Rain falling on the Mendip Hills sinks through fractured limestone. The deeper it goes, the hotter the surrounding rock gets, following the geothermal gradient. At Bath's fault line the water finds a fast path back to the surface — the faster that ascent, the less heat it loses to the cooler rock it passes on the way up.
Temperature at depth: T(d) = T0 + G x d
T0 = ambient ground temp (~10 C), G = geothermal gradient (C/km), d = depth (km)
Temperature at the outlet: T_out = T0 + (T(d) - T0) x R(flow)
R(flow) = heat-retention fraction, rises with flow rate
(a faster rise through the fault means less time to lose heat to the rock)
- Infiltration depth — how far down the fault the water is estimated to circulate; more depth means more time near hot rock.
- Geothermal gradient — how quickly temperature rises with depth in this part of the crust; Bath's fault taps unusually hot rock for the UK.
- Spring flow rate — modelled on Bath's real output of about 1.17 million litres a day; a faster flow keeps more of the deep heat by the time it resurfaces.
- Roman / Georgian toggle — swaps the buildings above the spring: the Roman-era temple and Great Bath, or the Georgian townhouses and crescent built 1,700 years later on the very same water.
Real-world application: this is the same reasoning hydrogeologists use to explain why Bath is the only place in the UK with naturally hot springs — the water that reaches the surface today fell as rain roughly 10,000 years ago.