Functional forms for approximating the relative optical air mass

This article constitutes a review and systematic comparison of functional forms for approximating the air mass from the zenith to the horizon. Among them, we find 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 air mass was recently proved by the authors. In total, we have compared 26 functional forms, and the fits have been done for three atmospheric profiles, an observer at sea level, and the median wavelength of the Sun’s spectral irradiance (0.7274 μm). As a result, the best of the uniparametric forms has more than three centuries of history; the best of the biparametric forms was recently introduced by one of the authors; the best of the tri‐ and tetraparametric forms were originally proposed for modeling the atmospheric delay of radio signals; and the best of the forms with more than four parameters is used here for the first time. On the basis of these, for the 1976 U.S. Standard Atmosphere (USSA‐76), we provide one‐, two‐, three‐, four‐, and five‐parameter formulas whose maximum deviations are 1.70, 2.91 × 10−1, 3.28 × 10−2, 2.49 × 10−3, and 3.24 × 10−4, respectively. Key Points Recalibration and comparison of 26 functional forms for approximating air mass Approximation of the air mass in terms of continuous variable New air mass approximation formulas with 1, 2, 3, 4, and 5 parameters