A new table and approximation formula for the relative optial air mass

Abstract

Summary. The mostly used table of the relative opticM air mass m as function of solar altitude y (or zenith angle 0 --90 ~ --y) was computed by BE~PO~AD [1,2,3] using values of the vertical air density profile up to 10 km height as they were known about the turn of the century, and taking the refractive index of the air at ground level no = 1.000293; this index refers to light of wavelength 0.54 ~ (peak of the visible spectrum) and to air of temperature 0 ~ and pressure 1013.25 rob.A new table is presented which is computed from the air density profile of the AI~DC Model Atmosphere, 1959 [4], up to 84 km height; no = 1.000276 is taken corresponding to air of 15 ~ and 1013.25 mb (ground level values of the ARDC ~ [odel Atmosphere, 1959) and to the wavelength 0.7 y.. This wavelength is more representative for the whole solar spectrum than 0.54 ~ because it divides the solar spectrum into two parts of equal energy.A new approximation formula for the relative optical air mass ~ as function of solar altitude y [deg] is presented also. The equation is re(y) = l/[sin y + @ a (y @ b) -c] in which a = 0.1500, b = 3.885, c = 1.253 are empirical constants. These constants were calculated from the new tabulated values of re(y) by successive approximation applying the method of least squares of the relative errors to obtain each approximation.The values of the relative optical air mass calculated from the approximation formula are in very good agreement with the tabulated values. The deviation is less than 0.1% for y > 4 deg. The highest deviation, 1.25%, occurs at y = 0.5 deg.The approximation formula can be applied as well to the old BE_~FO~D table and to the table of the relative optical water vapor mass computed by SCHNAIDT [5]; then the constants have the values a = 0.6556, b = 6.379, e = 1.757, and a = 0.0548, c = 2.650, e = 1.452, respectively. Die mit der N~herungsformel berechneten Werte der relativen optischen Luftmasse sind in sehr guter (;Tbereinstimmung mit den tabellierten Werten. Die Abweichung ist kleiner als 0.1% ffir y > 4 grad. Die htchste Abweichung, 1.25%, tritt bei y = 0.5 Grad auf.Die Ngherungsformel kann ebensogut auf die alte Bemporad-Tabelle und auf die Tabelle der relativen optischen Wasserdampfmasse, die yon SCHiNrAIDT des valeurs des nouvelles tables donnan~ m (7). Pour ce faire, on a u~tilis6 la m~thode du plus petit carrg de l'erreur relative afin d'obtenir chaque approximation. Les valeurs de la masse optique relative de Fair, calcul6es par la dire formule d'approximafion, correspondent parfaitement h celles de la table. La diff6rence en est inf6rieure ~ 0,1% pour y > 4 degr6s. La plus grande diff6rence est de 1,25% et se rencontre pour y = 0,5% Cette formule d'approximation peut aussi t r~s bien 6tre utilis@e pour calculer des valeurs se rapproehant soit de l' ancienne table de BE~CIPORAD, soit de la table 6tablie

UV and global solar radiation in Łódź, Central Poland

“…The data collected also include hourly values of cloud cover and type of clouds from visual observations for the 5-year study period. Kasten's (1966) formula for the calculation of optical air mass has been used. The relationship between daily UV and global solar irradiation has been analysed, and general linear models of the form y = a + bx is calculated.…”

Validation and Improvement of Satellite-Derived Surface Solar Radiation over the Northwestern Pacific Ocean

“…The relative atmospheric path length, m, is calculated by Kasten's (1966) formula: The transmittance due to Rayleigh scattering is given by the following: …”

Estimate of the atmospheric turbidity from three broad-band solar radiation algorithms. A comparative study

“…where k t is the hourly clearness index (defined as the ratio between horizontal global irradiance and horizontal extraterrestrial irradiance) and m a is the relative air mass given by Kasten (1966) and corrected for local atmospheric pressure (Iqbal, 1983). A cloudless sky is then defined as k t >0.7 (Molineaux et al, 1995).…”