A ball rolls in a landscape with two valleys: a cool summer regime and a hot (blocked) one. A weak yearly nudge is too gentle to push it over the hill on its own. But add the right amount of random weather noise, and the ball starts hopping between valleys in time with the nudge. That is stochastic resonance – the 1982 idea (Benzi, Parisi, Sutera, Vulpiani) for the ice-age cycle, here applied to UK summer heat. Find the noise sweet spot.
Left: the climate “pseudo-potential” – a curve with two dips. The ball sits in whichever dip it is in. The yellow tilt is the weak yearly forcing wobbling the curve; the red tilt is warming pulling the whole thing toward the hot dip.
Right: the regime over time. When the ball is up (hot) or down (cool), you see it switch. SR strength measures how well those switches lock onto the yearly nudge: it is near zero when the ball is frozen in one valley (too little noise) and when it rattles randomly (too much noise), and it peaks at an intermediate, “just right” noise level. That bell-shaped peak is the whole point.
The warming slider shows the honest result of the study: tilting the landscape toward hot makes the ball spend more time hot (the heatwave increase) and eventually removes the cool valley entirely (a tipping point) – but it does not create resonance. UK summer heat turns out to be metastable, not bistable: a single lopsided valley with a sticky hot tail and a floor that keeps rising. Warming shifts and tips; it does not resonate.
Full write-up, data and figures: Stochastic Resonance and UK Summer Heatwaves: A Double-Well Test (research preprint, paper [99]).