Radar and lidar data collected by instruments aboard the CloudSat and CALIPSO satellites are used to demonstrate statistics of the spatial variability of tropical tropopause layer (TTL) cirrus, along with their tendency to occur with or without lower clouds, during the period July 2006 through June 2007. This time period included a mild El Niño event. TTL cirrus occurrence patterns contain maxima over the tropical convective areas of South America, of Africa, and of the west Pacific. It is demonstrated from co-occurrence statistics that TTL cirrus events and general lower cloud events are nominally independent in a zonal average; however, tendencies toward co-occurrence between TTL cirrus and lower clouds that appear in specific base height and geometrical thickness bins do exist. Nominally independent of clouds based below 3 km, TTL cirrus become increasingly less likely to occur with lower cloud layers of increasing base height than they are to occur generally. The independence of TTL cirrus from clouds based in the boundary layer is due to the ubiquitous, unconnected co-occurrence of TTL cirrus with thin trade cumulus clouds. However, we find that TTL cirrus are more likely to occur with low-based clouds of moderate depth (3–10 km) than they are generally and less likely to occur with deep (thicker than 10 km), low-based clouds than they are generally. Results are used in commenting generally on the TTL cirrus maintenance and formation hypotheses of Hartman et al. (2001) and of Garret et al. (2006).
 Proposed formation mechanisms of TTL cirrus are subsumed within the general categories of condensate's detraining from convective clouds that penetrate the TTL [Danielsen, 1982] and of in situ formation due to synoptic-scale or gravity wave-scale ascent [Jensen et al., 1996]. A number of investigations have been made on the relative importance of these two mechanisms [e.g., Massie et al., 2002; and Spang et al., 2002]. Clark et al.  posited the relative importance of a mechanism to be a function of location and of pressure level. However, there also exists a class of hypotheses that combine both convective and synoptic-scale influences to explain the formation and maintenance of TTL cirrus. For instance, Jensen et al.  and others found the ubiquity of TTL cirrus difficult to explain without some means of adiabatic cooling such as would occur if radiative heating of cirrus volumes were converted into ascending motions. Hartmann et al.  suggested an additional mechanism for this cooling via a relationship in the co-occurrence of TTL cirrus with deep convective and thick anvil clouds: regardless of original formation mechanism, optically opaque thick lower-level clouds could act to shield TTL cirrus from IR radiation upwelling from the tropical boundary layer, thereby extending their existence and providing a means for dehydrating TTL air. Also, Garrett et al.  posited a possible formation mechanism whereby pileus clouds form above active convective cloud complexes. These last two hypotheses are conditioned on the co-occurrence of lower level clouds with TTL cirrus. With an eye on shedding some light on the feasibility of these hypotheses, we examine co-occurrence statistics using data from the CloudSat Cloud Profiling Radar (CPR) [Im et al., 2005] that has been combined with co-located data from the CALIPSO satellite's Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) lidar [Winker et al., 2007].
2. Data and Method
 As components of the Afternoon satellite constellation (or A-Train), CloudSat and CALIPSO follow Sun-synchronous orbits, crossing the equator at approximately 0130 and 1330 local time. The CPR on CloudSat is essentially insensitive to most TTL cirrus because of small sizes and low concentrations of ice crystals, the radar backscatter cross section in TTL cirrus volumes is insufficient to generate a return signal that rises above the CPR detection threshold. On the other hand, the CPR can sense and even fully penetrate nearly all cloud layers in the troposphere with the exception of moderately to heavily precipitating layers. The CALIOP, conversely, is able to sense most TTL cirrus without difficulty; and while the CALIOP measurement becomes attenuated in lower-lying optically thick clouds layers, it does allow for identification of boundary layer clouds that the CPR is unable to detect due to ground clutter. The complementarity of the two instruments makes them an excellent observing system for examining the co-occurrence statistics of TTL cirrus with lower cloud layers.
 Using the radar-lidar geometrical profiling product (RL-Geoprof [Mace et al., 2009]) from the period July 2006 through June 2007, counts of day and night cloud layer occurrence within CPR footprints (approximately 2.5 km along by 1.5 km across track) are accumulated into joint histograms for each 4° × 4° region within the 20°N–20°S latitude band according to the cloud base height and layer thickness bins shown in Table 1. Thus, within each averaging region so defined, the total number of occurrences of layers in each height and thickness bin as well as joint statistics between any two sets of base height and thickness bins is determined. We take the presence of any layer observed by either radar or lidar with base above 14 km and with geometrical thickness no greater than 3 km to indicate TTL cirrus. The 14 km base height is not chosen arbitrarily: This level indicates the top of the convective detrainment zone of most tropical deep convection [Hartmann and Larson, 2002]. Consistent therewith, Mace and Benson-Troth  find that the occurrence of cirrus in millimeter radar data collected in the tropics decreases to near zero above 14 km.
Table 1. Cloud Base Height and Cloud Thickness Bins Used
Cloud Base Height
 It should be noted that the time period investigated here included an El Niño event. Massie et al.  studied the effects of the 1997 El Niño event on upper tropospheric cirrus and deep convection, finding that the western Pacific centers thereof underwent correlated movement eastward toward the International Date Line [see also Mace et al., 2009]. While cloud system dynamics seem to shift spatially due to El Niño, it is not clear that the cloud system dynamics themselves change as a result of El Niño. Thus, while strictly speaking the data set used here represents a sample of cloud co-occurrence during an El Niño event, it is nonetheless assumed to be indicative of co-occurrence statistics in general.
 Details of A-Train sampling preclude auto- or cross-correlation analyses among the aggregated columns. It is possible, however, to make useful comparisons using conditional probabilities. For an atmospheric column, then, let the event T be defined as indicating the presence of TTL cirrus and let the event LBδz indicate the presence of some other lower layer with base height B and geometrical thickness δz on which the presence of TTL cirrus can be conditioned. If the two events are independent, then the difference P[T | LBδz] − P[T] will be zero; otherwise, the difference will indicate whether TTL cirrus is more or less likely given LBδz than they are without regard for LBδz. To determine the significance of such a difference, the null hypothesis H0 :P[T | LBδz] = P[T] is tested against the alternative hypothesis Hα :P[T | LBδz] ≠ P[T] via a two-sided exact binomial test of significance level α = 5% [Bain and Englehardt, 1992], where the sample size for each box derives from the number of A-Train transections thereof. This measure is mapped and discussed in the next section, but let the reader be careful and understand: This measure indicates statistical independence or dependence but cannot be used to imply causality.
 Zonal averages of the differences P[T | LBδz] − P[T] are also shown. These are computed using data taken around an entire parallel as the sample (i.e., an averaging bin that is 4° × 360° of longitude), rather than by averaging the differences computed for each 4° meridional bin. In computing the standard error for the zonal averages, the sample size used is the number of independent samples of that 4° latitudinal box, which is estimated by using the total number of orbits crossing that 4° latitudinal box. Also note that hereafter we use the shorthand notation PBδz to denote P[T | LBδz] − P[T] when possible, and Bδz will denote the zonal average of PBδz.
 Similar to previously noted studies, we find a maximum in TTL cirrus over the tropical west Pacific, with local maxima over tropical South America and over tropical Africa (Figure 1a). Relative to cirrus occurrence frequencies noted above, the maximum over the tropical west Pacific appears to have shifted eastward, toward the International Date Line, consistent with the findings of Massie et al. . While patterns are generally the same, the frequencies in Figure 1 are lower than those in the studies by Wang et al.  and Spang et al.  by anywhere from 15% to 30%. Those two studies, however, used data taken passively through the atmospheric limb and from much longer [Wang et al., 1996] or from much shorter [Spang et al., 2002] time periods, and so the differing reported frequencies are not necessarily significant. The frequencies in Figure 1 are also less than those of Eguchi et al. , who used the Geoscience Laser Altimeter System. However, their data came only from boreal autumn 2003, and they allowed for clouds with bases as low as 8 km within 15° of the equator and as low as 5 km without.
 As an aside, if the base height threshold is relaxed such that all thin cirrus with bases above 10 km are counted, then thin cirrus occurrence frequencies (not shown) increase to levels much closer to, but still less than, those reported in the study by Wang et al. . However, the 14 km base height threshold for TTL cirrus results in the selection of a certain type of cloud as TTL cirrus. Specifically, we have chosen cirrus in a region generally not affected by convection [e.g., Gettelman and de F. Forster, 2002]. This is confirmed at multiple tropical Atmospheric Radiation Measurement sites by Mace and Benson-Troth  and by Comstock et al. : Convective clouds, as a rule, reach their level of neutral buoyancy between 10 and 14 km. Thus, clouds found at higher levels exist in an increasingly stable zone rather than in an area of convective outflow and are both geometrically thin and visible only to lidar.
 Having made these considerations, we proceed with the originally stated base height threshold. The conditional probability of finding no lower clouds, given the presence of TTL cirrus, is shown in Figure 1b. Of all cirrus observed with bases higher than 14 km, nearly 100% had thicknesses less than 3 km (Figure 2). The zonal averages of Figure 1 are shown in Figure 3. Comparison of the two figures shows that the minimum near 5°N in the zonal nonoccurrence of lower clouds, given the occurrence of TTL cirrus, is associated with the Intertropical Convergence Zone in the Pacific and that the monotonically increasing probabilities at more northerly latitudes derive in part from a strong regional maximum over North Africa.
 Comparison of the probability of occurrence of TTL cirrus conditioned on the occurrence of any lower clouds with the marginal probability of occurrence of TTL cirrus shows that regional dependencies exist (not shown): Faint, negative, statistically significant differences (−6% ≤ PB<14kmδz>0 ≤ −4%) prevail over much of the convectively active Western Pacific and Indian oceans, signifying that TTL cirrus in these regions are less likely to occur with lower clouds than they are generally. Faint positive differences (5% ≤ PB<14kmδz>0 ≤ 7%) are found over convectively active continental regions such as South America and Africa as well as over the monsoon regions centered on the Bay of Bengal and on Northern Australia, signifying that TTL cirrus in these regions are more likely to occur with lower clouds than they are generally. The faintness of these patterns is reflected in the zonal mean, where B<14δz>0 is nearly indistinguishable from the marginal occurrence of TTL cirrus (Figure 5, solid line).
 Areas of weak, albeit statistically significant, negative values of PB≤3kmδz>0 are found in the regions that encompass the western Pacific deep convection zone (Figure 4a). These occur along with a generally faint, positive signal over the western hemisphere and local, statistically significant maxima in PB≤3km δz>0 over continental regions of sub-Saharan Africa, India, and Australia. The combined result is that B≤3kmδz>0 is generally indistinguishable from the marginal probability of TTL cirrus in all latitude bins (Figure 5, dotted line).
 TTL cirrus become increasingly less likely than their marginal likelihood of occurrence when co-occurring layer base heights are at higher levels in the troposphere. This is clearly seen in Figures 4 and 5. These results stem from regional minima in the differences P3km<B≤6kmδz>0, P6km<B≤10kmδz>0, and P10km<B≤14kmδz>0 over the western Pacific that result from an overall high coverage of upper tropospheric clouds relative to elsewhere in the tropics and from the apparently strong negative association between upper tropospheric layers and TTL cirrus in this region. Exceptions occur over northern Africa and over the subtropical oceans where either the differences are quite small or the null hypothesis is not rejected. Thus, while relatively independent of lower clouds generally (with a few regional exceptions of relatively small magnitude), TTL cirrus, when contrasted with their general occurrence statistics, are substantially less likely to co-occur with clouds whose bases are in the free troposphere.
 Having found a negative association between TTL cirrus and lower cloud layers with middle-to-high bases, we examine the occurrence of TTL cirrus with low-based clouds of varying thicknesses in Figures 6 and 7. B≤3kmδz≤3km is indistinguishable from null in a zonal average at most latitudes (Figure 7, solid line); however, local maxima of 10%–15% are found over sub-Saharan Africa, India, and Australia (Figure 6a). In the case where the low-based layer is deeper (3 km < δz < 10 km), we find that B≤3km3km≤δz≤10km is positive, particularly in the more subtropical latitudes over the southern hemisphere (Figure 7, dotted line). Figure 6b seems to show identifiable regional patterns in this statistic: PB≤3km3km≤δz≤10km ≈ 0 in the Western Pacific where TTL cirrus have their highest coverage, while the maxima in the subtropical latitudes are found primarily over the convectively active continental regions. Finally, it is interesting to note from Figures 6 and 7 that for low-based, deep clouds that would typically be classified as deep convection, PB≤3kmδz>10km < 0 (or is indistinguishable from zero) nearly everywhere. This seems especially the case in regions where TTL cirrus tend to occur the most. The exceptions found in the most southerly latitude bins are due to areas of positive difference over southern Africa and Australia (Figure 6c).
4. Conclusion and Discussion
 With data collected over an annual cycle containing an El Niño event, we have examined differences in the conditional and marginal probabilities of TTL cirrus and of co-occurring lower layers, reasoning that if TTL cirrus were independent of lower-level clouds in the same vertical column, this difference would be indistinguishable from a null hypothesis. Mathematically, these probability differences demonstrate either independence or a lack thereof between the events of finding TTL cirrus layers and of finding lower cloud layers with varying base heights and geometrical thicknesses. They cannot be used as measures of correlation or, in and of themselves, as indicators of causal relationships. One physical manifestation of this mathematical limitation is that the snapshot sampling scheme used in the collection of this data set admits the possibility of viewing TTL cirrus co-occurrence with lower cloud layers that have little to no physical connection with the overlying cirrus. This fact is underscored by the finding that TTL cirrus and low-based clouds are nominally independent, this finding stemming largely from the overwhelmingly commonplace co-occurrence of TTL cirrus with thin, low-based clouds (Figure 5) [Mace et al., 2009]. However, it is clear from this data set that there exists, in many locations, a statistically significant dependence between the events of TTL cirrus and of various underlying cloud layers.
 Specifically, although we found that TTL cirrus are indeed nearly independent of all lower-level cloud layers taken as a group, this apparent independence masks details that emerge when conditioning the probability of TTL cirrus on cloud types defined by layer base height and by layer thickness as defined in Table 1. This conditioning showed that TTL cirrus are significantly less likely to occur in the presence of upper tropospheric layers. This negative association also extends to co-occurrence with deep convective clouds—those layers that are based in the lower troposphere and that are more than 10 km deep. Conversely, a positive association in co-occurrence is found for low-based layers that are between 3 and 10 km deep, i.e., layers that could often be classified as cumulus congestus. This statistic maximizes especially over continental regions of the subtropics.
 While we must be careful not to invoke a causal relationship that can neither be proved nor disproved using these data alone, we can offer several interpretations in light of previously published hypotheses and modeling results. First, the mechanism proposed by Hartmann et al.  for dehydrating TTL air by causing radiative cooling, particle growth, and sedimentation as the TTL cirrus transit lower cloud layers would appear to be so efficient that the TTL cirrus do not long survive in such an environment. Our finding that TTL cirrus tend to be much less likely above high-level anvils and over deep convection suggests that the radiative cooling that would occur in the TTL cirrus layer as it transits deeper anvil cirrus or as anvil cirrus forms underneath them may result in fairly rapid dissipation of the TTL cirrus. This dissipation would occur via particle growth in the radiatively cooling environment and eventual sedimentation and sublimation of the ice crystals from within the TTL to lower layers. It would appear that the upwelling IR radiation from the tropical boundary layer leading to net heating of the layer containing the TTL cirrus would provide a plausible lofting mechanism and adiabatic cooling that would allow the TTL cirrus to persist as posited by Jensen et al. . We note, however, that due to the A-Train's equatorial crossing time, the daily periods of most mature convection over land and more especially over sea are generally not sampled (see, e.g., Hong et al. ), though a statistically significant number of deep convective events are included in the present results. The impact of this fact is not presently clear and suggests clearly the need for research into the diurnal nature of TTL cirrus clouds.
 These results shed very little light on the formation mechanisms of TTL cirrus. However, an increasing tendency toward co-occurrence is seen between TTL cirrus and moderately thick convective clouds (i.e., 0% < B≤3km3km≤δz≤10km ≤ 5%), but the association between TTL cirrus occurrence and the deepest convective clouds is decidedly negative (B≤3kmδz≤10km ≤ 0%). If it is assumed that the deepest convective clouds are past their most intense updraft stage and that the shallow convective clouds are still building and potentially strong over the subtropical continents, then the formation mechanism proposed by Garrett et al.  and by others, whereby TTL cirrus can form in a manner akin to pileus clouds, may merit further investigation.
 It can be stated that the event of finding a TTL cirrus cloud when there is a convective cloud present that extends into the upper troposphere seems to be relatively rare. However, it is not clear that this fact sheds any light on the hypothesis that overshooting convective moisture might intermingle with and cause the transformation of pileus cloud into longer-lived TTL cirrus or the hypothesis that overshooting tops contribute significantly to cirrus layers within the TTL. The along-track sampling of CloudSat and CALIPSO make this kind of analysis difficult. However, it is not uncommon in the merged CloudSat-CALIPSO data set to find extensive thin cirrus that extend downstream of deep convection. We have not tested for this type of association in this study.
 The data and work described thus far are only a beginning to a rigorous study of TTL cirrus. For future work, it would be appropriate to use meteorological data as a means of segregating forcing mechanisms, similar to studies done by Spang et al. , Clark et al. , Clark , Dessler et al. , Massie et al. , and Jensen et al. , wherein various combinations of satellite and model data were used to describe sea surface temperature, air temperature, water vapor, and ozone fields and to perform trajectory analyses of cirrus clouds in relation to convective sources. It is also possible to retrieve cloud microphysical and radiative properties using the instruments that detected the clouds to examine heating rates in and around TTL cirrus. For future work, though, a longer data set would be desired so that seasonal cycles could be examined; and a way of filtering daytime noise from CALIOP data would also be desired so that diurnal statistics could be studied.