Sun synchronous thermal tides in exosphere temperature from CHAMP and GRACE accelerometer measurements

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi:10.1029/2011ja016855, 2011 Sun synchronous thermal tides in exosphere temperature from CHAMP and GRACE accelerometer measurements Jeffrey M. Forbes, 1 Xiaoli Zhang, 1 Sean Bruinsma, 2 and Jens Oberheide 3 Received 18 May 2011; revised 24 August 2011; accepted 25 August 2011; published 10 November 2011. [1] This paper focuses on the sun synchronous diurnal (DW1) and semidiurnal (SW2) tidal components of neutral exosphere temperature derived from contemporaneous drag measurements made from the CHAMP and GRACE satellites. Densities are converted to exosphere temperatures using the parametric relationship that exists between density and temperature in the NRLMSISe00 empirical model. Daily, seasonal and solar cycle dependencies of DW1 and SW2 in exosphere temperature are elucidated, and similarities and differences with NRLMSISe00 are detailed. In addition, using TIMED/SABER measurements between 80 110 km and viscous tidal theory, it is demonstrated that the measured seasonal latitudinal variation of the semidiurnal exosphere temperature amplitude is dominated by the part excited in situ in the thermosphere, as opposed to those tidal components that propagate upwards from the lower atmosphere. Citation: Forbes, J. M., X. Zhang, S. Bruinsma, and J. Oberheide (2011), Sun synchronous thermal tides in exosphere temperature from CHAMP and GRACE accelerometer measurements, J. Geophys. Res., 116,, doi:10.1029/2011ja016855. 1. Introduction [2] The response of an atmosphere to changes in solar radiative forcing is one of the fundamental problems of solar planetary connections. The present paper concerns the neutral exosphere temperature response of Earth s thermosphere as determined from accelerometer measurements on the CHAMP and GRACE satellites as described below. Of specific interest are the longitude mean diurnal (24 h) and semidiurnal (12 h) periodic responses that arise due to planetary rotation. In addition, aspects of daily, seasonal and solar cycle changes in these responses are addressed that are due to variations in Earth orbit orientation and the originating solar flux. [3] Longitude mean solar driven tides are often referred to as Sun synchronous or migrating since they possess zonal phase speeds equal to the westward speed of the Sun to a ground based observer. Following recently adopted convention, e.g., of Forbes et al. [2003], we will refer to these migrating diurnal and semidiurnal tides, respectively, as DW1 and SW2 where D refers to diurnal, W denotes westward, and 1 and 2 are the zonal wave numbers for these oscillations that yield sun synchronous zonal propagation for their respective wave frequencies. Studies of non migrating tides have recently been published based 1 Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, Colorado, USA. 2 Department of Terrestrial and Planetary Geodesy, Centre National d Etudes Spatiales, Toulouse, France. 3 Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, USA. Copyright 2011 by the American Geophysical Union. 0148 0227/11/2011JA016855 upon CHAMP and GRACE accelerometer data [Forbes et al., 2008; Oberheide et al., 2009; Bruinsma and Forbes, 2010]. However, as we will see below, derivation of migrating tides from these data requires special consideration due to potential aliasing between temporal variations of zonal mean (i.e., 27 day, semiannual) and local time variations as measured from the satellite perspective. [4] DW1 in the thermosphere originates from two sources: (1) an in situ component driven by absorption of EUV radiation; and (2) a component propagating upwards from the lower atmosphere that mainly originates from troposphere IR radiation absorption and latent heating, with a smaller contribution from UV radiation absorption by stratospheric ozone [Hagan, 1996]. However, the upwardpropagating DW1 is strongly dissipated by molecular diffusion above 130 km, leaving in situ EUV absorption by far as the main driver of solar driven changes to DW1 in exosphere temperature. On the other hand, the SW2 contribution to exosphere temperature variations is thought to be strongly influenced by an upward propagating component excited mainly by UV absorption by stratospheric ozone in addition to a component excited in situ in the thermosphere [Forbes, 1982]. [5] Solar thermal tides in exosphere temperature have expected behaviors with respect to level of solar activity. Since the diurnal tide is almost exclusively excited in situ, its amplitude is expected to increase monotonically with solar activity, although the rate of increase is moderated by ion drag effects on the thermosphere wind system through heating and cooling terms in the thermal balance equation due to vertical motions [Hagan and Oliver, 1985]. For instance, Fesen et al. [1993] predict a factor of 3 increase in DW1 amplitude (from 80 K to 240 K) over the equator for an increase in 81 day average F10.7 solar radio flux from 72 sfu 1of14

to 215 sfu. Similar considerations apply for the semidiurnal tide excited in situ by absorption of EUV radiation. However, the semidiurnal tide propagating upwards from the lower thermosphere is expected to penetrate more easily into the upper thermosphere during solar minimum as opposed to solar maximum [Forbes and Garrett, 1978], thus producing the opposite dependence on solar cycle as the EUV driven component. Ion drag is also expected to influence the thermosphere semidiurnal tide excited in situ through nonlinear interaction with the diurnal tide and perhaps other mechanisms. There have been no studies to date that have attempted to ascertain the relative importance of in situ versus upward propagating components of the semidiurnal tide as a function of solar activity level, either experimentally or through numerical modeling. The present paper will provide some insight into this problem. [6] As noted previously, the purpose of this paper is to study the diurnal and semidiurnal components of the longitude mean local time variation of Earth s exosphere temperature, i.e., DW1 and SW2. The following section describes the data to be utilized and how it is processed for analysis. Section 3 deals with the diurnal tide, and provides insight into solar cycle, day to day, and seasonal variations. The semidiurnal tide is addressed in Section 4, where aliasing with the quasi 27 day variation in radiation due to solar rotation is addressed. Daily variations of the semidiurnal tide are not addressed due to inadequacies in sampling. However, it is shown that the derived seasonal latitudinal variation of SW2 from the CHAMP GRACE analysis agrees reasonably well with exosphere temperatures from the NRLMSISE00 model [Picone et al., 2002], but rather poor correspondence exists between this model and SABER derived SW2 amplitudes and phases at 100 km, i.e., the base of the thermosphere. Using CHAMP GRACE results for exosphere temperature, SABER temperature measurements at 100 km, and a numerical model that emulates the vertical propagation of tides from 100 to 400 km, an estimate is provided of the separated vertically propagating and in situ generated SW2 components. Section 5 is reserved for concluding remarks. 2. Data and Method of Analysis [7] The data to be employed in this study are thermosphere total mass densities inferred from accelerometer measurements on the CHAMP and GRACE satellites, which are in near polar orbits and have been supplying data since July, 2000 and March, 2002, respectively. See Bruinsma et al. [2004, 2006, and references therein] for various details relating to the derivation of densities from accelerometer measurements and related errors. Briefly, uncertainty in the drag coefficient is about 5 15% and is the most important systematic error. Errors relating to calibration, resolution, altitude, mass, and the satellite macromodel are all less than 1% for both systematic and noise errors. The largest source of error in inferring densities from in track accelerations is due to uncertainty in knowledge of neutral winds, which also contribute to the measured drag. Outside the polar/ auroral region and for quiet geomagnetic conditions, the effects of winds are estimated to be small. [8] There are several steps that must be taken to derive tides from the total mass densities inferred from the accelerometer measurements. First, the CHAMP and GRACE data must be inter calibrated to remove possible biases due to differences in drag coefficients and other effects. This is done by computing the mean ratios of the CHAMP and GRACE densities to the NRLMSISE00 empirical model [Picone et al., 2002], and adjusting the densities so that this ratio is unity. The mean measured/model density ratio was found to be constant (1.23*GRACE = CHAMP) for all the periods of analysis, and application of this ratio removed this bias. Second, since the measured densities come from different satellites at different altitudes, a conversion must be made from total mass density to exosphere temperature so that the data can be combined together in a least squares tidal fit. The idea of parametrically relating thermosphere densities and temperatures is not a new one, as it is the backbone of all empirical models to date, because the vertical distribution of thermosphere density is assumed to follow the barometric law. Furthermore, when temperature is independent of height (as it is for the 400 500 km altitude range considered here) the scale height of each constituent is constant, and a simple exponential dependence with height applies. The study by Forbes et al. [2009] was successful in producing results that were consistent with other data sets, and we will follow the same procedure in this study. That is, for each measured density, the F10.7 solar flux input to the model is varied iteratively in a loop until the model density converges on the measured density, and this then yields the equivalent exosphere temperature from the model. All of this is possible due to the parametric dependence between density and exosphere temperature. This procedure also assumes that atomic oxygen is the predominant constituent, otherwise composition errors in the model can affect the extracted temperatures. During the extremely low solar minimum beginning in 2008, densities measured by the GRACE satellite at 476 km were likely contaminated by the presence of Helium [Bruinsma and Forbes, 2010]. Therefore, the present study only extends to 2007. We recognize that these exosphere temperatures represent approximations to the true exosphere temperatures, and might contain biases imposed by the model. However, since we are interested in tidal perturbations about the mean exosphere temperature, we maintain that these tidal perturbations are relatively unaffected by any such biases that might exist. [9] As a result of the above procedure, exosphere temperatures are available every 80 km in latitude, nearly pole to pole at 4 local times and at approximately 16 longitudes per day for both the ascending and descending parts of each orbit. These are the basic data for analysis. The data are binned into 3 degree latitude bins since we are only interested in global structures, and this also helps to reduce noise. From this point we follow two different approaches, one involving daily fits, and the other involving fits during 72 day windows slid forward in time once per day. In each case, the longitude dependence is removed by constructing zonal means, since in this paper we are only interested in the Sun synchronous (longitude independent) tidal components. For the daily fits, at any given latitude one must perform a tidal analysis on data points at only 4 local times. Four data points is adequate to determine a daily mean and diurnal (24 hour) harmonic provided that these points are 2of14

Figure 1. Samples of fits to (red) CHAMP and (blue) GRACE zonal mean equatorial temperatures; the color dots with smaller black dot inside are the ascending nodes. The top plot shows the fit when the orbital planes are close to orthogonal, whereas the bottom plot corresponds to the case where the local times of CHAMP and GRACE are close to 3 hours separation. sufficiently separated, but are inadequate to additionally extract a 12 hour (semidiurnal) harmonic. We have found that stable and consistent results for the mean and diurnal harmonics are obtained with 4 data points (2 each on the ascending/descending parts of the orbit on opposite sides of the Earth) with a minimum 3 hour separation in local time between them. Two representative sample fits are shown in Figure 1. The ascending and descending portions of CHAMP and GRACE orbits precess through 24 hours of local time in about 260 and 320 days, respectively, so that the relative local times between them evolve slowly with time. The top plot in Figure 1 shows the fit when the orbital planes are close to orthogonal, whereas the bottom plot corresponds to the case where the local times of CHAMP and GRACE are close to 3 hours separation. However, since the relative local time precession rate between CHAMP and GRACE is rather slow, there are long periods of time ( 1 year) where the minimum 3 hour data point separation is, or is not, satisfied. These are illustrated in Figure 2. [10] In this paper we will use Hough Mode Extensions (HMEs) [Lindzen et al., 1977; Forbes and Hagan, 1982] to estimate the vertical extension of upward propagating tides into the thermosphere above about 90 km [Svoboda et al., 2005; Oberheide et al., 2009, 2011]. A HME can be thought of as an extension of a Hough mode from classical atmospheric tidal theory [Chapman and Lindzen, 1970] in that tidal dissipation due to molecular diffusion of heat and momentum is accounted for. Thus, a HME of given wave number and frequency is a self consistent latitude versus height set of amplitudes and phases for the perturbation fields in temperature, zonal, meridional and vertical winds, and density (T, u, v, w, r). For example, fitting HMEs to observed tides in T in a limited height and latitude range also results in tidal amplitudes and phases for (T, u, v, w, r) and at latitudes and altitudes not measured. This type of approach works well in the thermosphere where molecular dissipation is the dominant process affecting the structure of a vertically propagating tide. In our case, we will perform fits to temperatures from SABER measurements in 90 110 km height region, and utilize the HMEs to estimate the contribution of the upward propagating semidiurnal tide to the total semidiurnal tidal signal in exosphere temperature. HMEs and their successful application to TIMED and Figure 2. DW1 amplitudes (K) resulting from daily fits to CHAMP and GRACE exosphere temperatures when data points are at least 3 hours apart (cf. Figure 1). The occasional white vertical stripes occur when there are missing data, and the large white areas correspond to periods when local times of CHAMP and GRACE are less than 3 hours apart. 3of14

Figure 3. Latitude versus UT variation of DW1 exosphere temperature amplitude (K) for the period 3 Nov 2003 14 Jan 2004. (top) Amplitude and (bottom) phase derived from (left) CHAMP and GRACE data and from (right) NRLMSISE00 for the same period. The solid line indicates the daily value of F10.7, which ranges between 86 (min) and 190 (max). CHAMP data in this way are discussed by Oberheide and Forbes [2008] and Oberheide et al. [2009, 2011]. 3. The Migrating Diurnal Tide, DW1 [11] We now present results for DW1, first for the daily determinations and then for the 72 day sliding window results. SW2 is addressed in the following section. [12] Latitude versus UT variations of the DW1 temperature amplitude and phase for one segment in the first analysis period, namely 3 Nov 2003 14 Jan 2004, is illustrated in Figure 3. The left plots illustrate the amplitude and phase determined from the CHAMP GRACE measurements, and the right plots are the corresponding representations for NRLMSIS00. This period of time was chosen to illustrate the only example where the diurnal tide amplitude maxima occurred near +20 latitude rather than being centered around the equator, as in the model. It is furthermore noted that the sub solar point is in the Southern Hemisphere during this period. The reason for this behavior is unclear, but may be somehow related to modifications of the ionosphere thermosphere that likely took place during the magnetically disturbed periods between October 28, 2003 and November 22, 2003. Note that the observed diurnal maximum amplitude varies from about 80 to 160 K in response to the quasi 27 day solar flux rotation, whereas the corresponding amplitude range in the model is about 120 140 K. The observed phases are also somewhat more variable than the model during this period, although there is consistency in that the Southern Hemisphere phases ( 13.5 15.0 h) slightly lead those in the Northern Hemisphere ( 15.5 h). [13] Results for the 10/13/2007 12/14/2007 period are shown in Figure 4. Again the range of maximum diurnal amplitudes (at the equator) is greater in the observations ( 60 120 K) than in the model ( 83 100 K), but this time both modeled and observed amplitudes are symmetric about the equator and the corresponding phases reflect similar differences in temporal and latitudinal variability as in Figure 3. [14] It appears that there is a several day delay between DW1 amplitudes and major excursions in F10.7. We performed a lagged correlation analysis between the F10.7 and diurnal amplitude time series, and found that the temperature response (maximum correlation) occurred 1 day later than F10.7 in Figure 3, and 2 days later for Figure 4, for 4of14

Figure 4. Same as Figure 3, except for 13 Oct 2007 23 Dec 2007. The solid line indicates the daily value of F10.7, which ranges between 66 (min) and 94 (max). both the data and NRLMSISE00. The correlation analysis is probably affected by the shapes of these two time series, so that one cannot infer time delays simply by looking at peak values in Figures 3 and 4. [15] If one considers 72 day windows, then complete 24 hour local time coverage is obtained by combining CHAMP and GRACE exosphere temperatures together, continuously from 2003 through 2007. By sliding the 72 day window forward one day at a time, a depiction of the longterm trend in diurnal temperature amplitude and phase associated with solar cycle as well as seasonal variations is obtained, as illustrated in Figure 5. Also shown is the 72 day running mean value of F10.7 superimposed as a line plot. The diurnal tidal amplitudes clearly show a declining trend with solar activity, and the mean linear relationship between 72 day mean values of diurnal temperature amplitude (DW1) and F10.7: DW 1 ¼ 41:3 þ 0:789 * F10:7 (linear correlation coefficient = 0.84) is roughly the same as that for the daily values depicted in Figure 2: DW 1 ¼ 45:3 þ 0:792 * F10:7 [16] Furthermore, for the most part, the amplitude response is symmetric about the equator. There is not much of a seasonal trend observable in the amplitudes. The observed phases are generally of order 15.0 16.0 h at low latitudes, and have the tendency to be slightly earlier during local summer ( 14.0 h) than local winter ( 15.0 h) poleward of about 40 latitude in each hemisphere. NRLMSIS00 does a good job of capturing the mean characteristics of the observations. However, while the rate of increase of DW1 amplitude with solar activity is consistent with NRLMSISE00, it is somewhat less than that reflected in existing numerical simulations. For instance, if we assume a linear change in DW1 amplitude with 81 day averaged F10.7, then the solar minimum and maximum results from the model of Fesen et al. [1993] would predict an increase in DW1 amplitude from about 80 K to 160 K over the range of solar conditions depicted in Figure 5, whereas the range of CHAMP GRACE amplitudes extends from about 80 K to 140 K. 4. The Semidiurnal Migrating Tide, SW2 [17] As noted previously, it is not possible to determine the semidiurnal (12 h) wave component from only four measurements per day. The next best solution is obtained 5of14

Figure 5. 72 day running mean DW1 amplitudes (K) and phases (h) for the 2003 2007 time period considered in this study. The top two plots are the amplitude and phase derived from CHAMP and GRACE. The bottom two plots are the amplitude and phase derived from NRLMSISE00. The solid black line is the 72 day running mean of F10.7, which ranges between 67 (min) and 144 (max). 6of14

Figure 6. Representative exosphere temperature fits (using diurnal and semidiurnal sinusoids) within 72 day windows covering 24 hours of local time. The wavy line near the top of each plot is the semidiurnal part of the fit, but is shifted up by 1100 K. during 72 day periods when the relative precession between CHAMP and GRACE provides full 24 hour local time coverage. These occur within the periods of daily diurnal tide acquisition depicted in Figure 2. Some sample fits consisting of diurnal and semidiurnal tidal components, and that reflect the range of diurnal shapes and data variability encountered, are provided in Figure 6 for several of these 72 day windows. Our approach is to slide these 72 day windows through the data at each latitude so that latitude versus time depictions of SW2 amplitude and phase are obtained, as illustrated in Figure 7. However, the fits demonstrated in Figure 6 are made to data points that have been corrected for aliasing due to quasi 27 day variations in the data due to solar rotation changes in the solar flux. This aliasing removal process and final results for the semidiurnal tide are now presented. [18] The potential for aliasing of the quasi 27 day variation into the semidiurnal tide determination became apparent when we compared the seasonal latitudinal distributions of semidiurnal amplitudes and phases derived from CHAMP GRACE sampling of the NRLMSIS00 model (Figure 7, top plots) with the true 72 day mean solutions specified by the unsampled model (Figure 7, bottom plots). Note that significant differences exist between these two depictions. The middle plot illustrates the solution obtained by CHAMP GRACE sampling of NRLMSIS00 with the 27 day variation empirically removed according to NRLMSIS00. The extent to which the middle plot of Figure 7 agrees better with the bottom than does the top, provides a measure of to what degree contaminating effects from this source have been removed. Other differences are likely connected with the fact Figure 7. Latitude versus month depictions of SW2 exosphere temperature (left) amplitudes and (right) phases during December July 2006, when full local time coverage was realized during 72 day running mean windows. (top) From NRLMSISE00 values according to CHAMP GRACE sampling. (middle) From NRLMSISE00 values according to CHAMP GRACE sampling, but corrected for aliasing effects due to F10.7 related variations. (bottom) True result from NRLMSISE00 values, full sampled. 7of14

Figure 7 8of14

Figure 8. Same as Figure 7, except (top) from fitting CHAMP GRACE exosphere temperatures. (middle) From fitting CHAMP GRACE exosphere temperatures, but corrected for aliasing effects due to F10.7 related variations. (bottom) Predicted by Hough Mode Extensions (HMEs) fit to SABER temperature data between 80 and 110 km. The latter only contains that part of the total semidiurnal variation propagating upwards from below 100 km. that we are sampling a semidiurnal tide that is evolving in time due to changes in forcing or propagation conditions. [19] In approaching analysis of the actual measurements, we derived our own empirical relationship between daily residual F10.7 radio fluxes and exospheric temperatures from 81 day mean values, which turned out to reveal a linear relationship very close to that embodied in NRLMSIS00. A comparison between the uncorrected and corrected amplitude and phase distributions of the semidiurnal tide for the 2006 time period is provided in the top and middle plots of 9of14

Figure 9. Same as Figure 8, except for January July 2004. Figure 8, respectively. Note that many aspects of the amplitude and phase distributions revealed in the middle plots of Figure 8 are quite similar to those expressed in the model (Figure 7, bottom plots). For instance, maxima are found near +20 and 40 latitude during Northern Hemisphere winter, these maxima shift to +40 and 20 during Northern Hemisphere summer, and minimum amplitudes are found around March equinox. Phases are also in good agreement, including 2 3 hour shifts in each hemisphere between solstices. Similar results are obtained during a second period in 2004 when sampling is adequate to determine the semidiurnal tide during 72 day intervals (Figure 9). The seasonal asymmetry reflected in the measurements is likely due in part to well known seasonal asymmetries in the zonal mean winds of the middle atmosphere, but similar effects might exist in thermosphereionosphere propagation conditions as well. 10 of 14

[20] In comparing the F10.7 corrected results (Figures 8 and 9, middle plots) with NRLMSIS00, we conclude the following: The amplitude peaks in the model are all in the range of 20 30 K, whereas the measurements are all of order 35 45 K in Northern Hemisphere winter and 25 30 K in the Northern Hemisphere summer season. So, NRLMSIS00 appears to consistently underestimate by about 50% semidiurnal tidal amplitudes during December January, but otherwise provides a reasonable approximation of the semidiurnal variation in exosphere temperature during other months, and also reasonably emulates seasonal latitudinal phase structures. [21] We now turn our attention to deconvolving the semidiurnal structures analyzed above, and attempt to ascertain to what extent these structures originate from in situ forcing, or to that propagating upwards from the atmosphere below 100 km. To link the semidiurnal tidal temperatures near 100 110 km and those derived from density measurements around 400 km, we will employ what are called Hough Mode Extensions (HMEs), as described at the end of Section 2. As noted in Section 2, the u, w, v, T, r perturbation fields maintain internally self consistent relative amplitude and phase relationships for any given HME. So, if the amplitude and phase of the perturbation wind field is known for a given HME at a single latitude and height, then all the fields, u, w, v, T, r are known for all latitudes and all heights. So, by capturing the seasonal latitudinal structures of measured semidiurnal temperatures at 110 km, we can provide a reasonable estimate of the corresponding amplitudes and phases at 400 km, basically because this vertical extrapolation is dominated by the processes of molecular diffusion of heat and momentum, and since these effects on vertically propagating tides are reasonably well known, capable of being emulated by numerical modeling, and such extrapolations have been validated for other tidal components [Oberheide et al., 2009]. [22] Consider the 60 day mean amplitudes and phases at 110 km derived from SABER temperature data using the methods described in Forbes et al. [2008], as shown in the middle plots of Figure 10. It is immediately obvious from comparisons with NRLMSIS00 results in the bottom plots of Figure 10, that there is a large gap between the observed semidiurnal tide and that embodied in the most up to date model for that atmospheric region; in fact, significant differences exist in overall seasonal latitudinal structure as well as in temperature amplitudes and phases. This is not surprising, given the paucity of temperature data from these altitudes that were used in construction of NRLMSIS00 and its predecessor MSISE90 [Hedin,1991]. [23] Also shown in the top plots of Figure 10 are the reconstructed amplitude and phase structures obtained by fitting the first four semidiurnal HMEs (i.e., corresponding to the first two symmetric Hough functions widely known as (2,2) and (2,4), and the first two antisymmetric Hough functions (2,3) and (2,5). Because these fitting functions are close to orthogonal at 110 km, additional fitting functions would ultimately converge to emulate the fine details of the SABER observations, but here we are only interested in the aforementioned HMEs because higher order modes become preferentially dissipated above 110 km and do not contribute measurably to the exosphere temperature field. Similar results are obtained for the 2004 period (not shown) since 2004 and 2006 correspond to the same phase of the QBO and otherwise the 72 day mean semidiurnal tidal structures do not vary much from year to year [Forbes et al., 2008]. [24] Referring now to the bottom plots of Figures 8 and 9, these represent the semidiurnal tidal variation in exosphere temperature during 2006 and 2004, respectively, due to tidal components constituting the structures displayed at 110 km in Figure 10, as estimated by the superposition of the HMEs. Since the relative amplitudes of the (2,2), (2,3), (2,4) and (2,5) HMEs evolve differently with height in the thermosphere [Forbes and Hagan, 1982], the semidiurnal structures differ substantially between the two altitudes. Semidiurnal amplitudes are smaller in the upper thermosphere due to the effects of molecular dissipation, which preferentially damps higher order modes with shorter vertical wavelengths. Also, the exosphere temperature amplitudes do not differ substantially between 2004 and 2006 since the difference in molecular dissipation between these two levels of solar activity is insufficient to introduce perceptible influences on the HME vertical structures. [25] Summarizing to this point, the middle plots of Figures 8 and 9 represent the observed 72 day mean SW2 amplitudes and phases derived from CHAMP and GRACE data during 2004 and 2006, and the bottom plots represent the estimated contributions to these structures due to tidal components propagating upwards from the atmosphere below 100 km, as estimated from upward extrapolation of measured TIMED/SABER temperatures using a numerical dissipative tidal model. Therefore, the differences between the bottom and middle plots of Figures 8 and 9 are due to that part of SW2 that is excited in situ in the thermosphere. Taking vector differences, this in situ component of SW2 is depicted in Figure 11. The amplitude and phase structures are very similar between 2004 and 2006, although amplitudes are slightly larger for 2004, which corresponds to a higher level of solar activity. Note that amplitudes are broadly of order 20 40 K with maximum amplitudes tending to occur around 0 20 latitude during April July, and for a bifurcated structure to exist about the equator in the Northern Hemisphere winter months. As noted by Forbes and Garrett [1979], the in situ semidiurnal tide is likely not simply driven by solar EUV heating, but is also determined by the influences of ion drag. To the authors knowledge, numerical simulations have not been published that provide direct comparisons with these results. 5. Summary and Conclusions [26] This paper focuses on the Sun synchronous diurnal and semidiurnal tides in the upper thermosphere ( 400 500 km) as observed by accelerometers on the CHAMP and GRACE satellites during 2002 2007. The long lifetimes of these satellites, and the relative local time precession rates of their orbital planes, provides the opportunity to delineate interannual, seasonal, intraseasonal and daily time scale variations in the latitudinal structures of these tides. The primary results to emerge from this study are as follows: [27] (1) The variation in diurnal amplitude and phase with respect to solar activity averaged over several 27 day solar rotations is delineated, and found to be similar to that embodied in the NRLMSISE00 empirical model. [28] (2) The variation in semidiurnal diurnal tide analogous to (1) could not be retrieved from the data, due to 11 of 14

Figure 10. 60 day running mean SW2 temperature (left) amplitudes and (right) phases during the December 2005 July 2006 period. (top) HME fit to SABER SW2 shown in middle plot. (middle) SW2 derived from SABER data. (bottom) SW2 as predicted by NRLMSISE00. inadequate sampling with respect to local time over a sufficient range of solar activity conditions. [29] (3) The day to day variation of the latitude structure of the diurnal thermospheric tide is revealed for the first time. This variability appears mainly solar driven with a strong correlation with 27 day variations in daily 10.7 cm solar radio flux due to rotation of the Sun. In one illustrated period maxima in the diurnal amplitude were found in the hemisphere opposite to that of the subsolar point. Based on Kp levels it appears that this effect may be the result of some sort of interference between the solar and geomagneticallydriven responses of the thermosphere. 12 of 14

Figure 11. Vector differences between bottom and middle plots of (top) Figures 8 and (bottom) 9. These represent estimates of that part of SW2 excited in situ in the thermosphere. [30] (4) The seasonal latitudinal variation of the semidiurnal tide in the upper thermosphere has similar characteristics to those in the NRLMSISE00 model; but the model underestimates amplitudes during December January by about 50%. [31] (5) The seasonal latitudinal variation of the NRLMSISE00 semidiurnal tide in the lower thermosphere at 110 km has characteristics quite different from those found in TIMED/ SABER temperatures at the same altitude. [32] (6) TIMED SABER temperatures between 90 and 110 km are fit with a set of tidal theory based Hough Mode Extensions (HMEs), which are then used to estimate the upper thermosphere response to semidiurnal tides propagating upwards from the lower atmosphere. These estimates are vectorially removed from the total measured semidiurnal response in the upper thermosphere to reveal the seasonallatitudinal variation of thermospheric semidiurnal tide excited in situ in the thermosphere. [33] (7) All of the above results should prove useful to the ionosphere thermosphere modeling community for validation purposes. The tidal data products produced in this study are available to the community through requests to the authors. [34] Acknowledgments. This work was supported in part by Grant ATM 0719480 from the National Science Foundation under the Space Weather Program, and by AFOSR MURI Grant FA9550 07 1 0565. [35] Robert Lysak thanks the reviewers for their assistance in evaluating this paper. References Bruinsma, S. L., and J. M. Forbes (2010), Anomalous behavior of the thermosphere during solar minimum observed by CHAMP and GRACE, J. Geophys. Res., 115, A11323, doi:10.1029/2010ja015605. Bruinsma, S., D. Tamagnan, and R. Biancale (2004), Atmospheric densities derived from CHAMP/STAR accelerometer observations, Planet. Space Sci., 52, 297 312. Bruinsma, S., J. M. Forbes, R. S. Nerem, and X. Zhang (2006), Thermosphere density response to the 20 21 November 2003 solar and geomagnetic storm from CHAMP and GRACE accelerometer data, J. Geophys. Res., 111, A06303, doi:10.1029/2005ja011284. Chapman, S., and R. S. Lindzen (1970), Atmospheric Tides: Thermal and Gravitational, 200 pp., Gordon and Breach, New York. 13 of 14

Fesen, C. G., R. G. Roble, and E. C. Ridley (1993), Thermospheric tides simulated by the National Center for Atmospheric Research Thermosphere Ionosphere General Circulation Model at equinox, J. Geophys. Res., 98, 7805 7820. Forbes, J. M. (1982), Atmospheric tides. I. Model description and results for the solar diurnal component, J. Geophys. Res., 87, 5222 5240. Forbes, J. M., and H. B. Garrett (1978), Thermal excitation of atmospheric tides due to insolation absorption by O 3 and H 2 O, Geophys. Res. Lett., 5, 1013 1016, doi:10.1029/gl005i012p01013. Forbes, J. M., and H. B. Garrett (1979), Theoretical studies of atmospheric tides, Rev. Geophys., 17, 1951 1981. Forbes, J. M., and M. E. Hagan (1982), Thermospheric extensions of the classical expansion functions for semidiurnal tides, J. Geophys. Res., 87, 5253 5259. Forbes, J. M., X. Zhang, E. R. Talaat, and W. Ward (2003), Nonmigrating diurnal tides in the thermosphere, J. Geophys. Res., 108(A1), 1033, doi:10.1029/2002ja009262. Forbes, J. M., X. Zhang, S. Palo, J. Russell, C. J. Mertens, and M. Mlynczak (2008), Tidal variability in the ionospheric dynamo region, J. Geophys. Res., 113, A02310, doi:10.1029/2007ja012737. Forbes, J. M., S. L. Bruinsma, X. Zhang, and J. Oberheide (2009), Surfaceexosphere coupling due to thermal tides, Geophys. Res. Lett., 36, L15812, doi:10.1029/2009gl038748. Hagan, M. E. (1996), Comparative effects of migrating solar sources on tidal signatures in the middle and upper atmosphere, J. Geophys. Res., 101, 21,213 21,222. Hagan, M. E., and W. L. Oliver (1985), Solar cycle variability of exospheric temperature at Millstone Hill between 1970 and 1980, J. Geophys. Res., 90, 12,265 12,270. Hedin, A. E. (1991), Extension of the MSIS thermosphere model into the middle and lower atmosphere, J. Geophys. Res., 96, 1159 1172. Lindzen, R. S., S. S. Hong, and J. M. Forbes (1977), Semidiurnal Hough mode extensions into the thermosphere and their application, Memo. Rep. 3442, Naval Res. Lab., Washington, D. C. Oberheide, J., and J. M. Forbes (2008) Tidal propagation of deep tropical cloud signatures into the thermosphere from TIMED observations, Geophys. Res. Lett., 35, L04816, doi:10.1029/2007gl032397. Oberheide, J., J. M. Forbes, K. Häusler, Q. Wu, and S. L. Bruinsma (2009), Tropospheric tides from 80 to 400 km: Propagation, interannual variability, and solar cycle effects, J. Geophys. Res., 114, D00I05, doi:10.1029/ 2009JD012388. Oberheide, J., J. M. Forbes, X. Zhang, and S. L. Bruinsma (2011), Wavedriven variability in the ionosphere thermosphere mesosphere system from TIMED observations: What contributes to the wave 4?, J. Geophys. Res., 116, A01306, doi:10.1029/2010ja015911. Picone, J. M., A. E. Hedin, D. P. Drob, and A. C. Aikin (2002), NRLMSISE 00 empirical model of the atmosphere: Statistical comparisons and scientific issues, J. Geophys. Res., 107(A12), 1468, doi:10.1029/2002ja009430. Svoboda, A. A., J. M. Forbes, and S. Miyahara (2005), A space based climatology of MLT winds, temperatures and densities from UARS wind measurements, J. Atmos. Sol. Terr. Phys., 67, 1533 1543. S. Bruinsma, Department of Terrestrial and Planetary Geodesy, Centre National d Etudes Spatiales, 18 Ave. E. Belin, F 31401 Toulouse, France. (sean.bruinsma@cnes.fr) J. M. Forbes and X. Zhang, Department of Aerospace Engineering Sciences, University of Colorado, Campus Box 429, Boulder, CO 80309 0429, USA. (forbes@colorado.edu; xiaoli.zhang@colorado.edu) J. Oberheide, Department of Physics and Astronomy, Clemson University, 118 Kinard Laboratory, Clemson, SC 29634 0978, USA. (joberhe@clemson.edu) 14 of 14