Climatology of upward propagating diurnal and semidiurnal tides in the thermosphere

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi:10.1029/2011ja016784, 2011 Climatology of upward propagating diurnal and semidiurnal tides in the thermosphere J. Oberheide, 1 J. M. Forbes, 2 X. Zhang, 2 and S. L. Bruinsma 3 Received 26 April 2011; revised 5 July 2011; accepted 23 August 2011; published 5 November 2011. [1] A major challenge in delineating and understanding the space weather of the ionosphere thermosphere system is the lack of global tidal observations in the 120 400 km thermospheric gap between satellite remote sensing and in situ tidal diagnostics. This paper aims to close this gap by presenting an observation based Climatological Tidal Model of the Thermosphere (CTMT) of self consistent upward propagating migrating and nonmigrating diurnal and semidiurnal tides from 80 400 km and pole to pole for moderate (F10.7 = 110 sfu) solar flux conditions. CTMT includes the 6 (8) most important diurnal (semidiurnal) tidal components for temperature, density, and zonal, meridional and vertical winds and is based on Hough Mode Extension fits to 2002 2008 mean TIMED satellite tidal diagnostics in the mesosphere/lower thermosphere (MLT). Validation with independent 2002 2008 CHAMP tidal diagnostics (F10.7 = 105 sfu) around 400 km proves that the approach captures nonmigrating tides well, indicating that these waves propagate directly upward without significant tidal forcing occurring in the thermosphere. Notable exceptions are the DW2 and D0 components that are most likely generated in situ by nonlinear interaction forcing in the upper thermosphere. CTMT is suitable for driving upper atmosphere models that require self consistent tidal fields in the MLT region as a lower boundary condition. It does not include migrating tides due to in situ EUV absorption in the upper thermosphere but allows us to quantitatively assess thermospheric variability due to tides from the lower atmosphere. This is done by discussing longitude/latitude maps of reconstructed diurnal and semidiurnal tidal variations as function of altitude and local time. Citation: Oberheide, J., J. M. Forbes, X. Zhang, and S. L. Bruinsma (2011), Climatology of upward propagating diurnal and semidiurnal tides in the thermosphere, J. Geophys. Res., 116,, doi:10.1029/2011ja016784. 1. Introduction [2] Numerous observations and model studies during the past five years have unequivocally revealed that Earth s ionosphere thermosphere (IT) system owes a considerable amount of its longitudinal, local time, seasonal latitudinal and day to day variability to nonmigrating tides that propagate upward from the lower atmosphere. Climatologies of nonmigrating tides the non Sun synchronous and longitudedependent part of the tidal wave spectrum have been compiled from mesosphere/lower thermosphere (MLT) temperature and wind observations from the SABER and TIDI instruments on board TIMED [Forbes et al., 2008; Oberheide et al., 2006, 2007; Wu et al., 2008]. In situ tidal diagnostics 1 Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, USA. 2 Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, Colorado, USA. 3 Department of Terrestrial and Planetary Geodesy, CNES, Toulouse, France. Copyright 2011 by the American Geophysical Union. 0148 0227/11/2011JA016784 from CHAMP and GRACE data have resulted in comparable data sets of nonmigrating tidal temperature, density and zonal wind [Forbes et al., 2009; Oberheide et al., 2011; Häusler and Lühr, 2009], and more recently migrating temperature tides at 400 km [Forbes et al., 2011]. [3] However, the observational database to elucidate the connection between the MLT tides from TIMED and the in situ observations from CHAMP and GRACE is very limited because no global satellite borne observations of the neutral dynamics exist between 120 km and 400 km. The only suitable approach to date in obtaining at least observationbased tidal fields in this thermospheric gap is constraining a physics based empirical fit model with tidal observations made in the MLT region. This approach was successful in explaining several nonmigrating tides in the upper thermosphere, i.e., the DE3, DE2, and SE2 nonmigrating tides in exosphere temperature, neutral density and zonal winds [Forbes et al., 2009; Oberheide et al., 2009, 2011]. The tidal nomenclature used here is standard: DWs or DEs is a westward or eastward propagating diurnal tide, respectively, with zonal wavenumber s. For semidiurnal tides, D is replaced by S, and D0, S0 are zonally symmetric diurnal and semidiurnal tides, respectively. 1of21

[4] Several nonmigrating tides, including DE3, DE2, and SE2, are to a large extent forced by latent heat release in persistent, large scale tropical rainfall systems [Hagan and Forbes, 2002, 2003]. An important result of the above mentioned TIMED, CHAMP and GRACE based work was therefore the realization that nonmigrating tides provide a direct link between tropospheric weather and upper thermosphere neutral variability, by direct upward propagation. Nonmigrating tides also induce a significant longitudinal and local time variation in the low latitude F region plasma, as discovered by Sagawa et al. [2005] and Immel et al. [2006] using IMAGE FUV data. An important neutral plasma coupling process here is the longitudinal modulation of E region dynamo electric fields by nonmigrating zonal wind tides [Hagan et al., 2007; Jin et al., 2008] although there is growing evidence that F region meridional tidal winds and thermospheric tidal [O]/[N 2 ] variations also play an important role [England et al., 2010]. [5] Further progress in elucidating neutral plasma coupling and understanding the IT response to lower atmospheric wave coupling critically depends on an accurate knowledge of the global spectrum of thermospheric waves. Of particular interest are the thermospheric tidal winds because of dynamo interactions, filtering of small scale gravity waves, and their role in ionospheric instability and bubble seeding [e.g., Fritts et al., 2008]. Although a full characterization of the thermospheric wave spectrum has to await future dedicated satellite missions, it is nevertheless possible to provide observationbased estimates of the thermospheric tidal variability due to upward propagating tides. [6] The main purpose of the present work is to provide such tidal fields, in the form of a Climatological Tidal Model of the Thermosphere (CTMT). CTMT is based on tidal observations made in the MLT region that are extended into the thermosphere using Hough Mode Extension (HME) modeling. The latter can be thought of as constraining a tidal model with observations and produces self consistent tidal fields in temperature, neutral density, and zonal, meridional and vertical winds from pole to pole and from 80 400 km. A monthly tidal climatology is compiled from averaged 2002 2008 TIMED observations and validated with CHAMP neutral density tidal diagnostics at 400 km. CTMT accounts for contributions from solar radiation absorption in the troposphere and stratosphere, tropospheric latent heat release, and non linear wave wave interactions occurring in the MLT or below. It is valid for a solar radio flux of F10.7 = 110 sfu and includes the 6 (8) most important migrating and nonmigrating diurnal (semidiurnal) tidal components. As such it is suitable for driving upper atmosphere models that require self consistent tidal fields in the MLT region as a lower boundary condition or to study the effects of tidal density variations in the re entry region, to name just a few examples. [7] Thermospheric tidal forcing occurring above the MLT is not accounted for. CTMT, therefore, does not capture (i) migrating tides forced in situ by the absorption of solar EUV radiation, and (ii) nonmigrating tides forced in situ by nonlinear interaction processes. An example for the latter is the offset between the geographical and geomagnetic equator that modulates the migrating diurnal tide to produce nonmigrating tides as secondary waves. However, migrating tides due to EUV forcing can be linearly superposed from MSIS type models [Hedin, 1991], if required. In situ nonlinear interaction processes in the upper thermosphere mainly affect two diurnal nonmigrating components, DW2 and D0, but are comparatively unimportant for semidiurnal tides. Most nonmigrating tidal components propagate directly upward from their source regions into the upper thermosphere. Longitude/latitude maps of reconstructed diurnal and semidiurnal tidal variations as a function of altitude and local time thus allow us to quantitatively assess thermospheric variability due to nonmigrating tides from the lower atmosphere. [8] The paper is organized as follows. Section 2 overviews the baseline tidal data sets from TIMED and CHAMP. Section 3 introduces the HME methodology and discusses fit ranges, fit errors and limitations of the approach. Section 4 presents the CTMT tidal climatology for all individual components. Section 5 validates the climatology with CHAMP neutral density tidal diagnostics. Section 6 discusses CTMT/CHAMP differences in terms of thermospheric forcing, and the longitudinal and local time variability due to upward propagating tides in the MLT and upper thermosphere. Section 7 contains the conclusions. 2. Baseline Data 2.1. TIDI Zonal and Meridional Wind Tides [9] The TIMED Doppler Interferometer (TIDI) [Killeen et al., 2006] is the wind instrument on board NASA s TIMED satellite that was launched in December 2001. TIDI zonal and meridional winds in the MLT are based on Doppler shift measurements of green line emissions. Diurnal and semidiurnal tidal winds are routinely derived from 80 105 km and between ±75 latitude using the National Center for Atmospheric Research data version v0307a [Wu et al., 2008] and the two dimensional Fourier analysis described by Oberheide et al. [2006, 2007] who also provide details of amplitude and phase errors. As a rule of thumb, amplitude accuracy (precision) is about 10% (1 m/s) and phase precision is between 1 2 hours. Tides poleward of ±65 may be subject to aliasing from stationary planetary waves. For the present paper, we use tides that are averaged into 2002 2008 composite months. Diurnal tides include nonmigrating components DW5 to DE3 and semidiurnal tides components SW6 to SE3. The migrating tides DW1 and SW2 from TIDI are of limited quality, due to instrumental and sampling issues and are not used. TIDI tides have been successfully validated as part of the CAWSES tidal campaigns [Ward et al., 2010] by comparing them to ground based radar and lidar observations. 2.2. SABER Temperature Tides [10] Sounding the Atmosphere using Broadband Emission Radiometry (SABER) [Russell et al., 1999] on board TIMED measures temperature and selected trace constituents from 20 120 km from infrared emissions. SABER tidal temperature diagnostics is very similar to TIDI and provides diurnal tidal components DW7 to DE5 and semidiurnal components SW8 to SE4 with an amplitude error of 1 2 K. See the discussions of Zhang et al. [2006] and Forbes et al. [2008] for details. As for TIDI, SABER temperature tides used here are averaged into 2002 2008 composite months. They are based on SABER data version v01.07 and have been derived between ±50 latitude. 2of21

Figure 1. Amplitudes and phases for HME1 and HME2 of DE2. Amplitudes are normalized to a maximum zonal wind speed of 8 m/s. 2.3. CHAMP Neutral Density Tides [11] The Challenging Minisatellite Payload (CHAMP) satellite was launched in 2000 into a nearly circular orbit with an initial altitude of 450 km. CHAMP obtains full local solar time coverage every 130 days due to its slow orbit precession of 5.4 min/day. Neutral density in the upper thermosphere is measured in situ by the STAR accelerometer [Bruinsma et al., 2004]. These data are first normalized to a constant altitude of 390 km to account for the CHAMP orbit decay over time by using an empirical model and then Fourier analyzed for migrating and nonmigrating tides similar to TIDI and SABER. See Bruinsma et al. [2006] for details of the normalization and error discussion. A 50 km height normalization results in an uncertainty of only 3.5% in total mass density. This error does not play a role for tidal density diagnostics since (i) the latter use relative density variations (deviations from the zonal mean in per cent), (ii) tidal components are computed from 130 day running means (small orbit height variations) and (iii) tidal amplitudes are almost height independent in the upper thermosphere [Oberheide et al., 2009]. [12] CHAMP tides cover all the diurnal and semidiurnal tides included in CTMT and are used for validation purposes (section 5) by averaging them into 2002 2008 composite months. The mean 2002 2008 F10.7cm radio flux of 105 sfu is close to the 110 sfu used for CTMT which is important for reasons outlined in section 3.2 below. CHAMP tidal diagnostics are limited to ±60 latitude due to potential aliasing issues at higher latitudes and increasing contaminations induced by geomagnetic activity toward the poles. 3. Hough Mode Extension Fitting 3.1. Overview [13] Hough Mode Extensions (HME) represent the numerical solution (pole to pole, 0 400 km) to the linearized dynamical equations of the atmosphere taking into account dissipative effects above the forcing region and height dependent background temperature. Going back to Lindzen et al. [1977] and Forbes and Hagan [1982], an HME can be thought of as an extension of a classical Hough mode that represents the solution of Laplace s tidal equation in an isothermal atmosphere without mean winds and dissipation. Each HME is a self consistent latitude vs. height set of amplitudes and phases for the perturbation fields in temperature, zonal, meridional and vertical wind, and density (T, u, v, w, r). HMEs are computed as detailed by Svoboda et al. [2005] using a simplified version of the Global Scale Wave Model [e.g., Hagan and Forbes, 2002] that only maintains the tidal dissipation scheme including ion drag. Model background winds are set to zero and the standard model temperature and density profiles are replaced by global average MSISE90 profiles. Each HME is then computed using an arbitrarily calibrated simple tropospheric heat source with a latitudinal structure equivalent to that of a classical Hough Mode. Liu et al. [2009] found that longitudinal variations in ion drag have no measurable effects on the DE3 in the upper thermosphere observed by CHAMP. It is thus reasonable to assume that the same is true for all nonmigrating tides included in CTMT. [14] Zonal and meridional wind HMEs are exemplified in Figure 1 for the DE2 case. They correspond to the first symmetric (HME1) and first antisymmetric (HME2) Hough modes with symmetric and antisymmetric referring to the relative phasing of (u, w, T, r) across the equator. Meridional wind HMEs always have the opposite symmetry. Temperature, density and vertical wind HMEs (not shown) have a structure that is similar to the zonal wind case. Amplitudes and phases above 250 km are omitted in Figure 1, for better readability. This is justified because molecular diffusion becomes dominant in the upper thermosphere such that amplitudes and phases relax to constant values. Table 1 summarizes peak height, peak latitudes, and vertical wavelengths for all zonal wind HMEs used in this work. Note that non equatorial peaks in the upper thermosphere will generally shift toward higher latitudes compared to the MLT values in Table 1, again due to molecular diffusion. Further examples for the full latitude vs height structure of HMEs are given by Oberheide and Forbes [2008] and Oberheide et al. [2009, 2011], including the important DE3 and SE2 nonmigrating tides. [15] The HMEs for each tidal component are then leastsquares fitted to the observed tides in the MLT region, as detailed in section 3.4 below, and tidal amplitudes and 3of21

Table 1. Zonal Wind Characteristics of the HMEs a HME1 HME2 HME3 HME4 Component z (km)/l z (km) Latitudes (deg) z (km)/l z (km) Latitudes (deg) z (km)/l z (km) Latitudes (deg) z (km)/l z (km) Latitudes (deg) DW2 94/33 ±24 unstable unstable DW1 93/35 ±30 unstable unstable D0 94/32 ±30 105/69 ±30 DE1 164/149 0 101/45 ±24 94/29 0, ±30 DE2 105/70 0 101/35 ±24 DE3 106/42 0 102/28 ±18 SW4 107/50 0 104/38 ±30 100/32 0, ±42 100/29 ±18, ±48 SW3 111/65 0 104/45 ±36 100/36 0, ±48 100/32 ±18, ±54 SW2 111/90 ±24 104/54 ±48 100/42 0, ±54 100/37 ±24, ±60 SW1 100/96 ±90 100/87 ±90 100/59 ±18, ±90 100/45 ±30, ±90 S0 107/150 ±42 134/88 ±48 100/42 ±18, ±54 104/57 ±12, ±48 SE1 170/396 0 174/120 ±36 107/67 0, ±42 104/45 ±12, ±48 SE2 199/195 0 133/87 ±30 106/54 0, ±36 106/39 ±12, ±42 SE3 138/93 0 107/57 ±24 104/42 0, ±36 104/34 ±12, ±42 a Altitude z of maximum amplitude, vertical wavelength l z between 90 and 120 km, and latitudes of zonal wind peaks at z. Latitudes in italics indicate small, secondary peaks. HME1/3 is symmetric, HME2/4 is antisymmetric. phases are reconstructed as function of latitude, altitude and month. It should be noted that setting the mean winds to zero in the HME computation does not imply that the effects of mean winds are neglected in fitting the tides. Svoboda et al. [2005] show that the distortion of tidal structures due to mean winds can be viewed as mode coupling, that is, the excitation of higher order modes which combine together to approximate the distortion. These higher order modes, however, are unlikely to propagate into the thermosphere, for reasons outlined in section 3.3 below. In summary, HMEs represent an approach to constrain a linear tidal model with measured data in a self consistent manner. It is to date the only method to obtain at least observation based information about the global tidal spectrum in the 120 400 km gap between the upper boundary of TIMED tidal diagnostics and in situ tidal observations from the CHAMP satellite. 3.2. Dependence on Solar Flux Conditions [16] HMEs in the MLT region are almost independent of solar flux conditions but this is very different above 120 km. Amplitudes are smallest for high solar flux and largest for low solar flux, mainly due to the inverse dependence of vertical diffusion of heat and momentum on the background density. Solar min/max amplitude differences can exceed 100%. See Oberheide et al. [2009] for a more detailed discussion. All HMEs used in the present work have been computed for a F10.7cm solar flux level of 110 sfu which is close to the 2002 2008 average of 105 sfu. 3.3. Choice of HMEs [17] Most of the salient features of upward propagating tides are well described by fitting the first two HMEs (HME1 and HME2) to diurnal tides, with the exception of DW2, DW1 and DE1, and by fitting the first four HMEs (HME1, HME2, HME3 and HME4) to semidiurnal tides (Table 2). HME1 and HME3 are symmetric with respect to the equator, and HME2 and HME4 are antisymmetric since they resemble the latitudinal structure of their classical Hough Mode counterparts. Adding higher order HMEs would naturally improve the agreement between the HME fit results and the observed tides at MLT altitudes but it becomes increasingly difficult to compute stable HMEs for higher wave modes as the latter have comparatively short vertical wavelengths. Time constants of eddy and molecular diffusion are proportional to the square of the vertical wavelength of the tides. Short vertical wavelength modes and components therefore dissipate more rapidly and cannot propagate into the thermosphere. Higher order HMEs thus (i) become increasingly dependent on the eddy diffusion distributions used for their computation which are open to considerable uncertainty and (ii) have diminishing amplitudes in the thermosphere. [18] HME1 and HME2 are sufficient to describe the DE3 and DE2 tides [Oberheide and Forbes, 2008; Forbes et al., 2009]. This also applies to D0. DE1 requires the second symmetric mode (HME3) because the latter extends well into the thermosphere with a comparatively long vertical wavelength of 29 km. HME2 of DW2 and DW1 was unstable (short vertical wavelength, unimportant in the MLT and above) and only HME1 is used here. Semidiurnal tides on the other hand are generally more structured in latitude and always require HME3 and HME4. The vertical wavelengths of these modes (Table 1) often allow them to propagate into the thermosphere, although with smaller amplitudes than HME1 and HME2. Table 2. Height and Latitude Range and HMEs Used for the Least Squares Fits a Component Heights (km) Latitudes (deg) HMEs DW2 85 105 ±45 1 DW1 80 100 D0 85 110 1, 2 DE1 90 120 1, 2, 3 DE2 90 115 1, 2 DE3 90 115 SW4 90 120 1, 2, 3, 4 SW3 90 120 ±65 SW2 80 115 ±50 SW1 80 110 ±65 S0 80 120 SE1 95 120 ±50 SE2 80 115 SE3 90 115 a HME1 and HME2 correspond to the first symmetric and anti symmetric Hough modes, respectively. HME3 and HME4 correspond to the second symmetric and anti symmetric Hough modes. 4of21

3.4. Fit Method and Ranges [19] The CTMT climatology is computed by least squares fitting the chosen HMEs to individual 2002 2008 monthly mean (T, u, v) tidal components from SABER and TIDI in the MLT region. Exceptions are DW1 and SW2 (both migrating) that are based on SABER alone because of TIDI instrumental and aliasing issues that prevent a reliable analysis of migrating tidal winds. Note that the resulting fit coefficients are the same for (T, u, v, w, r) because of the self consistency of the HMEs, and are latitude and altitude independent. It is then straightforward to reconstruct the tidal component amplitudes and phases for (T, u, v, w, r) and at latitudes and altitudes not observed. This is done on a 5 latitude 2.5 km altitude grid. [20] Fitting temperature and wind tides simultaneously makes the results less dependent on the noise error of both tidal data sets (see section 2) and also levels systematic offsets. Furthermore, it increases the likelihood to capture amplitude maxima and/or altitudes and latitudes with significant changes in the tidal structure in the height and latitude range chosen for the fit. For example, DE3 in (T, u) is rather weak during boreal winter but strong in v and vice versa during boreal summer [Oberheide and Forbes, 2008]. [21] At a first look, the natural choice for the height and latitude fit ranges might be the common volume of SABER and TIDI tidal diagnostics, that is, 80 105 km and ±45. However, this weights the fit more heavily on the winds and, in addition, many tides maximize at altitudes above 105 km. The upper altitude of the fit range is thus extended toward higher altitudes (no winds but temperatures) as summarized in Table 2, with two exceptions. DW1 tidal temperatures from SABER show indications for a growing in situ forcing above 100 km that cannot be captured by HMEs (see section 3.5 below). DW2 rapidly decays above 105 km such that adding more temperature data would simply increase the noise level. All remaining temperature tides peak above 105 km and the fits are extended to either 110 km, 115 km or 120 km, depending on which value minimized the fit/observation difference. That these values differ from one component to another is due to a combination of growing tidal temperature uncertainties and amplitudes with height. SABER temperature errors increase rapidly toward 120 km due to increasing uncertainties in the non LTE retrieval [Remsberg et al., 2008]. The resulting effects on tidal temperature diagnostics are not completely understood because the temperature error itself most likely depends on the tidal activity, due to various feedbacks involving radiative transfer and atomic oxygen concentrations. One must therefore expect less agreement between HME temperatures and observations close to 120 km. However, larger tidal temperature amplitudes make the fits less dependent on noise at lower altitudes, particularly for those components that are rather small below 105 km, i.e., most of the semidiurnal tides. The optimum upper fit altitude is thus somewhere in between. The lower boundary of the fit range is chosen such that the observed amplitudes at this altitude exceed the errors of the observed tidal winds and temperatures. [22] Fits to diurnal tides are always confined to ±45 for reasons outlined above. Semidiurnal tides frequently maximize at higher latitudes and are often more structured in latitude. Fit ranges are thus extended to either ±65 or ±50. This weights the fit more heavily on the observed tidal winds but it is more important to capture all salient tidal features. 3.5. Limitations [23] The strength of the HMEs lies in extending upward propagating migrating and nonmigrating tides into the thermosphere but the approach has some inherent limitations. These limitations need to be emphasized here, in order to understand what processes and features the resulting CTMT tidal climatology includes and what processes and features are not described. [24] First, HME fitting can only account for tidal sources below the fit altitude [Svoboda et al., 2005]. It cannot capture tidal contributions originating from in situ (referring to the fit altitude) forcing or sources above. For example, HME fits to migrating tides only capture the upward propagating contributions due to tropospheric and stratospheric forcing but not the large contribution from in situ thermospheric EUV forcing. Furthermore, some nonmigrating tides might be affected by wave wave interaction forcing in the MLT. A prominent example is the SE2. This component is forced by latent heat release in the tropical troposphere, similar to the DE3, but also by the nonlinear interaction between DW1 and DE3 in the MLT [Hagan et al., 2009]. The latter forcing, however, produces a latitudinal SE2 structure that differs from the upward propagating part and, in addition, has a comparatively small vertical wavelength. As such, the in situ part does not propagate into the upper thermosphere. Oberheide et al. [2011] show that HMEs capture the upward propagating SE2 part well and produce realistic SE2 tidal fields in the upper thermosphere (within 10 15% of independent CHAMP tidal diagnostics) although the HME fit deviates from the observed SE2 tides in the MLT region. In general, MLT in situ forcing, if present, may contaminate the HME fit results (and thus the CTMT climatology) in the MLT but it is comparatively less important in the thermosphere. [25] Second, CTMT is only valid for 110 sfu due to the tidal dissipation sensitivity to thermospheric temperature. [26] Third, HME fits can only be performed for components DW2, DW1, D0, DE1, DE2, DE3, SW4, SW3, SW2, SW1, S0, SE1, SE2, SE3. Higher zonal wavenumber tides have small vertical wavelengths and the above mentioned difficulties related to the assumed eddy diffusion distribution in their computation prevent the computation of stable HMEs. These high zonal wavenumber tides are unlikely to propagate into the thermosphere but will add additional variability in the MLT not captured by CTMT. [27] It should also be noted that HMEs are not computationally feasible for stationary planetary waves since the latter do not belong to the family of solutions to Laplace s tidal equation. 3.6. Fit Errors [28] The HME fit error due to uncertainties in the observed tidal fields and due to the specific choice of the latitude/height fit range is on the order of 1 m/s for horizontal winds and 1 K for temperature amplitudes. The corresponding phase error is on the order of 1 hour for semidiurnal tides and 2 hours for diurnal tides. These values apply to individual tidal components and are based on previous work. Forbes 5of21

et al. [2009] compared 2005/06 TIMED based HME tidal temperatures for the DE3 and DE2 components to independent tidal temperature observations by the CHAMP and GRACE satellites at 400 km. The agreement was within 1 K and well within the error margins. Oberheide et al. [2009] did a comparison for five years of CHAMP DE3 zonal wind tides at 400 km and again, the agreement (1 2 m/s) was within the error margins when using solar flux dependent HMEs. A similar result was recently obtained for DE3 and SE2 neutral density tides by comparing 2008 HME fits to CHAMP observations [Oberheide et al., 2011]. A more detailed error analysis is not feasible here since unknown tidal sources may exist above the fit region. It is more meaningful to assess the CTMT climatology by comparing it to independent CHAMP tidal diagnostics in the upper thermosphere. This is done in section 5. 4. Climatological Tidal Model of the Thermosphere (CTMT) [29] The CTMT climatology includes amplitudes and phases for 6 diurnal and 8 semidiurnal tides as function of latitude (pole to pole) and altitude (80 400 km) for each month of the year, and for (T, u, v, w, r), respectively. Since it is impossible to present and discuss all of these fields (a total of 1680 latitude/altitude distributions), we will only overview the general characteristics of CTMT by discussing latitudinal/seasonal and vertical variations of amplitude spectra, and by providing an example for the latitude/altitude structure of the S0 tide. The full data set will be made available to the community via a web based interface once this paper has been published. 4.1. Latitudinal/Seasonal Characteristics 4.1.1. Diurnal Tides [30] The diurnal amplitude spectra in the thermosphere (Figure 2) are comparatively similar for (u, w, T, r) but very different for the meridional wind. The latter is dominated by a broad D0 between ±50 that maximizes in December. Other nonmigrating tides in v are relatively weak and only the migrating DW1 shows a noteworthy peak at high latitudes in March and September. As mentioned above in section 3.5, the DW1 in Figure 2 only includes the part that propagates upward from the MLT but not the part due to thermospheric EUV forcing. However, for DW1 molecular dissipation causes the propagating tide to maximize at the poles for u and v. [31] Low latitude tides in (u, w, T, r) are dominated by DE3 and DE2 with varying contributions that reflect the seasonal variation of these components in the MLT: two DE2 peaks in June and December; one DE3 maximum in September with still large amplitudes in March and June but vanishing DE3 in December [Oberheide et al., 2006]. High latitude tides poleward of ±40 in (T, r) are dominated by the D0 throughout the year with maximum amplitudes in December. The upward propagating DW1 is comparatively weak in (T, r) but becomes more important in (u, w) where its contribution equals or exceeds that of D0, particularly in u with its rather small D0 component. 4.1.2. Semidiurnal Tides [32] All semidiurnal amplitude spectra (Figure 3) show a strong signature of the upward propagating migrating SW2. Its latitudinal structure in (u, w, T, r) changes from two midlatitude peaks in June and September to a single low latitude maximum in March and December with u being somewhat broader. Nonmigrating tides in (u, w, T, r) are present at all latitudes throughout the year. The strongest components at low latitudes are SW4 and, to some extent, SW3. Both are most pronounced in March and December. Mid latitude nonmigrating tides are governed by a SE2 that does not change much from one month to another and by a SE3 that is similar in structure but only half of the SE2 amplitude. High latitude tides in (w, T, r) are dominated by the S0 that in most cases is stronger in the northern hemisphere. S0 is comparatively weak in u, similar to its D0 counterpart. Figure 3 also indicates the presence of a strong SW1 in (u, v) that maximizes in March and September at the poles with somewhat larger amplitudes in the southern hemisphere. [33] The meridional wind spectrum is similar to (u, w, T, r) in that the same tidal components are present with about the same seasonal variations. Its main difference to the other fields, as in the diurnal case, is the latitudinal distribution of the amplitude maxima. SW2 now maximizes at low latitudes in June and September with smaller secondary peaks around 50 S and 70 N. The low latitude peak disappears in March and December and only two maxima at about ±30 latitude remain. SE2 and SE3 maximize at the equator and S0 at about ±50. SW4 and SW3 in v are weak compared to (u, w, T, r) and no longer maximize at low latitudes but rather around ±30, if present. [34] Amplitudes will be further discussed in section 5 below, but by comparing Figures 2 and 3 it already becomes clear that semidiurnal nonmigrating are as important as diurnal nonmigrating tides in the thermosphere. Upward propagation from the MLT into the thermosphere is particularly important for the migrating semidiurnal tide as indicated by the large SW2 amplitudes in all fields. This is in contrast to the migrating diurnal tides since the upward propagating DW1 in Figure 2 is comparatively small. 4.2. Vertical Characteristics 4.2.1. Diurnal Tides [35] Diurnal spectra in the MLT region are exemplified in Figure 4 for 100 km and September. They differ in several important aspects from those in the thermosphere. In the MLT, DW1 shows the typical mid latitude zonal and meridional wind maxima and the three peaked (w, T, r) pattern that has been reported in many space borne observations of the MLT, i.e., LIMS [Hitchman and Leovy, 1985], UARS [Hays et al., 1994], CRISTA [Ward et al., 1999], and TIMED [Forbes et al., 2008]. This general structure is associated with the first symmetric mode (HME1) that dissipates rapidly above 110 120 km (Figure 5) because of its short vertical wavelength (35 km, Table 1) and is thus largely absent in the thermosphere. [36] A similar argument can be made for D0 and DW2. Only the antisymmetric HME of D0 has a sufficiently long vertical wavelength (69 km) to propagate into the thermosphere where it is causing the high latitude, antisymmetric signals in (u, w, T, r) and the strong symmetric signal in v. DW2 is very large in the MLT (Figure 4) but almost zero in the thermosphere (Figure 2) because it is associated with the first symmetric HME. The latter has a similar vertical wavelength compared to its DW1 counterpart and therefore 6of21

Figure 2. Diurnal amplitude spectra at 250 km. Negative (positive) zonal wavenumbers indicate westward (eastward) propagation. 7of21

Figure 3. Semidiurnal amplitude spectra at 250 km. Negative (positive) zonal wavenumbers indicate westward (eastward) propagation. 8of21

Figure 4. Amplitude spectra for September at 100 km. (a) Diurnal tide. (b) Semidiurnal tide. Negative (positive) zonal wavenumbers indicate westward (eastward) propagation. dissipates rapidly above 100 km (Figure 5). HME2 of DW2 does not play a role here since DW2 is fully symmetric in the MLT. The eastward propagating DE2 and DE3 tides, on the other hand, propagate straightforwardly into the thermosphere without changing their latitudinal structure much, due their long vertical wavelengths and corresponding less dissipation. Both components are dominated by the first symmetric modes with inviscid vertical wavelengths of 42 km (DE3) and 70 km (DE2) 9of21

Figure 5. (left) Diurnal and (right) semidiurnal zonal wind amplitude spectra for September between 90 km and 150 km. Negative (positive) zonal wavenumbers indicate westward (eastward) propagation. 4.2.2. Semidiurnal Tides [37] Semidiurnal tides generally peak at higher altitudes and show longer vertical wavelengths than the diurnal tides (Table 1). The four HMEs used for the fits usually have the long vertical wavelengths needed for upward propagation into the thermosphere although their relative importance may vary as function of height due to the specifics of vertical amplitude structures. This is different from the diurnal case where some HMEs completely dissipate. [38] For instance, the migrating semi diurnal tide SW2 in September evolves from a symmetric structure in the MLT with three peaks in (w, T, r) and two peaks poleward of ±50 in u (Figure 4) to a generally antisymmetric (phases not shown) structure in the thermosphere with two peaks equatorward of ±50 in (u, w, T, r) with a superposed broad, symmetric peak in u (Figure 5). The SW2 structure in the MLT is governed by HME3 because it maximizes at a lower altitude than HME1 and HME2. HME1 and HME2 on the other hand increase sharply in amplitude above 100 km and dominate SW2 in the thermosphere, with HME2 being more important in June and September and HME1 more important in March and December. [39] Nonmigrating semidiurnal tides are very weak at altitudes below 90 km but become important at 100 km and above (Figure 5). The nonmigrating part of the tidal spectrum in the MLT is dominated by westward propagating components. SW4, SW3 and SW1 maximize in the 100 110 km region but their vertical wavelengths are smaller than those of the eastward tides and S0 such that they propagate less efficiently into the thermosphere than the latter which, in addition, peak at higher altitudes (Table 1). S0 and the eastward tides thus become dominant in the thermosphere with SE2 being the single largest contributor. An exception from this general rule is SW1 which also has a long vertical wavelength and as such produces the large zonal and meridional wind signals evident at high latitudes in March and September (Figure 3). 4.3. S0 Amplitude and Phase Structure [40] Amplitudes and phases as function of latitude and altitude of the two single most important diurnal and semidiurnal nonmigrating tides, DE3 and SE2, have been presented before [Oberheide et al., 2011]. This work was focused on a single solar minimum year but the general structure is essentially the same for CTMT. The second most important nonmigrating diurnal tide, DE2, has been discussed by Forbes et al. [2009]. DE2 is responsible for the change from a wave 4 in September to a wave 3 in December frequently observed in fixed local time satellite observations of plasma densities [Pedatella et al., 2008]. The reader is thus referred to these papers for details about the DE3, DE2, and SE2 structure. Here, we want to exemplify the tidal structures of the second most important nonmigrating semidiurnal tide in the thermosphere, the S0. [41] S0 is excited by both latent heat release in the tropical troposphere [Hagan and Forbes, 2003] and nonlinear wavewave interactions, i.e., between the migrating SW2 and the stationary planetary wave 2 (SPW2). Observational results from TIDI and supporting modeling results in the MLT region indicate that latent heat and wave wave interaction forcing are about equally important [Oberheide et al., 2007]. As such, S0 is one of the more difficult components for HME modeling but the comparison with TIDI in Figure 6 indicates that its MLT structure is reasonably well captured. Amplitude differences above 95 km are on the order of 20% which is within the combined systematic errors of the TIDI tidal diagnostics (13% [Oberheide et al., 2007]) and the fit uncertainty (1 m/s). Deviations below 95 km, especially in the Southern hemisphere, are somewhat larger and may be the result of the above mentioned wave wave interaction processes. HME phases, however, are always well within the combined 2 hour observational and 1 hour fit errors and reproduce the observed three peaked symmetric S0 structure. A similar level of agreement is found for (u, T) and for the remaining months. [42] Figure 7 overviews the resulting (u, v, w, T, r) amplitudes and phases in the thermosphere. The overall S0 structure is largely dominated by the second antisymmetric mode (HME4) with some superposition from the other modes that lead to the generally larger amplitudes in the Northern hemisphere. Note that S0 produces large (w, T, r) amplitudes at polar latitudes which discerns it from most other tidal components that tend to maximize either at the equator or at mid latitudes. The increase in density amplitude above 10 of 21

Figure 6. (a, b) Meridional wind amplitudes and (c, d) phases of the zonally symmetric semidiurnal tide (S0) for September from TIDI and HME fitting. 200 km is simply a consequence of the constant temperature amplitudes combined with the ideal gas law and hydrostatic equilibrium. It does not indicate a tidal source in the thermosphere because the latter cannot be captured by the HME approach. 5. Comparison With CHAMP [43] The CTMT tidal climatology in the upper thermosphere is now evaluated by comparing all individual components to the independent tidal diagnostics of CHAMP in situ neutral density measurements introduced in section 2.3. Evaluating the HME fits by density alone is sufficient because of their self consistency in (u, v, w, T, r). A good match between HME and CHAMP density tides would also imply realistic temperature and wind tides from the former and a mismatch would imply unrealistic HME temperature and wind tides. [44] Table 3 summarizes the general level of agreement between CTMT and CHAMP, categorized as good, moderate, and poor for amplitude magnitude, seasonal and latitudinal amplitude variations, phase magnitude (phasing) and phase variations (i.e., symmetric vs. antisymmetric). Similarities and differences for each component are briefly described in the following thus specifying the meaning of the three categories. Comparisons for the four most important nonmigrating tides (DE3, DE2, SE2, S0) are exemplified in Figures 8 11, while similar figures for the remaining components are provided as auxiliary material, for space reasons. 1 1 Auxiliary materials are available in the HTML. doi:10.1029/ 2011JA016784. 5.1. Individual Components [45] DW2 is poorly described by CTMT because it is only composed of HME1 that completely dissipates when propagating upward. CHAMP, however, indicates the presence of a symmetric DW2 that maximizes at about 30 S with an annual variation that peaks at about 2.8% density amplitude in boreal winter. Since the independent zonal wind tidal analysis of Häusler et al. [2010] also shows a strong DW2 signal, it must be concluded that some thermospheric forcing processes play a role here that are not captured by CTMT. See section 6.1 for a more detailed discussion. [46] DW1, the migrating tide, is as expected poorly described because the thermospheric forcing by solar EUV absorption is not included in the HME formulation. CTMT amplitudes are negligible while CHAMP indicates DW1 density variations of up to 60%. [47] D0 amplitudes from CHAMP are on the order of 3% which is close to the CTMT amplitudes of 3.5 4%. However, CHAMP shows a broad, symmetric winter maximum across the equator while CTMT predicts very small equatorial amplitudes with a pronounced antisymmetric phasing. The limited latitudinal coverage of the CHAMP tidal density diagnostics does not allow one to assess the high latitude amplitude maxima in CTMT. D0 zonal winds [Häusler et al., 2010] show large maxima around 40 latitude which would be consistent with polar density maxima, as shown in Figure 2. It is thus likely that the high latitude density maxima are real, but that thermospheric forcing (see section 6.1) produces the equatorial density maximum in CHAMP. The general level of agreement for D0 is thus categorized as poor but it may be better at latitudes poleward of 60. [48] DE1 amplitudes in both data sets maximize around 1% density amplitude in the NH around equinoxes. SH amplitudes, in contrast, show a more semiannual variation. This is well captured by CTMT although the summer maximum in CHAMP is larger (1.4% compared to 0.7%). Phasing is always symmetric and agrees within 3 hours when the amplitudes are above 0.3%. The general agreement is thus categorized as good. 11 of 21

Figure 7. (a) Amplitudes and (b) phases of the zonally symmetric semidiurnal tide (S0) for September. [49] DE2 amplitudes and phases agree well, within 0.2% (amplitude) and 3 hours (phase). Phasing is always symmetric with a semiannual variation with maximum amplitudes of 2% in winter (Figure 8). [50] DE3 shows the same level of agreement as DE2, but with the well known annual variation that maximizes in September at about 2%. Phases are symmetric and agree within 2 hours (Figure 9). 12 of 21

Table 3. Level of Agreement Between Tidal Densities From CTMT and CHAMP at 390 km Altitude Component Amplitude Magnitude Amplitude Latitudinal/Seasonal Phase Magnitude Phase Latitudinal/Seasonal DW2 a poor poor poor poor DW1 a poor poor poor poor D0 a good poor poor poor DE1 good good good good DE2 good good good good DE3 good good good good SW4 good good good good SW3 good moderate good good SW2 a poor poor poor good SW1 good moderate poor good S0 good good good good SE1 good moderate good good SE2 good good good good SE3 good good good good a Poorly described components. [51] SW4 in CHAMP is well reproduced by CTMT, particularly the symmetric phases structure (within 2 hours), the magnitude of the winter amplitude maximum of 1.2%, and even the small secondary maximum in summer although the latter is larger in CHAMP. [52] SW3 amplitudes in CTMT maximize at 1.5% around equinoxes and 30 latitude. This is similar in CHAMP although the equinox maxima are shifted toward February and October/November. The main difference is the pronounced (2%) CHAMP maximum in summer at 15 N that is lacking in CTMT which only shows about half the amplitude then. Phases on the other hand are relatively well reproduced. The phasing across the equator is in between symmetric and antisymmetric with a larger symmetric contribution in CHAMP. Differences are on the order of 2 3 hours where the amplitudes are above about 0.4%. Phases and amplitude magnitudes in Table 3 are thus classified as good but amplitude structure as moderate only. The CTMT/CHAMP differences are probably caused by thermospheric forcing processes not captured by the HME approach (see section 6.1). [53] SW2, the migrating tide, is poorly described, similar to the DW1, because it does not include the thermospheric EUV absorption forcing. Tidal upward propagation and in situ forcing are about equally important for SW2 [Forbes et al., 2011]. [54] SW1 in CHAMP and CTMT maximize around 2.2 2.4%. Similar to SW3, the mid latitude maxima in the 30 60 latitude range occur approximately around equinoxes with a semiannual variation. This is evident in both data sets. The CHAMP amplitude maximum at 20 S and October is more pronounced and structured than in CTMT. The main difference is that CHAMP does not show the deep summer Figure 8. DE2 density (a, c) amplitudes and (b, d) phases at 390 km from CHAMP (Figures 8a and 8b) and CTMT (Figures 8c and 8d). Both data sets represent 2002 2008 averages. White dashed lines are to guide the eye. 13 of 21

Figure 9. DE3 density (a, c) amplitudes and (b, d) phases at 390 km from CHAMP (Figures 9a and 9b) and CTMT (Figures 9c and 9d). Both data sets represent 2002 2008 averages. White dashed lines are to guide the eye. minimum at low latitudes that is present in CTMT but rather constant background amplitudes of about 1.2%. The overall level of agreement in terms of amplitude structure is thus rated moderate. The relative phasing across the equator in both data sets is symmetric in summer and rather antisymmetric in winter, which is categorized as good. However, the absolute phase values disagree and are almost out ofphase. Possible reasons for the differences are discussed in section 6.1. [55] S0 CHAMP amplitudes are very small which is similar in CTMT that maximizes at the poles with amplitudes of 4.4% and a largely semiannual variation with peaks around equinoxes (Figure 10). Phases agree within 2 hours and are always symmetric. Although the lacking latitudinal coverage Figure 10. S0 density (a, c) amplitudes and (b, d) phases at 390 km from CHAMP (Figures 10a and 10b) and the CTMT (Figures 10c and 10d). Both data sets represent 2002 2008 averages. White dashed lines are to guide the eye. 14 of 21

Figure 11. SE2 density (a, c) amplitudes and (b, d) phases at 390 km from CHAMP (Figures 11a and 11b) and CTMT (Figures 11c and 11d). Both data sets represent 2002 2008 averages. White dashed lines are to guide the eye. of CHAMP does not provide a final proof for the S0 in CTMT, the latter apparently provides realistic signals in the ±60 latitude range and, due to the phase structure, most likely at higher latitudes. [56] SE1 maxima are on the order of 1.8 2% in both data sets and peak at the equator and ±60 latitude in summer. CHAMP amplitudes are largest in the SH while CTMT shows the largest amplitudes at the equator. The most obvious difference occurs in the NH because the climatological winter maxima are not present in CHAMP. The overall level of agreement in terms of amplitude structure is thus rated moderate. Phase agreement is good because both data sets show a symmetric phasing across the equator with a mean offset on the order of 2 3 hours. [57] SE2 amplitudes and phases (Figure 11) agree well with a somewhat larger month to month variability in CTMT. This may be due to the 130 day averaging window used for the CHAMP tidal diagnostics but the overall agreement is good. Phases are within 2 hours and amplitudes within 0.5%, compared to maximum amplitudes of 3%. [58] SE3 is similar to SE2. Amplitude magnitude (1.4%) and latitudinal/seasonal structure with peaks at ±30 in SH summer and NH summer and winter agree well. Phases are within 2 hours with a general antisymmetric behavior. 5.2. Summary of Tidal Density Comparisons [59] The individual component comparisons between CHAMP and CTMT can be summarized as follows. [60] First, the migrating diurnal and semidiurnal tides DW1 and SW2 are, as expected, poorly described, due to the lacking thermospheric EUV absorption forcing in the HME methodology. [61] Second, components that could be excited by a nonlinear wave wave interaction of migrating tide/spw1 type are not well described. This particularly applies to DW2 and D0, and to a lesser extent to SW1 and SW3. This will be discussed more closely in section 6.1 below. [62] Third, components that are less likely to be affected by wave wave interaction between migrating tides and Figure 12. (a) DW2 and D0 density amplitudes from CHAMP (solid) and HME (dashed) at 390 km and 30 S and 0 N, respectively. (b) Same as Figure 12a but for SW3 and SW1 at 15 N and 50 N, respectively. 15 of 21