Vol 1, No. 2, November 1998

*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
*f*_{o}*F*2,
*M*(3000)*F*2,
*f*_{o}*F*1, and
*f*_{o}*E*, are associated
in a systematic way with certain measurable quantities concerned
with solar and geomagnetic activity. However, different indices
should be used for
*F*2,
*F*1, 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
*f*_{o}*F*2 and
*M*(3000)*F*2. Usually it is assumed that what is best for
*f*_{o}*F*2 should also be best for
*M*(3000)*F*2, but this is not obvious.
For instance, the dependence of
*f*_{o}*F*2 and
*h*_{m}*F*2 on atmospheric
parameters is different, and one may expect that different indices
may turn out to be the best for
*f*_{o}*F*2 and
*M*(3000)*F*2.

Direct solar indices take into account solar activity level
expressed either by traditional sunspot number
*R* (usually a
12-month running mean
*R*_{12} is used) or by solar radiation in
selected spectral intervals (like
*F*_{10.7} or
*I*_{58.4} ). Keeping in
mind the physical mechanism of the
*F*2 region formation, the sunspot
number
*R*_{12} is far from being the best index for
*f*_{o}*F*2. 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
*F*2 layer heights. Research adherence to
*R*_{12} as the input parameter for empirical ionospheric
models like those of
* CCIR* [1967-1990]
or
* Chernyshov and Vasil'eva* [1973]
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
*F*2 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
*f*_{o}*F*2 with any direct
solar index. A well-known effect of hysteresis in solar cycle
*f*_{o}*F*2 variations
[*Rao and Rao*, 1969;
* Smith and King*, 1981]
may result in a 1-MHz difference for annual mean
*f*_{o}*F*2 at the same
*R*_{12}. For a particular month the
difference may be even higher: up to 1.5 MHz
[*Mikhailov*, 1993].
This means that
*f*_{o}*F*2 versus
*R*_{12} 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
*f*_{o}*F*2 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
*R*_{12} 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
*R*_{12} and monthly median
*f*_{o}*F*2 should
be used for
*R*_{12} < 150 and unchanged
*f*_{o}*F*2 for
*R*_{12} > 150 throughout the solar cycle. But linear
dependence is not valid in
many cases, and the recommended limitation on
*f*_{o}*F*2 at high solar
activity can give large errors in
*f*_{o}*F*2 prediction
[*Mikhailov*, 1993].
Despite all difficulties with
*R*_{12}, it is
considered the basic index of solar activity for ionospheric
modeling and prediction, and other indices are related to
*R*_{12} (see the references of
* Bradley* [1993]).

Since the end of the 1940s solar radio emission at
*l* = 10.7 cm
was measured regularly, the
*F*_{10.7} 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
*F*_{10.7}. 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
*F*_{10.7} values instead of
*R*_{12} does not improve
essentially the
*f*_{o}*F*2 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
*f*_{o}*F*2 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.* [1988],
where the dependence of
*f*_{o}*F*2 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
*F*2 region
formation, namely,photoionization. From this point of view, the
traditional 12-month running mean sunspot number
*R*_{12} 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
*f*_{o}*F*2 versus
*R*_{12} regression
accuracy can be improved using a nonlinear dependence instead of
a linear one
[*Jones and Obitts*, 1970;
* Mikhailov*, 1993],
and so
*R*_{12} 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
*IF*2 [*Minnis*, 1955;
* Minnis and Bazzard*, 1960],
the Australian index
*T* [*Caruana*, 1990;
* Turner*, 1968],
and index
*MF*2 [*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
*MF*2 give effective sunspot numbers which provide the
best regression accuracy for
*f*_{o}*F*2 in the course of a solar cycle.
The
*MF*2 index is
an effective noon
*f*_{o}*F*2 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
*R*_{12} for
monthly
*f*_{o}*F*2 [*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
*f*_{o}*F*2 with such
smoothed indices is not as good as with monthly ones. Thus the
overall accuracy gain with ionospheric indices use instead of
*R*_{12} is not too high: about 11% for predictions
6 months in
advance and 18% for predictions 12 months in advance for
*IG*_{12} [*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
*f*_{o}*F*2 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
*MF*2 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
*f*_{o}*F*2 and
*M*(3000)*F*2 ionospheric
model
*MQMF*2 over Europe
[*Mikhailov et al.*, 1996].
Comparison of
*MQMF*2 with the CCIR model (based on
*R*_{12} ) 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
*MF*2 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
*MF*2 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
*MF*2 long-term prediction convenient for
practical use.

The idea of
*MF*2 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
cos*c* 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
*MF*2 is found using the following
expressions:

*c*_{L} and
*c*_{MC} being solar
zenith angles at a given and
magnetically conjugate points at the same UT moment. The reduction
*f*_{o}*F*2 by
*M* factor gets in order to some extent
*f*_{o}*F*2 data on
ionosonde stations located in different latitudinal and
longitudinal zones. The new index
*MF*2 is defined as the
*f*_{o}*F*2/*M* value
found for an optimum
*Ch**c* which is so chosen for each month that
the standard deviation in the
*f*_{o}*F*2 versus
*MF*2 regression overall for
the ionosonde stations is minimized. Monthly indices
*MF*2 for
1945-1996 are listed in Table 1.

Monthly indices
*MF*2 show the regularity in seasonal and solar cycle
variations, and this feature is used in the
*MF*2 index prediction
method (see below). Figure 1 shows an example of this regularity in
*MF*2 variations during the 1969-1979 decade. Well-pronounced
semiannual peaks with relative minima during solstice periods are
similar to midlatitude median
*f*_{o}*F*2 variations. The difference is
seen in annual variations: unlike monthly median
*f*_{o}*F*2, summer
*MF*2 values are higher than winter ones. The "winter anomaly" effect for
*MF*2 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
*MF*2,
monthly index
*T* does not show as a rule any regularity in its
variation.

Two kinds of
*MF*2 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
*f*_{o}*F*2 with solar
activity level and (2) a comparison with smoothed 12-month running
mean indices which are used in practice for
*f*_{o}*F*2 and
*M*(3000)*F*2 modeling and long-term prediction. In both
cases, we will analyze
the regression accuracy of
*f*_{o}*F*2 (or
*M*(3000)*F*2 ) 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* = *f*_{o}*F*2_{ pred}
- *f*_{o}*F*2_{ obs}.

The results of the regression analysis of the first type are
given
in Table 2
for the ionosonde station Arkhangelsk (64.6^{o} N,
40.5^{o} E). Monthly ionospheric indices
*IF*2,
*IG*,
*T* ,
*MF*2 (old
version by
* Mikhailov and Mikhailov* [1995b]), and
*MF*2 (new
version, Table 1)
along with the traditional
*R*_{12} 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
*MF*2 indices give
very close results, being a little bit more efficient than
*IF*2 and
*IG*. Index
*T* is comparable with
*MF*2 and turns out to be even more
efficient in some cases. Index
*R*_{12} is systematically worse than
*MF*2, by 27% on average. The main result of this comparison is that
the newly developed index
*MF*2 is as efficient as the other
monthly ionospheric indices.

The second type of comparison is made with smoothed 12-month
running mean indices
*R*_{12},
*IF*2_{12} ,
*IG*_{12}, and
*T*_{12} 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
*MF*2 index may be
found in the work of
* Mikhailov et al.* [1996].

The results of
*MF*2 comparison with smoothed 12-month running mean
indices show that the
*MF*2 index provides systematically better
regression accuracy than any index in question, either direct
solar ( *R*_{12} ) or ionospheric. The other result is that
smoothed
ionospheric indices give rather little accuracy improvement compared
with
*R*_{12}.

The analysis has shown that such well-known
effects in
*f*_{o}*F*2 solar
cycle variations as "saturation" at high solar activity and
"hysteresis" in the course of a solar cycle related with
*R*_{12} use are absent when the
*MF*2 index is applied. This advantage of
the use of ionospheric indices
over direct solar indices was pointed out
earlier by
* Mikhailov and Mikhailov* [1994].

Similar regression analysis was made for the
*M*(3000)*F*2 parameter. It
should be kept in mind that
*M*(3000)*F*2 data are much less reliable
compared with
*f*_{o}*F*2 and they are not consistent at some ionosonde
stations. A comparison with inconsistent
*M*(3000)*F*2 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 (48.45^{o} N, 356.73^{o} 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
*R*_{12} provides the best
overall regression accuracy in comparison with other indices. The
gain is noticeable especially during daytime, equinox, and high
solar activity. Only
*MF*2 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
*MF*2 index seasonal and solar cycle
variations similar to monthly median
*f*_{o}*F*2 changes (Figure 1), a
method for its long-term prediction can be proposed. It is based on
the
*MF*2 relationship with any smoothed index
*R*_{12},
*IG*_{12},
*IF*2_{12}, or
*MF*2_{12}.
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
*MF*2 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
*MF*2 obtained from
*R*_{12},
*IG*_{12},
*IF*2_{12}, or
*MF*2_{12} 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
*R*_{12}. Long-term
prediction of
*MF*2_{12} can be carried out using the well-known
* McNish and Lincoln* [1949]
method, as four complete solar cycles
of observed
*MF*2 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
*MF*2 with
*R*_{12} relationship, a forecast of
*MF*2 indices
was made for solar cycle 23 (Table 6).
Space Environment Center (SEC)
prediction of
smoothed sunspot numbers
*R*_{12} [*Space Environment Center*, 1997]
was used for
*MF*2 calculations.

The final goal of all index considerations is to improve the
prediction accuracy for monthly
*f*_{o}*F*2 and
*M*(3000)*F*2. To estimate the
efficiency of the proposed approach, we performed
*f*_{o}*F*2 long-term
predictions for solar cycle 21 (1977-1985) using officially
predicted
*R*_{12} values. The
*R*_{12} forecast 3, 6, and 12 months in
advance published in Solar-Geophysical Data was used to
calculate
*MF*2 indices. The accuracy of the official
*R*_{12} forecast
and our
*MF*2 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
*R*_{12} and by 1.37 for
*MF*2 when
12- and 3-month forecasts are compared. This means that
*MF*2 is less
sensitive to errors in
*R*_{12} predictions. Naturally, the accuracy
of
*MF*2 indices obtained in a truly prediction mode is less than the
maximal (Table 7).
These predicted
*MF*2 indices were used as input
to the
*MQMF*2 model
(* Mikhailov et al.,* [1996])
for
the midlatitude ionosonde station Kaliningrad (54.7^{o} N,
20.62^{o} E) to calculate monthly
*f*_{o}*F*2. The same
*f*_{o}*F*2 calculations
were made with the CCIR model (based on the
*R*_{12} index) using the
officially predicted
*R*_{12}. The results of comparison with
*f*_{o}*F*2 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
*f*_{o}*F*2 versus
solar activity; the saturation effect at high solar activity level
and the hysteresis-type solar cycle variation of
*f*_{o}*F*2 are avoided
with monthly ionospheric indices use.
Smoothed
ionospheric
indices can be
predicted more accurately than the traditional sunspot number
*R*_{12} [*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
*F*2 region. It should be mentioned that the efficiency of some
of these physical processes is not yet well known.

The proposed index
*MF*2 seems to solve the dilemma between
regression accuracy and long-term predictability.
The monthly index
*MF*2 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
*MF*2 index shows a regularity in seasonal and solar cycle
variations similar to monthly median
*f*_{o}*F*2 and can be
predicted
in the long term
using the relationship with smoothed predictable
*R*_{12},
*IG*_{12}, and
*IF*2_{12} indices. Officially long-term predicted
ionospheric
*IG*_{12} or
*IF*2_{12} indices
by CCIR
may be recommended to
get
*MF*2, as they provide better accuracy than
*R*_{12} does. But even
the use of
*R*_{12} for
*MF*2 prediction can improve the
*f*_{o}*F*2 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,
*MF*2 prediction accuracy improvement
can be achieved if
*MF*2_{12} 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
*MF*2 indices, say, for the current
period, requires observed monthly median
*f*_{o}*F*2 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
*MF*2 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
*f*_{o}*F*2 observed over 10-20 representative
midlatitude ionosonde stations, local
*MF*2 indices can be obtained
via the
*f*_{o}*F*2 regression with
*MF*2 for these ionosondes; then the monthly
*MF*2 index
is calculated as an average over these local
*MF*2 indices.
One can get a monthly
*MF*2 index
by this way with pretty good
accuracy (mean relative deviation is about 3%). This approach was
used to derive
*MF*2 before 1957 and after 1988 (Table 1).

A comparable attempt to create a global ionospheric index (in megahertz)
was made by
* Lal* [1992].
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)*F*2 regression analysis (Table 4) has shown that the
traditional sunspot number
*R*_{12} provides the best overall
accuracy compared with other ionospheric indices; only
*MF*2 turns out
to be a little bit better in some cases. This does not seem
surprising, as all considered ionospheric indices are based on
*f*_{o}*F*2 observations. On the other hand,
*N*_{m}*F*2 and
*h*_{m}*F*2 (which determines
*M*(3000)*F*2 ) depend in a different way on the same aeronomic
parameters
[*Ivanov-Kholodny and Mikhailov*, 1986].
For instance,
*N*_{m}*F*2 is directly related to the EUV solar flux,
while
*h*_{m}*F*2 reacts to the EUV changes indirectly via changes
in all thermospheric parameters. Further,
*h*_{m}*F*2 is strongly controlled by
atmospheric temperature, while
*N*_{m}*F*2 only slightly depends on
*T*_{n}.
During nighttime hours,
*h*_{m}*F*2 variations
are mostly controlled by the
upward plasma drift resulting from thermospheric winds, while this
drift helps only to survive the nighttime
*F*2 region, preventing
*N*_{m}*F*2 from rapid decay. There are some other differences.
So a special
ionospheric index should be designed for
*M*(3000)*F*2, but meanwhile
*R*_{12} may be recommended. In comparison with other
indices,
*R*_{12} seems to reflect better the overall level of
solar and geomagnetic
activity and hence atmospheric temperature, density, and winds
responsible for
*h*_{m}*F*2 variations. The best efficiency of
*R*_{12} (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
*MF*2 provides as good
a regression accuracy for
*f*_{o}*F*2 as other monthly ionospheric indices
*IG*,
*IF*2, and
*T* and much better accuracy in comparison with smoothed
12-month running mean
*R*_{12},
*IG*_{12},
*IF*2_{12},
and
*T*_{12} 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"
*f*_{o}*F*2 in the
course of a solar cycle are avoided when
*MF*2 is used.

2. The monthly index
*MF*2 varies in a regular way with season in the
course of solar cycle similarly to the midlatitude monthly median
*f*_{o}*F*2. This opens the opportunity for its long-term
prediction. A
proposed method for
*MF*2 long-term prediction is based on the
*MF*2 relationship with
*R*_{12},
*IG*_{12},
*IF*2_{12}, or
*MF*2_{12}.
The accuracy of
*MF*2 derivation depends on the
solar cycle phase and equals 2-4% when observed
*R*_{12},
*IG*_{12},
*IF*2_{12}, or
*MF*2_{12} indices are used. In a truly
prediction mode applied to solar cycle 21, the
*MF*2 prediction
accuracy was shown to be 4-6% if the
*R*_{12} long-term
(3-12 months in advance) forecast is used. The prediction accuracy can be
further improved using the
*MF*2 relationship with
*MF*2_{12}, 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)
*f*_{o}*F*2 prediction for solar
cycle 21 has shown the advantage of the proposed approach over the
CCIR method based on the
*R*_{12} index. The
*f*_{o}*F*2 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
*f*_{o}*F*2 and
*M*(3000)*F*2 empirical
modeling and long-term prediction. This is due to the
different
dependence of
*N*_{m}*F*2 and
*h*_{m}*F*2 on main aeronomic parameters
responsible for the
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