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David P. Kratz, Ming-Dah Chou, and Michael M-H. Yan

Abstract

Fast and accurate parameterizations have been developed for the transmission functions of the CO2 9.4- and 10.4-μm bands, as well as the CFC-11, CFC-12, and CFC-22 bands located in the 8-12-μm region. The parameterizations are based on line-by-line calculations of transmission functions for the CO2 bands and on high spectral resolution laboratory measurements of the absorption coefficients for the CFC bands. Also developed are the parameterizations for the H2O transmission functions for the corresponding spectral bands. Compared to the high-resolution calculations, fluxes at the tropopause computed with the parameterizations are accurate to within 10% when overlapping of gas absorptions within a band is taken into account. For individual gas absorption, the accuracy is of order 0%–2%.

The climatic effects of these trace gases have been studied using a zonally averaged multilayer energy balance model, which includes seasonal cycles and a simplified deep ocean. With the trace gas abundances taken to follow the Intergovernmental Panel on Climate Change Low Emissions “B” scenario, the transient response of the surface temperature is simulated for the period 1900–2060. The minor CO2 and CFC bands contribute about 20%–25% of the total warming at the surface, which is comparable to the contribution from the CH4 and N2O bands. Collectively, these minor absorption bands account for 40%–45% of the total surface temperature increases. Thus, the climate warming due to absorption in these bands is comparable to that in the 15-μm CO2 band.

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Ming-Dah Chou, William L. Ridgway, and Michael M-H. Yan

Abstract

Water vapor contributes a maximum of 1°C/day to the middle atmospheric thermal infrared (IR) cooling. This magnitude is small but not negligible. Because of the small amount of mass involved and the extremely narrow molecular absorption lines at pressures less than 1 mb, only a few existing parameterizations can compute accurately the water vapor cooling in this region. The accuracy and efficiency of two IR parameterizations are examined in this study. One is the correlated-k distribution method, and the other is the table look-up using precomputed transmission functions. Both methods can accurately compute the cooling rate from the earth's surface to 0.01 mb with an error of only a few percent. The contribution to the cooling rate at pressures <1 mb comes from a very small fraction (<0.005) of the spectrum near the centers of the absorption bands, where the absorption coefficient varies by four orders of magnitude. It requires at least 100 terms of the k-distribution function to accurately compute the cooling profile. The method of table look-up is, therefore, much faster than the correlated-k distribution method for computing the water vapor cooling profile involving both the middle and lower atmospheres.

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Ming-Dah Chou, William L. Ridgway, and Michael M-H. Yan

Abstract

A medium-sized band model for water vapor and CO2 absorption is developed using the one-parameter scaling approximation. The infrared spectrum is divided into 10 bands. The Planck-weighted diffuse transmittance is reduced to a function dependent only upon the scaled absorber amount and fit by an exponential sum. By selecting specific sets of absorption coefficients for exponential-sum fitting, computations of fluxes and cooling rate are made very fast. Compared to a broadband model, the accuracy, speed, and versatility are all enhanced. With absorption due to water vapor line, continuum, CO2 as well as O3 included, the parameterization introduces an error of < 1.5 W m−2 in fluxes and <0.15°C day−1 in the tropospheric and lower stratospheric cooling rates.

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Ming-Dah Chou, Max J. Suarez, Chang-Hoi Ho, Michael M-H. Yan, and Kyu-Tae Lee

Abstract

Parameterizations for cloud single-scattering properties and the scaling of optical thickness in a partial cloudiness condition have been developed for use in atmospheric models. Cloud optical properties are parameterized for four broad bands in the solar (or shortwave) spectrum; one in the ultraviolet and visible region and three in the infrared region. The extinction coefficient, single-scattering albedo, and asymmetry factor are parameterized separately for ice and water clouds. Based on high spectral-resolution calculations, the effective single-scattering coalbedo of a broad band is determined such that errors in the fluxes at the top of the atmosphere and at the surface are minimized. This parameterization introduces errors of a few percent in the absorption of shortwave radiation in the atmosphere and at the surface.

Scaling of the optical thickness is based on the maximum-random cloud-overlapping approximation. The atmosphere is divided into three height groups separated approximately by the 400- and 700-mb levels. Clouds are assumed maximally overlapped within each height group and randomly overlapped among different groups. The scaling is applied only to the maximally overlapped cloud layers in individual height groups. The scaling as a function of the optical thickness, cloud amount, and the solar zenith angle is derived from detailed calculations and empirically adjusted to minimize errors in the fluxes at the top of the atmosphere and at the surface. Different scaling is used for direct and diffuse radiation. Except for a large solar zenith angle, the error in fluxes introduced by the scaling is only a few percent. In terms of absolute error, it is within a few watts per square meter.

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