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. Author manuscript; available in PMC: 2021 Jun 30.
Published in final edited form as: J Geophys Res Atmos. 2020 Apr 17;125(9):e2020JD032495. doi: 10.1029/2020jd032495

The Role of Vertically and Obliquely Propagating Gravity Waves in Influencing the Polar Summer Mesosphere

Brentha Thurairajah 1, Chihoko Yamashita Cullens 2, David E Siskind 3, Mark E Hervig 4, Scott M Bailey 1
PMCID: PMC8243719  NIHMSID: NIHMS1714398  PMID: 34211819

Abstract

Using an 8-year (2007–2014) data set from two different limb-viewing instruments, we evaluate the relative roles of vertically versus obliquely propagating gravity waves (GWs) as sources of GWs in the polar summer mesosphere. Obliquely propagating waves are of interest because they are presumed to be generated by the summer monsoons. In the high-latitude upper mesosphere, the correlation coefficient between the time series of ice water content (IWC) and GW amplitude is 0.48, indicating that the observed GWs enhance polar mesospheric clouds (PMCs). For vertically propagating waves, the correlation coefficient between IWC and stratospheric/lower mesospheric (20–70 km) GW amplitude at the same high latitudes becomes more negative with increasing altitude. This change in correlation from negative in the lower mesosphere to positive at PMC altitudes suggests the presence of another source of GWs. The positive correlation coefficient between the time series of IWC and GW amplitude from 0–50°N, 20–90 km shows a slanted structure suggesting oblique propagation. This slanted structure is more robust in some seasons compared to others, and this interannual variability may be due to the latitudinal gradient of the mesospheric easterly jet where steeper gradients allow for low-latitude tropospheric GWs to be refracted to the high-latitude mesosphere more efficiently. Gravity-Wave Regional or Global Ray Tracer (GROGRAT) ray tracing simulations show that more GWs propagate obliquely compared to vertically propagating waves that reach PMC altitudes. For obliquely propagating waves, GROGRAT simulations indicate that nonorographic tropospheric GWs with faster phase speed (>20 m/s) and longer horizontal wavelength (>400 km) have a higher probability of reaching the polar summer mesosphere.

1. Introduction

The role of gravity waves (GWs) in modulating the polar summer mesosphere is typically studied by analyzing the influence of GWs on noctilucent clouds, NLCs (or polar mesospheric clouds [PMCs] when seen from space) owing to the high sensitivity of these clouds to changes in the mesospheric environment. Previous observational studies include lidar measurements that have looked for a correlation between NLC brightness and stratospheric GW potential energy (Chu et al., 2009; Gerrard et al., 2004; Innis et al., 2008; Thayer et al., 2003). While no correlation between NLC parameters and stratospheric GW activity was reported at Davis, Antarctica (68.6°S, 78°E) (Innis et al., 2008), or at the South Pole (90°S) (Chu et al., 2009), Thayer et al. (2003) and Gerrard et al. (2004) reported an anticorrelation between NLC brightness and stratospheric GW potential energy at Sondrestrom, Greenland (67°N, 50.9°W). An anticorrelation was also reported by Chu et al. (2009) in Rothera, Antarctica (67.5°S, 68°W). The different correlations at Rothera and South Pole in Antarctica were attributed to the “latitudinal differences in background temperatures in the ice crystal growth region between the PMC altitude and the mesopause” (Chu et al., 2009), as GW-induced temperature perturbations either suppress or enhance ice crystal growth in warm and cold regions, respectively. Despite the seemingly contradictory results, these lidar studies all assumed that high-latitude stratospheric GWs would propagate vertically to reach the high-latitude mesosphere and influence NLCs. However, as noted by Gerrard et al. (2004), GWs that influence these clouds may not be the same waves observed in the stratosphere directly below.

More recently, Wilms et al. (2013) used common volume lidar and radar data over Andenes, Norway (69.3°N, 16°E), to study the correlation between NLC occurrence observed by lidar and GW kinetic energy derived from radar wind data at NLC altitudes. They reported no correlation and discussed the possibility that the observed NLCs might have been advected horizontally (Gerding et al., 2007), and therefore, the common volume GWs might not have had any influence on the formation of the observed NLCs. Wilms et al. (2013) also noted the different sources of GWs that could influence the polar summer mesosphere, that is, vertically propagating GWs, where the waves propagate directly above their source and non-vertically or obliquely propagating waves where the waves propagate vertically and latitudinally away from their source. This latitudinal or oblique propagation of GWs has been modeled in high-resolution GW resolving models (Sato et al., 2009; Siskind, 2014), the Gravity-Wave Regional or Global Ray Tracer (GROGRAT) ray tracing model (Kalisch et al., 2014), and discussed in several observational studies (e.g., Ern et al., 2011; Jiang et al., 2004; Sato et al., 2003; Thurairajah et al., 2017; Yasui et al., 2016). Sato et al. (2009) proposed that the tropical stratospheric GWs generated by monsoon convection (hereon referred to as monsoon GWs) would be refracted poleward due to the latitudinal shear associated with the prevailing summer monsoonal easterly winds. The slanted structure of the easterly jet (slanted from the stratosphere in the tropics to the mesosphere in the high latitude) would allow oblique propagation of these monsoon GWs to the polar summer mesosphere.

In this study we analyze the influence of GWs on the polar summer mesosphere using PMC and mesospheric GW data from the Solar Occultation for Ice in the Mesosphere Experiment (SOFIE) instrument on the Aeronomy of Ice in the Mesosphere (AIM) satellite (Gordley et al., 2009; Russell et al., 2009). We also study the potential sources of these polar summer mesospheric GWs by analyzing the influence of both vertically and obliquely propagating GWs using data from SOFIE and the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument (Russell et al., 1999) on board the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) spacecraft. The (AIM) mission was launched in April 2007 and provides an unprecedented global view of PMCs and their variability in both hemispheres, from both the Cloud Imaging and Particle Size (CIPS) experiment and SOFIE instrument. Chandran et al. (2009) used CIPS PMC images and reported an anticorrelation between the occurrence of GW structures and PMCs. They also reported a longitudinal variability in GW occurrence and PMC occurrence. A longitudinal variability in PMC response to mesospheric GWs was also reported by Liu et al. (2014) using SOFIE GW potential energy data in both the Northern and Southern Summer Hemispheres. More recently, Gao et al. (2018) extracted GWs with horizontal wavelengths of 20–150 km in CIPS images from 2007–2011 and found that small-scale GWs can amplify the albedo and ice water content (IWC) by 10.0–22.6%.

The TIMED mission was launched in 2002, and the long-term global temperature data from SABER have been demonstrated to be reliable for GW related studies (e.g., Ern et al., 2011; Ern et al., 2018; Preusse et al., 2009; Yamashita et al., 2013, and references therein). Recently, Thurairajah et al. (2017) reported on an observational case study of obliquely propagating GWs during the Northern Hemisphere (NH) 2007 PMC season using SABER GW and CIPS PMC measurements, with a high-resolution GW resolving model (the Navy Operational Global Atmospheric Prediction System-Advanced Level Physics High Altitude [NOGAPS-ALPHA] model). Thurairajah et al. reported the slanted structure of GW momentum flux from the tropical stratosphere to the high-latitude mesosphere using SABER measurements and confirmed the eastward and northward propagation of these waves using the NOGAPS-ALPHA model. The authors also reported a significant positive correlation between the time series of 50 km tropical GWs and the high-latitude 84 km PMC occurrence frequency and proposed that obliquely propagating monsoon GWs influence the summer mesosphere and hence PMCs. The present study investigates the influence of vertically and obliquely propagating GWs on PMCs using observations from eight (2007–2014) NH PMC seasons.

2. Data and Analysis

SOFIE, a limb-viewing solar occultation instrument, routinely measured high-latitude (~65–85°) temperatures from ~15–100 km during the NH 2007–2013 summers. During the NH 2014 PMC season SOFIE measurement latitudes were between 60°N and 65°N from 22 May to 10 July 2014 and increased poleward of 65°N after this date. During these years, in the NH, SOFIE observed 15 sunrise occultations per day with consecutive measurements separated by ~24° longitude (~96 min). The temperatures are reported at a vertical spacing of 0.2 km. Validation of SOFIE temperatures can be found in Stevens et al. (2012) and Hervig et al. (2016). SOFIE temperatures are used to derive GW amplitudes at the NH high latitude (60–85°N) from 20–90 km at a vertical resolution of 1 km. SOFIE IWC observations from ~60–85°N are also used to characterize the polar summer mesospheric variability. IWC is the column abundance calculated from the vertical integral of the ice mass density (Hervig & Stevens, 2014) and is reported at ~84 km. In this study we use the Version 1.3 temperature and IWC data.

SABER, a limb-scanning infrared radiometer, has measured continuous stratospheric and mesospheric (~20 to 100 km) temperatures in the latitude interval 50°N to 50°S since 2002. SABER temperatures are reported at 0.4 km resolution. Continuous SABER measurements in the high-latitude summer are not available due to the yaw cycle of the TIMED satellite that alternates between the NH and Southern Hemisphere (SH) high latitudes every 2 months. Validation of SABER temperatures can be found at Rezac et al. (2015) and Remsberg et al. (2008). SABER temperatures are used to calculate the global (50°N to 50°S) GW amplitude at a vertical resolution of 1 km and horizontal resolution of 2.5° latitude × 24° longitude. In this study we use the Version 2.0 Level 2A temperature data.

The influence of vertically propagating GWs on PMCs is studied using zonal mean SOFIE data (~60–85°N). The effect of obliquely propagating GWs on PMCs is studied using a combination of zonal mean GWs (0–50°N) from SABER and IWC from SOFIE. Figure 1 shows the proposed summer mesospheric GW sources and their direction of propagation. Combining SOFIE and SABER measurements provides a valuable opportunity to understand the effect of both vertically and obliquely propagating GWs as sources of the waves observed in the polar summer mesosphere.

Figure 1.

Figure 1.

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Gravity wave propagation paths in the summer hemisphere. The red vertical arrows indicate vertical propagation, and the blue arrows indicate oblique propagation.

GW parameters such as amplitude, potential energy, and momentum flux derived from SABER temperature perturbations have been widely used in various GW studies (e.g., Ern et al., 2011, 2013; Liu et al., 2017; Preusse et al., 2009; Yamashita et al., 2013, and references therein). The derivation of GW amplitude from temperature perturbations has been explained in detail in previous studies (e.g., Ern et al., 2013; Thurairajah et al., 2014; Yamashita et al., 2013) and is summarized here as follows. For each temperature profile, a temperature perturbation is calculated by first subtracting the contribution of the zonal mean component (wavenumber 0) and planetary wave (PW) (wavenumbers 1–7) components. This eliminates the influence of smaller-wavelength kelvin waves and larger-wavelength quasi-stationary PWs and tides. A wavelet analysis of the perturbation temperature fluctuations is used to estimate the first three dominant vertical wavelengths between 4 and 20 km. The dominant vertical wavelengths are then used in a harmonic fit analysis to calculate the GW amplitude. This method has been shown to effectively remove the influence of tides, equatorial waves, and quasi-2-day waves (e.g., Liu et al., 2014; Thurairajah et al., 2014, and references therein).

Wright et al. (2016) determined observational filters for a multi-instrument data set based upon the physical properties of each instrument, the radiative transfer (Preusse et al., 2002), and weighting function considerations. The authors noted that for vertical wavelengths between 4 and 20 km SABER is sensitive to GWs with horizontal wavelengths longer than ~500 km. However, depending on the distance between subsequent altitude profiles along the measurement track, GWs with horizontal wavelengths as short as 100 km can be observed (e.g., Ern et al., 2011, 2018; Preusse et al., 2009). Since different instruments are sensitive to different spectrum of GWs (Alexander et al., 2010; Wright et al., 2016), to meaningfully compare GW amplitudes from SABER and SOFIE, both instruments need to be sensitive to the same spectrum of waves. While previous SOFIE GW studies (e.g., Thurairajah et al., 2014) have assumed that SOFIE would be sensitive to the same spectrum of GWs seen by limb-viewing instruments such as SABER, here, we quantitatively test that assumption by estimating the sensitivity of SOFIE GWs using the analytical approach proposed by Preusse et al. (2002) for infrared limb measurements. Assuming a mean temperature of 230 K, the relative radiance sensitivity to a 1 K perturbation in the atmosphere is calculated using

S(H,k,m)=1B∂B∂Tc2c2+a24exp(−cb24(c2+a2)) (1)

where a = m/2RE, b = k, c = 1/(2HRE), k is the horizontal wavenumber, m is the vertical wavenumber, RE is the radius of the Earth, H is the scale height of 6.5 km, and B is the Blackbody radiation factor. B is evaluated at 4.3 μm, the CO2 measurement wavelength at which SOFIE temperatures are calculated. A detailed explanation of the derivation of equation 1 and the corresponding radiative transfer equations and assumptions can be found in Preusse et al. (2002).

Figure 2 shows the estimated sensitivity as a percentage deviation from the total radiance amplitude corresponding to a 1 K sinusoidal perturbation in the atmosphere. The sensitivity is shown as a function of horizontal and vertical wavelengths. Based on this analytical approach, in the vertical wavelength range of 4–20 km, SOFIE is sensitive to GWs with horizontal wavelengths greater than ~400–500 km. Thus, SOFIE and SABER are both generally sensitive to the same spectrum of GWs, and these two data sets in combination can be used to investigate both the vertically and obliquely propagating GWs as sources of summer polar mesospheric GWs.

Figure 2.

Figure 2.

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Estimated sensitivity of SOFIE as obtained from the analytical method proposed by Preusse et al. (2002).

3. Results

3.1. Seasonal and Interannual Variability

Figure 3 shows the time series of daily averaged zonal mean SOFIE IWC, SABER monsoon GW amplitude at 50 km, and SOFIE high-latitude GW amplitude at 50 and 84 km, during the NH 2007–2014 PMC seasons. The 50 km GW amplitude has been averaged over 48–52 km, and the 84 km GW amplitude has been averaged over 82–86 km. SABER GW is averaged over 15–30°N, and SOFIE GW is averaged over 60–85°N. Since PMC start and end dates vary year to year, to be consistent between different PMC seasons, we only show the time series from −30 to 70 days from solstice (DFS) or 22 May to 31 August, which is a typical PMC season. It is notable in Figure 3a that the IWC values of the NH 2007 and NH 2014 seasons are lower than average. The mid-season IWC reduction in 2007 was analyzed by Siskind et al. (2011) and shown to be likely the result of inter-hemispheric coupling due to enhanced PWs in the SH winter. For the NH 2014 PMC season, since the latitude of the SOFIE occultation had drifted slightly equatorward, this likely accounts for the later season onset. However, as with 2007, dynamical effects and inter-hemispheric coupling have been proposed to account for the mid-season 2014 IWC reductions (France et al., 2018). Finally, the increase in IWC after 40 DFS during the NH 2007 PMC season has been attributed to the increase in 5-day PW activity (Nielsen et al., 2010).

Figure 3.

Figure 3.

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(a) SOFIE IWC at 84 km and averaged over 60–85°N for the NH 2007–2014 PMC seasons. (b) SABER GW amplitude at 50 km and averaged over 15–30°N for the NH 2007–2014 PMC seasons. (c) Same as (a) but for SOFIE GW amplitude at 50 km. (d) Same as (c) but at 84 km.

Figure 3b shows the SABER daily averaged GW amplitude at 50 km and zonally averaged over the monsoon region (15–30°N). Ern et al. (2011) and Thurairajah et al. (2017) have shown that the zonal mean vertical GW flux of horizontal momentum associated with the monsoon convection in the NH summer maximizes in this latitude range. This area includes the Asian, African, and North American monsoon regions (Wright & Gille, 2011). These GWs have peak amplitudes of 2.5–3.0 K2 in early August (40 to 60 DFS), except for the NH 2007 monsoon GW amplitude, which has a peak between 20 and 40 DFS. The SOFIE daily averaged high-latitude 50 km GWs shown in Figure 3c have amplitudes varying from ~2–3 K2 from −30 to 70 DFS. The high-latitude 50 km GW amplitude in 2007 and 2014 is higher compared to other years.

Figure 3d shows the daily averaged high-latitude 84 km GW amplitudes. The GW amplitudes are more variable at the start of the general PMC season compared to the end of the season and show a summer cycle with peak amplitudes (>10 K2) in July (10 to 40 DFS). This summer peak in mesospheric GW activity at high latitudes has also been reported in other observations such as in the Microwave Limb Sounder (MLS) GW variance (calculated from saturated limb radiance measurements) at 80 km and averaged between 45°N and 75°N (Jiang et al., 2006), medium-frequency radar GW wind variance in the Arctic mesosphere and lower thermosphere (Dowdy et al., 2007), and medium-frequency radar GW wind variance at 70–78 km in the Antarctic mesosphere (69°S, 39.6°E) (Yasui et al., 2016). In general, as with 50 km, the 84 km GW amplitudes in 2007 and 2014 are higher than in other years. The reasons for this are as yet unexplained.

3.2. Vertically Propagating GWs

Most previous studies have correlated stratospheric GW activity (~40 km) with PMC brightness or occurrence frequency to understand the influence of GWs on these clouds (Chu et al., 2009; Gerrard et al., 2004; Innis et al., 2008; Thayer et al., 2003). The present study differs in that the simultaneous observation of GWs and IWC at the same PMC altitude by the SOFIE instrument provides a direct comparison between these parameters at the same location. Moreover, under the assumption that there is a linear relation between GW occurrence in the stratosphere/lower mesosphere and PMC occurrence in the upper mesosphere, we are able to analyze the influence of vertically propagating waves by correlating the time series of high-latitude GW amplitude at altitudes of 20–90 km with IWC at 84 km for all eight PMC seasons. This is shown in Figure 4. The GW amplitude and IWC from −30 to 70 DFS are smoothed by a 5-day running mean, which has the effect of removing PW effects such as the 5- and 2-day waves noted in Figure 3a.

Figure 4.

Figure 4.

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Correlation coefficient between the time series (5-day running mean) of high-latitude (~60–85°N) GW amplitude at each altitude between 20 and 90 km and IWC at 84 km.

Between ~75 and 85 km, time series of GW amplitude is positively correlated to IWC, with a significant correlation coefficient of 0.48 for data from all eight seasons (i.e., 8 seasons × 100 data points = 800 data points). The positive correlation implies that zonal mean mesospheric GWs at PMC altitudes can enhance IWC at least on a 5-day running mean time scale and thus support the formation of PMCs. Note that this increase in correlation coefficient is also seen when the correlations are calculated by removing the background signal (i.e., the underlying smoothly variable seasonal signature) implying that the seasonal time scale does not dominate the higher correlation coefficients. The positive correlations contradict Wilms et al. (2013), who reported that PMCs over Alomar (69°N) did not correlate with simultaneous measurements of GW kinetic energy at the same altitude. They concluded that the PMCs over ALOMAR, which is at the lower limit of the latitudes (~60–85°N) observed by SOFIE, were advected horizontally and not affected by co-located GWs. However, Wilms et al. reported PMC amplification during long-period GW occurrence in agreement with model simulations that have shown that short period GWs (<6.5 hr) tend to destroy PMCs, while long-period waves enhance PMCs (Chandran et al., 2012; Jensen & Thomas, 1994; Rapp et al., 2002; Turco et al., 1982). Upward vertical winds associated with long period GWs can last for a longer period and slow down the descent of ice particles while enabling these particles to stay in the supersaturated region and grow to the maximum size. In contrast, for short period GWs, ice particles are transported downward and out of the supersaturated region more rapidly thus diminishing the growth time.

For upward propagating GWs that reach the mesosphere, their variability is dependent on the filtering process of upward propagating waves by the background wind and temperature. Figure 4 shows that below ~45 km, the correlation coefficients (r) between GW amplitude at an altitude in the stratosphere and IWC at 84 km are either positively or negatively correlated for individual seasons. Above this altitude, r becomes increasingly negative with correlation coefficients reaching a minimum of −0.5 at 70 km for some summers. The differences in r could be due to differences in filtering of vertically propagating tropospheric GWs by winds, the presence of secondary waves, a different source of high-latitude summer mesospheric GWs, and/or constructive and destructive interference of multiple waves.

The present results are to some extent similar to previous lidar observations that showed negative or no correlations between stratospheric GWs and PMCs. The negative correlation between stratospheric GWs (40 km) and PMC backscatter from Sondrestrom at 67°N, 51°W (r = −0.35 with 95% confidence) (Gerrard et al., 2004) and Rothera, Antarctica (67.5°S, 68°W) (r = −0.49 with 98% confidence) (Chu et al., 2009) was based on calculations of GW strength characterized by a 2-hr averaged root-mean-square density perturbation in the upper stratosphere (30–45 km). Gerrard et al. proposed that a spectrum of GWs exists with greater wave strength that could sublimate existing clouds or inhibit the formation of PMCs, while weak waves had little influence on PMCs. Gerrard et al. (2004) also proposed that while strong GWs would reduce PMC brightness on short time scales (less than a day), that GWs may help enhance PMC formation via localized upwelling and cooling by providing sufficient zonal drag on longer time scales (days to weeks). Recall that the previous lidar studies were based on observations over periods of hours at one location and thus may have been observing a different spectrum of GWs. Differences between this study and previous results may therefore be consistent with differences in the PMC response to varying GW spectra combined with different observational time periods. Additionally, longitudinal variations in PMC occurrence are well known (e.g., Chandran et al., 2010; Liu et al., 2014), which cannot be addressed by lidar measurements at a fixed location. We therefore investigated the longitudinal variation in PMC response to GWs, but over all eight PMC seasons found no clear longitudinal variation in PMC response to GW activity, and thus, we do not further consider this in this study.

3.3. Obliquely Propagating GWs

GWs generated by monsoon convection have been shown to propagate obliquely from the low-latitude upper stratosphere/lower mesosphere to the high-latitude mesosphere (Thurairajah et al., 2017, and references therein). Model simulations (Sato et al., 2009) indicate that the oblique propagation of monsoon GWs is possible due to the latitudinal gradient of the mesospheric easterly jet. The wind gradients can refract the vertically propagating monsoon GWs, thus focusing these waves into the easterly jet and shifting the location of GW momentum flux deposition to high latitudes. As reported by Ern et al. (2011) and Thurairajah et al. (2017), both the GW total vertical flux of horizontal momentum and the GW temperature amplitude calculated from SABER temperature measurements have a slanted structure above ~50 km in the tropics. The maximum in momentum flux shifts poleward with increasing altitude. This slanted structure of the GW momentum flux and amplitude follows the slanted structure of the mesospheric easterly summer jet suggesting oblique propagation of GWs and is observed in all eight PMC seasons (not shown here; see Figure 2 of Thurairajah et al., 2017).

Model studies have suggested that the horizontal wind gradient can play a major role in the oblique propagation of GWs. Other mechanisms that cause oblique propagation of GWs include that by advection by horizontal winds perpendicular to the horizontal wavenumber vectors as shown implicitly by Smith (1980) and Eckermann and Preusse (1999), and explicitly by Sato et al. (2012) and that by GWs that originally have non-zero group velocity (e.g., Sato et al., 1999). Here, we analyze the role of the horizontal wind gradients. Figure 5 shows the latitudinal gradient of the zonal mean zonal winds from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) Version 2 data (Rienecker et al., 2011) from −30 to 70 DFS. MERRA is an atmospheric data assimilation system based on the Goddard Earth Observing System (GEOS) atmospheric General Circulation Model (GCM) integrated with the Gridpoint Statistical Interpolation (GSI) analysis. The latitudinal gradient, dU, is calculated as the difference in zonal mean zonal wind (U¯) at 20°N and 30°N, at 50 km altitude.

Figure 5.

Figure 5.

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Time series of zonal wind latitudinal gradient calculated between 20°N and 30°N at 50 km.

dU=U¯50km,20N−U¯50km,30N (2)

While the zonal wind gradients are similar to each other until ~10 DFS, the gradients after this day are larger during the 2010, 2012, 2013, and 2014 PMC seasons compared to other years.

Figure 6 shows the contour plots of correlation coefficients between the time series of GW amplitude at each NH latitude (0–50°N, 2.5° interval) calculated from SABER and the time series of IWC (averaged over 60–85°N) from SOFIE, for all eight PMC seasons (both time series are from −30 to 70 DFS). While there is significant interannual variability, there are some common patterns seen throughout. All the panels show an organized pattern in r, with peak values near 0.7 at 0.1 hPa (~65 km) from 10–40°N latitude. The GW-IWC correlation coefficients are higher with robust slanted structure in 2010, 2012, 2013, and 2014, compared to other years. Qualitatively, it appears that this pattern is associated with the years with stronger wind gradients shown in Figure 5. As noted previously, the interannual variability in correlation coefficients between the time series of stratospheric/lower mesospheric low-latitude GW and 84 km high-latitude IWC may be due to wind filtering, presence of secondary waves, and/or constructive and destructive interference from multiple waves. In addition, these GWs and their propagation could also be influenced by the teleconnections from the southern winter via inter-hemispheric coupling (e.g., Karlsson et al., 2009; Karlsson & Becker, 2016; Siskind et al., 2011). However, Figures 5 and 6 suggest that in general, the higher correlation coefficients between low-latitude upper stratospheric/lower mesospheric GWs and high-latitude upper mesospheric IWC can be associated with steeper wind gradients. The oblique propagation of GWs thus appears to depend on the strength of the horizontal wind shear of the mesospheric easterly jet, in agreement with the theory proposed.

Figure 6.

Figure 6.

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Contour of correlation coefficient between time series of GW amplitude at each latitude and altitude (0–50°N, ~25–95 km) and IWC (averaged over ~60–85°N, 84 km).

Note that Thurairajah et al. (2017) also showed a similar contour plot (their Figure 9) of the correlation coefficients between the time series of GW momentum flux at each NH latitude (0–50°N, 2.5° interval) calculated from SABER and the time series of PMC occurrence frequency (averaged over 60–85°N) from CIPS, for a single case study year of 2007. While the general slanted structure of the positive correlation is seen in both contour plots, the differences between Figure 9 of Thurairajah et al. (2017) and the first panel of Figure 6 for year 2007 may be due to factors such as differences in measurement local times, locations, and duration of observation between CIPS and SOFIE.

Figure 9.

Figure 9.

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Obliquely propagating GW ray-paths for phase speeds of (a, d) 0 m/s, (b, e) 20 m/s, and (c, f) 40 m/s that reached the upper mesosphere. Upper panels (a–c) show the number of low-latitude obliquely propagating waves that reached the mid-latitudes of 35–55°N. Lower panels (d–f) show the low-latitude obliquely propagating waves that reach the high latitudes of 60–85°N. The colors of the raypaths are the same as Figure 8.

3.4. GROGRAT Ray Tracing Results

To further examine the vertical and oblique propagation of GWs, we simulate GW raypaths using the GROGRAT ray tracing model (Eckermann & Marks, 1997; Marks & Eckermann, 1995). The GROGRAT model has been used to study GW propagation trajectories (e.g., Preusse et al., 2009; Yamashita et al., 2013) and changes in the distribution of GW drag under assumptions of oblique and vertical-only propagation directions (Kalisch et al., 2014). Trajectories in GROGRAT are based on the non-hydrostatic rotational GW dispersion relation, and the model considers the refraction of the wave vector due to the vertical and horizontal gradients of the background wind and temperature (Kalisch et al., 2014; Preusse et al., 2009). The dispersion relation for GWs is

ω^2=N2kh2+f2(m2+α2)kh2+m2+α2 (3)

where kh is the total horizontal wavenumber, m is the vertical wavenumber, N is the buoyancy frequency, f is the inertial frequency, and α = 1/2Hp, where Hp is the density scale height. The intrinsic frequency, ω^, is

ω^=kh(c−U(z)¯) (4)

where c is the ground-based horizontal phase speed and U(z)¯ is the background wind profile parallel to the horizontal wavenumber vector at altitude z. We use the background zonal and meridional wind, geopotential height, and temperature data from NOGAPS-ALPHA for the ray tracing simulations. NOGAPS-ALPHA is a forecast/analysis model that provides a synoptic analysis of the atmosphere from 1,000 to 0.001 hPa (~0–92 km) by assimilating observational data from SABER and MLS (Eckermann et al., 2009; Hoppel et al., 2008). The NOGAPS-ALPHA 6-hourly global analysis fields were generated at a spatial resolution of 2.25° latitude × 2.25° longitude for the years 2007–2009. Figure 7 shows a contour plot of the zonal mean zonal winds from NOGAPS-ALPHA on 1 July 2009. The slanted structure associated with the summer easterly jet is seen in the NH.

Figure 7.

Figure 7.

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Contour plot of zonal mean zonal wind on 1 July 2009 from NOGAPS-ALPHA model.

GWs were launched from the troposphere at 6 km (arbitrary altitude chosen to represent tropospheric GW source) and allowed to freely propagate until they dissipate or reach PMC altitudes. The growth of GW amplitude with altitude is dependent on the saturation scheme (i.e., saturation due to vertical dynamic instability) proposed by Fritts and Rastogi (1985). Moreover, Preusse et al. (2008) have shown that for GWs with short horizontal wavelengths, if the launch altitude is in the lower troposphere, for example, at 5 km compared to 20 km, the probability for the rays to propagate vertically and reach 80 km altitude is nearly a factor of 2 lower. This is attributed to the lower buoyancy frequency in the troposphere which will shift the boundary between the external, non-propagating waves and internal, propagating waves toward longer horizontal wavelengths, and the wind reversal line between the troposphere and stratosphere which adds to the critical level filtering of slow-speed waves. Although we do not expect our results to change significantly if the launch altitude was higher than 6 km but below the wind reversal line, changes (if any) will be investigated in future studies. Waves were launched in the tropical and sub-tropical latitudes (0–30°N) and high latitudes (60–85°N) with ground-based horizontal phase speeds (c) of 0, 20, and 40 m/s and horizontal wavelengths (λH) of 100, 200, 400, 600, 800, 1,000, and 1,200 km. The waves were launched at every 5° latitude and 10° longitude intervals, with the propagation direction uniformly distributed every 45° of azimuth. Thus, for a given phase speed, a total of 1,764 waves was launched between 0°N and 30°N, and a total of 1,512 waves was launched between 60°N and 85°N. The GWs were launched on 1 July of each year and allowed to propagate for up to 10 days. Previously, Preusse et al. (2008) have used GROGRAT simulations to investigate how GWs transport momentum flux from the lower atmosphere to the mesosphere lower thermosphere (MLT) at various ground-based phase speeds. While Preusse et al. (2008) considered GWs with short horizontal wavelengths (10–50 km) and vertical-only propagation direction, our study focuses on GWs with longer (>100 km) horizontal wavelengths and both vertical and oblique propagation paths of high-latitude and low-latitude tropospheric GWs.

Figures 8 and 9 show the raypaths of GWs that did not dissipate before reaching the upper mesosphere. Figures 8a–8c show the high-latitude raypaths that propagated vertically to reach the high-latitude (60–85°N) mesosphere, that is, the raypaths launched every 5° in the latitude band 60–85°N remained in the 60–85°N band in the mesosphere, for phase speeds of 0, 20, and 40 m/s, respectively. Similarly, Figures 8d–8f show the low-latitude raypaths that propagated vertically to reach the low-latitude (0–30°N) mesosphere, for all three phase speeds. Figure 9 shows the raypaths of GWs launched from the low-latitude troposphere and propagated obliquely to reach the mid-latitude (35–55°N) and high--latitude (60–85°N) mesosphere. The simulations suggest that GWs with a phase speed of 0 m/s or orographic GWs have a low probability of propagating vertically or obliquely to reach the upper mesosphere.

Figure 8.

Figure 8.

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Vertically propagating GW raypaths for phase speeds of (a, d) 0 m/s, (b, e) 20 m/s, and (c, f) 40 m/s that reached the upper mesosphere. Upper panels (a–c) show the number of high-latitude vertically propagating waves that reached 60–85°N. The total number of waves launched from the high latitudes are 1,512. Lower panels (d–f) show low-latitude vertically propagating waves that reached 0–30°N. The total number of waves launched from the low latitudes are 1,764. The black, dark blue, blue, green, light green, orange, and red lines indicate GWs with horizontal wavelength (λH) of 100, 200, 400, 600, 800, 1,000, and 1,200 km, respectively.

A comparison of Figures 8 (upper panel) and 9 (lower panel) shows that more non-orographic waves propagate obliquely to reach the high-latitude mesosphere, compared to vertically propagating high-latitude GWs. For example, for a phase speed of 40 m/s, 81 raypaths out of the 1,764 waves launched or 4.6% of the launched waves propagated obliquely from the low-latitude troposphere to reach the high-latitude mesosphere. In comparison, for the same phase speed, 30 raypaths out of the 1,512 waves launched or 2% of the launched waves propagated vertically from the high-latitude troposphere to reach the high-latitude mesosphere. Note that for the phase speed of 40 m/s, eight raypaths or 0.5% of the launched waves propagated obliquely from the high-latitude troposphere to the low-latitude mesosphere. A latitude-longitude analysis of the raypaths indicates that the direction of propagation of both the high-latitude vertically propagating GWs and the low-latitude obliquely propagating GWs is dominantly eastward.

For the case of low-latitude GW propagation, a comparison of Figures 8 (lower panel) and 9 shows that a larger number of low-latitude vertically propagating non-orographic waves reach the low-latitude upper mesosphere compared to the low-latitude obliquely propagating nonorographic waves that reach the high-latitude upper mesosphere. Kalisch et al. (2014) discussed the influence of the local Coriolis force on wave dissipation. From equation 3, waves can propagate only when ω^≫f: Under the assumption that the horizontal wavelength is much larger than the vertical wavelength (i.e., kh2 ≪ m2), the dispersion relation can be written as

m2=N2kh2ω^2−f2 (5)

Close to the equator f2 ≈ 0. With increasing latitude f2 is proportional to sin2(Φ) where Φ is the latitude. With f2 approaching ω^2, m grows to infinity or vertical wavelength becomes 0 and the wave dissipates. Equation 5 therefore suggests that for a given horizontal wavelength, poleward propagating low-latitude waves have a higher probability of dissipating compared to vertically propagating low-latitude waves.

Figures 8a–8c show that in the NH high-latitude summer, only GWs with short horizontal wavelengths (λH < 600 km) will propagate vertically to reach PMC altitudes. For obliquely propagating waves, Figure 10 shows the percentage of total rays from low latitudes that reach the upper mesosphere at all three latitude bands (0–30°N, 35–55°N, 60–85°N) as a function of phase speed and horizontal wavelength, for waves launched on 1 July 2009. The fraction of rays in a latitude band is defined as the number of rays at 84 km for each wavelength and phase speed divided by the total number of rays (includes all horizontal wavelength and phase speed) at ~84 km, in that latitude band. Note that the distribution of the total number of waves is similar in years 2007 and 2008 (not shown). The percentage of waves that reach the low-latitude (0–30°N) upper mesosphere increases with increasing phase speed but with a steeper increase at small horizontal wavelengths (λH < 400 km). The percentage of obliquely propagating waves that reach the middle-latitude (35–55°N) upper mesosphere increases with increasing phase speed in the horizontal wavelength range of 400–1,000 km. Only non-zero phase speed non-orographic waves with λH > 400 km reach the high-latitude (60–85°N) upper mesosphere, and the percentage of waves increases steeply with increasing phase speed at λH > 800 km. This wavelength range falls within the spectrum of GWs that can be observed by SABER and SOFIE.

Figure 10.

Figure 10.

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The percentage of total rays, originating in the low-latitude troposphere on 1 July 2009, that reach the (a) low-latitude (0–30°N), (b) mid-latitude (35–55°N), and (c) high-latitude (60–85°N) upper mesosphere as a function of horizontal wavelength and phase speed.

The ray tracing simulations suggest that for GWs with horizontal wavelengths greater than 100 km, those waves with fast ground phase speeds have the highest probability of reaching the upper mesosphere. This agrees with the results of Preusse et al. (2008) who investigated the transparency of the atmosphere to short horizontal wavelength (10–100 km) GWs. They reported that slower phase speeds are more prone to critical level removal, and waves with longer horizontal wavelength and faster phase speeds are more likely to reach the MLT, as expected from equations 4 and 5. GWs can dissipate and are absorbed into the background flow as they approach critical levels (zc) where their intrinsic phase speed (c^=c−Uz¯) and vertical wavelength approach 0. In the northern summer, orographic waves (c = 0) and westward traveling GWs are absorbed by the strong westward stratospheric jet, while eastward phase speeds from convection (c > 0) reach the upper mesosphere. Figure 10 also indicates that low-latitude tropospheric GWs with longer horizontal wavelength (λH > 400 km) will propagate obliquely to reach the high-latitude mesosphere. One explanation may be that if the waves have the same intrinsic frequency but different horizontal wavelengths, then from equation 5, at high latitudes when f2 is close to ω^2, obliquely propagating GWs with shorter horizontal wavelengths have a higher probability of dissipating (since m will be higher) compared to GWs with longer horizontal wavelengths. At low latitudes when f2 is close to 0, vertically propagating GWs with longer horizontal wavelengths will likely dissipate before reaching the low-latitude MLT (since m will be directly proportional to kH and thus will have a higher value) compared to GWs with shorter wavelengths.

4. Summary

In this study we show that a direct connection between the high-latitude stratospheric GWs and upper mesospheric IWC might not be the only source of polar summer mesospheric GWs and that obliquely propagating GWs presumably from monsoon convection also contribute to the polar summer mesospheric variability. However, the specific mix of vertical and oblique waves is a complicated function of GW wavelength, phase speed, and background wind. This complication may shed some light on the disparate results obtained from previous ground-based studies of mesospheric clouds and GWs.

Using data from eight NH PMC seasons, at PMC latitudes and altitudes, the GW amplitude is positively correlated to PMC IWC indicating that the observed GWs enhance PMC formation. The source of these high-latitude summer mesospheric GWs was investigated by analyzing the influence of vertically and obliquely propagating GWs. Observations from SOFIE indicate a negative correlation between the high-latitude stratospheric and lower mesospheric GWs and IWC. This correlation coefficient then becomes positive in the PMC region suggesting that there may be an additional source of polar summer mesospheric GWs.

Observations from SABER and SOFIE indicate a large interannual variability in the slanted structure of the positive correlation between GWs in the low- to mid-latitude stratosphere and lower mesosphere and IWC. Under the assumption that this slanted structure represents obliquely propagating waves, this variability could be associated with the strength of the latitudinal wind gradient, with steeper wind gradients allowing for more monsoon GWs to reach the summer polar mesosphere. The idea of oblique propagation of monsoon GWs is supported by GROGRAT ray tracing simulations. Our simulations indicate that more GWs propagate obliquely from low latitudes to reach the PMC regions compared to GWs that propagate vertically from high latitudes. Oblique propagation is favored for waves with faster phase speeds and longer horizontal wavelengths.

Key Points:

  • Obliquely propagating gravity waves influence the polar summer mesosphere

  • Steeper gradient of the mesospheric easterly jet allows for more efficient oblique propagation of gravity waves

  • Low-latitude tropospheric gravity waves with faster phase speeds have a higher probability of reaching the polar summer mesosphere

Acknowledgments

This work was supported by the NASA Grant 80NSSC18K0650 and NASA/AIM mission under Contract NAS5-03132. AIM was developed as part of the NASA Small Explorer Project. We thank the AIM SOFIE and TIMED SABER data processing teams. We thank Dr. Scott England for his help interpreting the GROGRAT results in terms of the wave dispersion theory. The SOFIE data can be found online (http://sofie.gats-inc.com/). The SABER temperature data can be found online (http://saber.gats-inc.com/). SABER gravity wave data and GROGRAT simulations can be found at Thurairajah (2019) (https://doi.org/10.7294/MHT5-EF87).

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