Mountain Fog and Visibility

What is modelled

Air can hold only so much water vapour, and that amount falls quickly as it cools. When the vapour pressure exceeds the saturation pressure at the new temperature, the surplus condenses onto particles as droplets. The droplets, a few micrometres across, are far larger than the wavelength of light, so each one removes about twice its own shadow from a beam. More droplets or larger droplets mean a stronger extinction and a shorter visibility.

Equations

• Saturation pressure es(T) = 6.112 exp[17.62 T / (243.12 + T)] hPa (Magnus form).
• Condensed water LWC = (e0 − es(T1)) / (Rv T1).
• Log-normal drops: ⟨r3⟩ = rg3 e4.5 ln2σ, ⟨r2⟩ = rg2 e2 ln2σ.
• Extinction β = Q N π ⟨r2⟩ with Q ≈ 2; visibility V = 3.912 / β (2 % contrast).

Checks run in the page

• Saturation pressure against the table and the dew point as its inverse.
• Log-normal moments by numerical integration against the closed forms.
• A full Mie series for water droplets giving an extinction efficiency near 2.
• The Koschmieder threshold: contrast 0.02 at 3.912 optical depths.

Honest simplifications

Condensation is taken as complete down to saturation with a fixed droplet number, so the droplet size follows from the water and the number; real fog also has activation, sedimentation and mixing. Wind, aerosol haze and the day-night colour of the light are ignored; the visibility is capped by a clear-air limit; and the 2 % contrast rule is a convention, not a property of every eye.

• Press Mountain fog, then Clean air fog: the same water in fewer, larger drops gives a longer visibility.
• Raise the cooling slider to condense more water and watch the posts disappear one by one.
• Lower the humidity: a drier start needs a deeper chill before any fog forms.