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Conjugate and closely-spaced observations of auroral radio absorption—II
Planet.
Space Sci. 1969,
Vol.
17, pp. 1485 to 1495.
Pergamon
Press.
Prmted
in Northern
Ireland
CONJUGATE AND CLOSEL;Y-SPACED OBSERVATIONS OF AURORAL RADIO ABSORPTION-II CORRELATION
Space Disturbances
Laboratory,
PROPERTIES
J. K. HARGREAVES* ESSA Research Laboratories, (Received
Boulder, Colo. 80302, U.S.A.
3 Murch 1969)
Abstract-Data on the aurora1 absorption events observed with riometers at and near the conjugate stations, Great Whale River and Byrd, are analyzed by means of correlation coefficients. The greatest correlation between conjugate regions, taking any displacement of conjugate point into account, is usually in the range 0.64.75; some, but not all, of the loss of correlation is attributed to a wandering of conjugate point by about 200 km. The analysis is unable to detect any loss of correlation as magnetic activity increases, although such a decrease has been reported in conjugate aurora1 observations by optical means. The paper points out, with examples, the difficulty of relating correlation patterns to the properties of the actual events. 1. SIGNIFICANCE
OF CORRELOGRAMS
1.1 introduction In many of the studies of aurora1 radio absorption which have been published to date, the spatial properties of the absorption regions were described by working out the correlation coefficients between pairs of riometer records taken simultaneously at separated stations, and the conjugate agreement was defined in terms of inter-hemispheric correlation coefficients. Correlation analysis differs from the gradient analysis used in Paper I (Hargreaves, 1969) in that it deals with variations of absorption rather than with the absorption itself. Thus it cannot show a simple difference of intensity, or even a spatial variation of intensity if the time variations at the spaced stations are coherent. It is a useful way of putting a number to the relative variability, but if absorption events are considered as sequences of discrete occurrences, as is the concept in these papers, the significance of the correlation coefficient needs to be carefully considered. This problem is considered in Section 1.2. Regarding the spatial properties within one hemisphere, the correlation approach has generally shown patterns several hundred kilometers across, though the shape and size vary from author to authort (Holt et al., 1961; Leinbach and Basler, 1963; Little et nf., 1965; Parthasarathy and Berkey, 1965; Hargreaves and Ecklund, 1968). We shall see, * Present address: Environmental
Services Department, University of Lancaster, Lancaster, England. t In attempting to reconcile the various measurements, which agree in broad outline but conflict in detail, it should first be remembered that the correlation coefficients have been worked out in different ways. Sometimes the absorption was read every hour, which is equivalent in practice to taking a random sample through the record. Sometimes hourly values were used onfy if they exceeded some threshold; this method excludes the Iong periods of zero absorption between events, and since the stations may show activity together but have no correlation of detail, this method will give correlation coefficients smaller than those derived by the previous method. In some cases the records were read only during events but then at short time intervais, a method which gives more weight to the temporal fine structure-though if the interval is only a few minutes adjacent readings are highly correlated and then the significance of the result may be much lower than appears at first sight. Also, the correlation pattern may vary from physical causes, changing with time of day, season, level of activity, and so on. 1485 4
1486
J. K_
RARGREAVES
however, that the size of the correlation pattern is not necessarily the same as the geographical extent of an average absorption event. In the study of conjugate properties, there is no obvious objection to taking points showing the best inter-he~spheric correlation as the median corresponding points (Leinbath and Baster, 1963 ; Little et tab.~ 1955 ; Hargreaves and Ecklund, 1968)-a definition of correspon~ng points as places where the variations are most simiIar seems as valid as one based on the spatial maxima of individual events. However, the value of that best corretation coefficient cannot be taken directly to indicate the measure of inter-hemispheric agreement, because it will also be affected by any wandering of the corresponding point (Hargreaves and Ecklund, 1968), which therefore has to be estimated and taken into account. Apart from the value of the correlation between corresponding points, an interesting question is whether it varies as the level of activity increases. Conjugate optical work (Belon et csl., I967,1368) suggests that the correlation decreases as the planetary magnetic activity increases, but such an effect has not yet been reported for radio absorption. The present paper presents a correlation analysis of the measurements of aurora1 radio absorption made at and near the auroral-zone stations Great Whale River (Canada) and Byrd (Antarctica) during 1966 and 1967. 1.2 ExampIes Before analyzing observational data we shall examine theoretica~y, by means of examples, how the correlation patterns are related to the actual absorption events. If the spatial variation of a given absorption event is described by A = A, exp
c
- &% 0
1
where A, is the absorption at the maximum, A is the absorption at the point x, and x0 is the width of the event, the correlation coefficient between observations at c, and X, is
=
A,Ag- - A;l&
[(AT
- A;z)(A,a - ,i2)]1’2
(2)
where A, = A, exp [--x12/2x02] and A, = A, exp [- x2”/2x02], and the bars represent averages over many readings. Variations from event to event can arise from a variation of magnitude (Ao), variation of position of the centre of the event (x) and variation of width (x0;). We consider these three effects separately. Case (1): only & varies. If all events are the same size (x0 = coast.) and fall at the same geographic position (x1, x2 = const.). it is easily seen that p = 1 for all values of x0, x1 and x2, In this case a correlogram gives no information about the individual absorption events. Case (2): only x1 and xa Yary. Now let all the events be of the same intensity (A, = const.) but vary in position, so that xl = xX’ + dx and x2 = x,’ + dx, x1’ and x~’ being the mean distances from the centres of the events. Let dx vary with distribution function N(dx) ==exp [-
g2].
OBSERVATIONS
OF AURORAL
RADIO
1487
ABSORPTION-II
Then, by integration,
P=
1
2/l + 2P - ---L exp [&])]“” (1 + P)
(3)
X, = X - AX/Z, where P = (dx,,/xJ2, Q = l/P, X, = x1)/x0, X, = x,‘/x,,. Putting X2 = X + AX/2, where AX is the separation of observing points measured in units of x,,, and X is the distance from the midpoint of the observing pair to the midpoint ofthe average event,
P= [
1
-
(1 + P)t’l
X2(4 + 3Q) -i- p exp
(1 + Q)(2 + Q)
QXAX (1 +
1 [ 1 [
@X2)(4 + 3Q>
exp
Q>P + Q>
40 + QG
+ exp
1
+ Q> ’
-QXAX
(1 + PI@ + Q)
l/2
’ (4)
If the events are centered
which is negative
over the midpoint,
if AX is large enough
X = 0, and
or P small enough,
@X2) > 4(1 + Q> In dlsp
i.e. if ;
p tends to -1 as P tends to zero. If the centres of the events are widely distributed with respect to the stations, P is large, and p=exp[-y]=exp[-s]
(7)
which is wider than an individual event by a factor 42. Thus the correlation coefficient can be used to measure x,, only if the events are spatially widely distributed. Curves of p are shown in Fig. 1. It is clear that the correlogram depends strongly on P and X as well as on the extent of the individual event.
1488
J. K. HARGREAVES
FIG. 1. CORRE~RA~S~OR
EVENTS WITH MOVING CENTRES.
Case (3): only x0 varies. We now consider A,, x1 and x2 to be fixed, and let .q, be uniformly distributed in the range x,,~to xoZ, with xoZ - .xol = 6x,. Then it can be shown that
\
(8) where H(z2, 21) =
exp (-z22> 22
exp (-z12) +
\G
(erf 2s = erf zl)
Zl
and 2 t erf z=-...--4; s 0 e-8Z d=Y and
Figure 2 shows curves of p against AX for this situation, where X, the distance of the midpoint from the centre of the events, is 0.0, 1.0 and 2-O. The correlation pattern is much broader than the average event, and is always unity for events centered overhead. Out of three examples, only in one (extreme) case is the correlogram simply related to the size of the events. Since the actual event-to-event variation of absorption over a riometer station presumably contains contributions from all three causes (Ao, x, x0), it is clearly not possible to deduce much about the spatial size of individual events from a
OBSERVATIONS
FIG.
2.
OF AURORAL
CORRELOGRAMS
RADIO
FOR EVENTS WITH
A~SORFTION-Ir
VARYING
1489
WIDTH.
measured correlogram. We may use the correlogram as an entity in its own right, as a measure of spatial coherence, but must not confuse it with the original events. 2. RESULTS
The data are the readings of peak absorption at Great Whale River and Byrd, 5 spaced readings being obtained at each station, as described in Paper I. The procedures used are described in Section 2.1 of that paper. Correlograms of the type shown in Figs. 3 and 4 were computed for sets of absorption values divided in several ways, according to time of year, time of day, and level of magnetic activity as indicated by K,. The value of k;, was taken to the nearest whole number, except that if K, changed at the time of the peak the earlier and later values were averaged and this introduced some half-integral values. The unit of separation or displacement is the distance between the effective points of an oblique antenna and the vertical (i.e. about 12.5km). The intra-liemispheric correlograms include data from both Great Whale River and Byrd. For example, the first group of points on Fig. 3(a) are cross-correlation coefficients between the pairs of channels Great Whale River (North)-Great Whale River (vertical), Great Whale River (vertical)-Great Whale River (South), Byrd (North)-Byrd (vertical), and Byrd (vertical)-Byrd (South); the points at two units of separation are from the pairs Great Whale River (North)-Great Whale River (South), and Byrd (North)-Byrd (South). In the inter-hemispheric correlograms, the extreme left-hand point on Fig. 3(a) is from the pair Great Whale River (South)-Byrd (South); the next points are Great Whale River (vertical)-Byrd (South, and Great Whale River ~South)-Byrd (vertical); and so on. Table 1 gives the results for 19 computations, performed in three groups. Initially, two periods of the day, 000~400 UT (the pre-midnight period) and 1000-1900 UT (covering morning and noon) were studied as a function of season. Since no marked seasonaf variations appeared, many months were put together and the data were then divided according to K,. The results are summarized as follows. 2.1 Width of intra-hemispheric correlogram The correlation pattern falls to 0.61 in a distance of a few hundred kilometers. Individual patterns may be elongated North-South or East-West, but the average pattern is almost circular except for the Byrd observations by night. The pattern tends to be broader by day
1490
J. K. WARGREAVES
t+o b)Kp=2$-3 l.
c-8 0.6
P
!
04
North-South
0.2
. b r
0
1
02
.
h&-
l
04 East -West 0.2
t
,L
f
Sfporolco”
separation
IWT
IO
P .
Q-8
i.
0.6 *
.
i
c-6
W.’
1
P6-
P
North-South
(
.
*
l
T
I
0.2
t1.
t
Eost
t
0.2 ‘
f
liorfh
South
~ west
East
too ~lK~=3$-9
.”
c-8-
f
2 %
K
P6-
‘j
P -
’
04 -
P North-South
iI4
$ 5
w
0‘2 -
I_
East-West
t
ok
Seporot lo” IQ
P
I
I
i O-4
J-J--fSeporotlon II)
P
I
FIG, 3. CORRELOGRAMSPOR MARCH-OCTOBERI~~~, fOOO-18OOUT. The bars indicate the standard error of the mean. One unit of separation or dispracement about 125 km.
is
OBSERVATIONS
OF AURORAL
RADIO
ABSORPTION-II
1491
19
li’ B
GWR
08
o$ P 04
East - West
c-z
t0r
P
P North-South
c-4
0.2 t
t
Ot---J-PO
Pi
Separation
T
North-South
Ot---J-
Sepmtlon ho-
P
At South
North Dwplocement
West
at GWR wth
I
t
respect to Byrd
t
East
--
*f
I West
Drsplocement at GWR with respect to Byrd
FIG. 4. CORRELOGRAMS FOR FEB. 1966JAN. 1967,0200-0500 UT. The bars indicate the standard error of the mean. One unit of separation or displacement about 125 km.
is
o-3 3.5-9 (r2 2.5-3 4.5-9
D-19 IO-19 D-19 10-19 IO-19
02-05 02-05 02-05 02-05 02-05
lo-19 02-05
3-10 3-10 3-10 3-10 3-10
2-13* 2-13 2-13 2-13 Z-13
3-10 02-13
330 350
:5’ 28
Camposite Composite
&9 O-9 220
250 200
370 250
320 250 150 370 450 370 240>450
260 340 140>450 >450 80>450 240 310
390 420 310 310 440
430 >450 220 >450 440
45 Jr
340450 >450 > 450 >450 >450 240 250 380 370>450
East-West CWR B
300 400 >450 275 >450 >450 280 400 430 200 >450
North-South GWR B
O-3 3.5-9 o-2 4.5-9 2-5-3
:: 33 29 6
3s; 33
;: 42 25 42
34
pso, of points
* Month ‘13’ is January of the following year.
:z 8-10 S-10
&9 Q-9 t-b9 o-9 &9 o-9 &9 O-9 O-9
O&-O6 10-19 00-06 lo-19 IO-19 00-06 lo-19 00-06 10-19
5-7 5-7 11-13 11-13 12-13
XV
UT
Months
-
Width of intra-hemispheric correlogram to p = 0.61 (km)
>150kmS 120 km 5 >60 km S
>25O km N -250 km N 60kmN >120kmN 100 km S
120kmS 120kmN 50km.S >150kmN
-
North-Sauth (km)
Corresponding
SO.75 ~~0.65 0.5 >0*75 0.7 0.7 :,06 075
? w ,250 km W Okm ? w 80kmE 60kmE :-250 km W MfkmE
point to Byrd at Great Whale River .-Greatest East-West interhemispheric p, i;,0.7 >250kmW 06 >150kmW >0*6
%+&3tfl1. SUWKY OF COWLOORAAIS
790 500
410
240 >SOO 260
North-South >5OO >SOO > 500 >500 >SOO 410 350 280 >500
200 :-500 280
500 240 i500 310
r5OO > 500 > 500 3500 > 500 250 >500 ;400 >5BO
East-West
Width of inter-hemispheric correlogram to 0.61 of max. p (km)
8
% 53
!z
6
OBSERVATIONS
OF AURORAL
RADIO
1493
ABSORPTION-II
than by night. An earlier study (Hargreaves and Ecklund, 1968) also found circular correlation patterns, larger by day than by night, in the vicinity of Great Whale River. The patterns were narrower than the present ones by a factor 1.7-2.0; the difference may be due to the use of hourly values of absorption rather than absorption peaks. It seems unlikely that the difference of night correlation patterns between Great Whale River and Byrd (Fig. 4) can imply a corresponding difference in the size and shape of the absorption patches. The variation of correlation coefficient with distance from the centre of activity, illustrated in Fig. 1, is likely to be a factor. 2.2 Position of maximum
inter-hemispheric
correlation
For the day events (1000-1900 UT) maximum correlation with Byrd is found 60 to >250 km north of Great Whale River and somewhat west of it-see Table 1 and Fig. 3. The displacements are very poorly defined, but the directions agree with the position of the also agree computed conjugate point (see Fig. 1 of Paper I, for example). The displacements as well as could be expected with the results of a gradient analysis, set out in Table 2, (Gradiperformed on the averages of the absorption values used in the correlation analysis. ent analysis is described in Section 2.1 of Paper I.) TABLET.
Average absorption Cdb)
GRADIENT ANALYSISFOR 1000-1900UT
at GWR Average absorption (db)
at Byrd
Position of Byrd corresponding point with respect to Great Whale River*
K, range
N
S
E
W
N
S
E
W
R’
R”
0.C2.0
1.28
1.25
1.25
1.37
1.62
1.60
1.68
1.42
1.03
0.77
7 kmN 60kmW
2.5-3.0
2.20
1.96
1.89
2.17
3.31
2.71
2.99
2.55
1.37
0.74
80kmN 75kmW
3.5-9.0
2.51
2.78
2.66
2.64
3.15
2.32
2.67
1.99
1.21
0.75
50kmN 70 km W
* For Ax = Ay = 250 km, x0 = y0 = 250 km.
For the night period (0200-0500 UT) maximum correlation is found to the south of Great Whale River, as shown in Fig. 4, whereas gradient analysis (Table 3) shows the corresponding point to be to the North. The situation at the two stations differs in that, according to the gradients over the stations, the events tend to be centered poleward of Great Whale River and equatorward of Byrd, but it is not clear how this could move the position of best coherence away from the corresponding point deduced by gradient analysis. 2.3 Conjugate
wandering and maximum
inter-hemispheric
correlation
The inter-hemispheric correlation patterns tend to be slightly wider than the intrahemispheric patterns. If the widths (to p = 0.61) are respectively d,(inter) and d,(intra), the average value of d,(inter)/d,(intra) is 1.25 for the North-South direction, and 1.05 East-West. According to the treatment by Hargreaves and Ecklund (1968), one-dimensional wandering of the conjugate point withstandarddeviation 11’widens the correlogram to d,(inter)
= (do2(intra)
+ ,v~)~‘~,
1494
J. K. HARGREAVES TABLE 3. GRADIENTANALYSISFOR0200-0500 UT
Average absorption (db)
at GWR Average absorption (db)
at Byrd
Position of Byrd corresponding point with respect to R" Great Whale River*
K, range
N
S
E
W
N
S
E
W
R'
0%2.0
1.54
0.77
1.11
1.05
1.41
1.37
1.47
1.35
2.06
0.97
180 km N 10 kmW
2.5-3.0
1.33
1.15
1.14
1.29
1.95
1.49
I-83
1.91
1.53
O-92
110 km N 20 kmW
35-9.0
1-79
I.86
1.92
1.63
2.18
1.87
2.14
1.93
1.12
l-06
30 kmN 20 kmE
45-9.0
1.94
2.03
2.16
1.57
2.02
2.09
2.17
1.91
0.93
1.21
20 kmS 50 kmE
*ForAx=Ay=250km,x,=y0=250km
and the maximum value of the inter-hemispheric
correlation coefficient is
$ = ~~(intra)~~~(inter). The 25 per cent widening observed in the present case implies w = O-74 d,(intra), or w .w 150-270 km; and B = 0% The observed maximum values of inter-hemispheric correlation are summarized in Table 1 for the cases when a maximum or a clear trend could be seen. These values are no less than 0.5 but have not been seen to reach as high as 0.X. Values in the range 0.6-0.75 are most common. This suggests some loss of correlation not due to wandering, and we infer that even if wandering did not occur the greatest inter-hemispheric correlation would be less than unity and probably in the region 0%-0~9. The results suggest that loss of interhe~spheric correlation at the instantaneous corresponding points, and wandering of the corresponding points, contribute about equally to the observed degradation of correlation between conjugate regions. (Treatments of the type used in Section 3 of Paper I lead to a similar conclusion, since the irregular variation of the inter-hemispheric absorption ratio, r, is about halved by deleting points showing large displacement of corresponding point.) 2.4 The efSect of K, Figures 3 and 4 show the correlograms for the day and night periods for different ranges of E;,. For both periods, the maximum correlation (8) increases between the first and second ranges of lis,. At zero displacement the correlation decreases again for lu, > 35, but in these cases the point of best correlation seems to have moved beyond the range of the plots and its value cannot be specified. It can at least be said that no marked decrease of correlation occurs as KD increases. A variation of K, affects neither the intra-hemispheric correlation pattern nor the position of best conjugate agreement for the day events. The shape and size of the night correlation patterns do change as K, increases. These changes might be related to the equatorward displacement of the centre of activity with increase of K, (Paper I) which, in the present situation, moves it closer to Great Whale River but further from Byrd. The gradient analysis of Table 3 shows the corresponding point to Byrd moving South and East across Great Whale River with increasing activity, but the trend does not shown in the correlograms.
03SERVATIO~S
OF AURORAL
RADIO ABSORPTION-1~
1495
3. CONCLUSION
This study has shown one or two results which are of interest concerning the conjugate properties of aurora1 phenomena, but also, by illustrating some difficulties of interpretation, it has provided comment on the correlation method itself. Apart from the measurements of the correlation patterns within a single hemisphere, which show general agreement with previous work and with the results of gradient analysis, the most useful results are probably: (1) the evidence that both wandering of conjugate point and loss of correIation between instan~neous conjugate points contribute (about equally) to the degradation of inter-hemispheric correlation to its typical value 06O-75-this provides some idea of the short term (i.e. event-to-event) variation of conjugacy both with respect to position and to coherence. (2) the lack of evidence for a decrease of coherence under disturbed conditions-in spite of one’s intuitive feeling that conjugacy might become ‘looser’ when the magnetosphere is more disturbed. On the face of it, this result is at variance with the optical results so far reported. It should be remembered, however, that there are detailed differences between the absorption and the luminous phenomena: in particular, they depend on different particle energies and have different spatial extent, absorption resulting from the more energetic electrons and appearing in patches that are broader than most luminous features. Comparison with results of the gradient analysis tends to show agreement for day events. For the night events, however, discrepancies and anomalies abound, with correlation patterns differing between hemispheres and changing with K,, and with the position of best inter-hemispheric correlation displaced from the corresponding points deduced by gradient analysis. We cannot be certain of the reason for these discrepancies, but circumstantial evidence suggests that differences and movements of the centres ofprecipitation with respect to the observation sites are a factor. We also know that the night events have a greater variation of width than the day events, although the average size is much the same (Paper I). The theoretical di~cL~lty of relating a correlation pattern to an average event was pointed out in Section 1.2. In practice the difficulty seems more acute for the night events, and caution is needed when interpreting correlation analyses in the night sector. An analysis based directly on absorption values is to be preferred before one based on their variations, Acknowledgements-The raw data were obtained during the observational programme described in Paper I, in which connection the author acknowledges with thanks the assistance of W. L. Ecklund. F. C. Cowlev. H. C. Swanson, the U.S. National Scienze Foundation and the Canadian National Research Coun& Mrs. S. Hargreaves wrote the computer programs used in the present study. REFERENCES A. E., DAVIS, T. N. and GLASS, N. W. (1968). Conjugacy of visual auroras during magnetically disturbed periods. Antarct. U.S.A. 3, 117. BELON, A. E., MAGGS, J. E., DAVIS, T. N., MATHER, K. B., GLASS, N. W. and HUGHES, G. F. (1969). Conjugacy of visual auroras during magnetically quiet periods. J. geophys. Res. 74, 1. HARGREAVES,J. K. (1969). Conjugate and closely-spacedobservations of aurora1 radio absorption-4 Seasonaland diurnal behaviour. Planet. Space Sci. 17,1459. HARGREAVES, J. K. and ECKLIJND,W. L. (1968). Correlation of amoral radio absorption between conjugate points. Radio Sci. 3, 398. HOLT, O., LAh?)hmRK, B. and LIED, F. (1961). Analysis of riometer observations obtained during polar radio blackouts. J. atmos. terr. Phys. 23, 229. LEINBACH,H. and BASLER, R. P. (1963). Ionospheric absorption of cosmic radio noise at magnetically conjugate aurora1 zone stations. J. geophys. Res. 68,3375. LITTLE,C. G., SCHIFFMACHER, E. R., CHIVERS,H. 3. A. and SULLIVAN,K. W. (196.5). Cosmic noise absorption events at geoma~etically conjugate stations. 2. geo&s. Res. 70,639. PART~ASARATHY, R. and BERKEY,F. T. (1965). Aurora1 zone studies of sudden onset radio wave absorption events using multiple station and muhiple frequency data. J. geophys. Res. 70, 89. BELON,
Space Sci. 1969,
Vol.
17, pp. 1485 to 1495.
Pergamon
Press.
Prmted
in Northern
Ireland
CONJUGATE AND CLOSEL;Y-SPACED OBSERVATIONS OF AURORAL RADIO ABSORPTION-II CORRELATION
Space Disturbances
Laboratory,
PROPERTIES
J. K. HARGREAVES* ESSA Research Laboratories, (Received
Boulder, Colo. 80302, U.S.A.
3 Murch 1969)
Abstract-Data on the aurora1 absorption events observed with riometers at and near the conjugate stations, Great Whale River and Byrd, are analyzed by means of correlation coefficients. The greatest correlation between conjugate regions, taking any displacement of conjugate point into account, is usually in the range 0.64.75; some, but not all, of the loss of correlation is attributed to a wandering of conjugate point by about 200 km. The analysis is unable to detect any loss of correlation as magnetic activity increases, although such a decrease has been reported in conjugate aurora1 observations by optical means. The paper points out, with examples, the difficulty of relating correlation patterns to the properties of the actual events. 1. SIGNIFICANCE
OF CORRELOGRAMS
1.1 introduction In many of the studies of aurora1 radio absorption which have been published to date, the spatial properties of the absorption regions were described by working out the correlation coefficients between pairs of riometer records taken simultaneously at separated stations, and the conjugate agreement was defined in terms of inter-hemispheric correlation coefficients. Correlation analysis differs from the gradient analysis used in Paper I (Hargreaves, 1969) in that it deals with variations of absorption rather than with the absorption itself. Thus it cannot show a simple difference of intensity, or even a spatial variation of intensity if the time variations at the spaced stations are coherent. It is a useful way of putting a number to the relative variability, but if absorption events are considered as sequences of discrete occurrences, as is the concept in these papers, the significance of the correlation coefficient needs to be carefully considered. This problem is considered in Section 1.2. Regarding the spatial properties within one hemisphere, the correlation approach has generally shown patterns several hundred kilometers across, though the shape and size vary from author to authort (Holt et al., 1961; Leinbach and Basler, 1963; Little et nf., 1965; Parthasarathy and Berkey, 1965; Hargreaves and Ecklund, 1968). We shall see, * Present address: Environmental
Services Department, University of Lancaster, Lancaster, England. t In attempting to reconcile the various measurements, which agree in broad outline but conflict in detail, it should first be remembered that the correlation coefficients have been worked out in different ways. Sometimes the absorption was read every hour, which is equivalent in practice to taking a random sample through the record. Sometimes hourly values were used onfy if they exceeded some threshold; this method excludes the Iong periods of zero absorption between events, and since the stations may show activity together but have no correlation of detail, this method will give correlation coefficients smaller than those derived by the previous method. In some cases the records were read only during events but then at short time intervais, a method which gives more weight to the temporal fine structure-though if the interval is only a few minutes adjacent readings are highly correlated and then the significance of the result may be much lower than appears at first sight. Also, the correlation pattern may vary from physical causes, changing with time of day, season, level of activity, and so on. 1485 4
1486
J. K_
RARGREAVES
however, that the size of the correlation pattern is not necessarily the same as the geographical extent of an average absorption event. In the study of conjugate properties, there is no obvious objection to taking points showing the best inter-he~spheric correlation as the median corresponding points (Leinbath and Baster, 1963 ; Little et tab.~ 1955 ; Hargreaves and Ecklund, 1968)-a definition of correspon~ng points as places where the variations are most simiIar seems as valid as one based on the spatial maxima of individual events. However, the value of that best corretation coefficient cannot be taken directly to indicate the measure of inter-hemispheric agreement, because it will also be affected by any wandering of the corresponding point (Hargreaves and Ecklund, 1968), which therefore has to be estimated and taken into account. Apart from the value of the correlation between corresponding points, an interesting question is whether it varies as the level of activity increases. Conjugate optical work (Belon et csl., I967,1368) suggests that the correlation decreases as the planetary magnetic activity increases, but such an effect has not yet been reported for radio absorption. The present paper presents a correlation analysis of the measurements of aurora1 radio absorption made at and near the auroral-zone stations Great Whale River (Canada) and Byrd (Antarctica) during 1966 and 1967. 1.2 ExampIes Before analyzing observational data we shall examine theoretica~y, by means of examples, how the correlation patterns are related to the actual absorption events. If the spatial variation of a given absorption event is described by A = A, exp
c
- &% 0
1
where A, is the absorption at the maximum, A is the absorption at the point x, and x0 is the width of the event, the correlation coefficient between observations at c, and X, is
=
A,Ag- - A;l&
[(AT
- A;z)(A,a - ,i2)]1’2
(2)
where A, = A, exp [--x12/2x02] and A, = A, exp [- x2”/2x02], and the bars represent averages over many readings. Variations from event to event can arise from a variation of magnitude (Ao), variation of position of the centre of the event (x) and variation of width (x0;). We consider these three effects separately. Case (1): only & varies. If all events are the same size (x0 = coast.) and fall at the same geographic position (x1, x2 = const.). it is easily seen that p = 1 for all values of x0, x1 and x2, In this case a correlogram gives no information about the individual absorption events. Case (2): only x1 and xa Yary. Now let all the events be of the same intensity (A, = const.) but vary in position, so that xl = xX’ + dx and x2 = x,’ + dx, x1’ and x~’ being the mean distances from the centres of the events. Let dx vary with distribution function N(dx) ==exp [-
g2].
OBSERVATIONS
OF AURORAL
RADIO
1487
ABSORPTION-II
Then, by integration,
P=
1
2/l + 2P - ---L exp [&])]“” (1 + P)
(3)
X, = X - AX/Z, where P = (dx,,/xJ2, Q = l/P, X, = x1)/x0, X, = x,‘/x,,. Putting X2 = X + AX/2, where AX is the separation of observing points measured in units of x,,, and X is the distance from the midpoint of the observing pair to the midpoint ofthe average event,
P= [
1
-
(1 + P)t’l
X2(4 + 3Q) -i- p exp
(1 + Q)(2 + Q)
QXAX (1 +
1 [ 1 [
@X2)(4 + 3Q>
exp
Q>P + Q>
40 + QG
+ exp
1
+ Q> ’
-QXAX
(1 + PI@ + Q)
l/2
’ (4)
If the events are centered
which is negative
over the midpoint,
if AX is large enough
X = 0, and
or P small enough,
@X2) > 4(1 + Q> In dlsp
i.e. if ;
p tends to -1 as P tends to zero. If the centres of the events are widely distributed with respect to the stations, P is large, and p=exp[-y]=exp[-s]
(7)
which is wider than an individual event by a factor 42. Thus the correlation coefficient can be used to measure x,, only if the events are spatially widely distributed. Curves of p are shown in Fig. 1. It is clear that the correlogram depends strongly on P and X as well as on the extent of the individual event.
1488
J. K. HARGREAVES
FIG. 1. CORRE~RA~S~OR
EVENTS WITH MOVING CENTRES.
Case (3): only x0 varies. We now consider A,, x1 and x2 to be fixed, and let .q, be uniformly distributed in the range x,,~to xoZ, with xoZ - .xol = 6x,. Then it can be shown that
\
(8) where H(z2, 21) =
exp (-z22> 22
exp (-z12) +
\G
(erf 2s = erf zl)
Zl
and 2 t erf z=-...--4; s 0 e-8Z d=Y and
Figure 2 shows curves of p against AX for this situation, where X, the distance of the midpoint from the centre of the events, is 0.0, 1.0 and 2-O. The correlation pattern is much broader than the average event, and is always unity for events centered overhead. Out of three examples, only in one (extreme) case is the correlogram simply related to the size of the events. Since the actual event-to-event variation of absorption over a riometer station presumably contains contributions from all three causes (Ao, x, x0), it is clearly not possible to deduce much about the spatial size of individual events from a
OBSERVATIONS
FIG.
2.
OF AURORAL
CORRELOGRAMS
RADIO
FOR EVENTS WITH
A~SORFTION-Ir
VARYING
1489
WIDTH.
measured correlogram. We may use the correlogram as an entity in its own right, as a measure of spatial coherence, but must not confuse it with the original events. 2. RESULTS
The data are the readings of peak absorption at Great Whale River and Byrd, 5 spaced readings being obtained at each station, as described in Paper I. The procedures used are described in Section 2.1 of that paper. Correlograms of the type shown in Figs. 3 and 4 were computed for sets of absorption values divided in several ways, according to time of year, time of day, and level of magnetic activity as indicated by K,. The value of k;, was taken to the nearest whole number, except that if K, changed at the time of the peak the earlier and later values were averaged and this introduced some half-integral values. The unit of separation or displacement is the distance between the effective points of an oblique antenna and the vertical (i.e. about 12.5km). The intra-liemispheric correlograms include data from both Great Whale River and Byrd. For example, the first group of points on Fig. 3(a) are cross-correlation coefficients between the pairs of channels Great Whale River (North)-Great Whale River (vertical), Great Whale River (vertical)-Great Whale River (South), Byrd (North)-Byrd (vertical), and Byrd (vertical)-Byrd (South); the points at two units of separation are from the pairs Great Whale River (North)-Great Whale River (South), and Byrd (North)-Byrd (South). In the inter-hemispheric correlograms, the extreme left-hand point on Fig. 3(a) is from the pair Great Whale River (South)-Byrd (South); the next points are Great Whale River (vertical)-Byrd (South, and Great Whale River ~South)-Byrd (vertical); and so on. Table 1 gives the results for 19 computations, performed in three groups. Initially, two periods of the day, 000~400 UT (the pre-midnight period) and 1000-1900 UT (covering morning and noon) were studied as a function of season. Since no marked seasonaf variations appeared, many months were put together and the data were then divided according to K,. The results are summarized as follows. 2.1 Width of intra-hemispheric correlogram The correlation pattern falls to 0.61 in a distance of a few hundred kilometers. Individual patterns may be elongated North-South or East-West, but the average pattern is almost circular except for the Byrd observations by night. The pattern tends to be broader by day
1490
J. K. WARGREAVES
t+o b)Kp=2$-3 l.
c-8 0.6
P
!
04
North-South
0.2
. b r
0
1
02
.
h&-
l
04 East -West 0.2
t
,L
f
Sfporolco”
separation
IWT
IO
P .
Q-8
i.
0.6 *
.
i
c-6
W.’
1
P6-
P
North-South
(
.
*
l
T
I
0.2
t1.
t
Eost
t
0.2 ‘
f
liorfh
South
~ west
East
too ~lK~=3$-9
.”
c-8-
f
2 %
K
P6-
‘j
P -
’
04 -
P North-South
iI4
$ 5
w
0‘2 -
I_
East-West
t
ok
Seporot lo” IQ
P
I
I
i O-4
J-J--fSeporotlon II)
P
I
FIG, 3. CORRELOGRAMSPOR MARCH-OCTOBERI~~~, fOOO-18OOUT. The bars indicate the standard error of the mean. One unit of separation or dispracement about 125 km.
is
OBSERVATIONS
OF AURORAL
RADIO
ABSORPTION-II
1491
19
li’ B
GWR
08
o$ P 04
East - West
c-z
t0r
P
P North-South
c-4
0.2 t
t
Ot---J-PO
Pi
Separation
T
North-South
Ot---J-
Sepmtlon ho-
P
At South
North Dwplocement
West
at GWR wth
I
t
respect to Byrd
t
East
--
*f
I West
Drsplocement at GWR with respect to Byrd
FIG. 4. CORRELOGRAMS FOR FEB. 1966JAN. 1967,0200-0500 UT. The bars indicate the standard error of the mean. One unit of separation or displacement about 125 km.
is
o-3 3.5-9 (r2 2.5-3 4.5-9
D-19 IO-19 D-19 10-19 IO-19
02-05 02-05 02-05 02-05 02-05
lo-19 02-05
3-10 3-10 3-10 3-10 3-10
2-13* 2-13 2-13 2-13 Z-13
3-10 02-13
330 350
:5’ 28
Camposite Composite
&9 O-9 220
250 200
370 250
320 250 150 370 450 370 240>450
260 340 140>450 >450 80>450 240 310
390 420 310 310 440
430 >450 220 >450 440
45 Jr
340450 >450 > 450 >450 >450 240 250 380 370>450
East-West CWR B
300 400 >450 275 >450 >450 280 400 430 200 >450
North-South GWR B
O-3 3.5-9 o-2 4.5-9 2-5-3
:: 33 29 6
3s; 33
;: 42 25 42
34
pso, of points
* Month ‘13’ is January of the following year.
:z 8-10 S-10
&9 Q-9 t-b9 o-9 &9 o-9 &9 O-9 O-9
O&-O6 10-19 00-06 lo-19 IO-19 00-06 lo-19 00-06 10-19
5-7 5-7 11-13 11-13 12-13
XV
UT
Months
-
Width of intra-hemispheric correlogram to p = 0.61 (km)
>150kmS 120 km 5 >60 km S
>25O km N -250 km N 60kmN >120kmN 100 km S
120kmS 120kmN 50km.S >150kmN
-
North-Sauth (km)
Corresponding
SO.75 ~~0.65 0.5 >0*75 0.7 0.7 :,06 075
? w ,250 km W Okm ? w 80kmE 60kmE :-250 km W MfkmE
point to Byrd at Great Whale River .-Greatest East-West interhemispheric p, i;
%+&3tfl1. SUWKY OF COWLOORAAIS
790 500
410
240 >SOO 260
North-South >5OO >SOO > 500 >500 >SOO 410 350 280 >500
200 :-500 280
500 240 i500 310
r5OO > 500 > 500 3500 > 500 250 >500 ;400 >5BO
East-West
Width of inter-hemispheric correlogram to 0.61 of max. p (km)
8
% 53
!z
6
OBSERVATIONS
OF AURORAL
RADIO
1493
ABSORPTION-II
than by night. An earlier study (Hargreaves and Ecklund, 1968) also found circular correlation patterns, larger by day than by night, in the vicinity of Great Whale River. The patterns were narrower than the present ones by a factor 1.7-2.0; the difference may be due to the use of hourly values of absorption rather than absorption peaks. It seems unlikely that the difference of night correlation patterns between Great Whale River and Byrd (Fig. 4) can imply a corresponding difference in the size and shape of the absorption patches. The variation of correlation coefficient with distance from the centre of activity, illustrated in Fig. 1, is likely to be a factor. 2.2 Position of maximum
inter-hemispheric
correlation
For the day events (1000-1900 UT) maximum correlation with Byrd is found 60 to >250 km north of Great Whale River and somewhat west of it-see Table 1 and Fig. 3. The displacements are very poorly defined, but the directions agree with the position of the also agree computed conjugate point (see Fig. 1 of Paper I, for example). The displacements as well as could be expected with the results of a gradient analysis, set out in Table 2, (Gradiperformed on the averages of the absorption values used in the correlation analysis. ent analysis is described in Section 2.1 of Paper I.) TABLET.
Average absorption Cdb)
GRADIENT ANALYSISFOR 1000-1900UT
at GWR Average absorption (db)
at Byrd
Position of Byrd corresponding point with respect to Great Whale River*
K, range
N
S
E
W
N
S
E
W
R’
R”
0.C2.0
1.28
1.25
1.25
1.37
1.62
1.60
1.68
1.42
1.03
0.77
7 kmN 60kmW
2.5-3.0
2.20
1.96
1.89
2.17
3.31
2.71
2.99
2.55
1.37
0.74
80kmN 75kmW
3.5-9.0
2.51
2.78
2.66
2.64
3.15
2.32
2.67
1.99
1.21
0.75
50kmN 70 km W
* For Ax = Ay = 250 km, x0 = y0 = 250 km.
For the night period (0200-0500 UT) maximum correlation is found to the south of Great Whale River, as shown in Fig. 4, whereas gradient analysis (Table 3) shows the corresponding point to be to the North. The situation at the two stations differs in that, according to the gradients over the stations, the events tend to be centered poleward of Great Whale River and equatorward of Byrd, but it is not clear how this could move the position of best coherence away from the corresponding point deduced by gradient analysis. 2.3 Conjugate
wandering and maximum
inter-hemispheric
correlation
The inter-hemispheric correlation patterns tend to be slightly wider than the intrahemispheric patterns. If the widths (to p = 0.61) are respectively d,(inter) and d,(intra), the average value of d,(inter)/d,(intra) is 1.25 for the North-South direction, and 1.05 East-West. According to the treatment by Hargreaves and Ecklund (1968), one-dimensional wandering of the conjugate point withstandarddeviation 11’widens the correlogram to d,(inter)
= (do2(intra)
+ ,v~)~‘~,
1494
J. K. HARGREAVES TABLE 3. GRADIENTANALYSISFOR0200-0500 UT
Average absorption (db)
at GWR Average absorption (db)
at Byrd
Position of Byrd corresponding point with respect to R" Great Whale River*
K, range
N
S
E
W
N
S
E
W
R'
0%2.0
1.54
0.77
1.11
1.05
1.41
1.37
1.47
1.35
2.06
0.97
180 km N 10 kmW
2.5-3.0
1.33
1.15
1.14
1.29
1.95
1.49
I-83
1.91
1.53
O-92
110 km N 20 kmW
35-9.0
1-79
I.86
1.92
1.63
2.18
1.87
2.14
1.93
1.12
l-06
30 kmN 20 kmE
45-9.0
1.94
2.03
2.16
1.57
2.02
2.09
2.17
1.91
0.93
1.21
20 kmS 50 kmE
*ForAx=Ay=250km,x,=y0=250km
and the maximum value of the inter-hemispheric
correlation coefficient is
$ = ~~(intra)~~~(inter). The 25 per cent widening observed in the present case implies w = O-74 d,(intra), or w .w 150-270 km; and B = 0% The observed maximum values of inter-hemispheric correlation are summarized in Table 1 for the cases when a maximum or a clear trend could be seen. These values are no less than 0.5 but have not been seen to reach as high as 0.X. Values in the range 0.6-0.75 are most common. This suggests some loss of correlation not due to wandering, and we infer that even if wandering did not occur the greatest inter-hemispheric correlation would be less than unity and probably in the region 0%-0~9. The results suggest that loss of interhe~spheric correlation at the instantaneous corresponding points, and wandering of the corresponding points, contribute about equally to the observed degradation of correlation between conjugate regions. (Treatments of the type used in Section 3 of Paper I lead to a similar conclusion, since the irregular variation of the inter-hemispheric absorption ratio, r, is about halved by deleting points showing large displacement of corresponding point.) 2.4 The efSect of K, Figures 3 and 4 show the correlograms for the day and night periods for different ranges of E;,. For both periods, the maximum correlation (8) increases between the first and second ranges of lis,. At zero displacement the correlation decreases again for lu, > 35, but in these cases the point of best correlation seems to have moved beyond the range of the plots and its value cannot be specified. It can at least be said that no marked decrease of correlation occurs as KD increases. A variation of K, affects neither the intra-hemispheric correlation pattern nor the position of best conjugate agreement for the day events. The shape and size of the night correlation patterns do change as K, increases. These changes might be related to the equatorward displacement of the centre of activity with increase of K, (Paper I) which, in the present situation, moves it closer to Great Whale River but further from Byrd. The gradient analysis of Table 3 shows the corresponding point to Byrd moving South and East across Great Whale River with increasing activity, but the trend does not shown in the correlograms.
03SERVATIO~S
OF AURORAL
RADIO ABSORPTION-1~
1495
3. CONCLUSION
This study has shown one or two results which are of interest concerning the conjugate properties of aurora1 phenomena, but also, by illustrating some difficulties of interpretation, it has provided comment on the correlation method itself. Apart from the measurements of the correlation patterns within a single hemisphere, which show general agreement with previous work and with the results of gradient analysis, the most useful results are probably: (1) the evidence that both wandering of conjugate point and loss of correIation between instan~neous conjugate points contribute (about equally) to the degradation of inter-hemispheric correlation to its typical value 06O-75-this provides some idea of the short term (i.e. event-to-event) variation of conjugacy both with respect to position and to coherence. (2) the lack of evidence for a decrease of coherence under disturbed conditions-in spite of one’s intuitive feeling that conjugacy might become ‘looser’ when the magnetosphere is more disturbed. On the face of it, this result is at variance with the optical results so far reported. It should be remembered, however, that there are detailed differences between the absorption and the luminous phenomena: in particular, they depend on different particle energies and have different spatial extent, absorption resulting from the more energetic electrons and appearing in patches that are broader than most luminous features. Comparison with results of the gradient analysis tends to show agreement for day events. For the night events, however, discrepancies and anomalies abound, with correlation patterns differing between hemispheres and changing with K,, and with the position of best inter-hemispheric correlation displaced from the corresponding points deduced by gradient analysis. We cannot be certain of the reason for these discrepancies, but circumstantial evidence suggests that differences and movements of the centres ofprecipitation with respect to the observation sites are a factor. We also know that the night events have a greater variation of width than the day events, although the average size is much the same (Paper I). The theoretical di~cL~lty of relating a correlation pattern to an average event was pointed out in Section 1.2. In practice the difficulty seems more acute for the night events, and caution is needed when interpreting correlation analyses in the night sector. An analysis based directly on absorption values is to be preferred before one based on their variations, Acknowledgements-The raw data were obtained during the observational programme described in Paper I, in which connection the author acknowledges with thanks the assistance of W. L. Ecklund. F. C. Cowlev. H. C. Swanson, the U.S. National Scienze Foundation and the Canadian National Research Coun& Mrs. S. Hargreaves wrote the computer programs used in the present study. REFERENCES A. E., DAVIS, T. N. and GLASS, N. W. (1968). Conjugacy of visual auroras during magnetically disturbed periods. Antarct. U.S.A. 3, 117. BELON, A. E., MAGGS, J. E., DAVIS, T. N., MATHER, K. B., GLASS, N. W. and HUGHES, G. F. (1969). Conjugacy of visual auroras during magnetically quiet periods. J. geophys. Res. 74, 1. HARGREAVES,J. K. (1969). Conjugate and closely-spacedobservations of aurora1 radio absorption-4 Seasonaland diurnal behaviour. Planet. Space Sci. 17,1459. HARGREAVES, J. K. and ECKLIJND,W. L. (1968). Correlation of amoral radio absorption between conjugate points. Radio Sci. 3, 398. HOLT, O., LAh?)hmRK, B. and LIED, F. (1961). Analysis of riometer observations obtained during polar radio blackouts. J. atmos. terr. Phys. 23, 229. LEINBACH,H. and BASLER, R. P. (1963). Ionospheric absorption of cosmic radio noise at magnetically conjugate aurora1 zone stations. J. geophys. Res. 68,3375. LITTLE,C. G., SCHIFFMACHER, E. R., CHIVERS,H. 3. A. and SULLIVAN,K. W. (196.5). Cosmic noise absorption events at geoma~etically conjugate stations. 2. geo&s. Res. 70,639. PART~ASARATHY, R. and BERKEY,F. T. (1965). Aurora1 zone studies of sudden onset radio wave absorption events using multiple station and muhiple frequency data. J. geophys. Res. 70, 89. BELON,