Cool Roof Surface Energy Balance

Roof Material

Solar albedo α 0.12

Thermal emissivity ε 0.90

Environment

Wind speed 2.0 m/s

Cloud cover 0%

Day speed 0.6 h/s

Live Readouts

Roof surface temp

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Air temp

32.0°C

Heat flux → building

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Solar irradiance

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Cooling benefit vs black roof

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How it works

Each roof patch obeys a steady-state surface energy balance, the same equation building-energy models (e.g. EnergyPlus, LBNL's Cool Roof Calculator) use to predict roof temperature:

(1-α)·G = ε·σ·T⁴ + h_c·(T - T_air)
absorbed solar   =  IR emission  +  convection

α is solar albedo (reflectance), G is incident solar irradiance (W/m², from sun elevation), ε is thermal emissivity, σ = 5.67×10⁻⁸ W/m²K⁴ is the Stefan–Boltzmann constant, and h_c ≈ 5.7 + 3.8·v_wind W/m²K is the convective heat-transfer coefficient. Each frame the sim solves this nonlinear equation for T by Newton–Raphson, then relaxes the displayed temperature toward it with a first-order thermal-mass lag so the roof heats and cools gradually rather than snapping to equilibrium.

Heat conducted into the building follows Fourier's law through the roof assembly's overall conductance U: q = U·(T_surface − T_indoor). A high-albedo, high-emissivity "cool roof" coating keeps T lower under the same sun, cutting q and the air-conditioning load — the core mechanic behind real cool-roof and urban-heat-mitigation programs.

Albedo / emissivity — the two material properties a cool-roof coating changes; raising either lowers steady-state temperature.
Wind — stronger convection carries heat away faster, especially on darker (hotter) roofs.
Cloud cover — patchy, drifting shading reduces local irradiance, which is why the tiled roof shows visible spatial temperature variation.

06:00

Surface temperature

cool → hot

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