Why is a green roof cooler, and what happens to a cloudburst? Compare it with the bare roof next to it.
Each button runs three hot days and then a one-hour cloudburst of 40 mm/h headless, for several values.
The science
Surface energy balance. For the top node: (1 − α) S + ε (L↓ − σ Ts⁴) − hc (Ts − Ta) − LE = G, with albedo α = 0.22 (green) or 0.12 (dark membrane), emissivity ε = 0.95 / 0.90, hc = 5.7 + 3.8 u (wind u in m/s), downward long-wave from a Swinbank-type clear-sky law L↓ = 5.31·10⁻¹³ T⁶ blended with σT⁴ under cloud. LE = λ·ET is the latent heat carried away by evaporation, zero for the bare roof.
Evapotranspiration. Priestley–Taylor reference rate ET0 = 1.26 Δ/(Δ+γ) Rn/λ with the FAO-56 Magnus slope Δ and γ = 0.0674 kPa K⁻¹; actual ET = Kc f(θ) ET0 and f(θ) = (θ − θwp)/(θfc − θwp) clipped to 0–1 (θwp = 0.08, θfc = 0.30, θs = 0.45; typical substrate values [перевірити за джерелом]).
Heat through the stack. One-dimensional conduction in 12–15 nodes (substrate, drainage mat, membrane, 10 cm insulation k = 0.035, 20 cm concrete k = 1.7), explicit finite volumes with 60 s steps, room at 24 °C behind a 0.12 m² K/W surface resistance. Substrate conductivity and heat capacity grow with moisture.
Water. A bucket model: rain fills the substrate up to saturation, anything above field capacity drains with a 15 min time constant into the drainage layer (10 min detention), then into the cistern; the cistern overflows to the storm drain; below half the plant-available water the cistern irrigates at 2 mm/h. The bare roof sheds 95 % of rain at once. Roof area drained to the cistern: 100 m².
Simplifications. One-layer bucket, fixed leaf area and crop coefficient, no snow, no lateral heat flow, no plant shading model, synthetic daily weather. Layer thicknesses in the picture are exaggerated about three times. Assets built with Blender; scene by Three.js.