The sentence 'Any trends in the feedback parameter detected on timescales shorter than ~100 years are indistinguishable from statistical noise' would be better phrased as '...indistinguishable from statistical noise when the feedback is estimated with the 30-year moving-window regression method considered here,' consistent with the recommended robustness changes.
  4. [Fig. 2 caption] Panels (c) and (d) are described in the text as 'Bias in feedback' and the vertical axis shows 'Feedback (Wm-2K-1),' but the plotted quantity is the difference between the two feedback curves; please label the axis 'Feedback bias' or 'Difference' for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; controlled experiments and Monte-Carlo null models are self-contained.

full rationale

The paper's central claims are established by controlled simulation experiments and Monte-Carlo null models, not by definitions or self-citations. The amip-piForcing versus coupled comparison (Sec. 3.1) uses pairwise identical SSTs as an external benchmark, and the failure to reproduce the coupled feedback is an empirical result. The Yule-Slutzky analysis (Sec. 3.2.1) fits Gaussian and VAR(5) models to N and T and then applies the same 30-year moving-window estimator to synthetic series; the resulting ~60-100 year decorrelation timescale is indeed specific to that estimator, but the demonstration that white noise can generate low-frequency feedback variability is a controlled null-model result, not a conclusion forced by the estimator definition. The SST-composite bootstrap (Sec. 3.2.2) tests against a null distribution. No load-bearing argument rests on a self-citation; cited prior work on Yule-Slutzky and pattern effects is external. The abstract's generalization to 'any trends ... shorter than ~100 years' omits the estimator caveat, but that is a limitation of scope, not circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard climate feedback theory and on statistical models fitted to the model output. The key free choices are the 30-year moving window and the smoothing/filter parameters, all standard or tested for robustness. No new physical entities are introduced.

free parameters (6)
  • VAR(5) coefficients (A1..A5, mu, Sigma_u) = not given numerically
    Fitted to CESM2 piControl N and T for Monte-Carlo synthesis (Sec. 2.3, Fig. 7d).
  • Bivariate normal mean and covariance = not given numerically
    Fitted to piClim-control N and T for Monte-Carlo synthesis (Sec. 2.3, Fig. 7b).
  • Moving-window length = 30 years
    Standard in literature (Gregory et al. 2004; Gregory and Andrews 2016); the paper does not test other lengths.
  • Savitzky-Golay smoothing window = 81 years, polynomial order 4
    Used to identify strengthening/weakening periods in Sec. 2.4; affects period selection, though robustness to period length 10-30 years is tested.
  • Butterworth high-pass cutoff frequency = 0.05 (period ~20 years)
    Used to decompose feedback into short and long timescales in Sec. 3.1.
  • Minimum period length for feedback trend selection = 20 years
    Sec. 2.4; robustness tested for 10 and 30 years.
assumptions (5)
  • domain assumption The linear forcing-feedback framework N = lambda*DeltaT + F (Eq. 4).
    Standard framework used throughout; the paper does not question it.
  • domain assumption The slope of the 30-year moving-window regression of N (or N-F) on DeltaT yields a meaningful instantaneous feedback lambda(t) (Eq. 6-7).
    This is the estimator whose noise properties the paper analyzes; the entire analysis conditions on it.
  • domain assumption The coupled historical and piControl runs serve as ground truth for the feedback evolution.
    The paper compares amip runs to coupled runs with identical SSTs; if coupled runs are biased, the comparison is still valid for testing the amip method, but the implication for observations assumes coupled runs reflect reality.
  • domain assumption The VAR(5) process adequately represents the joint autocorrelation of N and T in piControl.
    Sec. 2.3; spectral reproduction in Fig. 7d supports it, but it is a model choice.
  • domain assumption The RFMIP estimate of effective radiative forcing is unbiased for the coupled runs.
    Appendix A; sensitivity to two other F estimates is tested, qualitatively similar.

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Pith. "Pith review of Statistical Noise and Missing Forcing Limit Estimates of Earth's Feedback from Prescribed Sea-Surface Temperature Simulations." pith.science (2026). https://pith.science/paper/X4GLLPJT

@misc{pith2026260813219,
  author       = {Pith},
  title        = {Pith review of: Statistical Noise and Missing Forcing Limit Estimates of Earth's Feedback from Prescribed Sea-Surface Temperature Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X4GLLPJT}},
  note         = {Machine review of arXiv:2608.13219}
}
read the original abstract

Earth's feedback parameter measures how the Earth system responds to forcing and is inversely proportional to climate sensitivity. Sea-surface temperature (SST) patterns can modulate the value of the feedback parameter. Differences between observed and simulated SSTs have raised the question how the observed SSTs evolution impacts the global feedback. The standard method for estimating this effect uses observed SSTs prescribed to an atmospheric model with fixed pre-industrial atmospheric forcing. This method makes two assumptions: first, that the observed SSTs capture all relevant effects from the forcing, so that prescribing a time-varying forcing is unnecessary; second, that the temporal variations in the feedback parameter are driven by the evolving SST pattern and can be estimated via moving-window regressions. We test these assumptions by running controlled experiments in which SSTs from fully-coupled historical simulations are prescribed to an atmospheric model. We find that the prescribed-SST experiments fail to capture the coupled feedback evolution. This is explained by two effects: First, the absence of prescribed atmospheric forcing, and second, statistical noise arising from the computation of moving-window regressions. We find no evidence of any significant relationship between evolving SST patterns and changes in the feedback time series in a 4000-year pre-industrial control simulation. Any trends in the feedback parameter detected on timescales shorter than ~100 years are indistinguishable from statistical noise, making their attribution to the evolving SST pattern extremely difficult. Our results imply that prescribed SST simulations offer limited potential for inferring temporal changes in Earth's parameter over the observational period.

Figures

Figures reproduced from arXiv: 2608.13219 by the authors.

Figure 1
Figure 1. Results from amip-piForcing-histSST simulations (blue) compared to the CESM2 historical simulations (orange) with pairwise identical SSTs (i.e., amip-piForcing-histSST are forced with SSTs from CESM2 historical fully coupled simulations) for (a) global surface air temperature, (b) net TOA imbalance, (c) net TOA LW imbalance, (d) net TOA SW imbalance, and (e) radiative response R. For amip￾piForcing-histSST, R is ide… view at source ↗
Figure 2
Figure 2. (a) The feedback parameter in amip-piForcing-histSST runs (blue) compared to CESM2 historical runs with pairwise identical SSTs. Dotted lines show the feedback calculated on ensemble means of N and T (also in (b)). (b) The feedback parameter in amip-piForcing￾ghgSST (blue) compared to the CESM2 single-forcing GHG2 runs (orange), with pairwise identical SSTs. Panel (c) and (d): black line shows the difference in the … view at source ↗
Figure 3
Figure 3. Feedback parameter for three individual members (columns) with pairwise identical SSTs: amip-piForcing-histSST simulation (blue) and the corresponding coupled historical simulation (orange). Left column (a),(d),(g): the raw feedback parameter time series. Middle column (b), (e), (h): high-pass filter applied to the corresponding raw feedback parameter from the left column. The high-pass filter (But￾terworth filter) … view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Ensemble mean trends for the period 1980-2014 for the variables surface air temperature (a–c), net TOA flux (d–f), long-wave TOA flux (g–i), and short-wave TOA flux (j–l). The first column shows the trends in the amip-piForcing-histSST experiments. The middle column sh…
Figure 5
Figure 5. Figure 5: (a): like Fig. 2a, but with the ensemble mean and spread from amip-histForcing-histSST included in dark blue. (b-l): feedback parameter λ for individual members, all members in one panel have identical SSTs. Light blue lines show the amip-piForcing-histSST feedback, as…
Figure 6
Figure 6. Figure 6: Feedback calculated in the amip-piForcing-piSST run (blue) compared to the coupled piControl run with identical SSTs (orange). estimated feedback. Notably, there are periods—such as years 30–80, or years 200–240 of the simulation—during which the feedback time series d…
Figure 7
Figure 7. Figure 7: Spectral densities of the variables T (surface air temperature), N (net TOA imbalance) and the feedback λ, computed via 30- year moving window regressions of the N and T timeseries (Eq. 6), (a): for the 200-year long piClim-control simulation, (b): for synthetic timese…
Figure 8
Figure 8. Figure 8: Surface air temperature trend composites in the fully coupled piControl run during periods of feedback strengthening and weak￾ening. (a): the raw feedback time series (thin grey line), together with a smoothed feedback time series (thick black line), smoothed using a S…

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Pith tools

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