It has recently been suggested that observations of neutral density from satellite accelerometer data indicate a strong cooling occurred in the upper thermosphere during the January 2009 sudden stratospheric warming (SSW). The 2009 warming was a major event with winter polar stratospheric temperatures increasing by 70 K. This January period has been re-examined with three independent models: the NRLMSISE-00 empirical model; the physics-based coupled thermosphere, ionosphere, plasmasphere, electrodynamics model (CTIPe); and the whole atmosphere model (WAM). The analysis of this period and comparison with the neutral density observations reveals that there is, in fact, no evidence at any latitude for a large-scale or global decrease in upper thermosphere density or temperature in response to the SSW. The observed decrease in density and temperature can be amply accounted for by small changes in geomagnetic activity during this period. On the contrary, the WAM numerical simulations of the period suggest a possible small globally averaged upper thermosphere warming and neutral density increase by 5% during the SSW. This warming would have been difficult to discern in the local-time sampling of the CHAMP observations due to likely change in the diurnal density variation during the SSW, and due to a much larger contribution to the variability from geomagnetic sources. At this stage, therefore, it is not possible to ascertain if a cooling or warming occurred in the upper thermosphere in response to the stratospheric warming.
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 A sudden stratospheric warming (SSW) is a large-scale meteorological process that can disrupt the middle atmosphere global circulation [Matsuno, 1971]. During an SSW, the zonal mean flow in the winter stratosphere can reverse, and planetary waves with zonal wave numbers one and two usually grow in amplitude as they absorb some of the energy of the mean flow. The change in the stratospheric circulation and planetary wave activity, in turn, is likely to affect the vertical propagation of gravity waves and tides into the mesosphere and thermosphere. In the polar regions, mesosphere cooling and lower thermosphere warming have been predicted and observed [Liu and Roble, 2002; Siskind et al., 2010; Funke et al., 2010], and Conde and Nicolls  suggested a possible cooling in the upper thermosphere around 240 km. At middle latitudes, Millstone Hill radar observations reveal alternating regions of warming in the lower thermosphere and cooling above 150 km altitude [Goncharenko and Zhang, 2008]. Whole atmosphere model simulations of the January 2009 period (H. Wang, et al., First simulations with a whole atmosphere data assimilation and forecast system: The January 2009 major sudden stratospheric warming, submitted to Journal of Geophysical Research, 2011) [Fuller-Rowell et al., 2011] have also reinforced the concept of layering in the temperature response, with warming/cooling/warming in the stratosphere, mesosphere, and thermosphere, respectively. They also suggested that the amplitudes and phases of some of the tidal modes in the lower thermosphere undergo significant changes during the SSW. In particular, the terdiurnal migrating tide increased in magnitude at the expense of the more typical semidiurnal tide. The electrodynamic response to these changing tides agreed with the radar observations at Jicamarca [Chau et al., 2010], which served to validate the changes in the tidal fields in WAM.
 Whereas localized thermospheric temperature responses can be accommodated by changes in the amplitude and phase of tidal modes propagating into the thermosphere, larger scale temperature or density increases or decreases require either a change in the global circulation or changes in the heat sources and sinks in the region. Liu et al.  used observations of neutral density from the CHAMP and GRACE satellites to infer large scale, and strong, upper thermospheric cooling during the January 2009 sudden stratospheric warming. In this paper, we re-visit the analysis of the neutral density change from the CHAMP observations and come to a very different conclusion regarding the response in the upper thermosphere during this period, and whether the signature of the SSW is actually discernable.
 The NRLMSIS and CTIPe models are used to predict the likely response to the changes in solar and geomagnetic activity during this period. NRLMSIS is driven by the daily and 81-day average of the solar flux at 10.7 cm, and the time dependence of the 3-hour geomagnetic index Ap. CTIPe is a global, three-dimensional, time-dependent, non-linear, self-consistent model that solves the momentum, energy, and composition equations for the neutral and ionized atmosphere. The neutral atmosphere in CTIPe covers altitudes from 80 km to about 500 km, depending on solar activity. It uses the same solar 10.7 cm flux index as NRLMSIS to define the solar extreme ultraviolet (EUV) radiation for heating, ionization, and dissociation. For geomagnetic activity, the magnetospheric input is based on the statistical models of auroral precipitation and electric fields described by Fuller-Rowell and Evans  and Weimer , respectively. The auroral precipitation is keyed to the hemispheric power index (PI), based on the TIROS/NOAA auroral particle measurements. The Weimer electric field model is keyed to the solar wind parameters impinging the Earth's magnetosphere. The input drivers include the magnitude of the interplanetary magnetic field (IMF) in the y-z plane, together with the velocity of the solar wind. The propagating tidal modes are imposed at 80 km altitude with a prescribed amplitude and phase, and are invariant for the present study. In the simulations presented here, there is no forcing of NRLMSIS or CTIPe associated with the SSW.
 WAM is used to predict the possible consequences of the SSW on the upper thermosphere. WAM is a general circulation model of the neutral atmosphere from the surface to about 600 km altitude built on an existing operational Global Forecast System (GFS) model used by the US National Weather Service (NWS) for medium-range weather prediction. In order to predict the response to real atmospheric events, WAM was integrated into the NWS data assimilation system with some modifications (Wang et al., submitted paper, 2011). The WAM data assimilation and forecast system was used to simulate the January 2009 SSW interval, which followed the real SSW with high fidelity, and predicted the impact on the thermospheric winds and electrodynamics [Fuller-Rowell et al., 2011]. The simulation was conducted under constant and quiet geomagnetic and low solar activity conditions, thus eliminating any variability in the thermosphere forced from above.
 Between January 16th to 30th 2009, the CHAMP satellite sampled neutral densities over a range of altitudes from 320 to 350 km. Over this time period, the local time of the orbit precessed from 17 LT to 16 LT on the dayside and from 5 LT to 4 LT on the nightside. For comparison with the empirical and physical models, the CHAMP data were converted to a fixed altitude of 325 km. Figure 1 (top) shows the CHAMP neutral densities at 325 km altitude between 80°S and 80°N latitude in the afternoon (Figure 1, left) and pre-dawn (Figure 1, right) sectors. The latitude structure is consistent with expectations that the southern summer hemisphere is warmer with larger densities. The geomagnetic Ap index for the period is also shown in Figure 1 (bottom).
 The CHAMP data [Sutton et al., 2005; Sutton, 2011] show two clear peaks on January 19th and 26/27th, and a pronounced minimum in density between the 22nd and 25th, corresponding to the time of the peak in the stratospheric warming. Liu et al.  asserted the density minimum was a direct consequence of the SSW. In the present study, we use the three models to determine if this assertion is justified.
Figure 1 (second row) shows the neutral density at 325 km from the NRLMSIS empirical model in the same format as the CHAMP data. The model is driven by the changing F10.7 index and the time history of the 3-hour Ap index. The mean densities tend to be a little higher than the observations, presumably due to the unusually long and deep solar minimum [Solomon et al., 2011] and due to the stronger infrared cooling from the steadily increasing anthropogenic CO2 that is not expected to be captured in NRLMSIS. During this period the solar flux was fairly stable, and of course low, the 10.7 cm index gradually decreasing from 72 to 69 flux units. Most of the day-to-day changes in density from NRLMSIS are therefore coming from the changes in geomagnetic activity. Even though the Ap index was quite low, it did vary during the period from close to zero to occasional peaks near 20. What is striking is that minimum density near the peak of the SSW appears in the NRLMSIS model with similar, although slightly smaller, magnitude as the observations, and is due to the low geomagnetic activity, not the SSW. Emmert and Picone  showed that even small variations in geomagnetic activity at quiet-time levels and low solar activity can cause a significant density variation. Both Lei et al.  and Emmert and Picone  also suggest that the geomagnetic activity dependence in MSIS at low solar activity is actually too weak, which would further improve the comparison with the data. The results from the CTIPe model are also shown in Figure 1 (third row) in the same format and confirm the response. The mean CTIPe densities are again a little high compared with the observations, but the agreement in the structure with observations in Figure 1 (top) is very good. CTIPe reproduces the latitude structure reasonably well including the day-to-day changes in density. To eliminate the mean offset in CHAMP and CTIPe, Figure 2 (first two rows) show the relative percent density change compared with an average at each latitude over the 15-day period. The magnitude and timing of the neutral density response is captured well by CTIPe.
 Of course, one cannot rule out the possibility that the model may over or under predict the density response to geomagnetic activity, and that the residual could be attributed to the SSW. To further quantify the comparison, Figure 3 shows the correlation of the models with the CHAMP data. The correlation coefficient of CTIPe with CHAMP is close to 0.9 at nearly all latitudes on both the day and nightside. The scatter plots of CHAMP and CTIPe densities shown in Figure 3 (bottom) again show the strong correlation, particularly on the dayside where the slope of the linear fit to the data is close to 1.0. The NRLMSIS correlation with the data shown in Figure 3 (top) is also fairly high, with average values of 0.7 on the dayside, and about 0.6 on the nightside, over the range of latitudes. The empirical and physical model results and the quantitative agreement strongly reinforce the notion that it is the variation of geomagnetic activity that creates the main dip in density at the time of the SSW, and that it is not due to the influence of the SSW. If there is a neutral density response to the SSW, its magnitude is likely to be just a few percent, and therefore difficult to extract from the CHAMP data, and to separate from the relatively strong influence of geomagnetic activity.
 To investigate the likely change in density due to the SSW itself, the WAM numerical simulations have been used. As described by Wang et al. (submitted paper, 2011) the WAM model and data assimilation system is able to follow the response to the January 2009 SSW very well and is able to match the observed polar stratospheric temperature very closely. Fuller-Rowell et al.  were also able to infer that the changes in the lower thermospheric tides during the SSW were well simulated in WAM. This gives some confidence that the response in the upper thermosphere might also be reasonable. Note that in the WAM SSW simulation presented here, the solar flux and geomagnetic activity were both held constant, so any coherent density response can be specifically attributed to the forcing from the lower atmosphere.
Figure 4 shows snapshots of the global relative neutral density structure, compared with the zonal mean, in the upper thermosphere at 325 km altitude at 0 UT before the SSW on January 15th (Figure 4, top) and at the peak of the warming on the 23rd (Figure 4, middle). The inherent variability is apparent by the small-scale structure. Globally averaged, WAM predicts a density increase of about 5% from the 15th to the 23rd (hidden within relative density). The local time variation has also altered due to the changing amplitude of some of the important tidal modes, such as the semidiurnal and terdiurnal tides, which were discussed extensively by Wang et al. (submitted paper, 2011) and Fuller-Rowell et al. . There is also an increase in the amplitude of the diurnal variation. The change in local time variation appears to shift the late afternoon maximum in the southern hemisphere to slightly earlier local times, so the CHAMP orbit may not sample the real increase. CHAMP would also sample a deeper pre-dawn minimum again tending to underestimate any increase in the global mean. These features can be seen in Figure 4 (bottom), which shows the difference between the 23rd and 15th, and illustrate the consequences of the changes in the tidal structure.
Figure 2 (third row) shows what CHAMP would have seen in the afternoon (left) and pre-dawn (right) sectors by sampling WAM. Firstly, the WAM predicted response to the SSW is about one-third the magnitude (∼5%) of the observed response to geomagnetic activity (±15%, i.e., 30% from maximum to minimum). Secondly, although the peak dayside temperature response in WAM reached a maximum on the 23rd/24th (Figure 4, middle), CHAMP would not have seen a clear single peak due to the change in the local time structure of the density. In the afternoon sector, CHAMP would have actually seen a rather broadly distributed increase weakly correlated with the SSW. At some latitudes, WAM does actually show a small maximum at the peak of the SSW, but at other latitudes the maxima appear either a few days earlier or later. In the predawn sector, no obvious maximum is discernable at the peak of the SSW, but rather a gradual decrease in density over the two-week period (Figure 2, third row, right).
 The change in density during the SSW predicted by WAM has been used to scale the CTIPe values to determine if the predicted SSW density response would be discernable in the CHAMP observations. The result of a linear combination of CTIPe and WAM is shown in Figure 2 (bottom). Although the magnitudes are slightly different compared with the original CTIPe results (Figure 2, second row), the agreement with the CHAMP observations is still very good and the correlation still high and actually even better at some latitudes (see Figure 3, top). The varying geomagnetic activity is still the main driver of the day-to-day changes and the modest changes in density in response to the SSW could very easily be hidden in the CHAMP observations.
 Three models have been used to investigate the likely neutral density response in the upper thermosphere during the January 2009 sudden stratospheric warming. Previously, it had been asserted by Liu et al.  that CHAMP neutral density observations implied a cooling and a density decrease in response to the SSW of about 30% from the prewarming maximum. The NRLMSIS empirical model and the CTIPe model numerical simulations strongly suggest that the main decrease in density and temperature during the SSW observed by CHAMP is very likely due to the variation in geomagnetic activity, and not due to the SSW. Although the period was generally quiet, the geomagnetic activity index Ap did vary along with the solar wind and interplanetary magnetic field, and the variation was sufficient to reproduce the main signatures of the CHAMP observations.
 A whole atmosphere model simulation of the response to the SSW indicates instead a slight warming of 5% globally. The accompanying changes in the local time structure imply that CHAMP sampling of the density during the SSW would probably not have detected the warming. Changes in the amplitude and phase of tidal modes reaching the upper thermosphere could produce regional density decreases, in spite of a general warming. The combination of sampling along the CHAMP orbit and the contribution of variability from geomagnetic activity make it very difficult for the true signature of the SSW to be extracted from the data. The results presented clearly show the response to the SSW is small, and leaves open the question of whether an SSW actually cools or warms the upper thermosphere.
 Funding for this research was provided by NASA Heliophysics Theory and LWS Strategic Capabilities Programs, and AFOSR MURI NADIR project. The authors thank Eric Sutton of the Air Force Research Laboratory for providing the CHAMP satellite neutral density data.
 The Editor thanks the two anonymous reviewers.