Intercomparison of heating rates generated by global climate model longwave radiation codes
F. Baer, N. Arsky,1 J. J. Charney,2 and R. G. Ellingson
Department of Meteorology, University of Maryland College Park
Abstract. Longwave radiative heating, which has a pronounced impact on climate prediction, is represented in Global Climate Models (GCMs) by an algorithm which converts model input parameters to heating rates. Since each GCM has a unique longwave radiative heating parameterization, an intercomparison of seven frequently used algorithms designed to assess their variability to input data was performed. The algorithms' heating rate calculation, which is perhaps the most important aspect of the parameterization in that it is a principal part which the GCM actually incorporates into its climate prediction, was evaluated by subjecting each to identical input parameters and comparing the resulting output. It should be noted that the overall shape of a given heating rate profile depends strongly on the depth of the model layers over which the average conditions were determined. But since GCMs ultimately see the heating rates only at model levels, this aspect of heating rate calculations is transparent to the models themselves. For clear sky conditions, the algorithms were tested with a diverse range of input data taken from different geographic locations and seasons and with various distributions of vertical levels. Analysis of the results from these clear sky experiments indicated that heating rate profiles generated by the algorithms were similar, with maximum variations of the order of 0.5°K/d. The differences in algorithm output became substantially more pronounced when clouds at one or more levels with varying thickness were introduced into the input conditions, particularly if the clouds were thicker than one model level. Indeed, for some cloud configurations the resulting profiles of heating rates appear to have no correspondence whatsoever to one another. How important these differences are to ultimate GCM climate predictions is currently under study.
It is evident that large-scale global models have moved to the forefront as primary prediction tools for climate, and with regional models as variants, to the mesoscale as well. With the success these models have had in weather prediction, similar success was and is anticipated in the climate arena. However, important features of the model which had a lesser role on short timescales become more important on climatic timescales, shifting the emphasis from dynamics-dominated processes to the more persistent long-term forces which drive the climate system. These forces include radiative heating and cooling by long and short waves, as well as convective heating and cooling and boundary layer forcing due to variations in surface conditions. These forcing features all arise from a complex of physical and chemical processes, some of which are well understood while others are more obscure and difficult to interpret.
The longwave radiative forcing is particularly interesting and important because it depends, among other factors, on the distribution of the atmospheric aerosol and moisture in all phases throughout the atmosphere. As enthusiasm for climate prediction grew (stimulated in part by global warming research) and a corresponding awareness of how poorly understood and observed radiation was became evident, the Intercomparison of Radiation Codes in Climate Models (ICRCCM) project evolved and ultimately culminated in a comprehensive report by Ellingson and Fouquart (see Journal of Geophysical Research, 96, 8921-9157, 1991). Subsequently, The Department of Energy (DOE) launched a long overdue measurement program entitled Atmospheric Radiation Measurements (ARM). As a corollary, DOE also initiated the Computer Hardware, Advanced Mathematics, and Model Physics program to build more sophisticated and comprehensive climate models that would be prepared to exploit the improved understanding of the forces which drive the system.
The ICRCCM project collected existing radiation algorithms already being used in global climate models (GCMs) and attempted to compare them to a reference line-by-line model. Ellingson et al.  intercompared some 39 such models and demonstrated varying degrees of agreement using the standard soundings given by McClatchey et al. . They primarily examined the predicted fluxes at the bottom and top of the atmosphere. However, since radiative heating rates modify the entire atmospheric column as well as the top and bottom, the radiation parameterizatons must also function everywhere in order to properly determine the temperature tendency in a GCM. This fact becomes evident simply from considering the basic system prediction equations [see Washington and Parkinson, 1986]. Fels et al.  sought to make intercomparisons throughout the atmospheric column under limited input data conditions by comparing earlier versions of the Geophysical Fluids Dynamics Laboratory (GFDL), National Center for Atmospheric Research (NCAR), and Goddard Institute for Space Studies (GISS) models. They reported reasonable agreement amongst the models when compared to a line-by-line reference solution. Most recently, in attempting to find the best radiation model for the Nordic Climate Modelling Project (NOCLIMP) model, Räisänen  compared three models from European Center for Medium-Range Weather Forecasts (ECMWF), Action de Recherché Petite Echelle et Grande Echelle (ARPEGE), and DeutscheWetterdienst (DWD) with the GFDL line-by-line model using the ICRCCM data at a very high 106 level resolution. For those conditions, he found the ECMWF and DWD models to be reasonably accurate.
These attempts at identifying the quality of heating rates for use in GCMs have been made almost exclusively under clear sky conditions; Räisänen  did consider a few cases with clouds and their effect on the response at the top and bottom of the atmospheric column. However, it is well known that clouds have a profound impact on the vertical distribution of radiative heating rates and can critically impact climate predictions [Slingo and Slingo, 1988]. Although cloud observations are currently under intense study with exciting results on the horizon, their distribution and structure throughout the atmospheric column, are currently known to only a very limited extent and can thus provide only sparse estimates to the radiation models in GCMs. Cloud distribution may be essential to accurate calculations of heating rates, but current state-of-the-art modeling cannot yet provide accurate information nor can modelers test their hypotheses with the paucity of available observations. Nevertheless, radiation models must be able to provide realistic heating rates under the types of cloud conditions which can exist in order to achieve success in climate prediction.
As a supplement to the intercomparisons already noted and discussed above, we have studied a number of radiation models (algorithms taken from GCMs) more carefully with the intent of understanding the individual characteristics of the algorithms and assessing their degree of realism. These determinations can then be used to recommend areas where improvements should be made. These improvements will ultimately require implementation of the more accurate observations which are anticipated to evolve from the ARM program. For the present, the McClatchey et al.  soundings and a large set of observational data will be used to explore the variability in heating rates within any one season and/or region. We have also considered the variability of heating rates as they depend on the distribution of vertical levels in the atmospheric column, staying ,however, within the framework of distributions generally applied in GCMs. Finally, we consider the impact of clouds on the vertical distribution of heating rates produced by radiative heating algorithms. To represent their impact, we have arbitrarily introduced clouds at various levels and therefrom assessed and intercompared the behavior of the various radiation models for the same cloud distributions. Finally, using data derived from the ARM/Cloud and Radiation Testbed (CART) southern great plains site, we have intercompared heating rates produced by the models using real observed data.
Since our primary concern is to establish the sensitivity of GCMs to the radiation models they incorporate, and in particular the longwave radiation model algorithm (LWRM) , we have selected for study seven examples of radiation codes, most taken from active GCMs. These models and their source are listed in Table 1, and represent a broad spectrum of the GCMs currently in use. Each modeler provided us with a copy of their code so that the intercomparisons to be described could be made directly by us. The models (LWRMs) are all capable of performing calculations using different numbers and distributions of vertical levels, the choices limited only in that some of the models were unable to perform calculations significantly above the 1 -mbar level and one model could not handle more than 30 levels. All of the models are examples of broadband parameterizations to the longwave radiation processes in the atmosphere. They are contrasted to the line-by-line model of Clough et al.  (CLO), which we selected as the closest reference currently available to the true atmosphere under clear sky conditions. Although our program plan includes the development of a more accurate LWRM if such is needed, our study of intercomparison considers the LWRMs as "black boxes." Thus they all receive the same input data and their output data are subsequently compared. The salient details of the clear sky parameterizations in each LWRM are described below.
The MOR [Morcrette, 1990] and BLA [see Morcrette, 1990] models use identical longwave parameterizations, originally developed at the European Center for Medium Range Weather Forecasting [Morcrette, 1990]. Since the two models are identical with respect to their physics, any intervariation would be due to discrepancies in conversion calculations and round off errors resulting from different means of interpolation to the model layers. The broadband flux emissivity method is employed with six spectral intervals. Rotation and vibration-rotation water vapor bands and both p-type and e-type water vapor (continuum) absorptions are included.
The CCM model (CCM2) [Kiehl et al., 1994] employs the broadband absorption technique to calculate carbon dioxide and ozone emissivities and absorptivities. Water vapor calculations use a broadband absorptance method to determine water vapor absorption over the entire longwave region, accounting for overlap between water vapor and the other gases.
The CSU model [Harshvardhan et al., 1987] combines three different, independently formulated parameterizations for the three absorbers. It uses 10 spectral intervals, chosen to account for overlap between the water vapor, carbon dioxide, and ozone bands. The scheme includes e- and p-type water vapor absorptance, and the vibration-rotation and rotation bands of water vapor.
The ELL model [Ellingson and Gille, 1978] is based on the well-known Malkmus model. Nine overlapping spectral regions spread over 140 spectral intervals including both the rotation and vibration-rotation bands of water vapor, the vibration-rotation bands of carbon dioxide and ozone as well as absorption by methane and nitrous oxide. The water vapor continuum is employed to account for overlap regions. This model also includes e- and p-type continuum absorption [see Ellingson et al., 1994]. Although not used in a GCM currently, we include it to see how it differs or agrees with the other models.
The GAR model [Garand, 1983; Garand and Mailhot, 1990] provides for absorptivities in four spectral bands. Specialized approximations are employed where more than one absorber occupies a spectral region. Both the water vapor continuum and rotation and vibration-rotation bands are present in this model, as well as e- and p-type water vapor absorptances.
The NMC model [Schwarzkopf and Fels, 1991] operates on seven frequency bands. This model computes the absorptivity of the dominant absorber in each region and then calculates the other through a series of highly parameterized, approximate techniques. It includes an extended vibration-rotation water vapor continuum along with the other absorption lines. The code has p-type water vapor absorptance with an extensive e-type water vapor continuum.
The above descriptions refer to the general properties of the algorithms. In addition to these variations, each model (except ELL, which cannot represent cloud processes) also has its own characteristic method for the inclusion of clouds.
The BLA model includes subroutines for the generation of both stratiform and convective clouds. In our experiments we have chosen to prescribe the cloud distribution, so this aspect of the parameterization was not employed. The program requires the optical depth of each cloud layer and calculates cloud emissivity and liquid water content based on that optical depth. Since we did not specify optical depth, the clouds in this model had a default cloud emissivity of 1 (i.e., a black cloud). Clouds at single or multiple levels, variable cloud amounts, and prescribed or randomly overlapping clouds are also possible.
The CCM model has a very simple cloud treatment which does not account for liquid water content or drop size distribution. As input we provide the model with cloud amount and emissivity in each layer, with the emissivity always set to 1. The clear sky fluxes are then adjusted using cloud amount input for every layer with a cloud.
The CSU model requires the cloud fractions of convective and supersaturation clouds as input. The effective cloud fraction is the maximum of these two. The model does not contain any cloud or convective parameterization. The two cloud fractions noted above should be either climatological values or developed from a diagnostic relationship between cloud fraction and relative humidity, although there is no diagnostic relationship present in the code. Neither liquid water content, drop size distribution, or cloud emissivity are required as input, but there is an internal calculation of cloud emissivity based on temperature and pressure.
The GAR model treats clouds similarly to the CSU model. As an input we specify cloud amount and the cloud emissivity is then automatically prescribed. If the temperature is colder than 220 K or the cloud is above 100 mbar, the emissivity is 0.5; if not it is set to 0.97.
The MOR model is similar to BLA. As input it requires cloud amount. Although emissivity of the cloud is a function of liquid water content, all emissivities are assumed to be 1. The liquid water mixing ratio is diagnosed as a given fraction of the saturation mixing ratio.
The NMC model is different from all the others in that it can accommodate only three separate cloud layers. We can specify cloud top, bottom, and amount for low, middle, and high clouds as input information and whether the cloud is thick or thin. Cloud emissivity is included as input, but if it is not specified, it is prescribed inside the model. For low and middle clouds the default emissivity is 1. For high clouds it is set to 0.6 in tropical regions and 0.3 in polar regions.
To maintain consistency with the ICRCCM intercomparisons, we first selected the McClatchey data set for our tests with the LWRMs. This set provides five long-term average vertical profiles throughout the atmospheric column of temperature (T), moisture (Q) and ozone (O3). The profiles are representative of different seasonal and latitudinal locales: midlatitude summer (MLS), midlatitude winter (MLW), Subarctic summer (SAS), Subarctic winter (SAW), and tropical (TRP). Initial tests with these data, to be discussed subsequently, suggested that more detail was needed to establish the variability of heating rates derived from the characteristics of individual soundings. Consequently, additional data profiles were chosen from a set of 1600 instantaneous atmospheric profiles known as Phillips soundings [Phillips et al., 1988]. We selected four sets of 100 observations consisting of temperature, water vapor, carbon dioxide mixing ratio, and ozone mixing ratio soundings. The sets represented four different seasons and latitude bands, chosen for their similarity to the McClatchey soundings: midlatitude summer (MLS), midlatitude winter (MLW), tropical summer (TRS), and tropical winter (TRW). These data allowed us to calculate means, variances, and correlations for the calculated heating rates.
As a measure of the variability in the mean soundings, we display on Figure 1 the temperature and mixing ratios of the two extremes in the data sets, the tropics and midlatitude wintertime. Included are the McClatchey soundings for MLW and TRP, the mean Phillips soundings for MLW and TRS, and the standard deviations of the hundred soundings used for each of the Phillips' means. It is noteworthy that both in temperature and mixing ratio, the mean profiles of the two sets differ significantly, particularly in the winter data. Near the surface, the wintertime mixing ratios differ by almost a factor of 2 (although the values are small compared to the summertime) and the temperatures differ by as much as 5 throughout the troposphere. These differences are overshadowed by the standard deviations in the individual soundings, as exemplified by the Phillips data. Indeed, the large variability in individual soundings from the means will prove to be a severe test of the LWRM's ability to produce accurate heating rate profiles.
For vertical input to the LWRMs, we selected the 30 lowest McClatchey levels (M30) to meet the level distribution constraints of each model. Additionally, to determine the dependence of the heating rates on the number of levels we chose for comparison the 18 levels of the NMC model (N18). Not only is the NMC model a good reference for state-of-the-art GCM modeling, but many GCMs currently running have about 18 levels. Since our interest is to establish the impact of LWRMs on GCM prediction, this choice seems appropriate. The numerical values of the two sets of levels may be found in Table 2. McClatchey 30 level soundings were used for testing the models with clouds, as well as ARM/CART southern great plains site data from the period May 9-14, 1994.
Clear Sky Results
To begin the analysis, all seven models and the reference line-by-line model were presented with data on the 30 levels specified on Table 2. The profiles were interpolated from the five McClatchey sets and the four Phillips averaged sets under clear sky conditions. The calculated heating rate profiles in degrees Kelvin per day are summarized on the left panels of Figures 2 and 3; only MLW, MLS, and TRP (or TRS for Phillips' data) are shown as representative samples.
The heating rates produced using the McClatchey 30 level soundings (Figure 2) display a relatively small spread, although the spread does grow as the input moisture values increase. Moreover, the model profiles tend to distribute about the reference (CLO) profiles. Particularly for the wintertime soundings (MLW and supported by the SAW results), the profiles are very similar for all of the models, the entire spread falling within a 0.25°K/d range at all levels. This result is attributable to the relative scarcity of water vapor in this season and leads to the inference that the parameterization of water vapor absorption presents substantial difficulty and gives rise to the largest variations in output between the different models. In the absence of significant amounts of water vapor, the models tend to produce more similar results. However, the CSU model represents a notable deviation from this observation, particularly in the wintertime soundings. The CSU model displays more cooling in the middle troposphere for all seasons, regardless of latitude or (as we shall see) level distribution. Since the vibration rotation band plays a very minor role here, the differences noted could be due to differences in either the p-type continuum or the pure rotation band of H2O.
Careful comparison of the GAR profiles with those of the other models shows them to be somewhat smoother. This effect is most apparent in the TRP data cases but can also be seen in other seasons. As will be seen subsequently, the observation is even more pronounced in the N18 cases. This reduction in detail could be indicative of a hidden smoothing factor in the GAR model that is not present in the others.
The spread of the heating rate profiles is everywhere less than 1°K/d and most often less than 0.5°K/d. It is difficult to determine the significance of this difference because it is not evident that the models will provide heating rates of this difference systematically when employed in a GCM. Moreover, as we shall see, such differences are dwarfed when differences including clouds are presented. Systematic analysis of carefully designed GCM intercomparisons are needed here to determine the impact of these differences in the output of the algorithms. Note that other forcing functions interact with the longwave radiative heating in GCMs, thus adding to the difficulty in assessing significance to the observed results presented here.
Model Level Response
The sensitivity to level adjustment becomes apparent from the results depicted on the right hand panels of Figures 2 and 3, which are essentially the same as the left panels except that the heating rates were generated on the N18 level grid. Note that there is a potential pitfall when comparing the heating rates from the M30 to the N18 profiles. By definition, the heating rate represents an average value of the heating (or cooling) which occurs throughout a given layer. Therefore, if layers which have different boundaries are compared, even if they happen to overlap for most of the area, they will not necessarily have similar average heating rates. This interpretive problem can be bypassed by comparing only heating rate regions whose endpoints coincide exactly (i.e. profiles having the same level distribution). Heating rate comparisons in profiles with different level distributions must be evaluated with great caution and avoided if possible. In general, it is far preferable to remark on model profile comparisons using the same vertical discretization. Nevertheless, since a GCM uses the information that is provided by its incorporated LWRM, it is important to know how sensitive the heating rate profiles are to the vertical discretization.
The summertime soundings (MLS and also SAS) provide more apparent insight into the consequences of altering the vertical discretization. The ELL and GAR models display somewhat larger departures from the norm of all profiles in the N18 distribution than in the M30, suggesting a dependence on the vertical detail achieved in the M30 distribution. Specifically, the spread increases in the troposphere, again indicating a possible difficulty with the water vapor absorption. None of the other models display as marked an increase in variability for the summertime soundings.
The TRP heating rates further emphasize this sensitivity to the water vapor absorption parameterization, particularly as applied in the ELL, CSU, and NMC models. However, processes other than water vapor differences also appear to have an impact. The NMC model has a large spike in the M30 profile below 700 mbar, with substantially more cooling predicted than in the other models. But in the N18 sounding, the NMC profile actually predicts less cooling than the other models there. While this unusual variation is obviously tied to the water vapor absorption (since it does not appear in dryer soundings), there seems to be a strong dependence on the number and locations of the levels in the lower troposphere. It is particularly interesting that by changing from the M30 to the N18 distribution, the NMC model changes from giving much more cooling in the lower troposphere compared to the other models, to giving slightly less cooling. This is likely due to the way the model performs the integration over altitude. For example, the ELL model assumes the Planck function to vary linearly with optical path, whereas many of the other models simply assume a geometric average for the Planck function with altitude. Since water vapor absorption/emission varies in a nonlinear fashion with altitude, simply changing vertical resolution without modifying the altitude integration will lead to substantial errors in different altitude regimes, depending upon the amount of water vapor in the layer.
The mean heating rate results from the Phillips data sets for MLS, MLW, and TRS for both M30 and N18 are shown in Figure 3. Although the mean Phillips heating rate profiles are derived from instantaneous soundings whereas the McClatchey profiles are generated from long-term average soundings, the results from both are surprisingly similar over most of the domain. This is in part explained by a separate test wherein the Phillips soundings were first averaged and a heating rate was calculated therefrom; the difference between this heating rate and the average heating rate calculated from the individual soundings was negligible. The comparisons between the Phillips and McClatchey profiles are supported by all data sets and all LWRMs using the M30 distribution except for the NMC model, which shows a significant difference near the surface in the region where we have previously described an aberration. It should be noted however that the heating rate profiles derived from the two data sets are noticeably different in the stratosphere. Here we see a relative maximum of heating rate near 100 mbar from the Phillips data in the midlatitudes not seen in the results from the McClatchey data. This result may well be due to averaging of the vapor content in the soundings and particularly the averaging of the ozone distribution in the McClatchey data, although a review of the input data from Figure 1 does not make this interpretation obvious. Referring to the average Phillips heating rates, the CSU model again produces more cooling in the troposphere, as it did with the McClatchey data. The wintertime soundings are also more consistent than the summer. The TRS (and TRW) results do not show this trend as clearly as the other summer-winter pairs due to the significant water vapor present during both seasons.
The relative behavior of the models amongst themselves and as compared to the reference CLO model is summarized on Figure 4. In this figure we show the mean heating rates of all seven models and their standard deviations (inner error bars) calculated from the mean Phillips profiles for the TRS and MLW data for both the M30 and N18 distributions. Superposed on the M30 profiles are the CLO results. As noted from previous figures, the intervariability of the models is not particularly large except at the lowest levels in the tropics, and this deviation is attributed primarily to the aberration in the NMC model. However, the models seem to scatter more closely about their own mean than about the reference (CLO) profile; this is most evident in the TRS results. Thus using means from the various models in the tropics would probably not gain much of an advantage in a GCM, and would not likely yield heating rates closer to reality.
Sounding Variability Response
The variability of heating rates from one sounding to another within each data group was determined by calculating the standard deviation of heating rates generated from the 100 Phillips soundings in each chosen data set. Selected samples of standard deviations for each of the seven algorithms are presented on Figure 5. We show results for both the M30 and N18 distributions for TRS, MLS, and MLW. It is evident from this figure that although the models give similar results, the variability from the mean is sizable. Indeed, the magnitude of the deviation is substantially larger than the variability of the models from one another, as evidenced on Figure 4. On that figure we have presented the mean standard deviations of all the models as the outer error bars on the N18 profiles, which clearly are considerably larger than the model standard deviations (inner error bars).
The recurrent theme of soundings with high water vapor content giving the widest variations in heating rates is also evident in the variances, with perceptibly larger values appearing in the summertime soundings and in the tropics. Note that the standard deviations decrease systematically with height, as may be expected from observation that heating rates themselves have this property, but the relative variability with height remains sizable. From a radiative transfer point of view, the altitude of maximum cooling rate for a given spectral interval will occur at optical depth one. For a given water vapor distribution, different model-to-model heating rates imply substantially different absorption parameterizations, assuming the other parameterizations are approximately equal. Cooling by water in the middle and upper troposphere is dominated by the pure rotation band [see Clough et al., 1992]. Model-to-model differences in these regions are likely due to differences in the parameterizations of both the spectral lines and the continuum. Of further interest is that the models all exhibit a tendency toward reduced variability proceeding into the stratosphere, with heating rate values also diminishing. This minimum is probably attributable to the general similarities between the ozone parameterizations from model to model. Since ozone dominates the absorption in the region and the variation of ozone is small compared to other absorbers, the models all tend to predict very similar heating rates for each sounding. Since the variances increase at levels away from the stratospheric minimum, this phenomena highlights the increasing concentrations of other absorbers.
Several noteworthy observations from Figure 5 are the following:
The problem with the NMC model in the lower atmosphere in the presence of high water vapor concentrations becomes even more apparent in the standard deviation calculations for the M30 distribution. This aberration disappears when the model uses the N18 distribution, indicating an inability to handle high water vapor concentrations in the region using the M30 distribution.
The GAR model gives significantly smaller standard deviations in the troposphere for nearly all of the soundings and for both the M30 and N18 distributions. This is additional evidence suggesting an implicit smoothing factor in the model that is absent in its counterparts. Somewhat surprisingly, the ELL model displays a similar behavior but only in the N18 MLS sounding. Since there is no smoothing, this may be due to the model performing the altitude integral in nearly the same manner as for the 30-level soundings case, thereby placing the dependence of the cooling at the appropriate pressure level. The smaller standard deviation for the 18-level case is likely due to greater vertical separations masking the actual level where the spectral optical depth reaches 1.
There is evidence of a uniqueness in the CSU model's water vapor calculations in the upper troposphere; we note from several soundings, notably the M30 TRS sounding, that there is more variability in the CSU model near the 300 mbar level than in any of its counterparts.
Above 100 mbar there is good agreement in the variances for virtually all of the models. The numerics are probably best for the models here because absorption by water is in the weak line limit over most of the spectrum. Thus all of the model vertical integrations should lead to similar results.
There is a pronounced maximum of standard deviation in the boundary layer as seen from the N18 distributions on Figure 5. This implies high variability in heating rates there as calculated by the various algorithms and again suggests that mean soundings may not give a good representation of boundary layer longwave radiative heating. Since this region is particularly sensitive to the parameterization of the continuum, these differences are likely due to the combined effects of different physics and different numerical methods.
We have demonstrated that the individual models, with some notable exceptions, give on average both similar heating rates and similar standard deviations under clear sky conditions. However, it must still be established whether the models treat individual soundings similarly and not just in a statistical sense. To assess this issue we have correlated each model with all of the others for the entire data set of Phillips soundings, generating correlation coefficients which we have plotted as a function of model level. It would be ideal to correlate the models with the reference heating generated by the CLO model, but calculating that many LBL profiles is computationally too expensive. An alternative would be to correlate the models with the mean profiles generated from all the models. Since the MOR profiles are very close to the model means (see Figures 3 and 4), we elect to present on Figure 6 the correlations of each model with the MOR model for TRS and MLW data sets using both M30 and N18 levels. Since the ELL model uses a much higher spectral resolution than the other models, its correlation is difficult to interpret and not included here. Some significant differences in model results are highlighted from this figure, although it must be emphasized that these results do not draw comparisons to the real world. Since the nature of correlation coefficients precludes a full understanding of the model differences without additional statistical analyses, we will make no attempt to explain low correlations but instead merely point out where a more detailed study might be carried out.
Most of the correlation features are evident from Figure 6. We note that in general the correlations are reasonably good in the midlatitude winter domain, which is consistent with the observations of the mean results displayed on Figure 3. However, there are some disturbingly low correlations between the GAR and MOR models and lower correlations in general if the N18 distribution is used. The results are less encouraging in the tropics, however. There we find a number of reasonably poor correlations amongst the models, a result which is supported by other correlations which were made but not presented here. The NMC outlier previously seen on the TRS M30 profile is clearly evident. The GAR model in particular displays some widespread low correlations in the troposphere. Specifically, above 200 mbar there is significant variability in the correlations for the M30 soundings. This is probably due to the small values found there so that small differences show up as significant correlations. In general, these results are not very encouraging particularly since the correlations reflect only clear sky conditions.
We have repeatedly emphasized the algorithms' response to moisture as a source of possible differences and that the moisture profile in the sounding data is fundamental to the heating rates produced. To document this point we present Figure 7, which shows the heating rates generated by the McClatchey soundings for a representative subset of the models using the MLS and MLW data sets and M30 distribution. The profiles labeled "moist" represent results reproduced from Figure 2, and those labeled "dry" present the same calculations but with the moisture removed from the sounding data. It is apparent that longwave radiative cooling without moisture is substantially reduced the troposphere when compared to the cooling calculated with moisture, so one must thus infer that errors in the moisture profile could yield different heating rates. Moreover, the calculation of heating rates by the LWRM is highly sensitive to moisture, so slight variations in calculation procedures in the algorithms could explain some of the variations in results presented so far. It is noteworthy, however, that differences in the calculation of cooling even without moisture can yield differences of output amongst the algorithms, as seen by the NMC profile on Figure 7 which is a marked outlier.
Cloudy Sky Results
The LWRMs are all capable of handling complex cloud situations insofar as clouds of any density and character can be included within the levels specified by the LWRM. It is the response of the LWRMs to this input and how they compare for the same specification of clouds that we wish to investigate. Unfortunately, cloud observations are highly qualitative when it comes to creating a detailed profile over some 30 levels in the vertical column. We shall discuss meaningful observational data subsequently. For the moment, let us consider arbitrary cloud distributions superposed on our statistical clear sky data profiles,- -say the McClatchey profiles,- -and assess LWRM sensitivity to such "arbitrary" data. We have selected to place a cloud at a single level of the model and then move that cloud throughout the troposphere one level at a time. Thus for a given sounding of (T, Q) we add a cloud at each of the lowest 11 levels of the McClatchey 30-level TRP sounding, level by level. This yields 11 heating rate profiles which we superpose.
As expected, the models all exhibit a sharp cooling at the specified cloud level. This calculation was performed with all of the LWRMs except CLO and ELL; i.e., in six models (the latter two were omitted because it was not obvious from the versions available to us how clouds should be introduced into them). Using such a thin cloud, the models are able to produce comparable heating rate profiles. Only the GAR model has systematic differences, with reduced cooling at all levels similar to that seen previously. The BLA model is chosen as representative of the other models and we show its resulting heating rate profiles on Figure 8. Since the CCM tends to give somewhat anomalous results at higher levels of the atmosphere (see Figures 9-11 for example), we also include its profiles on Figure 8. Although the figure does not specify which profile is associated with a specific cloud, the distinct minima in heating rate clearly identify at which level the cloud was inserted. Note that only at the highest level ( ~ 250 mbar) does the effect of the cloud change the sign of the heating. These features have, of course, been noted before [see Ellingson, 1982].
Unfortunately, since clouds generally do not appear as thin bands at one level only, it is necessary to test for the effects of thicker and/or multiple cloud layers. Experiments with hypothetical distributions of clouds, because of the multitude of possible orientations, may appear as a rather random procedure but, after a number of such tests, do lead to some qualitative observations. As the clouds thicken in any layer the amplitude of the cooling at that layer begins to differ substantially amongst the various models, despite the fact that each received identical data. If clouds are introduced at two levels, the lower and the upper troposphere for example, not only are the heating rates at the cloud levels different for each of the models but the heating rate profiles between the cloud levels also differ substantially, with variations of the order of several degrees Celsius per day. This result appears to be independent of geographic region or season, as noted from tests using the McClatchey MLS, MLW, and TRP soundings. An additional shortcoming of this experimental approach is that it does not relate the temperature and moisture profiles with the cloud distributions, although there surely is a close functional relationship amongst these variables in the real atmosphere.
Having available a convenient data source of reasonable quality with cloud specification provided from the DOE ARM/CART site in the southern great plains, we have analyzed 1 week of that data from May 9-14, 1994, for use in testing the algorithms with real clouds. The relative humidity on each of the 30 vertical McClatchey levels was determined for each of the soundings available during the selected period. From that set we chose those soundings that have relative humidity greater than 75% at one or more levels for testing with clouds in the algorithms. By requiring a significant level of moisture in the sounding, we can be assured that the clouds will correlate well with the moisture distribution. The weather logs were checked to confirm that clouds were indeed present during the time of the sounding. In addition, cloud amounts were assigned for each level with clouds based on the weather log. Under some circumstances this was straightforward, but in the case of overcast sky with 100% low cloud coverage, it was difficult to establish cloud amount at higher levels. In those situations we made the determination based on cloud distributions at the most recent available previous time. Very few cases with only one level of cloud were found; most of the soundings have clouds at two or more levels. Generally, the cloud amount is less than 100%.
Based on that data set, 13 individual soundings were found to be applicable to our experiment and were used as input for the LWRMs. Figure 9 is a demonstration of the result if only a thin cloud layer near the Earth's surface (level 30) is present and is a realization of one of the experiments included on Figure 8. Relative to the scale of the abscissa on Figure 9, it appears that the models tend to yield very similar heating rate profiles, varying obviously only in the region very near the cloud. This is, of course, somewhat delusive since we have already demonstrated that the algorithms differ from one another under clear sky conditions by 0.5o to 1o K, but it does highlight the enormous difference noted when clouds are present. The cooling rate is decidedly sensitive to the density of the cloud (sometimes also denoted as cloud fraction or cloud amount), which can be seen by comparing Figure 9a with a cloud density of 1 to Figure 9b with cloud density of 0.5. However, the heating rate profile above cloud level is clearly determined by the temperature and moisture sounding data, a feature previously explained by Rodgers and Walshaw  and Ellingson and Gille  as resulting from a profile dominated by cooling to space. This is demonstrated by Figures 9c and 9d where the heating rates were determined from the same cloud distribution used for Figures 9a and 9b, but with the statistical sounding data from the McClatchey 30-level MLS profile in conjunction with the clear sky results rather than the (substantially different) observed profiles.
When clouds occur at more than one level, larger differences in the calculated heating rate profiles begin to appear. For two cloud levels, if the clouds are thin (i.e., each only one level thick), the model profiles are similar, as can be seen on Figure 10a and 10b. Figure 10a represents a thin low and a thin high cloud and Figure 10b a thin low and a thin middle cloud. When one of the cloud layers is thicker, as is the case for Figure 10c which includes a thick lower cloud and a thin high cloud, the heating rate profiles produced by the algorithms differ considerably in the region of the thick cloud. Above the thick cloud the algorithms' heating rate profiles tend to agree. With a thick cloud in the middle of the troposphere and a thin cloud at the bottom, as shown on Figure 10d, the heating rate profiles produced by the various algorithms differ significantly throughout the troposphere. This result is related to the flux calculations near cloud boundaries and is a familiar problem to most of the radiation community [see Fels and Kaplan, 1975].
Even when three cloud levels exist, provided that they are thin (only one level each), the algorithms are able to reproduce each others' heating rate profiles reasonably well; see, for example, Figure 11a which represents three thin cloud levels. However, when any one or two of the three cloud levels is thicker (see, e.g., Figure 11b where a thick lower and middle level cloud and a thin upper level cloud are present), the heating rates produced by the algorithms are substantially different. When the cloud is continuous throughout the troposphere, the heating rate profiles produced by the algorithms show little similarity; this observation is apparent from Figure 11c. Indeed the effect of this cloud distribution is so pronounced that it is difficult to distinguish the effect of the thermal and moisture profiles included in the data used by the algorithms. We saw from Figure 7 how sensitive the heating rate profiles are to the input profiles for clear sky conditions and even for thin clouds, as evidenced by Figure 9. However, note from Figure 11d, which uses the same cloud conditions as Figure 11c but substitutes the McClatchey 30-level MLS profiles for temperature and moisture, that the variation amongst heating rate profiles produced by the algorithms are comparable, although they are not necessarily the same as the profiles of Figure 11c. This result leads us to speculate that cloud effects dominate in the evolution of heating rate profiles, but the profiles of temperature and moisture cannot be ignored in the development of the heating rate profiles. Moreover, as the cloud distribution becomes more significant in any individual sounding, each LWRM produces a unique heating rate profile which differs from the corresponding profile produced by any other algorithm.
Conclusions and Recommendations
Based on the importance of longwave radiative forcing to global climate models and the ultimate climate they produce, we have studied and intercompared a number of longwave radiation model algorithms, most used by GCMs to produce the longwave radiative heating and cooling which influences the model's thermal field. In contrast to previous studies which have focused on heating impacts at the bottom and top of the atmosphere, we have concentrated on the heating rate throughout the entire atmospheric column. Because of the atmospheric sensitivity to thermal stability, heating rate profiles have a pronounced impact on the time evolution of the three-dimensional atmospheric field variables. Ideally, we should like to assess how accurately the algorithms used in the GCMs determine the heating rates due to longwave radiation, but unfortunately there are no observations of this quantity to use for reference. However, it is possible to intercompare the output of the algorithms and ultimately to establish how significant observed differences amongst them are in determining variations of predicted climate.
We have intercompared seven different algorithms, most of which were taken from their own current GCM. It should be noted that the ECMWF algorithm has undergone several versions and Morcrette  intercompared some of them. In addition, we had available a reference algorithm which is based on a line-by-line code (CLO) and which should by definition come closest to simulating the real atmosphere, albeit only under clear sky conditions. Since all of these models need identical initial profiles of temperature, moisture, clouds, and trace gases and/or aerosols, we selected a variety of atmospheric profiles with which to test the algorithms. Some profiles had been used in previous studies, while others were newly compiled by us. When tested under clear sky conditions, the models all gave similar heating rate profiles, varying from one another by about 0.5°K/d at most pressure levels but distributing somewhat more about the reference profile. However, notable exceptions were identified. Since the input profiles were varied according to season and geographic region, differences in the resulting heating rates were noted based on these variations. Moreover, the input data were based on statistical soundings. When variability in individual soundings which generated the statistical profiles was investigated, it was discovered that significant differences in heating rate output amongst the algorithms evolved. Thus, although the algorithms gave similar heating rate profiles for averaged input data, the algorithms yielded substantially larger differences when individual profiles from the statistical average set were utilized and the results were intercompared. Indeed, the standard deviations of the heating rates produced by any algorithm from soundings which made up the mean sounding were as large or larger than the variations of output from each algorithm when utilizing the mean input data.
Altering the location and distribution of the algorithms' vertical levels and noting the resulting differences in heating rates amongst the LWRMs was considered pertinent insofar as GCMs are developed with a variety of different level distributions. However, we were unable to establish firm evidence that such redistribution has a significant impact on heating rate calculations. Circumstantial evidence indicates that there are differences, but more study is needed to firmly establish the nature of these variations. Our lack of confidence in the observed differences arises from the fact that heating rates in layers with different boundaries cannot be directly compared. A logical next step in this assessment would be to compute heating rates for level distributions with the same heating rate levels but different numbers of calculation levels. The levels present in corresponding soundings could then be compared directly.
When clouds are included, the picture we have described for clear sky conditions changes dramatically. We tested the algorithms with statistical soundings of the clear sky experiments with arbitrarily assigned clouds and also with individual soundings which included real observations of clouds. If the clouds remain thin (i.e., only one level thick), the algorithms tend to reproduce heating rate profiles which are similar and exhibit variability comparable to those for clear sky conditions. However when the clouds become thicker, the heating rate profiles produced by the various algorithms differ substantially from one another, and often the profiles are so different that there is no recognizable comparison. These observations are based on algorithm output from identical input. Unfortunately, there are no observations against which the quality of these profiles can be established; we only have intercomparisons.
It is evident that more homogeneity and agreement
in output of the various algorithms would be desirable. Yet we
do not know with certainty that more accuracy in heating rates
would improve climate prediction, although speculation suggests
that this is so. Errors in heating would modify the thermal profiles
in a GCM and thus lead to differences in the evolving fields.
Since the errors from the heating rate algorithms are more than
likely systematic, the GCM predictions would then also evolve
to a systematically different climate. We are currently testing
this effect by performing twin climate integrations with a GCM.
The same GCM with identical initial and boundary conditions is
run twice with only the longwave radiative heating algorithm changed.
Currently, we use the CCM2 with the CCM and MOR algorithms interchanged.
This experiment should identify the range of sensitivity which
GCMs have to the heating rate algorithms studied in this report.
Acknowledgments. The research reported herein has been supported by the Environmental Sciences Division of the U. S. Department of Energy (under grants DEFG0590ER61075 and DEFG0294ER61746 to the University of Maryland College Park) as part of the Atmospheric Radiation Measurement Program.
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Phillips, N., J. Susskind, and L. McMillin, Results of a joint NOAA/NASA sounder simulation study, J. Atmos. Oceanic Technol., 5, 44-56, 1988.
Räisänen, P., Single column experiments with the ECMWF, DWD, and ARPEGE radiation schemes, Rep. DM-69, 67 pp., Dep. of Meteorol., Stockholm Univ., Stockholm, Sweden, 1994.
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N. Arsky, Platinum Technology, Inc., 4601 N. Fairfax Drive, Arlington, VA 22203. (e-mail: email@example.com)
F. Baer and R.G. Ellingson, Department of Meteorology, Computer and Space Sciences Building, University of Maryland, College Park, MD 20742. (e-mail: firstname.lastname@example.org; email@example.com)
J.J. Charney, Department of Meteorology, Pennsylvania
State University, University Park, PA 16802. (e-mail: firstname.lastname@example.org)
(Received October 27, 1995; revised June 18, 1996;
accepted July 25, 1996.)
Now at Platinum Technology, Inc., Arlington, Virginia.
at Department of Meteorology, Pennsylvania State University.,
Copyright 1996 by the American Geophysical Union.
Paper number 96DJ02511.
Copyright 1997 by the American Geophysical Union.
Paper number 96DJ02511.
Table 1. Set of Seven Models Intercompared in This Study
|BLA||Canadian Climate Center, Canada||J.-P. Blanchet|
|CCM||National Center for Atmospheric Research||D.L. Williamson|
|CSU||Colorado State University,||D. Randall|
|ELL||University of Maryland||R. Ellingson|
|GAR||Recherché en Prevision Numerique, Canada||L. Garand|
|MOR||European Center for Medium-Range Weather Forecasts, United Kingdom||J.-J. Morcrette|
|NCEP||National Centers for Environmental Prediction||K. Campana|
Table 2. Level Distributions Used
Data in Sigma units.
Figure 1. Data
used to test the longwave radiation algorithms. Data are examples
for the tropics (TRP) and midlatitude winter (MLW) and are taken
from the compilations of Phillips and McClatchey (see text).
McClatchey data are for mean profiles only. Since the Phillips
data include 100 soundings in each group, standard deviations
of that data set are included in addition to the mean (shaded
Figure 2. Heating
rates generated by the seven tested algorithms and the reference
algorithm (CLO) for the McClatchey data sets representing the
tropics, midlatitude summer and midlatitude winter. Profiles
using both 30 levels and 18 levels are shown.
Figure 3. Same
as Figure 2 except that the Phillips data sets were used.
Figure 4. Heating
rate profiles generated from the Phillips data sets. The two
left panels show the mean profiles of the seven tested algorithms
with their standard deviations compared to the reference model
profile using 30 vertical levels. The right-hand panels show
the same mean profiles and standard deviations but for 18 vertical
levels. The wider error bars here represent the mean of the standard
deviations of all the algorithms on each level.
Figure 5. Standard
deviation profiles of heating rates for the seven algorithms tested.
Phillips data sets for the tropics, midlatitude summer and midlatitude
winter were used, and results using both 30 levels and 18 levels
Figure 6. Correlation
coefficients of heating rate output from the five listed algorithms
with the MOR model. The Phillips data sets for TRS and MLW were
used to generate the heating rates, and correlations are displayed
for both the 30- and 18-level profiles.
Figure 7. Heating
rate profiles for four selected algorithms using McClatchey 30-level
data. Compared are the results for the given data (moist) and
for data with all the moisture removed (dry).
Figure 8. Heating
rate profiles using the McClatchey 30-level TRP sounding data
and including clouds one level at a time for all 11 levels in
the troposphere. Results using the CCM and BLA algorithms are
Figure 9. Heating
rate profiles generated by six algorithms from observed data including
clouds. Examples using data with low - thin clouds are presented
together with results using the same clouds but the McClatchey
30 level MLS data. Note cloud level/cloud density (Lxx/x.x).
Figure 10. Same
as Figure 9, but for two cloud level data and only for observed
Figure 11. Same
as Figure 10, but for multiple cloud level data.