Tropospheric tides from 80 to 400 km: Propagation, interannual variability, and solar cycle effects



[1] Recent observations and model simulations demonstrate unequivocally that non-Sun-synchronous (nonmigrating) tides due to deep tropical convection produce large longitudinal and local time variations in bulk ionosphere-thermosphere-mesosphere properties. We thus stand at an exciting research frontier: understanding how persistent, large-scale tropospheric weather systems affect the geospace environment. Science challenge questions include: (1) How much of the tropospheric influence is due to tidal propagation directly into the upper thermosphere? (2) How large is the interannual and the solar cycle variability of the tides and what causes them? These questions are addressed using solar maximum to solar minimum tidal wind and temperature analyses from the Thermosphere Ionosphere Mesosphere Electrodynamics and Dynamics (TIMED) satellite in the mesosphere/lower thermosphere (MLT), and from the Challenging Minisatellite Payload (CHAMP) satellite at ∼400 km. A physics-based empirical fit model is used to connect the TIMED with the CHAMP tides, i.e., to close the “thermospheric gap” of current spaceborne observations. Temperature, density, and horizontal and vertical wind results are presented for the important diurnal, eastward, wave number 3 (DE3) tide and may be summarized as follows. (1) Upper thermospheric DE3 tidal winds and temperatures are fully attributable to troposphere forcing. (2) A quasi-2-year 15–20% amplitude modulation in the MLT is presumably caused by the QBO. No perceivable solar cycle dependence is found in the MLT region. DE3 amplitudes in the upper thermosphere can increase by a factor of 3 in the zonal wind, by ∼60% in temperature and by a factor of 5 in density, caused by reduced dissipation above 120 km during solar minimum.

1. Introduction

[2] It is now well accepted that latent heating due to deep convection in the tropical troposphere is a major source of nonmigrating tides [Hagan and Forbes, 2002, 2003]. Convection largely depends on land-sea differences and the periodic absorption of solar radiation at the surface transforms to a longitudinal structure in raindrop formation at roughly the same local time of the day. The resulting spatiotemporal modulation of heat release excites tidal waves that propagate upward into the mesosphere and lower thermosphere (MLT) region where they reach their maximum amplitudes. Dissipation then leads to net momentum and energy deposition at these altitudes. Hence, nonmigrating tides are an important driver that redistributes solar energy back into the middle and upper atmosphere where it then competes with other drivers of solar and magnetic origin.

[3] The past 3 years have seen an increasing interest, even a boom, in nonmigrating tidal research. This was triggered by two discoveries. First, nonmigrating tides in the MLT region are much larger and hence more important to aeronomy than hitherto anticipated. Although earlier tidal diagnostics based on UARS and CRISTA satellite data [Talaat and Lieberman, 1999; Oberheide and Gusev, 2002; Forbes et al., 2003] already showed evidence for that, the full realization was mainly a result of Thermosphere Ionosphere Mesosphere Electrodynamics and Dynamics (TIMED) satellite observations. The two instruments of interest here are Sounding the Atmosphere using Broadband Emission Radiometry (SABER) [Russell et al., 1999] and the TIMED Doppler Interferometer (TIDI) [Killeen et al., 2006].

[4] SABER tidal analysis resulted in the first climatologies of diurnal, semidiurnal, and terdiurnal temperature tides up to zonal wave number 6 with a vertical extent (20–120 km) and a temporal coverage (7 years so far, 2002–2008) that was not possible before [Forbes et al., 2006, 2008; Zhang et al., 2006]. TIDI tidal analysis covers the same time span and resulted in the first climatologies of diurnal and semidiurnal zonal and meridional wind tides over a range of MLT altitudes (85–105 km) up to zonal wave number 4 [Oberheide et al., 2005, 2006, 2007]. Recently, Oberheide and Forbes [2008a] established the internal consistency of these tidal temperature and wind climatologies within the framework of the tidal theory. Their work was focused on the eastward propagating diurnal tide with zonal wave number 3 (DE3) alone but the general finding also applies to the other diurnal and semidiurnal components. The TIMED tidal diagnostics have since become the baseline data set for testing next generation models that in turn provided new insight into the physical mechanisms causing the seasonal variation of the nonmigrating tides [i.e., Du et al., 2007; Akmaev et al., 2008; Achatz et al., 2008] and on tidal momentum transport and transfer into the neutral atmosphere [Hagan et al., 2009].

[5] The second discovery was the observation of the four-peaked (“wave-4”) longitudinal structure of the F region equatorial ionization anomaly (EIA). It was first observed by Sagawa et al. [2005] in IMAGE/FUV satellite data. Shortly afterward, Immel et al. [2006] proposed DE3 tidal wind modulation of the E region electric fields as the governing process. This in turn modulates the equation image × equation image vertical plasma drifts that finally control the EIA structure. Here, it should be noted that any (quasi-) Sun-synchronous satellite observes the DE3 as a “wave-4” signature. See Oberheide et al. [2003] for details about tidal sampling issues.

[6] The “wave-4” has since been observed in a variety of ionospheric parameters: electron density profiles [Lin et al., 2007], in situ electron densities [Liu and Watanabe, 2008; Pedatella et al., 2008], total electron content [Scherliess et al., 2008; Wan et al., 2008], O+ airglow [England et al., 2006a], equatorial electrojet [Lühr et al., 2008], daytime electric fields [England et al., 2006b], and equation image × equation image drift velocities [Hartman and Heelis, 2007; Kil et al., 2008]. These observations and initial model simulations by Hagan et al. [2007] all support the tropospheric weather influence on the ionospheric F region, through DE3 electric field modulation in the E region. Hence, any variability or modulation of the tidal activity in the troposphere, stratosphere and MLT region will likely impose a similar variability or modulation on the F region ionosphere, competing with variability induced by solar and magnetic drivers from above.

[7] DE3 tidal signatures have also been identified in the neutral atmosphere above the MLT region. Lower thermospheric nitric oxide densities from the Student Nitric Oxide Explorer (SNOE) [Barth et al., 2003] show a pronounced “wave-4” signature at low latitudes that could be attributed to DE3 density variations [Oberheide and Forbes, 2008b]. In the upper thermosphere, the DE3 tide has been found in thermospheric neutral winds [Häusler et al., 2007; Häusler and Lühr, 2009] and temperatures [Forbes et al., 2009] based on in situ accelerometer measurements on the Challenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) satellites at ∼400 km. The amount to which the thermospheric tidal wind and temperature variations make an in situ contribution to the ionospheric F region “wave-4”, if any, has yet to be resolved. Forbes et al. [2009] were the first to demonstrate that the upper thermospheric DE3 temperature signal represents the direct vertical propagation of nonmigrating tides upward from the troposphere. Using 1 year of TIMED, CHAMP and GRACE data, and a methodology similar to the one used in the following, these authors could track the cause-and-effect chain over 400 km altitude.

[8] On the basis of the progress made and the data available, it is now possible to make the next step in our study of how geospace responds to persistent large-scale weather systems in the tropical troposphere. The science challenge questions addressed in the present work are: (1) How much of the tropospheric influence is due to tidal propagation directly into the upper atmosphere? This goes farther than the Forbes et al. [2009] analysis because the present study includes observation-based neutral wind and density estimates in the “thermospheric gap” between the TIMED (<120 km), and the CHAMP and GRACE (∼400 km) data. (2) How large is the interannual and the solar cycle variability of the tropospheric tides in the ionosphere-thermosphere-mesosphere (ITM) system and what causes them? This paper will demonstrate that key convectively driven tidal components indeed propagate into the thermosphere, and are affected by the solar cycle and, presumably, by the quasi-biennial oscillation (QBO).

[9] Data used are solar maximum to solar minimum (2002–2008) tidal wind and temperature diagnostics from TIDI and SABER on TIMED in the MLT region, and from CHAMP in the upper thermosphere. The latter diagnostics cover the time span 2002–2007, depending on variable. A physics-based empirical fit model to the TIMED tides that has been used before to study tidal characteristics in the MLT region [Oberheide and Forbes, 2008a, 2008b] has now been extended to 400 km altitude and updated for varying solar flux levels. It is used to close the “thermospheric gap” between TIMED and CHAMP as well as for the interpretation of the results. Presentation of the latter will be restricted to DE3 alone since it is the dominating nonmigrating tide in the low-latitude ITM over large parts of the year and for space reasons.

[10] The paper is organized as follows. Section 2 overviews the tidal temperature and wind diagnostics in the MLT. Section 3 introduces the Hough Mode Extensions used for the fit model. Section 4 presents the fit results. Section 5 discusses the interannual tidal variability in the MLT region. Section 6 connects the MLT tides with the CHAMP diagnostics and discusses the thermospheric results with emphasis on solar cycle dependence. Section 7 contains the conclusions.

2. DE3 Tidal Temperatures and Winds in the MLT

[11] The SABER tidal temperature (T) diagnostics used in the present paper are overviewed by Forbes et al. [2008] but have been extended to cover the March 2002 to December 2008 time span and updated to the most recent SABER data version v01.07 [Remsberg et al., 2008]. TIDI zonal (u) and meridional (v) tidal wind analysis is described by Oberheide et al. [2006] and has also been extended to March 2002 to December 2008 and updated to the most recent National Center for Atmospheric Research data version v0307a [Wu et al., 2008]. The uncertainties of the SABER and TIDI tidal diagnostics are unaffected by these updates: DE3 temperature error is ∼2 K [Forbes et al., 2008] and the DE3 wind accuracy (precision) is about 10% (1 m/s) as detailed by Oberheide et al. [2006].

[12] Figure 1 shows monthly mean time series of DE3 (T, u, v) amplitudes at about peak altitudes: 105 km (T), 100 km (u), 95 km (v). Amplitudes in all three variables always maximize around the equator with a distinct seasonal variation. Maximum amplitudes in (T, u) occur in August–September (late boreal summer) with smaller secondary maxima in spring. The latter are only present every 2 years (2003, 2005, 2007) and are more evident in T than in u. In contrast, meridional wind amplitudes maximize around December with two separate peaks in late fall and late winter. The different seasonal variation of (T,u) and v is consistent with the prediction of the classical tidal theory [Chapman and Lindzen, 1970] as it has been discussed in detail by Oberheide and Forbes [2008a].

Figure 1.

Times series of DE3 amplitudes at about peak altitudes. (a) Temperature from SABER at 105 km. (b) Zonal wind from TIDI at 100 km. (c) Meridional wind from TIDI at 95 km. White areas indicate missing data and/or latitudes not analyzed.

[13] A cursory inspection of Figure 1 already reveals a quasi-2-year pattern in tidal temperature with relative maxima in 2002, 2004, 2006, 2008 and relative minima in 2003, 2005, 2007. This is matched by the zonal wind amplitudes although it is less perceivable “by eye” in 2002 and 2007. Reasons for that will become clear in Figure 2. Meridional wind amplitudes do not show a quasi-2-year signature. These general findings are consistent with the results presented by Forbes et al. [2008] and Wu et al. [2008] and are not new, apart from adding one more year of data.

Figure 2.

Time series of DE3 amplitudes averaged between 5°S and 5°N. (a) Temperature from SABER. (b) Zonal wind from TIDI. (c) Meridional wind from TIDI. White areas indicate missing data and/or altitudes not analyzed.

[14] Figure 2 gives more insight into the interannual variability of the low-latitude DE3 tides. Temperature amplitudes always maximize around 107–108 km with a persistent quasi-2-year modulation throughout the MLT region. The zonal wind amplitudes show more peak altitude variability, i.e., from 100 to 105 km, with no clear correlation between magnitude and altitude of maximum amplitudes. However, zonal wind amplitudes are largest during the same years as for temperature. Again, meridional wind amplitudes do not show a distinct 2-year pattern throughout the MLT region. Neither (T, u) nor v show perceivable solar cycle dependencies by simple inspection of the raw data. Section 5 will present a more thorough analysis using the results of a fit model to the TIMED diagnostics based on Hough Mode Extensions.

3. Hough Mode Extensions

[15] The consistency of the (T, u) and v DE3 tides from SABER and TIDI in a climatological sense has recently been established by Oberheide and Forbes [2008a] using Hough Mode Extensions (HMEs) for moderate solar flux conditions. This approach is further extended in the present work by (1) extending the HMEs to 400 km altitude, (2) updating the HMEs for varying solar flux, and (3) fitting them to individual years of observations.

[16] An HME can be thought of as an extension of a classical Hough mode that in turn represents the solution of Laplace's tidal equation in an idealized (isothermal, windless and dissipationless) atmosphere. Introduced by Lindzen et al. [1977] and Forbes and Hagan [1982], HMEs account for dissipative effects above the forcing region and for the height variation of mean temperature. The HMEs are computed as detailed by Svoboda et al. [2005] using a stripped-down version of the Global Scale Wave Model [i.e., Hagan and Forbes, 2002]. The tidal dissipation scheme is maintained but background winds are set to zero and the standard model temperature and density profiles are replaced by global mean MSISE90 profiles. The tidal forcing in the model is substituted for an arbitrarily calibrated, simple tropospheric heat source with a latitudinal structure identical to that of the corresponding Hough mode. Hence, each HME of given wave number and frequency is a self-consistent latitude versus height set of amplitudes and phases for the perturbation fields in temperature, zonal wind, meridional wind, vertical wind (w), and density (ρ). For example, fitting HMEs to observed tides in (T, u, v) in a limited height and latitude range predicts tidal perturbations in parameters that have not been measured, i.e., ρ and w, and at latitudes and altitudes not observed.

[17] For DE3, two HMEs are sufficient to describe the observations: HME1 and HME2. HME1 corresponds to the first symmetric Hough mode and HME2 to the first antisymmetric. Figure 3 exemplifies their normalized latitudinal structure for (T, u, v) at 105 km altitude and for moderate solar flux conditions (110 sfu, sfu = 10−22 m−2 Hz−1). For latitude versus height amplitudes and phases see Oberheide and Forbes [2008a]. The latitudinal shape of the HMEs does not change appreciably with solar cycle (not shown). Note that the latitudinal structure of the normalized (T, u) components of HME1 and HME2 are almost identical. Similar to that, (ρ, w) components of HME1 are symmetric about the equator and antisymmetric in HME2 (not shown). In contrast, v is antisymmetric about the equator in HME1 and symmetric in HME2. This and the relative strength of HME1 and HME2 in the real atmosphere explain the different seasonal variation of (T, u) and v evident in Figure 1. HME1 dominates during boreal summer and HME2 during boreal winter [Oberheide and Forbes, 2008a].

Figure 3.

(a) Latitudinal structure of HME1 of DE3 for temperature (solid curve), zonal wind (diamonds), and meridional wind (dotted curve) at 105 km. Maximum amplitudes are normalized to +1 at 0°N and 20°N. (b) Same as Figure 3a but for HME2.

[18] HMEs have been computed for three F10.7cm radio flux levels: high (170 sfu), moderate (110 sfu) and low (60 sfu). Figure 4 shows the resulting HME 1 amplitudes and phases (in a sense analogous to the solution of the vertical structure equation in the classical tidal theory) at peak latitudes for T, ρ, u (equator) and v (20°N). They are not yet constrained by TIMED data but arbitrarily normalized relative to a maximum zonal wind amplitude of 10 m/s at 86 km. Peak altitudes are solar flux level independent and with 108 km (T), 103 km (ρ, u), 98 km (v) close to the observed ones in Figure 2. In the dissipative region above, (T, u, v) relax to a constant amplitude and phase when molecular diffusion becomes dominant in the thermosphere. In contrast, density amplitudes have a relative minimum at ∼200 km and increase again toward higher altitudes since they are given as percentage perturbation with respect to mean density.

Figure 4.

HME1 amplitudes and phases of DE3 for three F10.7 cm radio flux levels: 170 sfu (solid curve), 110 sfu (dotted curve), 60 sfu (dashed curve). Shown is the latitude of maximum amplitude, as indicated in each plot. Normalization is relative to a zonal wind amplitude of 10 m/s at 86 km. (a) Temperature amplitude. (b) Temperature phase. (c) Density amplitude. (d) Density phase. (e) Zonal wind amplitude. (f) Zonal wind phase. (g) Meridional wind amplitude. (h) Meridional wind phase.

[19] The most striking result in Figure 4 is certainly the solar flux dependence of the DE3 tidal amplitudes in the thermosphere. Amplitudes are smallest for high solar flux and largest for low solar flux, mainly owing to the temperature dependence (∝T2/3) of molecular thermal conductivity (see Forbes and Hagan [1982] for details). Temperature HMEs are the least sensitive with a ∼60% increase from 170 sfu to 60 sfu. Density (almost a factor of 5) and winds (a factor of 2–3) are more affected. The HME solar flux dependence in the MLT region is small with only a few percent (density, winds) or even less (temperature). HME phases are less sensitive to solar flux variations with only 2–3 h difference in the thermosphere (depending on variable) and virtually none in the MLT region. As for amplitudes, phases shown are arbitrary to within a single phase displacement appropriate to all fields at all altitudes and latitudes. The reference in Figure 4 is a zonal wind phase of 19.5 h at 86 km.

[20] Figure 5 overviews the corresponding HME2 results, also at peak latitudes (T, ρ, u: 20°N, v: equator). Normalization is relative to 10 m/s zonal wind amplitude and 12.5 h zonal wind phase at 86 km. HME2 is subject to larger dissipation compared to HME1 since the time constants of eddy and molecular dissipation are proportional to the square of the vertical wavelength which is considerably shorter for HME2. As a result, thermospheric HME2 amplitudes are only on the order of 1/10 of the peak amplitudes. The corresponding HME1 ratio for moderate solar flux conditions is on the order of 2–4.

Figure 5.

Same as Figure 4 but for HME2 of DE3.

[21] The solar flux–dependent HME computations therefore lead to three expectations for the thermospheric tides. (1) Tidal amplitudes should increase considerably from solar maximum to solar minimum, caused by reduced dissipation. (2) Winds and density should be more affected than temperature. (3) The latitudinal structure should be largely symmetric, i.e., governed by HME1. These predictions will be tested with CHAMP data in section 6. Toward this goal, and for an easier analysis of the observed interannual variation in the MLT region, the HMEs need to be constrained with TIMED tidal diagnostics by means of least squares fitting.

4. HME Fit Results in the MLT

[22] In a first step, the 170 sfu, 110 sfu and 60 sfu HMEs are linearly interpolated to the monthly mean F10.7cm solar flux levels from March 2002 to December 2008. HMEs are extrapolated for the 5 months in 2002 when the solar flux was above 170 sfu (maximum value: 190.17 sfu).

[23] The further fit approach essentially follows the method successfully applied to the SABER and TIDI DE3 climatologies [Oberheide and Forbes, 2008a]. For each month, HME1 and HME2 are fitted simultaneously to the observed (T, u, v) triplet. The effect of mean winds (set to zero in the HME computation) is inherently accounted for since the associated tidal distortion can be viewed as mode coupling. This has been discussed in detail and tested with model data by Svoboda et al. [2005]. Fit ranges are 90–110 km and 10°S–10°N. Above 105 km, only SABER DE3 temperatures are available but including the peak altitudes of all three parameters into the vertical fit range gives generally better results. The chosen latitudinal range is optimized for the low latitudes that are of interest here. However, the HME fits to the TIMED tides are robust and do not change considerably depending on the exact choice of vertical and/or latitudinal range.

[24] Figure 6 is the (T, u, v) result as function of time and latitude for the same altitudes and in the same color code as for the observed tides in Figure 1. The fit reproduces the basic features outlined in section 2, i.e., the (T, u) quasi-2-year variation in boreal summer amplitudes that is more pronounced in T and the occurrence of smaller low-latitude spring maxima every 2 years in 2003, 2005, and 2007. As in the observation, the fit v does not show a 2-year signature. Observed and fit amplitudes generally agree within one color scale which is about the error (see section 2) of the TIMED tidal diagnostics. The level of agreement comes not unexpected since it is the same as for the climatological DE3 analysis [Oberheide and Forbes, 2008a].

Figure 6.

Same as Figure 1 but for HME fit results. (a) Temperature at 105 km. (b) Zonal wind at 100 km. (c) Meridional wind at 95 km. Fit range: 90–110 km, 10°S–10°N.

[25] The vertical distribution of the low-latitude (T, u, v) fit amplitudes is shown in Figure 7, again in the same color code as for the observed tides (Figure 2). Note that the HME fits now provide tidal winds above 105 km. As for the horizontal time series, the general observation–fit agreement is good (within one color scale) throughout the whole MLT region, including the quasi-2-year amplitude variation in (T, u). There are, however, two noticeable exceptions. First, observed temperature amplitudes decrease more rapidly above 110 km than in the fit results. This may be an indication for more tidal dissipation in the real atmosphere than assumed in the HME computation. Second, the fits do not reproduce the interannual variability of the peak heights in the zonal and meridional winds. Physical reasons for the observed peak height variability, that is not present in tidal temperature, yet need to be explored and are not part of the present work.

Figure 7.

Same as Figure 2 but for HME fit results. (a) Temperature. (b) Zonal wind. (c) Meridional wind.

[26] Hence, HME fits do not capture every detail of the observations but they can nevertheless provide realistic observation-based estimates of tidal temperature and wind variations in the MLT region. One significant advantage of the approach is that one can express the temporal variation of the tides by time series of two complex fit parameters, one for HME1 and one for HME2. These fit parameters are the same for all tidal fields (T, ρ, u, v, w), even for those parameters that could not be measured, and are independent of altitude and latitude. The analysis of interannual tidal variability in section 5 can thus be reduced to two time series.

5. Interannual Tidal Variability in the MLT

[27] Figure 8a shows the absolute values of the complex HME1 and HME2 fit parameters and hence their excitation strength with respect to the normalization outlined in section 3. HME1 is a measure of the low-latitude variability in (T, ρ, u, w) since it is symmetric in these tidal fields. On the other hand, HME2 is a measure of the low-latitude variability in v since this field is antisymmetric in HME1 (Figure 3). Hence, HME1 reflects the temporal variability of (T, u) in Figure 7 and HME2 that of v. A quasi-2-year variation in HME1 is quite obvious with about 15–20% differences during boreal summer. It corresponds well with the quasi-biennial oscillation (QBO) in stratospheric mean zonal winds. A widely used proxy for the latter are Singapore radiosonde data at 30 hPa (Figure 8b). HME1 amplitudes are always larger during the westerly phase of the stratospheric QBO and smaller during the easterly phase. There is no such correspondence evident for HME2.

Figure 8.

(a) Absolute value of DE3 fit coefficients for HME1 (solid curve) and HME2 (dashed curve); mean fit errors are 0.03 and 0.05, respectively. (b) Singapore zonal wind at 30 hPa.

[28] Further insight into statistically significant periodic signals present in HME1 and HME2 comes from the computation of Lomb-Scargle periodograms [Scargle, 1982]. Briefly, Scargle power is a measure of the significance of a period in time series and not of its amplitude as it is for instance in Fourier transform. The false-alarm probability (FAP) over a range of periods that noise can produce the highest peak in the periodogram is FAP = 1 − (1 − eP)N where P is the Scargle power and N the number of independent periods in the period range of interest. Following Horne and Baliunas [1986], N is computed from the number of data points (N0 = 82) as N = −6.362 + 1.193 * N0 + 0.00098 * N02. The probability that the highest peak in the periodogram is caused by noise is eP.

[29] Here, it should be emphasized that Scargle power is only a measure for the significance of the highest peak in the periodogram. The detection of multiple periods Pi and the computation of their significance requires one additional step, that is, prewhitening of the data. It is summarized in Figure 9 and is basically the sequential removal of significant periods from the data until the noise level is reached. The decreasing resolution toward longer periods in the periodogram is accounted for by performing harmonic fits for a range of periods centered around the period of the highest peak. Pi is then assigned to the period that minimizes the variance of the resulting data–harmonic fit time series.

Figure 9.

Prewhitening flowchart. Pi are significant periods.

[30] HME1 periodograms are overviewed in Figure 10. Significant periods (FAP < 0.001) are detected at 12, 6, and 24.3 months. Other periods are insignificant with FAP > 0.1. Figure 11 shows the corresponding periodograms for HME2. Here, significant periods are at 12 and 5.9 months. There is no evidence for a quasi-2-year pattern. As a control test, similar analyses have been done on the observed low-latitude tides at various altitudes (not shown). Significant periods in (T, u) always equaled those of HME1 and v those of HME2. The annual and semiannual variations are a combination of tidal source and mean wind variability over the course of the year. Since they are not the focus of the present paper, the reader is referred to, i.e., Achatz et al. [2008] for a discussion of seasonal tidal variability based on model simulations.

Figure 10.

Lomb-Scargle analysis with prewhitening of HME1. Horizontal dotted lines and numbers indicate false-alarm probabilities of the highest peak in the spectrum (99.9%, 99%, and 90% significance). (a) Scargle power of HME1. Scargle power of HME1 after successively subtracting harmonic periods of (b) 12, (c) 6, and (d) 24.3 months. Significance of the remaining peaks in Figure 10d is below 90%. For details, see text.

Figure 11.

Lomb-Scargle analysis with prewhitening of HME2. Horizontal dotted lines and numbers indicate false-alarm probabilities of the highest peak in the spectrum (99.9%, 99%, and 90% significance). (a) Scargle power of HME2. Scargle power of HME2 after successively subtracting harmonic periods of (b) 12 and (c) 5.9 months. Significance of the remaining peaks in Figure 11c is below 90%. For details, see text.

[31] Of more interest here is the quasi-2-year variation. What is the reason? Why is it absent from HME2 and hence v? The eye-catching correspondence between QBO winds and HME1 (Figure 8) suggests that the tides are somehow affected by the QBO. Lomb-Scargle analysis (not shown) of the Singapore winds in Figure 8b yielded a March 2002 to December 2008 mean QBO period of 24.7 months (FAP < 0.001) which is close to the HME1 period. However, possible QBO effects are not necessarily imposed on the tides in the stratosphere. QBO variations extend into the MLT where they are out-of-phase with the stratospheric QBO winds [i.e., Burrage et al., 1996]. Indeed, a mesospheric QBO influence would be more plausible since this is the height region where dissipation sets in. In a model study, Ekanayake et al. [1997] found that eastward propagating diurnal tides are generally larger for easterly mean zonal winds because this Doppler shifts their frequencies toward higher values. They also noted that it is harder to dissipate a higher-frequency wave of comparable wavelength. Hence, a mesospheric QBO induced Doppler shift would be consistent with larger HME1 amplitudes during the westerly phase of the stratospheric QBO because the mesospheric QBO is easterly then. It also provides a tentative explanation of the lacking 2-year signal in low-latitude v. QBO effects in HME1 do not show up in the low-latitude v tide since the latter has a node there. HME2 is less affected by the mesospheric QBO since it has a low-latitude node in (T, u) and a comparatively short vertical wavelength leading to dissipation at lower altitudes. Hence, the Doppler shift mechanism described above will be less efficient for the upper mesospheric part of HME2.

[32] One can also think of alternative and/or additional QBO effects, including stratospheric filtering during upward propagation, i.e., vertical wavelengths distortions due to mean winds and hence altered dissipation [i.e., Forbes and Vincent, 1989]. Any closer examination of these processes and associated feedbacks between the tides, mean winds and dissipative effects will require more focused studies involving model simulations than is within the scope of this work. Model simulations are also required to unambiguously relate the observed 2-year amplitude variations to the QBO at all. The presented analysis supports a QBO interpretation but other (non-QBO) contributions are also possible, i.e., interannual variations in the tropospheric forcing. Lieberman et al. [2007] reported on interannual DE3 convective forcing variability and its relation to the El Niño/Southern Oscillation (ENSO) phenomenon, as indicated by a largely negative correlation between the Southern Oscillation Index (SOI) and latent heat release over the central and eastern Pacific. Performing a Lomb-Scargle analysis on March 2002 to December 2008 SOI data yielded a 26.8 month period at the 99% (FAP = 0.01) confidence level (not shown). This is not far from the 24.3 month period found in HME1 and certainly an issue worth to be pursued in the future.

[33] The analysis of variations on longer time scales, particularly of the solar cycle dependence, did not yield unequivocal results in the MLT. Various approaches (not shown) including wavelet analysis and fits to the observed tides and HMEs before and after subtracting the significant periods mentioned above indicated a slight amplitude increase with decreasing solar activity. The error bar, however, is compatible with no solar cycle dependence at all. More years of observations are necessary to conclusively separate it from variability due to the QBO and other sources. On the basis of current observation, there is no convincing proof for a significant solar cycle signal in the mesosphere/lower thermosphere DE3 tide.

6. Solar Cycle Tidal Variability in the Thermosphere

[34] The HME fits to the TIMED diagnostics in the MLT region now allow the prediction of the (T, ρ, u, v, w) tidal fields throughout the thermosphere into the exosphere. Figure 12 shows their latitude versus time distribution at 400 km altitude, based on the linearly interpolated solar flux–dependent HMEs in Figures 4 and 5 and using the HME fit coefficients from Figure 8.

Figure 12.

DE3 exosphere (400 km) amplitudes from HME1 and HME2. (a) Temperature. (b) Neutral density. (c) Zonal wind. (d) Meridional wind. (e) Vertical wind. For units, see color bar.

[35] The latitudinal structure of all fields is governed by HME1 because HME2 is subject to more dissipation at lower altitudes, as discussed in section 3. Hence, (T, ρ, u, w) still maximize at low latitudes and during boreal summer. The meridional wind tide, however, is very different compared to its MLT signature (Figure 6) since its horizontal shape has changed from HME2 (MLT) to HME1 (thermosphere). It now peaks at middle latitudes (compare Figure 3a) and times of maximum amplitude have changed accordingly from boreal winter to boreal summer. Note that a significant latitudinal broadening of the (T, ρ, u, v, w) structure occurs between the MLT region and 400 km. The horizontal shape of the amplitudes is independent of solar flux. All fields inherently show the quasi-2-year variation evident in the MLT results although it is partly masked by solar cycle induced amplitude variations, i.e., in density.

[36] The solar maximum to solar minimum amplitude increase in Figure 12 reflects the solar flux dependence of HME1, that is, the reduced dissipation for low F10.7cm levels, as has been discussed in section 3. Boreal summer amplitudes in T peak in 2008 at ∼7.5 K with lowest values in 2002 around 4.5 K. Density is much more sensitive, amplitudes increase from ∼1% in 2002 to ∼5.5% in 2008 and hence by roughly a factor 5. The solar cycle dependencies of (u, v) are large as well: u increases from ∼3 m/s to ∼10 m/s (factor 3). The midlatitude v amplitudes are somewhat larger in the Northern Hemisphere which reflects the small remaining contribution of HME2. At 40°N, amplitudes increase more than a factor 2, from ∼1.5 m/s (2002) to ∼3.5 m/s (2008). It is interesting to note that vertical wind amplitudes (∼11 cm/s) are almost independent (within 10%) of solar activity.

[37] Figure 13 overviews the vertical amplitude distribution at low latitudes and hence the tidal propagation characteristics from the MLT into the upper thermosphere and exosphere. Although this essentially reflects the vertical shape of the HME1 amplitudes in Figure 4, there are some noteworthy features evident here.

Figure 13.

DE3 amplitudes from HME1 and HME2, averaged between 5°S and 5°N. (a) Temperature. (b) Neutral density. (c) Zonal wind. (d) Meridional wind. (e) Vertical wind. For units, see color bar.

[38] 1. DE3 temperatures extend farther into the lower thermosphere than (ρ, u, v) owing to their relatively broad distribution around the peak. Amplitudes are still at the 9–10 K level at 150 km.

[39] 2. Density amplitudes rapidly decrease above the MLT peak but increase again in the upper thermosphere. This and the strong solar cycle dependence above the base of the thermosphere are of potential interest for reentry calculations.

[40] 3. Zonal wind amplitudes below 150 km, and hence throughout the ionospheric E region, are on the order of 10 m/s. Solar cycle effects become increasingly important with height. At 120 km, boreal summer amplitudes increase from 12 m/s (2002) to 15 m/s (2008) or 25%. At 150 km, the increase is about twice as large, from 7 m/s (2002) to 11 m/s (2008). This will likely introduce a considerable solar cycle effect on the E region dynamo modulation and hence on “wave-4” F region ionospheric properties.

[41] 4. DE3 meridional winds vanish at low latitudes and altitudes above 120 km.

[42] 5. DE3 vertical winds of about 15 cm/s persist throughout the thermosphere with a very broad vertical shape and a peak height of ∼250 km. How their vertical extent and magnitude contribute to “wave-4” ionospheric F region properties merits further exploration in the future.

[43] To date, HME fits are the only method to provide observation-based tidal estimates in the “thermospheric gap” between space-based observations in the MLT region and tidal diagnostics at ∼400 km based on accelerometer measurements. Revisiting older data sets, i.e., the WINDII on UARS observations, could make an important contribution at altitudes below 250 km to test the HME predictions in the dissipative region above the peak. However, validation is currently limited to comparisons with DE3 zonal wind and temperature tides from the CHAMP satellite. Note that these accelerometer measurements do not allow to derive meridional winds.

[44] CHAMP zonal wind tidal diagnostics at ∼400 km are overviewed by Häusler et al. [2007] and Häusler and Lühr [2009]. DE3 analyses are currently available from 2002–2005. Figure 14 compares them to the HME predictions at low latitudes. CHAMP and HME amplitudes maximize in boreal summer and reveal a similar solar cycle dependence. Observed amplitudes increase by 3 m/s from 2002 (4.5 m/s) to 2005 (7.5 m/s). This is matched by the 3 m/s increase of the predicted amplitudes from 3 m/s in 2002 to 6 m/s in 2005. Observed boreal summer maxima are about 1.5 m/s larger than the predicted ones with some variations from one year to another. This small offset is not a concern since it can easily be accounted for by HME errors and uncertainties in the TIMED tidal diagnostics. As outlined in section 2, TIDI DE3 amplitude accuracy is ∼10% and similar for SABER. HME1 fit error is ∼5% in boreal summer and on the order of 30% in boreal winter (Figure 8). These error sources already account for ∼0.5 m/s. CHAMP DE3 amplitude accuracy is 17% and the precision is ∼0.2 m/s [Häusler and Lühr, 2009]. This easily accounts for the remaining difference of ∼1 m/s between observation and prediction and is certainly a success, particularly when considering the inherent assumptions about dissipation and atmospheric background conditions in the HME computation. Within this limit, the results suggest that the low-latitude DE3 zonal wind tide in the upper thermosphere and exosphere can be fully attributed to direct tidal upward propagation from its tropospheric sources.

Figure 14.

Exosphere DE3 zonal wind amplitudes from CHAMP (solid curve) and from the HME analysis (dotted curve), averaged between 5°S and 5°N.

[45] Figure 15 shows the comparison between 2003 and 2007 CHAMP DE3 tidal temperature diagnostics and the HME predictions. CHAMP temperature tides are based on density data derived from accelerometer measurements [Bruinsma et al., 2006]. The densities are then further processed in a way to provide exosphere temperatures and the latter are finally analyzed on tides. See Forbes et al. [2009] for details.

Figure 15.

Exosphere DE3 temperature amplitudes from CHAMP (solid curve) and from the HME analysis (dotted curve), averaged between 5°S and 5°N.

[46] At a first glance, the temperature results in Figure 15 may look less satisfactorily than those for the zonal winds. HME predictions during boreal summer exceed the CHAMP results by ∼2.5 K or roughly a factor 2. Evidence for a high bias of ∼10% is already found in the MLT when comparing the HME fit results with the SABER observations (section 4) but this can only account for about 0.5 K in the thermosphere. Optimizing the vertical and horizontal fit ranges to give the best match to the observed CHAMP tides resulted in another 0.6 K and hence a total of 1.1 K. The remaining 1.4 K offset is in some parts related to the observed data. DE3 tides derived from combined CHAMP and GRACE densities yielded somewhat larger amplitudes, i.e., 3.7 K (CHAMP and GRACE) and 3.3 K (CHAMP) in August 2005 [Forbes et al., 2009]. The currently unexplained offset is therefore ∼1 K and on the same order as for the zonal wind but with opposite sign. Hence, HME predictions are somewhere in between DE3 zonal wind and temperature observations in the thermosphere and an indicator for the current level of consistency between the latter at low latitudes.

[47] CHAMP DE3 temperature tides do not show a pronounced solar flux dependence (note that 2002 is not included here) which is consistent with the HME prediction for the 2003–2007 time span. Lomb-Scargle analysis yielded a quasi-2-year variation of 23.4 months at the 95% confidence level which is not far away from the 24.3 months in HME1 (section 5). DE3 tides can apparently transport such interannual variability that is presumably caused by the QBO up into the exosphere. A similar analysis of DE3 zonal winds did not yield significant (<90% confidence) results because (1) the time series was too short (4 years instead of 5) and because (2) the quasi-2-year variation was masked by the large solar cycle signal.

7. Conclusions

[48] One of the overarching questions toward a better understanding of the climate and weather of the Sun-Earth system is the geospace response to variable waves from below. The present work demonstrates the effects of the important DE3 nonmigrating tide on the neutral part of the upper atmosphere. DE3 is forced by persistent, large-scale tropospheric weather systems and causes large longitudinal variations in MLT temperatures and winds, as observed by the SABER and TIDI instruments on the TIMED satellite. Using a physics-based empirical fit model, the TIMED measurements could be quantitatively linked to low-latitude DE3 tidal temperature and wind variations in the upper thermosphere. The results may be summarized as follows.

[49] 1. Observed upper thermospheric/exospheric DE3 tidal temperatures and winds are consistent with each other and fully attributable to direct tidal upward propagation from the troposphere.

[50] 2. A quasi-2-year 15–20% amplitude modulation in the MLT is presumably related to the QBO although a final proof requires further investigation. One likely cause for a QBO signal in the DE3 tides is enhanced (reduced) dissipation during the westerly (easterly) phase of the mesospheric QBO due to frequency Doppler shift.

[51] 3. The quasi-2-year signal extends up into the thermosphere and can be reconciled with DE3 temperature observations from CHAMP.

[52] 4. TIMED observations from 2002–2008 do not show a convincing evidence of a solar cycle effect in DE3 amplitudes at MLT heights.

[53] 5. Solar cycle effects become increasingly important above 120 km in the E region because of reduced tidal dissipation during solar minimum. In the thermosphere, density (factor 5) and horizontal winds (factor 3) are most sensitive whereas temperature (∼60%) and vertical wind (∼10%) are less affected.

[54] Tidal amplitudes on the order of 3 K and 7 m/s in the low-latitude thermosphere may not look very impressive but it should be emphasized that this is the DE3 contribution alone. Work in progress indicates that other diurnal and semidiurnal nonmigrating tides have similar effects. Aggregate tidal variations will therefore be much larger. The derived tidal density variations including their large solar cycle dependence are of potential interest for satellite trajectory and reentry calculations.

[55] Solar cycle effects become significant in the upper parts of the ionospheric E region where DE3 tidal winds modulate the electric fields. It is thus anticipated that “wave-4” longitudinal variations in F region ionospheric properties will increase with decreasing solar activity. The relative contribution of the 15 cm/s DE3 vertical winds throughout most parts of the low-latitude thermosphere yet needs to be explored.


[56] J.O. is supported by the DFG through its priority program CAWSES, grants OB 299/2-2 and OB 299/2-3. J.M.F. is supported under AFOSR MURI grant FA9550-07-1-0565, and grant NNX07AB74G from the NASA TIMED Program. K.H. is supported by the DFG through its priority program CAWSES, grant LU 446/9-1. Q.W. is supported by NASA grants NNX07AB76G and NNX09AG64G to NCAR. F10.7cm solar flux data are provided by Space Weather Canada. Singapore zonal winds are provided by Institute of Meteorology, Freie Universität Berlin.