a. In situ measurements

Tropopause cirrus layers were sampled near Kwajalein, Marshall Islands, using a high-altitude WB-57F high-altitude jet in the mid-1970s (Heymsfield and Jahnsen 1974; Heymsfield 1986). For the one case where original data are still available (18 December 1973), measurements were made between 16.2 and 16.7 km (temperatures of −83° to −84°C). There was a double tropopause, one at 16.7 km and another weak tropopause between 16.2 and 16.5 km. The 0.5-km thickness is very close to the average thicknesses of other subvisible cirrus observed during this project and during CEPEX and TOGA COARE; the particle sizes were similar to those observed during four other cases (A. J. Heymsfield 1998, personal communication).

For measuring ice crystals, the WB-57F aircraft was equipped with a particle measuring system axially scattering spectrometer probe (ASSP), which sized in the range 2–30 μm, and a one-dimensional cloud (1DC) particle probe sizing in the range 20–300 μm. Excellent information about the crystal shape was obtained with a formvar replicator since the small crystals did not break up on impact. Heymsfield (1986) reported an approximately 50% mixture of trigonal plates and columns for the larger ice crystals measured by the replicator. Examples of the trigonal ice crystals observed are depicted in Figs. 3 and 4 of that paper, and of columnar ice crystals in Fig. 5. A bullet polycrystalline form and plate crystal are also depicted in Fig. 4.

Figure 1 of this paper shows the size distributions measured at six different altitudes in the cirrus using the ASSP data presented by Heymsfield and Jahnsen (1974). Crystals larger than 17 μm were not detected by the ASSP, and most were smaller than 10 μm. However, particles with maximum dimensions up to 50 μm were occasionally detected by the 1DC and are presented in Fig. 1 assuming that the crystals are evenly distributed over sizes up to the maximum crystal length detected. The ASSP did not detect the larger particles because its sample volume is very small. Gayet et al. (1996) found that the ASSP/forward scattering spectrometer probe–type probes give reliable measurements consistent with other probes in the presence of small quasi-spherical ice particles. Although the replicator only provides size information about the larger ice crystals, the smaller numbers of large crystals measured by the 1DC, in situ observations of quasi-circular small ice crystals during CEPEX (Heymsfield and McFarquhar 1996), and the reasonable overlap of the 1DC and ASSP observations suggests that the number distributions plotted in Fig. 1 from the ASSP are reasonable.

The 1DC is used to estimate particle mass by combining the replica shape information with the 1DC measurements. A profile of ice water content (IWC) calculated from the measured spectra using Heymsfield and Jahnsen’s (1974) relationship between crystal length and crystal mass, is shown in Fig. 2. Both the contributions of small particles measured by the ASSP and the larger particles measured by the 1DC are included in the calculated profiles. While the ASSP measurements dominated the number concentrations, the 1DC measurements dominated the calculated mass. The double structure seen in Fig. 2, with a minimum in IWC at 16.5 km, was also observed with the mass densities estimated from the Stanford Research Institute ground-based lidar. Cirrus number densities derived from the lidar data agreed with the in situ densities within a factor of 2 when crystal information was considered (Uthe and Russell 1977).

The D_e [Fu and Liou (1993); Eq. (2.1)], is also shown in Fig. 2. There is no notable trend in altitude of typical particle sizes. The D_e are calculated using the Fu and Liou (1993) definition since their radiative code is used to calculate the radiative significance of this cloud; this definition assumes particles are hexagonal columns and represents the effective size as the mean-weighted crystal width. The visible optical depth, τ_vis, estimated from the microphysical data assuming Fu and Liou’s (1993) relationship between mean effective size (D_e), IWC, and volume extinction coefficient (β_ext), is 0.007, greater than averages seen during CEPEX from lidar data (0.0045), but well within the range of typical values and below the visible threshold. Mass-weighted terminal velocities of 1–2 cm s⁻¹ are estimated from the terminal velocities of the larger crystals (Heymsfield and Iaquinta 2000), corresponding to a descent of 1.7 km day⁻¹, suggesting that the presence of large-scale motions is needed to account for the ubiquitous nature of the subvisible cirrus.

Using the Aeromet Learjet, Booker and Stickel (1982) often noted a tenous cirrostratus in a thin and uniform layer just below the tropopause at Kwajalein, which was visible only at low sun angles or when flying above 10 km. On two occasions, the Learjet, instrumented with optical array particle measurement probes, was able to penetrate into and above the cloud layer. Figure 3 shows the IWC profile measured during a climb through the cirrus on 19 February 1981; a second tenuous layer 100 m thick at 15.4 km was not penetrated. From a rawinsonde sounding 6 h earlier, it is known that cloud temperature ranges from −70° to −80°C. The IWCs and D_es are remarkably similar to those depicted in Fig. 2;the maximum crystal lengths were up to 140 μm. Booker and Stickel (1982) noted an intensification of the layer during the course of the measurements, and the cirrus was visible from the ground after this profile was obtained. They also stated that this was the most intense example of subvisible cirrus observed during the several years of their experiments, probably because it was the lowest and hence is not really an example of tropical tropopause cirrus. Although τ_vis is 0.012, almost double that of Heymsfield and Jahnsen (1974), it is still below the visible threshold. The D_e is constant because Booker and Stickel (1982) only presented one size distribution averaged over the 9 min of ascent. For the other case analyzed by Booker and Stickel (1982), they presented only one averaged particle size distribution for the entire ascent on 16 June 1978. For this 400-m-thick cloud with 15.5-km cloud top, this corresponds to an IWC of 1.5 × 10⁻⁵, D_e of 7.9 μm, a τ_vis of 0.0036, and a maximum crystal size of approximately 30 μm.

b. Calculated radiative forcing

Fu and Liou’s (1993) δ-four-stream approximation for radiative transfer was used to investigate the broadband solar and infrared radiative properties of these clouds. The Fu and Liou (1993) code parameterizes the basic single-scattering properties of ice crystals using third degree polynomials in terms of mean effective size; in the development of the parameterization the results were computed from a light scattering program including geometric ray tracing for size parameters larger than 30 and an exact spheroid solution for size parameters less than 30. The use of the four-stream code is necessary because two-stream codes cannot properly consider the scattering for thin cirrus, which may be highly peaked in the forward direction for the observed crystal shapes. The calculated radiative properties implicitly assume that the ice crystals with size parameters larger than 30 have a hexagonal shape, which is reasonable given the shapes observed by Heymsfield (1986). The IWC and D_e profiles are the required inputs to their code. In addition, the water vapor mixing ratio, ozone mixing ratio, and concentrations of CO₂, CH₄, and N₂O are based on the environmental tropical profile of Ellingson et al. (1991). A clear sky albedo of 0.1 for the ocean surface was used. The solar zenith angles were 42.9°, 58.0°, and 13.7° for the 17 December 1973, 19 February 1981, and 16 June 1978 cases respectively, with the last angle being estimated for local noontime since the times of the measurements were not available.

Within a cloud, ice saturation mixing ratio is assumed. This assumption is reasonable since the persistence of the cloud layers indicates that the particles must not be evaporating. In addition, during CEPEX a Lyman-α hygrometer measured humidities near the tropopause during dives made by the ER-2, for some cases, near 100%. Humidities were measured during a dive when the lidar saw cirrus immediately before and/or after the dive. However, the lidar did not provide useful data during the descent, so although the data are consistent, there is no way to prove that the high humidities were associated with cirrus (E. Weinstock 1998, personal communication).

Ackerman et al. (1988) found that the atmospheric heating rates produced by cirrus clouds were sensitive to the IWC, thickness, and environmental conditions. Here, we use the in situ measured properties to calculate the heating rates. Figure 4 shows the calculated net heating rates (infrared plus solar) for all three cases, compared to the clear sky heating rates. The clear sky heating rates are computed assuming saturation vapor pressure for the cloud location to more clearly see the effects of the cloud particles. For the Heymsfield and Jahnsen (1974) measurements, a maximum heating rate of 1.8 K day⁻¹, compared to the clear sky maximum of 0.4 K day⁻¹, is observed. The majority of the additional heating due to the clouds occurs in the infrared wavelengths. This corresponds to a net cloud radiative forcing of 0.8 W m⁻², 1.4 W m⁻² in the infrared, and −0.6 W m⁻² in the visible. For the two Booker and Stickel (1982) observed cases, maximum heating rates of 0.6–0.5 K day⁻¹, representing rates of 1.0–0.5 K day⁻¹ greater than the clear sky values, are calculated. The corresponding cloud radiative forcings are 1.2 and 0.7 W m⁻², with 2.5 and 0.9 W m⁻² in the infrared, and −1.3 and −0.2 W m⁻² in solar channels.

The net radiative energy absorbed by subvisual cirrus results in a combination of local temperature change and induced upward vertical motion (Jensen et al. 1996). Assuming all of the absorbed energy results in the lifting of the cloud layer, for the observed potential temperature lapse rate of approximately 24 K km⁻¹ (Heymsfield 1986) for the case in Fig. 4a, the layer potential temperature will increase at a rate of about 7 K day⁻¹, and the parcel will rise about 300 m in 1 day, or at a rate of 0.35 cm s⁻¹. A comparison of two soundings, the first made 24 h before the measurement period, suggested that the air in the cloud layer cooled by about 3°C, and assuming cooling along dry adiabats, this corresponds to an ascent rate of 0.7 cm s⁻¹ (Heymsfield 1986), comparable to the calculated mass-weighted terminal velocities of 1–2 cm s⁻¹. Thus, it seems apparent that the large-scale dynamics should be considered in order to determine the influence of the absorbed energy. Rosenfield et al. (1998) also calculated similar radiative heatings to those calculated above and found that as a consequence water vapor increased in the lower stratosphere.

Jensen et al.’s (1996) maximum calculated heating rates are higher than those calculated for these three cases, on the order of 2 to 3 K day⁻¹, because their simulated optical depths, 0.028 and 0.023, are higher than those measured above. Because it is not known how representative these three cases of in situ cirrus measurements are, remote sensing measurements are used to derive a larger database of subvisible tropopause cirrus properties to further calculate their radiative impacts.

a. Lidar measurements acquired during CEPEX and TOGA COARE

During CEPEX and TOGA COARE, the NASA ER-2 was equipped with the CLS, a nadir-pointing Nd:YAG lidar, which operated at wavelengths of 0.532 and 1.064 μm with a vertical resolution of 7.5 m (Spinhirne et al. 1982). Figure 5 shows cloud boundaries detected by the lidar for selected time periods during CEPEX and TOGA COARE. Tropopause cirrus were sometimes detected during time periods when no other clouds were present (Fig. 5a), during time periods when thick clouds were present below them (Fig. 5b), and when thin clouds were present below (Fig. 5c). Following Heymsfield and McFarquhar (1996), clouds are classified as thick when the lidar beam is occulted before reaching the ocean surface; this corresponds to an optical thickness of greater than 3 or 4 (Kinne et al. 1992).

Wang et al. (1994) noted that the majority of high clouds detected by SAGE II occurred within the top 2 km of the tropical troposphere. The CEPEX data were used to estimate the fractional occurrence of the tropopause cirrus, by identifying a cloud as tropopause cirrus provided that the top and bottom of the echo detected by the lidar occurred above 15 km; this height was chosen as being approximately 2 km below the typical height of the tropopause in the Tropics. The bottom of the cloud also must be above 15 km to prevent the inclusion of high thick anvils (e.g., see Fig. 5d). Manual checks against the lidar data for a number of time periods suggested that this definition seemed reasonable.

Tropopause cirrus were present 29% of the time during CEPEX and had a mean thickness of 0.47 km. Although CEPEX was fundamentally interested in validating the “thermostat” mechanism (Ramanathan and Collins 1991) and in determining how cirrus regulate the energy below clouds, the flight paths consisted of western and eastern triangular trajectories that typically did not deviate to sample specific clouds. Thus, although the samples are somewhat biased toward anvils, the data are more representative of the equatorial regions than that from TOGA COARE when convection was specifically targeted. A double cirrus layer was observed 13% of the time that the tropopause cirrus was present (e.g., Fig. 5a at 1.65 UTC). The mean thickness of the tropopause cirrus was 0.47 km, and on average the thickness of the cloud layer below the tropopause cirrus was 1.9 km. Thick cirrus below was present 43% of the time when the tropopause cirrus occurred, and clear sky (here defined as no cloud layers between 5 and 14 km) for 36% of the time. For time periods where thick cirrus were present (i.e., the lidar beam was occulted before reaching the ocean surface), tropopause cirrus was present 25% of the time, and for time periods where clouds were absent between 14 and 5 km (and the ocean surface was detected), tropopause cirrus were present 32% of the time. This shows that although the presence of tropopause cirrus can coincide with thicker anvils, there are also ample examples where the tropopause cirrus are at least somewhat removed, at least in the vertical, from convection or thicker anvils. The large-scale uplift for these cases could also be generated by flow over large-scale convective systems or their associated stratiform regions (Churchill and Houze 1990). Winker and Trepte (1998) also found these thin cirrus layers both in clear air and above intense tropical thunderstorms, and in regions characterized by large-scale subsidence in the midtroposphere.

The estimates above do not use the 0.03 threshold for defining subvisible cirrus because direct estimates of τ were not available for computing these statistics. Attempts to use Prabhakara et al.’s (1993) split-window method for estimating τ and D_e for cases during CEPEX when no cloud was underlying the thin tropopause cirrus failed because no signal could be detected in the 11.0- and 12.0-μm channels of the moderate resolution imaging spectrometer airborne simulator (D. Duda 1998, personal communication); the limit of detectability of the split-window method is closer to 0.05 or 0.1 optical depth.

On 29 March 1993 between 0124 and 0148 UTC (Fig. 5a), the NASA ER-2 overflew a thin cirrus with no cloud layers below. This case offers an excellent opportunity for estimating cloud heating rates and optical depths because there is no interference from cloud layers below and because the cloud layers are not complex in structure. The lidar-attenuated backscatter is converted to an effective optical depth, τ_eff, following Spinhirne et al.’s (1996) technique. Here, the effective ratio of backscatter to extinction cross section for the CLS signal is obtained by solving a system of linear equations and applying the lidar molecular and aerosol scattering under the cloud for a boundary condition. Here τ_eff underestimates the true optical depth because the effects of multiple scattering are not accounted for, but these effects may not be that significant given the low thicknesses and optical depths.

Figure 6 plots the variation of τ_eff over the flight track. The τ_eff values range from 0.0002 to 0.015, with a mean value of 0.0036, and encompass the range of values estimated for the three in situ cases. Even if the actual optical thickness is twice τ_eff, these clouds would still constitute subvisible cirrus. An increase in τ_eff to almost 0.015 around 0136 UTC is seen and seems to be related to the increase in geometric thickness and to the occurrence of a double cirrus layer at that time.

b. Calculated radiative forcing

Figure 7 shows the average heating rate within the subvisible cirrus, assuming effective diameters from 5 to 25 μm, calculated with Fu and Liou’s (1993) radiative transfer code. The D_e are chosen to encompass the range of sizes that would be expected based on the particle sizes that were observed during all the Kwajalein missions, not just those depicted in Fig. 2 and Fig. 3. An average cloud base and top, and average solar zenith angle between 124 and 154 UTC were selected for the computations. The heating rates follow the τ_eff trends depicted in Fig. 7, showing maximum values of almost 4 K day⁻¹ when τ_eff exceeds 0.01 around 0138 UTC; the average heating rate is 1.1 K day⁻¹ for the time period plotted. The heating rates drop to as low as 0.2 K day⁻¹ when the observed τ_e drops to near 0.0001, essentially representing the clear-sky heating term (Fig. 4). The heating rates do not vary significantly for different D_e because τ, and not IWC, is held constant in the different simulations; there is some variation between simulations because of differences in the single-scattering properties. As for the simulations using the in situ microphysical data, the majority of the heating occurs in the infrared channels. At the time of maximum heating at 0138 UTC, of the 4.0 K day⁻¹ heating, 79.7% occurs in the infrared.

The top of the atmosphere cloud radiative forcings (CRF) were also calculated from the simulation results, as shown in Fig. 8. At the time of maximum τ_eff and heating rate, the total CRF reached almost 2.5 W m⁻², of which 3.5 W m⁻² was in the IR channels and −1 W m⁻² in the solar channels. The averages for the time period plotted were 0.53, 0.77, and −0.24 W m⁻², respectively.

In order to get a more representative database of heating rates and optical depths for these cirrus clouds, the above analysis steps were repeated for the three other cases during CEPEX amenable to this type of analysis (15 March, 3 April, and 5 April); a simple cloud structure with no underlying cloud layers was observed for time periods during all of these days. Figure 9 shows a histogram of cloud optical depths obtained for these time periods. The average τ_eff for these time periods is 0.01. Despite efforts to filter out the occurrence of visible cirrus, the tail of the distribution at 0.1 indicates that some visible cirrus are included in the statistics.

Figures 10 and 11 show histograms of the average cloud heating rate and cloud radiative forcing, respectively. Appropriate solar zenith angles, cloud tops, and cloud bases were selected for each date. The heating rates and CRFs depended on both the physical location of the cloud and the solar zenith angle. The smallest possible D_e of 5 μm was used for these calculations, but the results are not highly sensitive to values of D_e between 5 and 25 μm. Of the average heating rate of 1.66 K day⁻¹, 1.29 K day⁻¹ occurs in infrared channels, and 0.37 K day⁻¹ in the solar channels. The CRF is similarly dominated by absorption of infrared radiation;for the average CRF of 1.58 W m⁻², 2.19 W m⁻² is absorbed by the infrared, and 0.61 W m⁻² is reflected by the solar channels.

There was necessarily some subjectivity in deciding what constituted thin tropopause cirrus since the analysis times for Figs. 9, 10, and 11 were chosen from the lidar cloud images before the effective optical depths were calculated. For example, on 3 April 1993 during CEPEX, the times between 2030 and 2124 UTC were included in the analysis, but time periods greater than 2124 UTC were not. Figure 12 shows the lidar-derived cloud boundaries for this case; for increasing time as the plane moves east along the 2°S latitude line, the cloud becomes geometrically and optically thicker. For example, at 2109 UTC the cloud has a thickness of 500 m and τ_eff of 0.0108; at 2121 UTC, 700 m and 0.0093;at 2136 UTC, 2.0 km and 0.0301; and at 2148 UTC, 3.0 km and 0.0886. This suggests that the cirrus should be visible from the ground at the later times. After 2120 UTC, the tropopause cirrus seemed to be attached to this larger cloud system, which was increasingly visible, and hence time periods corresponding to the entire attached cloud were excluded from the analysis.

Because of uncertainties in the cloud populations that are subvisible, it is desirable to calculate the maximum radiative effect that may be associated with these cirrus. Because heating rate and cloud radiative forcing are highly dependent on τ_eff for the δ-four stream calculations, assuming τ_eff equals 0.03 gives a good indication of this effect. Figure 13 shows the relationship between τ_eff and average cloud heating rate for all four CEPEX cases for which the CLS retrievals were performed. Each point represents a 5-s average along the flight track. Four distinct sample populations may be inferred that represent different solar zenith angles and cloud thicknesses assumed for the computations. For a τ_eff of 0.03, the heating rate ranges from less than 3 to 7 K day⁻¹, with the maximum heating rates occurring for the lower zenith angles. A similar plot for CRF (not shown) showed values of between 4 and 6 W m⁻² for τ_eff of 0.03. Since τ > τ_eff, the the radiative effects of subvisible cirrus could be a bit larger. More scatter would be observed in the τ_eff–CRF–heating rate relationships if varying particle sizes and shapes were assumed.

The data used above still are limited to four cases during CEPEX. Hence, satellite data were used to develop a more representative climatology of the cirrus cloud properties.