We present direct, global observations of longitudinally averaged CHAMP zonal winds gathered between 2003 and 2007. A diurnal variation dominates the global zonal wind. Westward flows are observed from the early morning through afternoon hours, while eastward flows peak in the evening. A semidiurnal harmonic is also present, with magnitudes that are approximately one third of the diurnal harmonic. The time mean wind indicates westward winds over much of the globe, with weak superrotation (+E, or eastward winds) that is symmetric about the equator during equinox, and confined to the winter hemisphere at solstice. Diurnal and time mean CHAMP winds agree fairly well with the Whole Atmosphere Model. Some differences are observed in the semidiurnal and higher‒order tidal winds, that underscore the challenges of modeling the sources, sinks, and mean wind effects upon tides between the surface and 400 km.
 Thermospheric winds play an important role in ionosphere‒thermosphere coupling, through dynamo generation and transport of plasma along magnetic field lines. Knowledge of the thermospheric wind is therefore important for diagnosing ion‒neutral interactions, validating coupled models, and predicting the electrodynamics of the near‒Earth space environment.
 The CHAllenging Minisatellite Payload (CHAMP) mission studied the Earth's gravity field, magnetic field, and atmosphere/ionosphere between July 2000 and September 2010 [Reigber and Lühr, 2002]. Global, cross‒track winds have been derived from the Spatial Triaxial Accelerometer for Research (STAR) aboard CHAMP. With a local time precession rate of about 5 min day−1, CHAMP allows for a 24 h coverage in local time over 130 days [Häusler and Lühr, 2009]. We present the first global, monthly mean migrating diurnal and semidiurnal variations observed in thermospheric zonal winds, as well as the seasonal variations of the time mean winds. We compare these with predictions from the Whole Atmosphere Model (WAM) [Akmaev, 2011] and note the implications for thermospheric wind modeling.
2 Data and Analysis
 CHAMP was a 10 year mission managed by the GeoForschungsZentrum in Germany, whose primary goal was to map Earth's magnetic and gravity fields. The STAR measured non‒gravitational forces acting on the spacecraft, among which the drag is dominant. All aspects of the mission and the accelerometer experiment are described by Bruinsma and Tamagnan . Cross‒track winds have been derived from acceleration values by Liu and Lühr  and Doornbos et al. . Liu and Lühr  compared 2002–2004 CHAMP winds within 5° of the magnetic equator with the Horizontal Wind Model (HWM‒93) and documented the sensitivity of longitudinally averaged equatorial zonal winds to solar and geomagnetic activity. More recently, Doornbos and van den Ijssel  developed an iterative scheme to derive winds and densities from accelerometer measurements that operates independently of the instrument orientation in space. We examine the global wind field using this new data set, distributed at http://thermosphere.tudelft.nl/acceldrag/data.php?cat=CH_PN_R02.
 CHAMP was stabilized in a circular, near‒polar orbit, starting at about 450 km in 2000 and descending to 350 km by the end of 2007. Between roughly 65°S and 65°N, CHAMP ground‒relative orbit tracks are aligned north‒south, implying that the crosswind orientation is east‒west, or zonal. Daily measurements are fixed in local time, with a separation of approximately 12 h between the ascending and descending node observations. The orbital precession of CHAMP results in 24 h local time coverage within 131 days.
 This study utilizes winds between 2003 and 2007. Our analysis begins with the formation of daily longitudinal averages of the east‒west crosswind, which are then binned in 5° wide latitude bins by calendar month and by local time. Data are only used for conditions when the Kpgeomagnetic activity index does not exceed 3. The number of data points involved in a typical monthly calculation is roughly 42,000 or 1750 per hourly local time bin. An additional filter is imposed by retaining only crosswinds within two standard deviations of the 5 year mean. The longitudinal averaging removes perturbations in longitude, in particular non‒migrating tides (i.e., tides with universal time dependence). The resulting daily averaged winds represent motions that are invariant with respect to local time: the time mean wind and the migrating tides. At each latitude, monthly composite 24 h time series are Fourier transformed to obtain the time mean, diurnal, and semidiurnal harmonics, the latter commonly denoted DW1 and SW2, respectively.
 The crosswind error is mainly caused by errors in the cross‒track acceleration, either through the accelerometer calibration bias or through errors in the solar radiation pressure acceleration model [Doornbos and van den Ijssel, 2010]. These errors have a dependence on the orientation of the orbit plane with respect to the Sun and therefore on the local solar time at the measurement locations. In addition to this dependence on orbit geometry, the effect of cross‒track acceleration errors on the crosswind errors is modulated by the level of neutral density. When density is low, such as at high altitude, at nighttime hours and during low solar and geomagnetic activity, the aerodynamic accelerations from which the wind speeds are derived will be smaller, relative to calibration and radiation pressure acceleration model errors, and the resulting crosswind data will have larger errors.
 Attempts to quantify the complexity in the CHAMP crosswind error budget have been made by Liu and Lühr , Sutton and Nerem , and Doornbos and van den Ijssel , with each of these subsequent publications taking more details into account, which in general leads to larger error estimates. We will consider here an error estimate from Doornbos et al. , which was generated by propagating a 10 nm s−2acceleration offset over all data in the year 2004. This resulted in a 140 ms−1RMS crosswind error. This value was used to estimate the uncertainty of the time mean winds, and tidal wind amplitudes and phases (in hours). These estimates, summarized in Table 1, are obtained by iterating the analysis method 200 times upon a prescribed combination of time mean and tidal wave wind fields, perturbed by random fluctuations scaled by the 140 ms−1measurement uncertainty. The tabulated values have been averaged between 70°S–70°N. It is apparent that random errors are greatly reduced by the analysis method, due to the large sample size. A systematic part of the local solar time dependent cross‒track acceleration error will still be present in the CHAMP wind data. The magnitude of this type of error in the CHAMP wind data will remain uncertain until comparisons are made with independent observations.
Table 1. Uncertainties of the Time Mean Wind (in m s−1), Diurnal and Semidiurnal Amplitudes and Phases (in Hours)
 WAM is a general circulation model of the neutral atmosphere extending from the surface to the exobase at the average nominal height of about 600 km [Akmaev, 2011]. Built from the operational weather prediction Global Forecast System model, it has been demonstrated to realistically reproduce important tidal waves generated in the lower atmosphere [Akmaev and Fuller‒Rowell, 2008; Akmaev, 2011]. To represent the ionosphere‒atmosphere interactions, WAM incorporates empirical models of plasma density [Chiu, 1975] and dynamo electric fields (A. D. Richmond et al., unpublished data, 2009). For this study, the WAM zonal winds at a pressure level near 400 km are taken from a climatological annual run corresponding to quiet and low solar and geomagnetic conditions.
 The evolution of the longitudinally averaged zonal wind (denoted U) in local time is shown in Figure 1 for March and December. CHAMP's altitudes ranged between 350 and 400 km over the 5 year period when the winds were collected. Winds are generally directed away from the afternoon equatorial pressure bulge [Volland and Mayr, 1977] or from Earth's dayside to nightside. Poleward of 30°, westward winds are observed between 3 A.M. and 2 P.M., with eastward winds prevailing during the remaining hours. At low latitudes, the westward wind pattern contracts into a symmetric “hourglass” pattern in local time in March, with a narrow minimum of 120 m s−1near 7 A.M. during both seasons. Globally, the zonal wind pattern is symmetric in latitude at equinox, with local minima at the equator and stronger maxima and minima at higher latitudes, particularly for the eastward wind. At solstice, maxima are located away from the equator.
 The symmetric equinoctial global pattern is reflected in the time mean component of the zonal wind (Figure 1, second row). Time mean winds are westward over middle and high latitudes, and weakly eastward equatorward of 20°. The dominance of the westward winds is reflected in the global (70°S–70°N) mean U values indicated in the second row plots. The equatorial eastward wind represents the well known superrotation driven by the downward F layer dynamo electric field after the sunset [Rishbeth, 1971]. In December, the eastward winds shift to winter middle latitudes.
 Much of the global wind variability projects into the in situ generated diurnal harmonic (Figure 1, third row). The diurnal migrating tide exhibits key features of the total wind field: the dayside‒to‒nightside flow, the global symmetry at equinox, asymmetry at solstice, and maximum amplitudes of about 130 ms−1. The equatorial eastward flow driven by ion drag in the F layer during nighttime also projects into a diurnal variation. Standard decomposition of the eastward biased diurnal wind pattern into a mean and a diurnal sinusoid results in an apparent phase shift of DW1 at low latitudes: for example, the zero wind line shifts to later time in the afternoon to about 4 P.M. with a corresponding morning “tongue” extending eastward to 4 A.M. The semidiurnal migrating tide (SW2) is characterized by fairly uniform global structure at equinox with amplitudes of about 20 ms−1. At solstice, the maximum amplitudes reach about 50 ms−1at high latitudes in the winter hemisphere. The SW2 phase corresponds to maximum eastward winds at 4 A.M. or P.M.
 Figure 2 shows comparable fields from WAM. The model full‒wind field and migrating diurnal tide reproduce the salient morphological features of observed winds: the dayside‒to‒nightside flow, a local amplitude minimum at low latitudes and maximum amplitudes at high latitudes. The time mean component exhibits the same symmetric structure with equatorial superrotation turning westward poleward of 20–30° latitude as well as a more asymmetric distribution at solstice. Modeled wind values in general are weaker than CHAMP values. Most of the total wind variability arises from the diurnal tide generated in situ by absorption of solar extreme ultraviolet radiation. The lower amplitude of DW1 in WAM is likely explained by the fact that the model output corresponds to solar minimum conditions while the CHAMP data were collected during years of low to medium solar activity. The phase of WAM diurnal tides is generally quite consistent with values observed in CHAMP, including the equatorial phase shift to later hours.
 Amplitudes and phases of the modeled semidiurnal tide agree generally well with CHAMP at middle and low latitudes at equinox. However, the secondary amplitude maximum observed at higher northern latitudes is not seen in the model. The phase (hour of maximum) of the modeled semidiurnal tide tilts to later hours at high southern latitudes, unlike the observations. In December, the phase of the semidiurnal tide generally agrees with the observations in the northern hemisphere, however, WAM amplitudes in the winter hemisphere are weaker than observed. December WAM semidiurnal tides maximize in the southern hemisphere, where they exceed CHAMP values and are nearly out of phase with the observations.
 Unlike the diurnal oscillation, the semidiurnal tide is a superposition of the waves propagating upward from the stratosphere and generated in situ in the thermosphere [Volland and Mayr, 1977]. The SW2 tide excited in the middle atmosphere appears to be somewhat overestimated in WAM compared to satellite observations in the lower thermosphere, particularly at high latitudes [Akmaev and Fuller‒Rowell, 2008]. It is also known to be highly sensitive to the background winds and is affected by dissipative processes on its way to the CHAMP altitudes. The combination of all these factors may explain the deviations of the total modeled SW2 tide from the observations.
 The annual variation of the monthly mean zonal winds from CHAMP and WAM (Figure 3) shows excellent agreement. The most striking features in the mean wind evolution are the intensity of the CHAMP westward winds relative to the eastward winds (also noted in Figures 1 and 2) and the annual cycle at low and middle latitudes. Winter solstice periods are characterized by weakly eastward winds, while summer solstices are dominated by strong westward winds.
 We have examined CHAMP longitudinally averaged zonal winds sampled between 2003–2007 and compared them with WAM. CHAMP global winds are dominated by the diurnal tide, which accounts for the dayside‒to‒nightside flow. The time mean wind is predominantly westward, with weak superrotation (+E) that is symmetric about the equator during equinox, and confined to the winter hemisphere at solstice. The time mean and diurnal components in the CHAMP zonal wind agree fairly well with the WAM. Meriwether and Makela  have presented interferometer‒based winds over Brazil obtained for solar minimum conditions. The behavior of CHAMP nighttime winds at 5°S (not shown) is quite consistent with the winds reported for Brazil.
 A semidiurnal harmonic is also present in CHAMP observations, with magnitudes that are approximately one third of the diurnal harmonic. The semidiurnal tide is globally symmetric during equinox, but largely confined to the winter hemisphere during December. WAM simulations generally agree with CHAMP at middle and low latitudes at equinox. However, some differences exist, particularly at high latitudes and during solstice. In addition to the in situ generated tide, the semidiurnal and shorter‒period oscillations contain substantial components from sources in the lower atmosphere. These are affected by and potentially carry an imprint of a variety of processes ranging from the ozone radiative heating in the stratosphere to the distribution of mean winds and dissipative processes throughout the atmosphere. Unraveling this information will facilitate validation of “deep” atmospheric models as relevant observations become available.
 We thank Dr. Kathrin Häusler for helpful comments and guidance with the CHAMP data set. We would like to express our appreciation to Dr. Barbara Emery for her insightful review. This research was supported by NASA contract NNH12CF02C.
 The Editor thanks Barbara Emery and an anonymous reviewer for their assistance in evaluating this paper.