Spectrum analysis of the critical frequency of the F2-layer

Journal of Atmospheric and Terrestrial Physics, 1966. Vol. 28, pp. 447-4513. Pergamon Press Ltd. PrInted in Northern Ireland

Spectrum analysis of the critical frequency of the D.S.I.R.

C. H. CUMMACK Geophysics Division, Geophysical Observatory, Christchurch, New Zealand

F24ayer

P.O. Box 2111,

(Received 24 September 1965) Abstract-Spectrum analysis of the critical frequency of the FZ-layer, using the standard techniques of stationary time series, has yielded new information about the ionosphere. It has been established that within the sample, f,,FZ is not statistically homogenous in space. Trevelling disturbsnoes having velocity characteristics similar to those studied by MUNRO,but being greater in size by about an order of magnitude, exist in the F-region. These waves are highly dissipative. Irregularities of size about 4000-5000 km, moving at about l-2 km/min also exist. It is suggested that these arise from large scale atmospheric irregularities moving with the atmosphere.

TRAVELLINQ irregularities in the ionosphere have been the subject of much study. Most of this work has been carried out by the spaced receiver technique using a closely spaced aerial array. MUNRO (1958) has used a larger spacing and detected moving irregularities of dimensions about 500 km. while HEISLER (1959), by examining ionograms from an array of ionospheric stations, has detected isolated cases of ‘giant travelling disturbances’. Little seems to be known of the nature of these irregularities or the spectrum of sizes from which thay are derived. Irregularities of sizes in space and time between those detected by Munro and the solar or lunar tides, or even larger, remain unexplored. It is the purpose of this paper to show that large irregularities, having interesting properties, exist. The techniques used are the standard methods of stationary time series analysis. Estimates of the auto-correlation and the cross-correlation functions as well as spectral estimates of the power spectrum and cross-spectrum are the standard analytic tools. As these methods are treated in any text on meteorological statistics (e.g. PANOFSKY, 1958), discussion will not be repeated here. TRE

DATA

For a preliminary study, values of the critical frequency of the FZ-layer (f,,K?) from five stations in the Japsnese zone were chosen. The sampling periods were January 18-27 and April 6-16, 1964. These samples possessed the following advsntages: they showed interesting fine structure; they were at sunspot minimum and therefore minimized the influence of magnetic storms; they had almost continuous data, which could be read off the frequency plots at quarter-hourly intervals. Interpolation over spread P and missing values did nor exceed 6 per cent ; except for Taipei, where spread P is more prevalent, and interpolation did not exceed 10 per cent. Yamagawa was eliminated from the April sample for this resson. The geographic distribution of the stations was not ideal, having insticient spread in north-westerly and south-easterly direction. 447 2

C. H.

448

Chl’MACIi

Table 1. The ionospheric stations used for this analysis Geographic Long.

Station

Lat.

Wakkanai Akita Kokubunji Yamagawa Taipei

45”24’N 39”4d’N 35”42’N 31”21’N 26”OO’N

141”41’E 140”08’E 139”29’E 130’37’E 121”05’E

Geomagnetic Lat.

Station symbol

353”N 29.5”N 25.4”N 20.3”N 13.6”N

W A K Y r,1

As fJ2 is not & homogeneous measure it is desirable to devise a statistic giving equal weight to perturbations occurring at different times of the day. It is also desirable that the statistic retain some physical meaning. The statistic chosen was

where

fi,

is the F2-layer

critical frequency. i day index

j hour index f; mean hourly value over the sample. Using the familiar relation N,, = 1.24 x 104f,j2 where Nit is the maximum

electron density of the F2-layer, XijM&

we see that

1 AN...

Thus, we have devised a statistic which eliminates the diurnal variation of f,F2, normalizes the perturbations diurnally and may be expressed in physical terms. RESULTS The first step in the analysis of the data was to estimate the auto-correlation and cross-correlation functions for the two samples. Examples of these functions are given in Fig. 1. It was immediately obvious from these results that the auto-correlation functions were not homogeneous in space. Periods of several days were more apparent at the lower latitude stations while the shorter periods dominated at the other three stations. From the cross-correlograms it was also obvious that these shorter periods showed apparent motion. Long period components were thon smoothed out graphically and the space correlation functions estimated at time lags of zero hours and one hour for both samples. These are shown in Fig. 2.* It is obvious that large scale structures, of typical size about 4000 km exist in the F-region. These have the appearance of an aperiodic phenomenon, dissipating within a distance of about 2000 km or half a wavelength along the direction of travel. The velocity of movement is of the order of 10 km/mm directed south-south-west in winter and north-east in spring. From a consideration of Figs. 2(a) and 2(b) it appears that the patch is elongated, perhaps by a factor of two, in a direction perpendicular to the direction of travel. The inadequacy of the station array is obvious; for the * See note added in proof ou p. 456.

Spe&um analysis of the critical frequency of the PZ-layer

-Kckutwnjr

18-27th Jo?‘6

------Yomogawo?8-27thJan’G

24

?2

36

hr

Time, (4

_______mji-&&a

-Ycnnap,~-Tcipai

$-*thPJrilM

l6-27thJwt.W

(b)

Fig. I, (a) Examples of the &uto-co~elation fun&ions; (b) examples of the o~ossoorrelf&ionfunctions.

449

460

C.

H.

CUMMACK

207

PPRL ah-5th 20-N

006.

T= ohm-3

005 eo7

-0056

20-w

_.-

-

--

07. OBB

9x)

-357 357 3 ,’ ._

ZQ’E

04 O‘W

o-004

05-3

033

.-002

001

-002

(b)

Fig. 2. (a) The apace correlation function at zero and one hour time laga for January 18-17 1964; (b) the apace correlation function at zero and one hour time lage for April 6-16 1964. ample it merely establishes the direction of travel to be in the north-easterly quadrant. Cross-correlograms may be used to establish the mean time delay in the passage of events between stations. This method is far less satisfactory than constructing the space correlogram (BABBEB, 1966), as it is necessary to know the shape of the irregularity and its rate of decay before accurate velocities can be computed. As a first approximation the irregularities were assumed to consist of a striped pattern moving

second

Spectrumandyais of the criticalfrequencyof the PZ-layer

451

in a direction perpendicular to these stripes and having no decay. The results of these calculations are shown as the dashed vectors in Fig. 2. In Fig. (2a), as would be expected, the velocity is greater than the result obtained from the space correlation function. However, this method is useful in establishing the direction and upper limit of speed in the second sample (see Fig. 2 (b)) . Here again we find a typical speed of the order of 10 km/min. The long period components did not give good results by either of these two methods and consequently complete decomposition of the time series was attempted. From the auto-correlation functions estimates were made of the power spectra. In an effort to resolve the bands, high resolution but poor precision was chosen. The power spectra were computed to eleven degrees of freedom yielding values of power, for 90 per cent confidence level, lying between a factor of 2.6 and O-56of that estimated. The spectra in the period range of 2.26-0-6 hr showed only white noise accounting for about 6 per cent of the total power; this part of the spectra has not been reproduced. For further studies of this type quarter-hourly values are thus wasted effort. The spectra, shown in Fig. 3, give good consistency. Amplification of the long period components at both Taipei and Yamagawa, is statistically significant. As this shows a consistent latitudinal variation it appears to be a property of the lowlatitude ionosphere and consequently deserves future investigation. Next, the co-spectra and quadratic spectra were estimated from the crosscorrelograms. From these, and the power spectra, coherent bands were found. The results of these calculations are shown in Table 2 ; coherence for 95 per cent confidence or greater is indicated by an asterisk. Those bands coherent between 70 per cent or more of the available station pairs were then considered suitable for velocity determinations. The April sample gave inconsequential results; no new information was found, although the results obtained from the construction of the space correlation functions were verified. On the other hand the January sample gave more interesting results. Consequently all January determinations have been plotted in Fig. 4, and this will be used as a basis for further discussion. The velocities derived from the January sample fall into three groups. These will be discussed separately. The first group occur as isolated bands within the period range of 2.25-12.85 hr. These do not seem to be associated with any peaks in the power spectra. They travel with a velocity of lo-20 km/min in a southwards direction. This is similar to the velocity found from the space correlation function; thus this group is identified with the disturbances found by the previous methods. The mean of this group is shown as the dashed vector o in Fig. 4. For the sake of comparison the vector a, the velocity derived from the space-correlation function, and the vector b computed from the time delay method are also shown. This group we will call travelling disturbances. The second vector of interest, designated by 8 in Fig. 4, has a periodicity close to twelve hours. It is suggested that this band has arisen through the procedure adopted for normalizing the data. The application of equation (1) is mathematically equivalent to passing the data through a very narrow filter. A residue of the diurnal component is expected in the output if, for example, the diurnal variation is modulated by the length of the day. As the diurnalvariation provides the major part of

C. H. CUBMACK

452

Power soectro 18th - 27th Jan. 1964

S-----O

Taipei

c - - + Kokubunji o---a AkIlo

2 8

4

6

8

t0

I2

14

if

$

16

18

-

Wakkanai

x-x

Yamaqawa

20

22

24

26

28

30

32

34

36

38

(a)

Power 6th-16th

-

-

April, 1964

Tatpei

*----e o-

spectra

Kokubunji --4~

Aklta Wakkanai

\

6 4

it

0

O8

(b) Fig. 3. (a) Power spectra for all stations during the period January 18-Z 1964; (b) power spectre for all station8 during the period April 6-16 1964.

40

D 90 45 30 22.5 18 16 12-86 1l-25 10 9 818 7-60 6.92 6.43 6.00 6.63 5.29 5-00 4-74 4.60 429 4.09 391 376 3-60 346 3.33 321 3.10 3.00 2.90 281 2.73 2.66 2.67 2.60 2-43 2.37 2.31 2.26

(hr)

Period

*

l

*

*

*

* *

l

*

*

*

*

*

*

l

*

t

l

+

*

*

*

*

*

*

*

*

*

*

*

*

l

l

*

l

*

*

*

*

l

*

*

*

*

l

*

*

l

*

l

l

*

* * *

*

*

l

*

*

*

l

* * *

l

*

* *

l

l

l

Velocity

11 10 14

16

12

21 31

2 3

U=/mb)

1740 165” 1710

1910

2390

1710 266O

83O 187O

Bearing E ofN

*

+ *

l

l

* * L * *

l

* * * * +

l

l

* *

l l

*

l

l

*

*

*

e

l

*

*

l

*

*

l

*

1

l

*

l

l

l

1

l

l

*

l

*

t

*

*

l

l

*

l

*

.

l

*

*

l

*

*

*

l

l

*

*

*

*

*

*

*

l

*

*

*

l

* *

*

* *

*

*

April 6-16, 1964 W/H W/K W/T A/K A/T K/T

Velocities are also given for the highly coherent bands.

l

*

*

*

*

*

*

*

l

*

l

l

*

*

l

*

l

1

l

l

*

*

*

*

*

*

*

*

* l

l

l

l

*

*

*

*

l

*

l

*

*

l

*

*

*

l

*

* * * *

* *

l

l

*

*

*

*

*

*

l

* * * * * *

*

*

*

*

*

*

*

*

1

*

t

*

* * * *

*

l

*

l

*

* * *

*

*

*

l

January 16-27, 1964 W/A W/K W/Y W/T A/K A/Y A/T K/Y K/T Y/T

* Denotes coherence with confidence exceeding 90%.

0 1 2 3 4 6 6 7 8 9 10 11 12 13 14 16 I6 17 18 19 20 21 22 23 24 25 26 21 28 29 30 31 32 33 34 35 36 37 38 39 40

Band number

Table 2. Tbii gives the banda oohewnt between station pairs Velocity

11

29 39 28

(km/k)

93O

45” 62” 366’

Bearing EofN

454

C. H. CUMMACK

Kg. 4. Movement vectors for the coherent bands during January 18-27 1964. The ‘numbered’ vectors refer to band numbers, see Table 2. The lettered vectors are: a-the velocity computed from the space correlation function; b-velocity computed from cross correlogram time lags; c---mean of vectors 7, 22, 25, 38, 39,40; d-velocity of sun-rise lino across Japan. the raw data variability, this is not unreasonable. Vector d, also shown in Fig. 4, represents the velocity of the sunrise across Japan. It could also be suggested that this vector contains a travelling disturbance component as vector 8is roughly the addition of vectors c and d. In the 45-90 hr periodicity range large scale perturbations travel with a velocity This analysis is not particularly of 2-3 km/min in the south-easterly quadrant. suited for the study of irregularities of this size, but their existence has been definitely established. These irregularities carry the majority of the power at the low latitude stations, thus a direction eastwards rather than north appears more consistent.

From the previous statistical analysis, two classes of phenomena have emerged. They have been loosely called “travelling disturbances” and “large scale perturbations”. We will discuss these separately. The travelling disturbances have Fourier components of period from two hours to a little above twelve hours while their ‘typical size’ ranges from -900 to 6000 km. The term “travelling disturbance” is thus a misnomer, particularly for the large sizes. However, the phenomenon has much in common with those travelling disturbances studied by ?oIu,v~o (1958), so the term will be retained. The direction of travel for both the January and April samples is consistent with that found by Munro, though the velocity is some fift.y per cent higher. The dissipation rate per wave-length for both phenomena are comparable. Munro’s travelling disturbances however are of typical size about several hundred kilometres. These, though somewhat smaller were observed mainly in the Fl-region of the ionosphere while here we are concerned with disturbances situated somewhat higher. With these points in common, the two phenomena could well form part of the same spectrum and have a common

Spectrumandysis

of the oriticel frequency of the l%‘-lttyer

455

physical cause. It is interesting to note that these travelling disturbances have a low frequency cut-off at about the lunar and solar semi-diurnal variation frequency. At this low frequency it is difficult to imagine them as a travelling disturbance. If, however, disturbances are modulated by the solar and lunar tides, this would resolve the difficulty. WRIGHT (1962) found similar conditions in her study of night-time travelling disturbances at Rarotonga. It may be further suggested that, since the power available near the lunar and solar periods exceeds than in other bands, the energy input may arise from turbulence generated by tides. These suggestions, however, are consistent only with the January sample; other mechanisms could also generate these disturbances. The difference in scale size with Munro’s results could be due to difference in observability; only when the curvature of the iso-ionic contour reaches a certain critical size is multiple reflection possible. This would weight observability strongly towards the smaller sizes in Munro’s analysis. The large scale patches present some difficulties in the present study. Their existence is real, although their properties would be better studied from a longer sequence of data having a more widely spaced station array and a bigger sampling interval. Their velocity cannot be established with any certainty as they appear to move in the least favourable direction over an array with a spread far less than a wave-length. They appear to have a patch size of the order of 4000 km with a perturbation magnitude about ten times greater at the lower latitude stations. A southeasterly movement would require the patches to grow in depth as they moved. This does not seem plausible. A patch of this order of size and velocity is capable of only one physical interpretation. The order of magnitude is such as to preclude electrodynamic or acoustic perturbations. It is therefore suggested that these patches are due to large scale atmospheric irregularities reflected in ionospheric perturbations and moving with the atmosphere. This study is an initial survey to determine the parts of the f,,E”2 disturbance spectrum that are worth further investigations, the optimum station array necessary for this study, and, the data requirements. In this study only irregularities which travel along the line of stations have been found with any reliability. The results for other groups must be regarded as tentative. It is hoped to continue this work as suitable data and computing facilities become available. Acknowledgements-This work is part of the research programme of the Christchurch Geophysical Observatory, of the New Zealand D.S.I.R.; Superintendent, Mr. J. W. BEAQLEY. Thanks are due to Mr. M. D. LAWDENfor programming the IBM 1620 Computer and to Mr. B. A. M. MOON,Supervisor of the Mobil Computer Laboratory of Canterbury University, who made computing facilities available. REFERENCES BARBER N. F. HEISLER L. H. MUNRO G. H. PANOFSKY H. A.

1956 1969 1958

1968

Au&. J. Phy8. 11, 91. SomeApplicutiom of Stcltiatics to Meteorology. PennsylvaniaState University,

WRIUHT M. D.

1962

J. A&mph.

J. Atmmph.

Terr. Whys. 8, 318.

Nature, Lord

183, 383.

Pennsylva~.

Terr. Phye.

24, 857.

456

c’. H.

&LWdACK

Note a&led in proof

The method of estimating drift by examining the form of the correlation pattern in space for different lags is due to BARBER(1965). He showed that the original time series R(s, y, t) and t.he three-dimensional correlation function p(X, Y, T) are composed of the same set of moving sinusoids. Here X, Y are station separation co-ordinates while T is time lag. He also showed that the correlogram always has conjugate symmetry given by the relation p(X, Y, T) = p*( -x,

-Y,

V).

Since here p is a scalar quantity then p(X, Y, T) = p(-x,

-Y,

-7)

and p(X, Y,

-T)

=

f3( -x,

-Y,

T)

For a given lag we may read from a cross correlogram two correlation coefficients referring to the mirror image points (X, Y); (-X, - Y). By using a network of stations we may map the correlation coefficient at different lag times. A movement in the correlation contours has the same statistical properties as any moving patches in the original time series. The results of applying this method are shown in Fig. 2.