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- Author or Editor: Jason N. S. Cole x

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## Abstract

The full-spectrum correlated *k*-distribution (FSCK) method, originally developed for applications in combustion systems, is adapted for use in shortwave atmospheric radiative transfer. By weighting *k* distributions by the solar source function, the FSCK method eliminates the requirement that the Planck function be constant over a spectral interval. As a consequence, integration may be carried out across the full spectrum as long as the assumption of correlation from one atmospheric level to the next remains valid. Problems with the lack of correlation across the full spectrum are removed by partitioning the spectrum at a wavelength of 0.68 *μ*m into two bands. The resulting two-band approach in the FSCK formalism produces broadband rms clear-sky flux and heating rate errors less than 1% and 6%, respectively, relative to monochromatic calculations and requires only 15 quadrature points per layer, which represents a 60%–90% reduction in computation time relative to other models currently in use.

An evaluation of fluxes calculated by the FSCK method in cases with idealized clouds demonstrates that gray cloud scattering in two spectral bands is sufficient to reproduce line-by-line generated fluxes. Two different approaches for modeling absorption by cloud drops were also examined. Explicitly including nongray cloud absorption in solar source function-weighted *k* distributions results in realistic in-cloud heating rates, although in-cloud heating rates were underpredicted by approximately 8%–12% as compared to line-by-line results. A gray cloud absorption parameter chosen to fit line-by-line results optimally for one cloud or atmospheric profile but applied to different cloud combinations or profiles, also closely approximated line-by-line heating rates.

## Abstract

The full-spectrum correlated *k*-distribution (FSCK) method, originally developed for applications in combustion systems, is adapted for use in shortwave atmospheric radiative transfer. By weighting *k* distributions by the solar source function, the FSCK method eliminates the requirement that the Planck function be constant over a spectral interval. As a consequence, integration may be carried out across the full spectrum as long as the assumption of correlation from one atmospheric level to the next remains valid. Problems with the lack of correlation across the full spectrum are removed by partitioning the spectrum at a wavelength of 0.68 *μ*m into two bands. The resulting two-band approach in the FSCK formalism produces broadband rms clear-sky flux and heating rate errors less than 1% and 6%, respectively, relative to monochromatic calculations and requires only 15 quadrature points per layer, which represents a 60%–90% reduction in computation time relative to other models currently in use.

An evaluation of fluxes calculated by the FSCK method in cases with idealized clouds demonstrates that gray cloud scattering in two spectral bands is sufficient to reproduce line-by-line generated fluxes. Two different approaches for modeling absorption by cloud drops were also examined. Explicitly including nongray cloud absorption in solar source function-weighted *k* distributions results in realistic in-cloud heating rates, although in-cloud heating rates were underpredicted by approximately 8%–12% as compared to line-by-line results. A gray cloud absorption parameter chosen to fit line-by-line results optimally for one cloud or atmospheric profile but applied to different cloud combinations or profiles, also closely approximated line-by-line heating rates.

## Abstract

Solar flux densities and heating rates predicted by a broadband, multilayer δ-Eddington two-stream approximation are compared to estimates from a Monte Carlo model that uses detailed descriptions of cloud particle phase functions and facilitates locally nonzero net horizontal flux densities. Results are presented as domain averages for 256-km sections of cloudy atmospheres inferred from A-Train satellite data: 32 632 samples for January 2007 between 70°S and 70°N with total cloud fraction *C* > 0.05. The domains are meant to represent grid cells of a conventional global climate model and consist of columns of infinite width across track and Δ*x* ≈ 1 km along track. The δ-Eddington was applied in independent column approximation (ICA) mode, while the Monte Carlo was applied using both Δ*x* → ∞ (i.e., ICA) and Δ*x* ≈ 1 km. Mean-bias errors due to the δ-Eddington’s neglect of phase function details and horizontal transfer, as functions of cosine of solar zenith angle μ_{0}, are comparable in magnitude and have the same signs.

With minor dependence on cloud particle sizes, the δ-Eddington over- and underestimates top-of-atmosphere reflected flux density for the cloudy portion of domains by ~10 W m^{−2} for μ_{0} > 0.9 and −3 W m^{−2} for μ_{0} < 0.2; full domain averages are ~8 and −2 W m^{−2}, respectively, given mean *C* > 0.75 for all μ_{0}. These errors are reversed in sign, but slightly larger, for net surface flux densities. The δ-Eddington underestimates total atmospheric absorption by ~2.5 W m^{−2} on average. Hence, δ-Eddington mean-bias errors for domain-averaged layer heating rates are usually negative but can be positive. Rarely do they exceed ±10% of the mean heating rate; the largest errors are when the sides of liquid clouds are irradiated by direct beams.

## Abstract

Solar flux densities and heating rates predicted by a broadband, multilayer δ-Eddington two-stream approximation are compared to estimates from a Monte Carlo model that uses detailed descriptions of cloud particle phase functions and facilitates locally nonzero net horizontal flux densities. Results are presented as domain averages for 256-km sections of cloudy atmospheres inferred from A-Train satellite data: 32 632 samples for January 2007 between 70°S and 70°N with total cloud fraction *C* > 0.05. The domains are meant to represent grid cells of a conventional global climate model and consist of columns of infinite width across track and Δ*x* ≈ 1 km along track. The δ-Eddington was applied in independent column approximation (ICA) mode, while the Monte Carlo was applied using both Δ*x* → ∞ (i.e., ICA) and Δ*x* ≈ 1 km. Mean-bias errors due to the δ-Eddington’s neglect of phase function details and horizontal transfer, as functions of cosine of solar zenith angle μ_{0}, are comparable in magnitude and have the same signs.

With minor dependence on cloud particle sizes, the δ-Eddington over- and underestimates top-of-atmosphere reflected flux density for the cloudy portion of domains by ~10 W m^{−2} for μ_{0} > 0.9 and −3 W m^{−2} for μ_{0} < 0.2; full domain averages are ~8 and −2 W m^{−2}, respectively, given mean *C* > 0.75 for all μ_{0}. These errors are reversed in sign, but slightly larger, for net surface flux densities. The δ-Eddington underestimates total atmospheric absorption by ~2.5 W m^{−2} on average. Hence, δ-Eddington mean-bias errors for domain-averaged layer heating rates are usually negative but can be positive. Rarely do they exceed ±10% of the mean heating rate; the largest errors are when the sides of liquid clouds are irradiated by direct beams.

## Abstract

Upper-tropospheric ice cloud measurements from the Superconducting Submillimeter Limb Emission Sounder (SMILES) on the International Space Station (ISS) are used to study the diurnal cycle of upper-tropospheric ice cloud in the tropics and midlatitudes (40°S–40°N) and to quantitatively evaluate ice cloud diurnal variability simulated by 10 climate models. Over land, the SMILES-observed diurnal cycle has a maximum around 1800 local solar time (LST), while the model-simulated diurnal cycles have phases differing from the observed cycle by −4 to 12 h. Over ocean, the observations show much smaller diurnal cycle amplitudes than over land with a peak at 1200 LST, while the modeled diurnal cycle phases are widely distributed throughout the 24-h period. Most models show smaller diurnal cycle amplitudes over ocean than over land, which is in agreement with the observations. However, there is a large spread of modeled diurnal cycle amplitudes ranging from 20% to more than 300% of the observed over both land and ocean. Empirical orthogonal function (EOF) analysis on the observed and model-simulated variations of ice clouds finds that the first EOF modes over land from both observation and model simulations explain more than 70% of the ice cloud diurnal variations and they have similar spatial and temporal patterns. Over ocean, the first EOF from observation explains 26.4% of the variance, while the first EOF from most models explains more than 70%. The modeled spatial and temporal patterns of the leading EOFs over ocean show large differences from observations, indicating that the physical mechanisms governing the diurnal cycle of oceanic ice clouds are more complicated and not well simulated by the current climate models.

## Abstract

Upper-tropospheric ice cloud measurements from the Superconducting Submillimeter Limb Emission Sounder (SMILES) on the International Space Station (ISS) are used to study the diurnal cycle of upper-tropospheric ice cloud in the tropics and midlatitudes (40°S–40°N) and to quantitatively evaluate ice cloud diurnal variability simulated by 10 climate models. Over land, the SMILES-observed diurnal cycle has a maximum around 1800 local solar time (LST), while the model-simulated diurnal cycles have phases differing from the observed cycle by −4 to 12 h. Over ocean, the observations show much smaller diurnal cycle amplitudes than over land with a peak at 1200 LST, while the modeled diurnal cycle phases are widely distributed throughout the 24-h period. Most models show smaller diurnal cycle amplitudes over ocean than over land, which is in agreement with the observations. However, there is a large spread of modeled diurnal cycle amplitudes ranging from 20% to more than 300% of the observed over both land and ocean. Empirical orthogonal function (EOF) analysis on the observed and model-simulated variations of ice clouds finds that the first EOF modes over land from both observation and model simulations explain more than 70% of the ice cloud diurnal variations and they have similar spatial and temporal patterns. Over ocean, the first EOF from observation explains 26.4% of the variance, while the first EOF from most models explains more than 70%. The modeled spatial and temporal patterns of the leading EOFs over ocean show large differences from observations, indicating that the physical mechanisms governing the diurnal cycle of oceanic ice clouds are more complicated and not well simulated by the current climate models.