Influence of gravity wave temperature anomaly and its vertical gradient on cirrus clouds in the tropical tropopause layer – a satellite-based view

Negative temperature perturbations (T ′) from gravity waves are known to favor tropical tropopause layer (TTL) clouds, and recent studies have further suggested a possible role of dT ′/dz on facilitating TTL cloud formation and maintenance. With a focus on exploring the influence of dT ′/dz on TTL clouds, this study utilizes radio occultation temperature retrievals and cloud detection from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) to understand how 5 gravity wave perturbations modulate cloud occurrence. Cloud populations were evaluated in four phases corresponding to positive or negative T ′ and dT ′/dz. We find that 57% of TTL clouds are found where T ′ and dT ′/dz are both negative. Regions of frequent convection are associated with higher cloud populations in the warm phase T ′ > 0. The partitioning of cloud population among wave phases shows some dependence on the background relative humidity estimated using Aura Microwave Limb Sounder water vapor retrievals. Using effective radius 10 (re) retrievals from the CloudSat/CALIPSO 2C-ICE product, we find that re is distributed similarly among all wave phases but a smaller mode is found in the re distribution from the phase T ′ < 0 and dT ′/dz < 0. It is shown that the strongest mean negative T ′ anomaly is centered on the cloud top, resulting in positive dT ′/dz above the cloud top and negative dT ′/dz below. This negative T ′ anomaly propagates downward with time consistent with upward propagating gravity waves. Negative (positive) T ′ anomalies are associated with increased (decreased) probability of being 15 occupied by clouds. The magnitude of T ′ correlates with the increase or decrease in cloud occurrence, giving evidence that the wave amplitude influences the probability of cloud occurrence. While the decrease of cloud occurrence in the warm phase is centered on the altitude of T ′ maxima, we show that the increase of cloud occurrence around T ′ minima occurs below the minima in height, indicating that cloud formation or maintenance is facilitated mainly inside negative dT ′/dz. Together with existing studies, our results suggest that the cold phase of gravity waves favor TTL clouds mainly through the region of wave 20 anomalies where dT ′/dz is negative. 1 https://doi.org/10.5194/acp-2020-325 Preprint. Discussion started: 5 May 2020 c © Author(s) 2020. CC BY 4.0 License.

vertical bins. The r e estimates from 2C-ICE compare well to in-situ flight measurements with a retrieval-to-flight ratio of 1.05 (Deng et al., 2013). For quality control, we only use r e with uncertainty (given by the re_uncertainty variable) less than 20%.
Due to a battery failure CloudSat left the A-Train formation in 2011. After that it only operated in daytime and its footprint was no longer collocated to CALIPSO. For this reason we limit our analysis to 2C-ICE from 2007 to 2010 when nighttime data was available.
The Aura MLS H 2 O product provides retrievals of water vapor mixing ratio at pressures at and below 316 hPa with a preci-95 sion of 0.2-0.3 ppmv (4-9%) in the stratosphere (Lambert et al., 2007). We use the water vapor mixing ratio to estimate relative humidity with respect to ice (RH i ) using collocated RO temperature. Criteria for data screening follows all the recommendations outlined in section 3.9 of the official documentation (Livesey et al., 2017) found at https://mls.jpl.nasa.gov/data/v4-2_ data_quality_document.pdf. Although Aura was launched in 2004, the scan of the MLS did not align with that of CALIOP until May 2008. For this reason, all analysis involving this product uses data from 2008 to 2014.

Gravity wave temperature anomalies
Our method for obtaining temperature perturbations (T ) due to gravity waves is based on Alexander et al. (2008). Mean temperature profiles are calculated on grid boxes of 20 • longitude × 5 • latitude × 7 days centered on each day of year. Mean maps are made for each day between 1 Nov 2006 and 30 April 2014 during which COSMIC provided a large number of RO 105 observations. For an arbitrary RO temperature profile, the mean map centered on the same day as the RO profile is used to derive the corresponding mean-state profile through bilinear interpolation of the four grid boxes surrounding the location of the given RO profile. T is then obtained by removing the mean-state from the actual profile. Since we use a 7-day mean state, the resulting T can be thought of as representing variability on timescales less than seven days. After T is obtained, its vertical gradient is calculated to get dT /dz. Figure 1 shows one example of a temperature profile, its corresponding mean state, and 110 the resulting anomalies T and dT /dz.

Collocation of CALIPSO observations to RO profiles
The primary goal of this work is to study cirrus occurrence and properties in the four gravity wave phases defined in Figure   1. To accomplish this we collocate CALIPSO cloud observations to RO temperature profiles. The horizontal weighting of RO retrievals is mostly centered within 200 to 300 km of the perigee (tangent) point (Kursinski et al., 1997) where the ray temperature anomaly and its phases T'<0 and dT'/dz<0 T'<0 and dT'/dz>0 T'>0 and dT'/dz<0 T'>0 and dT'/dz>0 for analysis. Figure 2 gives an example of one RO profile, its perigee point at 17.25 km, and the collocated CALIPSO 5-km 120 footprints.
We collocate RO profiles to 2C-ICE cloud retrievals in a similar manner. Unlike the CALIPSO 5-km products, 2C-ICE provides cloud properties at 1-km footprints and vertical bins of approximately 250 m. Other than this difference, the collocation method is identical to that of CALIPSO and RO. In May 2008 the Aura MLS was aligned to within ± 10 km of CALIOP.
For analysis involving RH i , for each CALIPSO footprint with a RO collocation, we find the closest MLS footprint to that 125 CALIPSO footprint to calculate RH i .

Results
All results below were derived from data within 20 • of the equator. For convenience we will refer the the four gravity wave phases as follows. Phase 1: T < 0 and dT /dz < 0, Phase 2: T < 0 and dT /dz > 0, Phase 3: T > 0 and dT /dz < 0, and Phase 4: T > 0 and dT /dz > 0. Cold and warm phases refer to where T < 0 and T > 0, respectively.

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For the analysis presented in Section 4.1 and Section 4.3, the temporal restriction for collocation is that all the collocated data must be within two hours of each other. This restriction is not imposed in 4.2, and the time difference between RO and CALIPSO observations range from 0 to 36 hours with the purpose of examining how waves and cirrus clouds tend to evolve over time. This will be further elaborated in that section.

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As previously mentioned, K16 (their Figure 5) found that a majority of TTL clouds in the ATTREX data were observed in the cold phase T < 0 and that in the 2014 flight legs over the Western Pacific there was a higher frequency of ice inside dT /dz < 0 than in dT /dz > 0. To assess whether this tendency is general throughout the TTL or is limited to the regions observed by ATTREX, we evaluate cloud populations using collocated CALIPSO and RO observations that cover the TTL at all longitudes and over 2007-2014. Figure 3 shows the population of CALIPSO Cloud Profile vertical bins detected as clouds 140 in each wave phase extracted from collocated RO profiles. Considering all collocated observations between 1 Nov 2006 and 30 April 2014, 57% of clouds are observed to occur in Phase 1 throughout the entire TTL, as shown in Figure 3(a). When the cloud population is examined in 1-km vertical layers (14.5-15.5 km, 15.5-16.5 km, etc.), there is no obvious change with height and most clouds are found in Phase 1 followed by Phase 2 at all heights. Above 16.5 km there is a smaller fraction of clouds in the warm phase. A possible explanation for this may be that there are less convectively detrained clouds as altitude 145 increases, increasing the probability of clouds having been formed by gravity waves. In addition, the population in Phase 2 tends to increase with height, with 38% of clouds above 17.5 km in Phase 2. For comparison, using K16's Figure 5 one can infer that for clouds above 16.5 km the cloud fraction in Phase 1, 2, 3, and 4 are 56.25%, 31.25%, 9.375%, and 3.125% (calculated 6 https://doi.org/10.5194/acp-2020-325 Preprint. Discussion started: 5 May 2020 c Author(s) 2020. CC BY 4.0 License.
as the percentage in that phase divided by the sum all four phases), and for clouds below 16 km the percentages are 49.30%, 28.17%, 14.08%, and 8.45%. These ratios are similar to our findings, though we find less clouds in Phase 2 below 16 km.

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Cloud fractions in each phase are separated into six longitudinal belts in Figure 4. During December-January-February (DJF), the 120 • E-180 • E belt, which covers the Maritime Continent and Western Pacific, has the lowest cloud population in Phase 1 (52%) as well as the most clouds inside the warm phase (24%). Although this region is known for very low tropopause temperatures and high TTL cirrus frequency during boreal winter (Highwood and Hoskins, 1998;Sassen et al., 2009), there is also frequent deep convection (Ramage, 1968) which may generate clouds unrelated to gravity waves. This may explain populations of 63%/24% while February-March yielded 58%/20%. Over this region we were not able to find Phase 2 having more clouds as K16 did. It is not clear what causes this difference. Their T were calculated as the difference between aircraft in-situ temperature and 30-day mean temperature derived from RO, while we calculate it as the difference between RO-derived 165 temperatures and 7-day mean profiles. This difference in methodology may be a factor causing the contrasting findings.
Using the cloud top and base heights reported from the CALIPSO Cloud Layer product we calculate the vertical cloud fraction in each wave phase, defined as the amount of vertical overlap between the cloud boundaries and the line segments in Figure 1 corresponding to each phase. The distributions of vertical cloud fraction are shown in Figure 5 (for cloud fractions between 0 and 1) and Table 1 (for cloud fractions equal to 0 and 1). In this figure and table we only consider clouds with base 170 above 14.5 km and wave phase segments whose base height lie within 14.5 and 18.5 km. In phases of positive dT /dz, the number of samples tend to decrease as cloud fraction increases. This trend doesn't apply for negative dT /dz, and in Phase 1 there is a clear increase of samples with increasing cloud fraction. Phase 1 also has the most cases where the vertical cloud fraction is unity (19410 cases). Overall, Phase 1 is most distinct as it has most samples with cloud fractions of unity and it significantly favors higher values of vertical cloud fraction.

Composite time evolution of wave anomalies and cirrus occurrence
Since COSMIC observations are pseudo-random in time and space, it is possible to collocate CALIPSO observations to RO soundings with varying offsets in time. By binning the temperature profiles according to the time offsets, we can make a composite showing the mean time evolution of wave anomalies relative to the cloud observation. Such an approach of creating composite time series has been used to study the thermodynamic budget before and after tropical convection (Masunaga, 2012;180 Masunaga and L'Ecuyer, 2014), temperature anomalies associated with tropical deep convection (Paulik and Birner, 2012), and the interaction between atmospheric dust and tropical convection (Sauter et al., 2019).
We bin RO profiles in time bins of −35, −33, ..., −1, 1, ..., 33, 35 hours relative to the CALIPSO observations, where a negative value indicates that the collocated RO profiles precede the CALIPSO overpass. The composites of T , dT /dz, and buoyancy frequency N 2 anomaly for all collocations in 2006 to 2014 are shown in Figure 6. In making these composites we 185 only includes clouds with cloud base of at least 14.5 km to ensure that the included clouds are TTL clouds (instead of, for example, convection) Also, for statistical testing, we need the RO profiles used in each time bin to be unique. For this reason, only the CALIPSO footprint spatially closest to the RO profile is used. If this is not done, then the same RO profile may be reused several times since there are usually multiple CALIPSO footprints collocated to one RO profile as shown in Figure 2.
In Figure 6(a), the strongest cold anomaly is found close to the cloud top and is coldest near hour 0. The cold anomaly 190 contour with value below −0.6 K lasts approximately from −15 to +6 hours, and migrates downward with time consistent with the property of gravity and Kelvin waves with upward group velocity. The alternating cold-warm anomaly at heights of 2 December-January-February  Table 1. bin ( Figure 6(d)) has a 12-hour periodicity mainly due to Metop-A/B. When only using COSMIC observations to make Figure   195 6(a), (b),and (d), the anomaly patterns are largely the same so the periodicity does not affect the composites.
It is noteworthy that the mean cold anomaly is centered near the cloud top and not within the cloud. This results in a dipole structure in dT /dz (Figure 6(b)) and buoyancy frequency anomaly ( Figure 6(d)) with positive anomalies just above the cloud top and negative anomalies below. This structure shows that the inside of clouds (below cloud top) is likely to have negative dT /dz, consistent with the finding by K16 and Figure 3 that a majority of clouds are found in Phase 1. Although this 200 structure implies weakened stability (negative N 2 anomaly) inside the cloud, it is unclear whether this decreased stability has connections to cloud formation or maintenance. Since negative dT /dz also corresponds to upward vertical motion anomalies (assuming that these anomalies are from gravity waves), further study is required to separate the role of vertical motion and stability in how gravity and Kelvin waves influence TTL clouds.
Figure 7 is similar to Figure 6 except the anomalies are not composited relative to the cloud top height but rather on height 205 above mean sea level. In this composite, there are cold anomalies at TTL altitudes but the magnitude is weaker than that of Figure 6. This leads to weak anomalies in dT /dz (Figure 7(b)) and N 2 (not shown). Based on these results we suggest that gravity wave anomalies in Figure 6 are physically significant and have a close association with the vertical position of TTL cloud tops.
P18 argues that the upward vertical velocity in Phase 1 slows down the descent of ice crystal and tends to suspend them inside  of RO sounding, and use the CALIPSO cloud product to calculate the cloud frequency in each 2-hour time bin. In addition, instead of compositing relative to cloud top height, we composite on the altitude of the local minima or maxima of T . A 215 schematic of this compositing approach is given in Figure 8.
In the example shown in Figure 8(a), at day i there is a collocated RO sounding that occurred within 100 km of the CALIPSO footprint but ∆t i hours after. The position of the cloud top and base (solid and dashed magenta lines) is evaluated relative to a local T minimum. Since the CALIPSO overpass occurred before this RO profile, in the compositing (shown in Figure 8 i ]. If the collocated CALIPSO footprint has no clouds with base above 14.5 km, cloud fractions of zero are still binned in the appropriate time bin at all heights. Since any RO profile most likely has multiple local minima, the binning of cloud fraction is repeated for each local minimum in a T profile. The exact same procedure is conducted for local maxima to create a separate 225 cloud frequency composite. To focus on TTL clouds we only include clouds with base at or above 14.5 km. Also, we only consider local T extrema within 14.5 to 18.5 km since a majority of TTL clouds are inside this height range. The composites of cloud frequency made this way, shown in Figure 9 (Figure 9(a)-(c)) we find a lobe of enhanced cloud frequency and this becomes more evident as min(T ) decreases. Likewise, in the vicinity of max(T ) (Figure 9(d)-(f)) the cloud frequency is reduced, and this reduction also shows dependence on the magnitude of max(T ). In both cases, the increased or decreased cloud frequency displays a downward trend consistent with the expectation that gravity wave phases propagate downward with time. However, it is hard to quantitatively know which parts of these plots are true anomalies. For this reason 235 we devise a way for extracting the anomalies in these patterns and for statistical testing, as described below.
The cloud frequency composites in the top two rows of Figure 9 are made using the altitude of the T extrema as the zero height. To generate a composite where the vertical positon of T extrema has no relationship with cloud top/base height, for each T extremum we generate a random altitude using uniform distribution unif (14.5, 18.5) and make a separate cloud frequency time-height composite with the random altitude as zero height, shown in Figure 9(g)-(i). These plots can be interpreted as the 240 cloud frequency distribution one would expect if the vertical position of T extrema has no connection to cloud top/base height.
Then the statistically significant differences between the first/second row to the third row may signify a connection between wave anomalies and cloud occurrence. The distribution of cloud fraction in each time-height bin is similar to those shown in Figure 5 and therefore is not normal, so the Student's t-test cannot be used here. We use the two-sided two-sample Kolmogorov-Smirnov test (K-S test) (Hollander et al., 2015) which does not make any assumptions about the data distributions. This test 245 can be used to evaluate whether two continuous or discrete probability distributions differ from each other. The K-S test is employed to compare the discrete cloud fraction distribution in each time-height bin of the first/second row to the same bin in the third row. The null hypothesis is that the first/second row is not different than the randomly generated cloud frequency pattern in the third row.
The fourth row of Figure 9 (panels (j)-(l)) is the first row minus the third row, depicting the anomalies associated with 250 min(T ), and similarly the fifth row (panels (m)-(o)) shows the anomalies associated with max(T ). Colored portions of the contour denote regions with p < 0.05 (95% confidence) as estimated from the K-S test. In these anomaly patterns it is confirmed that there is enhanced cloud occurrence below min(T ), and, in addition, a weak reduction of cloud occurrence above it. For the subset of min(T ) < −0.5, the positive cloud frequency anomaly peaks at 3% whereas for min(T ) < −1.5 it peaks at 6%. The anomaly patters due to max(T ) also exhibit a dipole structure with negative anomalies centered on the altitude 255 of max(T ) and a weak positive anomaly below. The fifth row also suggests a dependence of cloud frequency anomaly with respect to the magnitude of max(T ), although the variation is not as large compared to that of min(T ). Both positive/negative anomalies associated with min(T )/max(T ) tend to migrate downward in time, although this trend is slightly more apparent in the enhanced cloud occurrence of min(T ).
One difference between min(T ) and max(T ) is that the positive anomalies in min(T ) occur below the altitude of 260 min(T ) while the negative anomalies in max(T ) are centered on it. Most of the enhanced cloud occurrence occurs inside Phase 1, and Phase 2 actually tends to have a negative cloud occurrence anomaly. Although the predictions of P18 suggests that it may be more likely to find clouds in Phase 2 under low background RH i , this global analysis suggests that on average the role of Phase 1 in facilitating TTL clouds is dominant.

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P18 suggests that (1) ice crystals within a confined range of r e are suspended approximately in Phase 1 and 2, and (2) background relative humidity with respect to ice (RH ib ) influences the phase at which these crystals are suspended. These two features are depicted in their Figure 2. To evaluate whether these predictions are consistent with satellite observations, we examine r e and RH ib in observations to see whether these quantities exhibit any correlations to gravity waves. Although here we present analysis motivated by P18, we note that their study assumes no background wind nor shear in their derivations and 270 simulations. Figure 10 shows normalized distributions of r e in the four wave phases as well as their mean and standard deviation. These distributions only contain nighttime 2C-ICE data, since the information toward thin cirrus are mostly from lidar backscatter.
Clouds above 17.5 km were omitted in this plot due to the low samples (∼0.6% of all TTL clouds). The distributions for all phases are very similar regardless of height. In 14.5-15.5 and 15.5-16.5 km, the r e distribution of Phase 1 has a peak near 16 275 µm. Above 16.5 km this peak is not evident, but the Phase 1 distribution has higher values around 15 µm and lower values between 20 to 25 µm, slightly differentiating Phase 1 from the other phases. The mean r e of Phase 1 is lower than all other three phases at all vertical layers, but the differences are small. In summary, characteristics of r e found here are qualitatively consistent with P18's findings, as Phase 1 tends to have a relative larger number of ice particles localized around a certain r e value. However we note that retrieving cloud properties of thin cirrus has large uncertainties and more research is needed to 280 explore the r e distribution in gravity waves phases using a variety of observations and models.  Figure 8. Schematic for creating the composite temporal evolution of cloud fraction with respect to T minima. In this example, as shown in (a), during day i there is a collocated pair of CALIPSO and RO observations. The RO observation occurs ∆ti hours after that of CALIPSO, and the vertical distance between the height of local T minimum and the cloud top and base is depicted by the dashed and solid magenta lines, respectively, with lengths h i . In the temporal compositing (b), in the time bin corresponding to ∆ti hours before observing T , the cloud fraction is binned according to how much each vertical bin overlaps with the interval [h The same procedure is carried out for the collocated pair at day j. Also see text for explanation.
As discussed in Section 4.1, K16 found that in the 2011 and 2013 flight legs over the Eastern Pacific there were slightly more clouds in Phase 2 than Phase 1, whereas in the 2014 flights over the Western Pacific a majority of clouds were in Phase 1. P18 argues that this may be due to the relatively low RH ib characteristic of the TTL over the Eastern Pacific. P18 solved a simplified set of equations describing the interaction of gravity wave perturbations and ice particle growth/sedimentation. Comparison 285 14 https://doi.org/10.5194/acp-2020-325 Preprint. Discussion started: 5 May 2020 c Author(s) 2020. CC BY 4.0 License. of the solution using values of RH ib = 0.85 or 0.64 (to represent Western and Eastern Pacific, respectively) showed that the former results in the ice crystals being suspended in Phase 1 where in the latter ice particles were situated closer to the T minimum which may result in more ice inside Phase 2. Motivated by these results we collocate the MLS water vapor retrieval to CALISPO and RO data to evaluate whether observations suggest a similar dependence on RH ib .
For each CALIPSO Cloud Profile bin identified as cloud, the water vapor mixing ratio from the Aura MLS product is log-290 interpolated (as suggested by the product documentation) to the height of the cloud bin. To evaluate the saturation mixing ratio, we interpolate the 7-day mean temperature to the cloud height since we are interested in the RH ib instead of the actual RH i (which would include wave influence). The Goff-Gratch equation (Goff and Gratch, 1946) is used to get the saturation vapor pressure, and subsequently the saturation mixing ratio and RH ib . Figure 11 shows the cloud population in each phase partitioned by RH ib values. The subsets with RH ib below 60%, between 60% to 80%, and above 180% tend to have less 295 clouds in Phase 1 compared to the other RH ib categories. The intermediate values of RH ib (between 80% to 120%) yielded the highest fractions in Phase 1. Qualitatively, this show some consistency with P18 since there are more clouds in Phase 2 for the lowest two RH ib categories, but we find only a slight dependence on RH ib with no clear trend. We conclude that our analyses on r e and RH ib does not prove or disprove P18's assertions but there is some qualitative consistency between P18 and our results.

Conclusions
This study uses multiple satellite datasets to evaluate the influence of gravity wave perturbations on TTL cirrus clouds. With a focus on understanding the role of dT /dz, the vertical gradient of the gravity wave temperature perturbation T , we extract T and dT /dz from RO observations and collocate them to clouds observed by CALIPSO and 2C-ICE to understand cloud occurrence and characteristics relative to wave anomalies. Similar to the results of K16, we find that the phase where T and 305 dT /dz are both negative (Phase 1) is most frequently occupied by TTL clouds. The second most populous phase is where T < 0 and dT /dz > 0 (Phase 2), followed by where T > 0 and dT /dz < 0 (Phase 3) and then T > 0 and dT /dz > 0 (Phase 4). We show that this relation among the four phases is more or less invariant with height or longitude.
A mean view of the temporal evolution of wave anomalies with respect to clouds is constructed by taking advantage of RO's pseudo-random distribution in time and space. We collocate CALIPSO cloud observations to RO soundings that occur 310 before and after the CALIPSO observation, and by averaging a large number of observations with different time separations, a composite time series of wave anomalies is presented. These composites show that, on average, the strongest cold anomaly due to gravity waves tends to be centered on the height of cloud top, and this cold anomaly descends with time consistent with the downward phase propagation of gravity and Kelvin waves having upward group velocity.
In the cloud frequency composites made with respect to local T minima or maxima, we find that the decrease of cloud 315 probability in the warm phase does not show clear dependence on the sign of dT /dz. This is distinct from the cold phase, where cloud probability is increased mainly below min(T ) where dT /dz is negative. Together with existing studies, this result adds support to the idea that Phase 1 facilitates cloud formation and/or maintenance. Although the downward migration of the increased cloud frequency may be due to ice sedimentation, this is unlikely to be the case for the decreased cloud frequency associated with the warm phase. Hence the downward migration of increased/decreased cloud frequency in the 320 temporal composites is most likely due to waves with downward phase propagation. We also show that the positive or negative cloud frequency anomalies strengthen with increasing magnitude of T minima or maxima, giving evidence on a global scale that the wave amplitude is connected to the probability of cloud occurrence.
Finally, using satellite estimates of r e from 2C-ICE we assess the predictions of P18 which implies that one may observe a narrower distribution ice crystal effective radius inside Phase 1. Their conclusion that the background relative humidity with 325 respect to ice affects the vertical position of clouds is also evaluated here by using RH ib based on the Aura MLS H 2 O product.
Among all phases, r e are distributed similarly but the distribution of Phase 1 had a notably sharper peak and than the other three phases and also a slightly smaller mean r e . The partitioning of cloud population among the four phases showed some variation with different values of RH ib , with Phase 1 having less clouds at very low or very high RH ib , but no clear trend is identified. Thus, while our satellite-based analysis has some qualitative consistency with the results of P18, it is insufficient for 330 verifying their assertions.
This study adds to the exist findings showing that Phase 1 has a distinct connection to TTL clouds. The findings of K16, based on aircraft data limited to specific regions and time span, have been extended by our study which shows that the large amount of clouds in Phase 1 is a general characteristic of the TTL. Based on our composite analysis using satellite data spanning eight years (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014), the connection between wave anomalies and cloud occurrence is evident: cold anomalies 335 are associated with the position of cloud top, and T amplitudes influence the increase or decrease in cloud frequency. The purpose of constructing composite temporal evolution by piecing together collocated temperature and cloud observations is an attempt to study processes occurring on a timescale typically unobserved by satellites. Although the resulting composites are not true time series, the anomalies patterns depict signatures consistent with wave propagation and enhances our understanding of how waves are connected to TTL clouds.

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Due to the spatial and vertical resolution of the RO technique, the waves analyzed here have relatively large wavelengths and low frequencies. Despite this, the findings here should be important for TTL processes as Dzambo et al. (2019) shows that the power spectrum of TTL gravity waves tend to peak at wavelengths of around 4-5 km, which is resolvable by RO soundings.
Nevertheless, it remains to be explored whether the Phase 1 of high-frequency waves are also distinct from other phases. Also, possible explanations for Phase 1 favoring clouds remain an open question. Since negative dT /dz corresponds to a positive 345 cooling rate (due to downward phase propagation as explained by K16), weakened stability, as well as upward vertical motion wave anomalies (according to the gravity wave polarization relationships), whether one has a stronger role in favoring clouds needs to be better understood. The fourth row (j)-(l) and fifth rows (m)-(o) are the cloud frequencies anomalies associated with cold or warm anomalies, calculated as the difference between the cloud frequency composites and the background cloud frequency. Contours in the bottom two rows are at intervals of 1% (dashed negative), matching the filled color contours which show values at or above the 95% significance level.   (h) 180% < RH ib Figure 11. Percentage of TTL clouds inside each wave phase categorized by background relative humidity with respect to ice (RH ib ).