1. Introduction
Radiative processes play a key role in the climate system. Radiative transfer theories can very accurately compute the radiative fluxes and heating rates provided that the input information is perfect. The input to a radiative transfer calculation includes information about the atmospheric thermodynamic state, the surface characteristics, and a description of the clouds. This description includes the microphysical properties of the clouds (i.e., phase, particle shape, and particle size distribution) and the macrophysical properties describing the geometry of the cloud fields. The geometry of the cloud fields in a climate model is customarily treated with a simple cloud overlap assumption in its radiative transfer code, which seriously impacts the accuracy of the radiative computation (e.g., Barker et al. 2003). Thus, the key factor limiting the accuracy of radiative fluxes and heating profiles is the deficient input to radiative transfer codes.
Recently, the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study Working Group 4 and the Atmospheric Radiation Measurement (ARM) program have performed a joint case intercomparison study, focusing on the midlatitude convective systems observed in the Southern Great Plains (Xie et al. 2002; Xu et al. 2002). Both cloud-resolving models (CRMs), which resolve most of the dynamics of clouds and their mesoscale organization, and single-column models (SCMs), which are single-column versions of general circulation models (GCMs), are compared. A major conclusion of this intercomparison study is that CRM simulations show very small intermodel differences compared to those of SCMs. All CRM simulations were performed with prescribed radiative heating rate profiles. Despite this simplification, different treatments of cloud microphysics were identified as the major reason for the intermodel differences among CRMs (Xu et al. 2002). The impact of these intermodel differences on radiation could not be examined because of the particular design of this intercomparison study.
In the present study, we attempt to quantify the impact of the intermodel differences on the radiative fluxes and radiative heating rates, as diagnosed from a single radiative transfer code, due to different treatments of cloud microphysics employed in the participating CRMs. The input data, including those describing the cloud fields, are averaged over the horizontal domain of each CRM (500 km). It is obvious that cloud–radiation interactions cannot be examined in this study because the radiative fluxes and radiative heating rates are diagnosed. Since a single radiative transfer code is used, one does not have to deal with difficulties associated with comparing different radiative transfer codes in CRMs. Once the intermodel differences are obtained, it is still difficult to identify the significance of the intermodel differences in the radiative fluxes and radiative heating rates without comparing them with the differences resulting from some assumptions used in the radiative transfer calculation.
Simulation of this intercomparison case performed by one of the participating CRMs provides outputs with the spatially varying structures of the simulated cloud fields. Data from this simulation will be used to examine the sensitivity of diagnosed radiative fluxes and heating rates to the cloud overlap assumption and the uniform hydrometeor assumption used in the diagnostic calculation with the domain-averaged output discussed above. These results will then be used to further quantify the intermodel differences in the diagnosed radiative fluxes and heating rates due to different treatments of cloud microphysics among the participating CRMs. The primary objective of this study is to quantify these intermodel differences among the CRMs. The second objective is to examine the sensitivity of diagnostic radiative properties to cloud overlap and uniform hydrometeor assumptions. The third objective is to quantitatively compare the consensus of the CRM results with available observations of all radiative fluxes obtained from the ARM program (Stokes and Schwartz 1994; Ackerman and Stokes 2003). This comparison is unprecedented because all radiative fluxes were simultaneously measured at the top of the atmosphere (TOA) and at the surface during an ARM intensive observational period (IOP).
The rest of the paper is as follows. Section 2 discusses methodology, observational data are described in section 3, results are presented in section 4, and a summary is given in section 5.
2. Methodology
Before the methodology is described, it should be pointed out that a single radiative transfer code, the state-of-the-art Fu–Liou scheme (Fu and Liou 1993), is employed for the diagnosis of radiative fluxes and heating rates in this study. Briefly, this broadband radiation model includes the δ-four-stream approximation for radiative transfer in nonhomogeneous atmospheres, the correlated-k distribution method for nongray gaseous absorption by H2O, CO2, O3, CH4, and N2O and the scattering and absorption properties of spherical liquid droplets and nonspherical ice crystals. The H2O continuum absorption is included in the spectral region 280–1250 cm−1. For liquid water clouds, a parameterization for the single-scattering properties is based on Mie calculations using the liquid water droplet size distributions in terms of cloud liquid water content and mean effective radius. For ice clouds, nonspherical ice particles in both the infrared and solar spectra are considered with cloud ice water content and generalized equivalent ice diameter as inputs (Fu 1996; Fu et al. 1998). There are 6 spectrum intervals in the solar (0.2–0.4 μm) range and 12 spectrum intervals in the infrared (2200–1 cm−1) range.
In one calculation called “detailed,” the input variables include the x–z distributions of temperature, specific humidity, and mixing ratios of cloud liquid water, cloud ice water, snow, graupel and rainwater at 5-min interval from one CRM simulation. (The CRM and the configuration of the model simulation will be described in section 3.) Cloud ice and snow mixing ratios are combined and treated as ice particles inside the radiative transfer code. The diameter of snow is assumed to be 150 μm, but that of cloud ice is a function of cloud ice content (Fu 1996). Calculations are performed for every single CRM column and the radiative fluxes and heating rates are averaged over the entire domain in horizontal space and 3 h or the entire simulation period in time. The radiative transfer code does not compute cloud optical properties when the cloud water/ice content is less than 10−8 kg m−3. Other inputs to the radiative transfer code are listed in Table 1.
In another calculation called “domain average,” all input variables are just functions of height, as provided by all participating CRM groups. They are the same variables as in the detailed calculation, except they are averaged over the entire CRM domain in the horizontal and over 3 h in time. An additional input variable is the cloud fraction, which represents the fraction of cloudy grids at a given height in the domain over the same 3-h interval. A 100% cloudy grid at a given height is diagnosed if the sum of cloud water and cloud ice mixing ratios exceeds 1% of the saturation water vapor mixing ratio with respect to liquid (Xu and Krueger 1991).
Because the original Fu–Liou scheme does not treat partially cloudy columns, a new procedure has to be adopted in order to distribute the cloud field horizontally and vertically. A method proposed by Yu et al. (1996) and modified by Klein and Jakob (1999) is used. The vertical profile of cloud fraction combined with a cloud overlap assumption provides information about what portion of clouds from each level contain no clouds above them. The horizontal domain is divided into 100 subcolumns in which the cloud fraction is assigned to be 0 or 1 at every level in order to allow the overlapping of clouds. The maximum-random overlap assumption is used to distribute the cloud field horizontally and vertically (Klein and Jakob 1999). The specification of which subcolumn contains cloud condensate at a given height is entirely consistent with the cloud overlap assumption, by stacking the cloud starting from the subcolumns farthest to the left. This procedure begins at the top layer of the atmosphere and ends at the surface. The radiative transfer calculation is then performed for each subcolumn and the result is averaged over all subcolumns.
A major assumption used in the domain-averaged calculation is that all hydrometeors are horizontally uniform in the cloudy subboxes at each level. Their local values are equal to the domain-averaged values divided by the cloud fraction. This is called the “uniform hydrometeor” assumption. Using output with spatially varying cloud fields from a CRM, an “intermediate” calculation is performed by assigning the horizontally averaged mixing ratios of hydrometeors to all grids where they are present. That is, the geometry of the cloud field is retained while the hydrometeor mixing ratios are homogenized. By comparing this calculation with the detailed calculation, one can estimate the impact of the uniform hydrometeor assumption on the diagnostic radiative properties. The impact of the cloud overlap assumption can then be estimated by comparing the intermediate and the domain-averaged calculations because the uniform hydrometeor assumption is used in both sets of calculations. To be more precise, the differences between the intermediate and domain-averaged calculations represent the differences between the maximum-random overlap and the exact overlap. For simplicity, however, the differences between these two sets of calculations are still referred to as those due to cloud overlap assumption. Thus, a comparison of the results from the three different methods can quantify the relative importance of the different assumptions used in the domain-averaged calculation.
Another input to the radiation scheme is the surface albedo for grasslands, which is 0.14 for the 0.2–0.7 μm wavelengths and 0.336 for other solar wavelengths at 60° solar zenith angle. The dependence of the surface albedo on the solar zenith angle is also included. These are based on Briegleb et al. (1986). The aerosol effects are not included in all calculations performed in this study. The rest of the input variables are summarized in Table 1.
3. Observational data
The ARM summer 1997 IOP covers a 29-day period starting from 2330 UTC 18 June to 2330 UTC 17 July (Julian days 170–199). Only 14 days of this IOP were simulated by the participating CRMs (Xu et al. 2002). There are two types of observations that are used to compare with diagnosed radiative properties in this study: satellite observations for the TOA radiative fluxes, cloud optical depth, and column cloud amount; and the ground-based measurements of surface radiative fluxes by ARM solar and infrared radiation stations (SIRS) and net radiative fluxes by energy balance Bowen ratio (EBBR) stations. The observed/derived products from the National Oceanic and Atmospheric Administration (NOAA) Geostationary Operational Environmental Satellite-8 (GOES-8) satellite are available at 4-km pixel resolution at half-hour frequency from the National Aeronautics and Space Administration Langley Research Center (Minnis et al. 1995). These quantities are then averaged over the Cloud and Radiation Testbed (CART) domain in horizontal space and 3 h (or 14 days) in time for comparison with the CRM results. The column cloud amount has an uncertainty of about 3% for the 14-day subperiod mean. Errors in cloud optical depths are less than 10%. Uncertainties are about 7 W m−2 for outgoing longwave (LW) radiative flux and 10% in reflected shortwave (SW) radiative flux, respectively. See Minnis et al. (1995) for a detailed description of the algorithms used in deriving these quantities.
The surface radiative fluxes are measured by SIRS and EBBR stations employed by ARM. The EBBR stations measure the surface broadband net radiative flux and surface sensible and latent heat fluxes. The SIRS instruments consist of pyranometers to measure the downwelling and upwelling hemispheric solar flux and of pyrgeometers to measure the downwelling and upwelling hemispheric broadband infrared flux (Long and Ackerman 2000). SIRS instrumentation was deployed at four extended facilities within the CART domain during the summer 1997 IOP. An average is performed from measurements taken every 15 s after filtering out unrealistic values. The uncertainties of these measurements are 2.5% or 4 W m−2 for upward and downward LW radiative fluxes, 6% or 10 W m−2 for downward SW radiative fluxes and 6% or 15 W m−2 for upward SW radiative fluxes. Additional uncertainties in SW radiative flux measurements will be discussed later. The net radiative fluxes measured from EBBR have an uncertainty of 5% of the measured values.
4. Results
a. Comparison of different calculations with a CRM simulation
The University of California, Los Angles–Colorado State University CRM is used to simulate the GEWEX Cloud System Study (GCSS)/ARM case 3 by the author. Output from this CRM is used to perform the three calculations discussed in section 2. This model includes two-dimensional anelastic dynamics, three-phase cloud microphysics, and a third-moment turbulence closure (Krueger 1988; Xu and Randall 1995). The model simulates the statistical behavior of midlatitude deep convective systems under observed large-scale conditions. Three subperiods of the ARM summer 1997 IOP are simulated with a duration of either 4 days (subperiod A) or 5 days (subperiods B and C). Details of the model configuration were provided in Xu et al. (2002).
The results from the detailed, intermediate, and domain-averaged calculations are provided in Table 2 for the 14-day means and in Figs. 1–6 for the time series of column cloud fraction, cloud optical depth, and all TOA and surface radiative fluxes for subperiod A. The time series can provide results at shorter time scales that are not revealed from the case-mean results. Two things must be kept in mind in comparing the case-mean and time series results: 1) uncertainties in observations are probably larger for the 3-hourly data than for the 14-day means and 2) errors in the diagnosed radiative fluxes can be much larger in the time series than for the 14-day means because of errors in the timing and the structures of the simulated cloud systems (Xu et al. 2002).
Before discussing the detailed results of radiative fluxes and heating rates, different definitions of column cloud amount are discussed. In the detailed and intermediate calculations, a 100% column cloud amount is diagnosed if the visible cloud optical depth (τvis) is greater than 1 in a CRM column, which is the detectable signal of satellite for thick cirrus clouds. Column cloud amount is obtained from the maximum-random overlap assumption in the domain-averaged calculation using the CRM-simulated cloud fraction profile. All numbers shown in Table 2 represent the averages over the horizontal domain in space and 14 days in time. It can be seen that thin cirrus clouds (see day 179 in Figs. 1a,c) contribute little to the column cloud amount in the domain-averaged calculation while they contribute to it in the other calculations. The column cloud amount is much larger in the intermediate calculation, compared to the detailed calculation (35% versus 21% for the combined 14-day period; Fig. 1a) because of the homogenization of hydrometeor mixing ratios. Please note that this difference can be diminished if the τvis threshold decreases. Table 2 also shows that the column cloud amount from the detailed calculation is larger than that of the domain-averaged calculation (21% versus 15.4%). One reason for this difference is that the cloud fraction profile used as input to the domain-averaged calculation excludes any contribution from precipitating hydrometeors, but they somewhat contribute to the τvis-based column cloud amount. Another reason is that the large thresholds used to diagnose the cloud fraction in the lower troposphere underestimate the cloud fraction there (Xu and Krueger 1991). The difference in column cloud amount between these two calculations is especially large at times during subperiod A (Fig. 1a) in comparison with the 14-day mean difference.
The cloud optical depth from the domain-averaged calculation is much lower (3.72 versus 6.33; Fig. 1c) than that of the detailed calculation. This result is related to the neglect of areas with precipitating hydrometeors in defining the cloud fraction (e.g., Julian days 179 and 181) and the underestimate of low-level cloud fractions. Implications of this difference in cloud optical depth to the diagnoses of radiative fluxes and heating profiles will be discussed in section 4b. Table 2 and Fig. 1c show that there is virtually no difference in cloud optical depth between the detailed and intermediate calculations. This is an expected result.
A first glance of Table 2 shows that the impact of the uniform hydrometeor assumption (fourth column) is larger than that due to the domain-averaged inputs (fifth column), in which both the cloud overlap and uniform hydrometeor assumptions are used. The values appearing in the fourth and fifth columns have opposite signs in nearly all radiative fluxes. They are, however, smaller than those due to the impact of cloud overlap assumption (sixth column). The exceptions are the surface upward and downward LW radiative fluxes. This is an important finding because more attention has been paid recently to the problem of cloud overlap (e.g., Hogan and Illingworth 2000; Mace and Bensen-Troth 2002) than to the problem of cloud heterogeneity (e.g., Cahalan et al. 1994; Barker et al. 1999; Pincus et al. 1999). Inspection of the time series of surface upward LW fluxes does not show any difference among the three calculations (Fig. 2a) because those fluxes are largely determined by the prescribed surface temperature. But the time series of surface downward LW flux shows that it is impacted more by the cloud overlap assumption (Fig. 2c), although the 14-day mean is nearly the same as that due to the uniform hydrometeor assumption (Table 2). This is because the flux differences between the domain-averaged and detailed calculations can be either positive or negative in the time series shown in Fig. 2c.
Both the uniform hydrometeor (fourth column) and cloud overlap assumptions (sixth column) have the opposite effects on the radiative fluxes although the latter assumption has a stronger effect. The time series plots largely support this result but it is difficult to see it in some of the plots (Figs. 4a,c; 5a,c; and 6c) because of the large temporal variations of these fluxes. For example, the effect on the TOA upward flux (Fig. 3a) is −13.5 W m−2 (for the uniform hydrometeor assumption) versus −22.4 W m−2 (for the cloud overlap assumption). This is primarily due to the much larger column cloud amount in the intermediate calculation (Fig. 1c), which reduces the TOA upward flux. These assumptions have an impact on the surface net LW radiation that is about 4 times smaller than at the TOA (Table 2; Fig. 3c). For SW radiation, the impacts are significant in all TOA and surface fluxes, except for the surface upward flux. The cloud overlap assumption has an impact on the SW radiative fluxes that is about 50% larger than that of the uniform hydrometeor assumption. For the combined LW and SW radiation, the cloud overlap assumption also has a larger impact on the TOA net fluxes (8.5 W m−2 versus 4.1 W m−2). Both assumptions have nearly equal impact on the surface net flux (−10.5 W m−2 versus −8.4 W m−2). Barker et al. (2003) showed that the maximum-random overlap produces smaller TOA albedo than the exact overlap. The results shown in Table 2 are consistent with their findings because the TOA SW flux for the domain-averaged calculation (99.2 W m−2) is smaller than for the intermediate calculation (114.1 W m−2).
The impact on the radiative heating rate, QR, which is averaged over the 14-day period, is slightly larger for the cloud overlap assumption than for the uniform hydrometeor assumption for most heights (Figs. 7a,b,c). The difference in QR between the detailed and intermediate calculations is as large as 0.5 K day−1 between 0 and 10 km. The difference is largely due to the LW radiation (Fig. 7a) with a small offset by the SW radiation (Fig. 7b), due to the homogenization of hydrometeor mixing ratios in the intermediate calculation (Fig. 1a). The difference in QR between the domain-average and intermediate calculations is almost negligible above 11 km. That is, the cloud overlap assumption plays a smaller role than the uniform hydrometeor assumption in the upper troposphere, implying that cirrus clouds are not homogeneous. However, the heterogeneity of these clouds has little impact on the SW heating rate (Fig. 7b).
By comparing the detailed and domain-averaged calculations, it is apparent that the radiative cooling above upper-tropospheric anvils and the warming (relative to the clear sky) below these clouds are overestimated by about 0.5 K day−1 above 7 km. The overestimates are largely due to the uniform hydrometeor assumption above 11 km and due to the differences between the cloud overlap and uniform hydrometeor assumptions between 7 and 11 km. Below 7 km, the difference in QR between the domain-averaged and detailed calculations is rather small, especially for SW radiation (Fig. 7b), which implies that the effects of cloud overlap and uniform hydrometeor assumptions nearly cancel each other out. The small differences (∼0.2 K day−1) in SW are consistent with Barker et al. (2003) for their tropical deep convective cloud; that is less heating below 5 km and more heating between 5 and 10 km for the exact overlap than for the maximum-random overlap. Therefore, the domain-averaged calculation can be used as a proxy for the detailed calculation of QR for the discussion presented in sections 4c if the differences above 7 km between these two calculations are taken into account.
b. Comparison with observations
In this section, results from the domain-averaged calculation are shown for the consensus of the 10 CRMs. The CRMs participating in the intercomparison project are listed in Table 3. A bulk representation is used in all cloud microphysics, with four or five condensate (e.g., cloud water, cloud ice, rainwater, snow, and graupel/hail) categories. The majority of CRMs use some variations of the Lin et al. (1983) and Rutledge and Hobbs (1984) schemes with five condensate categories: CNRM, CSULEM, GCE, LaRC, UCLA–CSU, and UKLEM (see Table 3 for definitions of these acronyms). The GFDL CRM predicts cloud water, snow/ice, and rainwater mixing ratios (Donner et al. 1999). The EULAG CRM uses a simple representation that is an extension of the classical Kessler (1969) scheme (Grabowski 1998). Both CRMs do not include graupel or hail. Further details of model descriptions can be found in Xu et al. (2002). It should be noted that other treatments in the CRMs such as cloud-scale dynamics and numerical schemes can also cause intermodel differences, in addition to those of cloud microphysics.
As shown in Table 2, the differences between the detailed and domain-averaged calculations are smaller than those due to the cloud overlap and uniform hydrometeor assumptions. The small differences may be related to the reduced cloud optical depths in the domain-average calculation, which is equivalent to the inclusion of the effects of cloud inhomogeneities (Cahalan et al. 1994; Tiedtke 1996). So, the domain-average calculations for all CRMs will be used as proxies for the detailed calculations of all CRMs, which are not possible for this study due to the fact that modelers were not asked to submit CRM outputs with spatially-varying cloud structures to the intercomparison study because of the large data volume.
Comparison of diagnosed radiative properties with observations is given for the ensemble means, or the consensus, of the 10 CRMs (second column in Table 4). The 14-day mean of column cloud amount (21.7%) is slightly higher than the “thick” cloud amount from GOES-8 (16.4%). For column thick cloud amount, only pixels with cloud liquid water paths greater than 0.01 kg m−2 (τvis ∼1.5) are included. Without this restriction, the GOES-8 cloud fraction is approximately 47% for the 14-day mean. That is, the satellite-observed optically thin clouds are twice as abundant as the optically thick clouds. As mentioned earlier, these clouds contribute little to the column cloud amount of the domain-average calculation, which may affect the comparison of some diagnosed LW fluxes with observations (see the early hours of Julian day 179 in Figs. 1–6). However, cloud optical depth has an excellent degree of agreement with GOES-8 retrievals for the optically thick clouds because the averaged cloud optical depth is largely determined by cumulonimbus clouds and their associated anvils. Their occurrence is more easily simulated by CRMs than that of optically thin cirrus clouds for the ARM summer 1997 IOP (Luo et al. 2003).
The consensus of all diagnosed radiative fluxes from 10 CRMs (second column in Table 4), agrees with observations to a degree that is close to the uncertainties of satellite- and ground-based measurements (first column) except for surface downward shortwave flux. For LW radiation, the ensemble means of surface upward, downward, and net fluxes differ from the surface-based measurements by 5.9, 3.2, and 2.7 W m−2, respectively, which are much smaller than the uncertainties of measurements (2.5% or 10 W m−2 for upward/downward flux, and 4 W m−2 for the net flux). For the TOA upward flux, the consensus of the models is higher than the observed by 12.5 W m−2, which is almost twice as large as the uncertainty of satellite measurements (7 W m−2). It should be pointed out that the TOA net SW fluxes are underestimated by a nearly identical amount (11.6 W m−2). As a result, the net SW and LW fluxes differ from the observations by only 1 W m−2. These results are related to the underestimate of optically thin clouds in the CRMs when the domain-averaged inputs are used in the radiative transfer calculation. Considering that the TOA upward LW flux from the domain-average calculation is 9.9 W m−2 higher than the detailed calculation (Table 2), the consensus of this flux is, thus, within the uncertainty of the measurements.
For SW radiation, the ensemble means of the TOA upward and net flux agree with observations to a degree that is very close to the uncertainties of satellite measurements (10% or 12 W m−2). The ensemble mean of the surface upward flux is within 1.8 W m−2 of that observed. The difference is also smaller than the uncertainty of measurements (3 W m−2). However, the surface downward and net SW radiative fluxes as well as the net SW + LW fluxes have significantly large differences from observations (46.8, 48.6, and 52.1 W m−2, respectively), which are much larger than the uncertainties of measurements (16 W m−2) discussed in section 3. These significantly large differences result from the models’ overestimate of the surface downward SW flux. An overestimate of the same magnitude was obtained with the same radiative transfer code by Charlock and Alberta (1996).
Possible reasons for the overestimate of surface downward SW flux are the underestimates of optically thin cirrus clouds and boundary layer clouds in the CRMs, 3D radiative effects, the lack of aerosols in the radiative transfer calculations, and additional uncertainties in measurements. Each of these reasons is briefly explained below. The 2D UKLEM results agree better with observations by 12–14 W m−2 than the consensus of CRMs because it has the largest cloud fraction among the CRMs (Table 4; Xu et al. 2002). It is common for CRM simulations to absorb too little solar energy in the atmosphere (e.g., Xu and Randall 2000). Xu and Randall (2000) attributed this mainly to the lack of boundary layer clouds in CRM simulations. Lack of aerosols could account for 12–20 W m−2 of the underestimate (Q. Min and T. Charlock 2004, personal communication). The domain-averaged calculation also overestimates the flux by 6.4 W m−2, compared to the detailed calculation (Table 2). The 3D radiative effects may have a larger magnitude than this. Additional uncertainties in measurements are related to the lack of the diffuse nighttime offset due to the overestimate of diffuse radiation. After all these uncertainties are considered, the overestimate may be reduced to a more reasonable range of 10–20 W m−2. Further studies will be needed to resolve this serious problem.
c. Intermodel differences
In this section, we discuss the intermodel differences in the diagnosed radiative fluxes and heating rates due primarily to different treatments of cloud microphysics among the CRMs (Table 4). First of all, the column cloud amounts show a large range from 13.8% (CSULEM-2D) to 33.5% (UKLEM-2D; Table 4). This range is very close to two standard deviations from the ensemble mean in the time series (Fig. 1b). The differences between 2D and 3D simulations are 6.9% in UKLEM, with a larger cloud amount in the 2D simulation, whereas they are only 2.4% in the CSULEM, but with a larger cloud amount in the 3D simulation.
The cloud optical depths also show large differences among the CRMs (Table 4; Fig. 1d). They are not correlated with column cloud amount (correlation coefficient is 0.05). For example, the GFDL, which has a column cloud amount close to the consensus, has the lowest cloud optical depth (2.6), while the GCE, which has a slightly lower column cloud amount, has the highest cloud optical depth (8.9). The rest of the models have a narrow range of cloud optical depths from 3.7 to 6.4. Differences between 2D and 3D simulations are negligible for cloud optical depth. This suggests that differences between 2D and 3D simulations are related to cloud macrophysics such as cloud structures, instead of cloud microphysics.
All the diagnosed radiative fluxes are shown as the differences from the consensus of all 10 CRMs in Table 4. For SW radiative fluxes, some adjustments were made before calculating the consensus to account for the small differences in the TOA downward solar fluxes among the CRMs as a result of slightly different time coordinates in their data. It should be pointed out first that there are very small differences (∼1 W m−2) among the models in the surface upward LW flux because the surface temperature is prescribed. The rest of the larger intermodel differences will be discussed in terms of their relationships with column cloud amounts and cloud optical depths. The magnitudes of the differences will also be compared with the differences between the calculation methods discussed in section 4a.
The surface downward LW fluxes exhibit very small intermodel differences from the consensus of the CRMs (−2.8 to 2.8 W m−2), as do the surface net LW fluxes (−2.6 to 1.7 W m−2). The magnitudes of these differences are slightly smaller than those due to the cloud overlap and uniform hydrometeor assumptions (3.4–5.3 W m−2; see Table 2). The differences of the downward (net) LW fluxes have small positive (negative) correlations with column cloud amount; 0.35 (−0.20), and cloud optical depth; 0.12 (−0.08).
The differences from the consensus TOA LW fluxes have much larger magnitudes (−10.8 to 5.8 W m−2). However, the magnitudes of these differences are still smaller than those due to the cloud overlap (−22.4 W m−2) and uniform hydrometeor assumptions (−13.5 W m−2). All results shown above suggest that the differences from the consensus are smaller than those due to the cloud overlap or uniform hydrometeor assumptions for all LW fluxes. This may be due to the fact that cloud macrophysical properties such as cloud base and top heights for optically thick clouds are well simulated by CRMs. It is noted that the spread from the lowest to the highest values is, however, comparable to that due to the cloud overlap or uniform hydrometeor assumptions. This can also be seen from the shaded areas in Figs. 2a,c and 3a,c in comparison with the corresponding plots in Figs. 2b,d and 3b,d.
The TOA LW fluxes are highly negatively correlated with column cloud amount (−0.86), but only slightly with cloud optical depth (−0.24). Their correlation with the averaged cloud-top height (not shown) is even smaller. This suggests that the LW radiation is more sensitive to cloud macrophysics than cloud microphysics. This is rather obvious if one compares the 2D and 3D results. However, a positive correlation between the TOA LW flux and column cloud amount appears in the GFDL and EULAG CRMs. This result is against physical intuition. It may be related to the fact that both models use simpler cloud microphysics than the other models.
The consensus of the TOA upward SW fluxes is smaller than that observed by 12.4 W m−2. The differences from the consensus range from −9.6 to 11.6 W m−2. This means that a majority of the CRMs underestimatethe TOA upward SW flux except for the UKLEMs. The magnitudes of these differences are higher than the magnitude of the uniform hydrometeor assumption (9.4 W m−2) but slightly smaller than the magnitude of the cloud overlap assumption (14.9 W m−2). The largest intermodel differences occur at large zenith angles as do the overall underestimates of the flux (Fig. 6b). The departures from the consensus are highly correlated with both the cloud optical depths (0.52) and the column cloud amount (0.63). This means that the underestimate of the TOA SW flux can be reduced by an increase of either cloud optical depth or column cloud amount. The intermodel differences in the TOA SW fluxes, as discussed below, can be reduced by improving both the cloud macrophysics and microphysics.
The surface downward SW fluxes differ from observations by 46.8 W m−2, which is very significant. Possible reasons for this were discussed in section 4b. The differences from the consensus are much smaller, from −14.1 to 12.4 W m−2. The magnitudes of these differences are smaller than that due to the cloud overlap assumption (−20.6 W m−2) but comparable to that due to the uniform hydrometeor assumption (−14.2 W m−2). On the other hand, the surface upward SW fluxes have smaller intermodel differences (−2.3 to 2.0 W m−2), the magnitudes of which are smaller than that due to the cloud overlap assumption (−4.8 W m−2), but comparable to that due to the uniform hydrometeor assumption (−2.4 W m−2). The intermodel differences in the surface net SW fluxes range from −11.8 to 10.4 W m−2, the magnitudes of which are also smaller than that due to the cloud overlap assumption (−15.8 W m−2), but comparable to that due to cloud heterogeneity (−11.8 W m−2). The intermodel differences in the net surface SW + LW fluxes range from −12.3 to 11.5 W m−2. The magnitudes of these differences are larger than that due to either the cloud overlap assumption (−10.5 W m−2) or the uniform hydrometeor assumption (−8.4 W m−2).
The most significant result for these radiative fluxes is that their departures from the consensus, as discussed above, are negatively correlated with both the cloud optical depth and the column cloud amount. The correlation coefficients range from −0.48 (between the net surface SW + LW flux and column cloud amount) to −0.63 (between surface downward SW flux and cloud optical depth). The GCE, GFDL, EULAG, and LaRC CRMs, however, show positive correlations between column cloud amount and these radiative fluxes. This suggests that an increase in column cloud amount alone cannot reduce the overestimate of these radiative fluxes shown in Table 4 for these models.
Finally, the intermodel differences in the 14-day mean radiative heating rates, as measured by the standard deviation from the consensus, are not larger than those due to either the cloud overlap or the uniform hydrometeor assumption, except for SW QR in the upper troposphere (Fig. 7). The ranges of intermodel differences (i.e., two standard deviations) are less than 0.5 K day−1 in LW radiation, 0.2 K day−1 in SW radiation, and 0.5 K day−1 in total QR for most heights. These ranges are very close to the differences due to the cloud overlap or uniform hydrometeor assumption (Figs. 7a,b,c). Thus, the intermodel differences in the radiative heating profiles are probably not negligible.
5. Summary
This study has examined the sensitivity of diagnosed radiative fluxes and heating rates to different treatments of cloud microphysics among CRMs. The domain-averaged CRM outputs from a model intercomparison study are used in this calculation. The results were compared to two other calculations that use outputs with spatially varying cloud fields from a single CRM. Comparison among the detailed, intermediate, and domain-averaged calculations has provided a benchmark that measures the sensitivity of diagnosed radiative properties to the cloud overlap and uniform hydrometeor assumptions, which has been used to compare with intermodel differences in the diagnosed radiative properties. The consensus of all 10 CRMs has also been compared with available radiation measurements from an ARM IOP.
It has been found that the cloud overlap assumption impacts the diagnosis more significantly than the uniform hydrometeor assumption for all radiative fluxes. This is also the case for the longwave radiative cooling rates except for a layer above 7 km where it is more significantly impacted by the uniform hydrometeor assumption. The radiative cooling above upper-tropospheric anvils and the warming (relative to the clear sky) below these clouds are overestimated by about 0.5 K day−1 using the domain-averaged data, compared to the detailed calculation. The differences in the radiative fluxes and the radiative cooling rate below 7 km are rather small between the domain-averaged and detailed calculations compared to those due to the cloud overlap and uniform hydrometeor assumptions. The small differences are likely related to the reduced cloud optical depths in the domain-averaged calculation, which is equivalent to the inclusion of the effects of cloud inhomogeneities (Cahalan et al. 1994; Tiedtke 1996).
The consensus of all diagnosed radiative fluxes among the 10 CRMs, except for surface downward shortwave, agrees with observations to a degree that is close to the uncertainties of satellite- and ground-based measurements. The large underestimate in the surface downward shortwave flux is a serious problem in CRMs because it impacts the surface radiation balance in CRMs. This may also have an implication on climate simulation when a CRM is embedded into a global climate model (Grabowski 2001; Khairoutdinov and Randall 2001). Further studies are needed to solve this problem.
The intermodel differences in the diagnosed radiative fluxes and heating rates have been extensively examined in this study. These differences are primarily related to different treatments of cloud microphysics in the 10 CRMs since differences between 2D and 3D simulations are generally small except for the TOA LW flux. The magnitudes of the intermodel differences in terms of the departures from the consensus of 10 CRMs are generally smaller than those due to the cloud overlap assumption and are comparable to those due to the uniform hydrometeor assumption for most SW radiative fluxes and the combined SW and LW fluxes. For all LW radiative fluxes, they are smaller than those due to the cloud overlap and uniform hydrometeor assumptions. This is also the case for the radiative heating profiles. However, the range (two standard deviations) of the intermodel differences in the radiative heating profiles is comparable to the difference due to the cloud overlap or uniform hydrometeor assumptions. The intermodel differences are thus not negligible. Therefore, treatments of cloud microphysics must improve in CRMs in order to provide reliable radiation budgets because several SW radiative fluxes and the TOA LW fluxes are significantly correlated with both column cloud amount and cloud optical depth. An improved treatment of cloud microphysics would yield more accurate cloud macrophysical and optical properties.
Because this is a diagnostic study, feedbacks of cloud–radiation interactions are ignored. It would be helpful to compare the performance of several CRMs using a single radiative transfer code to evaluate the impact of different treatments of cloud microphysics on simulations of cloud systems. A more straightforward comparison is to use a single CRM with multiple cloud microphysics packages. These are suggestions for a future model intercomparison study.
Acknowledgments
This research was partially supported by the Department of Energy’s ARM Program, under Interagency Agreement DE-AI02-02ER63318 and by the NASA EOS interdisciplinary study program. The submissions of intercomparison results from individual modeling groups (Drs. L. J. Donner, W. W. Grabowski, F. Guichard, D. E. Johnson, M. F. Khairoutdinov, J. C. Petch, C. J. Seman, W.-K. Tao, and D. Wang) are greatly appreciated. The author thanks Prof. Qiang Fu for providing the Fu–Liou radiative transfer code, Mr. John Yio for plotting some preliminary results, Dr. Yali Luo for providing satellite data, and Drs. Zachary Eitzen, Bing Lin, Yali Luo, Xiquan Dong, and an anonymous reviewer for providing valuable comments that helped to improve the manuscript.
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Time series of (a), (b) column cloud fractions and (c), (d) cloud optical depths for subperiod A of the GCSS/ARM case 3. In (a) and (c), the solid line is for the detailed calculation, the dotted line is for the domain-average calculation, and the dashed line is for the intermediate calculation. In (b) and (d), the ensemble means of simulated (solid gray) and observed (solid black) quantities are shown. The shaded areas represent −1 and +1 std devs from the ensemble means (solid gray).
Citation: Journal of the Atmospheric Sciences 62, 4; 10.1175/JAS3401.1
Same as Fig. 1 except for (a), (b) surface upward and (c), (d) downward LW radiative fluxes.
Citation: Journal of the Atmospheric Sciences 62, 4; 10.1175/JAS3401.1
Same as Fig. 1 except for (a), (b) TOA upward LW radiative and (c), (d) net surface LW radiative fluxes.
Citation: Journal of the Atmospheric Sciences 62, 4; 10.1175/JAS3401.1
Same as Fig. 1 except for (a), (b) surface upward and (c), (d) downward SW radiative fluxes.
Citation: Journal of the Atmospheric Sciences 62, 4; 10.1175/JAS3401.1
Same as Fig. 1 except for (a), (b) TOA and (c), (d) surface net SW radiative fluxes.
Citation: Journal of the Atmospheric Sciences 62, 4; 10.1175/JAS3401.1
Same as Fig. 1 except for (a), (b) TOA upward SW and (c), (d) surface net SW and LW fluxes.
Citation: Journal of the Atmospheric Sciences 62, 4; 10.1175/JAS3401.1
Vertical profiles of radiative heating rates for (a), (d) LW ; (b), (e) SW; and (c), (f) their sum averaged over the 14-day case-3 period. In (a), (b), (c) three different calculations from a CRM (solid, detailed calculation; dotted, domain-averaged calculation; and dashed, intermediate calculation) are compared, while in (d), (e), (f) the ensemble means of 10 CRMs are shown. The shaded areas represents −1 and +1 std devs from the ensemble means.
Citation: Journal of the Atmospheric Sciences 62, 4; 10.1175/JAS3401.1
Selected input variables for the radiative transfer calculations.
A comparison of detailed, intermediate, and domain-averaged calculations with data from the UCLA–CSU CRM. The differences from the detailed calculation are also shown in the fourth and fifth columns. The differences between the intermediate and domain-averaged calculations are shown in the sixth column. See text for an explanation of these calculation methods. Units for the SW (FSW) and LW (FLW) radiative fluxes are W m−2. Superscripts “up,” “dn,” and “net” denote upward, downward, and net fluxes, respectively.
A list of CRMs participated in the GCSS/ARM case-3 intercomparison project.
Differences from the ensemble means of SW (FSW) and LW (FLW) fluxes. Fluxes are in W m−2. All SW fluxes are normalized by the TOA downward flux before the deviations from the ensemble means are calculated. Superscripts “up,” “dn,” and “net” denote upward, downward, and net fluxes, respectively.
