Features of the proportionality coefficient in the relationship between visibility and liquid water content in haze and fog

Abstract

A wide set of size-distribution models of haze and fog droplets expressed in terms of the modified gamma distribu-tion function have been used for evaluating the proportionality coef-ficient b in the empirical relationship between visibility V and liquid water content LWC, that is V=b (LWC)ˉ2/3, as proposed by Eldridge (1966). The evaluations of b turn out to be consistent with the values proposed in the literature and give evidence for its close dependence on the shape-parameters of the droplet size distribution, especially as regards the mode radius and the width of the larger-droplet wing. Three average relationship curves are proposed respectively for dense haze, “dry and cold” fog and “wet and warm” fog.Corresponding to these cases, three correlation lines are presented between b and the ratio of the volume extinction coefficient at 3.70 µm wavelength to that at 0.55 µm, evaluated for the same uniform path in hazy and foggy atmospheres. Applied to measurements of infrared and visible transmission such correlation lines give the possibility of estimating the most proper value of b to be used in Eldridge’s relationship for different atmospheric conditions © Taylor & Francis Group, LLC.