The main external energy input to the terrestrial thermosphere is solar radiation, particularly in the extreme ultraviolet (EUV) band. The solar-driven circulation manifests as the flow across the isobars, in contrast to the geostrophic flow that dominates in the middle and lower atmosphere (Forbes, 2007). This is because the Coriolis force is much smaller than the pressure gradient term for the typical terrestrial thermosphere. Under absorption of solar daily cyclic forcing, the atmosphere also induces the solar tides, which refers to global-scale perturbations in atmospheric parameters with periods and zonal wavenumbers that are harmonics of a day and a zonal cycle. In addition to the local absorption of EUV radiation as the major source, the solar tides in the thermosphere also come from upward propagating waves excited in the middle and lower atmosphere, including the infrared absorption by tropospheric H2O and ultraviolet absorption by stratospheric O3 (Forbes and Zhang, 2022). Thus, the level of solar activity is expected to have a key impact on the dynamical variability in the thermosphere (Oberheide et al., 2009; Sun et al., 2022). However, when inspecting on timescales longer than the solar cycle, the influence from other secular variables, such as long-term changes in CO2 concentration and main geomagnetic fields, should not be ignored. It is then natural to ask how and to what extent these factors act on the thermospheric dynamics on long-term timescales, e.g., since the beginning of the Holocene.

CO2 plays a significant role in cooling the thermosphere, in contrast to the warming effect in the troposphere (Laštovička et al., 2006; Solomon et al., 2018). Since the first prediction by Roble and Dickinson (1989), many observational evidences and simulation experiments have been subsequently proposed to support the CO2 cooling effect using modern techniques and advanced models (Akmaev and Fomichev, 2000; Akmaev et al., 2006; Marsh et al., 2013; Ogawa et al., 2014; Qian et al., 2006, 2011; Solomon et al., 2015; Zhang et al. 2016). A well-established consensus is that every 10 ppm increase in CO2 concentration will result in a ∼1–3 K decrease in global mean temperature in the thermosphere (e.g., Solomon et al., 2018). As the issue of increasing CO2 becomes urgent (IPCC, 2014), researchers have also worked to elucidate the concomitant effects on the upper atmosphere (Zhou et al., 2022), and one of which is the thermospheric dynamics. Using the GAIA (Ground-to-topside Atmosphere Ionosphere model for Aeronomy) simulation, Liu et al. (2020) suggested that the doubling of CO2 concentration should strengthen thermospheric meridional circulation, enhance diurnal migrating tide, and weaken semidiurnal migrating tide. Kogure et al. (2022) further analyzed the underlying mechanism of the thermospheric zonal mean wind response, suggesting that the ion drag, molecular viscosity, and meridional pressure gradient forces as the three main factors are in the combined modulation. However, the impact of CO2 on the long-term evolution of the thermospheric dynamics during the Holocene is still poorly understood.

The secular variation of the geomagnetic field would produce considerable changes in the thermosphere temperature other than the CO2 effect. Although the geomagnetic variation does not act directly on the neutral atmosphere, it affects ion motion and thus ionospheric behavior (Cai et al., 2019; Elias et al., 2022; Yue et al., 2018; Zossi et al., 2018), which are coupled to the neutral atmosphere via ion-neutral collisions. The strength of the geomagnetic field determines the gyrofrequency and the ionospheric conductivity, thus influencing the Joule heating power and E×B drift velocities (Cnossen et al., 2012; Zhou et al., 2021). The geomagnetic tilt angle controlling the geographic distribution of the Joule heating should produce further changes in temperature and neutral winds (Cnossen and Richmond, 2012). The secular changes of geomagnetic field produce regionally both positive and negative changes; therefore in the global average their effect is negligible (Qian et al., 2021). Cnossen (2014) reported that the geomagnetic variation over the last century could cause a ∼±10 K change in the thermosphere temperature regionally, comparable to the -8 K decrease in global temperature due to increased CO2 over the same period. Analyses of recent decades (Cnossen et al., 2020) and projections in the coming decades (Cnossen, 2022) about the thermospheric climate change confirm the importance of the geomagnetic variation, although accelerating CO2 growth still plays a dominant role. Since the geomagnetic field has undergone a more complex evolution during the Holocene than in the present century (Korte et al., 2011), the impact on the evolution of thermospheric dynamics is expected to be more dramatic and therefore worth investigating.

The aim of the present study is to discuss the scenario of thermospheric dynamic changes due to the long-term changes in CO2 concentration and geomagnetic field during the Holocene. This paper is organized as follows: Sect. 2 will briefly introduce the numerical simulation settings. Section 3 will show the main results of the simulations, then Sect. 4 discusses the scientific key points. In the end, a short summary is given in Sect. 5.

Attempting to understand the long-term evolution of thermospheric dynamics affected by these two factors in the Holocene, we designed long-term time-slice simulations based on the Global Coupled Ionosphere–Thermosphere-Electrodynamics Model developed at the Institute of Geology and Geophysics, Chinese Academy of Sciences (GCITEM-IGGCAS; Ren et al., 2009, 2010, 2011, 2020). Detailed model description and settings are referred to in Yue et al. (2022) and Cai et al. (2023), which have carefully investigated the global thermal structure and density profile of the thermosphere and ionosphere, respectively. Here, we give a brief introduction to restate and to add key information. This 3-dimensional coupled thermosphere–ionosphere model self-consistently solves the global thermospheric and ionospheric behavior in the altitudinal coordinate, covering altitudes from 90 to 600 km. The ionospheric electro-dynamics are solved on the provided geomagnetic field configuration using magnetic apex coordinates (Richmond, 1995) based on a set of spherical harmonic coefficients. The calculation scheme requires the geomagnetic field to be dipole-dominated, so the situation of geomagnetic reversal is difficult to portray. The high-latitude electric potential and electric fields are specified by the empirical model of Weimer-96 (Weimer, 1996), which is driven by the hemispheric power (HP), solar wind speed (SWS), interplanetary magnetic field (IMF), and cross-polar cap potential (CPCP). At the lower boundary at 90 km, migrating tides in neutral temperature and density are given by the global-scale wave model (GSWM), while neutral winds are self-consistently calculated. Non-migrating tides are not included in this study. The solar EUV radiation is described by the empirical model EUVAC (Richards et al., 1994), which is driven by the proxy of solar flux at 10.7 cm (F10.7). The CO2 cooling is calculated under the assumption of the non-local thermodynamic equilibrium (NLTE) with a cooling-to-space approximation assumed. In this model, the CO2 level is specified by a given value for a fixed time under the assumption of diffusive equilibrium. This calculation formula follows Roble et al. (1988) and is also adopted by other thermosphere–ionosphere coupled models, such as NCAR-TIEGCM (Qian et al., 2017).

To diagnose the long-term effects of CO2 and geomagnetic field variations on the thermospheric dynamics, two control runs (CR1 and CR2) were performed under perpetual solar minimum and geomagnetic quiet conditions, which correspond to the CR2 and CR1 in Yue et al. (2022) and Cai et al. (2023). The driving parameters in the Weimer-96 model are set as HP = 10 GW, SWS = 300 m s-1, IMF By = 0 nT, IMF Bz = -0.5 nT, and CPCP = 20 kV for both cases, representing the extreme geomagnetically quiet condition of Kp=∼0.3. To eliminate the impact of solar variation, each case was performed under solar minimum, corresponding to the F10.7 setting to be a constant of 87 sfu (solar flux unit; 1 sfu = 10-22 W m-2 Hz-1). In CR1, realistic CO2 from a combined dataset drives the GCITEM-IGGCAS model with a fixed configuration of geomagnetic fields. Hence, the simulated variability of the thermosphere is derived exclusively from the CO2 changes. The CO2 dataset consists of three components: (1) estimations from the ice cores' recorded air composition since ∼80000 years before the present with a rough resolution of ∼100 years during the Holocene (Lüthi et al., 2008); (2) measurements in ice with high precision back to 2000 years before the present (MacFarling Meure et al., 2006); and (3) modern atmospheric measurements at Mauna Loa Observatory, Hawaii, since 1958 (Keeling et al., 1995). In CR2, the CO2 level is fixed to be 270 ppm, corresponding to the averaged value during the Holocene, while the geomagnetic fields are set to be varied with time. The specified geomagnetic field before 1900 is provided by the CALS10k.2 model developed by Constable et al. (2016), which is based on the archeo-magnetic and lake sediment data. Generally, this model roughly has spherical harmonics to degree and order of 10, and cubic B-splines parameterization is implemented with knots positioned every 40 years. After 1900, the geomagnetic fields are described by the International Geomagnetic Reference Field (IGRF) model (Alken et al., 2021). This model is based on the modern magnetic observations to describe the spatial distribution of geomagnetic fields by the spherical harmonic degree and order of 13 with the time resolution of 5 yrs. The secular variation of the geomagnetic field implemented in the CR2, including the dipole moment and the position of magnetic and geomagnetic poles, was illustrated in Fig. 1 of Yue et al. (2022), and the readers could refer to Constable et al. (2016) for more detailed information. A general scenario includes: (a) that the dipole moment fluctuated within 6.1–10.1 (1022 A m2) and has continuously decreased since 1700 by ∼13 %, and (b) that the geomagnetic/magnetic pole is located at latitudes larger than 78/70∘ and has drifted from the Western Hemisphere to the Eastern Hemisphere over the past century. Both cases were run every 100 years in the period of 9455 BC to AD 1945, and an additional run of AD 2015 was for the contemporary condition. Particularly, pre-runs of 15 d were performed as spin-up preparation to eliminate the influence from the initial conditions, and the outputs in the last day were used for analysis. Each case was running in two seasons, March and June, with the aim of discussing the seasonal dependence of the thermospheric dynamical response.

In this paper, two control runs, CR1 and CR2, were conducted to examine the response of thermospheric dynamics to long-term changes in CO2 and geomagnetic field during the last 12 000 years of the Holocene. The CO2 effect was revealed as an enhancement of the general circulation with increasing CO2 levels (Figs. 1 and 2), which agreed with the result of Liu et al. (2020). Rind et al. (1990) also found that an increase in CO2 similarly enhanced the mesospheric circulation. Both of them suggested that the increased eddy forcing and gravity waves (GWs) should play an important role. However, the GCITEM-IGGCAS model does not involve a parameterization scheme for GWs because the GWs mainly affect the mean flow in the mesosphere rather than in the thermosphere. Therefore, the changes in the circulation caused by CO2 variations in our results cannot be attributed to GWs. The interpretation by Kogure et al. (2022) should be responsible for the fact that the changes in ion drag, molecular viscosity, and meridional pressure gradient forces are in the combined modulation. An interesting founding is that the CO2 increase does not linearly accelerate the circulation and tends to be “saturated”, as shown in Fig. 3. The plausible explanation is that the molecular viscosity is non-linearly related to the temperature. As for the tidal response to the CO2 effect, the DW1 amplitude is positively correlated with CO2 variation (Fig. 4). A reasonable deduction is that the decreased viscosity due to the enhanced CO2 cooling should be less likely to dissipate tidal propagation from below. The latitudinal structure of the DW1 response to CO2 differs from that of Liu et al. (2020), partly because their results mixed the influences of changes in tidal sources from below, whereas our results reflected the internal thermospheric responses. In addition, this paper only considered the geomagnetically quiet condition, while the efficiency of CO2 forcing somewhat differs under low and high geomagnetic activity conditions according to GAIA simulations by Liu et al. (2021).

Figure 5 illustrated an asymmetric response in circulation to the geomagnetic variation. The change in neutral winds was larger in the hemisphere with a more distant geomagnetic pole shift. Given that the variation in the dipole component of the geomagnetic field is hemispherically symmetrical, it could logically be inferred that the hemisphere difference in circulation is contributed by the variation of the non-dipole component. The neutral temperature change due to geomagnetic variation has a similar pattern to the ion temperature in Cnossen (2014), which is also manifested to decrease around the day-time equatorial ionization anomaly (EIA) peaks. A possible causal linkage could be proposed that the geomagnetic variation affected the equatorial plasma drift velocity and then redistributed the electron density around the EIA region. As the electron density becomes large/small, the electron temperature changed conversely. The ion temperature change then should be more or less related to the electron temperature change. Generally, the smaller strength of the geomagnetic fields would induce stronger equatorial vertical drift (E×B/B2) and thus increase the electron density at the EIA peaks, and Yue et al. (2022) confirmed such a relationship. During the nighttime, the equatorial drift tended to be downward and the EIA structure disappeared in general. So, the above-discussed causality is not valid, and the night-time neutral temperature response should be different. The increased Joule heating related to the weakening of the geomagnetic field might be responsible. Hence, the geomagnetic variation would redistribute the temperature in the daytime and nighttime differently (Fig. 6), then causing the day–night difference in Figs. 6 and 7. The seasonal dependence of the day–night difference in temperature response to the geomagnetic variation is still puzzling and needs further explanation in the future. The temperature redistribution due to geomagnetic variation then causes the tidal responses in Figs. 8 and 9. At middle latitudes, both DW1 and SW2 manifest to be positively correlated to the dipole moment, partly because the cooler thermosphere caused by the strengthening geomagnetic field (Cai et al., 2023) modulated the tidal propagation from below. At the low latitudes, the effect from E×B drift at daytime becomes important as aforementioned, therefore different from that in middle latitudes.

As a tentative investigation of the long-term change of thermospheric dynamics during ∼12000 years, this paper still has some limitations and flaws, and one of them is the fixed lower boundary. In the present work, the migrating tides at the lower boundary (90 km) are set to be unvaried regardless of simulating different periods in the Holocene. To our knowledge, the long-term trend around the mesopause is still debated, and the understanding changed from no trend to a mild negative trend in general (Beig et al., 2003; Huang et al., 2014; Laštovička, 2017). This is partly because the temperature trends at these heights are sensitive to the changes in stratospheric ozone concentration (Lübken et al., 2013). A whole-atmosphere simulation performed by Solomon et al. (2018) also indicated there are very weak trends in the mesopause region. Hence, the perpetual lower boundary should be a conservative and compromised treatment, additionally considering that little evidence has been provided on how the atmospheric tides change during such a long-term historical time. Besides, the fixed lower boundary inferred that the tidal source from the lower atmosphere is constrained to be unvaried, so our results mainly describe the effect of propagation conditions and local excitation on the long-term dynamics change in the thermosphere. In the next step, simulation based on a whole-atmosphere climate model, like the WACCM-X (Liu et al., 2018) and GAIA (Jin et al., 2011), should give a much more realistic scenario of the long-term change in the thermospheric dynamics, nevertheless, the computation cost will increase substantially.

In addition, the empirical model describing the high-latitude input, Weimer-96, is based on modern satellite measurements. Although the geomagnetic intensity variation has not been taken into consideration by the model, the effect of the geomagnetic tilted angle has been included. The drift of magnetic poles and aurora region is thus considered, given that the Weimer-96 is based on a magnetic coordinate. The intensity of the geomagnetic field is examined as influencing the magnetosphere configuration and thus is expected to affect the energy input to the high-latitude thermosphere (Zhong et al., 2014; Cnossen et al., 2012). Vogt et al. (2009) summarized the potential impact of the geomagnetic field variation on the geospace by modulating the shielding of the energetic charged particles. During the simulated period, the dipole moment (M) is in the 6×1022–1×1023 A m2 range. As the sine of polar cap size (θ) is generally proportional to M-1/6, a rough estimation deduces that θ would change by ∼3∘, within latitudinal resolution (5∘) in the model. Theoretical scaling about cross-polar cap potential (Φ), Φ∝M1/3, infers that the Φ should varied from 18 to 21 kV during the Holocene if we set the Φ as 20 kV at the present era. Comparing a typical geomagnetically disturbed condition that Φ is ∼80 kV for Kp=4, the relative change in Φ above is quite small. Cnossen (2014) also declared that the magnetosphere–ionosphere coupling is only significant during the disturbed conditions. Given that our simulation is perpetually geomagnetically quiescent, the impact of geomagnetic variation on the high-latitude energy input should be limited.

In this work, the CO2 and geomagnetic fields were regarded as two independent external drivings to the simulation regardless of their interaction, although whether the interaction exists is still controversial. Zhou et al. (2021) proposed that the decrease in geomagnetic intensity would redistribute the CO2 in the upper atmosphere using the whole-atmosphere simulation. Their investigation suggested that the increased ionospheric conductivities due to the weakened geomagnetic intensity would induce much more Joule heating to warm the high-latitude lower thermosphere, which then should enhance the upwelling flow and bring rich CO2 from below. This result is based on the physical fact that the CO2 distribution becomes deviated from the well-mixed equilibrium above the mesopause (∼80–90 km), and the timescale of eddy diffusion becomes much larger in the upper atmosphere (Beagley et al., 2010; Rezac et al., 2015), so that the dynamical processes could modulate the CO2 distribution. However, until now, little observational evidence has been proposed to support the possible link between CO2 and geomagnetic fields. A simulation project conducted by the whole-atmosphere model in the next step could provide more information.

Responses of the non-migrating tides to the variation of CO2 and geomagnetic fields were not considered in this paper. The eastward propagating diurnal tides with a zonal wavenumber of 3 (DE3) should not be very sensitive to the CO2 change, according to the discussion by Liu et al. (2020). This result was expected, as the longitudinal variation of CO2 concentration is generally not obvious. On the other hand, geomagnetic fields crucially influence the non-migrating tidal propagation in the upper atmosphere, through the electro-dynamo or parallel-line transport. For example, Jiang et al. (2018) revealed that DE3 tide can induce the longitudinal wavenumber-3 (WN3) structure rather than the should-be WN4 structure through the electro-dynamical coupling with the geomagnetic field. Zhang et al. (2020) proposed that the significant role of parallel-line transport alters the interhemispheric symmetry as the enhanced planetary waves upward propagated during the 2009 sudden stratosphere warming (SSW) event. As the realistic geomagnetic field is much more complicated than the dipole or tilted dipole, a given non-migrating tide propagating into the thermosphere would broaden the spectra of wavenumbers. Yue et al. (2013) found that there were complicated longitudinal structures rather than simply the WN3 as the quasi 2 d wave with westward zonal wavenumber 3 propagating into the upper atmosphere. In this future work, the non-migrating tidal response to the long-term variation will be worth studying.

This paper diagnosed the long-term changes in the thermospheric dynamics caused by the secular variation of CO2 emissions and geomagnetic field during the Holocene, using the global coupled thermosphere–ionosphere model, GCITEM-IGGCAS. Two sets of long-term time-slice simulations covering ∼12000 years were performed by independently controlling the CO2 level and the configuration of geomagnetic fields, both under the perpetual condition of solar minimum and geomagnetic quiescence. The corresponding changes in the circulation and major solar tides in the thermosphere were then analyzed, and the main results were summarized as follows:

The CO2 increase/decrease generally strengthened/weakened the general circulation in the thermosphere, and notably the circulation has intensified dramatically with the steep increase in CO2 since the industrial revolution. The circulation increase due to the CO2 variation was found to grow non-linearly, which is expected to be caused by the non-linear relationship between temperature and molecular viscosity.