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  • View in gallery

    Liquid water and ice content 2D distributions for cloud fields used in study. Highlighted boxes represent regions discussed in detail within section 3b.

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    Multilayer cloud field as degraded in resolution from 0.2 to 20 km.

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    Cumulus cloud field (upper) shortwave heating rates and (lower) surface irradiance for model computational modes. Dark (light) line represents solar irradiance computed using 3D (ICA) approach.

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    Domain average (left) atmospheric absorption and (right) surface irradiance for (upper) 3D computation and (lower) 3D−ICA.

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    Domain average shortwave heating rates for 3D (solid line) and ICA (dotted line) computational modes for sza equals (left) 0° and (right) 60°.

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    (a) Liquid water and ice content 2D distributions and 3D−ICA heating rate differences for sza equals 0° and 60° for (top six panels) stratus, (middle six panels) broken stratus, and (bottom six panels) cumulus cloud fields; (left) 200-m and (right) 2-km model resolution. Images are for areas highlighted in Fig. 1. (b) Same as (a), but for cirrus, multilayer, and cumulonimbus cloud fields.

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    (Continued)

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    Surface irradiance difference (3D−ICA) for individual atmospheric columns distributed by percentile groupings for (top to bottom) different cloud conditions and for sza equals (left) 0° and (right) 60°. Results for each model resolution are presented as vertical bars. Dark (light) shaded box designates the range of values for the 20% of the columns having the maximum negative (positive) difference. White (black) dotted line indicates the fifth-percentile limit, and the dashed line represents the tenth percentile limit. Gray box represents the range of values for the middle 60% of the columns. The fifth- and tenth-percentile limits are not shown for resolutions coarser than 2 km. Elongated horizontal shaded box represents ±100 W m−2 as a reference for the eye.

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    Same as Fig. 7, except heating rate difference (3D−ICA) for individual cloudy cells. Elongated horizontal shaded box representing ±0.1 K h−1 is provided as a reference for the eye.

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The Impact of Model Resolution on Differences between Independent Column Approximation and Monte Carlo Estimates of Shortwave Surface Irradiance and Atmospheric Heating Rate

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  • 1 Institute for Computational Earth System Science, University of California, Santa Barbara, Santa Barbara, California
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Abstract

Within general circulation models (GCMs), domain average radiative fluxes are computed using plane-parallel radiative transfer algorithms that rely on cloud overlap schemes to account for clouds not resolved at the horizontal resolution of a grid cell. These parameterizations have a strong statistical approach and have difficulty being applied well to all cloudy conditions. A more physically based superparameterization has been developed that captures subgrid cloud variability using an embedded cloud system resolving model (CSRM) within each GCM grid cell. While plane-parallel radiative transfer computations are generally appropriate at the scale of a GCM grid cell, their suitability for the much higher spatially resolved CSRMs (2–4 km) is unknown because they ignore photon horizontal transport effects. The purpose of this study is to examine the relationship between model horizontal resolution and 3D radiative effects by computing the differences between independent column approximations (ICA) and 3D Monte Carlo estimates of shortwave surface irradiance and atmospheric heating rate.

Shortwave radiative transfer computations are performed on a set of six 2D fields composed of stratiform and convective liquid water and ice clouds. To establish how 3D effects vary with the size of a grid cell, this process is repeated as the model resolution is progressively degraded from 200 to 20 km. For shortwave surface irradiance, the differences between the 3D and ICA results can reach 500 W m−2. At model resolutions of between 2.0 and 5.0 km the difference for almost all columns is reduced to a maximum of ±100 W m−2. For atmospheric heating rates assessed at the level of individual model cells, 3D radiative effects can approach a maximum value of ±1.2 K h−1 when the horizontal column size is 200 m. However, between model resolutions of 2.0 and 5.0 km, 3D radiative effects are reduced to well below ±0.1 K h−1 for a large majority of the cloudy cells. While this finding seems to bode well for the CSRM, the results ultimately need to be understood within the context of how 3D radiative effects impact not only heating rates but also cloud dynamics.

Corresponding author address: William O’Hirok, Institute for Computational Earth System Sciences, University of California, Santa Barbara, Santa Barbara, CA 93106. Email: bill@icess.ucsb.edu

Abstract

Within general circulation models (GCMs), domain average radiative fluxes are computed using plane-parallel radiative transfer algorithms that rely on cloud overlap schemes to account for clouds not resolved at the horizontal resolution of a grid cell. These parameterizations have a strong statistical approach and have difficulty being applied well to all cloudy conditions. A more physically based superparameterization has been developed that captures subgrid cloud variability using an embedded cloud system resolving model (CSRM) within each GCM grid cell. While plane-parallel radiative transfer computations are generally appropriate at the scale of a GCM grid cell, their suitability for the much higher spatially resolved CSRMs (2–4 km) is unknown because they ignore photon horizontal transport effects. The purpose of this study is to examine the relationship between model horizontal resolution and 3D radiative effects by computing the differences between independent column approximations (ICA) and 3D Monte Carlo estimates of shortwave surface irradiance and atmospheric heating rate.

Shortwave radiative transfer computations are performed on a set of six 2D fields composed of stratiform and convective liquid water and ice clouds. To establish how 3D effects vary with the size of a grid cell, this process is repeated as the model resolution is progressively degraded from 200 to 20 km. For shortwave surface irradiance, the differences between the 3D and ICA results can reach 500 W m−2. At model resolutions of between 2.0 and 5.0 km the difference for almost all columns is reduced to a maximum of ±100 W m−2. For atmospheric heating rates assessed at the level of individual model cells, 3D radiative effects can approach a maximum value of ±1.2 K h−1 when the horizontal column size is 200 m. However, between model resolutions of 2.0 and 5.0 km, 3D radiative effects are reduced to well below ±0.1 K h−1 for a large majority of the cloudy cells. While this finding seems to bode well for the CSRM, the results ultimately need to be understood within the context of how 3D radiative effects impact not only heating rates but also cloud dynamics.

Corresponding author address: William O’Hirok, Institute for Computational Earth System Sciences, University of California, Santa Barbara, Santa Barbara, CA 93106. Email: bill@icess.ucsb.edu

1. Introduction

The interaction between clouds and solar radiation within large-scale climate models represents one of the largest sources of uncertainty in simulating the global climate (Houghton et al. 2001). Largely, the problem is one of integrating, in a statistical sense, small-scale physical features and processes to the grid cell resolutions used in general circulation models (GCMs). To account for unresolved clouds and their vertical distributions within a GCM atmospheric column, parameterizations have been developed based on various cloud overlap schemes (e.g., Geleyn and Hollingsworth 1979; Yu et al. 1996; Stubenrauch et al. 1997; Collins 2001). These are optimized, in part, so that the 1D shortwave radiative transfer algorithms used in GCMs can provide a best estimate of the domain average fluxes. However, in an extensive comparison of atmospheric solar radiative transfer models used in GCMs, no single 1D approach has been shown to perform well for all conditions (Barker et al. 2003).

The radiative transfer algorithms used in GCMs assume cloud layers to be homogeneous and plane parallel, but by ignoring horizontal fluctuations substantial biases may occur (Cahalan et al. 1994; Marshak et al. 1998; Pincus et al. 1999). While progress has been made to parameterize their radiative impact, these methods must depend on some statistical measure of the cloud-field horizontal variability (Oreopoulos and Barker 1999; Cairns et al. 2000). Optimally, the radiative transfer should be performed on individual subgrid atmospheric columns that represent the scale of the variability.

In a break from conventional cloud parameterizations, an innovative physically based cloud resolving convection parameterization or superparameterization has recently been introduced (Grabowski and Smolarkiewicz 1999; Randall et al. 2003). This method explicitly determines many of the subgrid cloud processes by embedding a high-resolution (2–4 km) 2D cloud system resolving model (CSRM) within a GCM grid cell. The embedded approach provides a physical basis for determining the vertical and horizontal structure of the cloud field. For each CSRM column, plane-parallel radiative transfer computations are performed using what is referred to as the independent column approximation (ICA). While in nature, photons can travel in all three spatial dimensions, this method ignores 3D radiative effects by preventing the horizontal transport of photons across column boundaries. This restriction vastly improves the efficiency of the radiation transfer code. For domain averages, the cost in accuracy is minimal for generally all but the most complex tropical convective systems, but at scales much smaller than a GCM can resolve the 3D radiative effects can produce small regions of intense local heating (O’Hirok and Gautier 1998; Barker et al. 1999; Fu et al. 2000; Vogelmann et al. 2001; Di Giuseppe and Tompkins 2003). If these occur at the resolutions used in a superparameterization, the heating rates produced using the ICA method may not be accurate enough to correctly drive the dynamics within an individual CSRM column. The model resolutions at which 3D shortwave radiative effects become important to atmospheric heating rates and surface irradiance is the subject of this research. For the purposes of this study, we use the expression 3D radiation to define 3D radiative transfer performed on a 2D cloud field.

In the research presented here, shortwave radiative transfer computations are performed on a set of six fields composed of stratiform and convective liquid water and ice clouds. For each cloud element within a field, the 3D radiative effect is established by determining the difference (3D−ICA) in the heating rates and surface irradiance derived from using the 3D and ICA approaches. To establish how 3D effects vary with the size of a grid cell, this process is repeated as the model resolution is progressively degraded. Ultimately, it is desirable to fully understand how these effects impact cloud field dynamics, but to obtain a complete solution requires incorporating a 3D radiative transfer code into a cloud-resolving model. An exercise of this type is a very large undertaking and is beyond the scope of this present study.

2. Methodology

a. Cloud fields

Six cloud fields representative of stratus, broken stratus, small cumulus, cirrus, cirrus overlying convective cells, and cumulonimbus are used in this study. Using the same approach as the embedded CSRM, the cloud fields are 2D and extend over a distance of 100 km. They are derived from observations rather than extracted from models that may be biased because of the current necessity to perform plane-parallel radiative transfer. A brief description of the cloud field derivation based on the method of O’Hirok and Gautier (2003) is now presented.

The structure of the cloud fields are derived from the Atmospheric Radiation Measurement (ARM) program millimeter cloud radar (MMCR) operating at the Southern Great Plains Central Facility. Based on the prevailing winds, the radar reflectivity, Z, is mapped onto a lattice structure with individual cells initially being 100 m across and 45 m high. Concurrent with the radar observations, the column integrated liquid water path (LWP) is obtained from a microwave radiometer and surface downwelling irradiance is measured by a multifilter rotating shadowband radiometer. For each cell, the liquid water content (LWC) is determined by using Z to map LWP. Column optical thickness (τ) is retrieved by matching the irradiance measurements to values computed from the plane-parallel cloud radiative transfer model, Santa Barbara DISTORT Atmospheric Radiative Transfer (SBDART; Ricchiazzi et al. 1998). Knowing the LWP and τ, the average column cloud droplet effective radius, 〈re〉, and average column particle number concentration, N, are computed. Through an iterative process, re can be estimated from LWC and N for each cell and adjusted until its column average (weighted by LWC) matches 〈re〉. From re and LWC, the particle extinction coefficient, κe, is obtained for each cell. For the ice, a simple empirical relationship is used that relates κe to Z. The mean ice particle size is fixed at 60 μm. The fraction of a cell that is composed of ice is a function of layer temperature and ranges from 0% at freezing level to 100% at −23°C.

The total LWC and ice water content (IWC) for all six cloud fields are displayed in Fig. 1. Shown here, the horizontal resolution for each column is 200 m. Atmospheric layers in top three panels of the figure have thicknesses of 45 m while those fields portrayed in the lower panels are composed of layers 90 m thick. The cirrus and multilayer cloud fields are originally from the same radar image. For the cirrus field the lower layer has been removed and IWC reduced. The cirrus, multilayer, and cumulonimbus cloud fields all contain ice with the freezing levels presented in Table 1. Cloud field τ and re statistics are also shown in this table.

To understand how computed radiative fields vary with model resolution, the cloud fields are progressively degraded in horizontal resolution. To keep the radiative computations consistent across the range of model resolutions used only the optical properties (re and κe) are averaged. Figure 2 demonstrates the regridding process for the multilayer cloud field as the model resolutions are decreased from 0.2 to 20.0 km.

b. Model computations

Shortwave atmospheric heating rates and surface irradiance are computed using a 3D radiative transfer model (SB3D) based on the Monte Carlo technique described in O’Hirok and Gautier (1998). A k-distribution method with 8–16 k-terms per spectral band is utilized for gaseous transmission (Yang et al. 1999). Atmospheric profiles of pressure, temperature, and water vapor are obtained from radiosondes launched during periods when the MMCR data were being acquired. All other atmospheric gases are from standard model profiles. For the surface, an ocean albedo is specified. An oceanic aerosol with an optical depth of 0.08 is included in the calculations. Cloud optical properties are computed directly from Mie theory for each spectral interval (Wiscombe 1980). Computations are performed at 5-nm resolution from 0.25 to 1.0 μm and 10-nm resolution from 1.0 to 5.0 μm. These are spectrally integrated to produce the broadband irradiances (0.25–5.0 μm).

Identical model inputs are utilized for both the 3D and ICA computational modes. The model runs are also the same with the exception of a cyclic boundary being employed for each atmospheric column of the ICA to prevent horizontal photon transport. For both modes, a cyclic boundary is incorporated at the edge of the model domain (i.e., the 0- and 100-km marks in Fig. 1). While the cloud fields are two-dimensional in the xz plane, the radiative transfer still occurs in 3D because the field has infinite length in the y direction. Photons traveling toward this direction will encounter cloud variability, but the spatial frequency of the variability will be reduced the further the trajectory is directed away from the xz plane. To some degree the use of a 2D cloud field will cause 3D effects to be underestimated, but its application here is appropriate since the embedded CSRM approach also utilizes a 2D field.

Because fluxes are being evaluated for individual columns rather than for the entire domain, an average of 5 × 108 photons are processed for each of the cloud fields. It is estimated that the accuracy for individual columns is between 1% and 3% for the field with 500 columns and becomes significantly better as the resolution of the field is degraded. Thus, the processing time of this study is high considering six fields are evaluated over seven model resolutions for both the 3D and ICA modes. Hence, only two solar zenith angles (sza) are selected (0° and 60°). Although these angles will not maximize all 3D effects for all fields, their use should bring out enough variability for the purposes of this study.

As a demonstration of the difference between the 3D and ICA computational modes, the shortwave heating rates and surface irradiance for the cumulus cloud field are presented in Fig. 3. These results should not be considered new since similar findings have been shown by investigators spanning more than three decades (e.g., McKee and Cox 1974; Welch and Wielicki 1989; O’Hirok and Gautier 1998; Varnai and Davies 1999; and others). They are presented here as an aid for the physical interpretation of the statistical quantities discussed further in this study.

The increased heating by gaseous absorption below approximately 2500 m is a function of the water vapor profile (Fig. 3). The most distinct 3D features are the cloud shadows being horizontally displaced, an enhanced diffusion of the radiative field and greater heating taking place where cloud elements are oriented toward the sun. At the surface, the difference in downwelling irradiance between the two modes is striking. For the 3D case the fluxes can exceed the ICA clear sky values because of photon leakage from the sides of the clouds. Still, notwithstanding large variations between the two modes approaching 500 W m−2 for individual columns, the domain average difference is only 2 W m−2.

3. Results

a. Domain averages

In this section only the GCM domain average irradiances are considered. Presented in the upper panels of Fig. 4 is the solar radiation absorbed in the atmosphere and the downwelling surface irradiance as computed using full 3D radiative transfer for the 200-m resolution fields. The lower panels represent the 3D effect (i.e., 3D–ICA results). Among the different fields used in this study, the amount of shortwave radiation absorbed in the atmosphere varies widely, ranging from 210 to 350 W m−2 for overhead sun and 125 to 170 W m−2 for the 60° sza. In contrast, the maximum difference between the 3D and ICA computations is less than 7 W m−2. For surface irradiance, the downwelling flux not surprisingly shows strong variations among the fields since this amount is largely a function of cloud optical thickness and cloud fraction. However, the difference between the 3D and ICA computation is again rather small except for the most complex cumulonimbus field where values between −20 and 10 W m−2 are found. Here, cloud photon leakage near the cloud gap produces positive values for overhead sun, but for the oblique solar beam the cloud field appears overcast causing the surface irradiance to be lower.

Domain average heating rate profiles for the 200-m resolution fields are plotted in Fig. 5 for both the 3D and ICA computational modes. Except in the upper portions of the cirrus and convective cloud fields, this figure demonstrates that 3D effects are almost imperceptible when averaged over the size of a GCM grid cell. This result supports previous findings that the ICA is a suitable approach for estimating domain average irradiances for most cloud fields (Barker et al. 1999; Fu et al. 2000). Interestingly, the heating rate (0.2 K h−1) for the cirrus cloud is insensitive to the location of the sun even though the solar input is 50% less when the sun is at 60°. Here, the cloud optical thickness is in a unique range that when it is doubled relative to the solar beam (because of the cosine of the solar zenith angle) the cloud absorptance is also nearly doubled. This relationship is true for both computational modes.

b. Column heating rates

Errors in atmospheric heating rates caused by neglecting photon horizontal transport between subgrid columns are now examined in detail. Figures 6a and 6b show images of cloud liquid water and ice content and heating rate differences for the model resolutions of 200 m and 2 km for both solar zenith angles used in this study. To highlight processes, only the areas bounded by the boxes in Fig. 1 are examined here. The heating rate difference contours (3D−ICA) are plotted in geometric steps and the plot scale can vary between the different cloud fields to bring out interesting spatial features.

While the stratus cloud field represents the closest approximation to a homogeneous plane-parallel cloud found in nature, internal horizontal variations in κe, and small undulations in cloud-top geometry can still produce 3D radiative effects (Fig. 6a). For overhead sun, some of the photons entering the less dense columns in the upper portion of the cloud will scatter into adjoining columns upon hitting cloud elements of higher optical density. This process causes an oscillatory pattern in the heating rate difference that shows error gradients of 0.25 K h−1 over a distance of 400 m. For the oblique solar angle, similar differences are observed but they are separated over a greater distance. These occur at the cloud top and are caused by cloud shadowing and the solar beam intercepting both the top and sides of some of the cloudy cells. All these effects take place when the model resolution is equal to 200 m. However, when the resolution is decreased to 2 km, the smoothness of the field reduces these values by a factor of 10 or ±0.025 K h−1.

Compared to the solid stratus field, the broken field has smaller variations in κe and lower column optical depth, but is geometrically more complex (Fig. 6a). Thus, heating rate differences are more pronounced for the lower sun angles with the most extreme values approaching ±0.3 K h−1. For the coarser model resolution, only a small area of 3D effects can be seen with maximum values near ±0.05 K h−1.

While the patterns for the small cumulus and stratus fields are similar, the 3D effects produced in the cumulus field are much more intense for the solar zenith angle of 60° (Fig. 6a). Here, the cumulus cloud elements oriented toward the sun produce positive values of 0.4 K h−1, while those in the shadows a kilometer away show a negative 0.2 K h−1. Below the cloud in the clear atmosphere, 3D effects impact gaseous absorption producing heating rate differences of ±0.1 K h−1. The positive values occur because 3D effects allow the direct beam to propagate horizontally below the cloud and it is negative because the same process allows clouds to cast shadows at an angle. Again, as found for the stratus fields almost all of the 3D effects are eliminated when the model resolution is decreased to 2 km.

The cirrus cloud results are similar to those of the broken stratus (Fig. 6b). For both cases τ is low and 3D effects for overhead sun are weak. Because the cloud is optically thin, κe in the cloud cells of low ice density is small enough that single scattering dominates. When these areas are adjacent to cloud cells with higher κe, optically the cloud appears to have a complex geometric top. For oblique sun angles, heating rate differences are near ±0.5 K h−1. When the field is smoothed to 2 km these effects are less noticeable.

For the multilayer case, the dominant feature is the shadowing of the lower convective layer by the overlying cirrus (Fig. 6b). Comparing the 3D to the ICA computations, photons will diffuse out of the sides of clouds and enhance the downwelling radiation in clear gaps while producing a deficit below the clouds. The effect is not strong and the difference is about ±0.1 K h−1. At the 60° solar zenith angle, the cirrus layer appears to be more solid for the 3D case and correspondingly less radiation reaches the top of the lower convective layer. At the coarser model resolution most of the heating rate differences are suppressed, but some negative values of −0.1 K h−1 arise because of oblique cloud shadowing.

Although the cumulonimbus cloud field is the most geometrically complex, the ice crystals in the upper portion of the field tend to reduce 3D effects for direct overhead sun (Fig. 6b). Here, the low optical densities of the cloud cells containing ice spread the differences between the 3D and ICA heating rates over a large vertical extent causing values no larger than ±0.1 K h−1. For the sza of 60°, the heating rate difference reaches extreme values of ±1.2 K h−1 causing intense local heating for the cloud cells oriented toward the solar beam. Variations of ±0.3 K h−1 are also produced in the upper third of the cloud field. At the lower resolution of 2 km some 3D effects are still be observed, but they are reduced to maximum values of approximately ± 0.3 K h−1.

4. Summary and conclusions

The objective of this study was to estimate the scale where the inclusion of horizontal photon transport in a shortwave radiative transfer model becomes no more accurate than the simpler ICA approach for progressively degraded cloud fields. To discern how these effects vary with model resolution, it is best to summarize the results within a single figure. In Fig. 7, the difference in surface irradiance between the 3D and ICA computational modes for each model horizontal column is presented in the form of percentile rankings.

For each model resolution, a bar is shown partitioned into three boxes of different shades. The dark (light) shaded box designates the range of values for the 20% of the columns having the maximum negative (positive) difference (3D−ICA) for surface irradiance. Within this box, the white (black) dotted line indicates the level where 5% of the columns have negative (positive) differences greater than this value. The dash line shows the 10% ranking. The gray box represents the range of values for the middle 60% of the columns. For fields of less than 50 columns, the 5% and 10% lines are not determined. For example, consider a dark box bounded by −400 and −200 W m−2 for a model resolution of 0.5 km (200 total columns). Within this box the white dash line is located at −350 W m−2. This pattern indicates that for 20%, or 40 of the columns, the ICA model overestimates the absorbed surface radiation by 200 to 400 W m−2 and for 10% or 20 of the columns it overpredicts by 350 to 400 W m−2. The lightly shaded rectangle across all the bars located between the −100 and 100 W m−2 marks is used as a point of reference to help guide the eye.

Across all model resolutions, 90% of the atmospheric columns for the stratus, broken stratus, and multilayer cloud fields show that 3D effects have a less than a 100 W m−2 impact on the amount of solar radiation reaching the surface. The largest discrepancies occur for the cumulus cloud field with negative and positive values initially greater than 100 W m−2 for more than half the field. It requires a model resolution of between 5 and 10 km before the leakage of photons from the sides of cloud is reduced to a level where all columns are below ±100 W m−2. The cirrus field results are similar to the cumulus, but with lower extreme values. From 200 m to 2 km the field is insensitive to model resolution. At coarser resolutions, the cloud gaps are filled and the 3D effects are reduced. While the cumulonimbus field contains large negative extremes for overhead sun, the overall bias is positive. For the 60° solar zenith angle, there is a consistent negative 3D bias that is also reflected in the domain average. At all the model resolutions for this cloud field, the impact of 3D effects for more than half of the columns is within the vicinity of ±10 W m−2. These low values occur because under the areas of deep convection, the total computed broadband surface irradiance can be less than 20 W m−2 for even overhead sun.

Percentile rankings for the difference in heating rates for individual cloudy cells are presented in Fig. 8. As in Fig. 7, a lightly shaded rectangle across all bars is used to provide a reference to the eye. Its limits are at ±0.1 K h−1 and approximate the maximum heating rate for a highly absorbing clear sky. For overhead sun, virtually all the heating rate differences for the stratus, broken stratus, and cumulus fields are smaller than ±0.1 K h−1. At 60°, about 10% of each field will exceed this value for the 200-m size column. A resolution of 2.0 km is required for the differences in all the cells to be less than ±0.1 K h−1. The cirrus field follows the same pattern for overhead sun as the cumulus. However, for the 60° solar zenith and model resolutions finer than 2.0 km, about 10% of the cells exhibit 3D effects that are equivalent to the maximum total heating rate (0.2 K h−1) for this field. For overhead sun, the multilayer and cumulonimbus fields require model resolutions coarser than 1.0 km to reduce 3D effects to values smaller than ±0.1 K h−1. At 60°, about 40% of the cells within multilayer cloud field have differences in the heating rate of ±0.1 K h−1 for resolutions higher than 2.0 km. The cumulonimbus field requires a model resolution of between 2.0 and 5.0 km to achieve the same result. At resolutions finer than 1.0 km, up to 20% of the cloudy cells show differences of ± 0.3 K h−1, which is nearly twice the maximum domain average heating rate computed for the cumulonimbus field.

While 3D radiative effects for GCM domain averages are generally unimportant, it is demonstrated here that at the local scale the impact of horizontal transport can be significant. For shortwave surface irradiance, the differences between the 3D and ICA results can reach 500 W m−2. At model resolutions of between 2.0 and 5.0 km the difference for almost all columns is reduced to a maximum of ±100 W m−2. If cloud fields were stationary such a number could be important to surface energy budgets and particularly to processes such as evapotranspiration. However, cloud fields are almost always in motion to some degree (except in the case of orographic clouds) and because of the high heat capacities of most underlying surfaces any 3D effects are likely to be transitory and insignificant.

At the highest model resolutions, the neglect of photon horizontal transport was found to produce errors that are magnitudes greater than the simulated 1D heating rate for individual cells. For cloud-resolving models having horizontal resolutions in the hundreds of meters, the integrated impact of 3D radiative effects on cloud dynamics is difficult to assess because of the very short time steps involved. As shown for the limited cases explored here, the greatest reduction in 3D effects occurs for model resolutions between 2.0 and 5.0 km, where almost all cloud cells show differences much smaller than ±0.1 K h−1. For the superparameterization method, this finding is fortuitous since the current embedded CSRM uses grid cells having horizontal resolutions on the order of 2–4 km. Likely at this resolution, the ICA assumption is sufficient for estimating the radiative field at the scale of individual columns for all but the most complex convective systems. Still, the accuracy of the radiative field computed at these lower resolutions cannot be any greater than the exactness of the cloud structure produced by the CSRM. These results ultimately need to be understood within the context of how photon horizontal transport effects impact not only heating rates but also cloud dynamics by incorporating a 3D radiative transfer algorithm within a cloud-resolving model.

Acknowledgments

This work was funded from the Department of Energy Grant 90ER61062 and the National Aeronautics and Space Administration Grant NNG04GE25G.

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Fig. 1.
Fig. 1.

Liquid water and ice content 2D distributions for cloud fields used in study. Highlighted boxes represent regions discussed in detail within section 3b.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 2.
Fig. 2.

Multilayer cloud field as degraded in resolution from 0.2 to 20 km.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 3.
Fig. 3.

Cumulus cloud field (upper) shortwave heating rates and (lower) surface irradiance for model computational modes. Dark (light) line represents solar irradiance computed using 3D (ICA) approach.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 4.
Fig. 4.

Domain average (left) atmospheric absorption and (right) surface irradiance for (upper) 3D computation and (lower) 3D−ICA.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 5.
Fig. 5.

Domain average shortwave heating rates for 3D (solid line) and ICA (dotted line) computational modes for sza equals (left) 0° and (right) 60°.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 6.
Fig. 6.

(a) Liquid water and ice content 2D distributions and 3D−ICA heating rate differences for sza equals 0° and 60° for (top six panels) stratus, (middle six panels) broken stratus, and (bottom six panels) cumulus cloud fields; (left) 200-m and (right) 2-km model resolution. Images are for areas highlighted in Fig. 1. (b) Same as (a), but for cirrus, multilayer, and cumulonimbus cloud fields.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 6.
Fig. 6.

(Continued)

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 7.
Fig. 7.

Surface irradiance difference (3D−ICA) for individual atmospheric columns distributed by percentile groupings for (top to bottom) different cloud conditions and for sza equals (left) 0° and (right) 60°. Results for each model resolution are presented as vertical bars. Dark (light) shaded box designates the range of values for the 20% of the columns having the maximum negative (positive) difference. White (black) dotted line indicates the fifth-percentile limit, and the dashed line represents the tenth percentile limit. Gray box represents the range of values for the middle 60% of the columns. The fifth- and tenth-percentile limits are not shown for resolutions coarser than 2 km. Elongated horizontal shaded box represents ±100 W m−2 as a reference for the eye.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Fig. 8.
Fig. 8.

Same as Fig. 7, except heating rate difference (3D−ICA) for individual cloudy cells. Elongated horizontal shaded box representing ±0.1 K h−1 is provided as a reference for the eye.

Citation: Journal of the Atmospheric Sciences 62, 8; 10.1175/JAS3519.1

Table 1.

Mean cloud optical thickness, mean cloud droplet effective radius, and freezing altitude.

Table 1.
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