Geomagnetic control of the foF2 long-term trends

. Further development of the method proposed by Danilov and Mikhailov is presented. The method is applied to reveal the f oF2 long-term trends on 30 Northern Hemisphere ionosonde stations. Most of them show signiﬁcant f oF2 trends. A pronounced dependence of trend magnitude on geomagnetic (invariant) latitude is conﬁrmed. Periods of negative/positive f oF2 trends corresponding to the periods of long-term increasing/ decreasing geomagnetic activity are revealed for the ﬁrst time. Pronounced diurnal variations of the f oF2 trend magnitude are found. Strong positive f oF2 trends in the post-midnight-early-morning LT sector and strong negative trends during daytime hours are found on the sub-auroral stations for the period with increasing geomagnetic activity. On the contrary middle and lower latitude stations demonstrate negative trends in the early-morning LT sector and small negative or positive trends during daytime hours for the same period. All the morphological features revealed of the f oF2 trends may be explained in the framework of contemporary F2-region storm mechanisms. This newly proposed F2-layer geomagnetic storm concept casts serious doubts on the hypothesis relating the F2-layer parameter long-term trends to the thermosphere cooling due to the greenhouse e(cid:128)ect.


Introduction
Long-term variations (trends) of the upper atmosphere and ionosphere parameters are widely discussed in recent publications due to the problem of global climate changes (see reviews by Danilov, 1997Danilov, , 1998Leshchenko, 1994, 1995;Ulich and Turunen, 1997;Rishbeth, 1997;Mikhailov, 1998, 1999;Bremer, 1992Bremer, , 1998Upadhyay and Mahajan, 1998). After the model calculations of Rishbeth (1990) and Rishbeth and Roble (1992) predicting the ionospheric eects of atmospheric greenhouse gas concentration increase, the researchers have been trying to relate the observed long-term trends in the ionospheric parameters to this greenhouse eect (Bremer, 1992;Givishvili and Leshchenko, 1994;Ulich andTurunen, 1997, Jarvis et al., 1998;Upadhyay and Mahajan, 1998). However an analysis has shown that the worldwide pattern of the F2 and E-layer parameter long-term trends is very complicated and cannot be explained suciently by this eect. Further analysis by Bremer (1998) of many European ionosonde stations and by Upadhyay and Mahajan (1998) of a global set of ionosonde stations has shown that the F2-layer parameter trends turn out to be dierent both in sign and magnitude for dierent stations and this cannot be reconciled with the greenhouse hypothesis. A contradiction with this hypothesis was revealed also by Leshchenko (1996, 1998) when analyzing the foE long-term trends. They found that observed foE trends may be related to the long-term variations in molecular oxygen abundance in the lower thermosphere. Therefore, the physical mechanism of the observed ionospheric trends remains unclear. Danilov and Mikhailov (1998) proposed a new approach to reveal foF2 trends. When referring to foF2 trends we mean linear trends everywhere. With this new approach they obtained negative trends for all 22 ionospheric stations considered and a pronounced dependence of the trend magnitude on geomagnetic latitude. This was the ®rst indication that F2-layer trends might be related to the long-term changes in geomagnetic activity. Further analysis of the foF2 trends is performed here to check this geomagnetic hypothesis.

The method and data
The method used for foF2 trend analysis is described by Danilov and Mikhailov (1999), but as it is being improved, the main points of the method are given. It should be stressed that dierent authors use dierent approaches to extract long-term trends from the ionospheric observations and the success of analysis depends to a great extent on the method used. The useful`s ignal'' is very small and the``background'' is very noisy, so special methods are required to reveal a signi®cant trend in the observed foF2 variations.
1. Relative deviations of the observed foF2 values from some model df oF2 f oF2 obs À f oF2 mod af oF2 mod 1 are analyzed rather than absolute values considered by Givishvily andLeshchenko (1994, 1995), Bremer (1998) and Upadhyay and Mahajan (1998). The advantage of using relative values instead of absolute ones are discussed by Danilov and Mikhailov (1998). 2. A regression of foF2 with the sunspot number R 12 (third-degree polynomial) is used as a model. Dependence on monthly Ap index was also added to this regression to try exclude the geomagnetic activity eects as was used in some papers (Bremer, 1992(Bremer, , 1998Jarvis et al., 1998), but this does not change the main results (see later).
3. A 12-month running mean hourly foF2 rather than just monthly hourly values are used for the analysis. This is a very important point not used by other researchers, which helps us in revealing long-term trends as it strongly decreases the scatter in observed foF2 data.
4. It was shown in our previous analysis Mikhailov, 1998, 1999) that only by selecting years around solar maxima and minima is it possible to obtain stable signi®cant trends, whereas for all years (including rising and falling phases of solar cycles) there is a chaos with various signs of the trends obtained at various stations (e.g. Bremer, 1998;Upadhyay and Mahajan, 1998). This approach is used in the present study as well, but it is shown that the inclusion of years around solar maximum also contaminates the picture of trends and better results may be obtained using the years around solar minimum only. Therefore, both year selections are used in the present study for a comparison. The chosen years of solar maximum and minimum are shown in Table 1. This selection of years diers to some extent from the M(3)+m(3) selection used in our previous analysis Mikhailov, 1998, 1999). The present one is based on the observed annual mean R 12 variations. Two to three years around solar cycle extrema with close annual mean R 12 values are selected for each solar cycle (Table 1). These years represent real solar cycle extrema as the annual R 12 are seen to dier from the neighbouring R 12 values belonging to the falling or rising phases of solar cycle.
5. Trends at dierent stations may be compared if only one precise time period is analyzed. A period 1965± 1991, which is the richest in observations over the worldwide ionosonde network was chosen for the main analysis. Observations at most of the selected stations (Table 2) overlap this 1965±1991 time interval. At some stations observations are available for earlier years and they were analyzed separately. On the other hand it should be stressed that the model (foF2 versus R 12 or R 12 + Ap regression) is derived over all years with foF2 observations available on a particular ionosonde station.
6. Gaps in the initial observational data are ®lled in using monthly median values from the MQMF2 model by Mikhailov et al. (1996) based on a new ionospheric index MF2 . This monthly median foF2 model was shown to demonstrate the greatest accuracy among the models compared and was accepted as a ®nal result of the COST-251 project (COST 251, 1999). Filling in gaps is necessary to ®nd 12-month running mean foF2 values used in the analysis. All foF2 observations (given in zonal or UT time) were converted to solar local time (SLT) using spline-interpolation. 7. To analyze foF2 trends one should exclude as much as possible the dependence on solar and geomagnetic activity. Thus, we have used two models, a regression of foF2 with R 12 (model 1) and with R 12 + monthly Ap (model 2) although we realize that both indices poorly represent the foF2 dependence on solar and geomagnetic activity (e.g. ProÈ lss, 1983) We discuss this issue later.
8. The test of the signi®cance of the linear trend parameter K (the slope) is made with Fisher's F criterion (Pollard, 1977) F r 2 N À 2a1 À r 2 2 where r is the correlation coecient between dfoF2 and year after Eq. (1), and N is the number of pairs considered. Although we are aware of the seasonal variations in trends (Danilov and Mikhailov, 1999), the later analysis has shown that diurnal variations may be much stronger than seasonal ones. Therefore, we have analyzed annual mean trends for a selected LT hours.

Geomagnetic control
Ground-based ionosonde observations at 30 European, North American and Asian stations are used in this study. The station list is given in Table 2. The selected stations are situated between 38°N and 81°N geographic latitude (30°N and 71°N geomagnetic latitude) and cover a broad longitudinal range, which provides a possibility to study spatial variations of the trend magnitude.
Regressions of dfoF2 with R 12 (model 1) and with R 12 + Ap (model 2) are used to ®nd the slope K (in 10 )4 per year) of linear regression for each station, 12 and 00 SLT. Some examples of annual mean linear trends for daytime (12 LT) and nighttime (00 LT) hours are given in Fig. 1, years of solar minimum being used for the analysis. Seasonal (over 12 months) scatter in dfoF2 is shown in Fig. 1 as well. Median dfoF2 over these 12 values is found and this value is considered as the annual mean value used in further analysis. Table 2 shows the results when years of solar maximum and minimum (Table 1) are analyzed together, while Table 3 gives the results on years of solar minimum and maximum separately. An F-test was applied to the annual mean slopes K to estimate the con®dence level. Such annual mean K values may be considered as independent as they refer to dierent years and solar cycles. As the number of pairs N is rather small (5±14) and the scatter of individual points sometimes is rather large the con®dence level may be less than 90%. Figure 2 gives the latitudinal dependence for annual mean slopes K (model 1) for three selections of years, 12 and 00 SLT. Figure 3 shows results for the same conditions but for model 2. Only signi®cant trends from Tables 2 and 3 are included in Figs. 2 and 3. The error bars present the standard deviation over 12 monthly slopes of K. High-latitude stations with positive nighttime trends (Tables 2 and 3) are not included in Figs. 2 and 3, these cases are discussed later. An analysis has shown that the invariant latitude (Table 2) usually provides better regression accuracy compared to regressions with geomagnetic or geodetic latitudes, so it was used in Figs. 2 and 3.
The trends revealed demonstrate a pronounced dependence on invariant latitude both for daytime and nighttime hours. Trends calculated over years of solar minimum (m) show a steeper latitudinal dependence and are more negative compared to (M + m) selection of years. In contrast, trends found over years of solar maximum (M) are more positive and are insigni®cant at the 90% con®dence level at many stations (Table 3). We have used stations with observations available for three solar cycles, that is with three extrema for (M) and (m) year selections. Trends for stations with two available solar extrema were not considered although they may be signi®cant according to the Fisher criterion.
Inclusion of the Ap index to the regression (model 2) makes the slopes K more positive in general and decreases the steepness of the latitudinal dependence for K. Sometimes it is even impossible to tell whether there is any latitudinal dependence for K, for instance, The main results of this analysis are the following: 1. The calculated signi®cant trends are negative for the stations considered (especially for m selection of years) and demonstrate a pronounced latitudinal dependence with the slope K being more negative at higher invariant latitudes regardless the year selections and model used; 2. Trends calculated over the years of solar minimum are more negative and signi®cant on more number of stations compared to the (M) selection of years. The (m) selection of years provides a more pronounced and steeper latitudinal dependence for the slope K. Therefore, we may conclude that the inclusion of (M) years to the trend analysis in fact contaminates the initial material although not to such extent as the years during falling and rising phases of solar cycle Mikhailov, 1998, 1999). Therefore, the (M+m) year selection may be used for foF2 long-term trend analysis as the additional (M) years increase the statistics.
3. The revealed dependence of trends on invariant latitude clearly indicates a geomagnetic control and possible relationship with F2-layer storms (see later). An inclusion of the Ap index in the regression in fact does not remove the geomagnetic dependence as Bremer (1992Bremer ( , 1998 supposed but only contaminates the analyzed material increasing the scatter of points around the regression line. When model M2 is used, K depends on geomagnetic latitude as well. Therefore, further analysis is made only with model 1 as it provides purer results. A well-pronounced dependence of foF2 trends on latitude tells us that the eect may be related to the F2layer storms due to the long-term increase of geomagnetic activity observed after 1965 (Fig. 4, top panel). Let us analyze the results obtained from this point of view. The main processes responsible for the F2-layer storm eects are known, they are neutral composition, temperature, and thermospheric wind changes at middle and lower latitudes while electric ®elds and particle precipitation strongly aect the high-latitude F2-region (see ProÈ lss, 1995, and references therein). The magnitude of negative storm eects increases with latitude due to a noticeable decrease in O/N 2 ratio. In contrast positive storm eects dominate at lower latitudes and they are mostly due to the increase of the equatorward thermospheric wind (see ProÈ lss, 1995;Mikhailov et al., 1995 and references therein). Therefore, the observed dependence of trends on invariant latitude (Figs. 2, 3) may be just related to this F2-layer storm mechanism. An additional support of this concept provides the foF2 long-term variation at Slough (Fig. 4) where observations are available from the early 1930s. Longterm variations of annual mean Ap 12 and dfoF2 were analyzed for (M+m) and (m) year selections. The least squares ®tting by the 4th (higher degree gives practically the same result) degree polynomial shows the anti-phase type of dfoF2 and Ap 12 long-term variations. As before error bars present the standard deviation over 12 monthly values. The periods of Only stations with signi®cant trends and a con®dence level ³90% are shown. Error bars present the standard deviation of seasonal (over 12 months) scatter of the slope K increasing geomagnetic activity (before 1945 and after 1965) are seen to correspond to negative foF2 trends while during the decreasing geomagnetic activity (1945±1965) small positive trend takes place. There is also a tendency for the trend to switch from negative to positive after 1990 in accordance with the change in geomagnetic activity (Fig. 4, top). This dependence is more pronounced for the (m) selection of years (Fig. 4, dashes) in accordance with the discussed results. Although ®tting curves give only a qualitative picture, the extrema in Ap 12 variations take place earlier or coincide with the extrema in dfoF2 variations con®rming the causal relationship between these parameters. Therefore, we may conclude that qualitatively foF2 trends at Slough station just re¯ect the long-term variation in geomagnetic activity. An increase of To check this conclusion diurnal variation of the trends was analyzed for the periods before and after 1965 at Slough, Moscow and Tomsk stations (Fig. 5). These three midlatitude stations are separated in longitude to demonstrate global character of the analyzed eect. Two (M+m) year selections over similar time intervals were chosen: 1947±1965 (18 years) and 1975± 1991 (16 years) to present the periods before and after 1965. The year 1965 is the turning-point in the long-term geomagnetic activity variation (Fig. 4. top) and if geomagnetic control of foF2 trends does exist these trends should be dierent for the two periods. Positive annual mean trends for all LT moments take place for the period prior 1965 and negative trends after 1965 for the three stations considered. Error bars give a seasonal (over 12 months) scatter in the trends. All hourly foF2 trends in Fig. 5 are signi®cant at the con®dence level ³75%. Annual mean K values were used for the F-test. Although the con®dence level is not high for some LT moments, the trends revealed demonstrate a consistent pattern of diurnal variation where individual K values seem not to be accidental.
Diurnal variations of foF2 annual mean trends at dierent invariant latitudes also clearly indicate a close relationship of these trends with geomagnetic activity. Figure 6 gives diurnal variations of trends for: (1) a subauroral station, Salekhard, (2) St. Petersburg station located in the transitional (auroral/midlatitude) zone, (3) a midlatitude station, Ekaterinburg, and (4) a lower latitude station, Tashkent. The period after 1965 is considered with (M+m) selection of years. Salekhard station has strong positive trends for nighttime hours and strong negative trends during daytime. Ekaterin-  . Diurnal variation of annual mean slope K at three stations for the periods of decreasing (1947±1965) and increasing (1975±1991) geomagnetic activity. Note dierent signs of trends for the two periods. Error bars present the standard deviation of seasonal (over 12 months) scatter in the slope K burg station demonstrates opposite behaviour with large negative nighttime trends and smaller trends during daytime hours. St. Petersburg shows mixed behaviour: the sub-auroral type for nighttime and midlatitude type during daytime hours. Low-latitude pattern of the trends is similar to the midlatitude one, but all values are more positive.
Let us consider a physical mechanism of these diurnal variations. Salekhard (F inv = 61.18°) is located in the main ionospheric trough during nighttime hours (Muldrew, 1965;Karpachev et al., 1996) next to the equatorial boundary of the diusive precipitation zone with the increased ionization produced by soft electrons (see for references Besprozvannaya, 1986). The equatorial boundary of this zone is known to shift to lower latitudes by about 2°per one unity of Kp increase (e.g. Andrews and Thomas, 1969). Thus, strong positive night-time trends (Fig. 6) just result from an intensity increase of soft electron precipitation due to the overall increase in geomagnetic activity after 1965 and the shift of the precipitation zone to lower latitudes. During daytime hours the equatorial boundary of this zone is located far to the north at F inv = 70±80°and we have strong negative foF2 tends resulting from the disturbed neutral composition and electric ®elds (ProÈ lss, 1980;Mikhailov and Schlegel, 1998).
Midlatitude trend diurnal variations (Ekaterinburg, Fig. 6) are due to disturbed neutral composition diurnal variations. Midlatitude negative F2-layer storm eects are known to be strongest in the post-midnight-early morning LT sector and they are much weaker in the afternoon (Wrenn et al., 1987;ProÈ lss, 1991, 1993, andreferences therein). This is due to the disturbed neutral composition with decreased O/N 2 ratio which is advected towards middle latitudes during night, rotates into Fig. 6. Diurnal variation of annual mean slope K for stations located at dierent invariant latitudes (given in brackets). Note strong and opposite types of diurnal variations for sub-auroral and midlatitude stations. Error bars present the standard deviation of seasonal (over 12 months) scatter in the slope K the day sector being shifted back to higher latitudes by diurnal varying thermospheric circulation (Skoblin and FoÈ rster, 1993;Fuller-Rowell et al., 1994;ProÈ lss, 1995). This eect is clearly seen for the afternoon hours with a tendency for trends to be even positive around 1500 LT.
St. Petersburg demonstrates the intermediate behaviour. In the 03±06 LT sector this station from time to time (depending on the level of geomagnetic activity) seems to be in the soft electrons precipitation zone like Salekhard and the trends are the least negative in this LT sector. On the other hand, the increasing geomagnetic activity after 1965 results in neutral composition and temperature perturbations and strong negative trends are seen in the morning LT sector. Negative trends are strongly decreased in the afternoon LT sector similar to the midlatitude station, Ekaterinburg.
As neutral composition perturbations decreases towards lower latitudes (e.g. ProÈ lss, 1980) the magnitude of negative trends is small even in the morning LT sector at the lower latitude station, Tashkent (Fig. 6). During daytime hours the increasing geomagnetic activity damps normal northward thermospheric circulation leading to positive F2-layer storm eects (ProÈ lss, 1995; and this results in positive foF2 trends at lower latitudes (Fig. 6). The existence of strong and latitudinal dependent diurnal variations in the magnitude of the trends is a strong argument against any manmade e.g. greenhouse origin of these trends. But such variations may be explained in terms of the F2layer storm eects related to the geomagnetic activity as was discussed earlier.

Discussion
A slightly modi®ed method earlier proposed by Danilov and Mikhailov (1999) was applied to the foF2 long-term trend analysis at 30 ionosonde stations. The slope K depends on latitude (Figs. 2, 3 and Tables 2, 3) with a pronounced decrease of the trend magnitude towards lower geomagnetic (invariant) latitudes for two models used in the analysis. Therefore, the proposed method of analysis with (m) or (m+M) selection of years allows us to ®nd systematic variations in trend magnitude. Meantime the other approaches (e.g. Bremer, 1998;Upadhyay and Mahajan, 1998) result in a chaos of various signs and magnitudes of the trends on various stations.
One of the key points of the proposed method providing its success is the use of 12-month running mean foF2 rather than just monthly medians. This strongly decreases the scatter in the analyzed material helping to reveal the trends. The application of an F-test to such smoothed observations to estimate the signi®cance of the trends may be questionable as the ®ltered data turn out to be dependent to some extent. However, it should be stressed that we use annual mean dfoF2 values belonging either to dierent solar cycles or dierent years, that is separated by 12 months. This span equals the ®ltering running interval and our values turn out to be at the opposite ends of the smoothing interval, virtually not aecting each other. Therefore, such annual mean dfoF2 values may be considered as independent. Due to relatively small number of pairs analyzed, the con®dence level is not high (about 75%) in some cases. But this is not important as the latitudinal and diurnal variations of the trends give, as a whole, a consistent picture showing the relationship to geomagnetic activity. On the other hand, one should keep in mind that all observed time series in geophysics and meteorology strictly speaking are never independent, nevertheless statistical methods are widely applied to such observations in practice (Panofsky and Brier, 1958). An example of the F-test application to the ionospheric trend analysis may be found in Bremer (1998). Estimating the signi®cance of the trends he used hourly F2-layer parameter observations which are known to be strongly correlated.
The sunspot number R 12 usually used in empirical ionospheric models is far from being the best  and in fact this index does not allow us to exclude completely the dependence on solar activity being used in foF2 versus R 12 regression. As thè`u seful signal'' is very small in the trend analysis this imperfection of R 12 results in scatter in analyzed points and various slopes K (both sign and magnitude) are obtained at various stations when all years are analyzed. The worst correlation of foF2 with R 12 takes place for the falling and rising phases of the solar cycles (the hysteresis eect), so these years were omitted from the analysis in the ®rst place Mikhailov, 1998, 1999). The years around solar maximum are also subjected to this uncertainty, but to a less extent and their inclusion to the trend analysis allows us, nevertheless, to obtain a consistent pattern of trends over all stations considered. Of course, the best way for the foF2 trend analysis would be not to use any reduction on solar activity with an index like R 12 . Our analysis for years of solar minimum when the solar activity reduction is the minimal gives the most consistent results: all signi®cant trends are negative with well-pronounced and steep dependence of K on invariant latitude (Table 3 and Figs. 2, 3). Acceptable results are obtained with the (M+m) selection of years as well. This tells us that the contaminating eect of the (M) years inclusion is not that strong. Indeed, a pronounced dependence of K on latitude takes place for (M) selection of years as well (Figs. 2, 3). Therefore, the (M+m) year selection may be recommended for the foF2 trend analysis as was proposed earlier by Mikhailov, 1998, 1999). An inclusion of (M) years may be important as well for stations where the period of observation is not long enough to work with (m) years only. For instance, we used the (M+m) selection of years in Fig. 5 to increase the number of points for the period before 1965.
Although there is an obvious relationship of foF2 trends with geomagnetic activity, the monthly Ap index is not a proper indicator for the F2-layer storm eects and its inclusion to the regression (model 2), in fact, does not remove the dependence on geomagnetic activity as supposed by Bremer (1998) and Jarvis et al. (1998). Indeed, a well-pronounced dependence of K on latitude takes place for model M2 as well (Fig. 3) with the decreased trend magnitudes only. Thus, we may conclude that the inclusion of Ap indices to the regression excludes the geomagnetic eect only partly without changing, in principle, the dependence of trends on geomagnetic (invariant) latitude. Moreover, the inclusion of Ap indices to the regression (model M2) inserts additional noise to the analyzed material increasing the scatter of points around the regression line (see Figs. 2 and 3, left hand columns). This is not surprising as the global Ap index cannot, in principle, take into account the whole complexity of F2-layer storm eects with positive and negative phases depending on season, UT and LT of storm onset, storm magnitude etc. Thus, the Ap index inclusion cannot be recommended for the F2-layer trend analysis.
It should be stressed that our conclusions contradict those in the recent publication by Bremer (1998). He found no latitudinal eect in the trends, but revealed a separation of the stations to two longitudinal groups with positive trends in Eastern Europe and negative ones in Western Europe. We found no such longitudinal eect as most of the revealed trends are negative regardless of longitude, but there is a well-pronounced latitudinal dependence. We believe that the reason for the contradiction with the results of Bremer (1998) lies in the dierences of approach. Bremer (1998) used absolute deviations from some model and all the years available for a given station. In this case the length of the data series used is inevitably quite dierent depending on the duration of the vertical sounding observations at this particular ionosonde. However, the sign of trends is dierent for the period prior to and after 1965, as follows from Fig. 5. This was the reason to separate these periods in our analysis. Further, Bremer (1998) analyzed annual trends averaging hourly and monthly values, but foF2 trends demonstrate strong diurnal variations as was shown earlier (Figs. 5, 6) and this inevitably will decrease the reliability of the trends revealed.
The proposed F2-layer storm induced mechanism for the foF2 long-term trends implies corresponding trends in hmF2. For the period with increasing geomagnetic activity and negative foF2 trends, as we have after 1965, one should expect positive hmF2 trends at middle and lower latitudes. The trends should be inverse for the period with decreasing geomagnetic activity. This follows from a well-known F2-layer negative storm mechanism related to neutral composition and temperature changes (e.g. ProÈ lss, 1995). Unfortunately, hmF2 trends inferred from M(3000)F2 are not as reliable as foF2 trends, nevertheless such analysis is being done and results will be published elsewhere. It is worth mentioning that there are indications of some long-term trends in the occurrence frequency of ionospheric storms (Sergeenko and Kuleshova, 1995;Sergeenko and Givishvili, 1997;Clilverd et al., 1998). This is in line with the proposed concept on the foF2 trends mechanism.
Total cooling of the upper atmosphere due to the greenhouse eect and related negative trend in hmF2 is discussed in some publications (e.g. Bremer, 1992;Ulich and Turunen, 1997). However, it may be shown that thermospheric temperature decrease would result in a positive trend in foF2 contrary to the observations. According to the isobaric F2-layer concept by Edwards (1989, 1990) the F2-layer peak follows, in its variations, the level of constant atmospheric pressure. This is a good approximation, at least during daytime hours, when vertical plasma drifts are not strong. Electron concentration NmF2 for a steady-state daytime midlatitude F2-layer is given by the expression of Rishbeth and Barron (1960): where q m and b m are given at the F2-layer maximum. For estimates it may be assumed that q µ [O] and b µ T 2 [N 2 ]. Then we may write using Eq (3) If [O] and [N 2 ] (molecular mass m 1 and m 2 ) are distributed in accordance with the barometric law where H = kT/mg and n 0 and T 0 are the concentration and temperature at the base height h 0 , the pressure and It follows from Eq. (6) that the ratio R remains constant at any ®xed value of pressure P and at any temperature height pro®le provided T 0 , n 10 and n 20 are constant. This is valid for any height and for hmF2 as well, so the ®rst term in Eq. (4) equals zero. Therefore, the expected temperature decrease due to the greenhouse eect should result in a positive NmF2 trend as follows from Eq. (4) Hierl et al. (1997) give weaker temperature dependence, but in any case this rate constant increases with temperature for usual ionospheric temperatures.

Conclusions
The main results of our analysis may be listed as follows: 1. A slightly modi®ed version of a method proposed earlier by Danilov and Mikhailov (1999) was applied to the foF2 long-term trends analysis on 30 mid-and highlatitude ionosondes of the Northern Hemisphere. Years of solar minimum (m), maximum (M) and (M+m) were analyzed separately. Trends for 12 and 00 LT calculated over the (m) years were shown to be more negative and signi®cant at a greater number of stations compared to the (M) selection of years. The inclusion of (M) years to the trend analysis in fact contaminates the initial material although not to such extent as the years of falling and rising phases of the solar cycle Mikhailov, 1998, 1999). The (M+m) year selection provides an acceptable result and may be recommended for foF2 long-term trend analysis. The present analysis con®rms our previous result on the dependence of the foF2 trends on geomagnetic (invariant) latitude with strong negative trends at high and small or positive trends at lower latitudes for the period analyzed 1965± 1991.
2. The revealed dependence of the foF2 trends on invariant latitude clearly indicates the geomagnetic control and relationship with F2-layer storm mechanisms. An inclusion of the Ap index to the regression does not remove the geomagnetic dependence as proposed in some publications, but only contaminates the analyzed material without changing the result obtained in principle.
3. It is shown, for the ®rst time, that there exist periods with negative and positive foF2 trends, which correspond to the periods of long-term increasing/ decreasing geomagnetic activity. The (M+m) analysis at Slough station for instance, gives the periods with negative foF2 trends: 1934±1948, 1967±1989 and periods with positive trends: 1950±1968, and after 1989 in accordance with the smoothed variation of annual mean Ap 12 index used as an indicator of geomagnetic activity. Dierent signs of the trends during the periods of increasing/decreasing geomagnetic activity take place for all LT moments at each individual station considered.
4. Strong diurnal variations in the trend magnitude are revealed for stations located at dierent latitudes. Strong positive foF2 trends in the post-midnight-early morning LT sector and strong negative trends during daytime hours take place for the sub-auroral stations for the period of increasing geomagnetic activity after 1965. In contrast middle and lower latitude stations demonstrate negative trends in the early morning LT sector and small negative or positive trends during daytime hours for the same period. The existence of such diurnal variations in the foF2 trend magnitude is a strong argument against any manmade (e.g. greenhouse) origin of such trends. 5. All the morphological features revealed of the foF2 trends may be explained in the framework of contemporary F2-region storm mechanisms. They include disturbed neutral composition, temperature and thermospheric winds variation (for middle and lower latitude stations) as well as soft electron precipitation for sub-auroral stations. This newly proposed geomagnetic storm concept to explain the foF2 long-term trends proceeds from a natural origin of the trends rather than an arti®cial one related to the thermosphere cooling due to the greenhouse eect.