Direct-normal solar irradiance (DNSI), the total energy in the solar spectrum incident in unit time on a unit area at the earth's surface perpendicular to the direction to the Sun, depends only on atmospheric extinction of sunlight without regard to the details of the extinction - whether absorption or scattering. Here we report a set of closure experiments performed in north-central Oklahoma in April 1996, wherein measured atmospheric composition and aerosol optical thickness were input to a radiative transfer model, MODTRAN-3, to estimate DNSI, which is then compared with measured values obtained with a normal incidence pyrheliometer. For 36 independent comparisons, the agreement between measured and model estimated values falls within the combined uncertainties in the measurement (0.2%) and model calculation (2%), albeit with a slight average model overestimate, (0.72 ± 0.81)%; for a DNSI of 839 W m-2, this corresponds to 6.0 ± 6.8 W m-2. The agreement is nearly independent of airmass and water-vapor path abundance. These results thus establish the accuracy of the current knowledge of the solar spectrum and atmospheric extinction as represented in MODTRAN-3. An important consequence is that atmospheric absorption of short-wave radiation is accurately parametrized in the model to within the above uncertainties.
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