1 Introduction

There is not only space weather but also space climate. Its part is the ionospheric climate, which changes with the 11-year solar cycle and with long-term trends. The main parameter of the ionosphere is its maximum electron density, NmF2. Because the ionosphere has been studied mainly by radio-physical methods, instead of NmF2 the directly measured critical frequency of F2 layer, foF2, has been dominantly used.

The dominant factor of foF2 climatological variability is solar cycle, for analysis of which we need intervals of at least a few solar cycles long. However, several decade long homogeneous measurements of the solar EUV fluxes are not available, so various solar activity proxies (solar activity indices) must be used in long-term ionospheric studies as climatology, long-term trend investigations or space climate change investigations. Solar activity indices are also used in various ionospheric models including the International Reference Ionosphere (IRI).

Here we shall deal with the selection of the most suitable solar activity proxy for analyzing long foF2 data series to be used for climatological and trend studies. There are several proxies of solar activity which have been used in various previous studies of relationships between foF2 and solar activity. The purpose of this paper is twofold: (a) Select the optimum solar activity proxy for investigating foF2 behavior. (b) To test (in)stability of the relationships between foF2 and individual solar activity proxies and to search for potential solar origin of possible instabilities.

Laštovička et al. (2006) and Mielich and Bremer (2013) came to conclusion that for investigating long-term evolution of foF2, F10.7 is a better solar proxy than the sunspot number R. Deminov et al. (2020) compared F10.7, R and the index of ionospheric activity T over solar cycles 23 and 24 and also came to conclusion that F10.7 is more appropriate for ionospheric studies. On the other hand, Danilov and Konstantinova (2020) used sunspot numbers and the solar Lyman-alpha flux to correct F10.7 in solar cycle 24 to get trends in foF2 consistent with trends from previous solar cycles. de Haro Barbas et al. (2021) analyzed foF2 from three Japanese stations and found the Mg II index to be better than Lα (solar H Lyman-α flux), R and F10.7. Perna and Pezzopane (2016) recommend Mg II for description of foF2 behavior in the deep solar minimum 2008/2009, when F10.7 is unable to describe the extremely low level of the solar EUV irradiance. However, these above authors did not consider solar activity proxy F30. Laštovička (2021a, 2021b) found Mg II and F30 to be the best solar proxies for the variability of yearly average and monthly median values for foF2 from three European stations. Vaishnav et al. (2019) used 12 different solar proxies and global total electron content (G-TEC) derived from IGS maps over 1999–2017. They found that at time scales of 16–32 and 32–64 days, He II was the best solar proxy followed by Mg II, Lyman-alpha flux and F30 as the seconds, all with time delay 1 day, whereas F1.8 and sunspot area indices poorly represented solar activity effect on G-TEC. Maruyama (2010), Lean et al. (2011), Laštovička et al. (2017), and Goncharenko et al. (2021) found Mg II to slightly outperform F10.7 for studying long-term changes of G-TEC using G-TEC calculated in two different ways. Gulyaeva et al. (2018) recommend Mg II as the best solar proxy for ionospheric modeling. Dudok de Wit and Bruinsma (2017) claim that F30, which correlates with Mg II better than F10.7, is more appropriate solar proxy for thermospheric density than F10.7.

The relationship between a solar activity proxy and foF2 had been assumed to be stable with time. However, some recent results indicate that this need not be the case in the 21st century. Elias et al. (2014) studied long-term trends in foF2 and found some changes of trends during the solar cycle 23 including the deep minimum 23/24, which they tentatively attributed to changes in the solar EUV-F10.7 relationship. Laštovička et al. (2016) investigated the behavior of long-term trends in foE. They obtained results consistent with the results of older papers only after dividing the whole analyzed interval into parts with different solar activity dependences of foE. Laštovička (2019) showed for three European stations that the relationship between foF2 and solar proxies F10.7 and Lα is clearly different in periods 1976–1995 and 1996–2014.

The Sun appears to change since the cycle 23. Not only the solar activity is now much lower than in the second half of the 20th century. Lukianova and Mursula (2011) observed changed relation between sunspot numbers, solar EUV/UV radiation and the total solar irradiance during the declining phase of solar cycle 23. Clette and Lefevre (2012) reported a change of the relation between sunspot numbers and F10.7 since about 2000 and substantially smaller drop in F10.7 than in Mg II in the extreme solar minimum 2008–2009. Tapping and Valdes (2011) also reported changes of relations between solar proxies during the decline of solar cycle 23. Balogh et al. (2014) reported a change in the relationship between sunspot numbers and F10.7, and a drop of the sunspot formation fraction parameter (introduced by Livingstone et al. (2012)) by ∼40% during the solar cycle 23 compared to the quasi-stable level in cycles 19–22. Traditional solar proxies R and F10.7 seem to describe solar EUV flux in the solar cycle 23 and particularly in the solar minimum 23/24 with some problems (e.g., Chen et al., 2011; Elias et al., 2014; Lukianova & Mursula, 2011). Laštovička (2019) found a different dependence of Mg II on F10.7 in 1979–1995 versus 1996–2014. Clette (2021) analyzed long data series of F10.7 and sunspot numbers and observed a jump in relation between them in 1980. Thus the relationships between various solar proxies need not be stable.

Section 2 deals with data and method. Section 3 presents results of search for the best solar activity proxy for variability of foF2. Section 4 treats the question of the stability of the dependence of foF2 on solar proxies. Section 5 deals with the stability of relationships among solar activity proxies. The results are discussed in Section 6. Section 7 contains conclusions.

2 Materials and Methods

Ionospheric critical frequency foF2 data obtained from a north-south chain of European stations Juliusruh (54.6°N, 13.4°W), Pruhonice (49.98°N, 14.55°E), and Roma (41.8°N, 12.5°E), US station Boulder (40.0°N, 254.7°E), Japanese station Kokubunji (35.7°N, 139.5°E) and Australian station Canberra (35.3°S, 149.0°E) are used for middle latitudes. Low/equatorial latitudes are represented by stations Okinawa (Japan; 26.3°N, 128.7°E), Chung-li (Taiwan; before 1983 Taipei; 24.9°N, 121.2°E), Townsville (Australia; 19.6°S, 146.9°E), Vanimo (Papua New Guinea; 2.7°S, 141.3°E), and Jicamarca (Peru; 12.0°S, 76.9°W). These data are analyzed together with solar proxies over the period 1976–2014, divided into two sub-periods 1976–1995 and 1996–2014, because the dependence of foF2 on F10.7 is somewhat different in these two sub-periods for European stations (Laštovička, 2019). It is necessary to mention that it was difficult to get data series without any year missing; thus for some stations data from some years are missing. For the first period, data sets of yearly data of Juliusruh, Pruhonice, Roma, Boulder, Canberra, Kokubunji, Chung-li and Vanimo are complete. Townsville has gap in 1985 and Okinawa in 1976. The Jicamarca data set had more gaps and was not used. For the second period, data sets of yearly data of Juliusruh, Pruhonice, Roma, Canberra, Kokubunji, Okinawa and Townsville are complete. The Boulder data set missed values for 2003 and 2012. The Jicamarca data set missed years 2001, 2002, and 2012. Chung-Li had more gaps; it was not used. Vanimo data series terminated in 2009. It was rather difficult to find in databases sufficiently complete data series, particularly for low and equatorial latitudes.

Figure 1 shows raw foF2 data for all six midlatitude stations. Their general evolution with time is the same with the quite dominant solar cycle effect even though there are some slight differences in fine structure.

Figure 2 shows raw yearly foF2 data for all five low-latitude stations. Only two of them, Townsville (black curve) and Okinawa (red curve) cover both periods, 1976–1995 and 1996–2014. Discontinuities in curves are caused by missing data. Again the solar cycle clearly dominates in foF2 evolution, which is generally similar for all five stations.

Altogether six solar activity proxies are used: F10.7 (solar radio noise at a wavelength 10.7 cm), F30 (solar radio noise at a wavelength 30 cm), R (sunspot number), Lα (solar H Lyman-alpha flux), Mg II (core-to-wing ratio of Mg II line), He II (solar flux in 26–34 nm dominated by the He II line at 30.4 nm). Re-calibrated sunspot numbers R is used (Clette et al., 2016). Again yearly average values are used. Data are available over the whole period 1976–2014 except for Mg II, which are available since late 1978. He II data are available only until April 2015, which is one of the reasons why the analyzed foF2 data series terminates with the year 2014.

Figure 3 shows evolution of solar activity proxies. Data are scaled in magnitude to make comparison possible; for example, the F10.7 curve shows values of 0.1 F10.7, whereas the Mg II curve presents values of 100 Mg II. The quite dominant solar cycle variation is clearly visible.

All ionospheric analyses are performed for noontime (11–13 LT) yearly average values. The yearly average values of ionospheric parameters are calculated as averages from monthly median values. This reduces effects of large deviations, particularly effects of geomagnetic storms. A simple linear regression, Equation 1, has often been used to remove solar cycle effect, for example, in calculating long-term trends in ionospheric parameters. As Laštovička (2021a, 2021b) demonstrated for the above European stations, Equation 1 with the optimum solar activity proxies describes a large majority of the total variance of foF2 for yearly values (99%); for non-European stations it describes also similar large majority of total variance of foF2 (see Section 3). The linear correlation between yearly values of solar activity proxies reaches typically value of 0.99 (Table 2). Therefore the simple linear regression, Equation 1, may be used in all further analyses of relationships between individual solar proxies or between foF2 and solar proxies:

(1)

where solar proxy is either F10.7, or F30, or Fα, or R, or Mg II, or He II index. When Equation 1 is not fully sufficient for foF2 (fully sufficient means that with at least one solar proxy Equation 1 describes 99% of total variance of foF2), the multi-parameter linear regression has to be used:

(2)

where Ap represents geomagnetic activity and “time” represents the linear long-term trend. In some cases even Equation 2 is not fully sufficient. Pedatella and Forbes (2009) found some impact of the El Nino Southern Oscillation (ENSO) on foF2 at low latitudes. The response of equatorial ionosphere to polar sudden stratospheric warmings is affected by the Quasi-Biennial Oscillation (QBO) (e.g., Yadav, 2019). Therefore Equation 3 is used:

(3)

The percentage of variance described by Equations 1 and 2 or Equation 3 is taken as the square of correlation coefficient. The average absolute differences between observed and model values of foF2 in Tables 3 and 6 are calculated as follows:

(4)

where ΔfoF2av is the average absolute difference between the observed foF2obs_i and model foF2mod_i (model = Equations 1 and 2 or Equation 3); n is the number of foF2obs values.

Solar Activity Index He II

The results of Laštovička (2021a) indicate that there might be problems with He II index in years 2011–2014; these years substantially reduce the correlation between foF2 and He II for European stations. Figure 4 shows the differences ΔHe II between the observed values of He II and He II values calculated from Equation 1. These differences display in the last 4 years the largest deviations from the zero level (no difference) for He II calculated using F10.7 (red line) as well as F30 (blue line). This may be considered to be evidence of some problems of He II in years 2011–2014. Therefore further analyses are carried out for 1996–2014 and also 1996–2010 (without 2011–2014).

3 The Best Solar Activity Proxy for Variability of foF2

The results are presented separately for middle and low latitudes because they are to some extent different.

4 Stability of the Dependence of foF2 on Solar Activity Proxies

Elias et al. (2014) found some changes of long-term trends of foF2 during the solar cycle 23 including the deep minimum 23/24, which they tentatively attributed to changes in the solar EUV-F10.7 relationship. Laštovička (2019) found for three European stations that the relationship between foF2 and solar proxies F10.7 and solar Lyman-α flux is clearly different in periods 1976–1995 and 1996–2014. Therefore we shall now investigate the stability of the dependence of foF2 on solar activity proxies separately for middle and low/equatorial latitudes by comparing the dependences in periods 1976–1995 (1979–1995 for Mg II) and 1996–2014 (1996–2010 for He II). The question of stability or non-stability of the dependence of ionospheric parameters on solar activity proxies/indices is analyzed in terms of the ratio B2/B1 = B(1996–2014)/B(1976/1995), where B is the slope from Equation 1 for relations between foF2 and solar activity proxies.

5 Stability of Relationships Among Solar Activity Proxies

Clette and Lefevre (2012) or Balogh et al. (2014) showed that the dependence of F10.7 on R (sunspot number) in the solar cycle 23 was different from that in previous period. Laštovička (2019) found a different dependence of Mg II on F10.7 in 1979–1995 versus 1996–2014.

Figure 5 is another example of different relationship between two solar proxies in 1979–1995 versus 1996–2014, here for sunspot numbers and F30. The slopes (parameter B of Equation 1) of dependence of R on F30 are 2.44 ±0 .09 for the first period and 2.15 ± 0.06 for the second period, that is, they are clearly different.

Table 10 summarizes the ratios B2/B1 = B(1996–2014)/B(1976/1995), where B is the slope of solar activity dependence from Equation 1, for relations between all solar activity proxies. For He II, values in parentheses are considered more representative. The B2/B1 ratio is close to 1.00 (no change of relationship) for some pairs of solar activity proxies, namely Mg II—F30, He II—Mg II, and Lα—He II. However, the B2/B1 ratio for majority of pairs of solar activity proxies differs from 1.00. For some of them the ratio differs clearly from 1.00, namely for pairs R—F30, F10.7—F30, R—Lα, and R—He II. Thus for majority (but not all) pairs of solar activity proxies the relationship between solar proxies differs between 1976 and 1995 (solar cycles 21 and 22) and 1996–2014 (solar cycles 23 and 24).

The origin of these changes of relationships among solar activity proxies is not clear. It might be related to the fact that different solar proxies are related to partially different parts of the solar irradiance spectrum and, therefore, to partially different parts of the solar atmosphere. Mursula (2022) found that the solar spectral irradiance in the range from the near ultraviolet through visible to the near infrared radiation changes its spectrum with time; some parts display positive, some parts negative and some parts no long-term trend over the period 2003–2019. Similar spectral changes in the EUV range (if they occur) could change the relationships between solar activity proxies. However, this is only speculation, more investigations of this problem are necessary.

6 Discussion

The results show differences between the optimum solar activity proxies for describing the variability of yearly values of foF2 between middle and equatorial latitudes. At middle latitudes, F30 and Mg II are the best solar activity proxies for evolution of yearly average values of foF2. All six stations from four continents confirm this result. This is consistent with finding of Dudok de Wit and Bruinsma (2017) that F30 is more appropriate solar proxy for thermospheric density than F10.7 and with Gulyaeva et al. (2018), who recommend Mg II as the best solar proxy for ionospheric modeling. Perna and Pezzopane (2016) recommend Mg II for description of foF2 behavior in the deep solar minimum 2008/2009. Maruyama (2010), Lean et al. (2011) and Laštovička et al. (2017) found Mg II to slightly outperform F10.7 for studying long-term changes of global TEC. However, authors who prefer Mg II did not consider in their analyses F30.

The latitudinal range of higher low latitudes (Okinawa, Townsville and Chung-Li) is a transition region between middle and equatorial latitudes, where differences between various solar proxies are mostly very small. Equatorial latitudes (Vanimo and Jicamarca) provide pattern, which differs from middle latitudes; the optimum solar proxy seems to be He II (Table 6). However, the results for low/equatorial latitudes should be considered as preliminary due to very limited available data.

Historical analyses of long-term trends in foF2 had been performed with F10.7 and R used for describing or removing the effect of solar cycle and old values of R before their re-calibration (e.g., by Clette et al. (2016)) were used. However, if Mg II and F30 are the best solar proxies for foF2 and if long-term trends of foF2 with application of Mg II or F30 can be somewhat different from trends calculated with F10.7 (an example is shown by Laštovička (2021a)), it might question reliability of historical results on trends in foF2 but also it could perhaps explain some of inconsistencies between previous trend results.

Table 7 shows that the stability of the dependence of foF2 on solar activity proxies in terms of ratio B(1996–2014)/B(1976–1975) principally depends on the solar proxy used. For F30 its median value from all six midlatitude stations is equal to 1.00, that is, the dependence of foF2 on F30 is stable. On the other hand, the median values of this ratio for F10.7 and R is 1.14 and 1.13, respectively, which means clearly steeper dependence of foF2 on these two proxies in 1996–2014. The standard deviations of values of parameter B is typically about 3%, which means that for F10.7 and sunspot numbers the difference between periods 1996–2014 and 1976–1995 is statistically significant. For Lα, Mg II, and He II, the 1996–2014/1976–1995 ratio is still mostly larger than 1.00, they are between F30 and F10.7. Thus F30 is the best solar activity proxy for midlatitudes from the point of view of stability of the relationship between foF2 and solar activity proxy.

Table 10 shows that relationships among solar proxies change, for some proxies more, for other less. There is even good quantitative agreement between the B(1996–2014)/B(1976–1975) ratio for changes of relationships among solar proxies and relationships between foF2 with solar proxies. The ratios of dependence of F10.7 and R on F30 are 0.89 and 0.88, respectively. The median ratios of dependence of foF2 on F10.7 and R are 1.14 and 1.13. If we replace F10.7 by 0.89 F30 and R by 0.88 F30, the median ratios change to 1.14 × 0.89 = 1.01 and 1.13 × 0.88 = 0.99, both numbers being practically equal to 1.00, which is the median ratio for dependence of foF2 on F30. This indicates that changes in relationships among solar activity proxies are likely the dominant contribution to changes in relationships between foF2 and solar activity proxies.

Thus Mg II and F30 are the best solar activity proxies for analyses of long-term variability of yearly values of foF2 at middle latitudes. F30 is the only solar proxy which provides the same dependence of foF2 on solar proxy for 1976–1995 and 1996–2014 but this dependence changes rather little for Mg II. F30 data are available over longer time interval (since March 1957) than Mg II (since November 1978). Dudok de Wit and Bruinsma (2017) recommend F30 as the best solar activity proxy for studying the thermospheric neutral density. Therefore we can recommend F30 as the optimum solar activity proxy and Mg II as the second one for analyzing yearly values of foF2 at middle latitudes, particularly for analyses of long data series, not the traditionally used parameters F10.7 and sunspot numbers.

7 Conclusions

The selection of the optimum solar proxy is expected to be important for models driven by solar proxies as IRI and for climatological studies, and it is important for long-term trend studies. All the above results are derived for yearly values of foF2. On daily time scale, the optimum proxies need not be the same due to some delays of ionospheric response as it was shown for example, for TEC (e.g., Vaishnav et al., 2021) and influences of other factors as geomagnetic activity and atmospheric waves. It has to be also mentioned that the optimum proxies need not be the same for all ionospheric parameters (Laštovička, 2021a).

Future investigations should focus on foE where, however, might be more data problems due to presence of the sporadic E layer, and on TEC required for the GNSS signal propagation, where the current problem is shorter data series and jump in the global TEC data series in 2001 (Emmert et al., 2017).

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.