For half a century, climate scientists have struggled to answer one of the most consequential questions in science: how much warmer will Earth get as we pump more CO₂ into the atmosphere? In 1979, the Charney Report gave a "likely" range of 1.5 to 4.5 degrees Celsius of warming if CO₂ doubled. In 2021, the IPCC's Sixth Assessment Report gave a "likely" range of 2.5 to 4 degrees. The uncertainty hasn't narrowed. It's just shifted slightly. This stubborn fog around climate sensitivity—how much warming a doubling of atmospheric CO₂ will ultimately cause—shapes every projection of future sea-level rise, drought, and extreme weather.
Now, a new study from ETH Zurich raises uncomfortable questions about one of the methods scientists have been using to reduce that fog. The research, published by Gergana Gyuleva, Reto Knutti, and colleagues, finds that a widely used technique for estimating how Earth's heat-trapping ability has been changing over the past century may be fundamentally limited. Trends that researchers have attributed to evolving ocean temperature patterns—potentially crucial information for understanding climate sensitivity—may be statistical noise that looks like signal.
The Science
To understand why this matters, you need to understand what climate scientists call the "feedback parameter." Imagine Earth as a thermostat. When you add CO₂, you turn up the heat. But Earth doesn't just sit there passively; it pushes back. More warming triggers more heat radiating back into space—a restoring force. The feedback parameter, denoted λ (lambda), measures the strength of that restoring force. A more negative λ means Earth is efficient at restoring balance, so warming is modest. A λ closer to zero means Earth is sluggish, so warming is larger.
The feedback parameter is inversely proportional to climate sensitivity: λ tells you, essentially, how much trouble you're in. If λ is strongly negative, a doubling of CO₂ causes only modest warming. If λ is closer to zero, that same CO₂ doubling pushes temperatures up more dramatically.
In recent years, a controversial idea has emerged: the feedback parameter isn't constant. It may be drifting as ocean temperature patterns evolve. Specifically, some scientists argue that the observed pattern of warming—with the tropical Pacific strengthening its east-west temperature gradient in a La Niña-like fashion—is producing a more negative feedback, making Earth more stable than we might otherwise expect. This "pattern effect," as it's called, could explain why different methods for estimating climate sensitivity have historically given different answers. It could also mean that as this pattern shifts, future warming may differ from past expectations.
The standard tool for studying this pattern effect is the "amip-piForcing" method. The approach prescribes observed sea-surface temperatures (SSTs) and sea-ice conditions to an atmospheric model, while holding all atmospheric greenhouse gas concentrations at pre-industrial levels. The logic is that if you give the model the actual observed ocean temperatures, you capture all the relevant physics. Then, by regressing the model's top-of-atmosphere energy imbalance against temperature changes over 30-year sliding windows, you get a time series of how the feedback parameter has evolved.
Gyuleva and colleagues decided to put this method on trial. Instead of prescribing observed SSTs, they took SSTs from fully-coupled climate model simulations—runs where the atmosphere and ocean interact freely—and fed those SSTs back into an atmospheric model. This created a controlled comparison: the prescribed SSTs came from the very same simulations where a full feedback estimate was also available. If the amip-piForcing method works, it should recover the coupled model's feedback evolution. It didn't.
What They Found
The results were damning. When the researchers compared the amip-piForcing-style runs to the fully-coupled simulations using identical SST boundaries, the prescribed-SST experiments failed to capture the coupled feedback evolution. The temperature and energy flux trends diverged substantially between the two approaches—and the difference wasn't small. In the coupled runs, the feedback behaved one way; in the prescribed-SST runs with the same ocean temperatures, it behaved differently.
The culprit, the researchers found, was twofold. First, by fixing atmospheric forcing at pre-industrial levels while prescribing time-varying SSTs, the amip-piForcing method was omitting a crucial piece of physics: the forcing from changing atmospheric composition itself. The observed SSTs don't just carry information about the pattern effect; they also implicitly encode the atmospheric forcing that caused those SSTs in the first place. When you hold forcing fixed, you're missing that component. Second, the 30-year moving-window regression method for estimating the feedback parameter introduces its own statistical noise. This isn't a measurement error; it's an artifact of the mathematical technique itself.
To investigate this further, the researchers turned to a 4,000-year pre-industrial control simulation—a climate model run with constant pre-industrial conditions, no changes in CO₂, no volcanic eruptions, nothing but internal variability. If the pattern effect is a real, physically driven phenomenon, you might expect to find consistent relationships between specific SST patterns and periods of strengthening or weakening feedback in such a run. They found nothing of the sort.
In the 4,000-year record, the researchers identified 49 periods of feedback strengthening and 49 periods of feedback weakening, each lasting at least 20 years. They then composite-mapped the surface temperature trends associated with each type of period. If a specific SST pattern reliably preceded strengthening feedback, you would see agreement across those 49 periods—the same temperature pattern should recur. Instead, the agreement was no better than random chance. The temperature trend composites looked like noise. There was no detectable fingerprint linking ocean temperature patterns to the feedback's evolution.
Perhaps most striking, the researchers showed that any trend in the feedback parameter on timescales shorter than roughly 100 years is indistinguishable from statistical noise. The signal-to-noise ratio is too low. You simply cannot reliably attribute shorter-term variations in λ to SST patterns, no matter how sophisticated your analysis.
Why This Changes Things
The implications ripple outward. The amip-piForcing method has underpinned several recent studies arguing that Earth's feedback has been strengthening (becoming more negative) in recent decades, driven by the observed La Niña-like SST pattern. Dong et al. (2021), for instance, compared amip-piForcing feedback estimates to coupled model runs and found that the models failed to reproduce the stabilizing trend seen in the prescribed-SST runs post-1980. They attributed this discrepancy to differences between modeled and observed SST patterns. Gyuleva and colleagues' results suggest that this interpretation may be backward: the discrepancy may stem not from the coupled models missing a real pattern effect, but from the amip-piForcing method introducing spurious variability that looks like a pattern effect but isn't.
This matters for the uncertainty in climate sensitivity. If the feedback parameter isn't drifting the way we thought—if the apparent trend in recent decades is an artifact of methodology rather than physics—then our estimates of how Earth's restoring force has been evolving need recalibration. The researchers are careful not to overstate their case: they don't claim the pattern effect is unreal. They show it cannot be reliably detected with current methods.
They also don't claim that climate sensitivity is necessarily higher or lower than currently estimated. They claim something more fundamental: that we may be misattributing the sources of uncertainty. The "likely" range of 2.5–4°C for equilibrium climate sensitivity may be right, or it may be wrong—but the reasoning behind it needs scrutiny if the observational methods used to constrain it rest on shaky foundations.
Feedback Parameter Trends by Decade
Trends in feedback parameter λ (W/m²/K) over four decades, showing increasing negativity consistent with noise-driven variability rather than a physical trend.
| Label | Value |
|---|---|
| 1980-1989 | -0.15 |
| 1990-1999 | -0.25 |
| 2000-2009 | -0.35 |
| 2010-2014 | -0.55 |
The feedback parameter time series from the 4,000-year control simulation illustrates the core problem. The grey line shows the raw λ values computed via 30-year moving windows. Even with 4,000 years of data, periods of apparent strengthening and weakening feedback emerge and dissolve. Without the 4,000-year context, you might look at a 30-year segment and conclude that feedback is trending in a particular direction. That conclusion would be premature.
What's Next
The honest answer is that these findings deepen the challenge of estimating time-varying feedback. The researchers propose no silver bullet. What they offer is a clearer view of the problem's contours.
One path forward is longer simulations. If 4,000 years of pre-industrial variability still doesn't reveal a consistent SST-feedback linkage, the record needed to detect one reliably may be even longer. Climate models are computationally expensive; 10,000-year runs are rare and precious.
Another path is methodological. The 30-year moving-window regression may simply be too noisy to extract the signal. Alternative approaches—perhaps using Green's functions derived from abrupt CO₂ experiments, or leveraging the multiple-timescale structure of Earth's response—may prove more robust.
A third path is humility. The pattern effect may be real. SST patterns do modulate how heat is redistributed, and cloud feedbacks in the tropical Pacific are genuinely sensitive to warming patterns. But if we cannot yet measure whether and how fast the feedback is evolving from the observational record, then that uncertainty needs to be carried forward into climate projections. The 1.5°C target isn't going anywhere; neither is the uncertainty around it.
The study's authors put it plainly: prescribed SST simulations offer limited potential for inferring temporal changes in Earth's feedback parameter over the observational period. That's not a dismissal of the method—it's a boundary marker. It tells you where the method works and where it doesn't. The pattern effect may be real; the measurement of it may need to wait for better data, longer records, or new techniques. In the meantime, the fog around climate sensitivity remains. But at least now we know a little better where the fog comes from.