Notice: Wiley Online Library will be unavailable on Saturday 27th February from 09:00-14:00 GMT / 04:00-09:00 EST / 17:00-22:00 SGT for essential maintenance. Apologies for the inconvenience.
 Wave-like disturbances in electron density ne have been observed in the thermosphere above Arecibo Observatory, Puerto Rico throughout its 45 year history. However, only recently has it become evident that these waves are continuously present in the Arecibo thermosphere. The wave characteristics are fairly constant between day and night and from season to season. High-resolution electron density measurements obtained by applying the coded long-pulse radar technique to photoelectron-enhanced Langmuir waves are presented. These new observations strongly suggest that the perturbations in electron density are the result of internal acoustic-gravity waves (AGWs) propagating through the Arecibo thermosphere. The AGWs appear to be broadbanded in wave number space. The downward phase trajectories of Δne/ne between 400 and 120 km combined with the low horizontal phase velocities obtained from airglow measurements support the idea that the AGWs are not ducted but rather are locally produced. In addition, the altitudes at which major peaks in Δne/ne are observed follow theoretical estimates for nonducted waves. The nominal period of the AGWs is ∼60 min at 250 km altitude, but periods of ∼20 min are also evident at lower attitudes. Classic sources of AGWs do not appear to be consistent with the Arecibo observations of a continuous flux of background AGWs. Ray tracing of the AGWs combined with 630.0 nm airglow observations point to a source location in the Atlantic Ocean that is roughly 2100 km east northeast of Arecibo. Internal ocean waves generated in response to the internal tide at the mid-Atlantic Ridge are the most likely source of Arecibo's thermospheric AGWs.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Previous observations have indicated that acoustic-gravity waves are continuously present in the thermosphere above Arecibo Observatory [Djuth et al., 2004; Livneh et al., 2007]. The waves appear in all incoherent scatter radar (ISR) observations that we have examined between 1991 and the present, and they may date back to the first acoustic-gravity wave (AGW) measurements made at Arecibo in May 1964 [Thome, 1964] or earlier. In a follow-on study, Thome and Rao  conducted 53 experiments at Arecibo during daytime hours over a 3 month period between May 1967 and August 1967. They report that “traveling ionospheric disturbances (TIDs) of clearly identifiable magnitude were present in about 70% of their tests” and conclude that “the TIDs are a manifestation of acoustic-gravity waves (AGWs) in the atmosphere.” These early measurements were quite rudimentary in comparison with observations made with modern ISR data acquisition and analysis methodologies. If Thome and Rao had access to the current state-of-the-art techniques at Arecibo, they might have concluded that these waves were present 100% of the time. Additional AGW experiments were conducted at Arecibo in May 1974, and these results were interpreted within the context of randomly occurring TIDs [Hearn and Yeh, 1977, 1978; Yeh et al., 1979]. These observations included electron and ion temperature measurements and were analyzed in great detail, but the basic format of the data was similar to that of Thome and Rao. TIDs were noted during all five observing runs, which spanned both daytime and nighttime hours. It was concluded that the source that generated the gravity waves was broad in bandwidth and was not related to any resonance process. The Arecibo wave activity was subsequently rediscovered in 1991 [Djuth et al., 1994] when a new technique involving photoelectron enhanced plasma lines (PEPLs) [e.g., Yngvesson and Perkins, 1968] was used to obtain very accurate electron density (ne) profiles in the thermosphere.
 Beginning in November 2004, several observing campaigns were launched at Arecibo Observatory to determine the characteristics of the waves and their frequency of occurrence. In this paper, attention is focused on PEPL experiments conducted at Arecibo on 5 and 6 June 2005. Previously, ISR data for this period were presented by Livneh et al. , which entailed the filtering of Barker-coded power profile data to obtain the ne signature of the thermospheric waves. This technique has the advantage of being able to detect induced ne perturbations under both daytime and nighttime conditions. However, simultaneous measurements of PEPLs with the coded long-pulse (CLP) technique [Sulzer, 1986a; Djuth et al., 1997] were also made during this interval. This method yields extremely accurate ne measurements having random errors of 0.01%–0.03% (or less) at most F region altitudes.
 The current work focuses on PEPL-CLP measurements in the altitude interval between ∼120 and ∼400 km. Prior PEPL-CLP observations of thermospheric waves at Arecibo were limited and directed toward studies of wave activity in the lower thermosphere between 117 and 220 km. In the lower thermosphere above Arecibo, background neutral waves couple to the ionospheric plasma, typically yielding ±3%–10% electron density images of the waves [Djuth et al., 1997, 2004]. Properties of the neutral waves such as their period and vertical wavelengths are closely mirrored by the electron density fluctuations. Frequency spectra of the fluctuations versus altitude exhibit a high-frequency cutoff consistent with calculated values of the Brunt-Väisälä frequency.
 Vertical half wavelengths are typically in the range 2–30 km between 117 and 150 km altitude. The detailed study of Djuth et al.  showed that the observed wavelengths were generally consistent with the simplified AGW theory of Hines . Large-amplitude waves were always in the zone unquenched by kinematic viscosity. However, there were some small-amplitude waves in the quenching zone. Hines  noticed similar features in sodium vapor trail observations and offered a more detailed explanation in his postscript to the Hines  paper. Calculations presented by Hickey and Cole  and Vadas  resolve this issue by taking into account the growth of the vertical wavelength above the altitude where dissipation starts to affect the AGW. The corresponding phase velocities of the observed electron density perturbations at Arecibo are always directed downward toward increasing time, and hence, energy flows upward. At altitudes above ∼170 km, the vertical half wavelength quickly becomes very large, exceeding 100 km at altitudes above 300 km altitude. Ultimately, the waves lose energy because of kinematic viscosity and heat conduction, which rapidly increase with altitude. The wave energy ends up heating the thermosphere.
2. Radar Data Acquisition and Processing
 The Arecibo PEPL-CLP data examined were acquired from 1200 to 1700 AST (local time) on 5 June 2005 and from 0830 to 1700 AST on 6 June 2005. The 3 h Kp values for these periods are listed in Table 1. Radar observations were made with the line feed, which was positioned for vertical measurements. The observing program made use of four types of radar pulses: (1) a coded long-pulse 500 μs in length with 1-μs bauds [Sulzer, 1986a]; (2) a multiple-frequency radar pulse (308 μs in length) used for multiple radar autocorrelation function (MRACF) analyses [Sulzer, 1986b]; (3) a 13-baud Barker-coded pulse (BKR) having a baud length of 4 μs [e.g., Gray and Farley, 1973], and (4) an 88-baud biphase code with a 2 μs baud used to assess wave activity in the D region [Zhou, 2000; Zhou and Morton, 2006]. The first three pulse types were cyclically transmitted in groups of 1000 within an interpulse period (IPP) of 10 ms; the D region measurements were made with 3584 pulses transmitted within an IPP of 4 ms. The cycle time for all four transmission sequences was ∼47 s. As noted above, the CLP is used with the PEPL to make very accurate measurements of ne with 150 m range resolution. MRACF is the standard ion line measurement program used to obtain electron temperature Te, ion temperature Ti, and vertical ion velocity vi. These observations are employed to make a second-order Te correction to the Bohm-Gross dispersion relationship discussed below. The BKR pulses yield ion line profiles having 600 m altitude resolution and high sensitivity. These data were used by Livneh et al.  in the initial assessment of wave activity above Arecibo.
Table 1. Kp Values During the Two Periods of Radar Observations
5 June 2005
6 June 2005
 Langmuir waves excited by daytime photoelectrons are responsible for the PEPL echoes. The excitation/damping of these waves in the ionosphere is discussed in detail by Yngvesson and Perkins  and Fremouw et al. . For the Arecibo observations of interest here, the plasma line frequency (i.e., the Langmuir wave frequency, ωr ≡ 2πfr) can be expressed to second order as [e.g., Yngvesson and Perkins, 1968]
where ωep and ωec are the electron plasma frequency and electron cyclotron frequency, respectively; θ is the angle between the radar line of sight and the geomagnetic field; k is radar wave number; me is electron mass; and Boltzmann's constant is represented as κ. Worst-case errors resulting from this approximation are on the order of 1 kHz, which are small compared with typical fr values measured in the Arecibo ionosphere (∼3.0 to >10 MHz). Radar echoes from PEPLs appear as narrow spectral peaks centered at 430 MHz + fr and 430 MHz − fr; the two peaks correspond to Langmuir wave vectors directed toward and away from the radar. In a homogeneous plasma, the spectral shape of the Arecibo plasma line is well approximated by a Lorentzian having a full width at half maximum of γ/π, where γ is the intensity damping decrement of the Langmuir waves. The principal contributions to γ come from electron Landau damping and electron-ion/electron-neutral collisions. At thermal energies in the electron distribution function, Landau damping is a strong function of Langmuir wave propagation relative to the geomagnetic field. Because the Arecibo radar detects Langmuir waves that satisfy the Bragg condition along its line of sight, the echo return is dependent on radar viewing angle relative to the geomagnetic field. The geomagnetic dip angle changes rapidly with time in the Caribbean region. The 2005 IGRF value for the dip angle at Arecibo is 45.6° at all altitudes of interest here. When Langmuir waves in the F region are monitored with a vertically directed beam, Landau damping from thermal electrons makes a dominant contribution to the overall damping decrement at frequency offsets from 430 MHz of ≲4–5 MHz (depending on electron temperature). At greater frequencies, the damping decrement is determined by a combination of Landau damping from photoelectrons and collisional damping. Typical values for Langmuir wave half-power spectral widths in a homogeneous F region plasma are ∼200–400 Hz.
 Only one 5 MHz band-pass receiver channel was used for the PEPL-CLP observations so that maximum altitude coverage could be achieved with the data acquisition rate that was available at the time. The receiver channel was centered at 435.5 MHz, and the radar coverage extended from 433 to 438 MHz. Thus, the radar was sensitive to photoelectron-excited Langmuir waves moving toward the radar and seen as PEPLs between 3 and 8 MHz. Aliasing of strong signals across the receiver band pass can extend the frequency coverage on either side of the filter by about 0.2–0.5 MHz. The high-frequency limit (∼8.0 MHz) is set at the point where significant losses are encountered in antenna line-feed gain. The low-frequency limit (∼3.0 MHz) corresponds to the detection of 3.1 eV photoelectrons with the Arecibo radar. This coincides with the point at which the photoelectron flux begins to overcome thermal electron Landau damping and generates PEPLs under solar minimum conditions; this is particularly relevant for PEPL excitation at high (400–450 km) altitudes. There is also a 3 MHz limit at low altitudes; electron-neutral collision frequencies tend to be large at altitudes where the local plasma frequency is 3 MHz. Electron-neutral collisions represent the principal PEPL loss process at altitudes below ∼110 km [e.g., Newman and Oran, 1981]. Landau damping by thermal electrons is dominant at altitudes where Te is ∼700 K or greater (i.e., at altitudes ≳130 km). At intermediate altitudes, electron Landau damping from nonthermal photoelectrons tends to dominate.
 The processing of the CLP data generally begins with an assessment of radar interference. This is accomplished by performing complex FFTs on undecoded data acquired within an IPP (∼13,500 point FFT). In principal, no mitigation strategy for interfering signals is required because any such signal will be randomized across a bandwidth of 1 MHz during the decoding process. However, the randomization of the interfering signal will add to the sum of system noise plus self-clutter noise, and in some cases, this can decrease the PEPL coverage at high and low altitudes. In processing the current data, we have set a threshold of ∼5% increase in noise per 1 kHz frequency bin for applying a mitigation technique. Such techniques do not significantly increase processing time. When the selected threshold is exceeded in the FFT of undecoded time series within an IPP, the frequencies of the primary interfering signals are identified and complex frequency values are set equal to zero. The inverse transform is then performed on the time series, and then the signal is decoded as normal. Nominally, FFTs zero-padded to 5000 points are performed on the data from each decoded range. In this investigation, data from 2174 range cells were decoded and Fourier analyzed per IPP. FFT results from 1000 IPPs (10 s interval) were subsequently averaged on a range-by-range basis to improve PEPL signal-to-noise ratio and thereby extend the altitude coverage. Approximately 1 billion decodes/FFTs are required to process 8 h of data.
 An example of the decoded spectrum measured in a single 150 m range cell is provided in Figure 1. The tallest spike in Figure 1 is the actual PEPL; an inset is used to expand the frequency scale near the peak. The broad hump is the clutter from randomized PEPL signals originating at other altitudes. After the CLP signals have been decoded and the power spectra calculated, the mean clutter + system noise spectrum at each range cell is fit by a polynomial of order 15 (or higher). The fitted function is subsequently subtracted from the data, which yields a level spectral baseline that facilitates the fitting of the PEPL spectral peak. However, as illustrated in Figure 1, the subtraction process does not reduce the random “noise” fluctuations that accompany the clutter. The CLP spectra are then nonlinear least squares fit to a triangle-square function to determine spectral frequency, width, and amplitude [e.g., Bevington, 1969; Djuth et al., 1994].
 The fitted frequency of the PEPL peak is fcenter = fr = ωr/2π. Electron density is obtained by solving (1) for ωep = (nee2/ɛome)1/2 using measured values of Te, where e is electron charge and ɛo is the permittivity of free space. Figures 2 and 3 show the ne results obtained on 5 and 6 June 2005. Black is used to demarcate regions where there are no recorded echoes. At higher altitudes, signal losses occur because the PEPL frequency is greater than ∼8.5 MHz, which is well outside of the band pass (3–8 MHz) of the Gaussian baseband filter and is at a frequency offset from 430 MHz where the line feed gain is rapidly declining. As noted earlier, this bandwidth limitation can be mitigated at Arecibo by using the Gregorian feed system along with planned enhancements in the Arecibo digital receiver system. Greater altitude coverage was achieved on 6 June due to the fact that the observations began earlier in the day when foF2 was less than 8.5 MHz. Nominal errors in the position of the PEPL are 250 Hz. This yields random ne errors of 0.02% and 0.006% at PEPL frequencies of 3 and 8.5 MHz, respectively.
Figures 2 and 3 reveal the presence of ionospheric structures that curve toward increasing time at lower heights even without any additional processing. Nevertheless, the ne perturbations are subsequently separated from the mean background ionosphere by independently detrending ne in each range cell versus time using a polynomial of fixed order. The results of this process are presented in Figures 4–6. Figure 4 shows the residual perturbations for the 5 June 2005 observations. The perturbations are plotted in an altitude-time-intensity (ATI) format and expressed as a percentage of background ne. In this particular case, a fourth-order polynomial was employed for detrending. In the case of the 6 June measurements (Figures 5 and 6), the PEPL data are segmented into two plots: one contains both low- and high-altitude results (between 0819 and 1155 AST), and the other utilizes only low-altitude results below ∼242 km (between 0819 and 1600 AST). Third- and fourth-order polynomials are used for the results presented in Figures 5 and 6, respectively. Note that if the selected order of the polynomial is too low, the ionospheric background variations become part of the perturbation profile, whereas if too high of an order is used the amplitudes of the perturbations are reduced and small perturbations remain in the background profile. The background plot corresponding to Figure 5 is shown in Figure 7. It is evident that the background component represents a smoothly varying plasma, and there is no sign of wave-induced perturbations.
 The above ATI plots show that the perturbations are highly structured as a function of time and altitude. In addition, the magnitudes of the perturbations are larger than those recorded in the past with the PEPL-CLP technique, but this is primarily due to the fact that altitude coverage has improved and the larger perturbations tend to be at higher altitudes. On 5 June, the amplitude range is +22% to −16%, with the high positive value arising from a single perturbation near 1300 AST. On 6 June, the amplitude range is approximately +14% to −15%. Also, it is clear that the most prominent features curve downward toward increasing time at lower altitudes. An analysis of the time series near 250 km altitude in Figure 5 yields an apparent wave period of ∼55 min. Below ∼220 km, there is also a striping effect in the data that consists of mostly vertical lines, but at heights below ∼155 km, the stripes often exhibit tilts toward increasing time with decreasing altitude. The time interval between the stripes ranges from 10 to 6.5 min, which corresponds to wave periods that are greater than and slightly less than the Brunt-Väisälä period. For the most part the striping is a relatively weak effect with the perturbations being on the order of 2%–3% or less. However, a 3% fluctuation in ne in this region of the ionosphere corresponds to a large number of points in the PEPL spectrum (∼97). Extensive testing revealed that this is not an artifact of the data processing. The fact that it is seen only at low altitudes rules out the possibility that it is contained in the radar transmission. No known characteristic of the radar receiver system or data acquisition system can account for this signal. In addition, the data were reprocessed with features such as the interference algorithm removed, yet the striping remained unchanged. Stripes similar to those shown have also been observed in past PEPL measurements of limited duration at Arecibo [e.g., Djuth et al., 2004].
 A complementary method for displaying the results of Figures 4–6 is a waterfall representation (Figures 8–10). This allows the downward phase progression of the waves to be followed in detail. For reference, expanded views of three residual ne perturbation (Δne) profiles from Figure 9 are presented in Figure 11. These results reveal that the observations of Figures 4, 5, and 6 consist of smoothly varying waves versus altitude and time. The complex nature of the ne perturbations below ∼230 km altitude is evident in Figures 4, 5, and 6; many overlapping waves coexist in this region of the atmosphere. In Figure 9, individual phase histories are tracked from the highest to the lowest altitudes. In one case at 1133 AST, it appears that two waves combine. The white dots with a black edge correspond to a significant local maximum that cannot be directly linked to any wave. This is related to the bifurcation of an ne wave in Figure 5 at 0913 AST (290 km altitude) and the patch of ionization near 400 km at 0944 AST. The four main structures in Figure 5 have identifiable phase histories in Figure 9 starting at high altitudes and ending near 120 km altitude. The average time between the phase paths yields the following apparent wave periods versus altitude: 20 min (130 km), 52 min (200 km), 55 min (250 km), 54 min (300 km), and 54 min (350 km). The number of zero derivative maxima becomes very sparse above 240 km, because the vertical wavelength becomes increasingly large at these heights. It is clear that below ∼180 km the ne perturbations are more structured in altitude owing in part to the simultaneous presence of multiple waves and to the decreasing vertical wavelength at lower altitudes. This makes the phase tracking of a single waveform from high altitudes to lower heights difficult without the guidance of Figure 5. The waves present between 120 and 125 km in Figures 8–10 and in the center/right panels of Figure 11 have short vertical wavelengths and oscillate between positive and negative Δne. These waves are unrelated to narrow metallic ion layers, which exhibit only positive Δne values.
4. Analysis of the Results
 The electron density structures discussed above mirror the characteristics of internal gravity waves [e.g., Hines, 1960, 1974; Yeh and Liu, 1974; Hocke and Schlegel, 1996]. Similar results from the lower thermosphere at solar maximum [Djuth et al., 1997] yielded temporal periods ≳8–10 min, with vertical half wavelengths in the range of 2–30 km depending on altitude. The current data set was secured at solar minimum and begins at approximately the same altitude near 120 km and extends well into the thermosphere to 400 km altitude. Apparent Δne periods range from ∼20 to ∼55 min. The phase velocity of the sinusoidal wave-like perturbations is directed downward (e.g., Figures 4–6 and 8–10) and curves toward increasing time. This is the result of the rapid increase in kinematic viscosity with altitude [e.g., Hines, 1968]; unquenched waves at lower altitudes have shorter vertical wavelengths, and therefore, the vertical phase velocity decreases with decreasing altitude. The upturning of the phase surface with increasing altitude arises because the real part of the vertical wave number approaches zero, and this prevents significant phase change with altitude. At the same time, the imaginary component becomes very large and ultimately leads to the total dissipation of the wave. Upon inspection of Figures 8–11, it is clear that the residual Δne profiles vary smoothly with altitude with no signs of nonlinearities caused by plasma instabilities. Consequently, it is of interest to examine these observations within the context of existing gravity wave theory. To this end the MSIS-E90 (mass spectrometer/incoherent scatter) model is employed to estimate neutral temperature, density, and mean molecular mass versus altitude on the days of the observations. The F10.7 (daily, 3 months) and the ap daily values used for these calculations were (99.8, 99.6), 17.0, and (108.6, 99.6), 10.2 for the 5 and 6 June observations, respectively.
 With the above neutral model, the Brunt-Väisälä frequency ωb is calculated using the nonisothermal expression [e.g., Yeh and Liu, 1974; Väisälä, 1925]
where g (acceleration of gravity), γ (specific heat ratio), and co (sound speed) are all functions of altitude z. The Brunt-Väisälä (BV) period τb ≡ (ωb/2π)−1 ranges from 3.7 min (120 km altitude) to 12.7 min (400 km altitude). Fourier analyses were performed on the data presented in Figures 5, 6, 9, and 10 to help quantify the wave periods present in the observations. Power spectra were calculated on an altitude-by-altitude basis. Each time series consisted of 280 data points. A Blackman windowing function (maximum sidelobe of −58 dB) was employed, and the data were zero-padded to 2048 points prior to the execution of a fast Fourier transform (FFT). The results are shown in Figure 12 for the initial ∼4 h period of complete altitude coverage on 6 June 2005; in Figure 13, results are presented for the lower altitude region below 242 km altitude. In the latter case, two 4 h data segments were averaged to produce the spectra. The weak broadband noise evident near 200 km altitude is caused by a small increase in measurement errors.
 Most of the spectral energy is located at periods in excess of τb (or frequencies less than fb = ωb/2π) consistent with the theoretical predictions for propagating AGWs, whereas waves at frequencies above ωb/2π are evanescent. The spectral structure in the propagating waves at a given altitude reflects the fact that the waves are not characterized by a single apparent frequency but rather represent a collection of several Fourier components having discrete frequencies and an underlying continuum. In addition, it is important to note that longer-period fluctuations (≳4 h) have been in part removed from the data by the detrending process discussed in section 3. The relatively good “fit” of the BV curve to the data indicates that there are no large altitude-dependent offsets in apparent frequencies/periods caused, for example, by large time-varying background winds. The calculated BV curve cannot be shifted a great deal while maintaining consistency with the spectral data. For example, removal of the second term in (2) would shift the BV curve farther to the left, and significant AGW spectral components would appear to the right of the curve.
 Because the spectra of Figures 12 and 13 are plotted on logarithmic scales, it may appear that there is substantial signal power beyond the BV frequency, but this is not the case. A line plot of the power spectrum at 234 km altitude in Figure 13 is presented in Figure 14 so that the full dynamic range (67 dB) of a typical spectrum can be seen. It is clear from the Blackman windowing function shown in Figure 14 that the power beyond the BV frequency is real and not a product of the digital signal processing. However, it is important to note that the signals immediately to the right of the BV frequency are 6000 times smaller than the AGW spectral line near 0.23 mHz (72 min period). Most of the power is contained in this peak, and only 0.07% of the total spectral power is located beyond the BV line. In Figure 12, the altitude-averaged power to the right of the BV curve is only 0.48% of the total, and in Figure 13, it is 0.77%.
 No background wind measurements were made during the current observations. Such winds are useful in inferring intrinsic frequencies, but in the present case the interpretation may be difficult because the AGWs have significant bandwidth in the frequency/wavelength domains. The background winds in the Arecibo thermosphere are dominated by the semidiurnal tide with a smaller diurnal component [e.g., Harper, 1979]. The tides vary with season and have a day-to-day variability of at least half the amplitude of the mean oscillation [e.g., Harper, 1981]. Thus, models of mean wind patterns are not good predictors of the winds at the time of the observation. During the 4 h required to develop the spectra shown in Figure 12, the background winds certainly changed at all altitudes. Some of the waves in the evanescent regime shown in Figures 12 and 13 may have been placed to the left of the BV curve had intrinsic frequencies been calculated for the time varying winds. In the future, measurements of ion drift velocities in both the lower thermosphere and in the upper F region will be made to determine neutral winds and their rate of change in the geomagnetic meridional plane and to infer zonal winds below ∼140 km [e.g., Harper, 1979; Harper et al., 1976; Zhou et al., 1997].
 The vertical wavelength of the ne perturbations versus altitude is also of interest to the current investigation. Theoretical estimates of the minimum vertical half wavelength λz/2 for internal gravity waves subject to damping by kinematic viscosity are provided by Hines [1964, 1974] and Vadas . At 120 km and above, it is assumed that kinematic viscosity dominates any contribution from eddy viscosity. The minimum vertical half wavelength λz/2 can be calculated by inserting experimentally measured and/or modeled atmospheric parameters into the simplified formula of Hines , that is,
where η is the kinematic viscosity, and ωg is the isothermal equivalent of ωb. Waves in the region to the left of the λz/2 versus altitude curve are quenched because they have too short of a wavelength whereas waves to the right are not. In the derivation of this equation, wave modes with severe dissipation are determined in the asymptotic limit kz2 ≫ ωa2/co2, where kz is the real component of the vertical wave number, ωa is the acoustic frequency, and co is the speed of sound. This limits the applicability of the expression to altitudes below ∼233 km in the current study. An inequality factor of 10 was used for this determination (i.e., kz2/(ωa2/co2) = 10). The elementary quenching criterion minimizes λz/2 in wave number and frequency (the minimum of the minimum) to establish the nominal quenching boundary. The above formula for λz/2 employs the special estimate ω = 3−1/2ωg or τ = 1.73τg, where ω and τ are the intrinsic angular frequency and period of the gravity wave, respectively. Because λz/2 scales roughly as (Tn/ρ)1/2 and MSIS-E90 is a self-consistent model (i.e., when Tn increases or decreases, ρ increases or decreases), the model values for Tn and ρ need not be perfect to obtain an accurate estimate of the λz/2 curve. Finally, Hines  points out in a postscript to Hines  that the dependence of λz/2 on horizontal wave number kH is not included in the above equation and that the limiting values of λz/2 may be up to 2/3 smaller than that suggested by the criterion.
 A separate formulation for λz/2 based on wave dissipation rates is provided by Vadas and Fritts [2005, 2006] and Vadas . Both kinematic viscosity and thermal conductivity are included in this work. The approach takes into account the growth of λz/2 above the Hines quenching altitude, which corresponds to the altitude at which dissipation begins to affect the gravity wave. The dissipation altitude of Vadas  is determined by solving the following approximate equation
where ma = 2π/λz.
 The experimental determination of λz/2 versus altitude from the observations is complicated by the fact that the wavelength rapidly increases with altitude. As a result, methods involving Fourier transforms of altitude series are not well suited for this study. The approach adopted here begins by identifying the residual ne zero crossings to determine λz/2. In processing data at altitudes below the lowest zero crossing, the first quarter wave oscillation is ignored and then the wave minimum (maximum) to maximum (minimum) is used to obtain λz/2. Above the highest zero crossing, the maximum to minimum approach is used immediately without consideration for the first quarter wavelength. As part of the analysis, the data are fit by a high-order polynomial (order of ∼11) to avoid the impacts of the very small random fluctuations in the observations. The altitude assigned to a vertical half wavelength is the midpoint between the two zero crossings or half the distance between a zero crossing or minimum (maximum) and the closest maximum (minimum).
 The results of this analysis for the data shown in Figures 5 and 9 are presented in Figure 15. Data points are represented as squares, and the area of each square is proportional to Δne. Thus, Δne scales as the square root of a square's side length. It is important to note that Δne is determined both by the magnitude of the AGW horizontal velocity and the logarithmic vertical gradient of ne. Theoretical results of Hines [1964, 1974] are plotted along with those of Vadas  using the MSIS-E90 model discussed above for neutral temperature and density. Viscosity was calculated using the empirical formula 6.5.12 of Rees . The Brunt-Väisälä frequency ωb in (2), which includes the vertical temperature gradient, was used for all model calculations. This correction moved the theoretical curves closer to optimum locations dictated by the observations. The Vadas  result for a horizontal wavelength of 500 km offers the best fit at altitudes between ∼170 and ∼310 km, and the shape of the quenching boundary at lower altitudes is best reproduced by the Vadas curves.
 The spatial structure and temporal behavior of the ne perturbations presented in the preceding two sections provide strong evidence that the observed waves result from the passage of AGWs over Arecibo Observatory. In Figures 4–6 and 8–10, it is evident that the phase of the wave as represented by Δne moves downward with time and rapidly curves toward increasing time at altitudes below about 160 km. Similar Arecibo results are found in the works of Thome , who supplies height-time contours of incoherent backscatter power; Livneh et al. [2007, 2009], who filters the incoherent scatter power; and Djuth et al. , who employ the same PEPL-CLP technique as in the current work but show data over a narrower altitude range down to a height of ∼120 km. Random error bars are more than 100 times smaller with the PEPL-CLP technique compared to standard incoherent scatter radar (ISR) measurements, so the PEPL-CLP method is best for obtaining the detailed properties of the waves. However, standard ISR measurements yield better altitude coverage, and observations made with filtered power profiles and profiles of vi, Te, Ti, indicate that the AGW-induced perturbations map up to altitudes greater than 650 km and down to altitudes near 117 km. It was noted earlier in section 3 that the curvature at low altitudes is largely related to the dispersion relation of gravity waves in the thermosphere and the key role played by kinematic viscosity and thermal conduction in dissipating waves that have too short of a vertical wavelength for continued propagation in the atmosphere [e.g., Hines, 1968; Clark et al., 1971; Klostermeyer, 1972; Kirchengast et al., 1996]. In the current study, the measured AGW phase path moves downward with time from the highest altitudes near 400 km to the lowest heights at ∼120 km as in the classic depiction in Figure 2 of Hines . As indicated by Hines  and Clark et al. , the downward phase paths shown in Figure 9 are associated with the upward propagation of nonducted AGWs from lower altitudes. Moreover, there is no evidence of the presence of thermospherically ducted G′i modes, or the imperfect ducting of gravity waves from the ground to the mesopause with leakage into the thermosphere [see, e.g., Francis, 1974, 1975]. The phase path of a thermospherically ducted AGW rotates to vertical between 250 and 300 km altitude and remains in this state to the lowest altitudes [e.g., Francis, 1973], which is not observed. In addition, for thermospheric AGWs having intrinsic periods between 10 and 60 min, the minimum horizontal phase velocity of the G′i mode is 250 m/s, whereas the measured horizontal phase velocities of waves near ∼240 km at Arecibo waves are only ∼30–60 m/s [e.g., Livneh et al., 2007]. The statement regarding leakage into the thermosphere is corroborated by simultaneous AGW measurements made in the D region, which show no sign of waves moving upward into the lower thermosphere or waves having periods near 55–60 min. We also note that the character of the waves does not change from day to night [Livneh et al., 2007, 2009], as one might expect for a ducted AGW. The observed downward phase paths of the gravity wave train illustrated in Figure 9 imply a local source at a lower altitude as opposed to a distant ducted source. The downward phase paths do not significantly change with time over time scales of hours, days, or years. At present there is a total of 19 similar Arecibo data sets obtained since 1991. Data acquired at solar maximum and solar minimum all exhibit the same repetitious downward phase paths separated in time by roughly 1 h at 250 km altitude. In addition, there are no identifiable seasonal variations. The AGWs propagating into the thermosphere are expected to dissipate over spatial scales of two to three horizontal wavelengths [e.g., Lognonné et al., 2006a, 2006b; Vadas, 2007]. This assumes that the continuous pumping of AGWs into the thermosphere is similar to the case of a single transient AGW propagating through the thermosphere.
where neo is the background electron density, ω is the intrinsic period of the gravity wave, ub = · , kb = · , is the wave velocity vector, is a unit vector in the direction of the geomagnetic field o, is the wave vector of the wave, and I is the geomagnetic dip angle. In general, kb is complex, and it can be written as kb = kbr + ikbi, where kbr and kbi are real. If one assumes that only the vertical component of is complex, then it follows that kbi = kzi sinI, where z is the vertical coordinate and I is taken to be positive in the Southern Hemisphere. In deriving the above equation, it is assumed that ∣′(O+)∣ ≅ ∣b∣, where ∣′(O+)∣ is the wave-induced O+ ion velocity parallel to o. This approximation is valid for most calculations except in the case where is nearly perpendicular to o. Finally, the divergence of ′(O+) is assumed to be small and therefore is ignored. Experimentally, kzi and kbr are not found to be strongly dependent on altitude near foF2 whereas ∂ln(neo)/∂z is. Thus, to first order one expects to encounter the greatest percentage fluctuation in ne at altitudes where ∂ln(neo)/∂z has the largest positive value (i.e., on the bottomside ionospheric gradient). However, the neglect of plasma diffusion generates increasingly large calculational errors at altitudes greater than ∼300 km [e.g., Clark et al., 1971; Hines, 1974 (Paper 32 Notes)]. Thus, (4) is not valid for determining the location of the greatest percentage fluctuation in ne on the topside ionosphere. In the linearized perturbation analysis of Hooke , the addition of plasma diffusion in the transport term of the continuity equation takes the form
where δM is the perturbed transport term and do and δd are background and wave-induced diffusion velocities. The inclusion of the diffusion terms transforms the continuity equation into a second-order differential equation that must be solved numerically. This calculation is beyond the scope of the current investigation.
Figure 7 shows that there are three regions where local maxima exist in ∣∂ ln(neo)/∂z∣. These include the topside region above 335 km (negative value for ∂ ln(neo)/∂z) and the bottomside region near the F region peak (200–250 km altitude) where the value is positive. In addition, a second positive zone exists at lower heights below 150 km. On average, the maximum value of ∂ln(neo)/∂z in the region 50–80 km below the F region is 0.0143/cm3 km and at lower heights the corresponding value is 0.0237/cm3 km. The two bottomside curves are plotted in Figure 5 along with the location of the F region peak. Even without the inclusion of wave-induced changes in the photoionization rate and dissociative recombination (at lower heights) in (4), the altitudes derived from this simplified equation are fairly close to the observational results. An important conclusion is that an increase in the magnitude of Δne in the residual profiles does not necessarily mean that the amplitude of the AGW is larger. An increase in ∂ln(neo)/∂z contributes to an increase in Δne. For example, the Δne range observed on 5 June 2005 is +22%, −16% (Figure 4), whereas on 6 June 2005 the values are +15%, −14% (Figures 5 and 6). The reason for the larger percentage range on 5 June is most likely related to larger ∂ln(neo)/∂z in the bottomside F region. The maximum percentage fluctuation in the plot is set by the value near 1252 AST at ∼240 km altitude where ∂ln(neo)/∂z is 0.0196/cm3km and the minimum is set by the value at the same altitude near 1620 AST. The latter case is the result of a growing trend in ∂ln(neo)/∂z that reached a value of 0.0212/cm3 km near the end of the negative Δne portion of the oscillation. These values are significantly greater than the nominal value of 0.0143/cm3 km observed on the following day.
 The topside maximum of ∣∂ln(neo)/∂z∣ in Figure 7 is in an altitude region where ∂neo/∂z is approximately linear. As a result, small changes in the gradient translate into a significant altitude variation in the max(∣∂ln(neo)/∂z∣). Upon comparison of the topside curve in Figure 7 with the observations of Figure 5, it is clear that the topside data do not match the results of (4). As noted above, this is expected because diffusion velocities are not included in the derivation of (4).
 The calculations made with (4) demonstrate that even a simplified model of the interaction of gravity waves with the bottomside F region plasma produces useful results for comparison with the data. Moreover, (4) is derived for the propagation of an AGW through the thermosphere in the absence of ducting. A similar calculation for ducted propagation yields much different results [e.g., Francis, 1975].
 In section 3, we showed that most of the AGW spectral energy is located at frequencies less than the Brunt-Väisälä frequency consistent with the predictions of AGW theory. In general, large amplitude AGWs dominate this region of the spectrum. In addition, lower amplitude oscillations were detected below about 220 km altitude that have an unknown origin (Figures 4 and 6) but are not likely to be a product of the data processing. These oscillations have periods in the range from 6.5 to 10 min, which correspond to wave periods that are greater than and slightly less than the Brunt-Väisälä period. They are present in most, if not all, of our Arecibo observations. The periodic fluctuations resemble buoyancy oscillations and may signal the presence of a parametric instability involving AGWs [e.g., Klostermeyer, 1990, 1991]. This phenomena is barely detectable in the spectral analysis shown in Figures 12 and 13, but it may account for the slight increase in signal strength at periods greater than the Brunt-Väisälä period below ∼220 km altitude. However, the oscillations are far too weak to account for the entire evanescent signal at periods less than the Brunt-Väisälä period. The evanescent waves to the right of the Brunt-Väisälä boundary in the spectral presentations are presumably decaying, nonpropagating AGWs. However, very weak signals (−56 to −60 dB) are most likely an artifact of the Blackman windowing function.
 The calculated cutoff boundary set by the nonisothermal acoustic resonance frequency for vertical propagation [e.g., Beer, 1974] is slightly (0.04–0.20 mHz) to the left of the Brunt-Väisälä curve throughout the altitude region displayed in Figure 12. Note that the acoustic curve is not displayed in Figure 12. The acoustic resonance frequency is lower than the BV frequency primarily because of an increase in the Brunt-Väisälä frequency resulting from high thermospheric lapse rates. Similar computational results have been reported in the past [e.g., Tolstoy and Pan, 1970]. However, both curves entail WKB approximations [Einaudi and Hines, 1971; Beer, 1974] and more detailed studies [e.g., Walterscheid and Hecht, 2003] are required to determine the exact locations of the two resonances and examine possible resonant coupling in the presence of high lapse rates. If most of the waves in the evanescent region are simply AGWs that have periods too short to propagate in this region of the atmosphere, then this implies that a wide range of wave periods is generated by the source extending from ∼3 to ∼90 min (0.2–5.6 mHz). This spread relative to the BV curve could also arise in part because of changes in the intrinsic frequencies of the waves. Figure 13 shows the results obtained by averaging two consecutive 4 h AGW spectra. It indicates that the averaging process smoothes out the spectra, and the frequencies of individual propagating/decaying waves are more difficult to distinguish. However, the basic nature of the spectrum remains the same as in Figure 12.
 Recently the so-called PEPL cutoff technique [Showen, 1979] was used at Arecibo to measure fluctuations in ne at the peak of the F region [Dyrud et al., 2008]. This technique has essentially no altitude resolution and requires that a consistent cutoff point in the spectrum be established to interpret the data. Both the line feed and the Gregorian feed were used for these measurements; the former feed was pointed south at 15° zenith and the latter north at 15° zenith angle. This yielded a beam separation of 160 km. A spectral peak was observed near 1.7 mHz that had an amplitude of 0.1% of the ne at the peak of the F region. This peak was interpreted in terms of ULF oscillations linked to the magnetosphere, but several caveats were also provided. The current paper shows that in the evanescent region beyond the Brunt-Väisälä frequency there are many peaks, and the frequencies of these peaks vary with altitude. In addition, in our case the Brunt-Väisälä frequency ranges from 1.59 mHz at 250 km to 1.38 mHz at 350 km. During the period of observations with the cutoff technique (1012–1332 AST) the height of the F region could have increased by as much as 50 km. The cutoff spectrum therefore represents the integration in altitude of many peaks similar to those shown in Figure 12. Within the context of the current work, correlation over spatial scales of 160 km is expected because AGWs with horizontal wavelengths of this dimension or greater are believed to travel continuously from the northeast to the southwest [e.g., Livneh et al., 2007]. We suggest that it might be useful for Dyrud et al. to repeat the ULF experiment using the PEPL-CLP technique with a supporting ground-based magnetometer. ULF oscillations of magnetospheric origin may exist, but they have to be separated out from the sea of AGWs above Arecibo.
 In Figure 15, the observed Δne vertical half wavelength (λz/2), which mirrors AGW vertical half wavelength, is shown along with the theoretical estimates of the quenching boundary offered by Hines [1964, 1974] and Vadas . This boundary arises because kinematic viscosity and thermal conductivity increase with altitude and eventually dissipate the AGWs. The curve demarcates the minimum unquenched vertical AGW half wavelength; waves to the left of this boundary are quenched whereas those to the right are not. The derivation of the Hines  curve is strictly valid up to ∼233 km; at 275 km moderate errors are anticipated, and at 300 km and above large errors are expected. The Hines  curve below 233 km altitude leaves some large amplitude waves in the quenched region. However, it is important to note that quenching of the neutral wave alone does not determine the amplitude of the Δne. As noted above, Δne is largest near maxima in ∂ln(neo)/∂z, so the strongest Δne perturbations lie at heights between 200 and 250 km and below 150 km altitude. In Figure 15, one can see trails of initially large amplitude waves moving upward and/or to the left in altitude in the 200–250 km zone near λz/2 ∼ 50 km. As the trail moves deeper into the quenching zone the amplitude rapidly decreases. Thus, waves entering the quenching zone may be quite large, but this situation quickly changes as they travel further into the zone. The 2/3 λz/2 “limiting” curve described in the Postscript to Paper 13 of Hines  yields an unacceptable result, and the curve of Hines  appears to deflect upward away from the data boundary at lower altitudes.
 The dissipation curves of Vadas  are also shown in Figure 15. They are calculated as a function of AGW horizontal wavelength λH (km), for λH = 150, 200, 250, 300, 500, 1000, and 2000. The envelope of the curves at λH = 150, 200, 300, and 500 km delineates the quenched/unquenched boundary the best. This implies that the horizontal wavelength spectrum extends from ∼150 to ∼500 km. As noted by Vadas , “although each solution is distinct because of the altitudinal ‘ceiling’ which prevents further vertical penetration of the AGWs with a fixed value of λH, the upward trends of the solutions are similar, with only small altitudinal differences.” In addition, it should be borne in mind that within the context of the Vadas  theory, most AGWs should be observable at heights of (1–2) H above the dissipation altitude. The value of H ranges from 26 km at 150 km altitude to 49 km at 300 km altitude in the atmospheric model adopted for the current observations. Thus, the Vadas  theory also sets altitude limits on detectable AGWs above the quenching curve that are consistent with the observations.
 The ceilings on the dissipative curves illustrate the difficulty in employing a fixed λH to model the Arecibo observations. In order to explain the results of Figure 9, one invariably needs short λH values to reproduce small λz/2 at lower altitudes but also long λH values to penetrate to the high altitudes at which the AGWs have been observed (>650 km). For example, if one employs a λH value of 200 km and uses an observed AGW period of 60 min, one finds that it is not possible to propagate the wave up to 250 km altitude without considerable dissipation. While this λH may succeed in producing the observed small λz/2 of ∼10 km at the lowest heights, it will not yield the much longer wavelength values of λz/2 at greater heights. Values of λH ≳ 500 km are required to satisfy this condition. This leads to the inescapable conclusion that the source must be very broadbanded in space.
 As noted earlier, the unique characteristic of the Arecibo AGWs is that they are continuously present above the Observatory. By definition the PEPL measurements presented above can only be made under sunlit conditions, but with the aid of filtered ISR power profiles [Livneh et al., 2007] we know that the waves are continuously present day and night. The filtered Barker power profiles recorded during the period of 5 through 6 June 2005 are displayed in Figure 16. In Figure 16, the daytime noise level is greater than at night because only ∼25% of the radar pulses were dedicated to the Barker program during the day (section 2), whereas 100% of the pulses were Barker-coded at night. In addition, there is reduced altitude coverage at night because of limitations imposed by the background ionosphere. Note that the character of the AGWs does not change between day and night. On the basis of our past observations, there does not appear to be significant change in the AGW electron density perturbations below ∼200 km altitude during periods of solar minimum and solar maximum. However, there are only three data sets at solar maximum; they were obtained with the PEPL-CLP technique in 1991, 1992, and 1993. The majority of the observations are from solar minimum. At solar maximum, AGWs are expected to penetrate to greater altitudes in the upper thermosphere because kinematic viscosity increases less rapidly with altitude and at the same time λz increases significantly [Vadas and Fritts, 2006]. Tests of this prediction will be made in a few years when the next solar maximum arrives.
 The presence of the continuous background of AGWs at Arecibo does not appear to be dependent on Kp index. However, the measurements made to date span a 3 h Kp range of only 0–5. In addition, we note that large-amplitude TIDs originating, for example, in the polar region pass over Arecibo on occasion [e.g., Harper, 1972; Nicolls et al., 2004] and overwhelm the background AGWs discussed here. There are no large seasonal variations in the Arecibo background AGWs [e.g., Djuth et al., 2004; Livneh et al., 2007, 2009]. In addition, previous nighttime observations of “plasma rain” by Mathews et al.  now appear to be related to AGWs.
 AGWs are also regularly observed at other large radar facilities. Observations made with the MU radar near Kyoto, Japan are reported by Oliver et al. . They indicate that ionospheric perturbations caused by AGWs are essentially always detectable to some degree with the radar. At Kyoto, these “waves appear to exist over a broad range of frequencies. During magnetically very quiet times, AGWs are weak at night but are often strong during the day. During even moderately disturbed times the waves appear both day and night, but they appear more sporadically. There seems to be little correlation between global geomagnetic indices and local wave activity, except for the aforementioned lack of strong wave activity at night during extremely quite times.” Oliver et al.  show that the wave speed remains around 240 m/s for all periods examined (40–130 min) in the altitude range examined (200–350 km) and that “the waves appear to be largely lossless” (i.e. not subject to dissipation). The MU radar results are similar to those at Arecibo in that the AGWs appear to be omnipresent with very little dependence on season or solar/geomagnetic conditions. However, Arecibo is different in that there is little change in wave amplitude between day and night and little variability in the waves over time scales of days, months, and years. In addition, kinematic viscosity plays an important role in the measurements at Arecibo.
 Recently, power profile data obtained with the Millstone Hill incoherent scatter radar were analyzed using filtering techniques similar to those employed for the Arecibo data in Figure 15 [Livneh et al., 2009]. The Millstone Hill data were acquired during a 30 day observation period extending from 4 October through 4 November 2002. Zhang et al.  describe the day-to-day variability of Ti, Te, and ne observed during this campaign. In addition, a quasiperiodic oscillation in ne and vertical vi having a period of greater than 1 day was also present throughout the observing period. The filtered power profile data of Livneh et al.  reveal the presence of oscillations having a period of ∼1 h at 250 km altitude, which is similar to that observed at Arecibo. At Millstone Hill the upturn of wave phase with increasing altitude is routinely observed, and the waves appear to be continuously present. Additional observations are planned at Millstone Hill to determine the nature and source of these waves as well as to assess the impact of the medium-scale traveling ionospheric disturbances described by Tsugawa et al.  on the 1 h periodicity.
 AGWs/TIDs are also commonly observed with the EISCAT incoherent scatter radar facility located near Tromsø, Norway [e.g., Kirchengast et al., 1995; Hocke et al., 1996; Hocke and Schlegel, 1996]. The reported measurements are made under quiet sunlit F region conditions with low E × B drift and low geomagnetic activity (Kp < 3−) [Hocke et al., 1996]. Analyses were performed on a group of 45 TIDs observed at altitudes between ∼150 and ∼500 km. The waves exhibited the distinctive upturning of the wavefront corresponding to the increase in λz with altitude. This behavior is similar to that of Arecibo. Moreover, perturbations in Ti, Te and vertical vi and ne were measured at EISCAT along with their relative phases versus altitude. The spread of the fluctuations in these four quantities was observed to be large, and the wave periods ranged from 30 to 150 min with minimal change in a given period versus altitude. These wave properties are unlike those at Arecibo. Ma et al.  obtained the directions of two TIDs over EISCAT: one was propagating toward the southeast, and the other was directed to the southwest. The source of the EISCAT AGWs has not been identified, but they are presumably auroral in nature.
 Measurements of Te, Ti, and vertical vi perturbations associated with the Arecibo AGWs yield nominal amplitudes of ∼50 K (∼3% of the mean background temperature), 20 K (∼1.5% of the mean background temperature), and 10 m/s (∼40% of the mean speed), respectively. These values are similar to those expected for AGWs propagating through the ionosphere under sunlit conditions [e.g., Kirchengast et al., 1996]. A more detailed description of these parameters is provided by Djuth et al. (Characterization of thermospheric gravity waves above Arecibo Observatory under quiet geomagnetic conditions, submitted to J. Geophys. Res., 2010). We also note that traveling fronts of 630.0 nm airglow observed with CCD imagers [Livneh et al., 2007; Seker et al., 2008] are locked in phase with the AGW ne perturbations simultaneously measured with the Arecibo radar. Additionally, the observations of Seker et al.  included supplemental GPS measurements of TEC. The airglow emission is proportional to and follows the regions of the AGW enhanced ionization, and in general, the wavefronts exhibit the behavior expected for a propagating internal gravity wave. The observed wavefronts have horizontal wavelengths of 100–200 km, a period near 60 min, and velocities in the range 30–60 m/s. The arrival direction is 31° north of east, and the waves travel from east northeast to west southwest. Additional 630.0 nm airglow wavefronts were measured at Arecibo in September and December 2005. Five events were analyzed and the average arrival direction was 30° north of east, and the mean horizontal velocity was 52 m/s. These results are similar to those of Livneh et al.  and Seker et al. . Moreover, an extensive series of 630.0 nm CCD airglow observations augmented by GPS TEC measurements led Garcia et al.  to conclude that the airglow above Arecibo was associated with medium-scale TID events, but that viable theoretical explanations were lacking. The Garcia et al.  measurements were made between January 1997 and March 1998. The earliest CCD observations of similar airglow bands were made in 1993 and reported by Mendillo et al.  and Miller et al. . A summary of the characteristics of all airglow wavefronts discussed above is as follows. The horizontal wavelengths measured optically near 240 km altitude are ∼100–200 km, and the wave period ranges from ∼50 to −70 min with a mean value near 60 min, which is the same as that observed with the Arecibo radar. The airglow fronts move from geographic east northeast to west southwest, and their nominal arrival direction at Arecibo is ∼30° ± 10° north of east. Typically, the fronts move at relatively low speeds in the range of ∼30–120 m/s with an average value near 60 m/s.
 In the past, a possible relation between the above airglow and the Perkins instability has been suggested, but it is difficult to interpret the observations solely within this framework [e.g., Garcia et al., 2000]. Under nighttime conditions, the gravity wave may be electrified as suggested by Kelley and Miller . This reduces ion drag. However, the radar observations of Livneh et al.  and Seker et al.  extended for 36 h and as usual AGW ne fluctuations similar to those shown in Figure 12 were continuously present day and night. There was no major change in the ne perturbations between day and night, which would be expected if the daytime process shown here to be of AGW origin was supplanted by a fundamentally different nighttime process. It is possible that instabilities are triggered under nighttime conditions by the AGW, but this does not appear to affect the progression of the large-scale (>100 km) ne fluctuations driven by the AGW.
 A key question is what is the source of the continuous AGW wave train over Arecibo? We have concluded above that the AGWs are not ducted but are propagating upward from lower altitudes, that is, they are “locally produced.” To estimate the source distance, we performed AGW ray tracing calculations that provided for a curved Earth, the inclusion of viscosity in the AGW dispersion relation [Pitteway and Hines, 1963], the use of the MSIS-E90 model for atmospheric parameters, and the inclusion of nominal thermospheric wind velocities for error assessment. Our ray tracing technique is similar to that described by Lighthill . As noted previously, we do not know the thermospheric wind profiles at the time of the observations. The preferred (and maximum) launch angle α for the AGW is given by α = tan−1(τ2τb−2 − 1)−1/2 [e.g., Hines, 1967; Francis, 1975], where τ is the period of the AGW. For AGW periods of 20 and 60 min, the nominal values of α for τ = 20 min and τ = 60 min are ∼17° and ∼6°, respectively. Under the assumption that all AGWs originate from the same region, the launch angle at sea level must be ∼6°, since waves having either period can be radiated at this angle. This places the source distance at ∼2100 km even though the optimum launch distance is ∼600 km for a 20 min wave. The estimated uncertainty of the 2100 km value is −250 km, +500 km, which corresponds to two to four horizontal wavelengths in the estimated Arecibo AGW spectrum. Uncertainties in the thermospheric wind profile above Arecibo contribute most to the above error bars.
 The ray tracing result combined with the wave direction obtained from 630.0 nm airglow images indicate that the AGW source region at sea level (including error bars) is located in the vicinity of 26.8°N (+2°, −1°), 48.5°W (+2°, −5°). Given the size of the current data base (19 data acquisition periods), it is difficult to argue that tropospheric storms are always present at just the right range (e.g., ∼2100 km) to account for all observations. A typical observation period is 48 h, so a storm would have to be active day and night for a relatively long period of time. In the case of the 5 June 2005 observations the weather was clear throughout the day in the region surrounding 27°N, 49°W. On 6 June 2005, this region was partly cloudy, and no major storm systems were present. In addition, ISR results similar to those of Figure 16 are presented in the study of Livneh et al. . During observations made between ∼2000 AST and ∼2300 AST on both 23 and 24 September 2005, the AGW thermospheric injection zone was under either clear-sky or partly cloudy conditions, yet no impact on the observations was noted.
 Trade winds blowing over orographic features and ocean corrugation are often mentioned as a possible source for Arecibo's AGWs. Ocean corrugation refers to the work of Maximenko et al. , which indicates that small (∼2 cm in height) stationary striations separated by ∼400 km are present in most regions of the world's oceans. These results are disputed by Schlax and Chelton . Wind flow over surface structure produces waves with ∼0 phase speed that propagate in the vertical direction. Such waves can propagate into the mesosphere (∼85 km altitude) and undergo nonlinear breaking. As part of this process, secondary waves having large spatial scales and high frequencies (intrinsic periods of ∼10–60 min) can be generated by the horizontal forcing mechanism suggested by Vadas et al. . These waves would be excited preferentially along and against the direction of the breaking waves [e.g., Vadas and Nicolls, 2009]. The secondary waves could subsequently propagate into the thermosphere over Arecibo. However, for an AGW having a 60 min period, the secondary wave source would have to be located ∼1000 km east northeast of Arecibo, and in this region the trade winds on average are directed toward Arecibo only during the months of December and January. Even for the optimum scenario where the source is located 1000 km due east/west of Arecibo, one would expect AGW activity to be greatly reduced during the months of December, January, and February because of a change in average wind direction. However, no significant seasonal AGW variations have been observed. Finally, we note that the direction of surface winds in this Caribbean region can be quite variable on a day-to-day basis and often deviate significantly from their mean westerly course. During the observations presented above, winds recorded at a NOAA/NOS/CO-OPS station in San Juan, Puerto Rico ranged from 6 to 11 m/s, and their direction varied from 63° to 106° with 90° being toward the west, but no commensurate changes were evident in the AGW observations. Overall, it appears that the trade winds are not a viable source for Arecibo's AGWs.
 Large tsunamis (50–60 cm amplitude on open water, 300–400 km in wavelength) such as the Sumatra tsunami of 26 December 2004 produce internal gravity waves in the neutral atmosphere that give rise to very large disturbances in the overlying ionosphere [Occhipinti et al., 2006]. However, even very small tsunamis (1–2 cm amplitude on open water) generate significant TIDs readily observable with a Global Positioning Satellite (GPS) network [Lognonné et al., 2006a, 2006b]. The sensitivity of the Arecibo ISR system is much greater than GPS, so spatially coherent ocean waves having amplitudes as low as 1–2 cm may be sufficient to generate the Arecibo AGWs. However, the dispersion relation of idealized gravity/infragravity waves on the open ocean surface [e.g., Webb, 1998; Knauss, 2005; Tanimoto, 2005] is incompatible with the horizontal wavelengths and periods of the AGWs measured at Arecibo. Gravity waves on the ocean surface near Arecibo have phase speeds near 216 m/s (for an ocean depth of 5000 m and a period of 60 min), whereas the average phase speed of the AGWs is ∼60 m/s. An unrealistically shallow water depth of ∼560 m is needed to produce the 60 m/s phase speed. Thus, freely propagating gravity waves on the ocean surface cannot explain the Arecibo results.
 Internal ocean gravity waves have lower phase speeds than surface gravity waves and are compatible with the Arecibo observations. The projected source location at 26.8°N (+2°, −1°), 48.5°W (+2°, −5°) lies directly above the western/central portion of the Kane fracture zone in the mid-Atlantic Ridge (MAR). Semidiurnal internal tides dominate the dynamics of the ocean near the MAR. The internal tides are generated by the surface tides, which move stratified water up and down the sloping topography. This produces waves at the tidal frequency in the interior of the ocean. The dispersion relation of the internal ocean waves can be written as [e.g., Knauss, 2005; Cushman-Roisin and Beckers, 2010]
where θ is the group ray direction relative to the horizontal, k and m are the horizontal and vertical wave numbers, respectively, N is the angular BV frequency, ω is the intrinsic frequency (very close to the apparent frequency), and f is the Coriolis period (2π/86,164 s). Thus, ω is limited to values between f and N. The BV period ranges from ∼1 min near the ocean surface to 3–5 h in the deep ocean, and the group velocity is always perpendicular to the phase velocity. Although internal waves are excited within the ocean, they are also manifested as and typically observed as perturbations on the surface of the ocean [e.g., Ray and Mitchum, 1996]. The preferred mode for AGW excitation is m ∼ 0, and therefore ω ∼ N and θ ∼ 90°. In this case, the phase velocity is parallel to the ocean surface and the group velocity is vertically downward. This mode is selective in that only waves near the BV frequency have the proper phase velocity orientation to excite the Arecibo AGWs. In the other extreme, k ∼ 0, a steady state exists with no phase propagation, and at intermediate values of θ the phase velocity is tilted upward relative to the seabed. In the AGW source region indicated above the estimated values of BV period are ∼1 h at 1500 m depth and ∼20 min at 150 m depth [Fu, 1981], which is consistent with our requirements for AGW generation.
 The internal tidal horizontal wavelength spectrum (2π/k) ranges from ∼80 to ∼1000 km [e.g., Ray and Mitchum, 1996; St. Laurent and Nash, 2004], and the exact spectral shape is dependent on whether the ratio of topographic slope to θ is greater than 1 or less than 1 [e.g., St. Laurent and Nash, 2003]. Future studies with the JASON satellite altimeter [Fu et al., 2003] will provide us with an independent assessment of the spatial spectrum in the projected region of AGW generation. Studies performed near our region of interest indicate that the MAR topography is very rough [e.g., Fu, 1981]. An important parameter in this regard is the ratio of the tidal length scale U/ωo to the length scale of the topography L, where U and ωo are the amplitude and the frequency of the barotropic tide, respectively. This parameter is used to determine whether conditions are favorable for tidal harmonic generation [e.g., Bell, 1975]. If we assume that L = ∼200 m (Ridge Multibeam Synthesis Project, http://ibis.grdl.noaa.gov/SAT/Bathy/noaa.html), ωo = 1.45 × 10−4 (12 h tidal period) and U = 0.16–0.32 m/s [Legg and Huijts, 2006], a ratio of 5.5–10.5 ≫ 1 is obtained, which is suggestive of strong harmonic generation. Simulations performed by Legg and Huijts  provide further support for the concept that very high harmonics of the tidal period are generated, and other parametric processes are expected to enhance harmonic production. In addition, within the error bars of the ocean current spectra of Fu et al. , it appears that their site at 27.4°N, 41.1°W, which is closest to our projected AGW source region, is especially prone to harmonic generation. A 1 h wave period is not unexpected in this part of the MAR.
 In summary, internal ocean waves generated by the barotropic tide can selectively produce the required 1 h (and perhaps 15/30 min) period with the proper range of horizontal wavelengths (∼200–500 km) to generate the Arecibo AGWs. The tidal forcing is also in the correct direction for AGW propagation toward Arecibo [e.g., Knauss, 2005]. Moreover, the suggested process is dependent only on the lunar tide and MAR topography and is therefore capable of generating the continuous AGW wave train observed at Arecibo.
 High-resolution radar measurements of ne made by applying the coded long pulse technique to photoelectron-enhanced Langmuir waves indicate that the large-scale ne perturbations that are continuously present in the Arecibo thermosphere are indeed acoustic-gravity waves (AGWs). Most of the wave energy is at periods greater than the Brunt-Väisälä period, and the change in vertical wavelength with altitude is consistent with theoretical expectations for waves that are damped by kinematic viscosity/thermal conduction. In addition, the altitudes at which major peaks in Δne/ne are observed follow theoretical estimates made with a simplified model for nonducted AGWs. This combined with the observed downward phase trajectories of Δne/ne and the horizontal phase velocities obtained from airglow measurements (40–50 m/s) are clear indicators that the AGWs are not ducted but rather are locally produced. No plasma nonlinearities have been observed in the ne waves; the waveform is approximately sinusoidal with wavelength increasing with increasing height. In the current work, waves are displayed from 120 to 400 km altitude; other Arecibo observations indicate that the full altitude extent is from ∼117 to >650 km. The source must be very broadbanded in wave number space to support AGW propagation over such a large altitude interval. On the basis of time series plots of Δne/ne at ∼250–275 km and vertical phase histories, the nominal apparent period of the AGW is ∼60 min. Below ∼160 km apparent wave periods of ∼20 min are often observed because of the appearance of additional AGWs having downward moving phase paths. This phenomenon is most likely related to the wave emissions generated at the source. In addition, oscillations having periods in the range from 6.5 to 10 min are observed, which correspond to wave periods that are greater than and slightly less than the Brunt-Väisälä period. The origin of these oscillations is unknown. However, they are commonly seen in the Arecibo observations and may be indicative of nonlinear processes in the neutral gas.
 All Arecibo measurements examined for “background” ne wave activity in the era beginning in 1991 until the present have revealed the continuous presence of AGWs having similar characteristics. These background measurements are made in the absence of large-scale traveling ionospheric disturbances and other induced changes to the midlatitude ionosphere caused by geomagnetic activity. The AGWs measured at Arecibo do not appear to be dependent on Kp index. However, the measurements made to date span a 3 h Kp range of only 0−5. There are no significant differences in the observations between day and night, and no significant seasonal changes are apparent. The maximum range of (Δne/ne) enhancements and depletions may vary from one observation to the next, but this appears to be primarily related to the background ionospheric gradient rather than the AGW wave amplitude itself.
 AGW ray tracing calculations indicate that the local source of the AGWs is about 2100 km (−250 km, +500 km) away from Arecibo Observatory, and 630.0 nm airglow measurements reveal that the waves are traveling from east northeast to west southwest. This yields a source location in the Atlantic Ocean that is above the western/central portion of the mid-Atlantic Ridge (MAR). Internal ocean gravity waves generated as a result of the dominant semidiurnal internal tides in this region are the most likely source of the AGWs seen at Arecibo. The internal waves are highly selective in that they generate surface perturbations having harmonics that are locked to the 12 h tide. Only waves having intrinsic periods of ∼1 h or less will have the properly oriented phase front necessary to excite AGWs. In addition, this source process is dependent only on the lunar tide and MAR topography; it is not subject to the large variability and impulsiveness encountered with the standard atmospheric/ionospheric sources. In contrast, it is a stable wave source capable of continuously transmitting the background AGW wave train seen for decades at Arecibo.
 Support from the NSF under grant ATM-0456085 is gratefully acknowledged by F.T.D. and L.D.Z. The work of J.D.M., D.J.L., and I.S. was supported by NSF grant ATM-0721613. The efforts of R.L.W. were supported by NASA grant NNX08AM13G-S02. S.M.S. acknowledges support under grant ATM-0509015 and thanks Mr. Raul Garcia for his efforts in maintaining the health of the Boston University all-sky imaging system. The Arecibo Observatory is part of the National Astronomy and Ionosphere Center, which is operated by Cornell University under cooperative agreement with the National Science Foundation.
 Amitava Bhattacharjee thanks David Fritts and another reviewer for their assistance in evaluating this paper.