Density-Temperature Synchrony in the Hydrostatic Thermosphere

Abstract

The paper presents a detailed analysis of the density-temperature (ρ-T) synchrony in the thermosphere using a hydrostatic general circulation model. The numerical models in general offer not only great potential for forecasting the transient response of the thermosphere but also are excellent tools for understanding the driving mechanisms of various thermospheric trends and features. This study investigates and isolates the dependency of the ρ-T synchrony on the season, altitude, space weather, high-latitude electrodynamics, and the lower atmospheric tidal spectrum. The results demonstrate that the previously reported ρ-T synchrony begins around 300-km (350-km) altitude at the equator (high latitudes). The effect of the lower atmospheric tidal spectrum on the ρ-T synchrony patterns seems to be only marginal and more noticeable during the equinox months. The study demonstrates that the ρ-T phase lag is larger in the high latitudes of the summer hemisphere and evolves through the day and is attributable to ion drag and temperature fluctuations via soft particle precipitation. The study provides physical insights into how the winds contribute to the ρ-T synchrony. In addition, the results show that geomagnetic activity contributes significantly to the ρ-T synchrony; the underlying mechanism may be related to temperature enhancements in the high latitudes via Joule heating and associated nonlinear interactions. While the ρ-T phase lags attributable to different solar activity levels are modest, the solar heating is the primary source that maintains the ρ-T synchrony in the low/middle latitudes via upward propagating thermal tides.

Key Points

• A detailed analysis of the neutral density-temperature (ρ-T) synchrony in the thermosphere is presented
• The ρ-T synchrony begins around 300 km near the equator and varies significantly with latitude, height, and season
• The ion drag and temperature fluctuations via electron precipitation alters the ρ-T synchrony in the high latitudes

1 Introduction

The thermosphere is a highly dynamic environment responsive to a myriad of processes interacting at many different time scales (e.g., Bauer & Lammer, 2004). An accurate forecast of the thermosphere/ionosphere is paramount to assure, among others, the safety of space assets vital to many technologies on Earth (e.g., Hejduk & Snow, 2018). During the past six decades or so, many advances have been made in our understanding of the variability and dynamics of the thermosphere and its coupling with the lower atmosphere and ionosphere/magnetosphere (see reviews by Liu, 2016, and Emmert, 2015). Early work (e.g., Mayr & Volland, 1972; Volland, 1988) has recognized and expounded the theories of relative amplitudes and phases of thermospheric variables such as neutral mass density (hereinafter density), neutral temperature (hereinafter temperature), and pressure. Numerical simulations and in situ and remote measurements are critical to understand the dynamics of the thermosphere and to improve our ability to develop better forecast models of the environment. The phase difference between density and temperature in the thermosphere is a uniquely complicated phenomenon, which has been investigated by some theoretical and observational studies (e.g., Akmaev et al., 2010; Chandra et al., 1979; Del Genio et al., 1979; Hickey et al., 2015; Mayr & Volland, 1972; Mayr et al., 1973). The general paradigms for the analysis presented here is an extension of those investigations.

Early observations revealed that the thermosphere is driven by external heat and momentum sources (Fuller-Rowell et al., 1997; Jacchia & Slowey, 1964; Jacchia, 1977; Slowey, 1983) akin to a stable linear oscillator system to a first approximation (unlike the lower atmosphere). In other words, the internal instabilities (e.g., in chemistry and nonlinear coupling) alone cannot describe much of the observed variability in the thermosphere (Volland, 1988). The absorption of solar radiation drives the majority of the diurnal pattern of, for example, temperature and winds in the thermosphere. Many recent studies have further elucidated that the lower/middle atmosphere forcing also contributes significantly to the thermospheric variability and sometimes even comparable with the variability imposed by the dissipation of solar wind energy via magnetosphere coupling (see Liu, 2016, and references therein). As pointed out in Liu (2016), studies on lower atmospheric forcing on the thermosphere, for the most part, have been limited by the scarcity of global measurements and observations, especially in the 100- to 250-km region.

Mayr and Volland (1972) using a crude diffusion model showed that the phase difference between density and temperature in the lower thermosphere (i.e., below 200 km) is greater than at higher altitudes (e.g., about 3 hr at 160-km altitude vs. 1 hr at 400-km altitude). Mayr and Volland (1972) attribute this large phase difference to thermospheric winds, which substantially alter the diffusive equilibrium for atomic oxygen, especially in the lower thermosphere. With increasing altitude, adiabatic thermal expansion subdues these circulation effects on diffusive equilibrium. Mayr and Volland (1973) showed that ion drag at higher altitudes and tidal forcing entering the thermosphere from below could further contribute to the phase discrepancy. Thermospheric variables, such as temperature, and horizontal (HW) and vertical (WN) wind measurements from the ground are typically inferred from interferometers and incoherent scatter radar (ISR; e.g., Meriwether, 2006; Salah & Holt, 1974). Even before space-based measurements were available, a strong correlation of the magnitude and direction of thermospheric wind upon the local time, season, and solar cycle was established through classical physics (Challinor, 1970; Geisler, 1966). As emphasized in Appendix Appendix A, the lack of sufficient local time and altitude coverage in, for example, temperature and density data, is an outstanding issue in model verification studies that focus on short periodic variations (e.g., diurnal and semidiurnal) of such variables by among others, season, altitude, and solar activity. Mayr et al. (1973) reported nearly identical phase differences at both 0° and 45° latitudes. The continuity equation suggests via the divergences of the HW field that the ion drag/electron density is latitude dependent. Therefore, the result in Mayr et al., 1973 (1973, Figure 6) is an artifact of the diffusion model used in their study.

Chandra et al. (1979), using temperature and composition measurements from the Aeros B satellite, showed a strong correlation between medium-scale gravity waves energized by auroral currents and the density-temperature phase difference in the auroral regions during July–August 1974. Chandra et al.'s (1979) phase difference study focuses on the heights approximately from 200 to 300 km and assumes exosphere temperature to be constant at 1000 K as well as atomic oxygen to be the major constituent. The phase difference results in Chandra et al. (1979) are likely to change in different seasons due to the significant seasonal difference in thermosphere winds in the middle-to-high latitudes. Hoegy et al. (1979), considering a horizontally stratified (i.e., disregarding dissipation) and isothermal thermosphere, found that the amplitudes and phase angles of density and temperature are not significantly modified with the exclusion of viscosity, thermal conduction, and ion drag terms. Hickey et al. (2015) numerically showed that the viscosity and thermal conductivity (while ignoring the Coriolis force and the ion drag) play a critical role in the relative phases and amplitudes between atomic oxygen and nitrogen densities in the altitude range 120–400 km. Atomic oxygen is the dominant species approximately from 200 to 500 km during solar minimum and 800 km during solar maximum and thus is critical to the specification of the density profile (Emmert, 2015). While physics-based models are capable of capturing the transient response of the thermosphere to external energy sources, the production of a comprehensive description of the phase difference has traditionally been challenging due in part to the limitations in models and sparseness of observations.

Furthering previous related studies, Akmaev et al. (2010) reported numerical results of the synchrony between midnight density maximum (MDM; Arduini et al., 1997) at 400-km altitude and midnight temperature maximum (MTM; Mayr et al., 1979) at 300-km altitude. The density-temperature (ρ-T) synchrony discussed in this paper is analogous to the synchrony reported in Akmaev et al. (2010) but broadly defined as the approximate east-to-west in-phase signature between density and temperature in the upper atmosphere above 300-km altitude (i.e., as opposed to the antiphase signature between, for example, 100–150 km). Akmaev et al. (2010) and Akmaev (2011) suggested that the altitudinal phase progression of MTM always leads that of MDM and as a result, MDM occurs above the MTM at the same longitude. This suggestion is backed by the hydrostatic equation of state, which forbids temperature and density maxima to cooccur at the same place (Mayr et al., 1973; Volland, 1988). The numerical results in Akmaev et al. (2010) are limited to two latitude regions and correspond only to constant unspecified low solar and geomagnetic forcing. It remains to ascertain a full global description of the magnitude and variability of the phase structure of density and temperature in the thermosphere aided by data.

Our work differs from earlier work in that it includes a fairly comprehensive description of the ρ-T synchrony in the thermosphere. The responsiveness of the ρ-T synchrony to various conditions including thermospheric winds and high-latitude electrodynamics are analyzed by season, height (100–500 km with 10-km resolution), multiple space weather conditions, and lower atmospheric tides using a state-of-the-art numerical model of the coupled thermosphere-ionosphere: thermosphere-ionosphere-electrodynamics general circulation model (TIE-GCM). The latter distinction is important for a detailed prognosis of the thermospheric trends given the tremendous improvement in the physics-based model over the years (Maute, 2017; Qian et al., 2014). The specific questions this paper address are as follows:

1. Does the east-to-west trend in density at a given altitude display a synchrony with temperature underneath at all latitudes and seasons?
2. How significant is the latitudinal variation of the ρ-T synchrony?
3. How significant is the impact of the lower atmospheric tidal forcing on the ρ-T synchrony?
4. How strong of a correlation do physically derived thermosphere wind patterns have with the ρ-T synchrony?
5. How significant are the impact of space weather drivers on the ρ-T synchrony?
6. How significant is the altitudinal variation of the ρ-T synchrony near the equator compared to high latitudes?

2 Model Descriptions

The phenomenon of ρ-T synchrony and associated physical features are mainly analyzed using TIE-GCM, which is a well-established, self-consistent, and physics-based model (e.g., Emmert, 2015; Maute, 2017; Qian et al., 2014). The reader is referred to Appendix Appendix A for a verification study that describes the appropriateness of the TIE-GCM for the results presented herein. The ρ-T synchrony results are also compared to the longstanding and widely used empirical Mass Spectrometer Incoherent Scatter Radar Model (NRLMSISE-00; Emmert, 2015; Picone et al., 2002).

2.1 TIE-GCM

The TIE-GCM is a three-dimensional, time-dependent model that couples the ionosphere and thermosphere using fluid mechanics and electrodynamics (Dickinson et al., 1981; Richmond et al., 1992). This study employs the TIE-GCM version 2.0—released on 21 March 2016. The reader interested in more details about TIE-GCM version 2.0 is referred to the website at http://www.hao.ucar.edu/modeling/tgcm/tiegcm2.0.

The vertical extent of TIE-GCM is approximately 97–600 km with a quarter of a scale height resolution. In this study, the model runs are performed on a 2.5° × 2.5° grid in latitude and longitude with Heelis et al. (1982) high-latitude ionospheric convection electric fields and auroral precipitation as described in Roble and Ridley (1987). TIE-GCM uses an implicit finite-difference numerical scheme on a uniform latitude-longitude grid with a tuneable model time step, which is set to 30 s in our simulations. The direction of flow of plasma flux describes the coupling with the plasmasphere at the upper boundary and the solar heat input to the system (i.e., irradiance and variability) is described using the extreme ultraviolet flux model for aeronomic calculations empirical solar proxy model (see Richards et al., 1994; Solomon & Qian, 2005). The lower boundary wave forcing is specified through numerically derived migrating/nonmigrating diurnal and semidiurnal tides using the Hagan et al. (2001) global scale wave model (GSWM). The dichotomy of migrating and nonmigrating tides is that migrating tides are sun-synchronous and nonmigrating tides are longitude dependent. Briefly, GSWM is a linearized numerical solution to the Navier-Stokes equations in response to specific zonal wave numbers and wave periods considering the zonal mean background atmosphere (Hagan et al., 2001). The forcing through GSWM includes dissipation due to ion drag, thermal conductivity, boundary layer friction, mean winds and meridional temperature gradients, molecular and eddy diffusion, and gravity wave drag (Hagan et al., 2001). In addition, the Qian et al. (2009) empirical formulation (i.e., eddy diffusion coefficient) that describes the seasonal variations in the advective and diffusive transport of primarily atomic oxygen is also imposed at the lower boundary.

Each TIE-GCM simulation is initiated with model's relevant benchmark conditions with a 15-day “settle-in” period, and only the model outputs after this period are considered here. Unless otherwise specified, the input of solar and geomagnetic variability to the model is based on observed F_10.7 proxy and Kp index, respectively.

2.2 Mass Spectrometer Incoherent Scatter Radar Model

The Picone et al. (2002) NRLMSISE-00 empirical model describes the atmosphere from surface of the Earth to the base of the exosphere and is constructed using multiple ground- and space-based sources of data including satellites, rockets, and radars from around 1961 to 1998. The model outputs depend on the Walker (1965) temperature profile with modifications to the parametrization of the extreme ultraviolet flux input by Picone et al. (2002). In this study, the F_10.7 solar flux and ap geomagnetic index for seven periods of anterior magnetic activity are used to drive the model runs.

3 Numerical Experiments

The numerical experiments reported here covers January, March, June, and September 2014, which belongs to the recent solar maximum period (sunspot cycle 24). The months are selected to roughly represent the winter and summer in both Southern and Northern Hemispheres and the periods around the two equinoxes. Following Akmaev et al. (2010), the ρ-T synchrony features are mainly analyzed in the altitude range 300–400 km and then completed with a description of the vertical profile extending from 100 to 500 km. In the model run referred to as T1, the thermosphere is simulated hourly for density, temperature, and winds using TIE-GCM driven by the GSWM tides and observed geophysical indices F_10.7 and Kp. A second TIE-GCM run (T2) without the GSWM tides specified at the lower boundary is used to compare the effect of these tides on the ρ-T synchrony. The phrase “TIE-GCM run” within the text only applies to the T1 run with the GSWM tides included unless explicitly stated as a T2 run. The NRLMSISE-00 estimated density and temperature are obtained with a matching spatiotemporal resolution to that of TIE-GCM outputs. While the NRLMSISE-00 can directly output results for a given altitude, the cubic spline interpolation scheme is used to map the TIE-GCM estimated quantities to the desired altitude. In order to avoid high geomagnetic activity levels influencing the monthly mean results, the following days with ap above 39 nT have been removed from the seasonal analysis: 8 and 18 June, and 12 and 19 September 2014 (hereinafter storm days).

An additional investigation on several other numerical experiments specifically devised to investigate the ρ-T synchrony during periods of enhanced space weather activities is presented. In this regard, 2 days from each month that falls into geomagnetically active and solar active periods have been selected. The day with the highest ap value of each month and the day with a relatively high F_10.7 value where the corresponding ap is relatively low are chosen to represent the geomagnetically active and solar active periods respectively. The chosen geomagnetically active days are 2 January, 13 March, 8 June, and 12 September 2014. The ap during the four solar active days remained significantly low with values less than 10 nT (Kp≈2) on 4 January, 11 March, and 12 June and 32 nT (Kp≈4) on 27 September 2014. The T1 run corresponding to these “active” days are compared against two climatologically representative controlled TIE-GCM runs, which are referred to hereinafter as No Dyn and No Dyn+Aur. In the No Dyn run, the ion drift velocities and electric potential (i.e., current due to plasma pressure gradient and gravity) have been set to naught. The No Dyn+Aur run is similar to the No Dyn run but without the Roble and Ridley (1987) auroral oval parameterization. In both controlled runs, the reference thermosphere is produced by forcing the TIE-GCM with GSWM tides at the lower boundary, and F_10.7 and Kp kept constant at 100 sfu and 2, respectively.

The percentage deviation of a given quantity (e.g., density or temperature) from the zonal mean is computed as , where A is the quantity at a specific location and is the mean across all the longitudes for the respective zone/latitude. The percentage deviation of density and temperature from the zonal mean are denoted as Δ ρ/ρ and ΔT/T, respectively.

The magnitude of the HW is computed as , where UN and VN are the zonal and meridional components of the horizontal wind, respectively. The flow direction of the HW is derived from the expression, , which describes the trigonometric relationship between the orthogonal velocity components UN and VN whose positive values are toward east and north, respectively.

The ρ-T synchrony (i.e., relationship between east-to-west trend in density and temperature) is investigated through a cross-correlation (CC) analysis. The phase lag is represented by the CC of density with respect to temperature. The CC is defined as

(1)

where Cov(X,Y) is the cross covariance of X with respect to Y and Var(X) and Var(Y) are the variances of X and Y, respectively. The quantities X and Y are both single dimension distributions with equal length. A unit variance scaling from −1 to 1 is applied on density and temperature prior to computing the CC.

The maximum CC indicates the position where the two distributions are best aligned. The number of steps l that the distribution X is shifted in order to gain the maximum CC is the lag/lead ϕ of X with respect to Y where . Given that n is the number of longitudinal bins, ϕ can be converted to degrees to describe the corresponding longitudinal shift. Thus, the longitudinal shift (phase lag) is obtained by multiplying ϕ with the resolution of the longitudinal axis, which is 2.5°.

4 Results

This section and the accompanying discussion are organized as follows to address the questions given in section 1. Figures 2 and 3 are used to answer the first three questions. Figures 4 are used to answer the fourth question. Figure 7 is used to answer the fifth question, and Figures 8 and 9 are used to answer the last question.

Figures 1a–1d display the daily F_10.7, 3-hr ap index and the hourly Dst index for January, March, June, and September 2014, respectively. Figure 1a shows that in January the solar activity was rather placid, apart from the two spikes over 200 sfu (sfu = 10⁻²²W·m⁻²· Hz⁻¹) early in the month. March shows the smallest variation in solar activity among the four months with June and September having amplitude differences of about 80 and 50 sfu through the month, respectively.

Figure 1

Space weather conditions for the months of (a) January, (b) March, (c) June, and (d) September 2014 demonstrated via F_10.7 solar flux (sfu = 10⁻²²W·m⁻²· Hz⁻¹), ap index, and the Dst (disturbance storm time) index. The times with ap above 39 nT are shaded in red. Source: OMNI data available at https://omniweb.gsfc.nasa.gov.

Except for the areas shaded in red in Figures 1c and 1d, the geomagnetic activity remained low/moderate (i.e., ap less than 39 nT; Kp less than 5). In both June and September, ap recorded a maximum of 94 nT but only in September, the corresponding Dst value dropped significantly. The Dst index also reached a low of approximately −50 nT once in March.

Figures 2a–2d show the TIE-GCM and NRLMSISE-00 outputs of temperature and density deviations at the latitudes of 70°N (brown), 70°S (green), and 0° (blue) for 6 UT in January, March, June, and September 2014, respectively. The 6 UT mean for the entire month (after removing the storm days) are shown as the percentage deviation from the zonal mean at altitudes of 400 and 300 km. It is clear from both models that near the equator the density variations are nearly in phase with the temperature variations underneath. A ρ-T synchrony is also apparent in the high latitudes; however, the aligning of density peaks/troughs with that of the temperature seems less pronounced. That is, for example, in Figure 2a the TIE-GCM temperature trough corresponding to 70°N occurring near 60°W is slightly shifted to the west compared to the trough in density above. Similarly, the temperature peak corresponding to 70°S occurring near 60°E is slightly shifted to the west compared to the density peak above. The synchrony patterns captured by both the physics-based TIE-GCM and the empirical NRLMSISE-00 seem to compare well with each other, although the empirical model shows a relatively more significant deviation from the equatorial mean for both Δ ρ/ρ and ΔT/T. The NRLMSISE-00 outputs for high latitudes also seem to be better synchronized than the corresponding TIE-GCM outputs.

Figure 2

(left) Physics-based T1 and (right) empirical model outputs of the percentage deviation of density (Δ ρ/ρ) and temperature (ΔT/T) from the zonal mean at 400- and 300-km altitudes, respectively. The 6 UT mean values for the specified months in 2014 are shown for geographic latitudes/zones at 70°N (brown), 70°S (green), and 0° (blue). The gray dashed line represents the zonal mean. TIE-GCM = thermosphere-ionosphere-electrodynamics general circulation model; NRLMSISE-00 = Naval Research Laboratory Mass Spectrometer and Incoherent Scatter radar Extended-2000.

A comparison similar to Figure 2 is given in Appendix Appendix B (Figure B1) where the ρ-T synchrony differences are compared in the geomagnetic reference frame for the TIE-GCM outputs. As in the geographic reference frame, a similar shift in density peaks/troughs in the high latitudes with that of temperature is also present in the geomagnetic reference frame.

In Figure 3, the phase lag of density at 400-km altitude with respect to the fiducial east-to-west trend in temperature at 300-km altitude is quantified latitudinally for 0, 6, 12, and 18 UT through January, March, June, and September 2014. The T1 (T2) phase lag profiles in Figure 3 correspond to the model run with (without) the diurnal/semidiurnal and migrating/nonmigrating tides from the GSWM specified at the TIE-GCM's lower boundary. As described in section 3, the phase lag is calculated as the CC between density and temperature. Therefore, for example, a positive phase lag indicates that the respective temperature leads that of density (i.e., temperature peaks to the east of that of density). Similarly, a negative phase lag indicates that the density peaks are shifted to the east of that of temperature. The uncertainty of the phase lag is ±2.5° longitudinally. The latitudinal resolution of the phase lag profile is also 2.5°. The occasions where the phase lag reach values beyond the chart are indicated separately.

Figure 3

The phase lag of density at 400-km altitude computed as the deviation from the fiducial east-to-west trend in temperature at 300-km altitude. (a–d) The mean phase lag as a function of geographic latitude at 0, 6, 12, and 18 UT (left to right) for the specified months in 2014. T1 (T2) denotes the physics-based model run with (without) the global scale wave model tidal forcing specified at the lower boundary. A positive lag indicates that the respective trend in temperature leads density. The precision of the phase lag is within ±2.5° longitudinally. The maximum value where the phase lag extend beyond the chart is indicated separately.

Figure 3 demonstrates that a distinctly clear in-phase signature between the temperature at 300 km and density at 400 km exists in the low and middle latitudes across all seasons. Figures 3a and 3c reveal a winter-summer asymmetry in the phase lag, where the phase lag is larger in the summer hemisphere high latitudes and nearly in phase in the winter hemisphere high latitudes. The 6-UT profile for January shows that the density trend begins to slightly lead the temperature trend between approximately 50°–70°N. In contrast, density begins to lead the temperature in the winter hemisphere in June at much lower latitudes and then reverses the trend around 50°S. Considering the T1 run (brown lines), the phase lag in the summer hemisphere in January seem to increase gradually from about 35°S toward higher latitudes (e.g., at 0 UT).

On the other hand, in the summer hemisphere in June the deviation seems to begin at much higher latitudes abruptly except at 18 UT (see Figure 3c). In January the mean behavior of the ρ-T synchrony patterns at 12 UT indicates that the density trend is leading that of temperature at the high southern latitudes, whereas an obverse trend is true at, for example, 0 and 6 UT. In contrast, the mean behavior at the high northern latitudes in June corresponding to T1 at all UTs indicates that temperature is leading at varying degrees of magnitude. A slight lead in the density trend can also be seen at the high southern latitudes in June (e.g., Figure 3c [12 UT]).

The overall synchrony patterns in the two equinox months (see Figures 3b and 3d) seem to be somewhat similar to each other with September showing relatively larger deviations in the high latitudes. Further, in both equinox months, density seems to be leading only at 12 UT in the Southern Hemisphere, whereas temperature seems to be leading most of the time in the high latitudes.

Considering the two runs T1 and T2, it can be seen that GSWM tides are responsible for the slight phase lags seen near the low/middle latitudes especially during equinox months (e.g., Figures 3b [12 UT] and 3d [12 UT]). The impact of GSWM tides on the ρ-T synchrony patterns at low/middle latitudes during January and June as well as high latitudes through all seasons seem to be insignificant except at 18-UT January.

The relationship between the ρ-T synchrony patterns and the horizontal and vertical winds is explored through Figures 4. As in Figure 2, the days corresponding to storm days have been removed from the comparison in Figures 4. The density at 400-km (temperature at 300-km) altitude shown in panel a (panel b) in Figures 4 are zonally normalized (i.e., along the latitude) and are referred to as and , respectively. Figure 4c (4d) shows the HW (WN) difference between 400- and 300-km altitudes. The positive values in panel c indicate that the corresponding HW at 400 km is faster than at 300-km altitude. The positive values in panel d represent the winds propagating upward in the zenith direction. Figures 4e and 4f show the mean flow direction (see section 3) of the HW at 400- and 300-km altitudes, respectively. The quantities considered in Figure 4 correspond to the 6 UT mean for January 2014. Figure 5 is similar to Figure 4 but for June 2014. While Figures 4 and 5 are based on the T1 run, Figure 6 is similar to Figure 5 except for T2 run. The −0.9 and 0 contours of corresponding is overlaid on panels a, c, and d in Figures 4.

Figure 4

(a, b) T1 outputs of the normalized density and temperature at heights of 400 and 300 km, respectively. (c) The difference between the horizontal wind speeds at 400- (HW₄₀₀) and 300-km (HW₃₀₀) altitudes. Positive values indicate that the corresponding HW₄₀₀ are faster. (d) Similar to (c) except for the respective vertical wind vectors (WN). Positive values indicate that the resulting vertical wind is propagating in the zenith direction. The −0.9 and 0 contours of are overlaid on (a), (c), and (d). (e, f) HW streams at heights of 400 and 300 km, respectively. No discernible change in the HW flow patterns between the two layers (e and f) but the magnitude of the difference is significant (c). All the latitude-longitude variations correspond to the 6 UT mean of the respective quantities for January 2014.

Figure 5

Same as Figure 4 except for June 2014.

Figure 6

Same as Figure 5 except for T2 outputs (i.e., the model run without the global scale wave model's migrating/nonmigrating diurnal and semidiurnal tides specified at the lower boundary).

It can be established from panels e and f in Figures 4 and 5 that no discernible difference in the average HW directions exists between the two altitude layers during the compared periods. On the other hand, panel c in both figures reveal a significant difference in the magnitudes of the HW between the two altitudes (i.e., from about −20 to 40 m/s). The difference in both direction and magnitude of the vertical winds between the two altitudes (i.e., from about 2 m/s downward to 1.5 m/s upward) shown in panel d in Figures 4 and 5 is considerable given that the TIE-GCM vertical wind velocities at these altitudes were typically between ±8 m/s.

The 0 contour lines in panels c and d in Figures 4 illustrate the resemblance between the wind difference patterns and the mean regions. For example, in Figure 4c, the HW speeds at 400-km altitude are in general faster along the 0 contour line. Interestingly, in Figure 4d, the downward vertical winds are slightly stronger especially near the 0° longitude in the low/middle latitudes along the temperature-minima region. The latitudinal zones where the ρ-T synchrony breaks (as shown in Figures 3a and 3c) are also apparent when peak-to-trough regions in density are compared with that of temperature in Figures 4 and 5. A striking similarity between ρ-T synchrony and the wind difference patterns is also apparent in June in Figure 5. For example, the HW at 400-km altitude is slower than that of at 300 km near the equator around the temperature minima and maxima regions. The wind difference is in general positively larger in the high latitudes around the temperature minima and maxima regions and in the winter hemisphere even more so.

Similarly, the vertical wind difference (Figure 5d) shows a slightly stronger downward trend near the equator around the temperature minima region, which also corresponds with the density minima region. Figure 5d also reveals a slight enhancement in the upward WN at 400-km altitude in the high latitudes near the temperature minima region. The similarity between wind difference patterns and the temperature is further illustrated in Appendix Appendix B where the profiles are compared for the equinox months March and September (Figures B2 and B3).

The secondary minimum in the equatorial region in Figure 5a is smoothed out in Figure 6a indicating the contribution of GSWM tides to the MDM. Figures 5e, 5f, 6e, and 6f also show that the tides imposed at approximately 96-km altitude are capable of altering the mean HW flow patterns even in the upper thermosphere (e.g., the shift in convergent and divergent points). Figures 5 and 6 are used to further the discussion on the impact of GSWM tides on the ρ-T synchrony and the wind difference patterns.

In Figure 7, the impact of relatively high geomagnetic and high solar activity periods on the ρ-T synchrony during different seasons is examined. As in Figure 3, the similarly computed phase lag of density with respect to temperature is shown in Figure 7 for specific space weather conditions alongside the controlled runs: No Dyn and No Dyn+Aur. The GSWM tides are considered for all model runs shown in Figure 7. The method applied in selecting geomagnetically active and solar active periods is described in section 3. The highest ap values for January, March, June, and September were 32, 27, 94, and 94 nT, respectively. The variation of the ap level during the respective active periods is shown on the right for each row in Figure 7 for a 24-hr period starting from 21 UT the day prior. Similar to Figure 3, the phase lag is shown for 0, 6, 12, and 18 UT for the specified months in 2014.

Figure 7

The phase lag as introduced in Figure 3 except for specific space weather conditions considering the global scale wave model tidal forcing specified at the lower boundary of the physics-based model. (a–d) The purple and green lines represent the phase lag during the specified high-ap and high-F_10.7 days, respectively. The orange and blue lines represent the controlled runs No Dyn and No Dyn+Aur, respectively. The controlled runs are based upon monthly mean conditions, and constant F_10.7 and Kp at 100 sfu and 2, respectively. The No Dyn run does not account for ion drift and electric potential while the No Dyn+Aur run additionally ignores the auroral oval parameterization. The variation of the ap level for the specified days are shown on the right for a 24-hr period starting from 21 UT the day prior. The corresponding F_10.7 values of the selected days are indicated separately. The maximum value of the few instances where the phase lag extend beyond the chart is indicated separately.

In Figure 7a, the phase lag on 2 January is much more pronounced than the phase lag on 4 January with an F_10.7 of 253 sfu, which is the highest among the four months. The fluctuations in ap on 2 January (purple) are larger compared to that of on 4 January (green) and these fluctuations seem to correlate with the phase lags with a time delay. For example, the increase of ap to 32 nT before 6 UT on 2 January seems to be reflected on the phase lag variations in the high latitudes at 6 UT, and similarly, the drop in ap to 8 nT before 12 UT can be associated with the phase lags at 12 UT. The evidence for the relationship of ap activity with the phase lag variations is also clear in Figure 7d. Interestingly, in Figure 7d, the phase lag corresponding to 6 and 12 UT in the Southern Hemisphere on 27 September shows slightly larger phase lags than on 12 September where the F_10.7 was relatively lower. However, an increase in ap approximately from 15 to 32 nT can also be observed on 27 September since about midnight (see Figure 7d). Although this increase in ap on 27 September is short-lived and may not reflect storm-time conditions, the phase lag patterns seem to correlate with the fluctuations in ap with a time delay (i.e., the ap increase before 6 UT and the phase lags over 30° at 6 UT; ap drops from 25 to 10 nT before 12 UT and large phase lags at 12 UT; ap is stable and quiet before 18 UT and phase lag is significantly reduced). Figure 7 highlights that the geomagnetic activity has a more significant impact on ρ-T synchrony in the high latitudes between 400- and 300-km altitudes more than the solar activity.

The comparison with the controlled runs No Dyn and No Dyn+Aur in Figure 7 investigates the driving mechanisms of the ρ-T synchrony in the high latitudes. The controlled runs represent monthly mean climatological conditions and are driven by constant solar and geomagnetic forcing (i.e., F_10.7=100 sfu and Kp=2). It can be seen that the controlled runs have largely eliminated the phase lags with the No Dyn+Aur run showing almost no sign of deviation at 0 and 6 UT. These controlled runs are used to extend the discussion on the contribution of ion drag and electron precipitation to the ρ-T synchrony.

In the altitude-longitude profiles shown in Figures 8 and 9, a unit variance scaling is applied to density, temperature, HW and WN along each altitude layer and are referred to as , , and respectively. The profiles are presented for 6 UT-mean in January and June each for 0° and 70°N latitudes respectively. The days corresponding to storm days have been removed from the comparison in both Figures 8 and 9. Selected contours of are overlaid on panels a, c and d in both figures. The −0.9 contour of is overlaid on panels d and h in both figures to illustrate the correspondence of -minimum region with vertical winds.

Figure 8

The relationship between patterns of density-temperature synchrony and winds as a function of altitude and longitude at 0° latitude. T1 outputs of (a, e) the normalized density , (b, f) temperature , (c, g) horizontal wind , and (d, h) the vertical wind . The profiles correspond to the 6 UT mean for (a–d) January and (e–h) June 2014. The vertical resolution of the profiles is 10 km. Where applicable, selected boundaries of and of the corresponding month are shown in magenta-dashed and black-dotted lines, respectively.

Figure 9

Same as Figure 8 except for 70°N latitude. Where applicable, selected boundaries of and of the corresponding month are shown in magenta-dashed and orange-dotted lines, respectively.

A more longitudinally uniform variation can be seen at the equator (see Figures 8a, 8b, 8e, and 8f) above 200 km for and 300 km for . It can also be seen that mean near longitude 0° (white areas in Figures 8a and 8e) move slightly eastward with increasing altitude starting from around 200 km to align with mean. In other words, near the equator, approximately from 300 km onward the east-to-west trend in density is nearly synchronous with that of temperature. The density and temperature approximately between 100 and 250 km show much more variation than at higher altitudes and even seem to be out of phase below 200 km (i.e., the density depletions corresponding to the temperature enhancements at a given altitude layer). At these low altitudes, temperature enhancements at a given longitude seem to correlate with density enhancements directly above. The vertical structure of both and in Figure 8 also reveal interesting similarities with the synchrony patterns (e.g., the correspondence at minimum region).

Similarly, in the Northern-winter Hemisphere (see Figures 9a and 9b), approximately above 350 km, both density and temperature seem to exhibit longitudinally uniform variation. In Figure 9a, the movement of mean to the east with altitude near longitude 0° starting from around 250 km seems to be with a less sharp gradient than at the equator. The longitudinal spread of below the zonal mean at altitudes between 250 and 300 km is less than that of . The minima (dark red) and maxima (dark blue) regions of both density and temperature above 300 km seem to align fairly closely preserving the phase structure. The ρ-T synchrony features are much more obscure in Figures 9e and 9f for the Northern-summer Hemisphere.

Unlike near the equator, as shown in Figure 9c, the peak values for at 70°N in January seem to occur around the minimum region. Figure 9g shows the better correspondence of maximum with minimum in comparison to that of January and the peaks in June also seem to be much more vertically uniform starting from a lower altitude than in January. The maximum in Figure 9d seem to agree well along the −0.9 contours of and above 300 km. On the other hand, in Figure 9h, the maximum ( minimum) aligns well with the minimum ( minimum) above 250 km.

5 Discussion

Akmaev et al. (2010) referred to ρ-T synchrony as the approximate in-phase signature between the east-to-west trend in density at a given altitude and that of temperature at a substantially lower altitude in the thermosphere. The phenomenon of synchrony between density and temperature underneath was illustrated in Figure 2 using the physics-based TIE-GCM and empirical NRLMSISE-00 models. A few fundamental characteristics of the ρ-T synchrony can be extracted from Figure 2. The Δρ/ρ troughs at the equator corresponding to both models are nearly twice as large as the peaks. The TIE-GCM diurnal temperature variations at the equator, on the other hand, are distributed in somewhat equal proportions between minima and maxima, while the NRLMSISE-00 shows more massive ΔT/T troughs than the peaks. Among the two models, NRLMSISE-00 shows the highest amplitude in the diurnal variation in both density and temperature during all four seasons. As mentioned previously, the NRLMSISE-00 outputs for high latitudes demonstrate better ρ-T synchrony than the TIE-GCM. This is expected as NRLMSISE-00 uses spherical harmonics to map the density, which is determined by the model's asymptotic exospheric temperature profile, to given geographic coordinates. Further, the contribution of nonmigrating tides is not included in the NRLMSISE-00 outputs. Thus, the NRLMSISE-00 is not well placed for a detailed analysis of the ρ-T synchrony.

In addition, the density-temperature variations when represented in the geomagnetic reference frame (see Appendix Appendix B) revealed that the temperature and density at these altitudes are more synchronous near the magnetic equator compared to high latitudes. The representation in the geomagnetic reference frame further supports the conclusion that the ρ-T synchrony is not an artifact of the model's geographic grid structure. Although some differences in the proportions and magnitudes of the variations exist, the general trends and features near the equator in Figures 2a and 2b largely agree with Akmaev et al.'s (2010) results for December and March.

The temperature variation at 70°N during the Northern Hemisphere summer (see Figure 2c) is relatively minimal. Although the two models seem to agree on where the troughs occur, TIE-GCM shows a slight rise in average temperature near 30°W. Interestingly, TIE-GCM estimated temperature compares outstandingly well with data at high latitudes in June (see Figure A1c). The data/model comparison presented in Appendix Appendix A with temperature data from six stations in the high and low latitudes at various altitudes ranging from 250 to 375 km shows that TIE-GCM is capable at reproducing the diurnal, zonal, and seasonal temperature variations observed during the analysis period.

The secondary peak in density and temperature in Figure 2 (e.g., blue lines between 120°W and 60°W) is known as the MDM and MTM, respectively. As hypothesized by the dynamical theory (see Mayr et al., 1973; Volland, 1988) and illustrated in Akmaev (2011), Figure 2 also shows that MTM and MDM near the equator occur approximately at the same longitude. The HW direction comparison presented in panels e and f in both Figures 4 and 5 revealed no discernible difference in the mean direction of TIE-GCM outputs of horizontal winds between the two altitude layers. Near the equator, the wind speeds are relatively small, and the zonal (east-west) component of HW is stronger, yet at the high latitudes, the winds are faster with a stronger meridional (north-south) component. An equatorward change in HW direction can be seen slightly to the west of longitude 0° (e.g., Figure 4e) and then converging around middle-to-low latitudes at approximately 60°W. This region (i.e., 60°–90°W) where meridional winds seem to be stronger also roughly coincides with the MTM/MDM locations. The MDM and MTM seem to occur between 22:00 and 02:00 local time (local midnight is at 90°W) in agreement with the occurrence times reported in Arduini et al. (1997) and Mayr et al. (1979). Figure 2 indicates that the MTM/MDM varies significantly with the season as also previously reported by, for example, Arduini et al. (1997) and Hickey et al. (2014). For instance, in March the average MDM is weak, and the MTM is barely noticeable compared to other months in the TIE-GCM runs. The MTMs corresponding to the NRLMSISE-00 runs are more defined than the MTMs in the TIE-GCM runs but shows less seasonal variability.

The MTM/MDM peaks visible at 70°N in January (see Figure 2) are also in agreement with, for example, Oliver et al. (2012) and Ruan et al. (2014) who showed the propagation of MTM/MDMs to middle/high-latitudes (up to around 60°N/S) during winter. The TIE-GCM results for March and June show that the MDMs occur around the same local time. Arduini et al. (1997) also highlight the similarity between equinox and solstice MDMs during high solar activity. Besides, our TIE-GCM results show that MDMs occur slightly earlier in January than in the solstice month of June.

Before proceeding further, it is necessary to examine the impact of lower atmospheric forcing on ρ-T synchrony as the previous ρ-T synchrony results of Akmaev et al. (2010) are entirely based on forcing from below with constant solar and geomagnetic energy inputs. The Figure 3 presents results for two cases: with and without the GSWM tides driving the lower atmospheric forcing in TIE-GCM. The main result of Figure 3 is the clear in-phase signature at the low/middle latitudes compared to the high latitudes apart from some minor deviations (e.g., Figures 3c [6 UT], 3b [12 UT], and 3d [12 UT]). Further, the density trend seems to be leading at the high southern latitudes at 12 UT during all seasons regardless of the presence of tidal forcing from below with June showing the lowest phase lag. The phase lag study presented here provides insights into the structure of the latitudinal variation of the ρ-T synchrony. As the proximity between two consecutive longitudes decreases with increasing latitude, the phase lag is more magnified at high latitudes than near the equator and thus becomes less meaningful at very high latitudes. Therefore, the results do not include the latitudes from the poles to 70°.

The impact of GSWM tides on the ρ-T synchrony patterns is more pronounced at the low/middle latitudes during the equinox months (see Figures 3b and 3d). The dynamical theory (e.g., Akmaev et al., 2010; Volland, 1988) explains that in the absence of the contribution to temperature perturbations from vertical tides, the HW follows the temperature gradient (i.e., the thermally driven winds). For example, the divergent and convergent foci of the HW in Figures 5e and 5f are more disturbed/turbulent than that of in Figures 6e and 6f, which are not influenced by the GSWM tides. The contribution from tides to the vertical wind shear near the equator is more substantial during equinox months due to the background zonal winds being more dominant in the equatorial region compared to other seasons. Appendix Appendix B (see Figures B2 and B3) provides examples of HW streams at higher altitudes (i.e., 300/400 km) during equinox months. The slower HW in the equatorial region also helps the propagation of vertical tides to higher altitudes before dissipation. The slight negative phase lags seen near low/middle latitudes in the T1 run in Figures 3b and 3d could be due to the temperature waves enhanced by vertically propagating tides. In corroboration, Salah and Wand (1974) using ground measurements of temperature showed that in the lower thermosphere the tidal-induced temperature fluctuations are larger during equinoxes and summer. Similarly, Friedman et al. (2009) in a study of the longitudinal thermal phase structure using the GSWM, and both ground and space measurements of temperature, showed that the effect of the (2, 4) Hough mode (see Forbes, 2013) amplitude is most dominant during equinox months.

Another significant result from Figures 5 and 6 is that even under solar maximum conditions tides have a significant impact on upper thermosphere HW magnitudes and circulation patterns as well as density. For example, the second density trough near 90°W around the equator in Figure 5 is vanished in Figure 6 thus suppressing the MDM signature. Ruan et al. (2015) showed a similar impact of tides on MDM and MTM but for March. The two figures also demonstrate that the impact of GSWM tides on WN is relatively subtle and minor.

The primary trough regions of seem to be in good agreement with in Figure 4 except in the high southern latitudes. The minimum in Figure 4a seems to move slightly westward away from the equator and then back eastward in the high southern latitudes. A similar movement is seen in the minimum in Figure 4b but not as further into the east as with density. As Figure 2a (TIE-GCM) indicates, these minima are also larger near the equator compared to the high latitudes. Such an agreement between and trough regions is also visible in June (see Figure 5) but somewhat less distinct than January due to the presence of other trends (e.g., the second trough near the equator). The second trough in Figure 5 is relatively deeper and more significant than the first trough (see Figure 2c). In June, unlike in January, the primary minimum and minimum seem to move westward from around 45°S to north. A second peak is also visible in Figure 5 in the high northern latitudes around 0° longitude.

Interestingly, a correlation between that second peak in temperature and the enhanced upward WN in the same region can be drawn (see Figures 5b and 5d). Panels a and d in both Figures 4 and 5 show that WN is, in general, upward where the at 400-km altitude is higher, which signifies the relationship between vertical winds and the ρ-T synchrony as WN is a mode of transport of neutrals between the different altitude layers. A day/night asymmetry is also evident in the WN difference patterns where the WN is in general upward (downward) on the dayside (nightside). The divergence/convergence resulting from the HW field partly set these WN patterns in motion as the HW must satisfy the conservation of mass for neutral species and ions at the same time (i.e., through the equation of continuity; Bauer & Lammer, 2004).

In Figure 4c, between 70°N and 70°S along the 0 contour of , the HW at 400-km altitude is faster (dark blue regions) compared to HW at 300-km altitude. Figure 5c shows a similar resemblance between faster HW and the mean region except for the faster winds near 0° longitude in the Northern Hemisphere seem to follow more along the −0.9 contour of . Following the thermal wind equation (see Volland, 1988), it is apparent that HW and at 300 km in Figures 4 are out of phase, more so in the low latitudes. The HW difference patterns in panel c in both Figures 4 and 5 are also out of phase with both and near the equator. The patterns in Figure 4a are not in full agreement with the 0 contour of in the high southern latitudes. Interestingly, a correlation between strong upward WN and depletion in density can be drawn in the southern polar latitudes between 0°–90°E longitudes (see Figures 4a and 4d). In summary, HW and WN play an important role in affecting trends in density and temperature where, for example, particles transported by WN may significantly alter the ion/neutral production and loss rates, and horizontal advection can transport these changed states (e.g., in composition) over long distances.

The investigation presented in Figure 7 was carried out to equitably capture the impact of space weather drivers on ρ-T synchrony. To the best knowledge of the authors, the literature lacks a quantitative demonstration of the relationship between solar and geomagnetic activities, and ρ-T synchrony. The results from Figure 7 showed that geomagnetic activity dramatically influences the ρ-T synchrony in the high latitudes between 400- and 300-km altitudes more than the solar activity (e.g., the comparison between 2 and 4 January in Figure 7a and 12 and 27 September in Figure 7d). Figure 7c shows further evidence of the impact of the geomagnetic activity on ρ-T synchrony. The phase lag on 12 June with an F_10.7 similar to 27 September but with shallow ap levels does not display large deviations indicating that the variation in geomagnetic activity is influencing the ρ-T synchrony patterns more than the magnitude of the solar flux (see 12 and 18 UT in Figures 7c and 7d). The erratic phase lag patterns in Figures 7c and 7d are likely a manifestation of the east-to-west temperature/density trend being greatly disturbed during times of high ap and thus eliminating any apparent signatures of the ρ-T synchrony between the two altitude layers. Figure 7b (11 March) provides another example of the correspondence between low geomagnetic activity and small deviations in the phase lag. Figure 7b (11 March) demonstrates that the ρ-T synchrony between the two altitudes can be in phase even through to high latitudes during periods of significantly quiet geomagnetic activity. The influence of geomagnetic activity on ρ-T synchrony may be due to the geomagnetic activity-induced Joule heating and associated temperature enhancements. Even small-scale current structures can cause substantial localized temperature increases due to the concentrated perturbation Poynting flux (Richmond, 2010).

To gain deeper insights, consider the controlled runs No Dyn and No Dyn+Aur, which are based upon climatologically representative lower atmospheric conditions and constant solar and geomagnetic forcing in Figure 7. The No Dyn results show that the ion drag velocities are mostly responsible for altering the ρ-T synchrony in the high latitudes. In the auroral regions, precipitating electrons are capable of enhancing the ionization and electron temperature and thus leads to enhancements in Joule heating (e.g., Liu et al., 1995; Zhang et al., 2012). Zhang et al. (2012) showed that the upflows associated with precipitating soft (less than 1 keV) auroral electrons lead to enhancements in density in the thermosphere. Our results for No Dyn+Aur, which ignores (in addition to ion drag) the contribution of electron precipitation, cusp precipitation, polar rain (drizzle), and ion precipitation to the total ionization and heating rates, also seems to reduce the phase lag further (e.g., compare the No Dyn and No Dyn+Aur in the high southern latitudes in June and September).

In TIE-GCM, inputs required to describe the high-latitude dynamics such as the high-latitude ion convection, hemisphere power, and the cross polar cap potential can be specified via multiple sources. In our simulations, the empirically derived Heelis et al. (1982) ionosphere convection model is used. Kodikara et al. (2018) discussed that, compared to accelerometer-derived densities, the performance of both Weimer (2005) and Heelis et al. (1982) ionosphere convection models are comparable under 2014/2015 geophysical conditions. Both Kodikara et al. (2018) and Wu et al. (2015) provided examples of the Weimer (2005) model outperforming Heelis et al. (1982) model during storm times. While the type of ionosphere convection model is not expected to influence the seasonal, monthly mean results much, it may have an impact on the storm time results. In this regard, a comparison with direct observations of ion velocities may provide an avenue to improve model sensitivity to ρ-T synchrony in the high latitudes.

Some physical insights into the vertical structure of the ρ-T synchrony are provided below. The altitude-longitude profiles shown in Figures 8 and 9 visualize the vertical structure of the ρ-T synchrony, and the relationship with the wind patterns at 0° and 70°N latitudes, respectively. The contours overlaid on Figures 8a and 8e show that at the equator the ρ-T synchrony in the upper atmosphere begins around 300-km altitude. Figures 8a, 8b, 8e, and 8f show that temperature trends are vertically uniform approximately above 200 km and that density and temperature are roughly antiphase below 200 km. The contours overlaid on Figure 9a aid to discern that the ρ-T synchrony begins around 350-km altitude at 70°N and that the density trough region approximately from 250- to 300-km altitude is considerably shorter in longitudinal spread than that of temperature. The ρ-T synchrony patterns in the Northern-summer Hemisphere high latitudes are much more obscure than in the Northern-winter Hemisphere. For example, in Figure 9e, has only one trough above 200 km, whereas in Figure 9f shows two peaks and troughs, albeit significantly different amplitudes. For brevity, the vertical profiles corresponding to equinox months have been omitted here. The magnitudes and trends in these vertical structures will likely be different in the equinox months due to the semiannual oscillations in density and temperature (e.g., Emmert & Picone, 2010).

As pointed out earlier, the vertical structure of and in both Figures 8 and 9 reveal interesting similarities with the synchrony patterns (e.g., the correspondence at minimum region). In Figure 8, the (panels c and g) is significantly lower around 0° longitude along the corresponding minimum region above 200 km. In contrast, Figure 9 shows that reaches higher wind speeds near the corresponding minimum region above 200 km in both summer and winter in the high northern latitudes. Figures 8d and 8h reveal an excellent agreement between minimum and minimum around 0° longitude above 200 km. In the Northern-winter Hemisphere (Figure 9d), is larger in the minimum region indicated by the −0.9 contour. However, in the Northern-summer Hemisphere (Figure 9h), has the lowest values in the minimum region above approximately 200 km. Further, is consistently low (i.e., below the mean) around minimum regions as illustrated by the black-dotted contours in Figures 8d and 8h. At 70°N, on the other hand, an obverse trend is seen where is higher along the minimum regions above 200 km (see Figures 9d and 9h).

The hydrostatic modeling of especially the WN has some inconsistencies with observations (e.g., Deng et al., 2008). For example, in TIE-GCM, which is a hydrostatic model, the vertical wind field is calculated from the divergence of the horizontal wind field and usually results in small magnitudes (i.e., less than 30 m/s) compared to observations ranging from many tens of meters per second downward up to 150 m/s upward (see Anderson et al., 2012; Deng et al., 2008). Deng et al. (2008) attributes this discrepancy in hydrostatic models to an imbalance between gravity and the gradient in pressure. There are also issues involving vertical wind measurements (see Anderson et al., 2012), which limits our understanding of the physical mechanisms of the global vertical winds. The correlations between winds and ρ-T synchrony in the thermosphere drawn here should be investigated further as the winds certainly play an essential role in the density/temperature trends.

6 Summary and Conclusions

This paper provides results from a detailed investigation of the mechanism for ρ-T synchrony in the thermosphere. Multiple numerical experiments with TIE-GCM were performed to isolate the dependency of the ρ-T synchrony features on the season, altitude, space weather conditions, high-latitude electrodynamics, and lower atmospheric tidal spectrum modulated via the GSWM. The present work focuses on different seasons in 2014.

The ρ-T synchrony results presented here agree well with the climatology patterns shown in Figures 1 and 2 of Akmaev et al. (2010). Our results extend the understanding of these patterns for different seasons and solar and geomagnetic activities and also clarifies the thermosphere behavior considering mean conditions. The ρ-T synchrony has a significant latitudinal and seasonal variation between 300 and 400 km, and the impact from lower atmospheric tides are only marginal and more noticeable during the equinox months. The phase lags between density and temperature are largest in the high latitudes of the summer hemisphere. The results also demonstrate that the previously reported (see Akmaev et al., 2010) ρ-T synchrony begins around 300-km altitude near the equator and at about 350-km altitude in the Northern-winter Hemisphere under solar maximum conditions. Therefore, the ρ-T synchrony is less latitudinally dependent, for example, above 350 km in January.

The effects from the GSWM tidal spectrum entering the thermosphere near 97 km are magnified during equinox months as the background zonal mean conditions are considerably quieter than other periods. The results also confirm the significant impact of lower atmospheric tides on MTM and MDM. Our numerical experiments demonstrated that addition of tides at the lower boundary of the TIE-GCM deposits momentum and heat into the zonal mean flow leading to significant circulation pattern changes and affecting the density and temperature trends even during solar maximum at altitudes as high as 400 km.

To the best knowledge of the authors, a quantitative demonstration of the relationship between solar and geomagnetic activities, and ρ-T synchrony across multiple seasons has not been treated in the literature before. The numerical experiments with separately forcing the TIE-GCM to ignore ion drift velocities, electric potential and auroral precipitation revealed that those sources are mainly responsible for affecting the ρ-T synchrony patterns in the high latitudes during all seasons considered in the study. The results also show that the phase lag between density at 400 km and temperature at 300 km is significantly affected by geomagnetic activity more than the solar activity. The hypothesis is that the underlying mechanism is related to temperature enhancements via Joule heating and associated nonlinear interactions.

Following the conclusions in Kodikara et al. (2018), one could expect the seasonal monthly mean results presented above to not change much based on the Weimer (2005) or Heelis et al. (1982) ionosphere convection models. Nevertheless, an extended comparison with different high-latitude forcing methods during storm/quiet times may help to quantify the sensitivity of ρ-T synchrony in the high latitudes even further. Particularly an analysis involving direct observations of ion velocities and a comparison with data-driven electrodynamics models (e.g., assimilative mapping of ionospheric electrodynamics; Richmond & Kamide, 1988) may provide further insights.

The paper provides some physical insights into how the horizontal and vertical wind contribute to the ρ-T synchrony. The correspondence of the ρ-T synchrony with winds was analyzed vertically and seasonally for both high and low latitudes. Three-dimensional wind, composition, and temperature measurements will allow a more critical evaluation of the density/temperature phase structures in the upper atmosphere.

Acknowledgments

This research was partially supported by a research scholarship awarded to T. Kodikara by the Cooperative Research Centre for Space Environment Management, SERC Limited, through the Australian Government's Cooperative Research Centre Programme. This research was also partially supported by an Australian Research Council Linkage grant (LP160100561) awarded to B. A. Carter, R. Norman, and K. Zhang. This research was also partially supported by the National Natural Science Foundation of China (NSFC) (project ID: 41730109) and the Jiangsu dual creative talents and teams programme projects awarded in 2017. This research was undertaken with the assistance of resources from the National Computational Infrastructure (NCI), which is supported by the Australian Government. The measurements Kp, ap, and F_10.7 are obtained from NOAA www.ngdc.noaa.gov. The IMF measurements are obtained from the OMNI database omniweb.gsfc.nasa.gov. Ingemar Häggström, Elizabeth Kendall, Robert Kerr, Jonathan Makela, Mike Sulzer, and Roger Varney are thanked for making the incoherent scatter radar (ISR) and Fabry-Pérot interferometer (FPI) measurements available via the CEDAR (Coupling, Energetics and Dynamics of Atmospheric Regions) Madrigal database: http://cedar.openmadrigal.org. The Resolute Bay North ISR is supported by the National Science Foundation (NSF) cooperative agreement AGS-1133009. The Cariri FPI is supported by the NSF CEDAR grants ATM-0940253, AGS-1138998, and AGS- 1452291. The Tromsø ISR facility is maintained by EISCAT, which is an international association supported by research organizations in China (CRIRP), Finland (SA), Japan (NIPR and STEL), Norway (NFR), Sweden (VR), and the United Kingdom (NERC). The National Center for Atmospheric Research, Colorado, is acknowledged for making the TIE-GCM freely available at www.hao.ucar.edu/modeling/tgcm/tie.php. The NRLMSISE-00 model is freely available at ccmc.gsfc.nasa.gov. The authors are very grateful to the reviewers for their helpful criticisms and suggested improvements to the manuscript.

Appendix A: Model Verification: A Comparison With Temperature Data

This appendix addresses the suitability of the physics-based TIE-GCM to perform a study about the ρ-T synchrony in the thermosphere. TIE-GCM's ability to reproduce the thermospheric density and temperature dynamics has been validated in some studies (see Emmert, 2015; Maute, 2017; Qian et al., 2014; Shim et al., 2012, and references therein). In particular, Kodikara et al. (2018) validated the TIE-GCM version 2.0 using accelerometer-derived density data for 2014/2015, which is part of the period considered in this analysis. Below is a comparison of ground measurements of thermosphere temperature from multiple stations with TIE-GCM.

The temperature product used in this work is independently derived from ISR and Fabry-Pérot interferometer (FPI) measurements from the following stations near the high latitudes and the equator: Resolute Bay North (RB, 75°N 95°W), Tromsø (TR, 69°N 18°E), Sondrestrom (SO, 67°N 51°W), Arecibo (AR, 18°N 66°W), and Cariri (CR, 7.5°S 37°W). The data are publicly distributed through the CEDAR (Coupling, Energetics and Dynamics of Atmospheric Regions) Madrigal database hosted at http://cedar.openmadrigal.org.

In processing the temperature data from each station, first, the data are binned hourly (local time) for each month. The above-mentioned storm days that are excluded from the model runs are also removed from the temperature data. Only the measurements that are within two standard deviations between ±50 km of a given height per hour is considered here. The measurements are then linearly interpolated to the given height. In the comparison given below, the monthly mean of the respective hours is compared with that of T1 outputs. TIE-GCM's performance is evaluated by comparing the data/model ratio such that ratio below 1 is a measure of the model's tendency to overestimate.

Figure A1 compares ISR and FPI temperature measurements from various stations at high latitudes and low latitudes with T1 outputs for January, March, and September 2014. In Figure A1c, data from only Sondrestrom in the high latitudes are shown for June 2014 due to unavailability of processed data from the other stations. Figure A1(left) compares the ISR data at 300-km altitude from stations at high latitudes. Figure A1(right) compares data from stations near the equator with ISR data at 375-km altitude and FPI data at 300- and 250-km altitudes. Where applicable, the mean ratio among multiple stations is displayed with a black dashed line. Where available, the aggregated hourly mean of the entire month is presented in Figure A1. However, the frequency of the data from all stations are not equal.

Figure A1

(a–d) Comparison of the ratio between temperature (TN) data with T1 outputs for the specified months in 2014. (left) The ratio between hourly mean incoherent scatter radar (ISR) measurements and model estimates of temperature compared at Resolute Bay North (RB, 75°N 95°W), Tromsø (TR, 69°N 18°E), and Sondrestrom (SO, 67°N 51°W) at 300-km altitude. (right) Similarly, the data/model ratio at Arecibo (AR, 18°N 66°W) and Cariri (CR, 7.5°S 37°W) at different altitudes using both ISR and FPI (Fabry-Pérot interferometer) measurements. No data for June (low latitudes). The days corresponding to storm days have been removed from the comparison. All values are adjusted to the local time at the respective station. Where applicable, the black dashed line indicate the mean ratio among the stations.

Figure A1 shows that the temperature measurements are generally in good agreement with the model outputs in all seasons. Figure A1b shows that the deviation from the ideal ratio is stronger at RB in March, especially during the morning hours. The long gaps in the ratios corresponding to the FPI measurements in Figures A1a(right) and A1b(right) are due to constraints on instrument's operational times. The comparison at AR in September shows that the model underestimate more during the heat of the day than other times.

The comparison with temperature data from six stations in the high and low latitudes at multiple altitudes ranging from 250 to 375 km shows that TIE-GCM is capable at reproducing the diurnal, zonal, and seasonal temperature variations observed during the analysis period. The availability of temperature data in the desired altitude range (300–400 km) is extremely sparse. The stations used in Figure A1 are among the very few where temperature data is available with a reasonable temporal coverage (i.e., at least covering multiple seasons hourly).

Appendix B: Additional Comparisons of ρ-T Synchrony

Figure B1 is similar to Figure 2 but density and temperature deviations are compared in the geomagnetic reference frame.

Figure B1

Physics-based T1 model outputs of the percentage deviation of density (Δ ρ/ρ) and temperature (ΔT/T) from the zonal mean at 400- and 300-km altitudes, respectively. The 6 UT mean values for the specified months in 2014 are shown for geomagnetic latitudes/zones at 50°N (red), 50°S (green), and 0° (blue). The magnetic coordinates are computed according to Emmert et al. (2010) but with IGRF-12 (International Geomagnetic Reference Field) coefficients.

Figures B2 and B3 are similar to Figure 4 but for March and September, respectively. The HW magnitudes in the high latitudes are significantly higher in September compared other months. The similarity between ρ-T synchrony and the wind difference patterns is evident in both figures.

Figure B2

Same as Figure 4 except for 6-UT March 2014.

Figure B3

Same as Figure 4 except for 6-UT September 2014.