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%.
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 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.