Middle and upper thermosphere density structures due to nonmigrating tides

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012ja018087, 2012 Middle and upper thermosphere density structures due to nonmigrating tides Jeffrey M. Forbes, 1 Xiaoli Zhang, 1 and Sean Bruinsma 2 Received 2 July 2012; revised 27 August 2012; accepted 19 September 2012; published 9 November [1] Density measurements from the SETA satellites near 200 km during , and the CHAMP and GRACE satellites between 350 and 550 km during , are used to investigate longitudinal structures in density due to nonmigrating tides, and to evaluate performance of the recently-created Climatological Tidal Model of the Thermosphere (CTMT). Amplitudes for the diurnal and semidiurnal tidal components fall roughly in the range of 4 10%. Diurnal tides at middle and low latitudes are often characterized by wave-3 and/or wave-4 structures, consistent with the presence of the eastward-propagating diurnal tides with zonal wave numbers s = 2 and s = 3 (DE2 and DE3, respectively) and with expected seasonal variability based on previous works. Semidiurnal structures often reflect the presence of the eastward-propagating tide with s = 2 (SE2), which gives rise to wave-4 structures that have a more antisymmetric relationship between N. and S. hemispheres. Similarities in structures between different years underscore the fact that the thermosphere is subject to repeatable and reproducible forcing by upward-propagating tides, but there are also occasions where considerable departures from climatology occur. Wave-2 structures at high latitudes likely contain signatures of the eastward-propagating diurnal tide with s = 1 (DE1) and the zonallysymmetric (s = 0) semidiurnal oscillation (S0) propagating upwards from below, but these and other waves that produce wave-2 can also be forced in-situ by high-latitude processes. The CTMT captures the salient features of the observations at middle and low latitudes, although with lower amplitudes that are likely due to phase cancelation effects resulting from averaging over multiple years ( ). We propose that some discrepancies between the CTMT and our observational results may be associated with wave components arising in-situ in the thermosphere as the result of nonlinear tide-tide interactions and plasma neutral interactions, the latter being especially prominent at high latitudes where the displaced geomagnetic frame is particularly influential. Modeling studies are required to validate these proposed mechanisms, however. Citation: Forbes, J. M., X. Zhang, and S. Bruinsma (2012), Middle and upper thermosphere density structures due to nonmigrating tides, J. Geophys. Res., 117,, doi: /2012ja Introduction [2] In recent works we demonstrated the existence of longitudinal density structures in total mass density and inferred exosphere temperatures in the upper thermosphere ( km), and their connection to upward-propagating tides as measured in the lower thermosphere between 90 and 100 km [Forbes et al., 2009; Oberheide et al., 2011a, 2011b]. The upper thermosphere measurements originate from 1 Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado, USA. 2 Department of Terrestrial and Planetary Geodesy, Centre National d Etudes Spatiales, Toulouse, France. Corresponding author: J. M. Forbes, Department of Aerospace Engineering Sciences, University of Colorado Boulder, Campus Box 429, Boulder, CO , USA. (forbes@colorado.edu) American Geophysical Union. All Rights Reserved /12/2012JA accelerometer data from the CHAMP and GRACE satellites, and the lower thermosphere data originate from temperature and wind measurements by the SABER and TIDI instruments from the TIMED spacecraft. In this paper we examine rare measurements of longitude structures in the middle thermosphere ( km) in the context of the above discoveries. As described in more detail later on, these measurements were made by the Satellite Electrostatic Triaxial Accelerometer (SETA) Experiment on two low-orbiting Air force satellites during [3] The longitude structures noted above are thought to be primarily generated by solar tides forced by troposphere heating [Zhang et al., 2010a, 2010b], although longitude-dependent tides can also be forced by nonlinear tide-tide interactions [Angelats i Coll and Forbes, 2002; Hagan et al., 2009]. Whatever the combination of sources, a spectrum of diurnal and semidiurnal eastward- and westward-propagating tides enters the thermosphere at 100 km, and this spectrum evolves 1of11

2 Figure 1. Tidal density perturbations (percent about the diurnal mean) versus height and longitude over the equator during September, as predicted by the climatological tidal model of the thermosphere (CTMT) [Oberheide et al., 2011a] for local solar times of (left) 1800 and (right) The horizontal white dashed lines at 90 and 110 km denote the range of altitudes wherein TIMED-SABER temperature and TIMED- TIDI wind measurements were used along with dissipative tidal theory to construct the CTMT, which extends the model results to 400 km. The dashed black lines at km denote the approximate altitudes where CHAMP data originate and where the CTMT was validated against CHAMP measurements for the DE3 and SE2 tidal components [Oberheide et al., 2011b] (see section 2 for a summary of tidal nomenclature). The solid black lines denote the km altitudes where the SETA density measurements in the present study originate. with height due to the effects of molecular dissipation, potentially moderated by the effects of mean winds. Molecular dissipation preferentially damps the waves with shorter vertical wavelengths, allowing the longest-scale waves to reach, e.g., CHAMP and GRACE altitudes. How the wave spectrum evolves with height, however, has never been measured. The SETA measurements near 200 km will provide a first but limited perspective on this evolution. Accelerometer measurements of densities and cross-track winds from the European Space Agency s GOCE (Gravity and Ocean Circulation Explorer) satellite near 250 km will also be available soon to provide insights on middle versus upper thermosphere differences. [4] In this paper insight into our current understanding of the tidal spectrum evolution with height will also be provided through upward extrapolation of the measured tidal spectrum between km using dissipative tidal theory. The framework for this already exists [Oberheide et al., 2011a, 2011b]. In these works, a set of physics-based functions called Hough Mode Extensions (HMEs) are fit to monthly climatologies of TIMED SABER tidal temperatures and TIMED TIDI tidal winds between 90 and 110 km, and the HMEs are used to extrapolate the tidal fields to 400 km; a climatological tidal model of the thermosphere ( CTMT ) thus results that corresponds to average solar conditions (F10.7 = 110 sfu). An example is provided in Figure 1, which also demonstrates that quantities that are not measured, such as total mass density, emerge from the fits as part of the dynamical relations that exist self-consistently internal to the HMEs. Within the CTMT, the HMEs for individual diurnal and semidiurnal tidal components (with a range of vertical wavelengths) are superimposed to provide the total tidal perturbations as a function of height, latitude, local time, longitude and month of the year for average solar conditions. Moreover, since the HMEs provide internally-consistent amplitude and phase information for the 3-dimensional wind field, temperature and density, all of these parameters are predicted, even in regions where observations do not exist. This is how global density perturbations can be estimated throughout the thermosphere from temperatures and winds measured in the lower thermosphere. [5] The horizontal lines in Figure 1 indicate the nominal , and km altitude regimes where the TIMED, SETA and CHAMP data originate. While the GRACE data used in the present study originate from roughly km, and thus beyond the upper altitude of CTMT, the differences in tidal density perturbations between CHAMP and GRACE are sufficiently small [cf. Bruinsma and Forbes, 2010] that their intercomparison with CTMT is still meaningful. One sees that these altitudes occur at different points in the evolution of the tidal spectrum with height, and that the SETA data occur at a good intermediary height between the lower and upper boundaries of the thermosphere height regime under investigation. Shorter-scale waves dissipate at the lower altitudes, leaving the longer-wavelength waves to penetrate to higher altitudes, eventually approaching asymptotically constant amplitudes and phases at the highest altitudes for the temperature and horizontal wind fields due to very efficient vertical diffusion of heat and momentum; however, the vertical wind and density perturbations do not follow this behavior. Note also that the spectral evolution with height not only varies with local time (Figure 1) but also with latitude during any given month. Figure 1 is just a typical example for illustration purposes. [6] In this paper we seek to evaluate our understanding of vertical tidal propagation in the thermosphere through comparison of CTMT density perturbations and those measured by the SETA, CHAMP and GRACE satellites. Keep in mind 2of11

3 Figure 2. A typical set of longitudinal density structures for June. The left 4 panels correspond to LST, while the right 4 panels correspond to LST. These local times pertain to the equatorial crossing. Local time differences as small as 8 hours occur at 80 latitude when the satellites pass over the polar regions. The top panels compare CTMT with CHAMP 2007 results, while the bottom panels compare CTMT with SETA2 measurements. As described in the text, wave-1 is removed from all data to better isolate wave-2, -3 and -4 structures, especially at high latitudes. that these density predictions are not based on density measurements, but only on temperatures and winds measured between 90 and 110 km altitude. Another objective of this work is to interpret the SETA, CHAMP and GRACE density measurements, and to identify the primary tidal oscillations that govern the observed tidal structures. [7] In the following sections we present a brief overview of the data used in this study, and provide an overview of the methodology employed to depict and interpret the presence of diurnal and semidiurnal tides in these data. 2. Data Description [8] The SETA satellites were in roughly km 1030/2230 LST (local solar time) Sun-synchronous orbits. The SETA-2 experiment provided accelerometer measurements of total mass density during May-November, 1982, and the SETA-3 data were collected during July, 1983 March, These data were described and analyzed previously with respect to geomagnetic activity [Forbes et al., 1996; Rhoden et al., 2000], wave structures [Forbes et al., 1995] and longitudinal variability [Forbes et al., 1999], but not in the context of nonmigrating tides. Solar activity levels during May 1982 March 1984 were similar to those that existed during the solar maximum periods. Only data for quiet geomagnetic conditions K p 3 are included in the analysis. To remove altitude variations and thus facilitate intercomparisons between data sets, the SETA data were normalized to 200 km using the NRLMSISE00 model [Picone et al., 2002]. Upon examination of these normalized SETA data, a fairly large wave-1 longitude component was evident that likely had its origins in differences in altitude and/or local time that were not removed by the model between ascending and descending parts of the orbit, and/or effects associated with geomagnetic versus geographic coordinate system displacements. In addition, the CHAMP and GRACE data primarily revealed wave-2, wave-3 and wave-4 structures as opposed to wave-1 structures. Therefore, in all the data to be displayed herein, density perturbations were cast in terms of percent deviations from the zonal mean, and the wave-1 component was removed. This also enabled better examinations of the wave-2-3, and -4 structures at high latitudes, whereas otherwise the wave-1 structure dominated the pattern. [9] The CHAMP and GRACE orbits covered the km and km orbital regimes, and were nearpolar. Since the perturbation densities are not strongly height dependent [Bruinsma and Forbes, 2010], no normalization using NRLMSISE00 was performed. Due to the local time precessions of the CHAMP and GRACE orbits, there occurred about two periods per year between 2002 and 2010 when each one was nearly co-planar (i.e., in a 1030/2230 LST orbit) with the SETA satellite. Representative samples from a few of these co-planar events that occurred during the month of June are illustrated in Figure 2. Only comparisons with CHAMP 2007 data are shown here, although similar results from CHAMP in 2002 and GRACE in 2004 and 2008 are also available. The full set of SETA-CHAMP-GRACE-CTMT comparisons for all 12 months of the year are available as an auxiliary file. 1 One will note that some depictions of SETA data are somewhat less smooth than CHAMP or GRACE. This is because CHAMP and GRACE are generally averaged over 10 days or 1 Auxiliary materials are available in the HTML. doi: / 2012JA of11

4 more, whereas for SETA, due to data gaps, averaging intervals are more typically in the 3 7 day range. [10] In Figure 2, the left 4 panels correspond to LST, and the right 4 panels to LST. These local times pertain to the equatorial crossing. Local time differences as small as 8 hours occur at 80 latitude when the satellites pass over the polar regions. The top panels correspond to the altitude of CHAMP (nominally 400 km), and the bottom panels to the altitude of SETA-2 (nominally 200 km). The corresponding results from CTMT are also shown. Note that most of the maximum amplitudes displayed in each panel fall within the range of about 4 7%. Comparing the CHAMP and SETA-2 morning ( LST) data, one can detect remarkable similarities given the difference in years (2007 for CHAMP versus 1982 for SETA-2). For instance, wave-3 structures of similar amplitude appear in the N. Hemisphere of both data sets, with some phase shift between them. In the S. Hemisphere some mixture of wave-2 and wave-3 prevails in the N. Hemisphere for CHAMP, but wave-3 obtains in the S. hemisphere for SETA-2. It is also noteworthy that many of the structures extend well into the auroral and polar regions. At some longitudes both data sets also indicate 180 phase shifts between hemispheres. The CTMT results share many of these same characteristics. There are also many similarities between the CHAMP and SETA-2 structures displayed in Figure 2 for the evening data ( LST). These similarities between altitudes and between widely-space time periods are consistent with the concept that the thermosphere is subject to regular and repeatable forcing from the lower atmosphere in terms of nonmigrating tides. What is also notable, though, is that while the CHAMP and SETA-2 longitude structures share many similarities within a given local time, the morning and evening structures at a given altitude (i.e., for each individual satellite) are not that similar. As a point of reference, given the 12-hour differences in local time over most latitudes, if these structures had resulted from a single vertically-propagating diurnal tide, then at each altitude the day and night structures would be identical and 180 out of phase. This is clearly not the case, and suggests that the observed structures contain a strong presence of semidiurnal nonmigrating tides, and mixtures of tides with different longitudinal characteristics. [11] Consistent with the above, we found it most informative to add one additional layer of processing to these data to facilitate interpretation. In the following we present results for both r diff =(A D)/2 and r avg =(A + D)/2, where A represents measurements along the ascending part of the orbit, and D represents measurements along the descending part of the orbit. For a 12-hour difference between A and D and considering the 24-hour period of diurnal oscillations and 12-hour period of semidiurnal oscillations, r diff provides a measure of the diurnal component of the density variation, whereas r avg primarily contains semidiurnal tides (the diurnal mean has been removed). In principle, the former can contain terdiurnal tides with zonal wave numbers s 2 and the latter can contain stationary planetary waves with s 2. However, based on our own analyses of CHAMP and GRACE data over periods of full local time coverage (130 days), we have no reason to believe that these waves regularly exist in the thermosphere with amplitudes comparable with those of diurnal and semidiurnal tides, although this does not preclude their sporadic occurrence. [12] At this point it is also necessary to introduce some tidal notation and remind the reader about the difference between a space-based perspective and a ground-based perspective of atmospheric tides, and to relate different types of longitude structures with various candidate waves. If a tide is defined as an atmospheric oscillation of the form A n;s cos nwt þ sl f n;s ð1þ where t = time (days), W = rotation rate of the earth = 2p day 1, l = longitude, n (= 1, 2,..) denotes a sub-harmonic of a solar day, s(=.. 3, 2,..0, 1, 2,..) is the zonal wave number, and the amplitude A n,s and phase f n,s are functions of height and latitude, then in the local time frame we have A n;s cos nwt LT þ ðs nþl f n;s ð2þ In this context, n = 1, 2, 3 represent oscillations with periods corresponding to 24 hours, 12 hours, 8 hours, and hence are referred to as diurnal, semidiurnal and terdiurnal tides, respectively. Eastward (westward) propagation corresponds to s <0(s > 0). Phase is defined as the time of maximum at zero longitude; in other words, the local time at Greenwich. We utilize the notation DWs or DEs to denote a westward or eastward-propagating diurnal tide, respectively, with zonal wave number s. For semidiurnal and terdiurnal oscillations S and T replaces D. The standing oscillations are denoted D0, S0, T0, and stationary planetary waves with zonal wave number s are expressed as SPWs. From a quasi-sun-synchronous space-based perspective (i.e., t LT constant in equation (2)), a tide with a frequency nw and zonal wave number s appears as an s n variation in longitude (i.e., s n maximaand minima); Thus, DE3, DW5, SE2, SW6 appear as wave-4; DE2, DW4, SE1, SW5 appear as wave-3; and DE1, DW3, S0, SW4 appear as wave-2. [13] Furthermore, note that from equation (2) that data from the ascending part of the orbit for a single diurnal tide with zonal wave number s can be expressed as and that the maxima occur at A asc cosðwt LT þ ðs 1Þl fþ; ð3þ l M ¼ f Wt LT s 1 þ M 2p s 1 where M =0,1, s and s 1. For ascending and descending parts of an orbit 12 hours apart in local time (i.e., polar orbit) A desc = A asc,sothatamplitudea of the tide is well approximated by r diff, and in fact since t LT is known, f can be derived from the observed longitude of maximum, provided a single wave number s is dominant. Moreover, since all of our forthcoming satellite-satellite and satellite-model intercomparisons are at the same local time, both amplitude and phase comparisons are possible. Note that the above means of deriving amplitudes and phases cannot be applied to the migrating diurnal tide since s = 1, there is no longitudinal wave pattern, and A asc and A desc can have maxima other than A n,s (in fact, even zero). Of course, when more than one wave component (value of s) is present, a quantitative comparison between satellite results is not necessarily definitive. Similar considerations apply for the semidiurnal tide. ð4þ 4of11

5 Figure 3. Diurnal tide estimates for September. Maximum percent density perturbation is shown at the top of each panel. The top panels illustrate upper thermosphere results for (a) GRACE 2006, (b) CTMT and (c) CHAMP The bottom panels compare middle thermosphere results for (d) SETA2, (e) CTMT, and (f) SETA3. [14] In the following section we now present and discuss several examples where r diff and r avg are compared between CHAMP, GRACE, SETA and CTMT, and are interpreted in terms of diurnal and semidiurnal tidal components where possible. 3. Results [15] Figure 3 presents a series of r diff ( diurnal tide ) depictions for SETA, CHAMP, GRACE and CTMT for September conditions, when wave-4 structures are known to be prevalent in the thermosphere-ionosphere system and DE3 is known to be the primary diurnal tide responsible for these structures [Forbes et al., 2009; Pedatella et al., 2008; Oberheide et al., 2011b]. The GRACE data for 2006 (Figure 3a) are characterized by a wave-4 structure mainly confined to 40 latitude and with amplitudes in the range 8%. These features transition to wave-3 and wave-2 structures at higher latitudes. Similar structures are predicted by CTMT (Figure 3b) at low to middle latitudes, with good agreement in phase but amplitudes more typically in the range 3%. In 2005 the CHAMP data (Figure 3c) reveal similar 4% wave-4 perturbations in the S. Hemisphere, but wave-3 between 0 30 and wave-2 at higher northern latitudes. The SETA-2 density perturbations near 200 km (Figure 3d) are of similar amplitude (4%) but dominated by wave-3; apparently DE3 is suppressed relative to DE2 during this particular period (see following discussion in connection with Figure 4, where similar structures are observed). The CTMT prediction at 200 km (Figure 3e) is phase-shifted with respect to that at higher altitudes (Figure 3b) as expected (cf. Figure 1) but underestimates the SETA-2 amplitudes by at least a factor of 2. The SETA-3 data on the other hand (Figure 3f) are dominated by wave-4 and in rather good phase agreement with CTMT, but with larger amplitudes (4%). Since the SETA satellites cover an altitude region ( km) where phase variations with height still exist (cf. Figure 1), tilted structures such as Figure 3f may actually reflect changes in height of the satellite with latitude and between the day and night sides of the orbit. [16] Figure 4 shows similar r diff results for the month of December. Here all of the displayed structures exhibit a predominance of wave-3, consistent with the expected dominance of DE2 propagating upwards from the lower thermosphere during December [Forbes et al., 2009; Pedatella et al., 2008]. As reflected in CTMT, DE2 possesses a broader latitudinal extent than DE3 (cf. Figure 3). The 2004 GRACE results (Figure 4a) and CTMT (Figure 4b) in the upper thermosphere are in very good agreement in terms of phase, but with CTMT (<2%) underestimating the observed amplitudes (4%) by over a factor of 2. The CHAMP 2009 amplitudes (6%) favor southern latitudes and are significantly larger than CTMT, but the phasing is in good agreement. CTMT is phase-shifted at 200 km (Figure 4d) with respect to its higher-altitude counterpart (Figure 4b), but with half the amplitude. SETA-3 5of11

6 Figure 4. Diurnal tide estimates for December. Maximum percent density perturbation is shown at the top of each panel. The top panels illustrate upper thermosphere results for (a) GRACE 2004, (b) CTMT and (c) CHAMP The bottom panels compare middle thermosphere results for (d) CTMT, and (e) SETA3. similarly exhibits a strong wave-3 signature, with amplitudes of order 4%, but with phasing similar to the observations at higher altitudes. It is interesting to note that between 60 and 80 latitude the observed structures tend to be more wave- 2-like. This was also noted in connection with Figure 2, and hints of this behavior can be seen in CTMT. These wave-2 structures may be due in part to DE1, which has still greater latitudinal extent than DE2. However, it cannot be discounted that in-situ processes may be at play at high latitudes. [17] In summary, given that the observations originate from different years, the illustrated diurnal density variations are consistent between the data sets examined here as well as with other observations. The September results are dominated by wave-4, consistent with the climatological dominance of DE3 during this month as revealed by CTMT. Amplitudes are generally of order 4 8%. Similar amplitudes are revealed in December, except with a preference for wave-3, consistent with the climatological expectation that DE2 is the predominant diurnal tide during this month. The primary departure from the above results is the strong presence of wave-3 during September near 200 km (Figure 4d) which suggests that there can sometimes be significant departures from climatology. In addition, while CTMT is accurate in terms of its phase predictions, its diurnal amplitudes underestimate observed ones by factors of 2 3. [18] We now turn to an examination of the complementary semidiurnal tide results for September (Figure 5) and December (Figure 6). Beginning with the September CTMT results at 400 km (Figure 5b), we again see a strong wave-4 presence, with one major difference from the diurnal tide results in Figure 3; whereas the diurnal tide structures tend to be more or less in phase between N. and S. Hemispheres, the semidiurnal results reveal a 180 phase shift between hemispheres that occurs within the equatorial region. Indeed the GRACE 2006 and CHAMP 2005 observations share this same characteristic, with amplitudes of order 9% and 7%, respectively, as compared with 5% for CTMT. In addition, both the model and data in the upper thermosphere indicate a strong signature of wave-4 in the S.Hemisphere, but less definitively so in the N.Hemisphere. The signature of wave-4 in CTMT is primarily due to SE2, and we suspect the same is true for the observations. The hemispheric differences and deviation from wave-4 in CTMT is primarily due to the presence of S0. As discussed in section 5, the non-zero equatorial wave-4 values and hemispheric differences are explicable in terms of an in-situ generated and symmetric SE2 component, which is not included in the CTMT. At 200 km, the CTMT (Figure 5e) retains a strong wave-4 structure, significantly phase-shifted from the higher altitudes. On the other hand, the SETA-2 results indicate a strong wave- 2 structure with largest amplitudes in the S. Hemisphere. We suspect that this is attributable to S0, but theoretically SW4 could be playing a role as well, especially at low latitudes. We cannot say whether the differences between Figures 5d and 5a are the result of an altitude effect, or because different years are compared. The SETA-3 structures are more consistent with the other results in Figure 5, revealing a predominant wave-4- like structure southward of +20 latitude, but less well-defined 6of11

7 Figure 5. Same as Figure 3, except for semidiurnal tide during September. Figure 6. Same as Figure 4, except for semidiurnal tide during December. 7of11

8 Figure 7. Diurnal tide estimates for June. Maximum percent density perturbation is shown at the top of each panel. The top panels illustrate upper thermosphere results for (a) GRACE 2004, (b) CTMT and (c) CHAMP The bottom panels compare middle thermosphere results for (d) CTMT, and (e) SETA2. behavior northward of this latitude. Similar to the diurnal tide results, both the data and CTMT reflect wave-2 characteristics at high (and sometimes middle) latitudes. At least for CTMT, this is due primarily to S0. In the case of the density data, other influences may be involved; these will be discussed later in section 4. [19] The December semidiurnal results at upper levels (Figures 6a 6c) also contain strong wave-4 signatures, this time in the N. Hemisphere. The GRACE 2004 and CHAMP 2009 observations shift to more wave-2-like structures in the S. Hemisphere, while CTMT retains a wave-4 character. Although, at 200 km (Figure 6d) CTMT is predominantly wave-3 due to the presence of SE1 and/or SW5, but does transition to wave-2 in the S. Hemisphere, mainly due to the influence of S0. Note also that the SETA3 data (Figure 6e) are strongly wave-3, consistent with CTMT in the middle thermosphere. [20] By and large the semidiurnal amplitudes in Figure 5 are as large as the diurnal counterparts in Figure 3, with amplitudes roughly of order 4 8%. However, semidiurnal phases tend to be more asymmetric in character compared to the diurnal tide results. And, whereas the diurnal tide shifted from predominance of wave-4 in September to wave-3 in December, the semidiurnal tide during December still contains strong signatures of wave-4, both in the data and CTMT. The CTMT captures most of the observed semidiurnal structures in both amplitude and phase, although some tendency to underestimate perturbation densities is still present for the semidiurnal tide. One departure is the stronger presence of wave-2 in the S. Hemisphere GRACE 2004 and CHAMP 2009 results (Figures 6a and 6c) as compared with CTMT, which likely reflects a much greater influence of S0. Finally, Figures 7 and 8 show the diurnal and semidiurnal tide results, respectively, for June. For the diurnal tide (Figure 7), a consistent feature is a strong negative density perturbation near 180 longitude flanked on either side by positive density perturbations (however, note that this feature is centered near 120 longitude in the CTMT at 200 km). The CHAMP 2007 (Figure 7a) and GRACE 2004 (Figure 7c) structures are remarkably similar, and consistent with CTMT, although the CTMT underestimates the observed amplitude structures. Both the model and data at these altitudes reflect some mixture of wave-3 and wave-4, indicating the likely presence of DE2 and DE3. Similar structures are seen near 200 km (Figure 7e for SETA2 and Figure 7d for CTMT), except with some phase-shifting to the west. The CTMT underestimates tidal amplitudes by about 25% in the upper thermosphere and more than a factor of 2 near 200 km. [21] The semidiurnal tide during June (Figure 8) reveals the following characteristics. The CHAMP 2007 (Figure 8c) and GRACE 2004 (Figure 8a) results are again remarkably similar in the amplitude and phase characteristics of their density structures, with a strong presence of wave-4 and a tendency for phase asymmetry between hemispheres. This behavior is also reflected in the SETA2 results at 200 km (Figure 8e) and in CTMT in both altitude regimes, suggesting the predominance of SE2. Again, one sees the predominance of wave-2 at high latitudes, likely reflecting the presence of S0. The 8of11

9 Figure 8. Same as Figure 7, except for semidiurnal tide during June. presence of S0 in CTMT also significantly distorts the SE2 wave-4 pattern, and shifts the negative density perturbations at high altitudes such that they occur near the equator (Figure 8b). This particular feature is not seen in the observations, and may be indication that S0 has different latitudinal structures between the observations and CTMT, and/or that a symmetric component to SE2 exists that is not in the CTMT (see following discussion). 4. Concluding Remarks [22] This paper presents and analyzes longitudinal structures in density based on accelerometer measurements during for the SETA satellite experiment near 200 km, and during for the CHAMP and GRACE satellites in the km height range. Based on the results presented here for June, September and December, and supported by similar results for other months contained in the auxiliary files to this paper (Figures S1 and S2), we summarize our results as follows: [23] 1. Longitude structures consistent with nonmigrating tides are prevalent throughout the thermosphere during all months and levels of solar activity. Moreover, these density structures are global in extent and sometimes extend well into polar regions. [24] 2. Diurnal tide amplitudes for CHAMP, GRACE and SETA are usually in the range 4 8% and often reflect the presence of the DE3 and/or DE2 tidal components. The preferential presence of DE3 and DE2 in the thermosphere is consistent with the long vertical wavelengths associated with these waves, and hence their penetration to high altitudes. Density structures associated with DE3 and DE2 tend to extend to high latitudes and often maintain phase coherence over wide latitude bands. [25] 3. Semidiurnal amplitudes are of the same order as diurnal amplitudes and often reflect the presence of SE2, which gives rise to wave-4 structures. Consistent with SE2, and in contrast to the diurnal tide, phase structures often exhibit phase asymmetries about the equator. However, there exists evidence for a symmetric component to SE2 as well (see item 6 below). [26] 4. There is often remarkable similarity between tidal structures spanning different years and altitude regimes. This is consistent with the concept that the thermosphere is subject to regular and repeatable forcing from the lower atmosphere in terms of non migrating tides. However, there are sometimes distinct departures from expected behavior which suggests that the thermosphere departs significantly from climatology on some occasions. These statements are consistent with the capability of the CTMT to capture the salient characteristics of many of the observed longitude structures at middle and low latitudes, except that it consistently underestimates observed amplitudes. However, the CTMT represents a fit to 5-year and 60-day mean tidal components, whereas the density structures analyzed here are averages over 5 10 days. It is quite possible that phase cancelation effects inherent in the averaging employed by the model account for this difference. [27] 5. Both the diurnal and semidiurnal density perturbations are often characterized by wave-2 at high latitudes (e.g., ) and sometimes middle latitudes. In the case of the semidiurnal tide, and based on diagnosis of the CTMT, as well as the fact that s = 0 structures have at least one 9of11

10 Figure 9. Schematic illustrating nonmigrating tides generated by SPW1 modulation of DW1 and DW2 and by-products. Wave-0, wave-1, wave-2 refer to the types of longitudinal structures (corresponding to zonal wave numbers s = 1, s = 2, s = 3, respectively) as viewed from the near-sun-synchronous satellite frame, and produced by the associated tidal components (DW1, DW2), (D0, DW2, SW1, SW3), and (DE1, DW3, S0, SW4), respectively. See text for further explanation. maximum at the pole in the density field, these wave-2 structures at high latitudes likely reflect the presence of S0. For the diurnal tide, some fraction of the high-latitude wave-2 structures are likely due to DE1, which extends to higher latitudes than DE2 or DE3. However, application of the present methodology to separate diurnal and semidiurnal tides at high latitudes could be somewhat flawed; since ascending and descending parts of the orbit are not as close to 12 hours apart as at lower latitudes, cross-contamination of diurnal and semidiurnal tides can occur in r diff (a measure of the diurnal tide) and r avg (a measure of the semidiurnal tide). Thus, for instance, the presence of S0 might (to some degree) leak into the wave-2 determination for the diurnal component. On the other hand, in many cases the structures at lower latitudes extend smoothly well beyond 60 latitude, suggesting that they arise from one and the same tidal component. Nevertheless, given the prevalence of a wave-2 signature in both the diurnal and semidiurnal components, it is likely that some degree of in-situ generation is present. [28] Quantitative determination of the different longitudinal wave number components that are generated in-situ at high latitudes is difficult given the complexity of this regime. For instance, at SETA altitudes low-density cells near dawn and dusk and high-density cells near noon and midnight were shown to exist in thermosphere general circulation simulations and in density measurements obtained by satellite accelerometers [Crowley et al., 1996; Schoendorf et al., 1996a, 1996b]; in other words, a semidiurnal variation. However, there are undoubtedly diurnal variations in conductivity and Joule heating, and all of these processes are ordered in a magnetic coordinate system displaced from the geographic frame. Nevertheless, we can ascertain in broad qualitative terms how components that contribute to a wave- 2 longitude structure from a Sun-synchronous orbit (e.g., DE1, DW3, S0, SW4) might be generated at high latitudes. Consider that some of the major components that likely exist at high latitudes consist of DW1, SW2, and SPW1, the former two arising from rotation of Earth with respect to the Sun, and the latter arising from the displaced geomagnetic coordinate system. Setting aside tide-tide interactions, modulation of either DW1 or SW2 by SPW1 (mathematically, cosl) gives rise to the sum and difference wave numbers, e.g., in the context of equations (1) and (2) we have: cosl cosðnwt þ sl fþ! cosðnwt þ ðs þ 1Þl fþ þ cosðnwt þ ðs 1Þl fþ ð5þ cosl cosðnwt LT þ ðs nþl fþ! cosðnwt LT þ ðs n þ 1Þl fþ þ cosðnwt LT þ ðs n 1Þl fþ ð6þ Figure 9 describes schematically the ramifications of equations (5) and (6). Beginning with SPW1 in the middle of the diagram, and following the circled number 1 s (which denotes primary interaction) up or down, one can see that SPW1 modulation of DW1 (n = 1, s = 1; up ) yields the secondary products D0 (n = 1, s = 0) and DW2 (n = 1, s = 2), and that SPW1 modulation of SW2 (n = 2, s = 2; down ) yields the secondary products SW1 (n = 2, s = 1) and SW3 (n = 2, s = 3). What this means is that if a dynamical structure (winds, temperature, or density) is defined by the sum of DW1 and SW2 in the geographic frame, and this structure is tilted into the geomagnetic frame (essentially wave-1 longitude variation in the geographic frame), then we would expect D0, DW2, SW1 and SW3 to constitute important components of this latter structure from the geographic frame perspective. As indicated in Figure 9, these tidal components are all observed as wave-1 longitude structures in the near-sunsynchronous satellite frame. One can imagine that these secondary products might also be modulated by SPW1 (following the circled number 2 s in Figure 9) to produce the tertiary products DE1, DW3, S0, SW4 in the same fashion. These tertiary products all appear as wave-2 from the Sun-synchronous 10 of 11

11 satellite frame (see equation (2)). Since the longitude-mean and wave-1 components are removed from the SETA data prior to analysis, it should not be surprising that wave-2 in the form of DE1 and S0 and/or DW3and SW4 should be present in the SETA data at high latitudes, and that such wave components would not be represented in the CTMT given its fundamental assumptions. This heuristic analysis would of course benefit from quantitative verification using a thermosphere-ionosphere general circulation model. [29] 6. There are additional ways in which wave components can be generated in-situ in the thermosphere, and thus account for some discrepancies in the results presented earlier. For instance, the observed September semidiurnal tide wave-4 structures attributed to SE2 in Figure 5 are stronger in the S. Hemisphere as compared with the N. Hemisphere, whereas this feature is missing from the CTMT. In addition, there are non-zero wave-4 amplitudes at the equator, in contrast to the near-zero values for CTMT; similar evidence for a non-zero equatorial SE2 exists in the June data in Figure 8. An SE2 symmetric component (which is not prominent in the CTMT) with non-zero equatorial values could explain both of these discrepancies, the hemispheric differences being accounted for by positive (negative) interference effects in the S. (N.) Hemispheres between symmetric and antisymmetric components. As shown by Hagan et al. [2009] using the National Center for Atmospheric Research (NCAR) Thermosphere Ionosphere Mesosphere Electrodynamics General Circulation Model (TIME GCM), nonlinear interaction between DE3 and DW1 can produce SE2 and SPW4 by this process with non-zero values at the equator. Note that SPW4 can also be seen as wave-4 in the r avg depictions in Figures 5 and 6. Creation of these products follows the same sum and difference rule employed to arrive at equations (5) and (6), except that both the frequency and zonal wave number are summed and differenced (see Hagan et al. [2009] for details). Along a similar vein, Oberheide et al. [2011a] deduced that D0 and DW2 also arise in part by in-situ processes, since CTMT significantly underestimates observed values. Through the same reasoning, nonlinear interaction between DE2 and D0 (DW2) can produce SE2 and SPW2 (S0 and SPW4). These sources of SE2 and SPW4 may be playing a role in producing differences in wave-4 structures between observations and CTMT as well. [30] As a second example, consider that the September diurnal tide wave-4 structure revealed by GRACE data in Figure 3 is confined within 40 latitude, more or less consistent with dominance of an upward-propagating DE3 as revealed in the CTMT. However, the wave-4 structures in the CHAMP and SETA3 data in the same figure extend to much higher latitudes, suggesting an additional wave-4 source at high latitudes, or existence of some mechanism that would extend the structures to high latitudes and that is not accounted for in the CTMT. SPW4 would yield wave-4 (see above), but the SPW4 generated in the Hagan et al. [2009] study is restricted to about 40 latitude, eliminating this SPW4 as a likely candidate. We noted previously the existence of a large wave-1 component that we removed from the data since we were unsure of its origin. It is likely that a significant part of this wave-1 exists in the form of SPW1 associated with the tilt of geomagnetic coordinates with respect to the geographic frame. Since DE2 extends to higher latitudes than DE3, SPW1 modulation of DE2 (following the same reasoning as in connection with Figure 9) could result in a high-latitude DE3 component that would also appear as wave-4 (accompanied by DE1 which would appear as wave-2, augmenting item 5 above). [31] 7. As a final note, it is obvious that many of the suggestions made above are conjecture, and require validation using a physics based model such as the TIME-GCM. It is possible that numerical experiments could be performed by varying tidal components specified at the lower boundary (i.e., DE3, DW1, DE2) and comparing solutions with a realistic magnetic field and one that is aligned with the geographic axis, to sort out some of these explanations. One could even sample the model along the SETA, CHAMP and GRACE orbits to ascertain the existence of any sampling or aliasing issues. It is our hope that the data presented herein provide the motivations for such studies. [32] Acknowledgments. 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