Implementing the Delta-Four-Stream Approximation for Solar Radiation Computations in an Atmosphere General Circulation Model

Tarek Ayash Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada

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Sunling Gong Air Quality Research Branch, Meteorological Service of Canada, Toronto, Ontario, Canada

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Charles Q. Jia Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada

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Abstract

Proper quantification of the solar radiation budget and its transfer within the atmosphere is of utmost importance in climate modeling. The delta-four-stream (DFS) approximation has been demonstrated to offer a more accurate computational method of quantifying the budget than the simple two-stream approximations widely used in general circulation models (GCMs) for radiative-transfer computations. Based on this method, the relative improvement in the accuracy of solar flux computations is investigated in the simulations of the third-generation Canadian Climate Center atmosphere GCM. Relative to the computations of the DFS-modified radiation scheme, the GCM original-scheme whole-sky fluxes at the top of the atmosphere (TOA) show the largest underestimations at high latitudes of a winter hemisphere on the order of 4%–6% (monthly means), while the largest overestimations of the same order are found over equatorial regions. At the surface, even higher overestimations are found, exceeding 20% at subpolar regions of a winter hemisphere. Flux differences between original and DFS schemes are largest in the tropics and at high latitudes, where the monthly zonal means and their dispersions are within 5 W m−2 at the TOA and 10 W m−2 at the surface in whole sky, but differences may be as large as 20 and −40 W m−2. In clear sky, monthly zonal means and their dispersions remain within 2 W m−2, but may be as large as 25 and −12 W m−2. Such differences are found to be mostly determined by variations in cloud optical depth and solar zenith angle, and by aerosol loading in a clear sky.

Corresponding author address: Tarek Ayash, Dept. of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, Toronto, ON M5S 3E5, Canada. Email: tarek.ayash@utoronto.ca

Abstract

Proper quantification of the solar radiation budget and its transfer within the atmosphere is of utmost importance in climate modeling. The delta-four-stream (DFS) approximation has been demonstrated to offer a more accurate computational method of quantifying the budget than the simple two-stream approximations widely used in general circulation models (GCMs) for radiative-transfer computations. Based on this method, the relative improvement in the accuracy of solar flux computations is investigated in the simulations of the third-generation Canadian Climate Center atmosphere GCM. Relative to the computations of the DFS-modified radiation scheme, the GCM original-scheme whole-sky fluxes at the top of the atmosphere (TOA) show the largest underestimations at high latitudes of a winter hemisphere on the order of 4%–6% (monthly means), while the largest overestimations of the same order are found over equatorial regions. At the surface, even higher overestimations are found, exceeding 20% at subpolar regions of a winter hemisphere. Flux differences between original and DFS schemes are largest in the tropics and at high latitudes, where the monthly zonal means and their dispersions are within 5 W m−2 at the TOA and 10 W m−2 at the surface in whole sky, but differences may be as large as 20 and −40 W m−2. In clear sky, monthly zonal means and their dispersions remain within 2 W m−2, but may be as large as 25 and −12 W m−2. Such differences are found to be mostly determined by variations in cloud optical depth and solar zenith angle, and by aerosol loading in a clear sky.

Corresponding author address: Tarek Ayash, Dept. of Chemical Engineering and Applied Chemistry, University of Toronto, 200 College Street, Toronto, ON M5S 3E5, Canada. Email: tarek.ayash@utoronto.ca

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