Persistence of planetary wave type oscillations in the mid-latitude ionosphere

Planetary wave type oscillations have been observed in the lower and middle atmosphere but also in the ionosphere, including the ionospheric F2 layer. Here we deal with the oscillations in foF2 analysed for two Japanese and two US stations over a solar cycle (1979-1989) with the use of the Morlet and Paul wavelet transforms. Waves with periods near 5, 10 and 16 days are studied. Only events of duration of three wave-cycles and more are considered. The results are compared with the results of a similar analysis made for foF2 and the lower ionosphere over Europe (Laštovička et al., 2003a,b). The 5-day period wave events display a typical duration of 4 cycles, while the 10and 16-day wave events are less persistent with typical duration of about 3.5 cycles and rather 3 cycles, respectively, in all three geographic regions. The persistence pattern in terms of number of cycles and in terms of number of days is different. In terms of number of cycles, the typical persistence of oscillations decreases with increasing period. On the other hand, in terms of number of days the typical persistence evidently increases with increasing period. The spectral distribution of event duration is too broad to allow for a reasonable prediction of event duration. Thus the predictability of the planetary wave type oscillations in foF2 seems to be very questionable. The longitudinal size of the planetary wave type events increases with increasing wave period. The persistence of the planetary wave type events in foF2 and the lower ionosphere is similar in Europe, but the similarity in occurrence of individual events in foF2 and the lower ionosphere is rather poor. Mailing address: Dr. Jan Laštovička, Institute of Atmospheric Physics, Academy of Sciences of Czech Republic, Bocni II, 14131 Prague, Czech Republic; e-mail: jla@ufa.cas.cz

Typical planetary wave periods are broad spectral peaks around 2, 5, 10 and 16 (very broad spectral peak) days, but the planetary wave spectrum is very variable and on individual days it can be much different.They roughly correspond to eigenfrequencies of the atmosphere, which slightly differ for various modes; for instance for the wave with the zonal wave number 1 they attain values of 1.2, 5, 8 and 12 days (these periods are Doppler shifted by the prevailing wind).All planetary wave periods are quasi-periods with the exact period varying within a period range.Amplitudes of planetary waves are unstable, as well; planetary waves typically occur in bursts of a couple of waves.The duration of such wave bursts in the critical frequency of the F2 region, foF2, in other words the persistence of the planetary wave type events, is the main topic of the paper.Las ˇtovic ˇka et al. (2003b) made such investigations for four representative European stations listed in table I.The primary aim of this paper is to make such investigations for representative stations from the mid-latitude U.S.A. and Japan in comparison with our previous results on the persistence of planetary wave events over Europe.
It should be mentioned that in the F region it is correct to use the term planetary wave type oscillations, because not all oscillations in the planetary wave period range are related to planetary waves in the neutral atmosphere; some of them are caused by periodic variability of geomagnetic activity (e.g., Altadill and Apostolov, 2003).Planetary waves cannot propagate directly to the F2 region heights.They have to propagate indirectly via modulation of other agents like upward propagating tides or gravity waves, vertical drifts, or the turbopause height and its properties.
Las ˇtovic ˇka et al. (2003a) studied the persistence of planetary wave events in the lower ionosphere over Europe.Data and methods used by Las ˇtovic ˇka et al. (2003a,b) allow examine the possible similarity of planetary wave type oscillations in the lower ionosphere and foF2, which is the second topic of the paper.The third topic is to use similarity and/or dissimilarity of planetary wave events in foF2 over Europe, Japan and the U.S.A. for rough estimate of the longitudinal size of planetary wave type events.

Data and methods
As the basic ionospheric parameter we use the main characteristics of the F2 region, the  1979, 1987/1988, 1988, 1988/89, 1989Akita 39.7°N 140.1°E 1984/1985, 1988/1989, 1989  For the «vertical» comparison of the planetary wave type oscillation events in Europe we need data representing the lower ionosphere.The radio wave absorption measurements obtained by the A3 method utilizing the oblique wave propagation are used.Data from two radio paths from central Europe are used.The path Luxembourg-Panská Ves has parameters as follows: f = 6.09MHz, feq= 2.1-2.2MHz (equivalent vertical frequency), reflection point 50°04lN, 10°18lE, transmitter-receiver distance 610 km.The path Deutschlandfunk-Panská Ves has different parameters: f=1539 kHz, feq=650-700 kHz, reflection point 50°16lN, 11°47lE, transmitter-receiver distance 390 km.The absorption along the former radio paths is formed very predominantly at altitudes of about 90-100 km, whereas the latter absorption is formed mostly at altitudes of about 85-90 km.
As a mathematical tool for the description of the persistence of planetary wave type oscillations within time series of foF we use wavelet analysis (Torence and Compo, 1998;Vidakovic, 1999).The Continuous Wavelet Transform (CWT) is an excellent tool for analysing changing properties of non-stationary signals.In analyses of signals, the wavelet representations allow us to view a time-domain evolution in terms of scale/period components.The CWT is a convolution of the data sequence with scaled and translated version of the mother wavelet.Varying the wavelet scale and translating along the localised time is possible to construct a picture showing both the amplitude of any feature versus the scale/period and how this amplitude varies with time.For a thorough introduction to wavelet transforms, the reader is referred, e.g., to Mallat (1998).
The wavelet transform of the data X(t, z) is defined as (2.1) where ψ0(t) is a mother-wavelet.In the present work, we used Morlet and Paul (complex) mother-wavelets, defined as where param counts the number of oscillations of the (real part of the) wavelet and provides the user with a degree of freedom that can be easily tuned to a given purpose.Wavelets, as building blocs of models, are well localized in both time and scale (period, frequency).As the Paul wavelet decays more quickly in the time-domain then Morlet, it enables better time localization.The greater difference is in frequency/ period domain.For the given count of evident oscillations in the wavelet the Paul wavelet is much less efficient.As a source Matlab code the wavelet software for Morlet wavelet computations provided by Torrence and Compo was used.Matlab codes are available at URL: http://paos.colorado.edu/research/wavelets/.
Since Las ˇtovic ˇka et al. (2003a) used only less suitable Meyer wavelet in analysis of the planetary wave activity in the lower ionosphere, we use for the «vertical» comparison over Eu-  (2003a,b).The Mayer (e.g., Daubechies, 1994) and Morlet wavelet transforms yielded the same statistical characteristics of the planetary wave type event persistence for foF2 over Europe (Las ˇtovic ˇka et al., 2003b).Commercial MATLAB-Wavelet software has been used to compute the Meyer wavelet transform.
The wavelet analysis is applied to consecutive 1-year long intervals, shifted by half a year (January-December 1979, July 1979-June 1980, January-December 1980, etc.).Thus for Slough and Juliusruh we have 21 partly overlapping intervals for the period 1979-1989, for other stations a bit less due to data gaps.Only wave events with duration of at least three wave cycles are taken into account.solute» power.However, the Morlet wavelet transform results are also evaluated in terms of «relative» power, when the seasonally variable level of the background foF2, shown in the top panel, is taken into account.We consider relative intensifications with respect to the vicinity of the events with duration of at least three wave cycles to be planetary wave type events.This allows us to compare the results of the relative and absolute power approach to interpretation of the results as it was done for European data by Las ˇtovic ˇka et al. (2003b).Figure 2 shows an example of the results of the Paul wavelet transform.The results of the Paul wavelet transform are evaluated in terms of the «absolute» power in the same way as Morlet results.

Persistence of planetary wave type events in foF2
The most pronounced feature of figs. 1 and 2 is a large temporal and partly spectral variability of the planetary wave activity.The migration of periods of planetary wave activity is also well visible.The large temporal variability of planetary wave activity has to result in a limited persistence of the individual planetary wave events.
The statistics of duration of individual events of the enhanced planetary wave activity for all yearly intervals and period bands centred at 5, 10 and 16 days is summarized in tables II, III and IV for Paul transform, «absolute» evaluation, Morlet transform, «absolute» evaluation and Morlet transform, «relative» evaluation, respectively.The tables present the number of events together with their mean, median and the most often occurring number of cycles for individual stations and the average values for all four stations.
Tables II-IV reveal for the 5-day wave the typical persistence of well-developed wave events to be of 4 cycles consistently for all three ways of analysis.For the 10-day wave, both the  median values and the most frequent occurrences provide the typical persistence of 3.5 cycles.For the 16-day wave, medians point to a typical persistence of 3.5 cycles and the most frequent values reveal a typical persistence of just 3 cycles.Thus the persistence in terms of the number of cycles slightly decreases with increasing period.
In terms of days the typical duration is 20 days for T=5 days, about 35 days for T=10 days and about 55-60 days for T=16 days.In other words, the duration of the wave events in terms of days is longer, not shorter for longer periods.The median, mean and most frequent values are mostly very similar for all four stations and in tables II-IV.This means that American and Japanese stations reveal essentially the same statistical characteristics of persistence of the planetary wave type events in foF2, and that the «absolute» evaluation of the Paul wavelet transforms and the «absolute» and «relative» evaluation of the Morlet wavelet transforms yield very similar statistical characteristics of the planetary wave type events.The only substantial difference is in the number of events derived by different methods, as tables II-IV clearly demonstrate.However, it does not affect the statistical characteristics of the persistence.One source of differences between the «absolute» and «relative» evaluation is the existence of relatively long intervals of high but variable activity.Such an interval is evaluated as one event in «absolute» way, but may provide two or even three events in «relative» way due to that internal structure of the interval.The different number of identified events for the Morlet wavelet transform compared with the Paul wavelet transform is probably influenced by different mother wavelets.
Tables V and VI show statistical characteristics of the persistence of the planetary wave type events over Europe obtained with the Morlet wavelet transform.They are either identical with or very slightly larger than such values from the U.S.A. and Japan for all three periods of waves.This means that the statistical characteristics of planetary wave type event persistence are essen-tially the same in all three geographic regions and, thus, may be considered to be representative for middle latitudes of the Northern Hemisphere.

Planetary wave type events in foF2
and the lower ionosphere over Europe As for the «vertical» comparison, we can compare the similarity of statistical characteristics of persistence of events, and of occurrence of individual planetary wave type events in foF2 and the lower ionosphere in Europe using data and results of Las ˇtovic ˇka et al. (2003a,b).The typical persistence of the 5-day wave in foF2 is four wave cycles (Las ˇtovic ˇka et al., 2003b).This is slightly less than the typical persistence of 5 cycles for the 5-day wave in the lower ionosphere (Las ˇtovic ˇka et al., 2003a).For the 10-day and 16-day waves, the typical persistence in foF2 and the lower ionosphere is identical.Thus the typical persistence of planetary wave type oscillations in the lower ionosphere and foF2 appears to be almost identical.
A quite different pattern is provided by comparison of individual events.The similarity of occurrence of individual events in foF2 and the lower ionosphere is mostly poor, worse than expected from the results of some studies, which compared neutral wind oscillations in the MLT region with oscillations in foF2 or in the radio wave absorption in the lower ionosphere (e.g., Pancheva et al., 1994).The quasi-simultaneous occurrence of events in foF2 and the lower ionosphere is rare.The reason might be that the absorption fluctuations are related to fluctuations in the prevailing wind (e.g., Pancheva et al., 1989), while those in foF2 seem to be related more to fluctuations in the tidal winds (e.g., Las ˇtovic ˇka and S ˇauli, 1999).The planetary wave type fluctuations in the prevailing wind and the tidal wind differ to some extent.Why and to what degree these fluctuations differ should be examined.
Another reason of the poor similarity might be the geomagnetic origin of a significant part of planetary wave type fluctuations in foF2 (Altadill and Apostolov, 2003), whereas the geomagnetic activity does not play a role in planetary wave type oscillations in the lower ionosphere (Pancheva et al., 1989).On the other hand, probably not all planetary wave type oscillations from the lower ionosphere have chance to be (indirectly) transported to heights of foF2.

Longitudinal size of planetary wave events
We analysed the planetary wave events for eight stations, which represented Europe, Japan, and the mid-latitude U.S.A. Similarity of occurrence (in the sense of simultaneous occurrence) of individual planetary wave type events observed in these three separated regions makes possible to estimate the longitudinal size of events or at least to put some constraints on that size.Altadill and Apostolov (2003) used another approach and found a typical longitudinal size of the planetary wave type events in foF2 as follows: T=5-6 days, 80°T =10 days, 100°T =16 days,180°w ith individual events covering up to the whole globe.
Our analysis reveals that there is almost no simultaneous occurrence of the T = 5 days events observed in Europe, Japan and US, even though statistical characteristics of their persistence are closely similar.Table VII shows an example of such a T=5 days event.The event first occurs in US (Wallops), immediately after the end of the event in US it appears in Europe, and a few days after the end of the event in Europe it appears in Japan, which looks like an eastward propagation of an event of limited longitudinal size.However, if we consider the longitudinal difference between the regions (stations) and the typical longitudinal size of 80°f ound by Altadill and Apostolov (2003), the observed absence of simultaneous occurrence of wave events coincides with the typical longitu- dinal size of such events established by Altadill and Apostolov (2003).
We analysed several T=7 days events.Such events observed at European, Japanese and US stations showed again almost no simultaneous occurrence of individual events.The T=10 days events also mostly displayed absence of simultaneous occurrence, as the event shown in table VII, in correspondence to their typical longitudinal size of 100°as found by Altadill and Apostolov (2003).
On the other hand, a few T=16 days events, which were studied, revealed much often simultaneous or partly simultaneous occurrence of wave events between European, US and Japanese stations.One such event happened in 1984 with beginning around day 60 and persistence of four wave cycles in Europe (at all four stations), and beginning slightly later and persisting again about four wave cycles for Wakkanai, Boulder and Wallops Island (at southernmost Akita persistence shorter than three wave cycles).This is consistent with their much larger typical longitudinal size found by Altadill and Apostolov (2003).

Discussion
We investigate the persistence of planetary wave type oscillations over Europe among others in order to clarify possible predictability of such oscillations with applications to the predictions of the radio wave propagation conditions.For the sake of predictions, not only the typical values of the persistence of planetary wave type events, but also the spectral distribution of persistence of individual events (= event duration) is required.An example of the spectral distribution of event duration is shown in fig.3, which presents for each region one station.The spectral distribution of event duration is too broad to allow a reasonable prediction of event duration from foF2 measurements themselves.Moreover, figs. 1 and 2 display many events of duration shorter than three cycles, which is the lower limit of studied events.Thus the predictability of the planetary wave type oscillations in foF2 from the measurements of fof 2 itself seems to be very questionable.We have to look for other predictors, which is complicated due to different physical origin of different planetary wave type events.Unfortunately, we will probably be unable to separate predictable planetary wave type events, which mean that they remain a part of the prediction noise.Improvement of the quality of radio wave propagation predictions in such a way seems to be rather impossible, or at least very difficult.
Some planetary wave events have sharp onset and end.Then the determination of planetary wave persistence depends on the time/period resolution of the used wavelet.Shape of selected wavelet influences how the wavelet captures/detects each wave-like event.However, the onset and end of most events is not so sharp and the accuracy of the determination of onset duration in such cases may be up to a few days, particularly for the «relative» evaluation.Therefore we can consider the accuracy of determination of the typical persistence of planetary wave events to be rather around half a cycle for 5-day waves, and better for longer periods in terms of wave cycles.

Conclusions
The basic characteristics of the F2 region, the critical frequency foF2, were analyzed for two US stations, Boulder and Wallops Island, two Japanese stations, Akita and Wakkanai, and the results were compared with the results of Las ˇtovic ˇka et al. (2003b) for four European stations Juliusruh, Slough, Pru °honice and Rome, and Las ˇtovic ˇka et al. (2003a) for the lower ionosphere above Central Europe.All data were analyzed over the period 1979-1989 (one solar cycle).Noontime average values (10-14 UT) of foF2 were used.The persistence of planetary wave type oscillations at periods near 5, 10 and 16 days and sometimes 7 days was studied with the use of the Paul, Morlet and Meyer wavelet transforms.Only events of duration of three cycles and more were considered.The main results are as follows: 1) There is a large temporal and partly spectral variability of planetary wave type activity.The migration of periods of planetary wave activity is also well visible.The large temporal variability of the planetary wave activity results in a limited persistence of the individual planetary wave type events.
2) For the 5-day wave, a typical persistence of well-developed wave events in foF2 is 4 wave cycles.For the 10-day wave, it is rather 3.5 wave cycles.For 16 days, the most frequent values provide typical persistence no more than 3 wave cycles.
3) In terms of the number of wave cycles in the planetary wave type events, the persistence decreases towards longer periods.However, the persistence of wave events in terms of days increases towards longer periods.
4) The planetary wave type wave persistence characteristics for Europe are either identical with or very slightly larger than corresponding values from the U.S.A. and Japan.
5) The spectrum of event duration is very broad.The character of the spectrum does not allow us to predict the duration of an event when we observe its beginning or, say, first 2-3 wave cycles.
6) The longitudinal size of the planetary wave type events increases with increasing period, making the 5-day and 10-day period events in Europe, America and Japan essentially dissimilar, and the 16-day oscillations much more similar among the three regions.
7) While the typical persistence of planetary wave type oscillations in foF2 and the lower ionosphere over Europe is similar, the correspondence of occurrence of individual events is rather poor.
only the results of the Mayer wavelet transform as published by Las ˇtovic ˇka et al.

Figure 1
Figure 1 presents an example of the normalized wavelet power spectrum for the Morlet wavelet transform.The Morlet wavelet transform results are evaluated for the normalized absolute power, i.e. we search for intervals with values larger than a fixed value.In terms of colours in fig. 1 it means that we consider only intervals with yellow and red colour of the duration of at least three wave cycles.Only results inside of the conus-of-influence (black thin curve) are taken into account.The border effects affect the information out of the thin curve.Even though the values shown in fig. 1 are normalized, the way of their interpretation with respect to a fixed level is hereafter called «ab-

Table I .
Co-ordinates of ionospheric stations and missing intervals from period1979-1989.

Table II .
Statistics of persistence of planetary wave type oscillations in foF2 for stations from the Northern America and Japan based on the Paul wavelet transform («absolute» evaluation).The average values for medians and the most frequent values are presented with a step of 0.5.

Table III .
Statistics of persistence of planetary wave type oscillations in foF2 for stations from the Northern America and Japan based on the Morlet wavelet transform (absolute values).The average values for medians and the most frequent values are presented with a step of 0.5.

Table IV .
Statistics of persistence of planetary wave type oscillations in foF2 for stations from the Northern America and Japan based on the Morlet wavelet transform (relative values).The average values for medians and the most frequent values are presented with a step of 0.5.

Table V .
Statistics of persistence of planetary wave type oscillations in foF2 over Europe based on the Morlet wavelet transform (relative values).The average values for medians and the most frequent values are presented with a step of 0.5.After Las ˇtovic ˇka et al. (2003a).

Table VI .
Statistics of persistence of planetary wave type oscillations in foF2 over Europe based on the Morlet wavelet transform (absolute values).The average values for medians and the most frequent values are presented with a step of 0.5.After Las ˇtovic ˇka et al. (2003a).
* = ∼220 days long period of persistent occurrence in 1980.

Table VII .
A T=5 days event and a T=10 days event, both observed in the second half of 1986, Morlet wavelet transform.Too short means shorter than 3.0 cycles; short bursts means only short, separated bursts occur.