A Simple Model to Calculate Visibility Reduction by Fog

Generally, fog is assumed to occur when visibility is less than 1,000 m. (Srisarakham and Exell page 75 – Thai Journal of Mathematics) The derivation for fog visibility is a simple one. (Jacobson page 315) Srisarakham and Exell page 77 have this equation as the starting equation from Jacobson, setting k = π r2 n, because k is the product of an effective across section of fog droplets π r2 and a number concentration of droplets n. k = total extinction coefficient.

d I’/d x’ = π r² n (Io - I’)

The integral is the following, using (CRC Handbook of Chemistry and Physics 1985-1986), page A-21 Eq. 27.

(Io – I) / Io = exp (- π r² n x)

This is where Io is the intensity of light emanating from a black object observed at distance x, where the light intensity is I. When the object cannot be discerned, that is the visibility limit. The contrast ratio Cratio is the following. The Koschmeider equation is Eq. (6).

Cratio = (Io – I) / Io

It is known from human experimentation that Cratio = 0.02. (See pages 314-315 of Jacobson.) There is meteorological data from the Don Muang Airport in Bangkok in the Thai article of which does not relate to this paper and it will not be included.