Article Type:
Research Article

Assessment and Optimization of the Gamma-Weighted Two-Stream Approximation

Howard W. Barker Cloud Physics Research Division, Meteorological Service of Canada, Downsview, Ontario, Canada

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Qiang Fu Atmospheric Science Program, Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

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Print Publication:
01 Apr 2000
DOI:
https://doi.org/10.1175/1520-0469(2000)057<1181:AAOOTG>2.0.CO;2
Page(s):
1181–1188
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Abstract

The two primary foci of this note are to assess the ability of the multilayer gamma-weighted two-stream approximation (GWTSA) to compute domain-averaged solar radiative fluxes and to demonstrate how its execution time can be reduced with negligible impact on performance. In addition to the usual parameters needed by a 1D solar code, the GWTSA requires ν ∈ R+, which depends on both the horizontal mean and mean logarithm of cloud water content. Reduced central processing unit (CPU) time is realized by simply rounding ν to the nearest whole number, denoted as [ν]. The experiment reported on here uses 120 fields generated by a 2D cloud-resolving model simulation of an evolving tropical mesoscale convective cloud system. Benchmark calculations are provided by the independent column approximation (ICA), and results are also shown for the conventional two-stream model.

The full GWTSA yields time- and domain-averaged broadband top-of-atmosphere albedo and surface absorptance values of 0.32 and 0.49, which are very close to the ICA values of 0.32 and 0.47. Correspondingly, the GWTSA using [ν] produces 0.34 and 0.46. In contrast, the conventional two-stream’s estimates are 0.56 and 0.20. While mean heating rate errors for the conventional two-stream average about −0.5 K day−1 near the surface and almost +2 K day−1 at 10 km, they are diminished at both altitudes to ∼0.25 K day−1 for the GWTSA regardless of whether ν or [ν] is used. For this simulation, the GWTSA using [ν] requires just ∼25% more CPU time than the conventional two-stream approximation.

* Additional affiliation: Atmospheric Science Program, Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada.

Corresponding author address: Dr. Howard Barker, Cloud Physics Research Division, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada.

Abstract

The two primary foci of this note are to assess the ability of the multilayer gamma-weighted two-stream approximation (GWTSA) to compute domain-averaged solar radiative fluxes and to demonstrate how its execution time can be reduced with negligible impact on performance. In addition to the usual parameters needed by a 1D solar code, the GWTSA requires ν ∈ R+, which depends on both the horizontal mean and mean logarithm of cloud water content. Reduced central processing unit (CPU) time is realized by simply rounding ν to the nearest whole number, denoted as [ν]. The experiment reported on here uses 120 fields generated by a 2D cloud-resolving model simulation of an evolving tropical mesoscale convective cloud system. Benchmark calculations are provided by the independent column approximation (ICA), and results are also shown for the conventional two-stream model.

The full GWTSA yields time- and domain-averaged broadband top-of-atmosphere albedo and surface absorptance values of 0.32 and 0.49, which are very close to the ICA values of 0.32 and 0.47. Correspondingly, the GWTSA using [ν] produces 0.34 and 0.46. In contrast, the conventional two-stream’s estimates are 0.56 and 0.20. While mean heating rate errors for the conventional two-stream average about −0.5 K day−1 near the surface and almost +2 K day−1 at 10 km, they are diminished at both altitudes to ∼0.25 K day−1 for the GWTSA regardless of whether ν or [ν] is used. For this simulation, the GWTSA using [ν] requires just ∼25% more CPU time than the conventional two-stream approximation.

* Additional affiliation: Atmospheric Science Program, Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada.

Corresponding author address: Dr. Howard Barker, Cloud Physics Research Division, Meteorological Service of Canada, 4905 Dufferin St., Downsview, ON M3H 5T4, Canada.

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  • Barker, H. W., 1996: A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part I: Methodology and homogeneous biases. J. Atmos. Sci.,53, 2289–2303.

  • ——, and Q. Fu, 1999: Modelling domain-averaged solar fluxes for an evolving tropical cloud system. Atmos. Oceanic Opt.,12, 211–217.

  • ——, B. A. Wielicki, and L. Parker, 1996: A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part II: Validation using satellite data. J. Atmos. Sci.,53, 2304–2316.

  • ——, J.-J. Morcrette, and G. D. Alexander, 1998: Broadband solar fluxes and heating rates for atmospheres with 3D broken clouds. Quart. J. Roy. Meteor. Soc.,124, 1245–1271.

  • ——, G. L. Stephens, and Q. Fu, 1999: The sensitivity of domain-averaged solar fluxes to assumptions about cloud geometry. Quart. J. Roy. Meteor. Soc.,125, 2127–2152.

  • Fu, Q., and K. N. Liou, 1992: On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres. J. Atmos. Sci.,49, 2139–2156.

  • ——, and ——, 1993: Parameterization of the radiative properties of cirrus clouds. J. Atmos. Sci.,50, 2008–2025.

  • ——, S. K. Krueger, and K. N. Liou, 1995: Interactions of radiation and convection in simulated tropical cloud clusters. J. Atmos. Sci.,52, 1310–1328.

  • Gradshteyn, I. S., and I. M. Ryzhik, 1980: Table of Integrals, Series, and Products. Academic Press, 1160 pp.

  • Liou, K. N., 1992: Radiation and Cloud Processes in the Atmosphere. Oxford University Press, 487 pp.

  • McClatchey, R. A., R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, 1972: Optical properties of the atmosphere. 3d ed. AFCRL Rep. 72-0497, 108 pp. [NTIS N7318412.].

  • Meador, W. E., and W. R. Weaver, 1980: Two-stream approximations to radiative transfer in planetary atmospheres: A unified description of existing methods and a new improvement. J. Atmos. Sci.,37, 630–643.

  • Oreopoulos, L., and H. W. Barker, 1999: Accounting for subgrid-scale cloud variability in a multi-layer, 1D solar radiative transfer algorithm. Quart. J. Roy. Meteor. Soc.,125, 301–330.

  • Pincus, R., S. A. McFarlane, and S. A. Klein, 1999: Albedo biases and the horizontal variability of clouds in subtropical marine boundary layers: Observations from ships and satellites. J. Geophys. Res.,104, 6183–6191.

  • Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, 1986: Numerical Recipes. Cambridge University Press, 702 pp.

  • Zdunkowski, W. G., R. M. Welch, and G. Korb, 1980: An investigation of the structure of typical two-stream methods for the calculation of solar fluxes and heating rates in clouds. Beitr. Phys. Atmos.,53, 147–166.

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