On the applicability of the koschmieder visibility formula

Abstract The inverse proportionality between the visibility and the extinction coefficient, first derived by Koschmieder, is only applicable under very limited conditions: the atmosphere must be illuminated homogeneously, the extinction coefficient and the scattering function are not allowed to vary with space, the object must be ideally black and be viewed against the horizon, and the eye of the observer must have a constant contrast threshold. A general formula, taking these facts in account has been derived and used to calculate possible errors which might arise if the simple Koschmieder Formula is used instead. The following results were obtained: inhomogeneous illumination generates errors smaller than 5 per cent. An inhomogeneous distribution only due to different dilutions of the aerosol gives no error if the average of the extinction coefficient is used. Using non black objects as visibility markers can give errors up to 50 per cent if they are illuminated by the sun, but the errors will be below 5 per cent if they are in their own shadow. The errors due to a varying contrast threshold of the eye can be considerable, if the visibility markers are too small. By proper selection of the visibility markers it will be possible to use the Koschmieder Formula to calculate the extinction coefficient from observed visibilities with an error of less than about 10 per cent.