Degrees per Metre: A Canyon Energy-Balance Model of Street-Level Heat and the Price of Cooling Interventions, with a Geometry-Locked Regime

A canyon energy-balance model gives pedestrian-level air temperature excess over a rural reference at peak afternoon conditions as a function of height-to-width ratio, sky view factor, surface albedo, thermal admittance, and anthropogenic heat. Across five geometries with height-to-width ratios from 0.5 to 4.0, the modelled excess rises from 2.73 K to 8.30 K. Interventions are priced per metre of street in degrees bought per unit cost: shade trees buy 1.01 K to 1.79 K at $225 per metre, with the best value of 7.956 degrees per $1,000 per metre ($125.7 per degree per metre) in the deep canyon; high-albedo surfaces buy 0.81 K in the shallow canyon falling to 0.18 K in the deepest. In the geometry-locked regime — canyons with ratios of 3.0 and 4.0, where trees cannot be planted — no surface intervention buys more than 0.25 K and 0.18 K respectively, below the stated 0.5 K threshold, while setback to a ratio of 1.0 at redevelopment buys 3.17 K and 4.07 K at $3,000 per metre. SIMULATED, NOT MEASURED: nothing was built, planted, or field-tested.