A 22-year cycle in the F layer ionization of the ionosphere

The double-sunspot-cycle variation in terrestrial magnetic activity has been well known for about 30 years. In 1990 we examined and compared the low-solar-activity (LSA) part of two consecutive cycles and predicted from this database and from published results the existence of a double-sunspot-cycle variation in total electron content (TEC) of the ionosphere too. This is restricted to noontime when the semi-annual component is well developed. Since 1995 we have had enough data for the statistical processing for high-solar-activity (HSA) conditions of two successive solar cycles. The results confirm the LSA findings. The annual variation of TEC shows a change from an autumn maximum in cycle 21 to a spring maximum during the next solar cycle. Similar to the aa indices for geomagnetic activity the TEC data show a phase change in the 1-year component of the Fourier transform of the annual variation. Additionally we found the same behaviour in the F-layer peak electron density (Nmax) over four solar cycles. This indicates that there exists a double-sunspot-cycle variation in the F-layer ionization over Europe too. It is very likely coupled with the 22-year cycle in geomagnetic activity.


Introduction
The main data source for the work on which this report is based was provided by the dierential Doppler eect on the signals of the US Navy Navigation Satellites (NNSS, formerly TRANSIT, in almost polar circular orbits with a height around 1100 km) (Leitinger et al., 1975;Leitinger and Putz, 1978).
Two European receiving stations have been in continuous coordinated operation since the beginning of 1975: Lindau/Harz in Germany (51X6 N, 10X1 E) and Graz in Austria (47X1 N, 15X5 E). The evaluation results are latitudinal pro®les of ionospheric electron content, which means sequences of data equidistant in latitude (data distance 0X5 in geographic latitude of the 400-km ionospheric points). Up to the mid-1980s the observations from Lindau gave more material and were used for the statistical investigation for the interval 1975±1986. The data of the station Graz were applied indirectly, namely to calibrate electron content by means of thè`t wo-stations method'' (Leitinger et al., 1975). For the high-solar-activity interval of 1988±92 the observations from Graz were used. For a given latitude there is no signi®cant dierence in monthly medians and quartiles calculated from Graz and Linda data.
For this report the electron-content values for the geographical latitudes 60 N, 55 N, 50 N and 45 N were selected. The data from Graz which reach 30 N show that the results are valid down to 35 N, where the in¯uence of the equatorial anomaly begins at HSA conditions. The total electron content (TEC) data used for this study are monthly medians gained over 2-h intervals. The data were divided into two classes: low solar activity (LSA) ( 40; nominal monthly mean sunspot number for modelling purposes: 20) and high solar activity (HSA) [130 170 (cycle 21), 120 180 (cycle 22), respectively, nominal value 150]. (The widening of the interval for HSA/cycle 22 was necessary in order to ensure data from at least 2 years for each month. Using data according to the criterion 130 12 170 ± all months from November 1988 to December 1991 ± leads to nearly identical results in statistical investigations.) The amount of TEC data from intermediate levels of solar activity (MSA) is not sucient to make clear statements about the ionization behaviour under these conditions. The results of investigations of peak electron density (x mx ) show that there is no substantial dierence between the annual variation for MSA and HSA.
These selection criteria enabled us to include all data from the years 1975 and 1976 and the data from July 1984 to December 1986 into the LSA class and data from 1978±1982 selected according to Table 1 and from 1988±1992 selected according to Table 2 into the HSA class. The comparatively large variation in HSA-might be a problem, especially when seasonal dierences are to be investigated. The month-to-month dierences in are cancelled out at least partially in averages: the cycle 21 vernal average (March 1979(March , 1982April 1980April , 1981 is 153, the autumnal one (September, 1978(September, , 1981October 1980October , 1981 158; the cycle-22 vernal average (March and April 1989, 1991 is 137, the autumnal one (September and October 1988, 1989, 1991 140. Both for monthly medians of TEC and of x mx (or foF2) one ®nds considerable dierences comparing data gained under comparable seasonal and solar activity (Y 12 or any other solar index) conditions. Therefore some averaging is necessary. In the TEC case this was done by selecting the observed data into (12 Â 9, cycle-21, or 12 Â 12 months, cycle 22) classes (the 12 months of the year and 9 or 12 LT intervals). Medians were calculated for each data class.
To extend the investigation to a wider range of solar cycles we obtained the annual variation of x mx with ionosonde scalings (hourly values of foF2) from several ionosonde stations (Table 3). For x mx linear regressions were applied to ®nd the relation between solar activity ( 12 ) and peak electron density for each month and for each hour of the day. From the linear regression relation x mx was calculated for a selected level of solar activity. The regressions were based on dierent data selections, e.g. all data of one solar cycle, data from the rising part of a cycle and data from the falling part, the interval around the solar maximum. Some regressions failed and gave negative slopes and/or negative 12 0 interception points. However, no failures occurred during daytime. For HSA ( 12 150) and intermediate levels of solar activity (e.g. 12 85) the 22-year periodicity is stable and does not depend on the data selection for the regressions: it appears when all data of one cycle are included, and in partial data (rising part, falling part, etc.). The examples used in this report show HSA ( 12 150) cases of one ionosonde station, Rome, Italy (41X8 N, 12X5 E).
An additional remark: attempts to ®nd a solar-cycle dependence in tropospheric dynamics (``weather'') have been based on the cycle-to-cycle dierences of the semiannual component of magnetic activity (Baranyi and LudmaÂ ny, 1992, 1995a, 1995b). An in¯uence on the ionosphere is much more likely than an in¯uence on the troposphere

Data Analysis
The results are discussed in terms of the Fourier transform of the twelve monthly medians of the annual variation (cosine terms 0 Á Á Á 6 , sine terms 1 Á Á Á 5 ) and reconstruction to order n: p n t n j0 j cosjxt n j1 j sinjxt 0 1 cosxt 1 sinxt 2 cos2xt 2 sin2x t Á Á Á g 0 g 1 cosxt À / 1 g 2 cos2xt À / 2 Á Á Á with g j 2 j 2 j q and tan / j j j X x 2p 12 t in months or x 2p 365X25 t in days  The Fourier decomposition gives the possibility to study asymmetries in the annual variation by means of the relation of the 1-year component to the 1/2-year component.

Behaviour of the amplitudes
The average values (g 0 0 ) increase with decreasing latitude. From solar cycle to solar cycle the change in value of the maximum of the average is less than 10%. The general level of ionization (averaged over 1 year) shows nearly no changes from solar cycle to solar cycle. A minimal value of the annual component (g 1 2 1 2 1 q ) appears around noon, therefore the semiannual component has a strong in¯uence for this timeinterval. For cycle 21, LSA, the positions of the absolute maximum of the semi-annual component (g 2 2 2 2 2 q ) and the noon minimum of the annual component coincide. For cycle 22, LSA, the annual component predominates during the whole day, except in the interval 1100±1300 LT. For HSA, predominance of the annual component over the semi-annual one exists only during night-time (Fig. 2, top). This is the reason why the annual variation shows distinct peaks during daytime. The annual variation has a well-de®ned semi-annual character (cf. Fig. 3) and the dierence between vernal and autumnal maximum is more pronounced than during LSA.
For HSA of cycle 22 the semi-annual amplitude reaches the maximum very late (1700±1900 LT), and therefore the semi-annual component is still visible in the annual variation up to midnight (Fig. 2). The vernal maximum shows up until 2200 LT, contrary to the cycle-21 case.    (Table 4). For the other daytime intervals we ®nd the maximal values between the ®rst half of July and the ®rst half of August (dierent from the following cycle). Higher latitudes show the same results. The high winter night values are caused by the strong semi-annual component with maxima in June and December.
For HSA there is a change in phase from day to night. From 1900 to 0900 LT the maximum of the annual component occurs in the ®rst half of June and from 0900 to 1700 LT between the ®rst half of December and the second half of February (Table 4, Fig. 2, top). The interval 1700±1900 LT is a transition between night-and daytime behaviour (Table 4). During 1978±1982 the phase of the annual component shows a clear leap from night to day but a smoother one from day to night. All latitudes give the same results.
During cycle 22 (LSA) the maximum of the annual component also appears during summer; from 1500 to 0900 LT during the second half of June (same result in cycle 21). For the other daytime intervals we ®nd the location of the maximal values in the ®rst half of June: one or two months earlier than in the previous cycle (Table 4). Higher latitudes show the same results. The annual variation is comparatively¯at around noon because the 4 month component has a maximum in summer (between the maxima of the semi-annual component).
For HSA there is a change in phase from day to night. From 1900 to 0900 LT the maximum of the annual component occurs in the ®rst half of June (like cycle 21) but from 0900 to 1700 LT between the second half of January and March: one or two months later than in the previous cycle (Fig. 3, Table 4). The interval   Fig. 2, bottom). The change of phase of the annual component is smoother than in cycle 21 and the change occurs earlier for 60 N than for 50 N.

Semi-annual component
For cycle 21 for LSA the maximum of the semi-annual part shows a dierent position for day and night. At night it occurs around the solstices (1900 to 0700 LT, second half of June), and during the day around the equinoxes (April, October). During the interval 0500± 0700 LT there is a night-to-day change (Table 4).
During the time of HSA the phase of the semi-annual component is very stable (April, October) ( Table 4). Only for high latitudes for 0100±0500 LT does the phase change to May (55 N) and June (60 N). The development of the``visibility'' of the autumn maximum occurs later (10 a.m.) than in the following cycle, and disappears earlier (Figs. 2 and 4, top).
For cycle 22 for LSA the maximum of the semiannual part shows almost the same behaviour as during the previous cycle (Table 4). The change from day to night behaviour is more distinct (1700±1900 LT, February).
During the time of HSA the phase of the semi-annual component is very stable too, but in daytime it occurs during this cycle half a month earlier (second half of March, ®rst half of April) (Table 4 and Figs. 2 and 5, bottom). Only for latitudes from 50 to 60 N does the phase change from 0100 to 0500 LT to June (Table 4).

4-month component.
During HSA the 4-month component also visibly in¯uences the annual variation. Cycle 21: the maxima occur at the end of October, February and June and intensify the autumn maximum with the annual variation. Cycle 22: the maxima occur at the begin of March, July and November and strengthen the spring maximum of the annual variation.

Long-term behaviour of geomagnetic activity
The long-term behaviour of geomagnetic activity follows roughly the solar activity. However, marked dierences were already found at the beginning of this century (e.g. Cortie, 1912). The maximum of geomagnetic activity is delayed when compared with the maximum of solar activity. Geomagnetic activity has a pronounced annual variation (dominant semi-annual component) whereas solar activity has none (Fraser-Smith, 1972). Re®ned studies revealed that the annual variation of geomagnetic activity is not due to an in¯uence of the atmosphere-ionosphere-magnetosphere system of the earth but is an eect of the earth-sun geometry (compare, e.g. Russell andMcPherron, 1973, Triskova, 1989). For the development of the semi-annual variation there exist two theories: the axial hypothesis (Priester and Cattani, 1962) and the equinoctial hypothesis (Bartels, 1963), which has been used for ionospheric investigations (e.g. Apostolov and Alberca, 1995).

Vernal-autumnal asymmetry in the seasonal variation of geomagnetic activity
A double-sunspot-cycle variation also occurs in terrestrial magnetic activity (Chernosky, 1966). Chernosky found that in even-numbered cycles the last half of the sunspot-number cycle is more active than the ®rst half, and the converse is true for the odd-numbered cycles. The curve of the 22-year cycle of magnetic activity is not symmetric to the minimum between two cycles. MuÈ nch (1972) found an annual wave in the odd-numbered sunspot cycles and explained its generation by an asymmetry in sunspot activity in the two solar hemispheres and by the inclination of the sun's equator with respect to the ecliptic. Meyer (1972) investigated C8 character ®gures and found two annual waves to exist in antiphase, with maxima around the equinoxes.
In 1988 the vernal-autumnal asymmetry in the seasonal variation of geomagnetic activity was investigated by L. T! riskovaÂ . In investigating the variation of geomagnetic activity, not from the viewpoint of solar cycles but with respect to the polarity of the main solar dipole, an annual wave can be observed with maxima alternatively in the periods of vernal and autumnal equinoxes. The phenomenon could be explained by the asymmetry in the main solar dipole ®eld and the result is a stronger in¯uence of the dominant polarity in one of the solar hemispheres. It enhances or attenuates one of the maxima of geomagnetic activity. After 1913 the dominant polarity of the southern solar hemisphere had a greater in¯uence which, under negative polarity (e.g. 1972±1980) enhances, and under positive polarity (e.g. 1960±1969, 1982±1987) attenuates the vernal geomagnetic activity maximum in comparison with the autumnal one (Triskova, 1989).

The in¯uence of magnetic activity on mid-latitude F-layer ionization
Assuming that a suitable geomagnetic index is an indicator for particle precipitation in higher latitudes, the (statistical) eect of the annual variation of geomagnetic activity on the annual variation of F-layer ionization could be based on the Joule heating eect of energetic particles reaching E-and D-layer heights. A widely accepted theory for F-layer``negative storm eects' ' (e.g. Taeusch et al., 1971;ProÈ lss, 1987;ProÈ lss and Roemer, 1987) assumes changes of the thermospheric wind system and changes of thermospheric neutral gas composition. The wind change depresses F-layer ionization in mid-latitudes because the plasma is pushed to lower altitudes, which results in increased recombination. The composition change decreases the , which also leads to a depression of ionization because recombination is enhanced as compared with production. The``negative storm eect'' is a typical phenomenon which is observed on the day following the day of the onset of a geomagnetic storm. In general it is observed in connection with moderate and severe geomagnetic storms. Usually the mid-latitude F-layer reaction to weak storms and to substorms is not directly observable because weak eects are masked by ionization variations not related to geomagnetic activity (day-to-day variability, TIDs, etc.). Experience with a large amount of European data (electron content, peak density) shows that``positive storm eects'', which can occur in the afternoon when the onset of the geomagnetic storm is in the (early) morning, do not cancel out the``negative eects''. We have reason to believe that the statistical eect of geomagnetic disturbances on F-layer ionization in (European) mid-latitudes is a depression of ionization. Therefore the annual asymmetry of F-layer ionization in mid-latitudes should be in anti-phase with the vernal-autumnal asymmetry of geomagnetic activity. This is what we have observed. The dominance of negative storm eects in summer was shown by Putz et al. (1990) for three European stations. At Stanford, USA (35 N), in summer, the negative eects were much larger than the positive ones (Titheridge and Buonsanto, 1988). Only in winter can positive eects dominate (Putz et al., 1990;Titheridge and Buonsanto, 1988). Since no reports on statistical studies of equinoctial storms were found, we made an investigation of the eect of geomagnetic disturbances in the following way. Long series of the quantity D x mx À x mx ax mx were calculated for given local time and compared with the daily geomagnetic disturbance index e p (x mx : monthly average). To account for the delay of ionospheric eects compared with geomagnetic eects we took the e p of the previous day. For each month we calculated the sum of D when e p was greater than a limit value. For the x mx data from Rome, Italy, from the time-interval 1958 through to 1994 we obtained, with e p limits between 5 and 30, very stable results: only winter sums of D are positive, all the others negative. No dierence was found between the months around the equinoxes (March, April, September, October) and summer. The D sum for the whole year is strongly negative.
We do not want to rule out other possibilities to explain the double sunspot cycle observed in electron content and in peak density, but it is unlikely that a pure solar-activity explanation can be found. There is no reason to believe in seasonal changes of the relation of a solar-activity indicator to the solar EUV output. For LSA of cycle 21 the maximum of the annual component occurs later in summer and therefore supports the development of an autumn maximum. For HSA of cycle 21 the maximum slips to the ®rst half of winter (December, January) and causes the same eect. The autumn maximum (cycle 21) and the spring maximum (cycle 22) is additionally increased by the same-season maximum of the 4-month component. The change of the time of the maximum is supported by data and descriptions published in previous publications for cycles 20 and 21 (Yuen and Roelof, 1967;da Rosa et al., 1973;Huang, 1979). The paper by Garriott et al. (1970) displays electron content from the Faraday eect on the signals of ATS-1. The data from 1968 show a clear spring maximum both for Stanford (34X2 N, 234.5 E) and Hawaii (19X8 N, 202X8 E). 1968 was a year with fairly uniform solar activity (103 12 111). Our Fourier analysis for the Stanford 1968 data is shown in Fig. 6. (Compare also Titheridge et al., 1996.) For Europe, GaldoÂ n and Alberca (1970) show a spring maximum for 1965for , 1966for and 1967cycle 20). The vernal-equinox values exceed the autumnal ones by more than a factor of 2. We suspect an overestimation because of arti®cial enhancement by the normalization to a constant level of solar activity. The European data were gained by means of the Faraday eect on the 40/41-MHz signals of a low orbiting satellite (Explorer 22) which coupled diurnal and annual variation. A comparison with the southern hemisphere brought no results for our investigations (Titheridge et al., 1996). There seems to be no marked dierence between vernal and autumnal maximum in the southern hemisphere.
The investigation of the annual variation of peak electron density (x mx : Fig. 7) also indicates the existence of a 22-year cycle in daytime F-layer ionization (considering data as early as solar cycle 19).
We show results for Rome (41X8 N, 12X5 E ± Fig. 7) and remark that the amplitude of the 22-year periodicity gets weaker when the latitude of the ionosonde station is increased [e.g. when the results for Slough (51X5 N, À0X6 E) are compared with those for Rome]. This seems to correspond with a decrease in the ratio of the amplitudes of the semi-annual component com-pared with the annual component (for TEC compare Fig. 2).
No distinct and persistent double-sunspot-cycle behaviour can be found for solar activity. In particular there is no signi®cant semi-annual component in solaractivity spectra. There is no indication of an annual variation in the relation between a solar-activity indicator (based on sunspot numbers or on solar radio¯ux) and the EUV output of the sun.
But, as already mentioned, the double-sunspot-cycle variation also occurs in terrestrial magnetic activity. Edwin Chernosky found an even cycle-odd cycle asymmetry in the average of``disturbed-day occurrence'' from grouped data for 1884±1963 (Chernosky, 1966). Ludmila T! riskovaÂ detected a very clear vernal-autumnal asymmetry in the average annual variation of the aa index (see Mayaud, 1972) and a change of the maximum from spring in odd cycles to autumn in even cycles. This behaviour was demonstrated for these parts of the solar cycles from 1873 to 1980 which have a well-developed solar dipole polarity (Triskova, 1989). An analysis of monthly medians of aa from solar cycles 18±23 using essentially the Fourier method was applied to the TEC, and x mx data shows that the phase of the annual component might be responsible for the 22-year period in geomagnetic activity (Fig. 8).
This aa-index behaviour might provide a basis for explanations of the double sunspot cycle in the total electron of the ionosphere, because the geomagnetic activity certainly in¯uences the ionospheric behaviour.
Qualitatively the relation between magnetic activity (described by a magnetic-activity indicator) and F-layer ionization can be explained by means of varying energy input into the high-latitude thermosphere (Joule heating and other particle precipitation eects). Quantitative explanations are a dicult task; for instance, the magnetic activity indicators available for long-term investigations have no direct relation to particle precipitation nor to current systems.