Presets
Playback
Sun and time
Time of day, latitude and day of year set the sun path.
Plaza design
Pavement, pool and sail, plus trees and irrigated lawn.
Weather
A clear-sky day with the chosen temperature range, humidity, wind and cloud.
Layers
Model checks
The science
Sun. Declination dec = 23.44 deg sin(2 pi (284 + d)/365); elevation from sin(el) = sin(lat) sin(dec) + cos(lat) cos(dec) cos(15 deg (t - 12)). Clear-sky beam (DNI) uses the Kasten-Young air mass with a Meinel-type attenuation 0.7^(AM^0.678); cloud cover c scales global radiation by 1 - 0.75 c^3.4 (Kasten-Czeplak) and moves the share toward diffuse light.
Shadows and sky view. Each 1 m cell casts a ray toward the sun and tests the building boxes (slab test), tree crowns (spheres with Beer's-law transmission exp(-0.45 s), s = path length in foliage) and the sail (transmission 0.15). The sky view factor is the mean over 16 azimuths of cos^2(horizon elevation) (Johnson-Watson); obstacle types are combined by multiplication, an approximation.
Surface energy balance of each cell, forward Euler with 120 s steps:
C dTs/dt = (1 - albedo)(DNI sin(el) f_sun + D SVF) + eps (L_down - sigma Ts^4) - h (Ts - Ta) - beta max(0,Rn) - kG (Ts - T_deep)h = 5.7 + 3.8 u (W/m2K, Juerges), L_down = SVF eps_sky sigma Ta^4 + (1 - SVF) sigma (Ta+2)^4 with Brutsaert sky emissivity 1.24 (e/Ta)^(1/7). Heat capacity C, albedo and evaporative share beta per material are illustrative round numbers (asphalt 0.08 / 1.2e5, concrete 0.30, cool pavement 0.55, lawn beta 0.7, water beta 0.7), not measurements of a specific site.
What a person feels. Mean radiant temperature by the six-direction method: Tmrt = [ sum W_i (eps_p L_i + a_k K_i) / (eps_p sigma) ]^(1/4), weights 0.06 up/down and 0.22 for each of four sides, a_k = 0.7, eps_p = 0.97, with beam, diffuse, reflected and long-wave fluxes from each direction. Then a black-globe temperature (ISO 7726 formula inverted), the Stull (2011) wet-bulb temperature and the outdoor WBGT estimate 0.7 Tnwb + 0.2 Tg + 0.1 Ta, with Tnwb approximated as Tw + 0.3 (Tg - Ta). Class limits 25 / 28 / 31 C are common rule-of-thumb flag values, not a medical standard.
Honest simplifications.
- Surfaces are lumped single-layer slabs with no lateral conduction between cells; facades are not modelled thermally (surroundings are taken as air + 2 K); inter-reflections between buildings and the plaza are ignored.
- The air temperature is a prescribed daily cosine (peak 15:00); trees, lawn and water change surfaces and shade but do NOT cool the air by evapotranspiration, which understates their real effect. Wind is a constant.
- Tree crowns are spheres of radius 3 m centred at 6.5 m; real canopies vary with species and season. A tree's own water use is not modelled.
- Clear-sky radiation formulas are standard approximations (a few percent to tens of W/m2 off in practice). The model is for understanding the ranking of measures, not for predicting a particular street.
- Cool pavements and Tmrt: in this model the cool surface lowers longwave emission but raises reflected shortwave on the pedestrian, so the net benefit for a standing person can be small. Published field studies report mixed results as well.
What to try
- Press "Play day" and watch the shadows of the four buildings sweep the plaza while the surface heats and cools.
- Compare the presets: dark asphalt, light concrete, cool pavement, twelve trees. The ground can get cooler while the person (Tmrt) hardly does, until shade is added.
- Click anywhere on the plaza to move the person (yellow ring) and read Tmrt and WBGT there.
- Run the design ladder to see each measure added in turn.