Clear-Sky Direct-Beam Solar Radiation Versus Altitude: A Proposal for Standard Soundings

William P. Lowry Department of Ecology, Ethology, and Evolution and the Institute for Environmental Studies, University of Illinois, Urbana 61801

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Abstract

The author reexamines Klein's (1948) quantitative statements relating clear-sky direct-beam solar radiation to altitude for the lower troposphere, which are of the form (transmissivity) = B + A log (altitude). Klein's summaries are judged to be the best general statements on the subject previously published, but the author proposes a different empirical formulation which is based on more direct physical reasoning and which yields a better statistical fit when applied to Klein's data. The author also proposes, for informal adoption, two standard soundings (moist and dry) of zenith path clear-sky direct-beam transmissivity τp as a function of pressure p in the form ln(Cτp) = InM + Np, where C is a constant with value near 0.975, the approximate transmissivity just below the high atmospheric ozone layer. For use in estimations of transmissivity tp with nonzero zenith angles, the author presents, as part of his proposal, altitude-dependent estimators for the adjustment parameter ap, suggested by Williams (1976) in the form lntp = (secZ) ln[τp + ap ln(secZ)] where Z is the zenith angle.

Abstract

The author reexamines Klein's (1948) quantitative statements relating clear-sky direct-beam solar radiation to altitude for the lower troposphere, which are of the form (transmissivity) = B + A log (altitude). Klein's summaries are judged to be the best general statements on the subject previously published, but the author proposes a different empirical formulation which is based on more direct physical reasoning and which yields a better statistical fit when applied to Klein's data. The author also proposes, for informal adoption, two standard soundings (moist and dry) of zenith path clear-sky direct-beam transmissivity τp as a function of pressure p in the form ln(Cτp) = InM + Np, where C is a constant with value near 0.975, the approximate transmissivity just below the high atmospheric ozone layer. For use in estimations of transmissivity tp with nonzero zenith angles, the author presents, as part of his proposal, altitude-dependent estimators for the adjustment parameter ap, suggested by Williams (1976) in the form lntp = (secZ) ln[τp + ap ln(secZ)] where Z is the zenith angle.

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