Middle Atmosphere Waves: A Physics Thesis

The study initially focused on the isotropy of internal gravity waves (IGWs), finding generally isotropic behavior below 80 km altitude. However, a significant departure from isotropy was observed between 80 km and 95 km, characterized by strong anisotropies. Crucially, these anisotropies exhibited the same directional pattern consistently across all months within this 80-95 km altitude range. Above 95 km, the anisotropies became less pronounced. While various explanations were considered for this observed behavior, none provided a fully satisfactory account of the phenomenon. The implications of this anisotropic behavior are further investigated throughout the study.

The study's key finding highlights the distinct altitude dependence of the observed anisotropy in internal gravity waves. The consistent anisotropic behavior between 80 km and 95 km, regardless of the month, is a striking feature. This suggests a persistent underlying mechanism influencing wave propagation within this specific altitude layer. The lack of complete explanation for this consistent directional anisotropy underscores a gap in our current understanding of IGW dynamics in the mesosphere and lower thermosphere. Further research is clearly needed to unravel the processes responsible for generating and maintaining this anisotropic pattern. The study's findings emphasize the complexities of IGW behavior in this region of the atmosphere.

Despite extensive investigation, the study reveals that no single explanation fully accounts for the observed anisotropy of internal gravity waves in the mesosphere and lower thermosphere. The research highlights the need for further investigation into the contributing factors that govern the anisotropic behavior observed, particularly in the 80-95 km altitude range. The consistent directional pattern observed across all months suggests a persistent and likely fundamental process influencing wave propagation in this region. The lack of a definitive explanation presents a significant opportunity for future research, potentially involving more detailed modeling and observational studies to uncover the underlying physical mechanisms.

The section begins by outlining the historical understanding of atmospheric temperature profiles. Until the late 19th century, it was commonly believed that atmospheric temperature decreased consistently with altitude. However, Teisserenc de Bort's work using registering barometers on balloons revealed a significant deviation from this assumption. His research (around 1904) demonstrated that at an altitude of approximately 10 km, the average atmospheric temperature ceased its decline and started to increase. This discovery marked a pivotal moment, leading to a more nuanced understanding of atmospheric temperature structure and paving the way for the division of the atmosphere into distinct height regions characterized by varying temperature gradients (increase, decrease, or stability).

A key focus of this section is the westward jet stream, identified as strongest during December and January. Reaching altitudes up to 80 km, it exhibits a potential amplitude maximum of 50-70 m/s near 75 km. The study notes a significant circulation reversal, transitioning from westward to eastward zonal winds, during the February-March period. This pattern, observed consistently over two years, is further explored at different altitudes. The reverse transition from eastward to westward winds occurs at higher altitudes, potentially linked to weak winds at the mesopause and lower thermosphere in spring. This transition is observed at 85 km in September-October and at 70 km in October-November across both years, showcasing the complex seasonal variations in wind patterns.

The data collected at Birdlings Flat show substantial agreement with the northern hemisphere data presented in the CIRA (COSPAR 1972) model. However, the study emphasizes the potential for significant hemispheric differences by comparing the Birdlings Flat data (Southern Hemisphere) with equivalent Northern Hemisphere months from the CIRA model. This comparison reveals variations, notably in the winter eastward jet, which exhibits an amplitude exceeding 85 m/s at altitudes between 65 km and 75 km in January (corresponding to July in the Northern Hemisphere). This suggests that the jet stream might appear at higher altitudes in the Northern Hemisphere. Furthermore, the transition from eastward to westward zonal wind conditions also differs between the hemispheres. The data presented highlights the importance of considering hemispheric differences when building comprehensive atmospheric models and understanding global atmospheric dynamics.

The study briefly explores the relationship between the solar cycle and its impact on the neutral atmosphere. While a connection between solar activity and particle activity is acknowledged, determining the influence of solar output variations on the neutral atmosphere proves challenging. A study by Venne et al. (1983) that compared 10.7 cm solar flux with 300 mbar winds found no statistically significant relationship. However, the document notes that other studies at higher atmospheric levels have yielded more positive results, suggesting the complexity of solar influence on different atmospheric regions. This underscores the need for further research to fully understand the extent of solar influence on atmospheric processes. The inherent variability and complexity of stratospheric and mesospheric time-series data require careful analysis and consideration.

The section introduces the quasi-biennial oscillation (QBO) as a significant phenomenon in the tropical stratosphere, also observable at latitudes between 60°N and 70°N (Kats 1968). The QBO's period is noted to vary, with Coy (1979a) reporting a range of 2 to 2.5 years, while Quiroz (1981) suggests a period between 21 and 34 months. At an altitude of 30 km, eastward winds typically prevail for 12 months, followed by westward winds for 15 months. Coy (1979a) also observes that the leading edge of the eastward shear zone tends to be sharper than that of the westward shear zone. The QBO's strength is highlighted as being strongest in the equatorial stratosphere, significantly weakening both above and below this region (Coy 1979a, Quiroz 1981). Outside the tropics, its influence further diminishes; however, Kats (1968) reports an amplitude of approximately 1K in the polar (70°N, S) stratosphere (50 mb), compared to an equatorial amplitude of about 2K at the same pressure level. Amplitudes in mid-latitudes are described as being very small. A downward phase propagation and latitudinal phase variations are also mentioned (McGregor and Chapman 1978).

Further detail is provided regarding the amplitude and phase variations associated with the quasi-biennial oscillation. McGregor and Chapman (1978) found amplitudes of 4K at the equatorial stratopause and up to 10K near the polar stratopause, illustrating the latitudinal variations in the QBO's impact. The study emphasizes that the discussion thus far has focused on long-period oscillations influencing mean monthly winds, which are considered as prevailing winds throughout the thesis. These prevailing winds are primarily attributed to the annual changes discussed in the preceding section. The inclusion of these long-period oscillations highlights their impact on the larger atmospheric circulation patterns and their importance in understanding the overall dynamics of the atmosphere. This sets the stage for a more detailed investigation of shorter-period oscillations.

This section delves into the characteristics of the two-day wave, utilizing data from various locations including Birdlings Flat, Adelaide, and Townsville. The study employs partial reflection drift measurements and Jicamarca radar data to analyze the wave's structure. A key aspect is the application of a simple mathematical model (Hines 1974), which predicts an exponential increase in wave amplitude with height. This increase is, however, contingent on the absence of a suitable damping mechanism; otherwise, the wave's amplitude growth would be constrained. The concept of wave breaking is introduced as a process where waves reach sufficiently large amplitudes to become unstable, leading to turbulence generation. Hodges (1969) suggests that this wave-breaking mechanism plays a significant role in restricting the growth of internal gravity waves in the mesosphere. The research also examines the role of turbulence in limiting wave amplitudes, and Hodges (1967) findings regarding velocity shear and the Richardson number are discussed in relation to the onset of turbulence.

The section focuses on the impact of wave breaking on internal gravity wave amplitudes. The research investigates the conditions under which wave breaking occurs, highlighting the role of the Richardson number as a key indicator of atmospheric stability and the onset of turbulence. The study notes that the observed momentum loss is greater at heights above 85 km compared to those below, raising questions about the factors governing wave amplitude increase. Two key hypotheses are presented: Firstly, the amplitude increase might be explained solely by unrestricted wave growth limited only by molecular viscosity. Secondly, significant seasonal or year-to-year variations in variance plots might offer clues. Understanding these variations is crucial for any theory explaining internal gravity wave breaking, requiring consideration of the seasonal and height changes, or lack thereof, in the variance spectrum. The study mentions reconciling observed temperature structure near the mesopause with radiative energy input as a relevant consideration.

The effects of breaking internal gravity waves on the general circulation in the mesosphere and lower thermosphere are examined. The study briefly addresses the challenge of reconciling the observed temperature structure near the mesopause with the radiative energy input to the atmosphere. The section mentions that the existing temperature structure in this region requires heating due to subsidence in winter and cooling due to net rising motion (Kellogg and Schilling 1951). The contribution of wave energy to this temperature regulation is considered significant and requires further investigation to fully understand the dynamics of this atmospheric region. The interaction between wave energy and the general atmospheric circulation remains a key area of focus in this section, indicating a complex interplay between various atmospheric processes and wave dynamics.

This section highlights the significant differences observed between the Northern and Southern Hemispheres in atmospheric data. The data used in this study covers latitudes from 30° to the pole, consisting entirely of Northern Hemisphere measurements. This limitation is explicitly noted as a potential source of bias, potentially significantly affecting models based on this data. To address this, Sehra and Hariharn (1981) compared rocket sounding data along lines of approximately constant longitude, contrasting Northern and Southern Hemisphere readings. They further compared data from longitudes between 40°E and 80°E with data from 40°W to 95°W. The CIRA (COSPAR 1972) temperature tables, compiled using data from various stations including Heiss Island, are referenced, acknowledging that the data used by Sehra and Hariharn (1981) comes from different years than the CIRA data. While not entirely independent, the large number of stations used in the CIRA model and the different years of data suggest that the Sehra and Hariharn data might not be representative of all Northern Hemisphere temperature data. However, because the Northern Hemisphere data used by Sehra and Hariharn appears typical, it is assumed that the Southern Hemisphere rocket data are also fairly representative of the mean temperature field in the Southern Hemisphere. Differences are observed below 70 km (the maximum height of the Sehra and Hariharn wind data), with the largest differences noticeable in winter, potentially due to stationary planetary waves. The observed decrease in the amplitude of these waves above 65 km (Houghton 1978) suggests increased zonal symmetry at higher altitudes.

This part describes the data acquisition and filtering processes employed in the study. Data were collected at heights below 80 km during daytime hours only, though echoes were observed outside these periods. A 2-hour filter could have sufficed; however, a 1-hour filter was used to retain a larger number of data points. This decision is justified by the need to minimize uncertainty introduced when subtracting the 1-hour mean from raw data to construct the mean. The selection of the averaging interval (1 hour) represents a compromise between obtaining the shortest possible period and utilizing enough data points to calculate reliable means. Tables 3.1 and 3.4 provide typical daily data, chosen by selecting a day of the month and calculating data occurrence per hour. December 22nd was used instead of December 11th due to unavailable data on the latter. The employed filters effectively pass a useful percentage of the signal within their intended frequency bands, with truncation being a greater issue for shorter period filters than for longer period filters.

The section details the spectral analysis techniques used in the study. The maximum entropy method (MEM) is emphasized as the primary technique due to the short length of some data series. The limitations of using MEM, including the difficulty of determining the optimal autoregressive filter length, are discussed. The selection of the filter length is shown to impact the resolution and reliability of the spectral analysis; if too few filter coefficients are used, resolution suffers; if too many are used, spurious peaks can be introduced. The researchers discuss using various criteria (FPE, AIC, CAT) to determine the best filter length, noting instances where these criteria disagreed, leading to potential uncertainties in the number of spectral peaks. Despite these challenges, the wavelengths obtained should be reasonably close to those present in the mesosphere and lower thermosphere and possibly be used for harmonic analysis.

The core of this section focuses on the spectral analysis techniques used to study wave amplitude variations. The maximum entropy method (MEM) is highlighted as the primary technique employed due to its suitability for analyzing short data series, a characteristic of some datasets used in this study. The choice of MEM is justified by its superior resolution compared to traditional methods like periodogram analysis and Blackman-Tukey (1958) spectral analysis, particularly when dealing with short data series or truncated sinusoids. However, a significant drawback of MEM is the challenge in objectively estimating the optimal length for the autoregressive filter. The text acknowledges that while the optimal filter length was used in most analyses, there were instances where the filter length was too short, impacting the resolution of the results. This highlights a trade-off inherent in spectral analysis between bias and resolution, a point the study directly addresses.

The analysis of spectral plots, categorized into two types based on the data used (3-hour wind averages), is discussed. The first type shows the semi-diurnal and diurnal tides, the two-day wave, and some long-period internal gravity wave activity. However, the consistency of the frequencies of the long-period internal gravity wave peaks is questioned. The spectral peaks related to the semi-diurnal tide consistently appear at periods of slightly less than 12 hours across all three heights (85 km, 90 km, 100 km). In contrast, 24-hour period peaks are only found at 85 km and 90 km, while a 20-hour peak is observed at 100 km, possibly also related to the diurnal tide. The diurnal tide peaks are consistently larger than the semi-diurnal tide peaks. Peaks are also observed in the 0.10 to 0.17 cycles per hour frequency range, with power appearing roughly constant across this range. The analysis of two-day wave activity reveals peaks centered at 48 hours (85 km and 90 km) and 33 hours (100 km), with the 48-hour peak exhibiting a high-frequency ledge, potentially indicating the influence of higher-frequency activity. The apparent 33-hour peak at 100 km might be a frequency-shifted diurnal tide peak. Spectral peaks are present in the 0.10 to 0.17 cycles per hour frequency range, and two peaks of just over 8 hours are found at different heights. Power across this range does not appear to vary with increasing frequency.

This subsection delves into the analysis of variance profiles and their relation to height variations. Figure 4.14, showing the change of variance with height in January, reveals a peak in planetary wave variance at around 50 km. The study suggests that if this variance increase is common in the summer mesosphere, it could be attributed to modes that become locally vertically propagating under summer wind conditions. The example of Geisler and Dickinson’s (1976) prediction of a locally vertically propagating 5-day zonal wavenumber 1 free mode (H1 mode) in the summer mesosphere is mentioned, explaining the increase in amplitude with height. Beyond these peaks, variance is generally low except for a small apparent increase above 95 km. The variances of planetary wave motions are significantly smaller than those of internal gravity waves above 80 km. This highlights the dominance of internal gravity waves in the upper atmospheric regions while establishing the importance of considering the interaction between various wave types.

This section explores the mechanisms that limit the amplitudes of internal gravity waves. A central concept is the role of the Richardson number, a measure of atmospheric stability, in determining the onset of turbulence. The study posits that when the Richardson number falls below a certain limiting value, turbulence arises, effectively restricting wave amplitudes. Lindzen (1981) observed neutral or unstable lapse rates above 50 km in winter and above 70 km in summer, suggesting potential wave breaking in these regions. The observed internal gravity wave variance profiles are then examined in light of this theory, considering the heights studied in the partial reflection drifts experiment, virtually all of which fall above these altitudes. The study notes that variance profiles generally do show effects consistent with wave breaking above these altitudes. The expected increase in variance with height, based on Hines' (1960) equations, is compared to the actual observations. Specifically, the expected relationship is discussed as exp(Z/2H) for amplitude and exp(Z/H) for variance; Table 5.1 provides a value of H (scale height) of approximately 6 km above 80-85 km. This section aims to assess whether a relatively simple wave-breaking model can sufficiently explain the observed variance profiles.

The analysis focuses on the variance profiles, divided into seasons, to investigate amplitude restrictions. The study notes that amplitudes increase notably near 77.5 km in winter and around 85 km in summer, with winter variances generally higher at almost all heights and a secondary maximum in summer. The least reliable variance values are those calculated at 65 km and 67.5 km due to limited data points. However, above approximately 90 km, where the data quality is more robust (up to 1000 data points per month after filtering), a decrease in variance is observed above 95 km across all months. This pattern in variance change is compared with theoretical expectations for wave-breaking scenarios. The effect of zonal winds, inducing a Doppler shift and modifying the intrinsic frequency of the wave, is discussed. Due to data limitations, precise calculations of phase velocity and horizontal wavelength are not feasible, which prevents a detailed quantitative analysis of the intrinsic frequencies and their influence on wave breaking. The observed maximum wave shear of around 20 ms⁻¹km⁻¹ is considerably lower than the 70-90 ms⁻¹km⁻¹ theoretically required for velocity shear instability, suggesting that convective instability might be a more dominant factor in limiting internal gravity wave amplitudes.

The section delves into both theoretical and experimental studies to understand wave-induced instabilities and their connection to wave breaking. The discussion covers the critical Richardson number, with some studies suggesting the onset of turbulence occurs at a value of 0.25 while others (e.g., Koop 1981) found turbulence arising when the Richardson number was 0.1. Woods' (1969) work on the transition from turbulent to laminar flow, where a Richardson number greater than unity always leads to a laminar condition, is mentioned. However, this is deemed unlikely to affect the onset of internal gravity wave breaking. The study by Fritts (1982) is referenced, which suggests that the region where the Richardson number is less than 0.25 develops almost simultaneously with, and becomes almost identical to, the region where the Richardson number is less than zero. Koop's (1981) experimental study on wave-induced instabilities found that low Richardson numbers caused convective instabilities and overturning, similar to Orlanski and Bryan's (1969) findings. The integration of these theoretical and experimental insights into the understanding of wave breaking dynamics is key to advancing the overall interpretation of the observations.