Vol 1, No. 3, August 1999

*A. D. Danilov*

**Institute of Applied Geophysics, Moscow, Russia**

*A. V. Mikhailov*

**Institute of Terrestrial Magnetism, Ionosphere, and Radio
Wave Propagation, Troitsk, Moscow Region, Russia**

The problem of long-term variations (trends) in parameters of the
upper atmosphere and ionosphere currently attracts attention (see
the reviews by
* Danilov* [1997]
and
* Danilov and Smirnova* [1997]).

The results of ionospheric measurements should play a leading role
in the analysis of long-term changes in the upper atmosphere. The
first indication of a presence of trends in the upper atmosphere
parameters was obtained merely on the basis of observations of
radio wave absorption in the
*D* region
[*Bremer*, 1992;
* Nestorov et al.*, 1991;
* Taubenheim et al.*, 1990].

The most frequently used ionospheric parameter is the
*F*2 layer
critical frequency
*f*_{o}*F*2. There are long enough series of
*f*_{o}*F*2 observations at several ionospheric stations
all over the globe, and
some attempts have been made during recent years to reveal
*f*_{o}*F*2 long-term trends
[*Bremer*, 1996;
* Danilov and Mikhailov,* 1998a, 1998b;
* Givishvili and Leshchenko*, 1993, 1994,
1995].

* Danilov and Mikhailov* [1998a, 1998b]
proposed a
principally new approach to derivation of
*f*_{o}*F*2 trends. In this
paper we further develop this approach, show that it leads to
principally new results (disappearance of the seasonal effect in
the trends and increase in its absolute values), and illustrate it
by the data of several ionospheric stations.

The first step in developing a new approach for looking at
*f*_{o}*F*2 trends was to use relative values of the critical
frequency instead
of the absolute values used by
* Bremer* [1996] and
* Givishvili and Leshchenko* [1993, 1994,
1995].
* Danilov and Mikhailov* [1998a]
proposed to look for trends not in
the absolute values of
*f*_{o}*F*2 but in the relative deviations of the
observed values from some mean (that is, constructed without any
allowance for long-term trends) model:

(1) |

This approach was
used
slightly earlier
by
* Danilov and Smirnova* [1997]
in looking for trends in the
*E* region ion
composition on the basis of rocket mass spectrometer measurements.

The principal advantage of the method suggested is the following.
Analyzing absolute values of
*f*_{o}*F*2, one cannot use jointly the data
for various LT moments and months, because there exist strong
diurnal and seasonal variations of this parameter. If the
deviations of observed
*f*_{o}*F*2 values from some mean model (created
without any allowance for possible long-term trends) are used, one
is able to analyze jointly all the data available, because the
absolute values are insignificant and only variations of the
*f*_{o}*F*2 deviations during several decades are sought.
Evidently, if any
trend does exist, deviations of one sign (relative to the mean
model) in earlier years and of the opposite sign in later
years should be seen.

The regression of the critical frequencies with respect to the
12-month running mean values of the sunspot number
*R* approximated
by the third power polynomial was used as a model.

Analyzing the
*f*_{o}*F*2 data,
* Danilov and Mikhailov* [1998a]
directly
used
the
*f*_{o}*F*2 monthly medians. A pronounced negative trend
was
derived in Moscow at the daytime hours for January, February, May,
June, July, August, and September, but the trend for other months
was close to zero or even positive. In fact, this conclusion on
different
*f*_{o}*F*2 trends in various months was similar to that
obtained by
* Bremer* [1996] and
* Givishvili and Leshchenko* [1993, 1994,
1995].

Later * Danilov and Mikhailov* [1998b]
proposed using for the
analysis not the initial monthly mean values, but smoothed 12-month
running mean values of
*f*_{o}*F*2. Since the 12-month running mean
sunspot number
*R*12 is used in the above mentioned regressions of
*f*_{o}*F*2, it seems reasonable to use also smoothed values
of the
critical frequencies as
*f*_{o}*F*2 (obs) in (1). The use of smoothed
*f*_{o}*F*2 reduces the scatter of individual points around
the regression
curve.

The next step in the development of a new approach to look for
*f*_{o}*F*2 trends
was the following. The reliability of the
*d**f*_{o}*F*2 values
obtained in the analysis
depends
to a great degree
on the
reliability of the model used, that is, on the reliability of the
*f*_{o}*F*2 regression with respect to
*R*12. It is widely known that there is
a so-called "hysteresis" effect in the solar cycle
*f*_{o}*F*2 variations.
The effect is seen at the rising and falling phases of a solar cycle
and, roughly speaking, is manifested in different values of
*f*_{o}*F*2 (under identical other conditions) under the
same value of
*R*12. The
effect may create significant noise in the model and distort the resulting
*d**f*_{o}*F*2 values.

* Danilov and Mikhailov* [1998b]
attempted to analyze
only the data for 5 years around the solar activity minima and
found that the negative trends for Moscow became better pronounced
for all seasons if such reduced data were used.

However, 5 years cover too long a period, and so parts of the
falling and rising phases of the solar cycle may
again
be
involved
in the analysis. On the other hand, one should not expect a
manifestation of the hysteresis effect also around solar maxima.
That is why we finally propose, looking for
*f*_{o}*F*2 trends, to use
three years around each maximum and minimum (1946-1948, 1953-1955,
1957-1959, 1963-1965, 1967-1969, 1975-1977, 1978-1980,
1985-1990, and 1995-1997). One can easily see that mainly the
years of long enough falling phases (for example, 1970-1974) are
excluded from the analysis. It appeared that such a reduction of
the data leads to fundamental changes of conclusions on the
*f*_{o}*F*2 trends.

Below we will consider in detail the results for the Moscow station to compare them with previous results and to demonstrate the effects of a new approach application and then summarize the results for other ionospheric stations.

We discuss here the data of the Moscow ionospheric station and, first, demonstrate the effects of new approach application to the data for 1200 LT and March.

Figure 1 shows the
*d**f*_{o}*F*2 values versus
time for all the years
available (1946-1996). A weak positive trend
( +1.8 10^{-4}
per
year; see Table 1)
is visually seen. It should be noted that
if one limits the analysis by 1990-1991 (that is exactly what has
been done by
* Givishvili and Leshchenko* [1993, 1994,
1995]
and
* Danilov and Mikhailov* [1998a, 1998b]),
one gets a weak negative trend for these data. The reversal of the
trend sign, when the data until 1996 are added, occurs mainly
because of the 1991-1994 points which correspond to the falling
phase of solar activity (see above).

Figure 2 shows the same data for the same period but with only
the
years around solar maxima M(3) and minima m(3)
left. The change of
the situation is dramatic. Now there is a well-pronounced negative
trend ( *k* = -6.7 10^{-4}).

Analyzing the data for Moscow,
* Givishvili and Leshchenko* [1993, 1994,
1995]
and
* Danilov and Mikhailov* [1998a]
obtained different values of the trend
(and even different sign of it) for different months. However, it
seems doubtful that the long-term changes in
*f*_{o}*F*2 during several
decades would have a pronounced seasonal behavior. In the scope of
current ideas one would rather expect that the
*f*_{o}*F*2 trends manifest
some systematic and single-directed changes of the entire upper
atmosphere (for example, a cooling, variations of transport
process, etc.), which should not depend on relatively short-term
seasonal variations. There is a danger that the seasonal effect in
the trends derived is due either to inhomogeneity of the initial
data distribution over seasons or to the method of trend derivation
itself.

Table 1 shows the slope
*k* of the linear approximation of the
*d**f*_{o}*F*2 data plotted
versus time for four months (representing all
seasons). Actually,
*k* gives a relative change in
*f*_{o}*F*2 per year. It
is evident from the third column of Table 1 that, with the new
approach proposed, one obtains negative trends of the same sign
(negative) and nearly the same magnitude (about
-6 10^{-4})
for all
seasons.

To illustrate the advantages of the new approach, the bottom
line
in Table 1
shows the
*f*_{o}*F*2 trends for winter. The principal results
do not significantly differ from those for individual months, but in
this case every point is a result of averaging over three winter
months; so its statistical provision is, roughly speaking, 3
times higher.

We checked our conclusions drawn for 1200 LT, using the data for other LT moments (1000 LT and 1400 LT), and obtained the same results. Actually, the method suggested makes it possible to use jointly all months and all LT moments to increase statistical provision of the results.

It is worth looking for possible changes with time of the
trend
magnitude. The last two columns of Table 1 show the
*f*_{o}*F*2 trends for
the period since 1965 only. Again, if the data for all years are
used, there is a contradiction even in sign between various months,
but the trend is negative and of the same magnitude if only the
M(3) and m(3)
years are used.

An important feature of Table 1 is that the values of the trends
since 1965 are about twice as high as those of the trends since
1946. This effect is even stronger for some other stations (for
example, St. Petersburg). This fact may mean that the
*f*_{o}*F*2 depletion during the three recent decades occurs
more rapidly than
during the preceding decades. The fact may be important while
looking for the causes of the trends described.

The method in question provides values of relative changes
in
*f*_{o}*F*2.
For example, the last column in Table 1 shows that since 1965
*f*_{o}*F*2 decreases, on the average, by 0.1% per year.
To compare this value
with the results of the absolute value analysis, we take the mean
value of
*f*_{o}*F*2 to be equal to 8.2 MHz. Then the
*f*_{o}*F*2 trend derived
is
8.2 10^{-3} MHz per year. This
value for the Moscow station is
higher than the value of
3 10^{-3} MHz per year given by
* Givishvili and Leshchenko* [1993]
and
* Danilov and Mikhailov* [1998a, 1998b].
This may be due to the more
sophisticated method used to look for
*f*_{o}*F*2 trends in this paper as
compared to the method used in the above indicated papers.

The same procedure as described in the previous section was applied to the data of four other stations: St. Petersburg, Alma-Ata, Rugen, and Sodankyla. The results are shown in Table 2.

One can see from Table 2, that the principal picture for all
stations is practically the same as described above for Moscow.
Inclusion into the analysis of all the years leads to small
positive or close to zero trends. Reduction of the data to only the
M(3) and m(3) years gives a stable negative trend with close
magnitudes for different months. Further reduction of the data
(only since 1965) leads to a further increase of the negative values
of
*k*. In the case of the St. Petersburg station this reduction
increases the magnitude of the negative trend by several times.

It is worth emphasizing that for all the stations considered the
scatter of the
*k* values in the case of all years used (the second
column) is very strong (up to 5 times), and in some cases there
is even a sign reversal, whereas for the M
(3)+ m(3) reduction of
the data, the difference in
*k* for various months is, as a rule,
relatively small (tenths of percents). We believe that this fact
may be considered as some additional argument in favor of the new
approach described.

It has
already
been
mentioned above that low values of the
*f*_{o}*F*2 trends had been obtained
by
* Bremer* [1996],
who used all the
years. This fact agrees well with the second column of Table 2. The
third column demonstrates that use of the data for the M(3) and
m(3) years only leads to negative trends of nearly the same
magnitude as for the Moscow and St. Petersburg stations. As an
example, Figure 3
shows the
*d**f*_{o}*F*2 variations
for Rugen for
July.

Comparison of the trends derived for all five stations
considered (Tables 1 and 2) indicates the presence of some
latitudinal variation of the trends. The least pronounced trends
are derived for the low-latitude Alma-Ata station ( *k* is about
-3 10^{-4} for the M
(3)+ m(3) years after 1965).
The signal is low, and
so the effects well seen at other stations are not so visually
pronounced on the noisy background.

The highest trends ( *k* 50
10^{-4}) are obtained for the
high-latitude Sodankyla station (see Figure 4 for illustration).
For this station, negative trends are seen even if all the years are
used. That agrees with well-pronounced trends obtained for this
station by
* Danilov and Mikhailov* [1998b].
And,
nevertheless, reduction of the data in the scope of the new
approach increases the trend magnitude by more than 2 times. The
midlatitude stations Rugen, Moscow, and St. Petersburg demonstrate
close values of the trends ( *k* = (1-2) 10^{-4}), which lie
between
the corresponding values for Sodankyla and Alma-Ata.

Five stations are not enough to derive solid conclusions on latitudinal effects in the trends, but we may state, at least, that there are some indications for the presence of such effects.

A new method for analyzing the long-term
*f*_{o}*F*2 trends is proposed. The
principal point of the method is to use relative rather than
absolute
*f*_{o}*F*2 variations and consider only the periods around
solar
maxima and minima in the cycles to avoid the distortion of the
*f*_{o}*F*2 values by the hysteresis effect at the rising
and falling phases of
a solar cycle. The vertical sounding data for the Moscow, Rugen,
St. Petersburg, and Sodankyla stations were analyzed with the help
of this method, and a pronounced negative trend for all months were
revealed. An averaged over all seasons negative trend in
*f*_{o}*F*2 for
Moscow was found to be
8.2 10^{-3} MHz yr
^{-1}.
This value is 2-2.5 times higher than that obtained earlier by
* Givishvili and Leshchenko* [1993, 1994,
1995]
and
* Danilov and Mikhailov* [1998a, 1998b].

Using the new method, in which relative (with respect to some
empirical model created without any allowance for trends)
*f*_{o}*F*2 variations are considered, one can increase
the statistical
provision of the conclusions, because it becomes possible to
consider jointly the data for different local times and seasons. If
only the years in the vicinity of solar activity minima and maxima
are considered (to reduce the influence of distorting effects, for
example, that of hysteresis), stable negative trends are derived for
all stations considered.

Some indications are obtained that there is a latitudinal effect in
the
*f*_{o}*F*2 trends (higher values at higher latitudes)
and that the
trends for the two recent decades may be higher than the average
ones derived for the entire period of observations.

Bremer, J., Ionospheric trends in mid-latitudes as a possible
indicator of the atmospheric greenhouse effect,
* J. Atmos. Terr. Phys., 54*, 1505, 1992.

Bremer, J., Some additional results of long-term trends in vertical incidence data, paper presented at the COST 251 Meeting, Prague, Sept. 1996.

Danilov, A. D., Long-term variations of the temperature and
composition of the mesosphere and lower thermosphere,
* Geomagn. Aeron., 37* (2), 1, 1997.

Danilov, A. D., and A. V. Mikhailov, Trends in the critical
frequencies of the
*F*2 region for the Moscow station,
* Geomagn. Aeron., 38* (1), 1998a.

Danilov, A. D., and A. V. Mikhailov, Long-term trends of the
*F*2 -layer
critical frequencies: A new approach, in
* Proceedings of the 2nd COST 251 Workshop "Algorithms and Models for COST 251
Final Product", 30-31 March 1998, Side, Turkey*,
p. 114,
Rutherford Appleton Lab., U. K., 1998b.

Danilov, A. D., and N. V. Smirnova, Long-term trends of the ion
composition in the
*E* region, * Geomagn. Aeron., 37*, 35, 1997.

Givishvili, G. V., and L. N. Leshchenko, Long-term trends of the
properties of the ionosphere and thermosphere at middle latitudes,
* Dokl. Ros. Akad. Nauk, 333* (1), 86, 1993.

Givishvili, G. V., and L. N. Leshchenko, Possible proofs of
presence of a technogenic impact on the midlatitude ionosphere,
* Dokl. Ros. Akad. Nauk, 334* (2), 213, 1994.

Givishvili, G. V., and L. N. Leshchenko, Dynamics of the climatic
trends in the midlatitude ionospheric
*E* region,
* Geomagn. Aeron., 35* (3), 166, 1995.

Nestorov, G., D. Pancheva, and A. D. Danilov, Climatic changes in
ionospheric absorption of radio waves in the SW range,
* Geomagn. Aeron., 31* (6), 1070, 1991.

Taubenheim, J., G. Cossart, and G. Entzian, Evidence of CO
_{2} induced progressive cooling of the middle atmosphere derived from
radio wave observations,
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