A measurement mast stands in a forest clearing. Follow one day: sunlight is absorbed leaf by leaf (Beer-Lambert), wind dies away inside the crowns, and three air layers heat, cool and exchange moisture with the air above.
A full day (after two days of spin-up) is run for several leaf area indices with the other settings as above.
The science
Sun. Declination δ = 23.45° sin(2π (284 + N)/365), sin β = sin φ sin δ + cos φ cos δ cos(15°(t − 12)). Clear-sky shortwave at the canopy top S = 1361 · 0.78^(1/sin β) · sin β, reduced by cloud cover c as (1 − 0.75 c3.4); photosynthetically active radiation is 48 % of it. The diffuse share is 0.15 + 0.85 c.
Light in the crowns (Beer-Lambert). The leaf area density a(z) is a Gaussian layer centred at 0.72 h whose integral is the leaf area index L. Light reaching a point with leaf area Lc above it is I = Idir e−k Lc + Idif e−kd Lc, with k = 0.5/sin β (spherical leaf angles) and kd = 0.8. Leaves absorb 85 % of the light lost in each layer. Gaps, sunflecks, clumping and the leaf-angle distribution are ignored.
Wind. Above the canopy a log law with displacement 0.67 h and roughness length 0.1 h, scaled so the speed at 2h is the value you set. Inside the canopy u(z) = uh exp(α (z/h − 1)) with α = 1 + 0.35 L (typical values are 2-3 for dense forest).
Air layers. Three well-mixed layers (floor 0-0.25 h, middle, crown 0.7-1 h) obey ρ cp Δz dT/dt = H − Uup + Ubelow, where H is the sensible heat from leaves (absorbed light times (1 − evaporative fraction), minus long-wave loss shared down the canopy by the same exponential) and U = ρ cp w ΔT is exchange between layers, with exchange velocity w = 0.12 u + 0.015 m/s. The top layer exchanges with the above-canopy air, prescribed as a daily sine wave, and the floor with a deep soil at the mean temperature (4 W/m²/K). Vapour follows the same exchange with a source from the latent heat (evaporative fraction of absorbed light). Saturation vapour pressure is the Magnus formula and the deficit is VPD = es(T) − e; condensation is capped at saturation.
Simplifications. A single layered profile with horizontal homogeneity (no edge effects or slopes), three air layers only, the above-canopy temperature and humidity are prescribed, constant long-wave loss, no rain, soil moisture or leaf phenology, and exchange velocities, evaporative fraction and the soil coupling are illustrative typical values. Results show how the model responds, not a specific forest. Models built with Blender, scene by Three.js.