## 1. Introduction

[2] More than two centuries ago *Laplace* [1805, p. 284] established that for an atmosphere with spherical symmetry whose density decreases exponentially with height, the logarithm for the intensity of incoming light from any heavenly body is proportional to its refraction divided by the cosine of its apparent elevation angle. According to *Young* [2006], this implies that

where *r* is the refraction of the light incident at an apparent zenith distance *z*_{a} and *m* is the air mass (relative optical air mass or obliquity ratio of the absolute optical air mass).

[3] The fact that relation (1) continues to hold true, at least in approximate terms, with atmospheric models more verisimilar than the exponential one [*Young*, 2006] has meant that recognized tables and formulae for estimating either of the magnitudes, whether atmospheric refraction or air mass, have been advantageously applied to the development of models for calculating the other magnitude [e.g., *Forbes*, 1842; *Kristensen*, 1998].

[4] On the other hand, in the field of radar tracking of objects in space from the Earth's surface, *Rowlandson and Moldt* [1969] showed that, assuming an atmosphere of spherical symmetry whose refractivity decays exponentially with height,

where *r*′ is the refraction of radio waves arriving at the tracking station with an apparent elevation angle ɛ_{a} and a delay *D*. As was the case by virtue of relation (1), relation (2) has likewise prompted that formulae designed to estimate either of the variables in question, whether atmospheric refraction or atmospheric delay, have been successfully applied to the development of models for calculating the other variable [e.g., *Marini*, 1972; *Yan*, 1996].

[5] Given that both light and radio signals are electromagnetic waves and that the elevation angle and zenith distance are complementary angles, it is remarkable that it has not been previously observed that for the same wavelength *D* ∝ *m* or its equivalent

where *M* is the absolute optical air mass. The closest statement has been given by *Young* [2006, p. 111], who notes that “the tropospheric corrections required in GPS calculations are more closely allied to air mass than to refraction.”

[6] This paper establishes that absolute optical air mass and hydrostatic atmospheric delay are proportional magnitudes, and, consequently, their respective obliquity ratios are identical dimensionless quantities. From this it can be demonstrated that the known formulae for calculating the atmospheric delay represent a good basis for the purpose of developing new models for the estimation of absolute optical air mass (and vice versa). To this end, we have found that when estimating air mass, the family of mapping functions for modeling atmospheric delay presented by *Herring* [1992] surpasses, among others, the model proposed expressly for the purpose by *Kasten* [1965]. Finally, the link established between absolute optical air mass and signal delay has allowed us to express the relation between this latter variable and its own atmospheric attenuation as a simple mathematical relation.