Illustrative numbers. The Carpathians are the flavour; the terrain is a stylised ridge with Carpathian-like proportions, not a survey of a real range. Vertical exaggeration x1.6; trees x5, houses x8 for visibility.
Dry and moist adiabats
Γd = g / cp = 9.8 K/km (unsaturated air)
Γm = g (1 + Lv rs / Rd T) / (cp + Lv² rs ε / Rd T²)
≈ 4-6 K/km (cold, high) ... 3 K/km (warm, low)
Rising unsaturated air cools at Γd. At the lifting condensation level (LCL) it is saturated, vapour condenses and releases latent heat, so it cools more slowly, at Γm.
Cloud base
Td = bγ/(a-γ), γ = ln(RH/100) + aT/(b+T) (Magnus)
z_LCL = z0 + 125 m/K x (T - Td) (Espy)
Rain on the windward side
Δr = r_s(T_LCL,p_LCL) - r_s(T_crest,p_crest) kg/kg condensed
R = εp · f(Fr) · ρ U D Δr / L_cloud mm/h
Fr = U / (N h), f = min(1, 0.4 + 0.6 Fr)
Depth D = 2000 m of air is lifted, the cloudy ramp is L_cloud (8 km x share above the LCL), εp = 0.7 of the condensate falls out. D, L, εp and f(Fr) are illustrative constants, not measurements. N = 0.011 s-1 is a typical value.
The foehn on the lee side
On the way down the air is warmed at Γm while it still holds cloud water, then at Γd once the cloud has evaporated. Because the rain has left, the descent starts from less water, so the air arrives in the lee valley warmer and drier than it started.
T_lee = T0 + (Γd - Γm)(H - z_LCL) (all condensate removed, constant Γm)
cp ΔT ≈ Lv Δr (latent-heat budget)
Rain-shadow ratio (lee / windward rain) = 0.25 (1-εp)/εp x min(1, U/10): a spill-over rule of thumb, illustrative.
Simplifications
- One parcel, no mixing, no entrainment, no mountain-wave drag; pressure from the standard atmosphere.
- The time-of-day clock moves the sun only; temperature does not change with it.
- Terrain lightmap is baked for a fixed late-morning sun and blended in; clouds are placed from the computed LCL, not simulated.
Independent numerical checks
Built with Blender 5.2 (village, spruce, cloud meshes, baked textures), Unity 6000.6 (terrain, 3 400-tree scatter, GPU lightmap) and Three.js r160. Hand-made models; no AI-generated assets.