A combination of satellite observations is used to study the global variation of polar mesospheric cloud (PMC) brightness and to determine its correlation with transient mesospheric dynamics. The observations include the PMC database from the Student Nitric Oxide Explorer (SNOE) satellite and measurements of atmospheric temperature made by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument onboard the Thermosphere-Ionosphere-Mesosphere-Energetics and Dynamics (TIMED) spacecraft. The analysis is unique in that we have contemporaneous measurements of PMCs by SNOE and atmospheric temperature by SABER for three summer mesosphere seasons (two northern, in 2002 and 2003; one southern, 2002–2003). The results show the presence of planetary wave activity in both PMCs and mesospheric temperature that are strongly coherent with each other. The dominant waves present in the polar summer mesosphere are the 5-day wave number 1 and the 2-day wave number 2 Rossby normal modes. The maximum amplitude of the temperature perturbations is small (2.0–3.5 K) but has a significant effect on the PMC brightness. The SABER temperature amplitude in the southern season is slightly larger than the northern seasons for both planetary waves with a corresponding increase in PMC planetary wave activity. The phase relationship between temperature and PMCs indicates that they are very close to 180° out of phase (cold temperatures coincide with bright PMC). This analysis establishes the importance of temperature as a forcing mechanism for planetary-scale variability in PMCs.
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 It is well established that mesospheric variability is driven by a combination of dynamical, chemical, and radiative processes [Andrews et al., 1987]. One of the most impressive examples of this interplay occurs near summer solstice when dynamical forcing by gravity waves reverses the zonal-mean zonal wind and causes the polar mesosphere to depart from radiative equilibrium. Associated with these temperature and wind changes are changes in meridional circulation and composition. In particular, adiabatic cooling due to mean upwelling causes the polar summer mesosphere temperatures to drop below the water vapor frost point (∼150 K), allowing for the formation of ice particles known as polar mesospheric clouds (when viewed from space) and noctilucent clouds (when viewed from the ground). Because the formation of PMCs requires supersaturated conditions, and because their growth rate is an exponential function of temperature, PMCs are an excellent indicator of small changes in the polar summer mesosphere [Turco et al., 1982].
 PMC formation is directly dependent on the available humidity, temperature, and nanometer size particles that form nucleation sites and, therefore, should serve as a visible sign of change in any of these parameters. PMCs are thought to be, in part, a direct effect of dynamical forcing of atmospheric variables. Application of lidar techniques in the last decade has contributed a great deal to our understanding of the small-scale structure and dynamics of mesospheric clouds, and observations from space have demonstrated that PMCs are highly variable on large spatial and temporal scales. Studies of the variability of PMCs can be separated into four time related classes: (1) less than 24 h, which includes tidal and gravity waves; (2) planetary-wave scales, i.e., periods of multiple days; (3) monthly to annual scales, including interhemispheric differences; and (4) multidecadal scales, which include the 11-year cycle as well as longer-term secular variations. All of these classes have been investigated and proven to be important in defining PMC variability. Gravity waves are responsible for the small-scale wave patterns seen by ground observers [Witt, 1962; Hines, 1965; Haurwitz and Fogle, 1969] and have a large effect on the microphysics of the clouds [Jensen and Thomas, 1994; Rapp et al., 2002]. Lidar has shown that atmospheric tides play a significant role, causing important local time effects [von Zahn et al., 1998; Chu et al., 2001, 2003; Thayer et al., 2003]. Satellite measurements generally do not provide information on the smallest scale of variability (class 1) because of the limitations of sampling from polar orbits nor on the largest scale (class 4) because of the relatively short lifetime of most space missions (with the exception of a few missions like, e.g., solar backscatter ultraviolet (SBUV) [DeLand et al., 2003] and Halogen Occultation Experiment (HALOE) [Wrotny and Russell, 2006]). However, large-scale waves (class 2) have been observed in both satellite and ground-based PMC observations, which indicate that cloud formation is highly variable on very large spatial scales [Gadsden, 1985; Kirkwood et al., 2002; Merkel et al., 2003; Kirkwood and Stebel, 2003; Petelina et al., 2006; von Savigny et al., 2007]. Most of the previous published work on planetary waves identified in mesospheric clouds highlight the 5-day or longer period waves (10-day, 16-day). This work will identify the dominant fast traveling (periods ≤ 5 days) planetary-scale variability in PMCs and correlate it with the observed transient mesospheric dynamics.
 With the Student Nitric Oxide Explorer's (SNOE) rich PMC database and global coverage (15 orbits per day and 2 local times) we investigate the role that planetary wave activity (class 2) has on global PMC variability. We couple this with an analysis of mesospheric temperature to identify the importance of temperature as a dominant dynamic forcing mechanism in PMC occurrence and to characterize the dynamical state of the summer polar mesosphere. An advantage of this approach is that we have contemporaneous measurements of PMCs from SNOE and atmospheric temperature from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument for three summer mesosphere seasons (two northern, in 2002 and 2003; one southern, 2002–2003). With sampling from polar-orbiting satellites and continuous observational sequences, both the SNOE and SABER data sets are well suited for utilizing Salby's  Fast Fourier Synoptic Mapping (FFSM) technique to identify the dominant planetary waves in the summer polar mesosphere.
 SNOE is a small scientific satellite that was launched on 26 February 1998 and had a lifetime of ∼6 years. SNOE reentered the atmosphere on 15 December 2003. The science objectives of SNOE include the study of nitric oxide in the lower thermosphere and the energy sources that drive NO variability, in particular solar soft X-ray irradiance and auroral energetic particles. SNOE was in a near-circular, sun-synchronous orbit with a near-polar data footprint that covered the range of latitude 82.5°S–82.5°N (with 0.75 degree resolution), with a fixed local equatorial crossing time of 1030 LT (ascending node) and 2230 LT (descending node). Because of the precession of the orbit, the local time of the equator crossing increased over the duration of the mission to 1330 at the end of the 2003 PMC season [Bailey et al., 2005]. The observation footprint covered 360° in longitude in 24 h (15 orbits per day). A description of the mission and its instrumentation may be found from Barth et al.  and Merkel et al. .
 The spinning motion of the spacecraft allowed the Ultraviolet Spectrometer to scan the limb, providing altitude profiles (200–0 km) of NO emissions and Rayleigh-scattered solar photons at 215 and 237 nm in the orbit plane with a vertical resolution of 3.3 km and a horizontal field of view of 33 km. The limb profiles were registered in altitude to 1.5 km accuracy as described by Merkel et al. . The ultraviolet spectrometer (UVS) observes scattered sunlight and, therefore, can detect PMC in the altitude profiles three months out of the year, during summer solstice, in each hemisphere. Light scattering from PMC particles is discernible above the Rayleigh background in the limb profile because the latter does not dominate the signal until below 70 km (i.e., below PMC altitudes). Details of the instrument, calibration, and PMC detection algorithm can be found from Merkel et al. , Merkel , Barth et al. , and Bailey et al. [2005, 2007]. We have an extensive PMC database that covers six northern PMC seasons from 1998 to 2003 and five southern PMC seasons from 1998 to 2002. All PMC Limb Scattering Ratio (LSR) values reported here apply to the 215 nm channel.
 Observations taken during the 2002 and 2003 northern seasons and the 2002–2003 southern season are used in the analyses presented here. For SNOE, the mapping analysis is performed on the brightness data (LSR) rather than on the occurrence of the clouds because the latter is a two-state parameter (1 or 0), which is not suited to Fourier analysis. LSR is reported as the ratio of the peak PMC radiance to the background radiance at the same height [Bailey et al., 2005]. On the other hand, the brightness parameter besides being a cloud indicator is also a continuous variable. It is noted that for the present analysis, all sampled SNOE PMC data are used and not filtered for altitude; however, the mean SNOE PMC altitude is near 83.5 km [Bailey et al., 2005].
 As described by Merkel et al.  and Bailey et al. [2005, 2007], because of the orientation of the SNOE orbit, the UVS detects forward scattered light in the Southern Hemisphere, thus making the mean LSR larger than in the north (where backscattered light is detected). Therefore, it is important to note that the apparent LSR amplitudes reported here for the southern season are an order of magnitude higher than in the north.
 Because SNOE measures scattered sunlight, the terminator is a limiting factor in PMC observations on the descending side of the orbit. To perform a mapping analysis with two local times, the latitude coverage is limited to 68°–80° in summer, when this range of latitude is sunlit. During the later part of the SNOE PMC season (1–15 August in the north; 1–14 February in the south) the lower latitudes 68°–71° are not analyzed because of a lack of sunlight (this will be evident in Figure 5). However, long periods of continuous PMC data from SNOE allow a mapping analysis of the whole PMC season. The SNOE observation periods used in this analysis are (1) 1 June to 15 August 2002, (2) 1 December 2002 to 14 February 2003, and (3) 1 June to 15 August 2003. Within these periods, the spectral analysis (Figure 4) and coherence analysis (Figure 9) are performed for periods of concurrent observations with SABER (defined in section 2.2). This allows direct comparison of PMC brightness to the temperature field.
 Included with this publication are time-lapse Animations 1–[link]3 of SNOE PMC brightness in LSR, globally mapped to illustrate the day-to-day variability of PMCs throughout the summer months. By using all data only from the ascending side (15 orbits per day per 0.75 degree latitude band), daily global composites of PMC LSR are produced. Although the FFSM analysis uses both the ascending and descending data products, for Animations 1–3 only the ascending data are shown. Figure 1 illustrates one frame (21 June 2003) of the 2003 time-lapse Animation 3. Each day illustrated is a global snapshot of the PMC LSR at ∼1106 LT for 2002, ∼1148 LT for 2002–2003, and ∼1254 LT for 2003 at 70° latitude [Bailey et al., 2005]. The local time changes with latitude as the observations approach the pole. Below the global map, the SNOE frequency of occurrence at 80° latitude is illustrated (as published by Bailey et al. ). Each season's animation (Animations 1–3) illustrates that the clouds are highly variable on time scales of a day. In addition, each season shows that the brightness and frequency of the clouds have an apparent westward (clockwise) motion around the pole. This indicates that the large-scale dynamical field influencing PMCs is westward propagating.
 SABER is one of four instruments launched onboard TIMED in December 2001 [Russell et al., 1999]. SABER's science objectives are to explore the global mesosphere and lower thermosphere and to better characterize the atmospheric structure (temperature, density, pressure), chemistry (oxygen and hydrogen families), and dynamics in this region. The instrument is a 10-channel broadband radiometer that scans the Earth's horizon every 58 s, producing vertical profiles of limb emissions from approximately 180 km down to the Earth's surface, with approximately 2 km vertical resolution.
 Retrieving temperature from SABER is challenging because infrared emissions from the CO2 vibrational rotational bands are in non-local thermodynamic equilibrium (non-LTE) in the mesosphere. This was shown to be very important for adequate retrievals of SABER temperature in the summer polar MLT [Mertens et al., 2001, 2004]. Kutepov et al.  pointed out that, even though non-LTE was accounted for in the SABER temperature retrievals, the results differed significantly from temperatures obtained from coincident falling sphere measurements taken during the MaCWAVE campaign in Andøya, Norway. They presented a reanalysis of the SABER non-LTE data for the summer mesosphere and produced an improvement in the mesospheric temperature retrievals by appropriately accounting for the CO2ν2 quanta V-V exchange. The analysis presented here uses SABER v1.07 temperature data, which include these enhancements. Because we are evaluating temperature perturbations, any error in the absolute temperature (such as a warm bias above 86 km discussed by Kutepov et al. ) does not affect our results.
 Because SABER measures temperature from infrared emissions, it does not suffer from the limitations described for SNOE (which can only observe sunlit latitudes). However, because the TIMED orbit precesses by ∼3° per day and SABER must keep its detectors from looking directly at the Sun, the spacecraft must perform a yaw maneuver every 63 days; this limits latitude coverage to either 52°S–83°N or 83°S–52°N. One yaw maneuver occurs in the middle of the PMC season in each hemisphere, such that there is continuous temperature data at polar latitudes only from the beginning to the middle of the PMC season. Thus, the SABER observation periods used in this analysis are restricted to (1) 1 June to 14 July 2002, (2) 13 December 2002 to 14 January 2003, and (3) 1 June to 14 July 2003. Figure 2 illustrates the zonal mean temperatures (altitude versus latitude) at solstice for each year of SABER data used in this analysis. The mean temperatures reach very low values (∼130 K) in the polar summer between 80 and 90 km. The mesopause is near 87 km in all seasons analyzed.
 The mapping analysis employed in this study uses Salby's  FFSM technique. FFSM is used to obtain synoptic spectra (in wave number and frequency) from the asynoptic sampling pattern inherent in polar orbiting satellites. FFSM requires extended periods of regularly sampled observations in space and time. While such continuous sampling is not often available from satellites, SNOE and SABER observations of PMCs and temperature include long sequences suitable for the FFSM technique. Using temperature data from all 15 orbits per day and both local times (ascending and descending orbit nodes), Garcia et al.  mapped SABER temperature using FFSM for several 1-month periods, including periods in the 2002 and 2003 summer mesosphere seasons. The analysis described in that paper uses the same technique employed here to map SABER temperature. The results presented here are an extension of the Garcia et al.  technique; however, our analysis and results focus on the dominant planetary wave activity in the summer polar mesosphere at altitudes where PMCs occur.
 The SNOE PMC mapping analysis of Merkel et al.  also employed FFSM. The results presented here are an extension of that work, as the two northern (2002 and 2003) and one southern (2002–2003) seasons have not been previously analyzed. In addition, the SNOE PMC mapping analysis was repeated using the same coded FFSM algorithm used for SABER temperature data by Garcia et al.  for consistency and comparability.
 The dominant planetary waves identified here have wave numbers and frequencies that fall within the Nyquist limits of asynoptic sampling. For both SABER and SNOE the zonal wave number limits range from 0 to 7. This follows from the fact that 15 longitudes are sampled at the local time corresponding to the ascending or descending node. The frequency limits for both data sets range from −1 to +1 cycles per day (cpd), where positive (negative) frequencies denote westward (eastward) propagating oscillations. The frequency limits are approximately equal to half the number of local time observations per orbit (two for both satellites). SABER and SNOE sampling are such that diurnal oscillations lie right at the Nyquist limit and may be contaminated from aliased oscillations. However, our results focus on periods longer than 1 day.
4.1. Wave Number–Frequency Spectrum
 The dominant planetary wave signatures identified by the FFSM are illustrated in Figure 3 for SABER and Figure 4 for SNOE. Figure 3 shows the normalized amplitude wave number–frequency spectrum of temperature at three latitude bands at 82 km altitude for each season analyzed. The temperature is normalized to the maximum amplitude in each season. In the summer MLT region a dominant source of variability occurs at periods near 2 days [Limpasuvan and Wu, 2003]. This is evident in the 48° latitude bin of Figure 3. Garcia et al.  showed that variance near 2 days in SABER temperatures not only peaks at ∼2 days and wave number 3 but is also accompanied by variance at other wave number–frequency pairs that tend to lie along a line of constant phase velocity (c ∼ 70 m s−1). This behavior is illustrated in Figure 3 by the black line in the 2002 season at 48°N, but it is present in all the seasons shown. Garcia et al. argued that this feature in the temperature spectra suggests that the 2-day wave is excited through the baroclinic instability of the summertime jet and manifests itself in a set of atmospheric normal modes that lie along a line of constant phase velocity [Plumb, 1983]. Included in the set is variance near 5-day wave number 1 and near 2-day wave number 2 Rossby normal modes, which is illustrated at 48° in Figure 3. Because the 2-day wave number 3 wave is a Rossby-gravity normal mode, it is confined to lower latitudes, and is not observed at the higher latitudes [Longuet-Higgins, 1969]. This is evident in the higher latitude bins in Figure 3, where the other two dominant modes (5-day wave number 1 and 2-day wave number 2) are still present, although relatively weak compared to the large amplitude of the 2-day wave number 3 that dominates the lower latitudes. All of the peaks identified in Figure 3 are statistically significant at the 95% level of the χ2 distribution with 6 degrees of freedom (d.o.f.). The spectral estimates in Figure 3 are obtained by smoothing the periodogram for each wave number with a three-point boxcar average. For 6 d.o.f. a spectral peak is statistically significant at the 95% level if the ratio of its magnitude to that of the local background spectrum is >2.1 [see Wilks, 2006, chapter 8 and Table B.3]. It is clear that the spectral peaks corresponding to the various normal modes discussed above meet this criterion. Any signal synthesized from frequencies surrounding a statistically significant peak (as shown in the next section) is presumed to be significant.
Figure 4 shows the normalized PMC brightness wave number–frequency spectrum at three increasing latitude bands. It is evident from Figure 4 that the dominant spectral peaks present in the SNOE PMC brightness data are found at 5-day wave number 1 and at 2-day wave number 2, consistent with those seen at the higher latitudes in the SABER temperatures. This distribution of variance in PMC brightness is evident in both northern seasons and the southern season. This comparison suggests that the planetary wave activity in PMC brightness is directly correlated to the variability in mesospheric temperature. Analysis of the seasonal characteristics of both waveforms in PMC and temperature gives an even stronger indication that they are related. As was the case with the temperature spectra of Figure 3, the peaks in the SNOE LSR spectra shown in Figure 4 are statistically significant at the 95% level (6 d.o.f.).
4.2. Seasonal Characteristics
 Using the output from the FFSM algorithm, the evolution of wave amplitude can be synthesized over any desired frequency bands. Figure 5 illustrates the RMS amplitude of PMC brightness in days from solstice (DFS) versus latitude for each of the three seasons. The waves are synthesized over the frequency bands that produce the maximum signal as indicated in Figure 5. Figure 5 (left) represents amplitude synthesized over the frequency range associated with the 5-day wave and Figure 5 (right) for the 2-day wave. The frequency range that produces a maximum amplitude for the 5-day wave number 1 for 2002 north is 0.18 to 0.24 cpd; for 2003 north it is 0.16–0.21 cpd; and for 2002–2003 south is 0.20–0.25 cpd (all associated with westward periods of 4−6 days). For the 2-day wave number 2 wave, the frequency range that yields the maximum signal is very consistent across all seasons: 0.46–0.51 cpd (westward periods of 1.9–2.2 days). The periods of maximum signal are highlighted in Table 1. Hereafter these waves will be referred to as the 5-day and 2-day wave. We emphasize again that in the case of the 2-day wave, we are referring to the wave number 2 Rossby normal mode rather than the wave number 3 Rossby-gravity mode.
Table 1. Wave Characteristics for Each of the Three Seasonsa
Period Range of Strongest Signal (days)
SABER MAX AMP (72°, 80–90 km)
SNOE MAX AMP
Mean SNOE LSR and SABER temperature are presented. The mean temperature is averaged over 82–90 km and 68°–80° latitude for the whole analysis period. The mean SNOE LSR is averaged over 68°–80° latitude. For each dominate wave feature the determined period (frequency−1) of the strongest signal, the max RMS amplitude of SABER temperature and the max SNOE LSR are presented. The reported SNOE maximum amplitude corresponds to the overlapping observation period from Figure 4. The SABER amplitude corresponds to the maximum at 72° latitude and altitude range of 80–90 km (determined from Figures 5 (left) and 6 (left)).
Figures 6 and 7illustrate the RMS amplitude of SABER temperature in days from solstice versus latitude and altitude for the 5-day wave and 2-day wave, respectively. It was determined that the frequency that produces the maximum amplitude in temperature at mesospheric altitudes is very similar to the frequency range for SNOE PMC in Figure 5. SNOE has continuous data over the whole PMC season (although limited in latitude); SABER does not. Therefore, the area identified by the dashed box in each contour plot in Figure 5 shows the overlapping detection period for SNOE and SABER. Because SABER has a more extensive coverage of the MLT in altitude and latitude, it is able to give a more complete picture of the seasonal evolution of these waves, although the seasonal coverage is shortened because of the yaw maneuver (with associated loss of polar coverage), which occurs in the middle of the PMC season as mentioned earlier. Figure 6 (left) and Figure 7 (left) illustrate the temperature amplitude as a function of altitude and days from solstice at 72° latitude. Figure 6 (right) and Figure 7 (right) illustrate the temperature amplitude as a function of latitude and days from solstice at an altitude of 82 km.
 The 5-day wave in SNOE appears in every season both in the north and the south [Merkel et al., 2003]. However, as shown in Figure 5, the maximum amplitude occurs in bursts of activity throughout the season and varies from year to year. This is consistent with the variability of the 5-day wave in SABER temperature (Figure 6) and similar to findings by Wu et al. . Comparing the seasonal evolution of the detected planetary wave in SNOE and SABER, it is evident that the periods of maximum amplitude from both measurements are consistent. For example, the 5-day wave in 2002 (Figure 5, top left) reaches significant amplitude twice in the overlapping time period at ∼0 and 20 DFS. In Figure 6, SABER season 2002 (top), the maximum in the 5-day temperature amplitude between 70°–80° latitude and 80–90 km (PMC altitudes) also occur near these same days. In the 2003 northern summer, the 5-day wave occurs in both SNOE LSR and SABER temperature (Figure 5, middle left; Figure 6 middle) reaching maximum amplitude twice in the overlapping time period: −15 DFS and 10 DFS. The southern summer of 2002–2003 shows the same behavior, maximizing once in the overlapping period near solstice (0 DFS). The variability of the 5-day wave differs year to year and the seasonal evolution visually correlates between SNOE LSR and SABER temperature.
 The SABER temperature FFSM results give a good view of the variation of the 5-day wave in altitude and latitude. Figure 6 (left) shows that the maximum amplitude at 72° latitude occurs between 75 and 90 km in all seasons. Although the full altitude range is not shown here, it appears that the 5-day wave is isolated in the mesosphere (not propagating from the lower altitudes). Figure 6 (right) shows that the amplitude at 82 km does not always reach a maximum at latitudes poleward of 68°. However, it is evident from Figure 6 that the wave variation does extend to the highest latitudes, where it is coincident with SNOE observations. The temperature amplitude is relatively small between 40° and 80° latitude ranging from 1.5 to 3.5 K.
 The 2-day wave behaves very similarly to the 5-day wave in both PMC and temperature in that the observed seasonal evolution visually correlates in both signals. As shown in Figure 5 (right) and Figure 7, the 2-day wave does not always have large amplitude at the same time (within the summer season) as the 5-day wave. However, both waves are dominant in the summer polar mesosphere. Comparing the 2-day wave seasonal variation in both SNOE and SABER, the same results are observed for the 5-day wave. The seasonal evolution in PMC and temperature coincide and the maximum amplitude in temperature may occur at latitudes equatorward of 68° but they are still present at the highest latitudes coincident with SNOE. In addition, in all seasons presented here, both planetary waves are present at PMC altitudes (80–84 km) although sometimes they are more evident at mesopause heights rather than at PMC altitude. This is the case, for example, for the 2003 2-day wave in Figure 7.
 A recent study showed a coincident 5-day wave variation in both temperature and PMC frequency by means of a wavelet analysis of SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Cartography) PMC frequency and MLS (Microwave Limb Sounder) mesopause temperatures for the 2005 northern summer season [von Savigny et al., 2007]. This study is complementary to our results in that von Savigny et al. show 5-day wave variance in both mesopause temperature and PMC frequency from a different data set and year than presented here. While their current analysis does not provide wave number information, spatial extent (latitude, altitude) of the 5-day amplitude, or information on other wave periods faster than the 5-day wave, we believe we are investigating the same phenomenon. Further comparison of these data sets will be important to understanding the characteristics of planetary waves in the summer mesosphere.
Figures 5, 6, and 7 illustrate that the evolution of planetary wave activity in PMCs over a summer season correlates in time and space with the transient mesospheric dynamics measured from SABER temperatures. Figures 5–7 isolate periods where both data sets observe strong planetary wave activity. Using these periods, we can determine if the variation observed in SNOE PMCs is directly related to a change in temperature. Figure 8 shows a Hovmoller diagram of one of the periods in the Northern Hemisphere in 2002 (0–20 DFS) where both data sets contain a strong 5-day wave. Figure 8 (left) illustrates SNOE LSR amplitude, and Figure 8 (right) illustrates SABER temperature amplitude. Figure 8 shows the evolution of amplitude in PMC LSR and temperature synthesized over the frequency band 0.18–0.24 cpd. Both images show a clear westward propagating wave signature. It is evident from Figure 8 that the SABER temperature and SNOE LSR variation are visually correlated in time and space and are near 180° out of phase (low temperatures tend to coincide with bright cloud). However, a coherence analysis is used next to quantitatively determine how the variation in PMC brightness is related to the variation in temperature in time and space.
4.3. Coherence and Phase
 Cross-spectral analysis provides a way of quantitatively evaluating the relationship between SABER temperature and SNOE PMCs. It provides a frequency-dependent measure of the correlation between observed signals, represented by the squared coherence. We use the method of Hayashi . The mean power spectra (2Sn for SNOE, 2Sa for SABER), the cospectrum (K2SnSa, SNOE versus SABER), and the quadrature spectrum (Q2SnSa, SNOE versus SABER) were computed from the m = 1 and m = 2 components of the synoptic spectra obtained from the FFSM for the overlapping measurement periods illustrated in Figure 8 (0–20 DFS, 2002 north). The average cross spectra are shown in terms of squared coherence (coh2) and cross-spectral phase (ϕ) at frequency (f), where
In Figure 9, we show the coherence between SNOE and SABER (top) and their phase relationship in degrees (bottom). Confidence limits for the squared coherence are calculated as explained by Julian . The 95% confidence limits are denoted by the dashed line in Figure 9. The top left image represents the coherence versus frequency for wave number 1 and the top right for wave number 2. It is evident from this analysis that SNOE and SABER spectra are highly coherent for this period in north 2002 at the appropriate wave numbers and frequencies. Analyses for all the other seasons considered in this study produce similar results. The bottom row illustrates the phase relationship between SNOE and SABER. The phase value at the frequency where the highest coherence occurs is positive, indicating that the temperature perturbation leads the PMC brightness variation. The 5-day wave phase relationship indicates they are ∼150° out of phase while the 2-day wave phase analysis indicates the signals are 165° out of phase. A 180° (out of phase) or greater phase difference between PMC brightness and temperature might have been expected because cold temperatures (and possibly higher water vapor mixing ratios) at the wave crests are most favorable for supersaturated conditions and particle growth. However, our results show that the cloud brightness actually maximizes about 10 h before the temperature minimum for the 5-day wave and 2 h before the temperature minimum for the 2-day wave. This result is consistent and apparent in all the seasons considered in this study.
 Currently, we do not have a quantitative explanation why the maximum in PMC brightness occurs before the minimum in SABER temperature, but we may speculate on a couple of possible reasons. PMC formation depends on both temperature and the supply of water vapor. The motion field of planetary waves that drives PMC brightness variations will also produce changes in temperature and water vapor. These perturbations depend on the relative magnitude of the background gradients of these variables and on the phase of the horizontal and vertical velocity components. So the maximum in the available water vapor may not coincide with the coldest temperatures, possibly causing a phase relationship illustrated here. Alternatively, rapid particle growth along the temperature wave trajectory could exhaust the available water vapor supply and/or cause sedimentation, preventing or even reducing further PMC growth. This would cause a maximum in PMC brightness to be reached before the coldest temperature perturbation. Because microphysical processes are complex, nonlinear functions of local temperature and the available water vapor, which are both susceptible to changes from dynamics, a 3-D model study incorporating PMC microphysics is needed to fully understand these results. First results of such a study with the 3-D PMC LIMA (Leibniz Institute Middle Atmosphere) model show that both the variable background atmosphere and the redistribution of water vapor are important factors in the geographical distribution of PMCs [Berger and Lübken, 2006]. Further analysis of the role that temperature and water vapor play in defining the determined phase relationship is underway using the Whole Atmosphere Community Climate Model (WACCM) (D. Marsh, private communication, 2007).
 The coherence analysis demonstrated that the variation observed in SNOE PMCs is directly related to the change in temperature. This section discusses the PMC brightness amplitudes associated with the temperature change. Table 1 lists the maximum amplitude of the 5-day and 2-day waves in both SNOE and SABER. The maximum temperature amplitude shown in Table 1 corresponds to the maximum near 72° latitude and the altitude range of 80–90 km (for comparison to SNOE PMC latitudes and altitudes). The SNOE maximum amplitude corresponds to the overlapping observation period as highlighted in Figure 5 at all latitudes. Included in Table 1 is the zonal mean SABER temperature averaged over 82–90 km and 68°–80° latitude for the overlapping observation period. The zonal mean SNOE LSR averaged over 68°– 80° is also shown in Table 1. To compare PMC brightness and temperature perturbations, we consider the fractional or normalized changes in these variables given by
Using the values in Table 1, the ratio δPMC/δT = 16.4 (5-day), 16.0 (2-day) for 2002 and 13.0 (5-day), 11.4 (2-day) for 2003. These results suggest a somewhat greater sensitivity of PMC brightness to temperature perturbations in 2002 compared to 2003. The planetary wave activity in both the 5-day and 2-day waves appears to be comparable, indicating that both planetary waves are dominant in the summer polar mesosphere. The third row in Table 1 shows the amplitude characteristics for the southern summer 2002–2003 PMC season. The zonal mean temperature is 143 K in the south, about 3–8 K warmer than the Northern Hemisphere, in agreement with previous north/south comparisons of summer mesospheric temperatures [Lübken et al., 2004; Hervig and Siskind, 2006; Xu et al., 2007]. The zonal mean SNOE LSR in the south is 10.0, which is larger than in the north because of forward scattering as mentioned earlier. Normalizing the activity as illustrated above, ∂PMC/∂T = 22.4 (5-day) and 17.8 (2-day), indicating a larger sensitivity of PMC brightness to temperature changes than in the northern seasons. Several observational studies have indicated prominent differences in PMC characteristics between the north and the south [Bailey et al., 2007, and references therein]. Complementary to this study, Bailey et al.  indicates that these differences are probably due to the small zonal mean temperature difference between the two hemispheres.
 Although it is apparent from this analysis that PMC brightness variation is directly related to the temperature variation on planetary scales, it is difficult to calculate the expected PMC brightness response from SNOE to a temperature change without a 3-D microphysical model. The variation of temperature combined with available water vapor induces a saturated environment that is conducive to particle growth, thus affecting the particle size distribution and, therefore, the apparent brightness of the cloud. Since the scattering cross section is proportional to the third to sixth power of the PMC particle size in the mid-UV (depending on the angle of observation), the change in SNOE brightness is representative of a change in particle size for the forward scattering geometry and the volume of ice for backward scattering geometry [Englert and Stevens, 2007]. This relationship along with WACCM/PMC modeling will be instrumental in defining the observed PMC brightness relationship to the presented temperature perturbation and how the relationship translates to the cloud microphysics.
 The data presented show that the summer polar mesosphere is a site of planetary wave modulation of temperature and PMC brightness. Time-lapse Animations 1–3 of SNOE PMC brightness maps indicate that the general motion of PMC is westward with strong zonal variations that change daily, indicating planetary scale variance. Along with previous analyses [Garcia et al., 2005] of SABER temperature measurements, this analysis shows a population of planetary waves in the summer mesosphere presumably forced by the baroclinic instability of the summer time jet. Dominant among these planetary waves at midlatitudes is the Rossby-gravity 2-day wave number 3 [Limpasuvan and Wu, 2003; Garcia et al., 2005]. While this planetary wave has been thoroughly documented, it is not the most important forcing mechanism when it comes to producing PMC variability on planetary scales. The 2-day wave number 3 has the largest amplitude at the lower latitudes (equatorward of 60° [Longuet-Higgins, 1969]), far from the latitudes of highest PMC occurrence. Although not shown here, a 2-day wave number 3 modulation in temperature may affect PMC brightness below 60° latitude.
 The planetary wave features most important to PMC variability on planetary scales are the Rossby normal modes 5-day wave number 1 and 2-day wave number 2 excited from the same source as the 2-day wave number 3. These 2-day and 5-day waves in temperature behave very similarly in that their variance extends to high latitudes (68°–80°) in the summer mesosphere. The amplitude of these waves is small (2.0–3.5 K) and the variance seems to be isolated between 80 and 90 km (PMC altitudes). Merkel et al.  estimated that a 7 K temperature change in an environment with a water vapor mixing ratio of 4 ppmv was enough to produce supersaturated conditions for particle growth at mesopause altitudes. Here we show that observed temperature perturbations much smaller than this estimate are sufficient to produce a measurable change in cloud brightness. This suggests that a temperature perturbation estimate based on an assumption of a fixed background environment may not be a good representation of the conditions encountered by air parcels following a wave trajectory.
 SABER temperature and SNOE LSR dynamical signatures are highly coherent, indicating that temperature is a controlling mechanism for PMC brightness. In addition, temperature and PMC brightness are 150° (5-day wave) and 165° (2-day wave) out of phase, indicating an almost antiphase relationship between PMC brightness and temperature.
 The seasonal evolution of the anomalies in PMC brightness and temperature coincide, and the seasonal variability is evident. Year-to-year differences are noticed, with the 2002 northern season being slightly more active than the 2003 northern season. Comparing the two wave features, the 2-day wave temperature amplitude is slightly less than the 5-day wave (∼0.5 K); however, the ratio of normalized PMC to temperature perturbations (δPMC/δT) is comparable. In the southern summer season the zonal mean temperature is slightly higher, the amplitude of the temperature perturbations is slightly greater (∼1 K), and the ratio δPMC/δT is larger than in either of the northern summers. These results suggest that PMC brightness is very sensitive to small changes in background temperature and perturbation temperature. Future modeling studies will be instrumental in explaining the coupling of dynamical and microphysical processes. In addition, using the SABER water vapor product (to be released in the next version of the data) in a similar study will help identify the role that water vapor plays in PMC variability on a global scale.
 While previous analysis has shown that the 5-day global mode does not maximize in the summer but rather near equinox [Garcia et al., 2005; Riggin et al., 2006], it is important to note that this wave does occur in the summer polar mesosphere and we have further established that it is an important forcing mechanism of planetary-scale PMC variability. The zonal variation of PMC brightness and the day-to-day variability in geographic locations from planetary wave activity should be considered when analyzing observations of PMCs.
 We thank the reviewers for constructive comments on the manuscript. This research was supported by the National Science Foundation under the Coupling, Energetics, and Dynamics of Atmospheric Regions (CEDAR) postdoctoral grant conducted at the National Center for Atmospheric Research. The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. SNOE was managed for NASA by the Universities Space Research Association. We thank the SABER data processing team for their work to provide the high-quality temperature product used in this analysis. We thank Ruth Lieberman, Scott Palo, and Gary Thomas for their suggestions with this analysis and manuscript.