Slant path absorption correction for low elevation angles

Slant path attenuation at millimeter wavelengths due to the gases oxygen and water vapor is often estimated by multiplying the zenith attenuation by the cosecant of the elevation angle. This flat-earth approximation is not valid at low elevation angles. The error produced by this approximation is examined. It is assumed that the actual atmosphere can be represented by a uniform surface layer with an effective height such that the attenuation through the layer is equal to that through the actual atmosphere. An expression for calculating this effective height is provided and with the effective height specified, the error produced by the approximation is determined. The percent error is then plotted as a function of effective height for a set of elevation angles above
2\deg
.