Introduction

Variations of mid-latitude noontime monthly median foF2 in the course of the year manifest a combination of three components: annual - responsible for “December anomaly”, seasonal - responsible for “Winter anomaly”, and semiannual component responsible for semiannual foF2 peaks. This was shown in the extensive morphological analysis1,2,3. The December anomaly with global foF2 values larger in the vicinity of December solstice than around the June one was firstly reported by the authors4,5. Although it is obvious that the effect is related to the Sun-Earth distance today after many decades a formation mechanism of December anomaly is still discussed in the literature6,7,8. The explanation of the Seasonal anomaly with winter foF2 values larger than summer ones in terms of yearly variations of thermospheric composition was proposed9,10. Later this idea was confirmed by model simulations11. Further attempts in this direction have resulted in a beautiful explanation of seasonal variations in the ionospheric F2-region12. The mechanism includes global from summer to winter Hemisphere thermospheric circulation, the total insolation, and auroral heating with its crucial role in longitudinal/latitudinal foF2 yearly variations. Available global ionospheric and thermospheric observations in general confirm the validity of this mechanism.

The situation with semiannual variations in thermosphere and ionosphere looks more complicated. The semiannual foF2 variations in the course of the year were described long ago1, while semiannual variations in the thermosphere were revealed using harmonic analysis of satellite drag observations13. The authors12 have considered 6 mechanisms of semiannual variations ever proposed. The final conclusion of their analysis – “the circulation-driven mechanism provides a reasonably complete explanation of the observed pattern of F2 layer annual and semiannual quiet-day variations”. However, a comparison of STIP simulation results used in their analysis with monthly median NmF2 observations manifest a difference up to factor of 2 during equinoxes even at a normal mid-latitude station Slough for noontime14. Further, STIP simulations give equal magnitudes for equinoctial NmF2 peaks while they may be different in observations. Therefore global thermospheric circulation alone is not sufficient to provide a satisfactory (at the quantitative level) explanation to semiannual NmF2 variations. Noontime NmF2 at middle latitudes manifest the state of the surrounding thermosphere (mainly atomic oxygen concentration) therefore observed semiannual foF2 peaks directly point to the corresponding peaks in atomic oxygen and neutral density which is mainly presented by atomic oxygen at F2-layer heights. Therefore problems with the description of semiannual foF2 peaks mean problems with the description of thermospheric parameters during equinoxes.

The most straightforward explanation of semiannual peaks in neutral gas density, atomic oxygen and correspondingly in foF2 is eddy diffusion with its minimal intensity around equinoxes. The possibility of eddy diffusion to control the thermospheric neutral composition is known long ago15,16,17. Unfortunately up to now very few are known about spatial and temporal variations of this process. The ‘thermospheric spoon’ mechanism18 tells about minimal mixing of the thermosphere during equinoctial periods seemingly confirming the idea of decreased eddy diffusion during equinoxes. In his mechanism a semiannual variation of O/N2 is generated by the inter-hemispheric circulation. TIE-GCM simulations qualitatively reproduce O/N2 and neutral density semiannual variations but they are much smaller than observed ones19. This was also mentioned in relation with a comparison of STIP simulation results with NmF2 observations14.

Further steps were done by the authors19,20 who varying eddy diffusion coefficient have fitted TIE-GCM and TIME-GCM model simulation results to satellite neutral density observations. Both analyses manifested yearly variations of eddy diffusion (Kedd coefficient) with minima around equinoxes20. Recent results21 are also inclined to the same conclusion: “Results produced by TIE-GCM are closest to the observations when seasonally varying eddy diffusivity is considered in the model.” Of course, technically it is always possible to prescribe the difference between simulation results and observations to any unknown process. But who could vouch for the fact that incorrect Kedd specified in the original versions of TIE-GCM and TIME-GCM models is the only drawback that prevents the simulation results to coincide with neutral density observations? Along with this yearly varying eddy diffusion looks as the most plausible basic mechanism to explain global occurrence of semiannual variations in the thermosphere and correspondingly in the F2-region as this is discussed in the paper.

The aims of the paper may be formulated as follows.

  1. 1.

    To check is there a statistically significant difference between vernal and autumnal foF2 peaks at middle latitudes during noontime hours.

  2. 2.

    To specify the aeronomic parameters responsible for the difference between vernal and autumnal foF2 peaks.

  3. 3.

    To discuss possible mechanism(s) forming the vernal and autumnal foF2 peaks in the thermosphere-ionosphere system.

Observations and results

It is well-known that vernal and autumnal foF2 peaks manifest large variations depending on geophysical conditions. We confined our analysis by four mid-latitude North Hemisphere stations Boulder (40.00N, 254.70E, Φ = 48.10 Φ is the magnetic latitude) Rome (41.80N, 12.50E, Φ = 41.90), Wakkanai (45.40N, 141.70E, Φ = 36.90), Juliusruh (54.60N, 13.40E, Φ = 54.00 ) and two mid-latitude South Hemisphere stations Hobart (42.90S, 147.30E, Φ =-50.20) and Port Stanley (51.70S, 302.20E, Φ =-42.00), located in different longitudinal sectors with respect to the magnetic pole. Figure 1 as an example gives noontime monthly median foF2 yearly variations for similar geophysical conditions under moderate solar and geomagnetic activity but quite different foF2 variations during equinoctial periods. It is seen that the larger foF2 peak may occur either in spring or in autumn.

Fig. 1
figure 1

Observed noontime monthly median foF2 variations in three longitudinal sectors for two periods with similar monthly F10.7 and Ap indices (lower panels) but different foF2 equinoctial peaks.

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It is known that semiannual foF2 variations dominate at lower latitudes and in the Southern Hemisphere while the contribution of seasonal component increases with geomagnetic latitude and semiannual foF2 peaks may merge to create a single winter foF2 maximum12,14,22,23.

For this reason the vernal foF2 peak may be often absent at Boulder, a ‘near-pole’ station. Therefore, we have selected only years when the vernal peak is clearly present in yearly foF2 variations. For this reason the number of points at Boulder is less compared to Rome for the same (1958–2022) period in question. Figure 2 gives years with monthly median foF2 used at each station in our analysis.

Electron concentration in the noontime mid-latitude F2-layer maximum NmF2 ~ IEUV × [O]4/3 where NmF2 = 1.24 × 104(foF2)2, IEUV is the intensity of ionizing EUV radiation, atomic oxygen concentration [O] is taken at a fixed height in the thermosphere24. According to theory, solar IEUV and atomic oxygen are the main contributors to daytime mid-latitude NmF2.

Fig. 2
figure 2

Years with monthly median foF2 at each station used in our analysis.

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The vernal and autumnal foF2 peaks are separated by half of a year in time and solar ionizing EUV radiation is different in two peaks especially during rising and falling phases of a solar cycle. Therefore at first, it is necessary to remove the dependence on solar EUV impact. Calibrated total solar EUV (100–1200) Å flux observations are available for the (2002–2017) period25. Observed monthly median EUV manifests a good correlation with the effective F10.7eff = (F10.7 mon + F10.7 3mon)/2 solar index. A similar solar activity index is used in the EUVAC model26. In our case the correlation coefficients between monthly median EUV and F10.7eff is ~ 0.986 ± 0.02 for the equinoctial months. According to the Ceddok scale this is practically a functional dependence and ~ 97% of the EUV variability is explained by F10.7eff. Therefore monthly F10.7eff may be used as a proxy for monthly solar EUV radiation for the periods not covered with EUV observations25. The reduced NmF2/EUV values may be further reduced bearing in mind that the amount of produced atomic oxygen via O2 dissociation depends on the intensity of FUV solar radiation as [O] ~ Idiss × [O2]. The Schumann-Runge continuum is actually the major cause of the O2 dissociation above 100 km. The characteristic time of this process τdis ≈ 1/JO2 < 3 days above 120 km height27, i.e. this is a fairly fast process and month-to-month variations of the atomic oxygen abundance should depend on month-to-month variations of the intensity of dissociation radiation. A recently developed model of solar EUV and FUV radiation28 is based on HLα (λ = 1216 Å) solar emission as the input parameter. The model shows that the intensity of FUV radiation is linearly related to HLα. Therefore it is possible to use directly observed HLα29, also LISIRD database https://lasp.colorado.edu/lisird/data/composite_lyman_alpha/) as an indicator of dissociation radiation for the NmF2/EUV ratio further reduction. The results with double reduced monthly median NmF2 values are given in Fig. 3.

Vernal foF peaks may occur in the course of three months while autumnal peaks occur only during two months (see later). For this reason the maximal reduced NmF2/EUV/HLα value over February-April was considered as the vernal peak, while the maximal NmF2/EUV/HLα value over October-November was considered as the autumnal peak in the Northern Hemisphere. Seasons are shifted by 6 months in the Southern Hemisphere. Hobart manifests very unusual foF2 yearly variations with the main and well-pronounced autumnal peak always in April and a secondary smaller vernal peak which may or may not occur in the course of 5 months from August to December. However, we analyzed only peaks that occurred in the vicinity of the vernal equinox in August-October. All cases are divided into three levels of solar activity: maximal (Feff > 150), medium (110 ≤ Feff ≤ 150), and minimal (Feff < 110). The EUV flux is used in 1010 ph cm-2s-1 and HLα flux in 1011 ph cm-2s-1 units.

Points in Fig. 3 are distributed with respect to the bisector which manifests the absence of a difference between vernal and autumnal NmF2/EUV/HLα peak values. Figure 3 gives that points are clustering around the bisector under elevated and high solar activity while the points are mainly located above the bisector under low solar activity. This means that the autumnal NmF2/EUV/HLα peak is on average larger than the vernal peak under solar minimum. All points are above the bisector at Hobart for any level of solar activity.

Apart from the dependence on solar radiation, monthly median NmF2 also depends on geomagnetic activity via neutral composition, mainly atomic oxygen. The relationship of NmF2 with monthly Ap indices is not straightforward but depends on solar activity, season, local and storm time, and geomagnetic latitude of a station. Moreover, unlike NmF2 day-to-day variability when geomagnetic activity impact is well-pronounced, geomagnetic effects may not be seen in monthly median NmF2 due to the very procedure of NmF2 medians derivation. Monthly median NmF2 clearly manifests the disturbance effects if only half of days in a month were really disturbed and this is not often. For this reason NmF2 monthly median empirical models like IRI30 or the model31 do not include the dependence on geomagnetic activity.

However the impact of geomagnetic activity on monthly median NmF2 under different levels of solar activity may be interesting in the framework of our analysis. Although this impact is small due to a weak relationship between noontime monthly median NmF2 and Ap indices Table 1 gives the results of such correlation analysis.

Table 1 Correlation coefficients between NmF2/EUV/HLα and monthly Ap indices under solar minimum and maximum. The total correlation is estimated on the Ceddok scale.
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Table 1 gives that correlation coefficients between NmF2/EUV/HLα and monthly Ap in general are low although they may be significant. Positive correlation coefficients take place under solar minimum while they are negative (when significant) under solar maximum. In general the correlation is ranging between moderate and weak on the Ceddok scale. For this reason any further reduction of NmF2/EUV/HLα on geomagnetic activity gives no visible results even under solar minimum – the number of points above the bisector in Fig. 3 is not increased. Therefore the distribution of points given in Fig. 3 may be considered as the final one for our further analysis.

Figure 3 indicates a systematic dependence of autumnal NmF2/EUV/HLα versus vernal ones. All correlation coefficients are significant at the 99.9% confidence level and vary from 0.680 ± 0.168 at Boulder to 0.896 ± 0.060 at Hobart with the correlation ranging between noticeable and close according to the Ceddok scale.

Another interesting aspect is the timing of vernal and autumnal peaks occurrence. Table 2 gives the number of peak occurrences at six stations for vernal and autumnal months over all years in question. Double reduced NmF2 were used in this statistics.

Fig. 3
figure 3

Scatter plots of reduced monthly median NmF2/EUV/HLα autumnal values versus vernal ones at six stations for three levels of solar activity.

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Table 2 The probability (in %) of NmF2/EUV/HLα peaks occurrence during vernal and autumnal months. The total number of analyzed years at a given station is given in brackets.
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Table 2 manifests that the vernal peak may occur in the course of three months in both Hemispheres while the occurrence of the autumnal peak is confined by two months. Hobart station demonstrates an interesting behavior. Along with results given in Fig. 3 where all autumnal points are larger than vernal ones under all solar activity levels, Table 2 shows that all these autumnal points belong to one month, April.

Summarizing the morphological part of our analysis it is possible to conclude that the NmF2 autumnal peak on average is larger than the vernal one in both Hemispheres at least under solar minimum. The autumnal NmF2 peak independently on solar activity always occurs within two months while the vernal peak may occur in the course of three months. An additional analysis has shown that Hobart manifests the main and well-pronounced autumnal peak always in April and a secondary smaller vernal peak which may or may not occur in the course of five months from August to December. This peculiarity of Hobart requires a special analysis.

Interpretation

According to theory day-time mid-latitude NmF2 manifests the intensity of solar EUV radiation, the state of surrounding neutral composition, and vertical plasma drift related to thermospheric winds24,32. The (2008–2009) period was selected for our analysis. That was a deep solar minimum with very low geomagnetic activity. Moreover CHAMP/STAR neutral gas density (ftp://anonymous@isdcftp.gfz-potsdam.de/champ/) and solar EUV observations25 are available for this period.

Figure 4 gives observed yearly variations of noontime foF2 at Juliusruh and Port Stanley during July - December 2008 and January - June 2009. Both stations are located in the ‘far-from-pole’ longitudinal sector. The polynomial approximation of foF2 variations manifests the results earlier given in Fig. 3 for solar minimum conditions - the foF2 autumnal peak is larger than the vernal one in both Hemispheres. This difference is not related to solar EUV fluxes which are close for the two periods. Averaged over February-March and October-November daily Ap = 4.93 ± 3.66 nT and 5.38 ± 5.85 nT, correspondingly. Student’s t-parameter = 0.499 under the degree of freedom m = 118 indicates the absence of any statistically significant difference between two arrays of Ap indices. Therefore the observed foF2 difference in the two peaks should be attributed to the difference in thermospheric parameters not related to solar and geomagnetic activity.

Figure 4 gives that two foF2 peaks in both Hemispheres are shifted towards the December solstice with respect to the equinoctial dates. This clearly indicates the contribution of the annual component responsible for the December anomaly in atomic oxygen and foF2 yearly.

variations8. However this does not explain the excess of the autumnal foF2 peak over the vernal one. At Port Stanley the autumnal peak occurs in March i.e. two months later than the peak of the annual component occurring in December.

Aeronomic parameters responsible for the formation of daytime mid-latitude F2-layer are required to explain the observed yearly NmF2 variations. Our method THERION33 with further improvements34 was used to specify these parameters. The method was repeatedly used in our previous publications 34,35,36 and its description is not given here. The idea is based on solving an inverse problem of aeronomy to extract a self-consistent set of aeronomic parameters from bottom-side Ne(h) profile and satellite neutral gas density observations. Among these parameters are [O] and [N2] column densities calculated above the height with column [N2] of 1017 cm− 2 37 and basic aeronomic parameters in the F2-layer maximum which are obtained in the course of the fitting process. The results of calculations for Juliusruh are given in Fig. 5. Figure 5 gives that the main peak in the atomic oxygen column abundance takes place in November and the other not a peak but an inflection point is in February. In accordance with present-day understanding (see Introduction) the November peak is a sum of three components: semi-annual, seasonal, and annual, while the February inflection point is formed by semi-annual and seasonal components of yearly variations. Yearly NmF2 variations manifest peaks which are close in time to peaks in column [O] density (Fig. 5b) but they do not exactly coincide. This is understandable as NmF2 depends on atomic oxygen concentration at the F2-layer maximum height rather than on column [O] density38. The NmF2 peaks are closer in time to q(O+)max peaks (Fig. 5b) in accordance with a well-known expression39

Fig. 4
figure 4

Yearly variations of noontime foF2 at Juliusruh and Port Stanley during. July-December 2008 and January-June 2009. Polynomial approximation of observed foF2 is given for better visualization of yearly variations. Monthly median Ap and total solar EUV variations are given in the bottom of the plot. Vertical lines indicate the dates of equinoxes.

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Fig. 5
figure 5

Noontime aeronomic parameters for the (2008–2009) period. Column atomic oxygen abundance and [O] concentration in the F2-layer maximum - a); observed NmF2, total rate of [O+] ion production qmax and linear loss coefficient βmax in the F2-layer maximum – b); vertical plasma drift W, hmF2, and exospheric temperature Tex – c). Solid lines are polynomial approximations given for better visualization. Vertical dashed lines – 27 October 2008 and 26 December 2008 (see text).

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$${N_m}{F_2}=0.75\frac{{{q_m}}}{{{\beta _m}}}$$

where qm – O+ ion production rate and βm – linear loss coefficient, both taken at hmF2. A similar expression can be also obtained using an analytical solution of the stationary continuity equation for electron concentration in the mid-latitude daytime F2-region24. This expression does not take into account the effects of vertical plasma drift W. However it can be used for qualitative estimates. Figure 5,b shows that q(O+)max is larger in the autumnal NmF2 peak (October-November) than in the vernal one although [O]max are similar in the two peaks (Fig. 5,a). Partly this is due to different solar zenith angles − 63.70 in the middle of October and 67.10 in the middle of February. An additional contribution to this difference in NmF2 provides βmax which is larger in January-February than in October-November. The difference in βmax may be related to different hmF2 which are larger in October-November than in January-February (Fig. 5,c). The main contributors to hmF2 are Tex and vertical plasma drift, W24,40. Figure 5,c gives that Tex are practically the same (~ 700 K) for the two periods but W related to horizontal thermospheric winds are different. Downward plasma drifts W are ~ -20 m/s in October-November but W are ~ -25 m/s and even down to -35 m/s in January-February (Fig. 5,c). Stronger downward W transfers O+ ions to lower altitudes with larger [N2] and [O2] concentrations and correspondingly larger β = γ1[N2] + γ2[O2]. Therefore larger q(O+)max and smaller βm (which is related to larger hmF2 via a weaker downward plasma drift W = VnxsinIcosI) in October-November compared to January-February values may be considered as the reasons for larger autumnal NmF2 peak compared to the vernal one.

The leading role of the atomic oxygen abundance in the NmF2 difference in two peaks manifests a comparison of 10 October 2008 to 17 March 2009 at Juliusruh. Observed noontime NmF2 for these dates are close to October/November and February/March noon monthly median NmF2, correspondingly (Fig.,5b). Observed EUV25, daily Ap, calculated hmF2 and W are close for the two dates to exclude as much as possible their possible impact (Table 3).

Table 3 Observed and retrieved aeronomic parameters for the two dates in the autumnal and vernal peaks at Juliusruh to demonstrate the leading role of atomic oxygen in the difference between two NmF2 peaks. The parameters are explained in the text.
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The NmF2 difference between two peaks is 18.7% which is mainly the 11.2% difference in qm and − 6% in βm. It should be noted that the solar zenith angle χ is larger in October than in March however qm is larger in October indicating the leading role of [O] in the qm difference between two dates. The autumnal (10 October, 2008) date also manifests larger column atomic oxygen abundance.

Similar results manifests Table 4 for two dates 18 March, 2009 and 25 October 2008 located in the autumnal and vernal peaks at Port Stanley, correspondingly. The observed NmF2 are close to noon monthly median NmF2 (Fig. 4). The list of aeronomic parameters is the same as in Table 3.

Table 4 Same as Table 3 but for Port Stanley for the dates in the autumnal and vernal peaks.
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The NmF2 difference between two peaks is 17.5% which is mainly the result from larger qm and smaller βm on 18 March, 2009 compared to 25 October, 2008. The other parameters (hmF2, W, and EUV, Ap) are close for the two dates and this should exclude their possible impact on the difference in NmF2. Similarly Juliusruh the solar zenith angle χ is larger in autumn (18 March) than in spring, however qm is larger in March indicating the leading role of [O] in the qm difference between two dates. The autumnal date (March 18) also manifests larger column atomic oxygen abundance compared to the vernal date. Therefore both Hemispheres manifest the dominance of NmF2 in the autumnal peak over the vernal one and this is due to larger qm and smaller βm in autumn.

A two-hump NmF2 variation with a trough in December-January (Northern Hemisphere) is a key point of yearly NmF2 variations. Without such a trough we would have a well-pronounced “winter anomaly” with midwinter NmF2 values larger than summer ones. This type of yearly NmF2 variation is observed under solar maximum at middle-high latitudes in the Northern Hemisphere and this issue was repeatedly discussed in the literature14,41.

According to12 the winter NmF2 trough is due to large solar zenith angle during midwinter: ”The zenith angle effect is especially important in longitudes far from the magnetic poles. Here, the downwelling occurs at high geographic latitudes, where the zenith angle effect becomes overwhelming and causes a midwinter depression of electron density, despite the enhanced atomic/molecular ratio. This leads to a semiannual variation of NmF2”.

However, our analysis shows that solar zenith angle is important but not the only factor leading to the midwinter NmF2 depression. Table 5 contains necessary aeronomic parameters taken from Fig. 5 to do such estimates. We took 27 October 2008 when q(O+)max and NmF2 reached maximal values and 26 December 2008 when both parameters were much smaller. Table 5 gives that the observed NmF2 depression is ~ 35% which is mainly resulted from a decrease of q(O+)max and an increase of βmax. Firstly let us check the contribution of the solar zenith angle, χ. To sufficient accuracy for present purposes, the production q(O+)max may be written as.

q(O+)max = I∞Ch(Zmax,χ)[O]max.

where I∞ is the total ionization flux at the top of the atmosphere, [O]max denotes the concentration of atomic oxygen at the F2-layer maximum height, and Ch(Zmax, χ) is the ‘Chapman function’ of the solar zenith angle at the hmF2 height.

Table 5 The list of aeronomic parameters necessary to estimate the contribution of solar zenith angle to the q(O+)max decrease.
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The production rate q(O+)max should be reduced on I∞ and [O]max to estimate the contribution of solar zenith angle to the q(O+)max decrease. After this reduction the contribution of Ch(Zmax,χ) to the q(O+)max decrease is ~ 4% while the q(O+)max difference is ~ 54% between the two dates.

Bearing in mind that I∞ are close for the two dates the q(O+)max difference is due to the [O]max difference (Table 5). Therefore the observed midwinter NmF2 through ~ 35% at Juliusruh (Fig. 4,b) is mainly related to the [O]max decrease from 27 October to 26 December. The contributions of βmax and W are small compared to [O]max (Table 5). The difference in [O]max cannot be related with different hmF2 which are close for the two dates (Table 5). Therefore the midwinter NmF2 trough is a manifestation of low [O] concentration in December-January relative to October/November (Northern Hemisphere) values rather than the solar zenith angle effect.

Table 2 shows that the vernal peak may occur in the course of three months in both Hemispheres while the occurrence of the autumnal peak is confined by two months. This is due to the difference between summer-to-winter and winter-to-summer transitions in the thermosphere. We do not have direct observations of the seasonal transition in global thermospheric circulation but atomic oxygen which is directly related to this circulation may serve as an indicator of this process. According to42 there are winter and summer types of foF2 diurnal variations and analyzing day-by-day foF2 diurnal variations it is possible to specify the dates of summer-to-winter and winter-to-summer transitions in the thermosphere. It was shown42 that the summer-to-winter foF2 transition at Juliusruh in 2008–2009 took place within ~ 12 days while the winter-to-summer transition lasted for ~ 36 days i.e. the autumnal transition is much shorter than the vernal one.

Figure 5,(c) gives that the W transition from summer ~ -10 m/s to winter ~ -20 m/s values occurs very fast during one month (September) and this period corresponds to a steep increase in the atomic oxygen abundance (Fig. 5,a) indicating the process of the atomic oxygen transfer from summer to winter Hemisphere. Although W manifests diurnal variation of thermospheric winds which are not responsible for seasonal inter-hemispheric transfer of atomic oxygen12 nevertheless W indicates seasonal changes in global thermospheric circulation resulting in variation of the atomic oxygen abundance. Vertical drift W does not manifest any pronounced variations during January-April (Fig. 5c) being around ~ -20 m/s. During this period NmF2 demonstrates small month-to-month and large day-to-day variations (Fig. 5,b). Under such a scatter the NmF2 peak may occur in any month (February-April) in the vicinity of the vernal equinox.

All analyzed stations (apart from Hobart) manifest the dominance of the autumnal peak over the vernal one only under solar minimum conditions (Fig. 3). This may be related to the geomagnetic activity impact. Low solar activity is normally associated with low geomagnetic activity and low heating of the auroral zone. Therefore global thermospheric circulation is mainly solar driven and along with yearly varying eddy diffusion (see our discussion later) provide the corresponding variations of atomic oxygen when the autumnal [O] is larger than the vernal one. Under elevated and maximal solar activity geomagnetic activity increases resulting in increased auroral heating. A comparison of monthly Ap indices for the (1958–2022) period for the dates with elevated and high solar activity to dates with low activity gives average Ap = 15.74 ± 6.68 nT and Ap = 11.38 ± 5.03 nT, correspondingly, which differ significantly at the 99.9% confidence level according to t - test. There is a linear relationship between Joule heating and Kp indices43. In accordance with the well-known F2-layer storm mechanism 44,45,46,47,48,4944–49,12 the [O]/[N2] ratio (which is directly related to NmF2) decreases with increasing geomagnetic activity. Therefore depending on the station and the intensity of auroral heating the NmF2 points may turn out to be above or below the bisector line in Fig. 3 under elevated and high solar activity.

Comparing foF2 (Fig. 4) and column [O] yearly variations (Fig. 5) it is seen that two peaks are shifted towards the December solstice with respect to the equinoctial dates. This may be related with contribution of the annual component responsible for the December anomaly in atomic oxygen and correspondingly in foF2 yearly variations. However according to GUVI O/N2 ratio observations50 “…in the northern hemisphere (NH) low latitudes, the first “equinox peak” clearly shifts toward the December solstice, whereas in the southern hemisphere (SH) low latitudes, the “equinox peaks” shift toward the June solstice (JS), forming the hemispheric asymmetry characteristics of the annual and semiannual variation”. No explanation to such inter-hemispheric asymmetry is suggested by the authors.

Discussion

The undertaken analysis has shown that the difference between vernal and autumnal NmF2 peaks is mainly due to the difference in the atomic oxygen abundance. Atomic oxygen is totally produced and lost in the upper atmosphere above 70 km27. Therefore we will consider variations of the column [O] abundance above this level using the empirical thermospheric model MSISE0051. The column [O] abundance, unlike the concentration at a fixed height does not depend on the neutral temperature height profile therefore this characteristic is more convenient for our analysis.

Let us consider yearly variations of the atomic oxygen abundance given by the empirical (based on observations) thermospheric model MSISE00. It should be noted that the choice of MSISE00 for our analysis rather than MSIS 2.052 is not principal. The difference between two models in the thermosphere is not large: “ In the thermosphere, N2 and O densities are lower in NRLMSIS 2.0; otherwise, the NRLMSISE-00 thermosphere is largely retained”. With respect to atomic oxygen that is mostly interesting for our analysis, it is said “The upper thermospheric MSIS 2.0 O densities are ~ 10% less overall than MSISE-00”. A comparison of MSISE00 and MSIS 2.0 with CHAMP and GOCE neutral density observations has shown that “Overall, MSIS 2.0 mass densities are ~ 2% larger than GOCE and ~ 9% larger than CHAMP”. But this difference is within the inaccuracy (10–15)% of CHAMP neutral density observations 53. A comparison of neutral density yearly variations given by two models just indicates a small systematic bias52. On the other hand, GOLD observations of daytime thermospheric effective temperature and ΣO/N2 under deep solar minimum from 13 October 2019 to 12 October 202054 have revealed obvious differences between observations and MSIS 2.0. Therefore there is no reason to give preference to any of the models.

Figure 6 gives noontime MSISE00 model variations of the total atomic oxygen abundance above 70 km in the European and American longitudinal sectors for both Hemispheres (top panel), and separately for the Northern and Southern Hemispheres under solar maximum (1980) and solar minimum (2009). The years were selected to have close monthly F10.7 and Ap indices for both equinoctial periods. The global atomic oxygen abundance mainly manifests semiannual variations with close magnitudes in the two peaks in both sectors under solar maximum and minimum. This is an important result clearly indicating the global increase of the total atomic oxygen abundance during equinoxes. Such an increase cannot be attributed to any redistribution of atomic oxygen in the thermosphere as we have the absolute global scale [O] increase. Another interesting result – the magnitudes of the two peaks are practically equal. This tells us that the dominance of the autumnal peak over the vernal one revealed in our analysis also seen in [O] total abundance in the two hemispheres (Fig. 6, middle and bottom panels) is related to seasonal thermospheric circulation. The annual component which maximizes in the vicinity of the December solstice provides January [O] abundance larger than July one (Fig. 6, top panels). On the other hand, the seasonal component related to the summer-to-winter transfer of [O] is not seen under the global consideration of the atomic oxygen abundance.

Yearly variations of the [O] abundance with the main peak in November and the secondary peak in March are seen in the Northern Hemisphere (see also Fig. 5,a). The Southern Hemisphere manifests semiannual variations with the main peak in April and the secondary in September. Therefore the empirical model MSISE00 confirms our earlier obtained result that the autumnal peak in NmF2 and column [O] is larger than the vernal one. In accordance with the foF2 global morphology14,41,47 the MSISE00 model properly describes seasonal variations of the atomic oxygen total abundance (Fig. 6, middle and bottom panels). Seasonal (winter/summer) difference is large in the Northern Hemisphere where the Seasonal and December components are working in phase and this difference is small in the Southern Hemisphere where two components are anti-phase.

It should be stressed that Fig. 6 (top panel, similar variations may be obtained for other longitudes) gives the global total content of atomic oxygen which cannot be attributed to any seasonal redistribution of [O] by global circulation. Therefore we should speak about the absolute global increase or decrease of the [O] abundance in the course of the year which cannot be attributed to any redistribution of [O] by global circulation as this was suggested12,18.

Fig. 6
figure 6

MSISE00 model variations of the noontime column atomic oxygen abundance above 70 km along the zero meridian in both Hemispheres (top panel) and separately in the Northern and Southern Hemispheres for solar maximum and solar minimum.

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An obvious question arises – where does this additional [O] come from around two equinoxes? Atomic oxygen is totally produced and lost in the upper atmosphere above ~ 70 km27. Therefore, either this is newly produced [O] or its loss is decreased near equinoxes, there is no other possibility. The rate of [O] production is limited by the intensity of solar far UV radiation which depends only on solar activity28 and it may be considered as a constant under fixed solar activity (Fig. 6). On the other hand the rate of [O] association is not limited and any amount of [O] transferred downward will be lost via a three-body collision O + O + M → O2 + M, where M is a total number density of neutral species mostly presented by [N2], the rate of this process exponentially increases with decreasing height. The transfer of [O] is provided by molecular diffusion down to the turbopause level (around 120 km) and further by eddy diffusion, the latter being a fairly fast process. Theoretically it was shown that the maximal value of the time average eddy diffusion coefficient in the thermosphere could not exceed 3 × 106 cm2/s 55 and this was confirmed experimentally - the annual mean eddy diffusion coefficient is ~ 4 × 106 cm2/s at 85–100 km56, the same estimate was earlier obtained15. This gives the characteristic time for the eddy diffusion transfer of [O] τedd ~ H2/Kedd ~ 1 day at ~ 100 km. It means that newly produced [O] is very efficiently redistributed over the thermospheric column. Therefore the downward transfer of [O] by eddy diffusion is the process globally controlling the amount of [O] in the whole thermosphere. Anyway it is not seen any other way to explain the global increase of the total amount of [O] during equinoxes as no redistribution of [O] by global circulation can produce additional [O] in the thermosphere.

The results19,20 apparently confirm this conclusion. The minimal intensity of eddy diffusion in the vicinity of equinoxes qualitatively agrees with the ‘thermospheric spoon’ mechanism18 basing on a reasonable idea that under a symmetric heating of the thermosphere during equinoxes global turbulence should be at the minimal level. However TIE-GCM simulations only qualitatively reproduce O/N2 and neutral density semiannual variations as they are much smaller than observed ones19. But the very idea of yearly varying eddy diffusion gives a straightforward explanation to the observed variations of the total [O] abundance (Fig. 6).

According to the mechanism12 during equinoxes one should expect a strong upwelling from the equatorial latitudes due to strong thermosphere heating. Such upwelling inevitably should be accompanied by a decrease of the [O] abundance. However MSISE00 gives peaks of the total atomic oxygen abundance at the equator during equinoxes under any level of solar activity. Figure 7 gives observed noontime foF2 monthly medians along with MSISE00 [O] column concentration (above 70 km height) at the equatorial station Boa Vista (2.80N, 299.30E) under solar minimum in 2019 and maximum in 2014.

Fig. 7
figure 7

Yearly variations of noontime foF2 monthly medians are given along with MSISE00 [O] column concentration under solar minimum (2019) and maximum (2014) at the equatorial station Boa Vista.

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Figure 7 gives well-pronounced foF2 equinoctial peaks of equal magnitude both under solar minimum and maximum which just manifest the corresponding peaks in the total [O] column content. Notice that column [O] reaches its maxima at equinoxes when the upwelling from the equator is supposed to be the largest according to12 while minimal column [O] content takes place in summer when the subsolar point (and so maximal heating) is far from the equator. This is an obvious contradiction with the mechanism of the atomic oxygen redistribution by global thermospheric circulation12. But such variations of atomic oxygen can be explained by seasonal variations of eddy diffusion with minima at equinoxes.

Conclusions

The results of our analysis of semi-annual noontime foF2 variations at four mid-latitude North Hemisphere stations (Boulder, Rome, Wakkanai, Juliusruh) and two South Hemisphere stations (Hobart, Port Stanley) may be formulated as follows.

Reduced solar activity NmF2 values manifest a close relationship between autumnal and vernal NmF2 peaks at the stations in questions. All correlation coefficients are significant at the 99.9% confidence level and vary from 0.680 ± 0.168 at Boulder to 0.896 ± 0.060 at Hobart with the correlation ranging between noticeable and close according to the Ceddok scale.

The NmF2 autumnal peak on average is larger than the vernal one in both Hemispheres at least under solar minimum. The observed NmF2 difference in the two peaks is attributed to the difference in thermospheric parameters not related to solar and geomagnetic activity.

Larger q(O+)max and smaller βmax in autumn compared to spring may be considered as the reasons for larger autumnal NmF2 peak compared to vernal one. The abundance of atomic oxygen plays the leading role in the difference between NmF2 in the two peaks.

The vernal peak may occur in the course of three months in both Hemispheres while the occurrence of the autumnal peak is confined by two months. This may relate to a fast summer-to-winter transition of the thermosheric circulation which transfers atomic oxygen from summer to winter Hemisphere while the winter-to-summer transition is a more prolonged process under analyzed deep solar minimum conditions. This results in small month-to-month and large day-to-day NmF2 variations in spring. Under such a scatter the monthly median NmF2 peak may occur in any of three months in the vicinity of the vernal equinox.

A two-hump NmF2 variation with a trough in December-January (Northern Hemisphere) is a manifestation of low [O] concentration in December-January relative to October/November values rather than the solar zenith angle effect as this was suggested12. Solar zenith angle provides some contribution to this NmF2 decrease but this is not the main factor leading to the midwinter NmF2 depression.

The global atomic oxygen abundance given by the empirical (based on observations) MSISE00 thermospheric model mainly manifests semiannual variations with close magnitudes in the two peaks both under solar maximum and minimum. This indicates the global increase of the total atomic oxygen abundance during equinoxes. Such an increase cannot be attributed to any redistribution12,18 of atomic oxygen in the thermosphere as we have the absolute global scale [O] increase.

6. The downward transfer of [O] by eddy diffusion is the process which can globally control the amount of [O] in the thermosphere. Anyway it is not seen any other way to explain the global increase of the total amount of [O] during equinoxes as no redistribution of [O] by global circulation can produce additional [O] in the thermosphere.