Future-proofing Interpretations of the Paris Agreement’s Limit of Well Below 2°C
A new analysis shows how the Paris Agreement’s “well below 2°C” target can drift toward 2°C as climate uncertainty shrinks — and how to fix it.

The Paris Agreement’s temperature language has always carried a degree of productive ambiguity — “well below 2°C” is at once a legal ceiling, a political aspiration, and a scientific benchmark. But as climate modeling has grown more sophisticated and observational records have lengthened, a quiet problem has emerged in how that language gets operationalized. Policy documents, legal proceedings, and international negotiations have increasingly converged on a probabilistic interpretation: keeping warming below 2°C with a likelihood of 66% or higher. That sounds rigorous.
The trouble, as Robin Lamboll and Joeri Rogelj argue, is that it is not future-proof. As uncertainty in climate projections narrows over time — a natural consequence of accumulating observations — the emissions pathways compatible with a given probability of staying below 2°C actually widen. The target, paradoxically, appears to relax as science improves. The result is a built-in drift toward 2°C, rather than well below it.
Key Findings
Probabilistic targets converge toward 2°C as uncertainty shrinks
When warming uncertainty is high — as it was at the Paris Agreement’s adoption in 2015 — a 66% or 90% probability of remaining below 2°C translates to relatively strict emissions limits and a median projected warming well under 2°C. As observational data accumulate and uncertainty ranges narrow, the same probability thresholds allow higher emissions while still technically satisfying the target. Without any change in ambition or legal interpretation, the effective ceiling drifts upward toward 2°C itself.
A logistic relationship links median warming to exceedance probability
The authors use the MAGICC and FaIR simple climate models — calibrated against both AR5-era knowledge (reflecting the science available at the Paris Agreement’s adoption) and the more recent AR6 database — to quantify this relationship precisely. A logistic function reliably maps each probability level to a corresponding median peak warming. Across models and calibrations, a 66% probability of keeping warming below 2°C corresponds to a median peak warming of approximately 1.83–1.85°C; an 83% probability corresponds to roughly 1.63–1.67°C; and a 90% probability to around 1.54–1.58°C.
Median warming targets are more stable through time
The paper’s central recommendation is to reframe the LTTG in terms of median — or expected — warming rather than a probabilistic threshold. Because the median is anchored to the central estimate of projected warming rather than to a tail of the distribution, it does not systematically drift as uncertainty resolves. This approach translates the level of scientific uncertainty at the Paris Agreement’s adoption into a fixed temperature benchmark, adjusting emissions limits when new science requires it without implicitly relaxing ambition.
Paris-consistent warming lands in the 1.65–1.8°C range
Applying this framework to the best available science at the time of the Paris Agreement’s adoption — MAGICC calibrated to AR5 knowledge with SR1.5 scenarios — the authors show that “well below 2°C” translates most faithfully to a median peak warming in the 1.65–1.8°C range. The specific value depends on how broadly one interprets “well below”: a 66% probability threshold implies a median of roughly 1.83°C, while tighter interpretations pushing toward 83% or 90% converge on medians closer to 1.63–1.65°C. The benchmark the authors consider most historically defensible is approximately 1.5–1 standard deviation above the median — a median warming of no more than 1.63°C.
The 1.5°C target serves as an important guardrail
Most scenarios that comply with the 1.5°C end-of-century target carry a currently assessed probability above 66% of remaining below 2°C throughout the century. This means the 1.5°C target functions as a natural guardrail against ambition backsliding — its pursuit keeps the “well below 2°C” limit meaningful regardless of how probabilistic interpretations evolve.
A Benchmark That Doesn’t Move With the Science
What Lamboll and Rogelj have identified is a subtle but consequential design flaw in how the Paris Agreement’s temperature goal has been put to work — one that grows more consequential precisely as climate science improves. By anchoring the target to a probability rather than a median outcome, existing interpretations have inadvertently built in a mechanism for loosening ambition without any political decision to do so.
Their solution — reframing “well below 2°C” as a median warming target in the 1.65–1.8°C range — is technically modest but politically significant: it makes the goal robust to exactly the kind of scientific progress it was meant to respond to. As Lamboll & Rogelj show, future-proofing the Paris Agreement’s limits isn’t about changing what countries committed to — it’s about making sure the math doesn’t quietly change it for them.
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