Extinction, refraction, and delay in the atmosphere

Abstract

[1] This paper establishes that absolute optical air mass and hydrostatic atmospheric delay of electromagnetic waves are proportional magnitudes, and, consequently, their respective obliquity ratios are identical dimensionless quantities. This means that a potential source for developing new models for relative optical air mass can be found in the formulae for the atmospheric delay in electromagnetic signals (and vice versa). In this respect, for estimating relative optical air mass, we demonstrate that Herring's (1992) family of mapping functions for modeling atmospheric delay is more accurate than functional forms devised expressly for the purpose, such as that of Kasten (1965).

Functional forms for approximating the relative optical air mass

“…Introduced by Kasten [1965], this functional form was applied by Kasten and Young [1989], Rapp‐Arrarás and Domingo‐Santos [2008], and Rapp‐Arrarás [2009, chapter 4]. We will refer to it as Ka‐3, and its mathematical expression, as a function of the apparent zenith distance, is Kasten [1965] also provided an obliquity function for the optical mass of atmospheric water vapor following this model.…”

“…Adopted by Ifadis [1986, 2000] for modeling the atmospheric delay of radio signals, the triparametric version of the truncated continued fraction by Marini [1972] was applied by Rapp‐Arrarás and Domingo‐Santos [2008]to approximate air mass. We will refer to it as Ma‐3, and its mathematical expression, as a function of the apparent zenith distance, is …”

“…Nevertheless, generally these tables and graphics have the disadvantage of not considering the contribution of each error source mentioned above to the total error of approximation. Thus, for instance, apart from the research article by Rapp‐Arrarás and Domingo‐Santos [2008], there are no published works specifically examining the first error source.…”

“…This article constitutes a review and systematic comparison of functional forms for approximating the relative optical air mass. Among them, we have considered the most meaningful forms in atmospheric optics, geophysics, meteorology, and solar energy science, as well as several forms arising from the study of the atmospheric delay of electromagnetic signals, whose relationship with the optical air mass was shown by Rapp‐Arrarás and Domingo‐Santos [2008].…”

Primary and Albedo Solar Energy Sources for High Altitude Persistent Air Vehicle Operation

“…is the original light beam intensity β e is the extinction coefficient over the medium thickness h. To calculate transmissivity, β e ∆h for each distinctive layer of the atmosphere Liou [27], Rapp-Arraras [28] need to be determined to give the total extinction, as in Equation (2). Alternatively, Aglietti [29] shows that a global extinction coefficient of 0.32 can be derived using standard test conditions since the SPP is known at the TOA, 1366 Wm −2 , and the AM1.5 direct beam component at MSL; 850 Wm −2 is specified for testing PV panels.…”