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The science
Surface energy balance. Each 50 m cell is a thin slab of areal heat capacity C that obeys C dTs/dt = (1 - α) S + ε Ldown - ε σ Ts&sup4; - h (Ts - Ta) - LE. S is shortwave on the cell (direct sun if not shaded plus diffuse), Ldown = 0.75 σ Ta,rural&sup4; is clear-sky longwave, h = 5.7 + 3.8 u W/m²/K is the convective coefficient, and LE is evaporative cooling: an evaporative fraction times the available radiation (grass 0.7, trees 0.9, pond 0.35, pavement and roofs 0). What is not carried away as H or LE is stored in the surface.
Sun and shade. Declination δ = 23.44° sin(2π(284 + N)/365) and hour angle give the sun's elevation and azimuth. Clear-sky direct beam is 1361 · 0.761/sin e W/m² on the normal. A cell is shaded when a building upwind (toward the sun) satisfies (hobstacle - hcell) > d tan e; trees stop 70 % of the beam. Roofs are taller than the ground, so they are rarely shaded.
Why parks are cold islands. Grass and trees reflect more than asphalt and cool by evaporation; tree canopies also shade what is below. A cooler surface sends less sensible heat to the air: H = h (Ts - Ta).
Air temperature. A column of air of depth zmix = 40 m blows through the district at speed u. Each cell adds the excess of its sensible heat flux over a rural grass reference: ΔT = (H - Hrural) Δx / (ρ cp u zmix), so air downwind of hot pavement is warmer and downwind of a park is cooler. This is a first-order advective budget, not a fluid-dynamics solution: no turbulence, no canyon geometry, no building heat storage or air-conditioning waste heat, no humidity feedback.
Honest simplifications. Clear-sky day, flat terrain, surfaces horizontal (walls are not modelled: a roof stands for the whole building), constants are typical values for asphalt, concrete roofs, grass and water rather than measurements of one city, no wind-direction change in the day. The cold-island effect in real cities is typically 1-3 K in air temperature and much more in surface temperature; the model reproduces that order of magnitude, not a specific park.