Interactive · from CO₂ forcing to the Central England Temperature record
What's actually driving UK heatwaves
The textbook way to picture a climate regime is a ball in a double-welled landscape: a cool valley and a hot one, with random weather knocking it between them. That is the stochastic-resonance idea (Benzi et al., 1982), and the companion demo lets you play it by hand. This page asks what the real Central England record does with that picture. Greenhouse gases warm the planet; the warming slides the whole summer distribution past a fixed heatwave line (more hot summers) and tilts the landscape so the hot regime sticks (longer spells). Drag the year – the warming is not invented, it comes from a real CO₂ trajectory run through a causal Earth-model response. By the end the data has returned a verdict on the lens itself.
2020
CO₂ –forcing –global warming –
1 · The rising floor
The real CET summer distribution (faint = 1900s baseline) slides right as the planet warms. Area past the heatwave line = how often a summer is “hot.”
hot-summer chance, this year
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summer mean (UK)
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heatwave line 16.4°C (fixed)
2 · Sticky weather (blocking)
One simulated summer of daily temperatures at this year's warmth. Red = a hot day. Toggle blocking off to see the same heat scatter instead of forming spells.
weather
hot days this summer
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longest heatwave
– days
3 · The landscape underneath (the double-well lens)
The two stories above told as one shape. A ball sits in whichever valley it is in; synoptic weather is the noise that knocks it across; the seasonal cycle is the weak yearly nudge. Here the slider does something the standalone demo cannot: the warming you compute below tilts this landscape in real time.
the landscape · ball = today's regime
regime over time · gold = the seasonal nudge
time in hot regime
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tracks panel 1's rising floor
phase-lock (SR strength)
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resonance needs two valleys
cool valley
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fills in as the planet warms
This panel is the hypothesis, idealised. Hold the climate fixed and the right amount of noise makes the ball hop in step with the season – stochastic resonance, and the phase-lock meter climbs. Now crank the year: warming tilts the well, the cool valley fills, the ball just sits hot, and the phase-lock collapses. The real record never shows the symmetric two-well this lens assumes – panels 1 and 2 show one skewed valley with a sticky hot tail. UK summer heat is metastable, not bistable: warming shifts and tips, it does not resonate.
Addendum · the Earth model behind the warming (causal & perturbative)
No black box. The warming above is a real reduced-complexity Earth model: CO₂ → radiative forcing → temperature, where temperature is the forcing perturbation convolved with the planet's response kernel (its Green's function). It is causal (only the past forces the present), nonlinear (forcing grows with log CO₂, not CO₂), and diffusive (a fast surface response plus a slow ocean tail, so warming lags and keeps coming).
global temperature now
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radiative forcing
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5.35·ln(CO₂/278) W/m²
UK summer warms
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faster than global (regional)
Inset (top-right): the climate's Green's function – the temperature kick from a single year's forcing pulse. The sharp spike is the surface mixed layer; the long tail is heat diffusing into the deep ocean. The temperature curve is that kernel convolved with the whole history of forcing. Parameters are AR6-style; CO₂ is the dominant term; years past 2021 follow a mid-range emissions path.
What am I looking at?
The rising floor (panel 1) drives heatwave frequency. The distribution's shape barely changes; warming shifts it bodily, and a fixed threshold catches a larger slice of the tail. The real hot-summer rate climbs ~10% → 11% → 16% across the 1800s, 1900–1990 and 1990–now; the curve's markers show those.
Sticky weather (panel 2) sets heatwave duration. UK summer days are strongly autocorrelated (lag-1 ~0.77): a blocking high parks overhead and the same hot air sits for days. In the real record, hot spells reach 18 days; destroy that memory by shuffling and the longest collapses to about 6.
The landscape (panel 3) is those two stories told as one shape, and it is where the stochastic-resonance lens meets the data. Hold the climate fixed and, at the right noise level, the ball hops between valleys in step with the season – that is resonance, and the phase-lock meter lights up. Tilt the same landscape with real warming and two things happen together: the ball spends ever more time in the hot valley (panel 1's rising floor), and past a threshold the cool valley vanishes entirely (a metastable collapse). The telling part is that the resonance dies as it tilts – the ball simply sits hot. That is the honest result of the study: warming shifts and tips, it does not resonate.
The addendum is the honest causal chain, and it is deliberately a perturbative one: we do not run a full coupled climate simulation, we treat the climate as a system perturbed by a forcing and read off its linear response through its Green's function. That keeps causality intact (the kernel is zero for the future) while staying tractable in your browser. The double-well in panel 3 is the candidate mechanism the study tested; the verdict from the real record is that UK summer heat is metastable, not bistable. Full study: Stochastic Resonance and UK Summer Heatwaves: A Double-Well Test (paper [99]).
abhishek-shivakumar.com · data: Met Office Hadley Centre CET · CO₂ ice-core + Mauna Loa · runs entirely in your browser