Clock 19:00Air 0 °CDew point 0 °CRH 0 %Pool depth 0 mVisibility 0—FPS 0

Drag to orbit, wheel or pinch to zoom. Blue arrows and streaks are cold air draining down the slopes; the white layer is the liquid-water fog, drawn where the terrain lies below the cold-pool surface. Orange arrows over the fog top appear after sunrise: sun heating lifts and thins the layer (burn-off).

Mountain Valley Fog: Cold-Air Pool and Burn-Off Lab

From dusk to late morning: does the valley fill with fog, how thick does it get, and when does the sun burn it off?

Air mass

Sky and wind

Time

Live readouts

Temperature and dew point

Cold-pool depth and visibility

Experiments

Each button runs the whole night headless (19:00 to 11:00) for several values and reports when the fog forms, how dense it gets and how long it lasts.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. Three camera presets jump to a ridge, the valley floor or a top-down map.
Presets set the evening air, dew point, wind and cloud together. Every slider can be changed while the night runs; the model reacts at once.
Time scale is simulated minutes per real second; the clock runs from 19:00 to 11:00 and then holds.

The science

Dew point and saturation. Saturation vapour pressure (Magnus form): e_s(T) = 6.112 exp(17.62 T / (243.12 + T)) hPa, T in °C. Dew point from relative humidity: T_d = 243.12 γ / (17.62 − γ), γ = ln(RH/100) + 17.62 T/(243.12 + T). Saturation mixing ratio q_s = 0.622 e_s / (p − e_s) with p = 1000 hPa.

Radiative cooling. The air layer (thickness h = 60 m) loses heat to the clear sky: F = ε σ (T⁴ − T_sky⁴)(1 − 0.8 c) β f_w, with ε = 0.97, T_sky = 0.0553 T^1.5 (Swinbank clear-sky form, T in K), cloud cover c, a coupling factor β = 0.5 for the share of the loss not returned by the ground (illustrative), and a wind factor f_w = 1/(1 + (u/3)²) for turbulent mixing. The ground returns sensible heat H = 6 (T₀ − 2 − T) W m⁻² K⁻¹ (illustrative). Then ρ c_p h dT/dt = −F + H. Once the air is saturated, condensation releases latent heat and slows cooling by Γ = 1 + (L/c_p) dq_s/dT.

Liquid water and visibility. Total water is conserved: q_l = max(0, q_t − q_s(T)), LWC = ρ q_l. Kunkel (1984): Vis [km] = 1.002 / (LWC [g m⁻³] · N [cm⁻³])^0.6473, with droplet number N adjustable. Extinction used for drawing: 3.912 / Vis.

Cold-air drainage and pool. Slope flows follow a Prandtl-type balance: U = √(g′ δ sin α / C_D), g′ = g (T₀ − T)/T, δ = 8 m flow depth, α = 12° wall slope, C_D = 0.05. Only ε = 20 % of the drained cold air is trapped (the rest leaves down-valley; illustrative). Cross-section of a trapezoidal valley: A = W₀ D + D²/tan α, W₀ = 600 m, and the pool grows by dA/dt = 2 ε U δ. The fog is drawn only where the terrain lies below the pool surface.

Sunrise. Absorbed shortwave 0.4 × 900 W m⁻² × sin(elevation) (halved inside fog) warms the layer until q_l returns to zero. Simplifications: one-box layer, no fog-top longwave cooling, no advection, no soil heat store, no vertical mixing of the pool, flat pool surface. Typical constants only — spot-check them before quoting. Assets built with Blender; scene by Three.js.