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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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Roger Davies, William L. Ridgway, and Kyung-Eak Kim

Abstract

The spectral of solar radiation in typical water clouds is determined using a radiative transfer model based on LOWTRAN transmission functions at a 20 cm−1 resolution and Monte Carlo simulations of photon pathlength distributions. Relative absorption by the vapor and droplets within each cloud is obtained, and both plane-parallel and horizontally finite clouds are considered.

Results indicate slightly lower absorption than found previously, with boundary layer clouds typically absorbing 9% of the extraterrestrial insolation for overhead sun. Cloud absorption depends strongly on the presence of water vapor above the cloud top and solar zenith angle, moderately on cloud aspect ratio, and (provided the cloud is neither tenuous nor broken) weakly on cloud type and thickness. The droplets, not the vapor, are shown to be the dominant absorbers within the cloud, except in the absence of water vapor above the cloud top, in which case the vapor and droplets make similar contributions to the low cloud absorption. For many of the cases modeled, the sum of the cloud and atmospheric absorption remained invariant, allowing the net solar radiation budget at the surface to be deduced from broadband satellite measurements of albedo. An explanation for this behavior is found in the analysis of the spectral absorption by the different components.

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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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Robert F. Cahalan, William Ridgway, Warren J. Wiscombe, Thomas L. Bell, and Jack B. Snider

Abstract

An increase in the planetary albedo of the earth-atmosphere system by only 10% can decrease the equilibrium surface temperature to that of the last ice age. Nevertheless, albedo biases of 10% or greater would be introduced into large regions of current climate models if clouds were given their observed liquid water amounts, because of the treatment of clouds as plane parallel. Past work has addressed the effect of cloud shape on albedo; here the focus is on the within-cloud variability of the vertically integrated liquid water. The main result is an estimate of the “plane-parallel albedo bias” using the “independent pixel approximation,” which ignores net horizontal photon transport, from a simple fractal model of marine stratocumulus clouds that ignores the cloud shape. The use of the independent pixel approximation in this context will be justified in a separate Monte Carlo study.

The focus on marine stratocumulus clouds is due to their important role in cloud radiative forcing and also that, of the wide variety of earth's cloud types, they are most nearly plane parallel, so that they have the least albedo bias. The fractal model employed here reproduces both the probability distribution and the wavenumber spectrum of the stratocumulus liquid water path, as observed during the First ISCCP Regional Experiment (FIRE). The model distributes the liquid water by a cascade process, related to the upscale cascade of energy transferred from the cloud thickness scale to the mesoscale by approximately 2D motions. For simplicity, the cloud microphysical parameters are assumed homogeneous, as is the geometrical cloud thickness; and the mesoscale-averaged vertical optical thickness is kept fixed at each step of the cascade. A single new fractal parameter, 0 ≤ f ≤ 1, is introduced and determined empirically by the variance of the logarithm of the vertically integrated liquid water. In the case of conservative scattering, the authors are able to estimate the albedo bias analytically as a function of the fractal parameter f, mean vertical optical thickness Tν, and sun angle θ. Typical observed values are f = 0.5, Tν = 15, and θ = 60°, which give an absolute bias of 0.09, or a relative bias equal to 15% of the plane-parallel albedo of 0.60. The reduced reflectivity of fractal stratocumulus clouds is approximately given by the plane-parallel reflectivity evaluated at a reduced “effective optical thickness,” which when f = 0.5 is T eff ≈ 10.

Study of the diurnal cycle of stratocumulus liquid water during FIRE leads to a key unexpected result: the plane-parallel albedo bias is largest when the cloud fraction reaches 100%, that is, when any bias associated with the cloud fraction vanishes. This is primarily due to the variability increase with cloud fraction. Thus, the within-cloud fractal structure of stratocumulus has a more significant impact on estimates of its mesoscale-average albedo than does the cloud fraction.

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