A. V. Mikhailov
Institute for Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Troitsk, Moscow Region, Russia
V. V. Mikhailov
Institute of Applied Geophysics, Moscow, Russia
Empirical ionospheric modeling and prediction widely use various indices to specify the variations of ionospheric parameters. Monthly, weekly, daily, and even hourly indices are used in practice [Bradley, 1993; International Radio Consultative Committee (CCIR), 1990; Mikhailov et al., 1990a; Secan and Wilkinson, 1997; Turner and Wilkinson, 1979; Wilkinson, 1986a]. The idea of index use is based on the assumption that key ionospheric characteristics, such as foF2, M(3000)F2, foF1, and foE, are associated in a systematic way with certain measurable quantities concerned with solar and geomagnetic activity. However, different indices should be used for F2, F1, and E layer parameters [CCIR, 1990], because physical mechanisms of their formation are different and independent to a great extent. The same is valid for foF2 and M(3000)F2. Usually it is assumed that what is best for foF2 should also be best for M(3000)F2, but this is not obvious. For instance, the dependence of foF2 and hmF2 on atmospheric parameters is different, and one may expect that different indices may turn out to be the best for foF2 and M(3000)F2.
Direct solar indices take into account solar activity level expressed either by traditional sunspot number R (usually a 12-month running mean R12 is used) or by solar radiation in selected spectral intervals (like F10.7 or I58.4 ). Keeping in mind the physical mechanism of the F2 region formation, the sunspot number R12 is far from being the best index for foF2. It is not related directly to solar EUV radiation which is responsible for the ionization and to a great extent for the state of the upper atmosphere at F2 layer heights. Research adherence to R12 as the input parameter for empirical ionospheric models like those of CCIR [1967-1990] or Chernyshov and Vasil'eva  probably is explained by the fact that long and continuous observations were available only on sunspot numbers at the time that these models were developed. The ionospheric F2 region is known to be governed by solar ionization radiation, highly variable thermospheric neutral composition, and dynamical processes. That is why there is no one-to-one relationship for foF2 with any direct solar index. A well-known effect of hysteresis in solar cycle foF2 variations [Rao and Rao, 1969; Smith and King, 1981] may result in a 1-MHz difference for annual mean foF2 at the same R12. For a particular month the difference may be even higher: up to 1.5 MHz [Mikhailov, 1993]. This means that foF2 versus R12 regression accuracy cannot be improved in principle as it is limited by this hysteresis effect. A physical explanation for the hysteresis type of solar cycle foF2 variation is proposed by Mikhailov and Mikhailov [1994, 1995a], but it is stressed that the effect may be considered as a result of improper solar index application.
The other problem with R12 use is the "saturation effect" at high solar activity level. According to CCIR recommendations [CCIR, 1967-1990] also used in the International Reference Ionosphere (IRI) [Bilitza, 1990], a linear relationship between R12 and monthly median foF2 should be used for R12 < 150 and unchanged foF2 for R12 > 150 throughout the solar cycle. But linear dependence is not valid in many cases, and the recommended limitation on foF2 at high solar activity can give large errors in foF2 prediction [Mikhailov, 1993]. Despite all difficulties with R12, it is considered the basic index of solar activity for ionospheric modeling and prediction, and other indices are related to R12 (see the references of Bradley ).
Since the end of the 1940s solar radio emission at l = 10.7 cm was measured regularly, the F10.7 index, expressed in units of 10-22 W m-2 Hz-1, is widely used in aeronomy as an indicator of solar activity level. All modern thermospheric models as well as models of solar EUV radiation are based on the index F10.7. This is due to the fact that solar radio emission at l = 10.7 cm is generated in about the same areas on the Sun as EUV radiation responsible to a great extent for the state of the upper atmosphere and ionosphere. Nevertheless, analysis [CCIR, 1990; Kouris et al., 1994; Mikhailov et al., 1990a] has shown that the use of monthly or 12-month running mean F10.7 values instead of R12 does not improve essentially the foF2 versus solar activity regression accuracy.
The use of solar flux at l = 58.4 nm, which is proportional to the total flux in the spectrum range of l 100 nm as an index for foF2 regression, turned out to be not very efficient [Mikhailov et al., 1990a]. A similar conclusion follows from analysis of results obtained by Lakshmi et al. , where the dependence of foF2 versus the measured solar flux in the l= 17-19 nm interval was used. Such results are not surprising, as solar EUV radiation reflects only one side of the F2 region formation, namely,photoionization. From this point of view, the traditional 12-month running mean sunspot number R12 seems to be more preferable than other direct solar indices as it serves implicitly as an indicator not only of ionization efficiency, but of the overall state of the upper atmosphere. On the other hand, it should be kept in mind that the foF2 versus R12 regression accuracy can be improved using a nonlinear dependence instead of a linear one [Jones and Obitts, 1970; Mikhailov, 1993], and so R12 can be efficiently used in practice.
Ionospheric indices are derived from observed trends in ionospheric characteristics measured by the worldwide ionosonde network. Two types of ionospheric indices exist: truly ionospheric indices such as IF2 [Minnis, 1955; Minnis and Bazzard, 1960], the Australian index T [Caruana, 1990; Turner, 1968], and index MF2 [Mikhailov and Mikhailov, 1995b] and model-oriented indices such as IG [Liu et al., 1983], and RESSN [Mikhailov et al., 1990b]. All ionospheric indices except for MF2 give effective sunspot numbers which provide the best regression accuracy for foF2 in the course of a solar cycle. The MF2 index is an effective noon foF2 over the northern hemisphere normalized by a magnetic factor M. Model-oriented indices are developed to work with particular empirical models: IG with the CCIR [1967-1990] model and RESSN with MUF Forecast [Chernyshov and Vasil'eva, 1973], used for HF communication prediction. All ionospheric indices (especially monthly) were shown to provide much better regression accuracy in comparison with to R12 for monthly foF2 [Liu et al., 1983; Mikhailov et al., 1990a, 1996; Wilkinson, 1986b]. But there is a problem with using ionospheric indices in practice. Only smoothed 12-month running mean indices can be predicted in the long-term with acceptable accuracy, but the regression of foF2 with such smoothed indices is not as good as with monthly ones. Thus the overall accuracy gain with ionospheric indices use instead of R12 is not too high: about 11% for predictions 6 months in advance and 18% for predictions 12 months in advance for IG12 [Liu et al., 1983] and about 13% when RESSEN 12 was used [Mikhailov et al., 1990b]. So the problem is to derive such an ionospheric index which could demonstrate the merits of monthly indices (that is high regression accuracy of foF2 with solar activity) and which could be predicted in the long-term (1-12 months in advance) with acceptable accuracy as well.
An attempt to produce an appropriate ionospheric index MF2 was undertaken in the framework of the European PRIME (COST-238) project by Mikhailov and Mikhailov [1995b]. This new index was used to develop monthly median foF2 and M(3000)F2 ionospheric model MQMF2 over Europe [Mikhailov et al., 1996]. Comparison of MQMF2 with the CCIR model (based on R12 ) in a retrospective mode (16,000-18,000 comparisons) gave an overall standard deviation decrease by 30-50%. Comparison with the CCIR approach for long-term (3-12 months in advance) predictions for the rising phase of solar cycle 22 gave essential improvement of prediction accuracy when the MF2 index was used. So this proposition seems to be very promising and is worthy of further development. The aim of this paper is to try to improve the MF2 index by taking into account additional ionosonde observations, to make a comparison with other direct and ionospheric indices used in practice, and to propose a method for MF2 long-term prediction convenient for practical use.
The idea of MF2 index derivation is given by Mikhailov and Mikhailov [1995b]. The only difference of the new approach is in using the Chapman function of the solar zenith angle instead of cosc for the "magnetic factor" M [Besprozvannaya, 1966; Rothwell, 1962] calculation. This allowed us to include additional high-latitude ionosonde stations in the procedure of index derivation. So the new index MF2 is found using the following expressions:
cL and cMC being solar zenith angles at a given and magnetically conjugate points at the same UT moment. The reduction foF2 by M factor gets in order to some extent foF2 data on ionosonde stations located in different latitudinal and longitudinal zones. The new index MF2 is defined as the foF2/M value found for an optimum Chc which is so chosen for each month that the standard deviation in the foF2 versus MF2 regression overall for the ionosonde stations is minimized. Monthly indices MF2 for 1945-1996 are listed in Table 1.
Monthly indices MF2 show the regularity in seasonal and solar cycle variations, and this feature is used in the MF2 index prediction method (see below). Figure 1 shows an example of this regularity in MF2 variations during the 1969-1979 decade. Well-pronounced semiannual peaks with relative minima during solstice periods are similar to midlatitude median foF2 variations. The difference is seen in annual variations: unlike monthly median foF2, summer MF2 values are higher than winter ones. The "winter anomaly" effect for MF2 takes place only during years of very high solar activity (1957-1958 and 1990-1991; see Table 1). Ionospheric index T variations are given in Figure 1 for comparison. Unlike MF2, monthly index T does not show as a rule any regularity in its variation.
Two kinds of MF2 index comparison with other indices should be done: (1) a comparison with monthly ionospheric indices which are known to provide the best regression accuracy for foF2 with solar activity level and (2) a comparison with smoothed 12-month running mean indices which are used in practice for foF2 and M(3000)F2 modeling and long-term prediction. In both cases, we will analyze the regression accuracy of foF2 (or M(3000)F2 ) versus any chosen index. A polynomial of the third degree is used for the regression [Mikhailov, 1993]. A special procedure was developed to prevent the regression curve from unnatural behavior at the ends of the index interval (at low and high solar activity). Although such model-oriented indices as IG are supposed to be used with their own "mother" models, they may be considered independently as well for our regression analysis like other indices. We will operate with standard e (in megahertz) and relative mean d (in percent) deviations given by expressions
where D = foF2 pred - foF2 obs.
The results of the regression analysis of the first type are given in Table 2 for the ionosonde station Arkhangelsk (64.6o N, 40.5o E). Monthly ionospheric indices IF2, IG, T , MF2 (old version by Mikhailov and Mikhailov [1995b]), and MF2 (new version, Table 1) along with the traditional R12 were used for comparison. Three parts of the day, three seasons, and three levels of solar activity during the 1957-1990 period were analyzed. The number of comparisons (ranging from 1600 to 3100 depending on conditions) is sufficient to consider the results statistically significant. The analysis shows that new and old MF2 indices give very close results, being a little bit more efficient than IF2 and IG. Index T is comparable with MF2 and turns out to be even more efficient in some cases. Index R12 is systematically worse than MF2, by 27% on average. The main result of this comparison is that the newly developed index MF2 is as efficient as the other monthly ionospheric indices.
The second type of comparison is made with smoothed 12-month running mean indices R12, IF212 , IG12, and T12 which are really used in practice for long-term HF radio communication predictions (Table 3). Some additional stations (Sofia, Sverdlovsk) were used in the analysis and gave similar results not listed here. The results of similar comparison for Moscow, Slough, Uppsala, and Athens ionosonde stations with the old version of the MF2 index may be found in the work of Mikhailov et al. .
The results of MF2 comparison with smoothed 12-month running mean indices show that the MF2 index provides systematically better regression accuracy than any index in question, either direct solar ( R12 ) or ionospheric. The other result is that smoothed ionospheric indices give rather little accuracy improvement compared with R12.
The analysis has shown that such well-known effects in foF2 solar cycle variations as "saturation" at high solar activity and "hysteresis" in the course of a solar cycle related with R12 use are absent when the MF2 index is applied. This advantage of the use of ionospheric indices over direct solar indices was pointed out earlier by Mikhailov and Mikhailov .
Similar regression analysis was made for the M(3000)F2 parameter. It should be kept in mind that M(3000)F2 data are much less reliable compared with foF2 and they are not consistent at some ionosonde stations. A comparison with inconsistent M(3000)F2 data may result in a wrong conclusion about the tested index. So a thorough examination was made to select reliable stations for further index comparison. Among them is Lannion (48.45o N, 356.73o E); the results on this station for the period 1957-1990 are given in Table 4.
The results of our comparison for various geophysical conditions show that traditional sunspot number R12 provides the best overall regression accuracy in comparison with other indices. The gain is noticeable especially during daytime, equinox, and high solar activity. Only MF2 provides comparable accuracy in some conditions; the other indices are systematically worse. Similar results were obtained for some other European ionosondes.
Using the regularity in the MF2 index seasonal and solar cycle variations similar to monthly median foF2 changes (Figure 1), a method for its long-term prediction can be proposed. It is based on the MF2 relationship with any smoothed index R12, IG12, IF212, or MF212. Analysis has shown that the best results can be obtained if different phases of the solar cycle are analyzed separately for each month. The period of 1957-1988 was chosen for the analysis when the amount of ionosonde observations was sufficient to get monthly MF2 with the highest accuracy. Three phases of the solar cycle were considered: minimum plus rising phases (1963-1967, 1975-1978, 1985-1988), maximum phase (1957-1959, 1968-1970, 1979-1981), and falling plus minimum phases (1960-1965, 1971-1976, 1982-1986). The results of regression analysis are given in Table 5.
It is seen that MF2 obtained from R12, IG12, IF212, or MF212 can be found with prediction accuracy ranging from 2.2 to 3.6%, which may be considered acceptable for practical use. Ionospheric indices provide better accuracy than R12. Long-term prediction of MF212 can be carried out using the well-known McNish and Lincoln  method, as four complete solar cycles of observed MF2 indices are available now. It should be stressed that Table 5 gives an estimate of the maximal accessible accuracy as it was obtained in retrospective mode for observed smoothed indices.
Using the MF2 with R12 relationship, a forecast of MF2 indices was made for solar cycle 23 (Table 6). Space Environment Center (SEC) prediction of smoothed sunspot numbers R12 [Space Environment Center, 1997] was used for MF2 calculations.
The final goal of all index considerations is to improve the prediction accuracy for monthly foF2 and M(3000)F2. To estimate the efficiency of the proposed approach, we performed foF2 long-term predictions for solar cycle 21 (1977-1985) using officially predicted R12 values. The R12 forecast 3, 6, and 12 months in advance published in Solar-Geophysical Data was used to calculate MF2 indices. The accuracy of the official R12 forecast and our MF2 index prediction for the 1977-1985 period is given in Table 7.
Table 7 shows that the prediction accuracy falls with increasing the lead time by a factor of 2 for R12 and by 1.37 for MF2 when 12- and 3-month forecasts are compared. This means that MF2 is less sensitive to errors in R12 predictions. Naturally, the accuracy of MF2 indices obtained in a truly prediction mode is less than the maximal (Table 7). These predicted MF2 indices were used as input to the MQMF2 model ( Mikhailov et al., ) for the midlatitude ionosonde station Kaliningrad (54.7o N, 20.62o E) to calculate monthly foF2. The same foF2 calculations were made with the CCIR model (based on the R12 index) using the officially predicted R12. The results of comparison with foF2 observations for four UT moments are given in Table 8.
Ionospheric indices are known to be advantageous in comparison with direct solar ones. They provide better regression accuracy for foF2 versus solar activity; the saturation effect at high solar activity level and the hysteresis-type solar cycle variation of foF2 are avoided with monthly ionospheric indices use. Smoothed ionospheric indices can be predicted more accurately than the traditional sunspot number R12 [Liu et al., 1983]. All of these merits of ionospheric indices are due to the fact that ionosphere works as a smoothing filter and ionospheric indices reflect the entire impact of all processes in the F2 region. It should be mentioned that the efficiency of some of these physical processes is not yet well known.
The proposed index MF2 seems to solve the dilemma between regression accuracy and long-term predictability. The monthly index MF2 provides as a high regression accuracy as the other monthly ionospheric indices (Table 2), which are not predicted in the long term,\linebreak
\noindent and much better regression accuracy in comparison with 12-month running mean indices (Table 3), which are predicted in the long term.
The monthly MF2 index shows a regularity in seasonal and solar cycle variations similar to monthly median foF2 and can be predicted in the long term using the relationship with smoothed predictable R12, IG12, and IF212 indices. Officially long-term predicted ionospheric IG12 or IF212 indices by CCIR may be recommended to get MF2, as they provide better accuracy than R12 does. But even the use of R12 for MF2 prediction can improve the foF2 long-term prediction accuracy by 30% on average compared with the CCIR approach, as was shown for solar cycle 21 at Kaliningrad station. This result is much better than can be obtained using smoothed ionospheric indices [Liu et al., 1983; Mikhailov et al., 1990b]. Further, MF2 prediction accuracy improvement can be achieved if MF212 long-term prediction is established using the McNish-Lincoln approach, but this requires access to current ionospheric observations on the worldwide ionosonde network.
A general way to derive a new set of MF2 indices, say, for the current period, requires observed monthly median foF2 at many northern hemispheric ionosonde stations, including equatorial and high-latitude ones. Such an approach was applied to the 1957-1988 period, and so this set of MF2 indices is considered the most reliable. When the amount of ionosonde observations is not sufficient for some reasons the other approach can be applied. Using monthly median foF2 observed over 10-20 representative midlatitude ionosonde stations, local MF2 indices can be obtained via the foF2 regression with MF2 for these ionosondes; then the monthly MF2 index is calculated as an average over these local MF2 indices. One can get a monthly MF2 index by this way with pretty good accuracy (mean relative deviation is about 3%). This approach was used to derive MF2 before 1957 and after 1988 (Table 1).
A comparable attempt to create a global ionospheric index (in megahertz) was made by Lal . Unfortunately, it is difficult to evaluate its efficiency. But it should be noted that a lot of approaches can be proposed for retrospective ionospheric parameter variation description, but not all of them can be efficiently used in practice for ionospheric long-term prediction.
The M(3000)F2 regression analysis (Table 4) has shown that the traditional sunspot number R12 provides the best overall accuracy compared with other ionospheric indices; only MF2 turns out to be a little bit better in some cases. This does not seem surprising, as all considered ionospheric indices are based on foF2 observations. On the other hand, NmF2 and hmF2 (which determines M(3000)F2 ) depend in a different way on the same aeronomic parameters [Ivanov-Kholodny and Mikhailov, 1986]. For instance, NmF2 is directly related to the EUV solar flux, while hmF2 reacts to the EUV changes indirectly via changes in all thermospheric parameters. Further, hmF2 is strongly controlled by atmospheric temperature, while NmF2 only slightly depends on Tn. During nighttime hours, hmF2 variations are mostly controlled by the upward plasma drift resulting from thermospheric winds, while this drift helps only to survive the nighttime F2 region, preventing NmF2 from rapid decay. There are some other differences. So a special ionospheric index should be designed for M(3000)F2, but meanwhile R12 may be recommended. In comparison with other indices, R12 seems to reflect better the overall level of solar and geomagnetic activity and hence atmospheric temperature, density, and winds responsible for hmF2 variations. The best efficiency of R12 (Table 4) during high solar activity and equinox periods, when geomagnetic activity is enhanced, confirms this conclusion.
The main results of our consideration are summarized as follows:
1. The monthly improved ionospheric index MF2 provides as good a regression accuracy for foF2 as other monthly ionospheric indices IG, IF2, and T and much better accuracy in comparison with smoothed 12-month running mean R12, IG12, IF212, and T12 indices usually used for long-term ionospheric and HF radio communication predictions. Distinct from direct solar indices, such effects as "saturation" at high solar activity and "hysteresis" foF2 in the course of a solar cycle are avoided when MF2 is used.
2. The monthly index MF2 varies in a regular way with season in the course of solar cycle similarly to the midlatitude monthly median foF2. This opens the opportunity for its long-term prediction. A proposed method for MF2 long-term prediction is based on the MF2 relationship with R12, IG12, IF212, or MF212. The accuracy of MF2 derivation depends on the solar cycle phase and equals 2-4% when observed R12, IG12, IF212, or MF212 indices are used. In a truly prediction mode applied to solar cycle 21, the MF2 prediction accuracy was shown to be 4-6% if the R12 long-term (3-12 months in advance) forecast is used. The prediction accuracy can be further improved using the MF2 relationship with MF212, but this is possible on the basis of a prediction center where current worldwide ionospheric observations are available.
3. Long-term (3-12 months in advance) foF2 prediction for solar cycle 21 has shown the advantage of the proposed approach over the CCIR method based on the R12 index. The foF2 prediction accuracy is improved by 36, 26 and 24% on average for 3, 6, and 12 months of lead time, respectively. This is better than what may be obtained using smoothed 12-month running mean ionospheric indices.
4. Different indices are required for foF2 and M(3000)F2 empirical modeling and long-term prediction. This is due to the different dependence of NmF2 and hmF2 on main aeronomic parameters responsible for the F2 region formation. A special ionospheric index should be designed for M(3000)F2. Meanwhile, MF2 for foF2 and R12 for M(3000)F2 indices may be recommended for practical use.
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