1. Introduction
Understanding the radiative effects of clouds on the earth–atmosphere system is of crucial importance to improving the accuracy of general circulation models (GCM) to predict our current climate and to better comprehend climate change issues (Stackhouse and Stephens 1991). The chief radiative properties of clouds are expressed in terms of their visible cloud optical depth τ and infrared absorption emittance ε. Although these parameters depend on cloud microphysical content by way of variations in particle phase, size, and shape, or as expressed in many models by mass content and effective particle size, it is ambient temperature that, to a large extent, governs radiative transfer because of the strength of the adiabatic process. Thus, temperature is a basic factor in the parameterization of cloud radiative properties, and relations describing these temperature dependencies can be used to help to validate model calculations.
One important element in this endeavor is related to the component of cirrus clouds inhabiting the upper troposphere (Liou 1986). The essential radiative properties of these ice clouds are that they are optically thin (τ < ∼3.0) in the visible and are gray emitters (ε < ∼0.85) in the infrared (Platt et al. 1987; Sassen 2002). Nonetheless, cirrus clouds are globally widespread and are well positioned in the upper troposphere to modulate the fluxes of incoming shortwave and outgoing longwave radiation (Wylie et al. 1994). Because of this, uncertainties related to the manner in which their radiative properties are treated in GCMs have become an important issue. Stephens et al. (1990), for example, related the relevance of the radiative properties of clouds to climate feedback, and Lohmann and Roeckner (1995) used a GCM to illustrate how different cirrus cloud emissivity parameterizations could have a large impact on the predicted global climate and sensitivity to climate change.
The infrared absorption coefficient σa is a basic cloud property from which the radiative transfer of infrared flux through a cloud can be calculated. It is convenient and most accurate to measure the cloud vertical emittance, and thus absorption coefficient, in a narrow band of wavelengths in the atmospheric window region. This value can then be related to broadband flux emittance and various reflectance considerations through theoretical or experimental values of spectral variation and diffusivity calculations (e.g., Platt and Dilley 1981).
Here we present results from an extensive remote sensing dataset based on combined Raman lidar and millimeter-wave radar measurements of cirrus and using a newly developed algorithm to infer cirrus cloud content (Wang and Sassen 2002a). Our results are compared with similar parameterizations developed from combined lidar and infrared radiometer (LIRAD) datasets from Platt and Harshvardhan (1988) and Sassen and Comstock (2001). Although the equations are significantly different, we show how they can be reconciled by addressing the numerical form of curve fitting and confining the datasets to proper cirrus clouds [as defined in Sassen (2002)].
2. The lidar–radar dataset
Figure 1 provides the results of this analysis in terms of the dependence of σa on ambient temperature T in 1.0°C intervals. For this first result, we show the standard deviations for each data value, which indicate the considerable variability that exists in σa at all cloud temperatures. Frequency distributions of the σa at four selected temperatures (within 3.0°C temperature bins) are given in Fig. 2 to further illustrate this point. The distributions broaden with increasing temperature in a manner very similar to that reported for the visible extinction coefficient in Wang and Sassen (2002b). A basic property of scattering and absorption in cirrus, then, is their strong variability even at a given temperature, which reflects the action of cloud microphysical process involving ice particle nucleation, growth, and vertical transport. Factors such as the cirrus cloud generating mechanism and the cloud-top temperature and relative position within the cloud (Sassen et al. 2002), also have impacts. As shown in Platt et al. (1987), the standard deviation of experimental uncertainties is typically much smaller than the natural variability of σa in clouds.
In Fig. 3, the dependence of σa on midcloud temperature Tm is shown, also in 1.0°C intervals. As in Fig. 1, the expected gradual decrease in average σa with decreasing temperature is clearly in evidence. Note that since both radar and lidar data are needed in the analysis, less accurate data occur at less than −65°C because of the bias in the radar measurements to sense only the densest cold cirrus (Wang and Sassen 2002b). In addition, anomalously high σa are found at the warmest Tm because this cloud sample appears to have included some relatively dense midlevel clouds (Sassen et al. 2001a; Sassen and Comstock 2001).
3. Current cirrus cloud σa parameterization
Using a second-order polynomial function to fit the extended datasets in Figs. 1 and 3, the results of our parameterizations of σa(km−1) in terms of T and Tm (both in degrees Celsius) are shown by the solid lines in Figs. 1 and 3, respectively. The fitted equations are σa = 0.3949 + 5.3886 × 10−3T + 1.526 × 10−5T2 and σa = 0.2896 + 3.409 × 10−3Tm.
4. Comparison with LIRAD parameterizations
The LIRAD method has been used previously to derive the relation between σa and Tm in primarily midlatitude cirrus clouds (Platt 1973; Platt and Dilley 1981; Comstock and Sassen 2001). (Note that, because this approach combines range-resolved lidar with path-integrated infrared radiometer measurements, it is only possible to provide information with respect to Tm.) With this method, simultaneous coaligned measurements of narrow-field-of-view infrared brightness temperature and lidar backscatter cross section are combined to estimate τ and ε. The derived lidar cloud backscatter coefficient βc, which is strongly dependent on the backscatter-to-extinction ratio k and multiple scattering parameter η, is related to σa by assuming σa(z) = ζβc(z). Final values of σa(z) are obtained by iterating ζ and the combined parameter k/2η until measured and model radiances agree. Cloud emittance is then calculated directly from σa(z), and τ is calculated using the final value of k/2η and integrating βc between cloud base and top. The LIRAD method computes ε with an uncertainty of about 10% (Platt and Dilley 1981).
The LIRAD method, as described in Platt and Dilley (1981), provides values of ε and improved estimates of τ by assuming a single value of k/2η for the entire cloud system, which is obtained from the integrated attenuated backscatter as ε tends to unity (Platt 1973). The ratio k/2η can also be obtained for each individual lidar profile by comparing the average backscatter coefficient above the cloud to the expected molecular signal, as described Comstock and Sassen (2001). This method produces an uncertainty of about 24% in τ. The results given here from the University of Utah Facility for Atmospheric Remote Sensing (FARS; Sassen et al. 2001b) dataset are calculated using this new LIRAD approach.
Figure 3 compares the results of the parameterization from our radar–lidar analysis of cirrus clouds from the SGP CART site (solid line) with those from midlatitude and tropical cirrus in Australia [dotted line; from Platt and Harshvardhan (1988)] and the total cirrus cloud sample from the FARS site in northern Utah [dashed line; from Sassen and Comstock (2001)]. The FARS dataset has been restricted to only visually identified cirrus clouds. There are obviously significant differences in the σa-versus-Tm predictions offered by these cirrus cloud parameterizations.
5. Discussion
To help to evaluate the reasons for the differences in the curves in Fig. 3, we first provide, in Fig. 4, a comparison of the original data points composing the FARS and SGP CART datasets (see inserted key). Although the parameterized results are divergent, it can be seen that the data values are in very good agreement over the −20° to −70°C midcloud temperatures appropriate for these midlatitude cirrus clouds (Sassen and Comstock 2001).
Similarly, Fig. 5 compares the individual data points from Platt and Harshvardhan (1988) to the lidar–radar-based parameterization (solid line) from the SGP CART site. In this case, data corresponding to Tm < ∼−30°C are in reasonable agreement with the SGP and FARS parameterizations, although at warmer temperatures the Southern Hemisphere data increase considerably faster.
Thus we conclude that the significant differences in the parameterized curves in Fig. 3 are primarily a result of the earlier convention used to fit the LIRAD datasets. In addition, because of the inclusion of relatively warm cloud data in Platt and Harshvardhan (1988), which violates our working definition of cirrus clouds (Sassen 2002), this particular parameterization has also been affected during curve fitting by the relatively high σa values at the warmer temperatures. It is clear that if the use of a minimum cirrus cloud temperature (of ∼−80°C) for σa = 0 is avoided, then the two LIRAD-derived datasets appropriate for midlatitude cirrus clouds are in good correspondence with our current lidar–radar data based on a different approach. As a matter of fact, the dashed line in Fig. 4 represents the reanalysis of the FARS LIRAD dataset using a linear fit: the result is practically indistinguishable from the current curve.
It is of interest to note that the southern midlatitude LIRAD data from which the Platt and Harshvardhan (1988) parameterization was drawn included some cirrus cloud systems that evolved into deep altostratus clouds with greater optical depths. Such clouds at higher temperatures can be expected to contain larger ice crystals and their aggregates and thus to have higher absorption coefficients. This common evolution in cloud type, then, has been captured in this dataset and can be used to parameterize the development of high cloud systems into midlevel cloud systems. The dashed line in Fig. 5, which clearly curves away from the FARS and SGP results at warm temperatures, provides the following parameterization appropriate for these conditions: σa = 2.6282 exp(0.064Tm).
Last, note that the same concerns regarding minimum cirrus temperature constraints also apply to the parameterization of other cirrus cloud radiative properties such as τ or visible extinction coefficient σe, as was recently pointed out in Wang and Sassen (2002b). We therefore provide the following new parameterization of cirrus cloud σe versus Tm based on the extensive LIRAD data reported in Sassen and Comstock (2001): σe = 0.49 + 0.0052Tm. This equation is based on a linear curve fit but reflects the growth of cirrus clouds at temperatures <−80°C and produces results that are very similar to the second-order polynomial function developed in Wang and Sassen (2002b) using the same lidar–radar dataset as here.
6. Conclusions
The accurate parameterization of the visible extinction and infrared absorption coefficients versus cirrus cloud temperature is crucial for modeling the radiative effects of these upper-tropospheric clouds. Unfortunately, recent analyses of remote sensing datasets have generated significantly different relations.
However, we have been able to show that what appeared to be an inharmonious set of cirrus cloud σa-versus-Tm parameterizations is in effect mainly a consequence of the data curve fitting approach used in each case. The σa data derived previously from the LIRAD approach, which were stated to be valid over the range of observed temperatures, were assumed to go to zero at the frigid (i.e., for midlatitudes) temperature of about −80°C. Of course, the adiabatic process continues to produce ice mass at colder temperatures, as is especially clear in the occurrence of tropical cirrus clouds down to temperatures as cold as about −90°C (Sassen et al. 2000). Because of the drawbacks associated with minimum temperature constraints, we have provided a reanalyzed cirrus cloud σe-versus-Tm relationship based on extended LIRAD data from FARS.
It is also indicated that care must be taken to properly identify cloud type (e.g., cirrostratus versus altostratus) in the creation of parameterizations from extended measurements (Sassen 2002). In the case of the data from Platt and Dilley (1981) and Platt et al. (1987), the cloud sample included cirrostratus that developed into altostratus over the observation period. However, the Platt and Harshvardhan (1988) parameterization remains valid for these prefrontal cirrus/altostratus clouds observed at midlatitudes, and a new exponential σa-versus-Tm fit describing this common transition is offered here, with the following caveat. These clouds contained frequent layers of high backscatter and low depolarization (Platt et al. 1987), pointing to the presence of horizontally oriented ice crystals that could cause a larger emittance than for equivalent particles with random orientations using zenith lidar measurements.
We believe that additional research is needed to determine whether other types of cirrus clouds, particularly those derived from tropical deep convection, will need to be treated as distinct from the midlatitude cirrus considered here. Although the relatively small sample of tropical cirrus clouds from northern Australia in Platt et al. (1987) appears to be consistent with the midlatitude data presented in Fig. 5, because differences in radiative properties as a function of cirrus cloud generation mechanism have been identified in Sassen and Comstock (2001), it may prove useful for GCMs to stratify their treatment of cirrus clouds according to latitude or other factors. Recent observations of tropical clouds in Papua, New Guinea (Platt et al. 1998), for example, have indicated higher values of σa at the lower temperatures as compared with midlatitude clouds. We stress that the basic cirrus cloud generation process to a large extent controls the cloud microphysical conditions that ultimately determine their radiative properties.
Acknowledgments
This research has been funded by DOE Grant DEFG0394ER61747 from the Atmospheric Radiation Measurement Program and by NSF Grant ATM-0119502. Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy.
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Dependence of 1.0°C-average infrared absorption coefficients on ambient temperature derived from approximately 1000 h of combined Raman lidar and millimeter-wave radar data from the SGP CART site. Bars give the standard deviations for each point, and the solid curve shows the result of our parameterization
Citation: Journal of the Atmospheric Sciences 60, 2; 10.1175/1520-0469(2003)060<0428:POIAIM>2.0.CO;2
Frequency distributions of the infrared absorption coefficient for four selected ambient temperatures, showing strong variability at any given temperature
Citation: Journal of the Atmospheric Sciences 60, 2; 10.1175/1520-0469(2003)060<0428:POIAIM>2.0.CO;2
Comparison of midcloud temperature vs absorption coefficient parameterizations from the current study (solid curve and 1.0°C-average σa), Platt and Harshvardhan (1988), and Sassen and Comstock (2001)
Citation: Journal of the Atmospheric Sciences 60, 2; 10.1175/1520-0469(2003)060<0428:POIAIM>2.0.CO;2
Comparison of data points from the current study at the SGP CART and FARS sites for midlatitude cirrus clouds. Also shown are the new parameterized results for the two datasets
Citation: Journal of the Atmospheric Sciences 60, 2; 10.1175/1520-0469(2003)060<0428:POIAIM>2.0.CO;2
Absorption coefficients from Platt and Dilley (1981) and Platt et al. (1987) plotted against midcloud temperature, as compared with the current SGP CART parameterization and a new exponential fit to the Southern Hemisphere data (dashed line) considered to be appropriate for high-level clouds that evolve into midlevel clouds
Citation: Journal of the Atmospheric Sciences 60, 2; 10.1175/1520-0469(2003)060<0428:POIAIM>2.0.CO;2