1. Introduction

Diurnal thermal tides are global-scale inertia–gravity waves that oscillate with a period of one day. Solar thermal tides can be thought of as migrating and nonmigrating. The migrating diurnal tide is an oscillation with zonal wavenumber 1 that travels westward with the sun. Nonmigrating diurnal tides include any oscillation that is not traveling with the sun; examples are wavenumbers other than 1 or eastward propagating modes. Nonmigrating tides are functions of universal time, with or without zonal variation. Further theoretical descriptions of solar thermal tides can be found in Chapman and Lindzen (1970).

The strongest forcing of migrating tides is due to solar radiation absorption by tropospheric water vapor and stratospheric ozone (Lindzen 1967). The migrating (or sun-synchronous tide) is generated when the heating constituent is zonally uniform. Longitudinal variations in these constituents due to land–sea differences, topography, or latent heat release of diurnal oscillating clouds excite nonmigrating tidal modes (Kato et al. 1982; Forbes and Groves 1987; Kato 1989; Tsuda and Kato 1989; Lindzen 1978; Hamilton 1981). Lieberman and Leovy (1995) investigated several forcing mechanisms in a classical model with Newtonian cooling that extended into the lower mesosphere. Boundary layer sensible heat contributed the most to the nonmigrating surface pressure tide, while in the middle atmosphere the largest response was due to solar absorption with a weaker signal from latent heating. Williams and Avery (1996) used a dissipative f-plane model to investigate nonmigrating tides forced by the latent heat associated with diurnal oscillations of deep convective clouds. The superposition of nonmigrating tides was found to be of comparable amplitude to the migrating tide in the mesosphere and lower-thermosphere (MLT) region. Hagan et al. (1997) expanded the study by using the latent heat release functions of Williams and Avery to force tidal oscillations in a two-dimensional, linearized, steady-state tidal model. The nonmigrating components were strong enough to modulate the migrating tide zonally. Ekanayake et al. (1997) forced nonmigrating tides in a two-dimensional model using tropospheric forcing obtained from a GCM and found that in the low-latitude zonal wind, eastward diurnal tides were preferentially propagated over westward nonmigrating tides due, in part, to filtering by the mean zonal wind.

Departures from migrating diurnal structure in observational studies have suggested the presence of nonmigrating tides. Wallace and Tadd (1974) analyzed 12-h differences in rawinsonde data and found higher-order zonal structure, which they believed was due mainly to nonmigrating tides. Khattatov et al. (1996) postulated that differences between High Resolution Doppler Imager (HRDI) and medium-frequency radar determination of tides could be explained by nonmigrating components of significant amplitude. Lieberman (1991) analyzed nonmigrating tides in the stratosphere and lower mesosphere using Limb Interferometer Monitor of the Stratosphere (LIMS) data. The most prominent mode observed was the zonally symmetric diurnal tide, a standing wave uniform in longitude that oscillates with a period of one day. At low latitudes, the nonmigrating tides were observed to be vertically propagating. The features found in LIMS data exhibited some properties such as upward or no vertical phase propagation that could not be explained by a classical tidal model (Lieberman and Leovy 1995).

This study extends the global picture of nonmigrating tides into the equatorial MLT region using winds and temperatures measured by HRDI. A description of the data and the method of analysis used follow in section 2. Section 3 presents results from the analysis and section 4 includes a discussion and summary.

2. Data and analysis

This study uses horizontal wind and temperature measurements by HRDI on board the Upper Atmosphere Research Satellite (UARS). HRDI measures daytime winds and temperatures from 50 to 115 km and nighttime winds at 95 km. The longitudinal sampling is nominally 24°, and sampling along the orbital track is 500 km. Winds and temperatures are reported every 2.5 km in the vertical. HRDI (Hays et al. 1993) is a triple etalon Fabry–Perot interferometer, which infers mesospheric and lower-thermospheric winds from Doppler shifts in the O₂A band emission lines (Abreu et al. 1989). The precision of HRDI winds in the MLT region is roughly 5 m s⁻¹ (Burrage et al. 1996b). Temperature and band volume emission rate (VER) are derived from the brightnesses of two rotational lines in the O₂A band (Ortland et al. 1998). A forward model is constructed to model brightness, and the difference between the initial computed brightnesses and those measured is inverted via perturbation theory to derive both temperature and VER. An individual profile is recovered with an error of 7 K.

UARS is in a slowly precessing orbit and samples roughly the same local time at every point along a latitude circle. A typical HRDI day of sampling, 15 August 1994, is presented in Fig. 1a. HRDI has full coverage of equatorial latitudes and samples 24 h of universal time. Figure 1b indicates the positions of each orbit as a function of latitude and longitude. From Figs. 1a and 1b, it can be seen that a complete latitude circle is sampled over 24 h of universal time.

The analysis of HRDI data requires several steps in order to retrieve a quantitative picture of diurnal nonmigrating tides. For a given day, the zonal mean wind and temperature are removed from each latitude and altitude. Because each point around a latitude circle is sampled at the same local time, by removing the zonal mean, the migrating tide is also removed (Morton et al. 1993; Hays et al. 1994; Lieberman and Riggin 1997). At each latitude and each altitude, data are then compiled to form monthly composites with respect to a satellite-relative (asynoptic) coordinate (Salby 1982) defined as

where λ is longitude, t time, and c₀ the angular velocity of the satellite (≈−6.37 rad day⁻¹ day for UARS).

Figure 2a presents the composite at the equator for a representative month, December 1992. This composite is averaged within the grid lines shown to obtain the s_a coordinate. Within each bin, several hours of universal time are averaged together resulting in some dilution of the spectra. The loss of signal is quantified as a function of the time spread in Fig. 2b for different zonal wavenumber, s, eastward diurnal tides.

A Fourier harmonic in the satellite-relative coordinate, labeled k_sa, is related to ground-based frequency, σ, and zonal wavenumber, s, by

An observed peak in the satellite spectrum (k_sa) can correspond to a number of wavenumber–frequency pairs, (s, σ), that are aliased to that particular k_sa by the satellite motion relative to Earth (Salby 1982). For example, the zonally symmetric diurnal (s = 0, σ = −2π) is aliased to k_sa ≈ 1, as is a stationary (σ = 0) s = 1 zonal feature (k_sas are generally noninteger; but for discussion purposes, they will be referred to by their nearest integer value). Table 1, adapted from Lieberman (1991), presents the zonal wave components retrieved from HRDI data and some of their possible aliases. The s = 0 and eastward diurnal tides s = 1–3 are aliased to k_sa = 1–4. Stationary s = 1–4 waves are observed at their true wavenumber. Westward s = 2–5 diurnal tides are also aliased to k_sa = 1–4. Smaller-scale and faster waves are assumed to be averaged out by the composite.

Salby (1982) has shown that if data are sampled at two different local times (e.g., on the ascending and the descending nodes of the satellite orbit) it is possible to separate the contribution of two waves in the absence of the third. In general, HRDI samples at one local time per day for all altitude ranges; except at 95 km, where nighttime horizontal wind measurements are enabled. In theory, double-node separation of the winds is then possible at 95 km. However, the presence of a third wave would still alias into the retrieved spectra of the other two. In order to successfully resolve the contribution of three waves, sampling of data taken at three or more local times is required.

In the absence of a quantitative method of determining which wavenumber–frequency pair is present in the data, this decision is based upon comparison of the wind and temperature fields with theoretical features of the waves in question.

3. Results

Prominent equatorial structures are found in k_sa = 1–4 winds and temperatures. Figure 3a displays an altitude–latitude cross section of k_sa = 1 meridional wind field for November 1994 at 0000 UTC. In this representative plot, the meridional wind is antisymmetric about the equator, peaks at roughly 20°, and extends to about 40° on either side of the equator. This corresponds well to the theoretical meridional wind structures of the zonally symmetric diurnal tide. Figure 4 presents k_sa = 1 wind vectors at 85 km overlaid with contours of temperature perturbation. This retrieval is plotted as a function of longitude and universal time. The convergence and divergence of the horizontal wind at the equator and the corresponding temperature perturbation are strong tidal characteristics. At low latitudes, k_sa = 1–4 are believed to be predominantly tidal with correlating features in temperature and at least one horizontal wind component. In the following sections, these tidal features are referred to as eastward tides, as the observations generally suggest the presence of eastward over westward tides (section 4 has further discussion of this assumption).

Nonmigrating tides are observed in zonal and meridional winds and temperature from February 1992 to March 1995. Interannual variability can not be readily discerned from the dataset partly due to large gaps in the sampling; therefore, 3 yr of data are used to construct one composite year by averaging the spectra of individual months together. The results presented for diurnal s = 0–3 tides are those that exhibited organized and repeatable patterns in at least two out of the three fields observed.

4. Summary and discussion

Asynoptic Fourier analysis of HRDI winds and temperatures reveals features that are consistent with classical predictions of nonmigrating diurnal tides. The zonally symmetric (s = 0) tide is the most prominent nonmigrating component, with maximum amplitudes of 6 K in temperature and 30 m s⁻¹ in meridional wind. Eastward diurnal tides exhibit similar properties in temperature and in zonal and meridional winds. Classical tidal theory predicts that the temperature amplitude (in Kelvin) would roughly equal that of the winds (in meters per second). The observed meridional wind amplitude is five times that of temperature. The zonal winds generally have slightly lower maximum amplitudes than the meridional wind, and they peak at higher altitudes. The zonal wind is strongest in the s = 3 tide, with peak amplitudes of 30 m s⁻¹. The eastward diurnal modes generally showed decreasing phase with height, suggesting upward energy propagation.

The dominant symmetric modes in s = 0 meridional wind and temperature, V⁰₂ and T⁰₂, show increasing phase with altitude. If the phase, ϕ, is interpreted in terms of vertical wavenumber, m, so that ϕ ∼ mz, where z is altitude, then m > 0. From linear tidal theory, an eastward frequency and positive vertical wavenumber imply that the averaged vertical energy flux is downward (Wilkes 1949). The HRDI observations interpreted as s = 0 diurnal tides, suggest in situ or higher-level forcing. However, it is also possible that this feature corresponds to another alias, namely, a westward diurnal s = 2 oscillation (Table 1). The presence of the westward mode is suggested by the phase structure, since a westward frequency and positive vertical wavenumber imply forcing from levels below and therefore consistency with present knowledge of forcing mechanisms.

As mentioned, at 95 km HRDI has well-defined coverage of the horizontal winds at two local times. As a result, it should be possible to separate the contribution of two waves in an observed wave field. However, for k_sa = 1, such double-node analyses suggest the presence of three separate waves. The presence of a third wave heavily aliases into the spectra of the two waves retrieved. Hence, using data from only two local times is insufficient to accurately decompose the observed wave field into the possible aliases listed in Table 1, and, therefore, we are unable to resolve the question of westward aliasing.

Forcing for both the westward s = 2 and the s = 0 tides is predicted by the solar excitation of tropospheric water vapor and the diurnal cycle of latent heat release in the Tropics (Forbes and Groves 1987; Lieberman and Leovy 1995; Williams and Avery 1996). Ekanayake et al. (1997) find that GCM tropospheric forcing produces a weak MLT westward s = 2 zonal wind tide (relative to eastward and migrating components) and a negligible s = 0 response. The global-scale wave model (GSWM) predicts the s = 0 and the westward s = 2 diurnal tides (Hagan et al. 1997), as a response to latent heat release. The meridional wind amplitudes of the model s = 0 and s = 2 responses are comparable to each other, thus bearing out a westward s = 2 interpretation of k_sa = 1. However, there are major differences between the GSWM tides and HRDI observations. The model tides are a factor of five less than those found in HRDI data. Furthermore, the latitudinal structure of both model tides is inconsistent with the dominant mode found in HRDI data. The question of aliasing in the s = 0 field by a westward s = 2 tide cannot be resolved as available studies of forcing and theoretical predictions do not provide conclusive support for one interpretation over the other.

The GSWM also predicts some of the Kelvin structure seen in the s = 3 zonal wind from forcing due to diurnal deep convective activity. The latitudinal structure of the model zonal wind during October was symmetric and centered at the equator. Moreover, model tidal amplitudes are significant above 95 km. Both these features correspond well to HRDI observations of the gravest symmetric mode in the zonal wind, though the model predicts a slightly lower peak amplitude at a higher altitude. Ekanayake et al. (1997) predict that the eastward s = 3 zonal wind is the strongest nonmigrating response in the low-latitude zonal wind.

This study establishes the presence of nonmigrating tides in s = 0–3 MLT winds and temperatures. Recent modeling studies of nonmigrating tides agree with some of the features exhibited in HRDI tides. However, questions about the amplitudes and the variable phase behavior observed in the tides still remain. The amount that aliasing contributes to such variability would hopefully be resolved by future satellite observations that sample on three or more nodes. Further study of forcing mechanisms can possibly align model results more with HRDI observations.