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A long-term trend in the F2-layer critical frequency as observed at Alma-Ata ionosonde station


In this study, we combine monthly median values for the F2-layer critical frequency (foF2), measured at Alma-Ata ionosonde station [43.25°N, 76.92°E] between 1000 and 1400 (local time), with historical data on the monthly mean values for solar radio flux at 10.7 cm (F10.7) and the geomagnetic activity index (Ap) (available at, over the period from 1957 to 2012. These data are used to derive long-term trends in the upper ionosphere and to discuss their importance in the context of coupling between solar and geomagnetic activity in the ionosphere at middle latitudes.


Since Rishbeth (1990) and Rishbeth and Roble (1992) predicted an effect on HF/VHF radio propagation due to the ‘greenhouse cooling’ associated with lowering of the F2-layer, the long-term variations in the upper atmosphere's and ionosphere's parameters have been the subject of a number of observational and modeling studies (Mikhailov 2006; Lastovicka et al. 2008a; Danilov 2012; and references therein). These studies employed a variety of methods, approaches, and datasets to extract long-term trends in the F2-layer critical frequency (foF2) and peak height (hmF2) for the ionospheric F2-layer, and the majority were conducted using ionosonde observations. Table 1 summarizes these studies.

Table 1 List of authors who derived long-term trends in foF2 and their findings

Potential drivers of long-term trends in foF2 are widely discussed by Yue et al. (2006), Lastovicka (2009), Danilov (2012), and references therein and include long-term variations in solar and geomagnetic activity, increasing concentrations of greenhouse gases (e.g., CO2, CH4) and anthropogenic changes to the ozone layer and the distribution of water vapor. Our study focuses on the role of solar and geomagnetic activity in long-term foF2 trends, using foF2 data routinely measured over Kazakhstan at the Alma-Ata ionosonde station [43.25°N, 76.92°E]. Data used in this study cover about five solar cycles between 1957 and 2012. Data measured at the Alma-Ata station between 1958 and 1994 have already been used to derive long-term trends, independent of geomagnetic activity (e.g., Danilov 2003). However, this study is the first to use the extended dataset up to the year 2012 to derive long-term trends in foF2 (we assume the trend is a long-term linear change in foF2 over the period between 1957 and 2012).


For this study, we used monthly median values of foF2 averaged over 5 h, between 1000 and 1400 (local time) (Figure 1a). Monthly mean values of the solar radio flux at 10.7Â cm (F10.7) and geomagnetic activity index (Ap) (available at were also studied as the characteristics of solar and geomagnetic activities can strongly affect the ionosphere (Figure 1b,c). As expected, Figure 1 shows that the temporal variations in all three parameters are dominated by changes in solar activity related to the solar cycle. Assuming a second-order polynomial dependence on F10.7, foF2′ is defined as follows (see the regression line in Figure 2a):

Figure 1
figure 1

Monthly median near-noon foF2 (a), monthly mean F10.7 (b) and Ap (c) values.

Figure 2
figure 2

Monthly median near-noon foF2 values versus monthly mean F10.7 (a); monthly absolute deviations ΔfoF2 (b).

foF 2 =a+b× F 10.7 +c× F 10.7 2

A higher-order (cubic) regression, as used by Chen et al. (2014), does not provide any significant improvement to the fit: R2 = 0.810324 for a second-order regression versus R2 = 0.810385 for a third-order regression). The regression defined in Equation 1 was then used to remove variations in foF2 related to the solar activity effect, allowing monthly absolute deviations (defined as ∆foF2 = foF2 - foF2′), which can potentially reveal long-term trends in foF2, to be calculated (Figure 2b). However, Figure 2b shows that the correlation between foF2 and F10.7 determined via Equation 1 only accounts for around 80% (R2 = 0.810324), of the variations in foF2 and the majority of the ∆foF2 variability linked to the 11-year solar cycle. Therefore, to obtain an independent picture of long-term trends in the upper ionosphere, the 11-year (132 months) running mean values of the monthly absolute deviations (∆foF2 132 ) were calculated over the entire dataset according to the method set out by Mikhailov (2006). This 11-year smoothing technique was also applied to the F10.7 and Ap datasets but reduced the available period for study to between 1962 and 2006.

Results and discussion

Figure 3 presents the calculated values for ∆foF2 132 , F10.7 132 , and Ap 132 . Figure 3 shows a pronounced similarity in the ∆foF2 132 , F10.7 132 , and Ap 132 variations, which display negative correlations with time and a repeating pattern with a period of ca. 30-32 years. This implies that geomagnetic activity and the Earth's ionosphere are strongly controlled by solar activity. However, it should be noted that the negative trend in geomagnetic activity found here contradicts the generally accepted increase in geomagnetic activity observed throughout the twentieth century (e.g., Clilverd et al. 1998). However, in detail, the geomagnetic activity increased throughout the first half of the twentieth century (along with solar activity) then stabilized (with some increase in Ap seen at the end of the 1950s), and then decreased until the beginning of the twenty-first century (with another smaller Ap peak observed in the 1980s) (Figures 3 and 4). This study spans the interval from 1957 to 2012, and our data match the overall decrease in Ap observed over these years. The trend with a period of ca. 30-32 years is likely to have a solar origin, as it matches a period of 31.1 years that has been found elsewhere in sunspot number spectral analyses (Echer et al. 2004; Clúa de Gonzalez et al. 1993). It has also been suggested that this period of 31 years is the origin of the 35-year Brückner climatic periodicity (Raspopov et al. 2000). Figure 3 shows evidence of the same solar periodicity in foF2 long-term variations. The Fisher (F) parameter for foF2 data confirmed that the clear negative trend (ca. –0.0038 MHz y-1) was significant with a confidence level of 95%-99%.

Figure 3
figure 3

The 11-year running means of variations.

Figure 4
figure 4

Annual mean values for F10.7, Ap and foF2 (a), and their 11-year running means (b).

Using a similar method to that described for foF2 above, we calculated the dependence of monthly mean Ap on F10.7, allowing the variations in Ap related to the solar cycle to be clearly seen (Figure 5). Assuming a linear dependence, we defined (Ap)′ as a function of F10.7 and obtained absolute deviations (∆Ap) as follows:

Figure 5
figure 5

Correlation of monthly means Ap and F10.7 (a). Long-term variations in (Ap)′ (b) and ΔAp (c).

A p =a+b×F10.7
ΔAp=Ap- A p

Figure 5 displays the observed Ap values (black crosses) versus F10.7, together with the linear regression line (solid line), the variations in Ap related to solar forcing, and the variations in ∆Ap with time. Approximately 16% of the variations in the geomagnetic field can be explained by the linear relationship between geomagnetic and solar activities (R2 = 0.15798, Figure 5a) and the majority variations in ∆Ap are linked to the 11-year solar circle. Peaks in ∆Ap are slightly shifted (by about 2 to 3 years) relative to the falling phase of the 11-year solar cycle (Figure 5c). Taking this shift into account for the regression calculation did not result in a significantly better fit (R2 = 0.1698). These results show that the geomagnetic activity (described by Ap) is strongly linked to the solar cycle phase (solar activity is described by F10.7) and in this study, we were unable to exclude variations in foF2 related to geomagnetic activity. Analyzing geomagnetic data observed at Kakioka (Japan) and Gnangara (Australia) over almost five solar cycles, Yamazaki and Yumoto (2012) recently found that solar activity controls not only the stationary component of the geomagnetic solar quiet daily variation field (S q ) but also the annual and semi-annual components. They report that all three components have a positive linear correlation with sunspot numbers. Thus, the positive linear correlation between Ap and F10.7 found in this study confirms Yamazaki and Yumoto's findings and shows the existence of a long-term coupling between solar and geomagnetic activity that could be used to further our understanding of solar-terrestrial relations.

Our results also show that foF2 strongly depends on solar activity and shows a negative temporal trend between 1957 and 2012 (about -0.0038 MHz y-1), although the magnitude of this trend is probably too small value to be of practical use. However, it should be noted that the sign of the deduced trend can be dependent on choice of time period for trend analysis. Periods of increasing solar activity (1970-1984) are seen to correspond to positive trends in foF2 and periods of decreasing solar activity (1956-1968, 1986-2004) to negative trends in foF2 (Figure 3). Therefore, periods of several solar-cycle observations should be used to obtain reliable trend estimates from the data series.

In addition to the material presented above, we derived a picture of long-term changes in the upper ionosphere using annual mean values for Ap and F10.7 (Ap(12) and F10.7(12)) and annual median values for foF2 (foF2(12)). Following a similar method to that described above, Figure 4a,b shows the variations in the 11-year running means foF2(12) 132 , F10.7(12) 132 , and Ap(12) 132 for the analyzed period. Figure 4b shows that long-term trends are similar to those seen in Figure 3, which supports our conclusion that variations in Ap and foF2 are dominantly affected by solar cycles as represented by F10.7. One exception to this conclusion is the somewhat higher foF2 trend (-0.0075 MHz y-1) than that found using the regression method and including an F10.7 correction (-0.0038 MHz y-1). Table 1 shows that the higher foF2 trend is close to those calculated by Danilov (2002, 2003), Lastovicka et al. (2006, 2008b), Khaitov et al. (2012), and Ghabahou et al. (2013), whereas the weaker foF2 trend more closely matches that calculated by Mielich and Bremer (2013). Here, we can only note that twice removing the solar element of variations in foF2 (using the regression method and the 11-year running mean) provides a weaker foF2 trend than that obtained using only the 11-year smoothing.

Additionally, we calculated regressions for foF2(12) 132 as a function of F10.7(12) 132 for different periods. Figure 6a shows that for the total interval (07.1963 to 08.2006), the correlation between the two variables forked into two distinct point groups assuming different relationships between foF2(12) 132 and F10.7(12) 132 for different phases of the ca. 32-year cycle, a coefficient of determination (R2) of 0.81 was obtained. Figure 6b,d shows linear relationships for the intervals showing a decrease (1964-1967; 1980-2007) and increase (1968-1979) in solar activity. It was found that 95% and 99% of the variations in foF2(12) 132 could be explained by linear relationships between foF2(12) 132 and F10.7(12) 132 for the decreasing and increasing intervals, respectively. The remaining variations in foF2(12) 132 are not explained by solar activity.

Figure 6
figure 6

Plot of foF2(12) 132 versus F10.7(12) 132 for periods: 1964-2007 (a), 1964-1967 (b), 1968-1979 (c), and 1980-2007 (d).


In this study, we derived a picture of long-term trends in foF2 for the ionosphere, using data from the mid-latitude ionosonde station at Alma-Ata [43.25°N, 76.92°E] observed over about five solar cycles between 1957 and 2012. We showed that solar activity (as represented by F10.7) is significantly correlated with variations in foF2 and Ap. In addition to the well-known 11-year solar cycle, the Sun also exhibits a cycle of about 30-32 years, which matches the period of trends observed in Ap and foF2. A negative trend is seen in long-term variations in foF2 between 1957 and 2012, and the magnitude of this trend was found to be -0.0038 and -0.0075 MHz y-1 for monthly absolute deviations (∆foF2) and annual mean median foF2, respectively. This trend is considered too small to have practical meaning. It was found that 95% and 99% of the total variation in foF2(12) 132 could be explained by linear relationships between foF2(12) 132 and F10.7(12) 132 for periods increasing and decreasing solar activity, respectively. The remaining variations in foF2(12) 132 cannot be explained by solar activity.


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We thank two anonymous reviewers for their careful reviews that helped significantly improve this manuscript. This research was supported by the Kazakhstan National Center for Space Research and Technology and funded through the Institute of Ionosphere (Research Project 011200290).

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Correspondence to Galina I Gordiyenko.

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Gordiyenko, G.I., Vodyannikov, V.V., Yakovets, A.F. et al. A long-term trend in the F2-layer critical frequency as observed at Alma-Ata ionosonde station. Earth Planet Sp 66, 125 (2014).

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