Abstract
Photosynthetically active radiation (PAR) incident at the surface is crucial for understanding and modeling the Earth's climate and ecosystems. In this article, a general parameterization scheme suitable for PAR estimation under cloudy skies is proposed based on an elaboration on the PAR radiative transfer (RT) processes above, in, and beneath cloud layers. Its most important novel property is that all RT processes in cloudy atmospheres are explicitly explained, including ozone absorption, Rayleigh scattering, cloud single scattering, cloud multiple scattering, aerosol scattering, and cloud reflection. Theoretical accuracy evaluations show over 95% of errors (against rigorous RT calculations) lie within ±20 W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and an operational application with multisource satellite products as inputs shows the root-mean-square error (RMSE) of ≤42 W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> on the hourly timescale. Therefore, the parameterization scheme is accurate both in theory and actual applications.
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