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## Abstract

Hourly measurements of particulate matter that is smaller than 2.5 *μ*m in diameter (PM_{2.5}) have been made at air-monitoring sites in Hamilton and Burlington, Ontario, Canada, since 2003. These sites are separated by ~6 km; Burlington is right on Lake Ontario while Hamilton has, directly to the east, very heavy industry between it and Lake Ontario. Hence, by taking the difference between measurements at Hamilton and Burlington, it is possible to isolate, during east-wind conditions, PM_{2.5} that result from emissions from the industrial sectors (primarily steel mills) located in Hamilton’s northeast end. After screening the data for east winds off Lake Ontario, it was found that median background values of PM_{2.5}, of 5–10 *μ*g m^{−3} are increased by an additional 5–10 *μ*g m^{−3} by emissions from local sources. On the contrary, however, industrial contributions to PM_{2.5} in Burlington during south winds are much smaller at ~3 *μ*g m^{−3} (industrial sectors are due south of Burlington). This difference is likely due either to wind direction–dependent local circulation patterns or to alignment of sources that can concentrate PM_{2.5} into Hamilton. It was also found that throughout much of 2009, but especially during spring and early summer, the industrial contribution of PM_{2.5} at Hamilton was reduced relative to other years by amounts that are statistically significant at the 95% confidence level, even when measurements are augmented with large amounts of Gaussian noise. These reductions are consistent with documented reductions in steel production during the global economic crisis that peaked in the first half of 2009.

## Abstract

Hourly measurements of particulate matter that is smaller than 2.5 *μ*m in diameter (PM_{2.5}) have been made at air-monitoring sites in Hamilton and Burlington, Ontario, Canada, since 2003. These sites are separated by ~6 km; Burlington is right on Lake Ontario while Hamilton has, directly to the east, very heavy industry between it and Lake Ontario. Hence, by taking the difference between measurements at Hamilton and Burlington, it is possible to isolate, during east-wind conditions, PM_{2.5} that result from emissions from the industrial sectors (primarily steel mills) located in Hamilton’s northeast end. After screening the data for east winds off Lake Ontario, it was found that median background values of PM_{2.5}, of 5–10 *μ*g m^{−3} are increased by an additional 5–10 *μ*g m^{−3} by emissions from local sources. On the contrary, however, industrial contributions to PM_{2.5} in Burlington during south winds are much smaller at ~3 *μ*g m^{−3} (industrial sectors are due south of Burlington). This difference is likely due either to wind direction–dependent local circulation patterns or to alignment of sources that can concentrate PM_{2.5} into Hamilton. It was also found that throughout much of 2009, but especially during spring and early summer, the industrial contribution of PM_{2.5} at Hamilton was reduced relative to other years by amounts that are statistically significant at the 95% confidence level, even when measurements are augmented with large amounts of Gaussian noise. These reductions are consistent with documented reductions in steel production during the global economic crisis that peaked in the first half of 2009.

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## Abstract

A 1D infrared radiative transfer model that handles clouds with subgrid-scale horizontal variability is developed and tested. It assumes that fluctuations in cloud absorptance optical depth *κ* across layers (and collections of layers) can be described by gamma distributions. Unlike homogeneous clouds, flux incident at a level inside a horizontally inhomogeneous cloud requires explicit computation of transmittance to all other levels in the cloud. Consequently, in addition to estimates of variability for each layer, variability between any two levels must be specified too. Scattering by hydrometeors and a general treatment of cloud overlap are included in this model. Solutions for isothermal and nonisothermal Planck source functions are presented.

For the synthetic cloudy atmospheres used here, the new model produces errors for outgoing longwave radiation (OLR) and cloud cooling rates that are typically more than an order of magnitude smaller than those associated with the conventional homogeneous cloud model (as used in all GCMs at present). It is shown that up- and downwelling fluxes and cloud cooling rates can depend much on subgrid-scale variability. For high overcast clouds with realistic variability, OLR can be up to 20 W m^{−2} more than that predicted by a conventional homogeneous model using the same mean *κ.* At the same time, cooling rate errors at cloud top and cloud base due to the homogeneous assumption can be up to ±25%; the sign depending primarily on mean *κ* and magnitude of variability. For lower, thicker clouds, the homogeneous assumption leads primarily to errors in cloud-top cooling. The new code usually remedies these errors greatly. This model, and its solar counterpart, are used currently in the Canadian Centre for Climate Modelling and Analysis GCM.

## Abstract

A 1D infrared radiative transfer model that handles clouds with subgrid-scale horizontal variability is developed and tested. It assumes that fluctuations in cloud absorptance optical depth *κ* across layers (and collections of layers) can be described by gamma distributions. Unlike homogeneous clouds, flux incident at a level inside a horizontally inhomogeneous cloud requires explicit computation of transmittance to all other levels in the cloud. Consequently, in addition to estimates of variability for each layer, variability between any two levels must be specified too. Scattering by hydrometeors and a general treatment of cloud overlap are included in this model. Solutions for isothermal and nonisothermal Planck source functions are presented.

For the synthetic cloudy atmospheres used here, the new model produces errors for outgoing longwave radiation (OLR) and cloud cooling rates that are typically more than an order of magnitude smaller than those associated with the conventional homogeneous cloud model (as used in all GCMs at present). It is shown that up- and downwelling fluxes and cloud cooling rates can depend much on subgrid-scale variability. For high overcast clouds with realistic variability, OLR can be up to 20 W m^{−2} more than that predicted by a conventional homogeneous model using the same mean *κ.* At the same time, cooling rate errors at cloud top and cloud base due to the homogeneous assumption can be up to ±25%; the sign depending primarily on mean *κ* and magnitude of variability. For lower, thicker clouds, the homogeneous assumption leads primarily to errors in cloud-top cooling. The new code usually remedies these errors greatly. This model, and its solar counterpart, are used currently in the Canadian Centre for Climate Modelling and Analysis GCM.

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## Abstract

A new radiation scheme is proposed that uses the correlated-*k* distribution (CKD) method. The definition of the *k*-distribution function, the transformation between frequency space and *k* space, and the upper limit of the absorption coefficient in cumulative probability space (CPS) are discussed. The corresponding relation between each interval in CPS and the heating rate profile provides a method for determining the width of intervals in CPS. Three schemes are discussed for handling the spectral overlap of gases. Method 1 rearranges the appropriate combination of gaseous absorption coefficients when the spectral overlap of two gases is extensive. Method 2 applies to most overlapping gases and addresses the most important aspects of each gas’s spectrum in each interval of CPS. Method 3 applies to weak gases only and seeks to adjust the main absorption coefficients in order that radiative forcing at the surface and the top of the atmosphere is correct. This model is quite efficient because 1) relatively few intervals in CPS are used (up to 1 mb, only 35 intervals for solar radiation, and 46 for infrared); 2) for some intervals with very large absorption coefficients, the radiative transfer process is simplified by ignoring scattering; 3) the water vapor continuum is dealt with efficiently by neglecting its effect in some nonimportant intervals in CPS and at high altitudes; and 4) gaseous overlap methods are simple and effective. Moreover, this model contains a proper treatment of spectral overlap between solar and infrared radiation. For both solar and infrared radiation, heating rate errors are generally less than 0.2 K day^{−1}, and errors in flux at the surface and the top of the atmosphere are generally less than 1 W m^{−2}.

## Abstract

A new radiation scheme is proposed that uses the correlated-*k* distribution (CKD) method. The definition of the *k*-distribution function, the transformation between frequency space and *k* space, and the upper limit of the absorption coefficient in cumulative probability space (CPS) are discussed. The corresponding relation between each interval in CPS and the heating rate profile provides a method for determining the width of intervals in CPS. Three schemes are discussed for handling the spectral overlap of gases. Method 1 rearranges the appropriate combination of gaseous absorption coefficients when the spectral overlap of two gases is extensive. Method 2 applies to most overlapping gases and addresses the most important aspects of each gas’s spectrum in each interval of CPS. Method 3 applies to weak gases only and seeks to adjust the main absorption coefficients in order that radiative forcing at the surface and the top of the atmosphere is correct. This model is quite efficient because 1) relatively few intervals in CPS are used (up to 1 mb, only 35 intervals for solar radiation, and 46 for infrared); 2) for some intervals with very large absorption coefficients, the radiative transfer process is simplified by ignoring scattering; 3) the water vapor continuum is dealt with efficiently by neglecting its effect in some nonimportant intervals in CPS and at high altitudes; and 4) gaseous overlap methods are simple and effective. Moreover, this model contains a proper treatment of spectral overlap between solar and infrared radiation. For both solar and infrared radiation, heating rate errors are generally less than 0.2 K day^{−1}, and errors in flux at the surface and the top of the atmosphere are generally less than 1 W m^{−2}.

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## Abstract

Monte Carlo simulations of solar radiative transfer were performed for a well-resolved, large, three-dimensional (3D) domain of boundary layer cloud simulated by a cloud-resolving model. In order to represent 3D distributions of optical properties for ∼2 × 10^{6} cloudy cells, attenuation by droplets was handled by assigning each cell a cumulative distribution of extinction derived from either a model or an assumed discrete droplet size spectrum. This minimizes the required number of detailed phase functions. Likewise, to simulate statistically significant, high-resolution imagery, it was necessary to apply variance reduction techniques. Three techniques were developed for use with the local estimation method of computing reflectance *ρ.* First, small fractions of *ρ* come from numerous, small contributions of *ζ* computed at each scattering event. Terminating calculation of *ζ* when it falls below *ζ*
_{min} ≈ 10^{−3} was found to impact estimates of *ρ* minimally but reduced computation time by ∼10%. Second, large fractions of *ρ* come from infrequent realizations of large *ζ.* When sampled poorly, they boost Monte Carlo noise significantly. Removing *ζ* − *ζ*
_{max}, storing them in a domainwide reservoir, adding *ζ*
_{max} to local estimates of *ρ,* and, at simulation's end, distributing the reservoir across the domain in proportion to local *ρ,* tends to reduce variance much. This regionalization technique works well when the number of photons per unit area is small (nominally ≲ 50 000). A value of *ζ*
_{max} ≈ 100 reduces variance of *ρ* greatly with little impact on estimates of *ρ.* Third, if *ζ* are computed using exact (e.g., Mie) phase functions for the first *N* scattering events, and thereafter a blunt-nosed corresponding phase function (e.g., Henyey–Greenstein) is used, production of large *ζ* is thwarted resulting in reduced variance and time required to achieve accurate estimates of *ρ.*

## Abstract

Monte Carlo simulations of solar radiative transfer were performed for a well-resolved, large, three-dimensional (3D) domain of boundary layer cloud simulated by a cloud-resolving model. In order to represent 3D distributions of optical properties for ∼2 × 10^{6} cloudy cells, attenuation by droplets was handled by assigning each cell a cumulative distribution of extinction derived from either a model or an assumed discrete droplet size spectrum. This minimizes the required number of detailed phase functions. Likewise, to simulate statistically significant, high-resolution imagery, it was necessary to apply variance reduction techniques. Three techniques were developed for use with the local estimation method of computing reflectance *ρ.* First, small fractions of *ρ* come from numerous, small contributions of *ζ* computed at each scattering event. Terminating calculation of *ζ* when it falls below *ζ*
_{min} ≈ 10^{−3} was found to impact estimates of *ρ* minimally but reduced computation time by ∼10%. Second, large fractions of *ρ* come from infrequent realizations of large *ζ.* When sampled poorly, they boost Monte Carlo noise significantly. Removing *ζ* − *ζ*
_{max}, storing them in a domainwide reservoir, adding *ζ*
_{max} to local estimates of *ρ,* and, at simulation's end, distributing the reservoir across the domain in proportion to local *ρ,* tends to reduce variance much. This regionalization technique works well when the number of photons per unit area is small (nominally ≲ 50 000). A value of *ζ*
_{max} ≈ 100 reduces variance of *ρ* greatly with little impact on estimates of *ρ.* Third, if *ζ* are computed using exact (e.g., Mie) phase functions for the first *N* scattering events, and thereafter a blunt-nosed corresponding phase function (e.g., Henyey–Greenstein) is used, production of large *ζ* is thwarted resulting in reduced variance and time required to achieve accurate estimates of *ρ.*

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## Abstract

Overcast cloud optical depths *τ* are inferred from hourly, broadband surface pyranometer measurements of global irradiance for 21 Canadian stations. A radiative transfer model that treats the atmosphere as plane-parallel and horizontally homogeneous is used so inferred *τ* are *effective* values that should resemble those used by GCM radiation routines. Results are presented mostly for June, July, and August (JJA), thus minimizing the impact of surface albedo errors that arise from unreported sea–ice and ground snow. Measurement periods for several sites exceed 20 yr. Frequency distributions of *τ* for JJA can be described well by gamma distributions with mean values *τ*
*τ*
*τ* (dayside) are negligible for most sites but exceed 5 for some. There is some evidence of weak, yet occasionally significant, increases in monthly mean *τ* from the late 1960s to early 1990s. Annual results for four coastal sites exhibit maximum monthly mean *τ* during autumn.

The International Satellite Cloud Climatology Project (ISCCP)-CX optical depths *τ*
_{sat} (means of ∼10 km cloudy pixel values inside 1° × 1° cells centered roughly on pyranometers) are compared with collocated surface-inferred values *τ*
_{srf} (means of two hourly values that flank ISCCP snapshots). Data for JJA of 1989 at a continental and a maritime site are considered. For the majority of cases, 1.25 < *τ*
_{srf}/*τ*
_{sat} < 2.25 echoes an independent study. Many occurrences of *τ*
_{sat} ≪ *τ*
_{srf} have ISCCP IR temperatures >273 K so cloud phase is not an issue. Moreover, for most of these cases, variances for the 10-km pixel optical depths suggest weak horizontal variability of cloud. A full explanation of this systematic discrepancy is beyond the scope of this study.

## Abstract

Overcast cloud optical depths *τ* are inferred from hourly, broadband surface pyranometer measurements of global irradiance for 21 Canadian stations. A radiative transfer model that treats the atmosphere as plane-parallel and horizontally homogeneous is used so inferred *τ* are *effective* values that should resemble those used by GCM radiation routines. Results are presented mostly for June, July, and August (JJA), thus minimizing the impact of surface albedo errors that arise from unreported sea–ice and ground snow. Measurement periods for several sites exceed 20 yr. Frequency distributions of *τ* for JJA can be described well by gamma distributions with mean values *τ*
*τ*
*τ* (dayside) are negligible for most sites but exceed 5 for some. There is some evidence of weak, yet occasionally significant, increases in monthly mean *τ* from the late 1960s to early 1990s. Annual results for four coastal sites exhibit maximum monthly mean *τ* during autumn.

The International Satellite Cloud Climatology Project (ISCCP)-CX optical depths *τ*
_{sat} (means of ∼10 km cloudy pixel values inside 1° × 1° cells centered roughly on pyranometers) are compared with collocated surface-inferred values *τ*
_{srf} (means of two hourly values that flank ISCCP snapshots). Data for JJA of 1989 at a continental and a maritime site are considered. For the majority of cases, 1.25 < *τ*
_{srf}/*τ*
_{sat} < 2.25 echoes an independent study. Many occurrences of *τ*
_{sat} ≪ *τ*
_{srf} have ISCCP IR temperatures >273 K so cloud phase is not an issue. Moreover, for most of these cases, variances for the 10-km pixel optical depths suggest weak horizontal variability of cloud. A full explanation of this systematic discrepancy is beyond the scope of this study.

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## Abstract

The Earth Clouds, Aerosol and Radiation Explorer (EarthCARE) satellite’s Broadband Radiometer (BBR) consists of three telescopes and a rotating chopper drum (CD). Together they yield alternating measurements of total wave (TW; 0.25 to >50 *μ*m) and shortwave (SW; 0.25–4 *μ*m) radiances with point spread functions that translate to ^{2} domains. Correspondingly, the average longwave (LW) radiances are the differences between TW and SW averages. It is shown that impacts on domain-average nadir radiances resulting from alternating samples of TW and SW signals for realistic cloudy atmospheres are sensitive to the variance of cloudy-sky radiances, CD rotation rate, and along-track length of averaging domains. Over domains measuring 5 × 21 km^{2} and at a 50% rotation rate, uncertainties reached up to 3.2 and 4.1 W m^{−2} sr^{−1} for SW and TW radiances, respectively. The BBR’s design allows for in-flight alteration of the CD rate. An approximate method is provided for estimating SW and LW uncertainties resulting from the CD rate. While the nominal rotation rate meets EarthCARE’s mission requirements, reducing below

## Abstract

The Earth Clouds, Aerosol and Radiation Explorer (EarthCARE) satellite’s Broadband Radiometer (BBR) consists of three telescopes and a rotating chopper drum (CD). Together they yield alternating measurements of total wave (TW; 0.25 to >50 *μ*m) and shortwave (SW; 0.25–4 *μ*m) radiances with point spread functions that translate to ^{2} domains. Correspondingly, the average longwave (LW) radiances are the differences between TW and SW averages. It is shown that impacts on domain-average nadir radiances resulting from alternating samples of TW and SW signals for realistic cloudy atmospheres are sensitive to the variance of cloudy-sky radiances, CD rotation rate, and along-track length of averaging domains. Over domains measuring 5 × 21 km^{2} and at a 50% rotation rate, uncertainties reached up to 3.2 and 4.1 W m^{−2} sr^{−1} for SW and TW radiances, respectively. The BBR’s design allows for in-flight alteration of the CD rate. An approximate method is provided for estimating SW and LW uncertainties resulting from the CD rate. While the nominal rotation rate meets EarthCARE’s mission requirements, reducing below

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## Abstract

The Monte Carlo Independent Column Approximation (McICA) method for computing domain-average radiative fluxes is unbiased with respect to the full ICA, but its flux estimates contain conditional random noise. Results for five experiments are used to assess the impact of McICA-related noise on simulations of global climate made by the NCAR Community Atmosphere Model (CAM). The experiment with the least noise (an order of magnitude below that of basic McICA) is taken as the reference. Two additional experiments help demonstrate how the impact of noise depends on the time interval between calls to the radiation code. Each experiment is an ensemble of seven 15-month simulations.

Experiments with very high noise levels feature significant reductions to cloudiness in the lowermost model layer over tropical oceans as well as changes in highly related quantities. This bias appears immediately, stabilizes after a couple of model days, and appears to stem from nonlinear interactions between clouds and radiative heating. Outside the Tropics, insignificant differences prevail. When McICA sampling is confined to cloudy subcolumns and when, on average, 50% more samples, relative to basic McICA, are drawn for selected spectral intervals, McICA noise is much reduced and the results of the simulation are almost statistically indistinguishable from the reference. This is true both for mean fields and for the nature of fluctuations on scales ranging from 1 day to at least 30 days.

While calling the radiation code once every 3 h instead of every hour allows the CAM additional time to incorporate McICA-related noise, the impact of noise is enhanced only slightly. In contrast, changing the radiative time step by itself produces effects that generally exceed the impact of McICA’s noise.

## Abstract

The Monte Carlo Independent Column Approximation (McICA) method for computing domain-average radiative fluxes is unbiased with respect to the full ICA, but its flux estimates contain conditional random noise. Results for five experiments are used to assess the impact of McICA-related noise on simulations of global climate made by the NCAR Community Atmosphere Model (CAM). The experiment with the least noise (an order of magnitude below that of basic McICA) is taken as the reference. Two additional experiments help demonstrate how the impact of noise depends on the time interval between calls to the radiation code. Each experiment is an ensemble of seven 15-month simulations.

Experiments with very high noise levels feature significant reductions to cloudiness in the lowermost model layer over tropical oceans as well as changes in highly related quantities. This bias appears immediately, stabilizes after a couple of model days, and appears to stem from nonlinear interactions between clouds and radiative heating. Outside the Tropics, insignificant differences prevail. When McICA sampling is confined to cloudy subcolumns and when, on average, 50% more samples, relative to basic McICA, are drawn for selected spectral intervals, McICA noise is much reduced and the results of the simulation are almost statistically indistinguishable from the reference. This is true both for mean fields and for the nature of fluctuations on scales ranging from 1 day to at least 30 days.

While calling the radiation code once every 3 h instead of every hour allows the CAM additional time to incorporate McICA-related noise, the impact of noise is enhanced only slightly. In contrast, changing the radiative time step by itself produces effects that generally exceed the impact of McICA’s noise.

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## Abstract

A method is introduced for inferring cloud optical depth *τ* from solar radiometric measurements made on an aircraft at altitude *z.* It is assessed using simulated radiometric measurements produced by a 3D Monte Carlo algorithm acting on fields of broken boundary layer clouds generated from Landsat imagery and a cloud-resolving model. The method uses upwelling flux and downwelling zenith radiance measured at two solar wavelengths where atmospheric optical properties above *z* are very similar but optical properties of the surface–atmosphere system below *z* differ. This enables estimation of cloud reflectance into nadir for upwelling diffuse flux and, finally, *τ* above *z.* An approximate one-dimensional radiative Green's function is used to roughly account for horizontal transport of photons in all, even broken, clouds. This method is compared to its surface-based counterpart and shown to be superior. Most notably, the aircraft-based approach deals easily with inhomogeneous land surfaces, is less susceptible to poor sampling, and need not account for aerosol below *z.*

The algorithm appears as though it will have little difficulty inferring high-resolution time series of *τ* ≲ 40 for most (single layer) clouds. For larger values of *τ,* biases emerge; particularly, underestimation for the statistically infrequent interiors of cumuliform clouds as photon leakage through cloud sides is not addressed. For the cumuliform and stratiform clouds used here, mean bias errors for retrieved *τ* are ∼1 (or ∼15%) and ∼0.3 (or ∼3%), respectively. For stratiform clouds with textured bases, performance is likely to improve slightly for flights just up from mean cloud base.

## Abstract

A method is introduced for inferring cloud optical depth *τ* from solar radiometric measurements made on an aircraft at altitude *z.* It is assessed using simulated radiometric measurements produced by a 3D Monte Carlo algorithm acting on fields of broken boundary layer clouds generated from Landsat imagery and a cloud-resolving model. The method uses upwelling flux and downwelling zenith radiance measured at two solar wavelengths where atmospheric optical properties above *z* are very similar but optical properties of the surface–atmosphere system below *z* differ. This enables estimation of cloud reflectance into nadir for upwelling diffuse flux and, finally, *τ* above *z.* An approximate one-dimensional radiative Green's function is used to roughly account for horizontal transport of photons in all, even broken, clouds. This method is compared to its surface-based counterpart and shown to be superior. Most notably, the aircraft-based approach deals easily with inhomogeneous land surfaces, is less susceptible to poor sampling, and need not account for aerosol below *z.*

The algorithm appears as though it will have little difficulty inferring high-resolution time series of *τ* ≲ 40 for most (single layer) clouds. For larger values of *τ,* biases emerge; particularly, underestimation for the statistically infrequent interiors of cumuliform clouds as photon leakage through cloud sides is not addressed. For the cumuliform and stratiform clouds used here, mean bias errors for retrieved *τ* are ∼1 (or ∼15%) and ∼0.3 (or ∼3%), respectively. For stratiform clouds with textured bases, performance is likely to improve slightly for flights just up from mean cloud base.

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## Abstract

A new radiation package, “McRad,” has become operational with cycle 32R2 of the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). McRad includes an improved description of the land surface albedo from Moderate Resolution Imaging Spectroradiometer (MODIS) observations, the Monte Carlo independent column approximation treatment of the radiative transfer in clouds, and the Rapid Radiative Transfer Model shortwave scheme. The impact of McRad on year-long simulations at *T*
_{
L
}159*L*91 and higher-resolution 10-day forecasts is then documented. McRad is shown to benefit the representation of most parameters over both shorter and longer time scales, relative to the previous operational version of the radiative transfer schemes. At all resolutions, McRad improves the representation of the cloud–radiation interactions, particularly in the tropical regions, with improved temperature and wind objective scores through a reduction of some systematic errors in the position of tropical convection as a result of a change in the overall distribution of diabatic heating over the vertical plane, inducing a geographical redistribution of the centers of convection. Although smaller, the improvement is also seen in the rmse of geopotential in the Northern and Southern Hemispheres and over Europe. Given the importance of cloudiness in modulating the radiative fluxes, the sensitivity of the model to cloud overlap assumption (COA) is also addressed, with emphasis on the flexibility that is inherent to this new RT approach when dealing with COA. The sensitivity of the forecasts to the space interpolation that is required to efficiently address the high computational cost of the RT parameterization is also revisited. A reduction of the radiation grid for the Ensemble Prediction System is shown to be of little impact on the scores while reducing the computational cost of the radiation computations. McRad is also shown to decrease the cold bias in ocean surface temperature in climate integrations with a coupled ocean system.

## Abstract

A new radiation package, “McRad,” has become operational with cycle 32R2 of the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). McRad includes an improved description of the land surface albedo from Moderate Resolution Imaging Spectroradiometer (MODIS) observations, the Monte Carlo independent column approximation treatment of the radiative transfer in clouds, and the Rapid Radiative Transfer Model shortwave scheme. The impact of McRad on year-long simulations at *T*
_{
L
}159*L*91 and higher-resolution 10-day forecasts is then documented. McRad is shown to benefit the representation of most parameters over both shorter and longer time scales, relative to the previous operational version of the radiative transfer schemes. At all resolutions, McRad improves the representation of the cloud–radiation interactions, particularly in the tropical regions, with improved temperature and wind objective scores through a reduction of some systematic errors in the position of tropical convection as a result of a change in the overall distribution of diabatic heating over the vertical plane, inducing a geographical redistribution of the centers of convection. Although smaller, the improvement is also seen in the rmse of geopotential in the Northern and Southern Hemispheres and over Europe. Given the importance of cloudiness in modulating the radiative fluxes, the sensitivity of the model to cloud overlap assumption (COA) is also addressed, with emphasis on the flexibility that is inherent to this new RT approach when dealing with COA. The sensitivity of the forecasts to the space interpolation that is required to efficiently address the high computational cost of the RT parameterization is also revisited. A reduction of the radiation grid for the Ensemble Prediction System is shown to be of little impact on the scores while reducing the computational cost of the radiation computations. McRad is also shown to decrease the cold bias in ocean surface temperature in climate integrations with a coupled ocean system.

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## Abstract

A 3D broadband solar radiative transfer scheme is formulated by integrating a Monte Carlo photon transport algorithm with the Fu–Liou radiation model. It is applied to fields of tropical mesoscale convective clouds and subtropical marine boundary layer clouds that were generated by a 2D cloud-resolving model. The effects of cloud geometry on the radiative energy budget are examined by comparing the full-resolution Monte Carlo results with those from the independent column approximation (ICA) that applies the plane-parallel radiation model to each column.

For the tropical convective cloud system, it is found that cloud geometry effects always enhance atmospheric solar absorption regardless of solar zenith angle. In a large horizontal domain (512 km), differences in domain-averaged atmospheric absorption between the Monte Carlo and the ICA are less than 4 W m^{−2} in the daytime. However, for a smaller domain (e.g., 75 km) containing a cluster of deep convective towers, domain-averaged absorption can be enhanced by more than 20 W m^{−2}. For a subtropical marine boundary layer cloud system during the stratus-to-cumulus transition, calculations show that the ICA works very well for domain-averaged fluxes of the stratocumulus cloud fields even for a very small domain (4.8 km). For the trade cumulus cloud field, the effects of cloud sides and horizontal transport of photons become more significant. Calculations have also been made for both cloud systems including black carbon aerosol and a water vapor continuum. It is found that cloud geometry produces no discernible effects on the absorption enhancement due to the black carbon aerosol and water vapor continuum.

The current study indicates that the atmospheric absorption enhancement due to cloud-related 3D photon transport is small. This enhancement could not explain the excess absorption suggested by recent studies.

## Abstract

A 3D broadband solar radiative transfer scheme is formulated by integrating a Monte Carlo photon transport algorithm with the Fu–Liou radiation model. It is applied to fields of tropical mesoscale convective clouds and subtropical marine boundary layer clouds that were generated by a 2D cloud-resolving model. The effects of cloud geometry on the radiative energy budget are examined by comparing the full-resolution Monte Carlo results with those from the independent column approximation (ICA) that applies the plane-parallel radiation model to each column.

For the tropical convective cloud system, it is found that cloud geometry effects always enhance atmospheric solar absorption regardless of solar zenith angle. In a large horizontal domain (512 km), differences in domain-averaged atmospheric absorption between the Monte Carlo and the ICA are less than 4 W m^{−2} in the daytime. However, for a smaller domain (e.g., 75 km) containing a cluster of deep convective towers, domain-averaged absorption can be enhanced by more than 20 W m^{−2}. For a subtropical marine boundary layer cloud system during the stratus-to-cumulus transition, calculations show that the ICA works very well for domain-averaged fluxes of the stratocumulus cloud fields even for a very small domain (4.8 km). For the trade cumulus cloud field, the effects of cloud sides and horizontal transport of photons become more significant. Calculations have also been made for both cloud systems including black carbon aerosol and a water vapor continuum. It is found that cloud geometry produces no discernible effects on the absorption enhancement due to the black carbon aerosol and water vapor continuum.

The current study indicates that the atmospheric absorption enhancement due to cloud-related 3D photon transport is small. This enhancement could not explain the excess absorption suggested by recent studies.