Long-term trends in the ionospheric F 2 region with different solar activity indices

A new comprehensive data collection by Damboldt and Suessmann (2012a) with monthly foF2 and M(3000)F2 median values is an excellent basis for the derivation of long-term trends in the ionospheric F2 region. Ionospheric trends have been derived only for stations with data series of at least 22 years (124 stations with foF2 data and 113 stations with M(3000)F2 data) using a twofold regression analysis depending on solar and geomagnetic activity. Three main results have been derived: Firstly, it could be shown that the solar 10.7 cm radio flux F10.7 is a better index for the description of the solar activity than the relative solar sunspot number R as well as the solar EUV proxy E10.7. Secondly, the global mean foF2 andhmF2 trends derived for the interval between 1948 and 2006 are in surprisingly good agreement with model calculations of an increasing atmospheric greenhouse effect (Rishbeth and Roble, 1992). Thirdly, during the years 2007 until 2009, the mF2 values and to a smaller amount the foF2 values strongly decrease. The reason for this effect is a reduction of the thermospheric density and ionization due to a markedly reduced solar EUV irradiation and extremely small geomagnetic activity during the solar cycle 23/24 minimum.


Introduction
Long-term trends in the upper atmosphere/ionosphere have been initiated by model calculations of Roble and Dickinson (1989), Rishbeth (1990), and Rishbeth and Roble (1992).They predicted a lowering of the F2 peak height hmF2 by −10 to −20 km and a reduction of the critical frequency foF2 by about −0.2 to −0.5 MHz for a doubling of the greenhouse gas CO 2 in the Earth's atmosphere.These model predictions can be tested by long-term ionosonde observations which are available at many stations around the world partly available since about 1940.A lot of investigations have been done in the past with data of single stations (e.g.Bremer, 1992;Hall and Cannon, 2002) as well as analyses with different stations (e.g.Bremer, 2004;Ulich, 2000).Additional references of such analyses can be found in recent papers by Qian et al. (2011) and Bremer et al. (2012).
An important point in the ionospheric trend analyses is the elimination of the solar and geomagnetic activity-induced parts.Different methods have been used such as different regression analyses (Bremer, 1992;Alfonsi et al., 2002;de Adler et al., 2002), a statistical inversion method (Ulich, 2000), a neural network model (Yue et al., 2006), and two different methods for elimination of geomagnetic long-term effects (Mikhailov et al., 2002;Danilov, 2002Danilov, , 2003)).
In most of the published ionospheric trend analyses, the solar sunspot number R has been used as proxy of the solar EUV radiation.However, there are also other indices such as the solar 10.7 cm radio flux or the E10.7 index developed by Tobiska et al. (2000).Whereas Bremer (2001) did not detect essential differences in the trends derived with different solar activity indices for one station, Jarvis et al. (1998) and Ulich et al. (2006) found, however, slightly less noisy results if F10.7 was used instead of R.
As the influence of the solar activity causes marked variations in different ionospheric key parameters foF2 and hmF2, it is necessary to use the optimum solar activity index to derive the small ionospheric long-term trends.In the present paper, trend analyses are carried out for more than 100 worldwide distributed ionosonde stations using their foF2 and hmF2 data series collected in a new databank with monthly median values of these parameters (Damboldt and Published by Copernicus Publications on behalf of the European Geosciences Union.Damboldt and Suessmann (2012a).Dots indicate stations with foF2 and M(3000)F2 data, and crosses indicate stations with foF2 data only.
Suessmann, 2012a).These analyses have been made for the above-mentioned different solar activity indices, the solar sunspot number R, the solar 10.7 cm radio flux F10.7, and the solar EUV proxy E10.7 to find the most appropriate solar index for trend analyses.This is the first main topic of this paper.The second main point is the derivation of mean global trends of foF2 and hmF2 and their comparison with model predictions of an increasing atmospheric greenhouse effect.The third topic is directed to the investigation of the unusual behaviour of the ionospheric parameters foF2 and hmF2 during the solar cycle 23/24 minimum.Some data of the databank of Damboldt and Suessmann (2012a) have been used for the first time by Bremer et al. (2012).Here trend results have been compared from analyses with two different methods for a limited data set (37 stations).In these analyses the solar sunspot number R has been used as solar activity index.From these results mean global trends have been estimated, and the variation of hmF2 during the low solar cycle 23/24 minimum was analysed.Some of these investigations are continued in this paper, however, on an essentially larger data basis and with the solar F10.7 index instead of the solar sunspot number R. The markedly enhanced data volume (113 stations with hmF2 and 124 stations with foF2 values) will increase the significance level of the derived mean trends.The investigation of the ionospheric variation during the solar cycle 23/24 minimum is extended, including now for the first time in addition to hmF2 also the variation of foF2.
In Sect. 2 of this paper, the trend analysis method is shortly described together with some details of the used ionospheric database and the different solar indices.In Sect. 3 the trend results are presented followed by a discussion of the derived trends in Sect. 4. Conclusions with the main results are given in Sect. 5.

Method of trend analysis
For a detection of ionospheric trends, it is necessary to remove the influence of the solar (and the geomagnetic) activity.As introduced by Bremer (1992), this part can be approximated by a twofold regression equation: Here X is the ionospheric parameter foF2 or hmF2, SA the solar activity parameter R, F10.7, or E10.7, and Ap is the global geomagnetic activity index.Then the differences between the observed ionospheric parameter X exp and the corresponding model value X th are calculated according to For each hour and each month, such data series are calculated (i.e. 12 × 24 data series).These data series can be analysed separately, but often yearly X mean values are used (as in this paper) to derive linear trends according to Here E is the trend parameter in km year −1 for hmF2 data and in MHz year −1 for foF2 values.

Ionospheric database
The trend analyses presented in this paper are based on the data collection of Damboldt and Suessmann (2012a)  It is difficult for a foreign user to check the quality of the data in the data collection of Damboldt and Suessmann (2012a).If we, however, found some discontinuities in individual data series, these series have been removed from the trend analyses.Examples of such discontinuities have been found in previous investigations (Bremer, 2001(Bremer, , 2004 In the trend analyses we did not use the M(3000)F2 data but hmF2 values derived from the M(3000)F2 values according to the well-known formula of Shimazaki (1955): There are of course more complicated and even more accurate formulas for the derivation of the F2 peak height using additional information about the underlying ionization (e.g.Bilitza et al., 1979).But such data are not available in the used databank of Damboldt and Suessmann (2012a).Therefore, we had to use the simple Eq. (4).

Solar activity indices
In Fig. 2 the yearly variations of the solar activity indices F10.7 and R are presented together with the variation of the geomagnetic Ap index for the time interval between 1948 and 2010 thus consisting of nearly 6 solar cycles (mainly cycles 18-23).Here the variation of R and F10.7 is very similar, confirmed by the highly significant correlation between both yearly mean data sets (correlation coefficient r = 0.99).
If we, however, consider the dependence between R and F10.7 separately for the time interval from 1948 to 2000 and for the interval from 2001 to 2009, then we can observe marked differences as shown in Fig. 3.Here the yearly R values from 2001 to 2009 (dots connected with a polynomial fit of second order) are markedly smaller than the correspond- ing data of the interval from 1948 to 2000 (crosses connected with a polynomial fit of forth order).These smaller R values during 2001 to 2009 are strongly confirmed by Floyd et al. (2005) and Lukianova and Mursula (2011).These authors detected, in comparisons between the solar sunspot number R and different EUV indices (F10.7,MGII core-to-wing ratio, HeI 1083 equivalent width), marked differences during the period from 2001 until 2008 thus demonstrating that the R values underestimate the solar EUV radiation during this period.
In spite of the strong correlation between the yearly R and F10.7 values mentioned above in connection with Fig. 2, some differences may occur between these solar indices as demonstrated in Fig. 3. Therefore, it is an essential point of this paper to compare ionospheric trends derived with R or F10.7 indices.Additionally, the solar EUV proxy E10.7 (Tobiska et al., 2000) has been tested in selected trend analyses.

Comparison of trends with different solar indices
In the first two of three subsections, trends in hmF2-and foF2 data series are separately derived by use of the solar sunspot number R as well as the solar 10.7 cm radio flux F10.7.In a third subsection we investigated if the solar EUV proxy  E10.7 (Tobiska et al., 2000) can also successfully be used in such trend analyses.

Trends in hmF2 data with solar indices R and F10.7
For all 113 stations with hmF2 data series of at least 22-yr duration during the time interval from 1948 until 2009, trends have been estimated by use of the two solar activity indices As can be seen from these histograms together with the corresponding median values, the hmF2 trends(F10.7) are generally smaller (more strongly negative) than the corresponding hmF2 trends(R).From all 113 individual hmF2 trends, mean global trends are estimated for both solar indices.These global mean trends are presented in Fig. 5, in the upper part mean trend using F10.7 values, in the lower part mean trends using R values.As to be expected from the results presented in Fig. 4, also here the global hmF2 trend(F10.7) is more strongly negative than the global hmF2 trend(R).The mentioned mean hmF2 trend values are summarized in the upper part of Table 1.For the global trends in this table, also the error values ε t deduced from the Student's t test are added via the following formula: with X = hmF2 in this subsection and X = foF2 in the following subsection, the number of years  (Taubenheim, 1969).In the upper part of Table 1, also the median values of the individual trends (as shown in Fig. 4) are included as well as the mean values of the individual trends together with their error values derived by the following formula: with the number of stations N, the standard deviation of the individual trends STD, and the t value for 95 % reliability t 95 (N − 1) (Taubenheim, 1969).As partly remarked above (see Figs. 4 and 5), all three mean hmF2 trend parameters are more strongly negative if the F10.7 values have been used in the trend analyses.Also the significance levels are higher for these trends than those of the corresponding hmF2(R) trends.

Trends in foF2 data with solar indices R and F10.7
Similar trend analyses as for hmF2 data series presented in Sect.3.1.1have also been carried out for all available 124 ionosonde stations with long-term foF2 observations.In the upper part of Fig. 6, histograms of the derived foF2 trends of the individual stations are separately presented for analyses with F10.7 or R. In the lower part of Fig. 6, the trend differences, foF2 trend(F10.7)-foF2 trend(R), are shown.Nearly all of these differences are negative.In each case the corresponding median value is marked by an arrow.Whereas the median of the foF2 trends(R) is slightly positive (not significant as shown in the lower part of Table 1), the median of the foF2 trends(F10.7) is negative and significantly different from zero.A similar result was also obtained from the mean values of the individual trends as to be seen in the lower part of Table 1.Therefore, we observe qualitatively comparable results as for the hmF2 trends reported above.
The global mean foF2 trends are shown in Fig. 7. Also here the foF2 trend(R) is slightly positive, but not significantly different from zero.The global foF2 trend(F10.7),however, is significantly negative (for details see Table 1).

Trends by use of the solar EUV proxy E10.7
In trend analyses of selected ionospheric data series, we normally detected very similar results if we used F10.7 or E10.7 data.However, we got different results for the years 1957 and 1958.In the upper part of Fig. 8, the long-term variations of yearly averaged F10.7 (dots) and E10.7 data (crosses) are presented.The ordinate of the E10.7 data set is slightly shifted to get nearly the same level for both indices at solar minimum conditions.There is in general a satisfying agreement between both data series.Only for the years 1957-1958 the E10.7 data are markedly more enhanced than the corresponding F10.7 data.This behaviour is more clearly seen in the monthly variation shown in the lower part of Fig. 8. Especially during the months September 1957 until January 1958, the E10.7 data are markedly more strongly than the corresponding F10.7 data.
These large E10.7 data are responsible for problems in the trend analyses as demonstrated by the trends for the station Juliusruh presented in Fig. 9.Here the trends have been derived for two different data intervals: in the left part for 1957 to 2009, in the right part for 1959 to 2009.In the upper part the hmF2 trends are shown and in the lower part the foF2 trends.The trend analyses have been carried out for both solar indices (F10.7 marked by dots, E10.7 marked by crosses).The hmF2 trends (see upper part of Fig. 9) agree in nearly all cases; only the hmF2 trend(E10.7)for the full data interval between 1957 and 2009 is reduced due to the extremely high E10.7 value during the year 1957.A similar behaviour can also be seen in the foF2 trends in the lower part of analyses with E10.7 data are carried out without the years 1957 and 1958, the results are in agreement with the corresponding trends using F10.7 data.Another phenomenon has to be remarked.The foF2(E10.7)data show a stronger 11yearly variability than the corresponding foF2(F10.7)data, thus suggesting that the solar cycle has only partly been eliminated.In the hmF2(E10.7)data, this 11-yearly variability is smaller but can also be observed.Altogether, we conclude that ionospheric trend analyses with F10.7 data give more reliable results than the analyses with E10.7 data.

Trends in dependence on data length
Up to now we presented only trends from the interval between 1948 and 2009.In the following we will investigate trends for data intervals with different lengths.In these analyses we use only F10.7 data for the elimination of the solar activity-induced parts.At first we estimate hmF2 trends for constant interval length of 22 years continuously shifted by one year from the yearly hmF2 data shown in the upper part of Fig. 5.In the upper part of Fig. 10, such hmF2 trends are presented together with their error limits.The trends (marked by full dots) have been drawn for the last year of the 22-yr interval (i.e. the analysed interval started 21 years before).Whereas the hmF2 trends before about 1979 are significantly negative, the trends become positive between about 1980 and 1996 (significant only between about 1983 and 1988) and become again negative after about 1997 (significant from about 2000 to the final year 2009).
In a second step we analyse the hmF2 trends for different data lengths from the yearly hmF2 data shown in the upper part of The foF2 trends for different data lengths in the lower part of Fig. 11 are nearly all negative.Whereas the significance level of the global trends before about 1988 is markedly smaller than 95 %, after 1990 the significance becomes better with values near about 95 %.This phenomenon is markedly caused by the fact that the error limit becomes smaller due to an increasing number of years N in the trend analyses.

Ionospheric changes during solar minimum 2007-2009
In the upper part of Fig. 5, the hmF2 values are markedly reduced during the solar minimum years 2007-2009, which have never been observed during the previous solar minima.
A similar reduction can also be observed in foF2 values in the upper part of Fig. 7.However, this lowering of the foF2 values is not as strong as in the hmF2 values.The special behaviour of the hmF2-and foF2 values during the solar cycle 23/24 minimum can be demonstrated by a superimposed epoch analysis.Here the solar minima (1954, 1964, 1976, 1986, 1996; shown by vertical dashed lines in Fig. 2) are used as key year zero.The parameters hmF2, foF2, F10.7, and Ap are separately averaged for the years −5 until +5 to get mean reference values.For each year also the corresponding error limits according to Eq. ( 6) have been calculated.N is here, however, the number of years.These reference values (dots with error bars) are presented in Fig. 12  than the corresponding reference values.For foF2 the decrease is by about 0.2 MHz also significantly different from zero but not so pronounced in comparison with the hmF2 deviations.Also the solar and especially the geomagnetic indices (F10.7 and Ap) are significantly smaller during the years of the solar minimum at the end of the solar cycle 23 and the beginning of the cycle 24.

Discussion
Long-lasting ionosonde observations at worldwide distributed stations are very important for the derivation of trends in the ionospheric F2 region.Especially the new data collection with monthly median values of M(3000)F2 and foF2 by Damboldt and Suessmann (2012a) is very helpful for such investigations.Nevertheless, a lot of open questions have to be solved to understand the physical background of the derived trends.Some of them will be discussed in the following subsections.

Solar activity indices
As shown by Floyd et al. (2005) and Lukianova and Mursula (2011), the solar sunspot number R underestimates the solar EUV flux during the years between 2001 and 2009.This phenomenon can also be confirmed by the comparison between R and F10.7 in Fig. 3. Multiscale comparisons between F10.7, R, MGII and SOHO/SEMEUV flux by Wintoft (2011) concluded that F10.7 is the best solar EUV proxy for investigations with long time scales (>1.4 years).Also in comparisons of foF2 trend analyses with different methods (Lastovicka et al., 2006), it was proposed that F10.7 may be a better solar index than the solar sunspot number R for trend analyses.This statement was also confirmed by trend analyses of Jarvis et al. (1998) and Ulich et al. (2006) 6 and 7 for foF2 trends, the use of F10.7 instead of R data will make the trend values more strongly negative.The correlation coefficients between individual trends derived with R and F10.7 are, however, strongly significant with r = 0.99 for both hmF2 data sets and r = 0.91 for both foF2 data sets (not shown here).Nevertheless, the differences between the data sets can clearly be seen (e.g. in the lower parts of Figs. 4 and 6).
As shown in Figs. 8 and 9, the use of the solar EUV proxy E10.7 is only reasonable if the years 1957 and 1958 are excluded in the trend analyses.In conclusion we prefer the use of F10.7 data for time intervals starting after 1948 (more exact after 14 February 1947).

Length of data interval
At the beginning of our trend analyses, we believed in agreement with Lastovicka et al. (2006) that in trend analyses with data length of about 22 years the influence of the solar cycle can satisfyingly be removed.The global foF2 trends with constant length (upper part of Fig. 11) show, however, variations with a nearly 11-yearly period and small indications of a trend variation with a longer period.
Also in the hmF2 trends (upper part of Fig. 10) periodical variations can be seen.Here, however, the long-term variation is more pronounced with negative values at the beginning and the end of the analysed time interval and positive values in the middle of the investigated interval.A nearly 11yearly trend variation is markedly smaller but can also partly be detected.
The reason for the periodical 11-yearly variations in the foF2-and hmF2 trends is probably caused by the 11-yearly solar cycle which could not totally be removed in the trend analyses of the 22-yearly intervals.The reason for the longer trend variation (most markedly detected in the hmF2 trends, but also to be seen in the foF2 trends) is still unclear and requires further investigations.
The trends for increasing data intervals of the analysed data sets in the lower parts of Figs. 10 and 11 show more stable variations and suggest that the derived mean hmF2and foF2 trends are more reliable for longer data intervals as the error bars become smaller with increasing number N of years.Therefore, for tests of an increasing atmospheric greenhouse effect (see Sect. 4.5 below), ionospheric data series of about 50-60 year duration are necessary to get significant long-term trend results.This result is in general agreement with Jarvis et al. (2002).

Solar activity minimum 2007-2009
As shown in Fig. 12 the observed hmF2 values are during the solar cycle 23/24 minimum up to about 13 km lower than the corresponding reference values deduced from the preceding solar minima.Also the foF2 values are about 0.1 to 0.3 MHz smaller than the estimated reference values.
A similar unusual behaviour of the upper atmosphere has been reported by Emmert et al. (2010)  detected density reductions up to −30 % during the solar cycle 23/24 minimum.The reason for this effect is not conclusively resolved.According to Solomon et al. (2010), the unusually low EUV irradiances during the solar minimum of the solar 23/24 cycle may play an essential role.
The extreme lowering of the hmF2 values is strongly connected with the observed thermospheric density reduction.Due to typical density profiles of the COSPAR International Reference Atmosphere (CIRA, 1972), a density reduction by about 30 % corresponds to a height lowering of about 7-10 km.The abovementioned ionospheric effect with about 13 km is markedly stronger.The ionospheric effect is probably caused by the lowering of the atmospheric density together with a markedly reduced ionization due to the extremely low solar radiation as well as geomagnetic activity (see corresponding F10.7 and Ap curves in Fig. 12).The reduced foF2 values during the solar cycle 23/24 minimum could also be caused by the extremely low solar and geomagnetic activity.Such reduced foF2 and hmF2 values at low solar activity conditions can be expected due to the well-known positive correlation between these parameters and the solar activity (corresponding figures can be seen in Hargreaves, 1979, andBremer, 2001).
For an investigation of this unusual ionospheric effect during the solar cycle 23/24 minimum in dependence on latitude, we estimated for each station the hmF2-and foF2 trends from the data between 1948 and 2006.With these linear equations we calculated the theoretical values for the years 2007, 2008 and 2009 and estimated the differences to the corresponding experimental values of these three years.From these three difference values, we estimated the minimum value hmF2(min) and foF2(min) for each station.In Fig. 13 these values are shown in dependence on latitude (more correct: on the absolute value of the latitude.Due to the limited number of values N, the min-data of both hemispheres are not separately presented).The hmF2(min) values are nearly independent of latitude.The mean hmF2(min) value at the pole with about −13 km is only slightly lower than at the Equator with about −12 km.This difference is statistically insignificant.In contrast to the hmF2(min) values, the foF2(min) values strongly depend on the latitude as shown in the upper part of Fig. 13.Whereas the mean foF2(min) value at the pole is nearly zero, at the Equator the mean foF2(min) value is about −1.0 MHz.Due to the smaller solar zenith angle at the Equator, the reduced EUV irradiation is more effective there and causes a stronger decrease of the foF2(min) values than at the pole.As easily shown by the statistical Student's t test (Taubenheim, 1969), the dependence of the foF2(min) values on the absolute values of the latitude is strongly significant.The dependence of hmF2(min)-and foF2(min) values on geomagnetic latitude (not shown here) is nearly identical with the results shown in Fig. 13.Damboldt and Suessmann (2012b) recently estimated also global hmF2-and foF2 trends with data of the same databank (Damboldt and Suessmann, 2012a) as used in this paper.However, these authors utilised another analysis method.They eliminated the solar cycle influence by means of a CCIR ionospheric prediction model (ITU, 2009).Nevertheless the results of both data analyses agree quite reasonably with global negative hmF2-and positive foF2 trends, however, only if the solar sunspot number R is used in both data analyses (in agreement with investigations of Bremer et al. (2012) with a markedly smaller data volume).Using, however, F10.7 values in the data analyses presented in this paper, the global trends of hmF2 and foF2 are both negative (see upper parts of Figs. 5 and 7) and agree with model results as shown in the next Sect.4.5.Unfortunately, the CCIR model can only be run with R but not with F10.7 data.

Comparison with other trend analyses
As shown in the upper parts of Figs. 10 and 11, the trends deduced from shorter time intervals (here 22 years) demonstrate with periodical variations marked deviations from the global mean trends estimated from the full data interval.Deviations from the mean trends have also been found by Damboldt and Suessmann (2012b) (1948-2009 and 1948-2006).
Parameter Trend type Trend (1948-2009) Trend (1948-2006) hmF2 trends before and after 1964 (negative trend before 1964 and positive trend after this year).This behaviour can also be seen in the lower part of Fig. 5 where R is used as solar activity index.If F10.7 is used in the trend analyses, more detailed trend variations were found as can be seen in the upper parts of Figs. 10 and 11.
It can be concluded that both methods reasonably agree only if R values are used.As mentioned above differences occur, however, if different solar activity indices are used, in the CCIR method R values and in our regression analysis F10.7 data.Some additional differences may result from the fact that the influence of geomagnetic activity is not included in the CCIR method.Also the investigated data volumes are slightly different.Whereas in this paper only data series with more than 22 years have been analysed, in the paper of Damboldt and Suessmann (2012b) all available stations are included even if the data series are very short.

Comparison with model results
As remarked in Sect.4.3, the years 2007 until 2009 show an anomalous behaviour which is not caused by long-term variations in the Earth's atmosphere/ionosphere.Therefore, these years will be excluded from investigations of long-term trends and their comparison with long-term model results.In Table 2 the corresponding hmF2-and foF2 trends are shown for the time interval from 1948 until 2009 as well as for the interval from 1948 until 2006.As to be expected from the trend results shown in the upper parts from Figs. 5 and 7, the trends without the years 2007-2009 are not so strongly negative compared to the trends that include these three years.Also the significance levels of the trends  are smaller than those for the trends .Nevertheless for some trends  the significance level is more than 95 % (global hmF2 trend, individual mean foF2 trend), for the individual mean hmF2 trend slightly below 95 % and for the global foF2 trend about 87 %.
According to an excellent review paper by Qian et al. (2011), there are different theories to explain the ionospheric trends in the F2 region: a cooling of the atmosphere by an increasing greenhouse effect (Rishbeth and Roble, 1992;Qian et al., 2009); long-term changes of the Earth's magnetic field (Cnossen and Richmont, 2008); changes of the geomagnetic activity (Mikhailov, 2002); and the influence of non-migrating tides (Bencze, 2009).
If we expect that the mean hmF2-and foF2 trends are caused by an increasing greenhouse effect, we have to compare the mean trend values in the right column of Table 2 with available model results.Unfortunately, the model results are normally carried out for a doubling of the atmospheric greenhouse gases.Therefore, we have to extrapolate our trend values to an interval corresponding to such a doubling of the greenhouse gases.According to Houghton et al. (2001) and Brasseur and de Rudder (1987), the content of the atmospheric greenhouse gases increased about 20 % during 40 years.Assuming a linear relationship between the amount of the greenhouse gases and the ionospheric effect, then for the doubling of the greenhouse gases the experimental trends have to be multiplied by 200 to get the ionospheric effect which can be compared with the model values.In Table 3 there are presented the experimental trends (Exp.trends, derived from the right column of Table 2), the extrapolated experimental changes (Exp.2xCO 2 effect), and the model values from Rishbeth and Roble (1992) (Th.2xCO 2 effect).The agreement between the experimental effects with the model results is very reasonable.Therefore, the global long-term mean hmF2-and foF2 trends strongly confirm the importance of the atmospheric greenhouse effect.This agreement could, however, only be achieved if F10.7 data are used in the trend analyses.The mean foF2(R) trends, however, are slightly positive (see Table 1) and disagree with the model predictions.Qualitatively, the same result was also detected by trend analyses in dependence on R with a reduced data volume (Bremer et al., 2012)  As remarked above (see upper parts of Figs. 10 and 11 and comments in Sect.4.2) in trends with shorter data series, variations can be detected which cannot be explained by an increasing atmospheric greenhouse effect.

Conclusions
The presented results of trends in the ionospheric F2 region are based on a recently available data collection by Damboldt and Suessmann (2012a).From this databank with monthly median values of foF2 and M(3000)F2, trend analyses with a twofold regression method have been carried out for 113 different stations with hmF2 data (derived from M(3000)F2 values) and for 124 stations with foF2 data.The following main results were obtained: -The elimination of the solar-induced variations can preferably be made with the solar 10.7 cm radio flux.
Especially during the years from 2001 until 2009, the relative solar sunspot number R markedly underestimated the solar EUV flux.The E10.7 data are in general very similar to the F10.7 data.However, the E10.7 values during the solar maximum years 1957 and 1958 are strongly enhanced and cause erroneous trend estimations.The trends derived by means of the solar 10.7 cm radio flux give the most reliable ionospheric trend results.Therefore, we recommend the use of the F10.7 index in atmospheric/ionospheric trend analyses.
-Global mean hmF2-and foF2 trends derived from the time interval between 1948 and 2006 are significantly different from zero with reliability from about 87 % up to a level greater than 95 %.These trends are in surprisingly reasonable agreement with model results, thus demonstrating that long-term variations in the atmosphere/ionosphere can be explained by the atmospheric greenhouse effect.
-During the solar cycle 23/24 minimum (years 2007-2009), a marked lowering was detected of hmF2 up to 13 km and of foF2 up to about 0.3 MHz compared with previous solar activity minima conditions.This phenomenon is mainly caused by a thermospheric density reduction detected in satellite drag observations by Emmert et al. (2010) together with a reduced ionization due to extremely low solar and geomagnetic activities.
In the present paper the investigations have mainly been restricted to the derivation of global mean trends.Regional differences of the hmF2-and foF2 trends will be discussed in a planned paper in near future.

Fig. 1 .
Fig. 1.Ionosonde stations with observations of at least 22 years from the databank of Damboldt and Suessmann (2012a).Dots indicate stations with foF2 and M(3000)F2 data, and crosses indicate stations with foF2 data only.

Fig. 3 .
Fig. 3. Relation between yearly mean values of the solar 10.7 cm radio flux F10.7 and the solar sunspot number R. The values from 1948 until 2000 are marked by crosses and are adapted by a polynomial fit of fourth order (continuous curve); the values from 2001 until 2009 are marked by full dots and are adapted by a polynomial fit of second order (dashed curve).

Fig. 4 .
Fig. 4. Histograms of hmF2 trends by use of F10.7 or R data in the trend analyses (upper part) as well as a histogram of the differences of both hmF2 trends (lower part).The corresponding median values are marked by arrows.

Fig. 5 .
Fig. 5. Global mean hmF2 trends by use of F10.7 (upper part) or R data (lower part) in the trend analyses.

Fig. 6 .
Fig. 6.Histograms of foF2 trends by use of F10.7 or R data in the trend analyses (upper part) as well as a histogram of the differences of both foF2 trends (lower part).The corresponding median values are marked by arrows.

Fig. 7 .
Fig. 7. Global mean foF2 trends by use of F10.7 (upper part) or R data (lower part) in the trend analyses.

Fig. 10 .
Fig. 10.Global mean hmF2 trends with error bars for constant intervals of 22 years continuously shifted by one year (upper part) and for intervals with increasing data length (lower part).The trend values are drawn in both cases at the upper end of the intervals investigated.

Fig. 11 .
Fig. 11.Global mean foF2 trends with error bars for constant intervals of 22 years continuously shifted by one year (upper part) and for intervals with increasing data length (lower part).The trend values are drawn in both cases at the upper end of the intervals investigated.

Fig. 12 .
Fig. 12.Comparison of global yearly mean values of foF2, hmF2, F10.7, and Ap values from the years 2003 until 2009 (crosses connected with dashed lines) with corresponding reference values derived by a superimposed epoch analysis from the previous solar minima (full dots with error bars connected with continuous lines).

Fig. 13 .
Fig. 13.Minimum values of foF2 and hmF2 from the years 2007-2009 in dependence on the absolute values of the latitude of the investigated stations (N: number of stations, r: correlation coefficient).

Table 1 .
Estimated mean trend values of hmF2 and foF2 with error bars using two different solar activity indices in the trend analyses of 113 stations with hmF2 and 124 stations with foF2 data for the time interval from 1948 until 2009.
N, the Ann.Geophys., 31, 291-303, 2013 www.ann-geophys.net/31/291/2013/standard deviation STD X and STD year , and the t value for 95 % reliability level t 95 (N − 2) , who found a smaller variance if F10.7 values were used instead of R.As shown in detail in Figs.4 and 5for hmF2 trends and in Figs.
Therefore, it can be concluded that F10.7 data should be preferred in long-term trend analyses.The only disadvantage is that the F10.7 data series starts only in 14 February 1947.For investigations of longer data series therefore solar sunspot numbers have to be used.Ann.Geophys., 31, 291-303, 2013 www.ann-geophys.net/31/291/2013/

Table 2 .
Estimated mean trend values of hmF2 and foF2 with error bars using F10.7 data as solar activity index in the trend analyses of 113 stations with hmF2 values and 124 stations with foF2 data for two different time intervals