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Secular trends in daily geomagnetic variations
Ioumal of Ahnosphcric and Ten&h1 Physics Vol. 42, pp. 689-695 Pergamon Press Ltd.1980. printed in Northern Ireland
Secular trends in daily geomagnetic variations R. SELLEK Geomagnetism Unit, Institute of Geological Sciences, Murchison House, West Mains Road, Edinburgh EH9 3LA, Scotland and Department of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, England (Received 22 October 1979; in reuised form 18 January 1980) act-After removal of seasonal and sunspot cycle effects, the solar (S) and lunar (L) daily geomagnetic variations at Hermanus, Huancayo and San Juan are found to have significant secular changes. The solar variations are shown to be more closely fixed to local magnetic coordinates than to geographic coordinates. Many of the secular changes can be qualitatively accounted for by simple considerations of the physical processes involved in the generation of S and L.
1. INTRODUCTION The solar and lunar
daily geomagnetic variations (denoted S and L respectively) have previously been studied in some detail but the possibility of long term trends in the variations does not appear to have been considered. The presence of such secular changes would be of considerable importance when analysing long data sets to find values for S and L coefficients. Most of the analyses of long series of data have been of D, H and Z (declination, horizontal intensity and vertically downward intensity, respectively) on the implicit assumption that S and L are fixed relative to these local magnetic elements. However, some analyses (GUPTA and CHAPMAN, 1970) have been made in terms of X, Y and Z, where X and Y denote the geographic north and east intensities respectively, and here the implicit assumption is that S and L are tixed relative to geographic co-ordinates. Since the angle between geographic and local magnetic north changes with time (for example, in London D changed from 11”E in 1576 to 24”W in 1820), it is clearly of importance to ascertain which is the better assumption. Besides such geometrical considerations, it is probable that the amplitudes of S and L show changes with time. While there may exist some appreciable contribution to both S and L of magnetospheric origin, it seems probable that electric currents flowing in the ionosphere are primarily responsible for the generation of S and L. These currents depend only on (i) the main geomagnetic field, (ii) the ionospheric conductivities, and (iii) winds in the upper atmosphere. The distribution of dynamo emf’s driving the currents will be affected by a change in the configuration of the main field and, with the exception of the direct conductivity, the ionospheric conductivities 689
(Pedersen, Hall and Cowling) depend on the total intensity of the main field (MATSUSHITA and CAMPBELL, 1967). Both S and L are known to have a dependence on sunspot number and this is taken into account in the analysis described later in this paper. Variations in other parameters such as the number density of charged particles and that part of the solar flux responsible for the thermal excitation of the S winds will also affect the ionospheric dynamo. However, at present there does not appear to be any evidence to suggest that these parameters exhibit long term changes. Thus, at least two of the quantities which exert a direct influence on S and L, namely the main field and the conductivity tensor, show long term variations and so one may reasonably expect secular trends to be present in S and L. The magnetospheric dynamo will also be influenced by variations in the main field and hence its contributions to S and L may also be expected to show secular trends. Here we present results which show such trends and suggest possible physical processes which may account for this effect. 2. THE DATA To have most chance of detecting significant secular changes in S and L it is reasonable to select stations where the main field elements show large temporal changes. Also, we need a long series of data from the same site. It is important that there should be no change of site since the induced currents associated with S and L depend on local geography and even a small change of site can produce marked changes in S and L as was found for example between Greenwich and Abinger (LEATON, MALIN and FINCH, 1963). The series needs to be long in order that the parameters of S
1able I
The observatories
Geographic Station
!ili
Hermanus Huancayo San Juan
34’25.2’S 12” 2.7’S 18” h.X’N
long. E
19*13.5’ 284O39.6’ 293”s 1.O’
and L can be determined as accurately as possible, and that a sufficiently long baseline is available for the determination of secular changes. Both S and L are influenced by the sunspot cycle and thus it is necessary not only to take account of this effect, but also to use data spanning at least one complete sunspot cycle. Integral numbers of years of data have been used to eliminate seasonal changes which are of the same order of magnitude as the sunspot effect. The stations used are Hermanus, Huancayo and San Juan. All these observatories have long enjoyed a reputation for producing high quality data. The geographic and geomagnetic coordinates of the stations are shown in Table 1 together with the time span of the data used in each case. Hermanus is a southern mid-latitude observatory where there are large secular variations in H and Z. At San Juan, a northern mid-latitude observatory, large secular changes in D and Z are found. Although further machine readable data for San Juan are available beyond 1964. these are from a new site and so have not been used. Huancayo is close to the geomagnetic equator and has large secular changes in D and Z. Near the geomagnetic equator, S and L are generated almost entirely by currents flowing in the overhead equatorial electrojet (FORBUSH and CASAVERDE, 1961). Thus temporal changes in the position or magnitude of the electrojet current are likely to produce changes in S and L. Hourly mean values of D, H and Z at Hermanus and San Juan were supplied in machine readable form by the World Digital Data Centre in Edinburgh. The hourly mean values of D, H and 2 from Huancayo were punched from year books at the University of Exeter. The Huancayo data are tabulated according 75th meridian mean time from 1923-1947 and in universal time from 1948-1961. This is merely a change of format and does not involve any discontinuity or site change. However, for computational convenience, the two parts of the data.,have been analysed separately. 3. ANALYSISAND Rk%JLTs The solar daily variation may be adequately represented by the first four harmonics of a Fourier
Geomagnetic lat. long.
33.3” 0.6” 29.6”
E
Period --___.._.
8CJ.5”
1941-1976
353.X” 1923-196 1 3.1” 1929-1964
series: S=&.=i(A, “=I
n=l
cos 2rnt + B, sin 2rrnt)
ilj
where A, and B, are the amplitudes of the components of the nth harmonic and t is measured in mean solar days from Greenwich midnight. The principal harmonic of L has a period of half a lunar day, and may be similarly represented in terms of the amplitudes of the in-phase and quadrature components of a sine wave. Here we have used the least squares method of MALIN and SCHLAPP(1980) for the determination of the values of A and B. We wish to find whether A and B show secular change, but first we must take account of the known variation of these coefficients with the sunspot cycle. Figure 1 shows plots of the B, solar coefficient obtained for Z at San Juan and the annual mean sunspot number for each year from 1929-1964. By comparing the two curves, it is obvious that the magnitude of B,(Z) is closely tied to the sunspot cycle. Similar variations are present in all the coefficients of D, H and Z at each station. From Fig. 2 which is a plot of B,(Z) against annual mean sunspot number, R, we see that we can reasonably assume a linear relationship between these quantities. Annual mean sunspot numbers are used as a basis for subdivision of the sunspot cycle since this is the parameter recommended for the determination of the dependence of the daily variations on solar activity (ALLDREDGE. 1973). For the main analysis we assume that, for the lunar semidiurnal and first 2 solar harmonics, A, = a0.n + a,,(r-
I)+ a,,(R
- B)
and 8, = br,, + b,,,(r - t, + bR,n(R - I?‘)
(2)
where i and B denote the mean vales of t and R over the interval analysed, and ao,n and bo., are constants to be determined from the data. (It was considered improbable that any sunspot or secular
691
Secular trends in daily geomagnetic variations
variations of the higher solar harmonics could be significantly determined). In this study, we are particularly concerned with the coefficients a,, and b,, which represent a linear fit to the secular changes in S and L. The solar and lunar coefficients au,_, a,,, aR,_, bo,., b,,+, bR,, were calculated simultaneously using the method of MALIN and SCHLAPP (1980) modified to include the sunspot and secular terms, and applied to the full runs of data. The coefficients of interest for the present study are presented in Table 2. The significance of the secular variation coefficients can only be assessed by comparing them with their error estimates. Hence, it is of particular importance that the standard deviations should be reliable, so we will examine the method employed for their determination. Following MALIN and SCHLAPP(1980) the data were divided by randomly allocating each successive hourly mean value to one of ten sets. The required coefficients were determined from each of the sets, and the quoted error is the standard deviation of the mean of the ten separate determinations. The only assumption made here is that the separate determinations are statistically independent.
i=
z
ci-
I
I
1
I
2oolk
5
160-
I .
l \ lv
:
lz
i“? .
80_
40- i
?
\
120i
I
I
1
I *\
0.' 1930
l\.
* .'I
I\ l
.,
l
\
\ Ia,
i
I x._i
II'
\
t,
I
,940
I 1950
1
l \.
t,i
I
I 1960
Year Fig. 1. The variations of the B,(Z) coefficient at San Juan and the annual mean sunspot number from 1929.5 to 1964.5.
"0
20
40
60
80
IO0
120
140
160
180
200
Sunrpot number
Fig. 2. A plot of the B,(Z) coefficient at San Juan versus annual mean sunspot number. The least squares straight line fit to the points is also shown.
The average time separation between data from any two sets is about 10 h. By ‘time separation’ we mean the interval between t, and t2 where t1 is the time of an hourly mean value in one set, and t2(>t1) is the time of the nearest subsequent hourly mean value in the other set. If there is appreciable serial correlation between data separated by this interval, the data sets will not be statistically independent and the standard deviations will be underestimated. A convenient and direct way of checking the independence of the data sets is to vary their number (thus changing the average time separation) and see if the estimated standard deviations change significantly. The same data were analysed using 5, 10, 15 and 20 sets and it was found that only 4.2% of the standard deviations showed significant differences. Thus, it was concluded that the data sets used were statistically independent at the 95% confidence level. From Table 2 we can see that, as expected, the largest secular change coefficients are those for S, and S2 (the solar diurnal and semidiurnal harmonics, respectively) and a large majority are significant at the 5% level. In the next section we shall discuss the physical significance of these results and relate them to simple theory. It can also be seen that although several of the L secular change coefficients are statistically significant, the overall evidence of secular change is less convincing than for Sr and S2, and the L2 results will not be discussed
further.
hY2
K. SEl.l~k l’able 1. C‘oeffic~rnls obtamed
____
__-_._
II -...__
_
s,
A B A B A B
S* L*
_
IL!>\.I),:,% ‘1
3.69A2.56
- 2.03 -20.79 6.53 2X.7 1 3.39 1.3x
- 3.89zt 1.48 lC).i.ii2.12 JY.1212.51 1.8? I 2.23 l,.hiii- 1.41
-___A B A B A
s, S, L,
-4.78 f 0.94 --4.3X + 1.27 X.55 Il.28 12.81 f 1.21 1.55k 1.46 - 1.391 1.38 _ _____-
-1.97 -7.82 -2.99 3.30 1.73 0.68
data set\ z
%tx.hw
IlIT,
(lO~‘nT.tl~‘,
Hermanus
( 194 I - 1Y76)
-1.45 11.33 4.09 3.45 0.66 11.6-I
1.74r0.76 -4.34iO.76 -0.97 * 1.00 --X.92 * 0.93 -1.181tO.75 --0.X2 0.93
atn. ‘L %n. h0P1 (10 ’ nT (1~’ 1 f il.TI
- 3.64 3.95 4.67 0.34 -0.75 --0.32
X.OX.k0.?3 1.86. I.01 --9.06rtO.54 -2.19*0.Y5 ~-2.17rO.hlt 1.6X*o.oi
_______-.____-
.~
~-
of the complete
I/
_ ~. -. (1s ,I. 4 ,,
% “- hl 1, IIO~’ arcsin) (10 “arcsin.d
from analyses
._..-_. _-_
Huancayo (1923-1947) ____-12.11 f 1.76 45.88*3.56 16.54i3.30 -26.521t2.07 1.11 zt2.07 1.55 *2.85
-- 19.38 -40.40 - 16.74 15.81 5 .os 4.17
_-_.__.-3.32 X.h7 5.23 0.57 --0.69 -2.24
-_-.
Huancayo
4.67 * 0.68 64.21 zt0.79 40.91 iO.56 -- 12.OOk 0.68 6.75 f 0.X0 -9.54* 1.01
--.
_._..__
(1948-19613
__A B A B A B
S, S, L,
-3.67 -9.48 -3.45 4.05 1.70 1.31
-24.32 + 3.07 -4.16k3.53 19.0753.28 20.21* 3.51 7.26 k 2.94 X.49 i 2.46 --___--____
---21.52 -53.72 -21.2X 18.80 5.42 4.3 1
San Juan
17.29 f 8.45 -4.59zk 9.29 12.2116.17 --0.2217.25 5.15i5.88 X.26*6.1 1 -._
3.54* 1.99 19.81*2.(11 14.2Xrt2.70 - 5.731 1.40 0.04 + 1 .xu --3.70i2.17 -1.55 .__ .___--..__
-4.55 6.11 3.77 1.58 -0.27
(1929-1964) --
%
A B A B A B
S, L*
--Il.92 6.82 10.11 6.40 2.02 -1.92
X.12+0.62 3.OlzkO.64 -5.53kO.82 -6.46 L+C 0.39 --3.50* 1.07 0.60 * 0.89
-1.55 --I.67 0.99 2.29 --0.91 0.X4
4. DISCUSSION
shall examine whether the solar daily variation is more closely tied to a local magnetic or geographic coordinate system. For this purpose we use the results from San Juan, where D, the angle between local magnetic north and geographic north, changed by over 3” between 1929 and 1964. Since we have taken linear fits to the secular changes in the daily variations we shall also take a linear fit to D, and this gives a change of -2.97”* 0.03” from 1929.5 to 1964.5. Figure 3 illustrates how D and the direction of a harmonic component of the daily variation are related at different epochs, tl and t2. We see that First
we
1.23ztO.47 -0.42*0.X2 0.981 1.06 -2.87~tO.87 1.2Xi 0.49 1.65kO.84
3.2X 4.65 0.71 -3.09 -0.01 -0.80
-0.2 1 + 0.40 0.58*0.31 - 1 .Ol i 0.23 0.53 * 0.35 -1.10*0.2x -0.11*0.31
the direction of the horizontal component of the main field (denoted H) changes from Dt, to % relative to the geographic axis between the epochs. The position and magnitude of a harmonic component of the daily variation are represented by the vectors V,, and V,,. The directions of these components relative to the magnetic north are denoted by @,,, and @,2 respectively, where @ =: tan.-’ {A,(D)/A,(H)j for the in-phase component, and Cp= tan-’ {B,(D)/B,(H)} for the quadrature component; the letter in parenthesis indicates the appropriate element. If the direction of V remains fixed relative to the local magnetic north, then a,, --a,, = /3 = 0; alternatively. if V is fixed relative
693
Secular trends in daily geomagnetic variations
Table 3. The angles through which the in-phase and quadrature components of S1 and St at San Juan move with respect to magnetic north (fi) and geographic north (0) between 1929.5 and 1964.5
-
Fig. 3. The relationship between the horizontal component of the main field and the in-phase component of the nth harmonic of the daily variation at two epochs tl and 12. to geographic
coordinates,
a,, -a,,
t D,, - D,2 =
8=0.
Values of A, and B, have been synthesized for 19292 and 1964.5 from equations (2), assuming R = R and used to determine the values of p and 6 given Table 3. Clearly the values of /3 are smaller than those of 8, favouring the hypothesis that the solar daily variation is tied to local magnetic coordinates. Two of the quantities which exert a direct influence on S, namely the tensor ionospheric conductivity and the horizontal electric field in the ionosphere, depend on the magnitude and direction of the Earth’s main field. The above result implies that these are of greater importance in determining
Coefficient
P(“)
A, B, ‘4, B,
1.51kO.32 0.52* 1.55 1.35* 1.47 -0.89* 1.64
different epochs San Juan Coefficient ‘4, BI A2
J%
C 1964.5
5
(nT) 8.31kO.07 4.89 f 0.05 1.21*0.11 3.98 f 0.08
4.48 f 3.49* 4.32* 2.08*
0.32 1.55 1.47 1.64
the morphology of S than the wind pattern, which remains fixed relative to the geographic coordinate system. Next we shall consider the temporal changes in the amplitudes of the first two solar harmonics. The tensor ionospheric conductivity is dependent on F, the total intensity of the main field, while in midlatitudes the horizontal electric field depends on Z. Hence we may reasonably expect to see significant secular changes in the magnitudes of the harmonic components of S at stations where F and IZI show large temporal variations. At San Juan, where changes in H have been small, IZl has decreased by over 6% between 1929 and 1964. At Hermanus, decreases of about 24% and 13% have occurred in H and ]ZI respectively between 1941 and 1976. The results from Huancayo will be discussed later. The magnitude of the in-phase component of the nth harmonic is given by C= {[A,,(H)]‘t [A,(Z)]2}“2; for the quadrature component the A’s are replaced by B’s. The values of C for 1929.5 and 1964.5 at San Juan and for 1941.5 and 1976.5 at Hermanus have been synthesized at R = R using equations (2), and are presented in Table 4. At San Juan, only the B2 term shows a significant change. The change in this term is consistent with a 6% decrease, corresponding to that in Z. A 6% change in A2 would not be significant, whereas such a change would be detectable in A, and B, but is not seen. At Hermanus ail the changes are significant, and all except the smallest term (B,) change in the same sense as H and JZ(. However
Table 4. The amplitudes of the in-phase and quadrature components of S, and S, at
C 1929
W)
8.17rtO.07 4.99 f 0.05 1.23zt0.12 3.72ztO.08
Hermanus C 1941.5 C 1976S (n7-I 6.OlztO.11 12.20*0.10 6.62kO.11 2.92hO.13
5.53zto.11 11.75*0.10 5.83iz0.12 4.02ztO.13
R %L.I.Ph
694
there is no obvious quantitative reiation between these changes and those in H and IZ/. At Huancayo, most of the daily variation 1s a direct result of currents flowing in the equatorial electrojet, so we would expect any secular changes in S and L to be the result of either changes in the magnitude of these currents or movements of the electrojet. From the N-S gradient of Z. we infer that an increase of 1 nT corresponds to a 1 15 m movement of the geomagnetic equator (and hence the electrojet) in the N-S direction towards Huancayo. Using the observed values of Z, and representing the electrojet by an E-W current at a height of 110 km and showing no secular change of amplitude, we deduce that AH and AZ (the amplitudes of the daily variations in H and Z) should vary as shown in Fig. 4. The main points to note are a decrease in AH and an increase in AZ between 1923 and 1947, and very little change between 1948 and 1961. Precisely these changes are seen in the values of AH and AZ for S, and S, given in Table 5, suggesting that secular changes in S at Huancayo are closely related to movements of the electrojet. These values were synthesized from the data of Table 2 via equations (2), again assuming R = R and taking AH = {[A,(H)]2+[B,(H)]*}1’2 and AZ = {[A,(Z)]Z+[B,(Z)]2}“2 5. CONCLUSIONS Significant secular trends have been detected in both the solar and lunar daily geomagnetic variations. The statistical evidence of secular change in S seems conclusive and the reality of the effect is confirmed by its qualitative agreement with the predictions of simple theory. The results for L have less statistical weight and might possibly be improved in the future by the analyses of longer series of data. The secular changes in the solar daily variations
r [
!
“l
-c/ I
J\- - - - ___. - - - _. _
I
i-
:
:
1
,’
L__
__,_____-~-. - ----__.
--- - AZ AH , 1930
I
1 ,
1940
,950
1 i
are more closely related to local magnetic
coordinates than to geographic coordinates. Thus, for the analysis of long series of data it is more appropriate to use D and H rather than X and Y. The secular changes in S and L appear to result from changes in the main geomagnetic field, although possible long term variations in other parameters may also contribute to these effects. If similar studies were made for a wider distribution of observatories, each with its characteristic pattern of main field secular change, it should be possible to establish an empirical relation betweeen secular changes in main field elements and the daily variations. This would lead to a better understanding of physical processes in the dynamo region of the ionosphere. Acknowledgements-The author wishes to thank Dr S. R. C. MALIN, who provided the initial stimulus for the work, for his invaluable guidance and advice. Thanks are also due to Dr D. M. SCHLAPPfor many helpful comments, Dr C. A. GREEN for his assistance with the computation, and Miss S. A. JEFFERYwho helped with the preparation of the paper. The author is funded by a Science Research Council grant.
1947.5
1948.5
(nV 46.86kO.32 24.31 kO.26 6.84 f 0.08 3.60 f 0.05
t
1960
Fig. 4. The variations of AH and AZ at Huancayo as predicted from N-S movements of the equatorial electrojet. The arrow marks the temporal division of the two data sets.
different epochs
AH@,) AHW AZ@,) AZ&)
_I
Year
Table 5. The amplitudes of AH and AZ at Huancayo for S, and S2 at 1923.5
--‘.‘-T”.-~
1961.5 (nT)
42.78 f 0.32 21.67zt0.26 1190~0.08 7.02*0.05
57.90*0.46 28.63 f 0.36 7.30*oo.09 3.84kO.11
57.80 f 0.46 28.19kO.36 7.95 f 0.09 4.35*0.12
Secular trends in daily geomagnetic variations
hLDREDOEL. R. FOREIUSHS. E. and CASAVERDEM. GUPTA J. C. and CHAPMAN S.
B. R.,
LEATON MALIN
MALIN
S.
R. C. and FINCH H. F.
S.R. C. and SCHL,QP D. M.
MATSUSHITA
MCNISH
S. and CAMPBELLW. H.
1973 1961 1970
1963 1980 1967
1936
695
I.A.G.A. Bull. 35, 105. Carnegie Inst. Wash. Publ., 620. Manual of the coefficients of rhe first four harmonics of the solar and lunar daily geomagnetic uariations computed from IGY/C and certain other data. National Centre for Atmospheric Research, Boulder, Colorado. R. Obs Bulls. 63 Geophys. .I. R. astr. Sot. 60,409. Physics of Geomagnetic Phenomena. Vol. 1, pp. 381-388, Academic Press, New York and London. I.U.G.G. Bull. 10,271.
Secular trends in daily geomagnetic variations R. SELLEK Geomagnetism Unit, Institute of Geological Sciences, Murchison House, West Mains Road, Edinburgh EH9 3LA, Scotland and Department of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, England (Received 22 October 1979; in reuised form 18 January 1980) act-After removal of seasonal and sunspot cycle effects, the solar (S) and lunar (L) daily geomagnetic variations at Hermanus, Huancayo and San Juan are found to have significant secular changes. The solar variations are shown to be more closely fixed to local magnetic coordinates than to geographic coordinates. Many of the secular changes can be qualitatively accounted for by simple considerations of the physical processes involved in the generation of S and L.
1. INTRODUCTION The solar and lunar
daily geomagnetic variations (denoted S and L respectively) have previously been studied in some detail but the possibility of long term trends in the variations does not appear to have been considered. The presence of such secular changes would be of considerable importance when analysing long data sets to find values for S and L coefficients. Most of the analyses of long series of data have been of D, H and Z (declination, horizontal intensity and vertically downward intensity, respectively) on the implicit assumption that S and L are fixed relative to these local magnetic elements. However, some analyses (GUPTA and CHAPMAN, 1970) have been made in terms of X, Y and Z, where X and Y denote the geographic north and east intensities respectively, and here the implicit assumption is that S and L are tixed relative to geographic co-ordinates. Since the angle between geographic and local magnetic north changes with time (for example, in London D changed from 11”E in 1576 to 24”W in 1820), it is clearly of importance to ascertain which is the better assumption. Besides such geometrical considerations, it is probable that the amplitudes of S and L show changes with time. While there may exist some appreciable contribution to both S and L of magnetospheric origin, it seems probable that electric currents flowing in the ionosphere are primarily responsible for the generation of S and L. These currents depend only on (i) the main geomagnetic field, (ii) the ionospheric conductivities, and (iii) winds in the upper atmosphere. The distribution of dynamo emf’s driving the currents will be affected by a change in the configuration of the main field and, with the exception of the direct conductivity, the ionospheric conductivities 689
(Pedersen, Hall and Cowling) depend on the total intensity of the main field (MATSUSHITA and CAMPBELL, 1967). Both S and L are known to have a dependence on sunspot number and this is taken into account in the analysis described later in this paper. Variations in other parameters such as the number density of charged particles and that part of the solar flux responsible for the thermal excitation of the S winds will also affect the ionospheric dynamo. However, at present there does not appear to be any evidence to suggest that these parameters exhibit long term changes. Thus, at least two of the quantities which exert a direct influence on S and L, namely the main field and the conductivity tensor, show long term variations and so one may reasonably expect secular trends to be present in S and L. The magnetospheric dynamo will also be influenced by variations in the main field and hence its contributions to S and L may also be expected to show secular trends. Here we present results which show such trends and suggest possible physical processes which may account for this effect. 2. THE DATA To have most chance of detecting significant secular changes in S and L it is reasonable to select stations where the main field elements show large temporal changes. Also, we need a long series of data from the same site. It is important that there should be no change of site since the induced currents associated with S and L depend on local geography and even a small change of site can produce marked changes in S and L as was found for example between Greenwich and Abinger (LEATON, MALIN and FINCH, 1963). The series needs to be long in order that the parameters of S
1able I
The observatories
Geographic Station
!ili
Hermanus Huancayo San Juan
34’25.2’S 12” 2.7’S 18” h.X’N
long. E
19*13.5’ 284O39.6’ 293”s 1.O’
and L can be determined as accurately as possible, and that a sufficiently long baseline is available for the determination of secular changes. Both S and L are influenced by the sunspot cycle and thus it is necessary not only to take account of this effect, but also to use data spanning at least one complete sunspot cycle. Integral numbers of years of data have been used to eliminate seasonal changes which are of the same order of magnitude as the sunspot effect. The stations used are Hermanus, Huancayo and San Juan. All these observatories have long enjoyed a reputation for producing high quality data. The geographic and geomagnetic coordinates of the stations are shown in Table 1 together with the time span of the data used in each case. Hermanus is a southern mid-latitude observatory where there are large secular variations in H and Z. At San Juan, a northern mid-latitude observatory, large secular changes in D and Z are found. Although further machine readable data for San Juan are available beyond 1964. these are from a new site and so have not been used. Huancayo is close to the geomagnetic equator and has large secular changes in D and Z. Near the geomagnetic equator, S and L are generated almost entirely by currents flowing in the overhead equatorial electrojet (FORBUSH and CASAVERDE, 1961). Thus temporal changes in the position or magnitude of the electrojet current are likely to produce changes in S and L. Hourly mean values of D, H and Z at Hermanus and San Juan were supplied in machine readable form by the World Digital Data Centre in Edinburgh. The hourly mean values of D, H and 2 from Huancayo were punched from year books at the University of Exeter. The Huancayo data are tabulated according 75th meridian mean time from 1923-1947 and in universal time from 1948-1961. This is merely a change of format and does not involve any discontinuity or site change. However, for computational convenience, the two parts of the data.,have been analysed separately. 3. ANALYSISAND Rk%JLTs The solar daily variation may be adequately represented by the first four harmonics of a Fourier
Geomagnetic lat. long.
33.3” 0.6” 29.6”
E
Period --___.._.
8CJ.5”
1941-1976
353.X” 1923-196 1 3.1” 1929-1964
series: S=&.=i(A, “=I
n=l
cos 2rnt + B, sin 2rrnt)
ilj
where A, and B, are the amplitudes of the components of the nth harmonic and t is measured in mean solar days from Greenwich midnight. The principal harmonic of L has a period of half a lunar day, and may be similarly represented in terms of the amplitudes of the in-phase and quadrature components of a sine wave. Here we have used the least squares method of MALIN and SCHLAPP(1980) for the determination of the values of A and B. We wish to find whether A and B show secular change, but first we must take account of the known variation of these coefficients with the sunspot cycle. Figure 1 shows plots of the B, solar coefficient obtained for Z at San Juan and the annual mean sunspot number for each year from 1929-1964. By comparing the two curves, it is obvious that the magnitude of B,(Z) is closely tied to the sunspot cycle. Similar variations are present in all the coefficients of D, H and Z at each station. From Fig. 2 which is a plot of B,(Z) against annual mean sunspot number, R, we see that we can reasonably assume a linear relationship between these quantities. Annual mean sunspot numbers are used as a basis for subdivision of the sunspot cycle since this is the parameter recommended for the determination of the dependence of the daily variations on solar activity (ALLDREDGE. 1973). For the main analysis we assume that, for the lunar semidiurnal and first 2 solar harmonics, A, = a0.n + a,,(r-
I)+ a,,(R
- B)
and 8, = br,, + b,,,(r - t, + bR,n(R - I?‘)
(2)
where i and B denote the mean vales of t and R over the interval analysed, and ao,n and bo., are constants to be determined from the data. (It was considered improbable that any sunspot or secular
691
Secular trends in daily geomagnetic variations
variations of the higher solar harmonics could be significantly determined). In this study, we are particularly concerned with the coefficients a,, and b,, which represent a linear fit to the secular changes in S and L. The solar and lunar coefficients au,_, a,,, aR,_, bo,., b,,+, bR,, were calculated simultaneously using the method of MALIN and SCHLAPP (1980) modified to include the sunspot and secular terms, and applied to the full runs of data. The coefficients of interest for the present study are presented in Table 2. The significance of the secular variation coefficients can only be assessed by comparing them with their error estimates. Hence, it is of particular importance that the standard deviations should be reliable, so we will examine the method employed for their determination. Following MALIN and SCHLAPP(1980) the data were divided by randomly allocating each successive hourly mean value to one of ten sets. The required coefficients were determined from each of the sets, and the quoted error is the standard deviation of the mean of the ten separate determinations. The only assumption made here is that the separate determinations are statistically independent.
i=
z
ci-
I
I
1
I
2oolk
5
160-
I .
l \ lv
:
lz
i“? .
80_
40- i
?
\
120i
I
I
1
I *\
0.' 1930
l\.
* .'I
I\ l
.,
l
\
\ Ia,
i
I x._i
II'
\
t,
I
,940
I 1950
1
l \.
t,i
I
I 1960
Year Fig. 1. The variations of the B,(Z) coefficient at San Juan and the annual mean sunspot number from 1929.5 to 1964.5.
"0
20
40
60
80
IO0
120
140
160
180
200
Sunrpot number
Fig. 2. A plot of the B,(Z) coefficient at San Juan versus annual mean sunspot number. The least squares straight line fit to the points is also shown.
The average time separation between data from any two sets is about 10 h. By ‘time separation’ we mean the interval between t, and t2 where t1 is the time of an hourly mean value in one set, and t2(>t1) is the time of the nearest subsequent hourly mean value in the other set. If there is appreciable serial correlation between data separated by this interval, the data sets will not be statistically independent and the standard deviations will be underestimated. A convenient and direct way of checking the independence of the data sets is to vary their number (thus changing the average time separation) and see if the estimated standard deviations change significantly. The same data were analysed using 5, 10, 15 and 20 sets and it was found that only 4.2% of the standard deviations showed significant differences. Thus, it was concluded that the data sets used were statistically independent at the 95% confidence level. From Table 2 we can see that, as expected, the largest secular change coefficients are those for S, and S2 (the solar diurnal and semidiurnal harmonics, respectively) and a large majority are significant at the 5% level. In the next section we shall discuss the physical significance of these results and relate them to simple theory. It can also be seen that although several of the L secular change coefficients are statistically significant, the overall evidence of secular change is less convincing than for Sr and S2, and the L2 results will not be discussed
further.
hY2
K. SEl.l~k l’able 1. C‘oeffic~rnls obtamed
____
__-_._
II -...__
_
s,
A B A B A B
S* L*
_
IL!>\.I),:,% ‘1
3.69A2.56
- 2.03 -20.79 6.53 2X.7 1 3.39 1.3x
- 3.89zt 1.48 lC).i.ii2.12 JY.1212.51 1.8? I 2.23 l,.hiii- 1.41
-___A B A B A
s, S, L,
-4.78 f 0.94 --4.3X + 1.27 X.55 Il.28 12.81 f 1.21 1.55k 1.46 - 1.391 1.38 _ _____-
-1.97 -7.82 -2.99 3.30 1.73 0.68
data set\ z
%tx.hw
IlIT,
(lO~‘nT.tl~‘,
Hermanus
( 194 I - 1Y76)
-1.45 11.33 4.09 3.45 0.66 11.6-I
1.74r0.76 -4.34iO.76 -0.97 * 1.00 --X.92 * 0.93 -1.181tO.75 --0.X2 0.93
atn. ‘L %n. h0P1 (10 ’ nT (1~’ 1 f il.TI
- 3.64 3.95 4.67 0.34 -0.75 --0.32
X.OX.k0.?3 1.86. I.01 --9.06rtO.54 -2.19*0.Y5 ~-2.17rO.hlt 1.6X*o.oi
_______-.____-
.~
~-
of the complete
I/
_ ~. -. (1s ,I. 4 ,,
% “- hl 1, IIO~’ arcsin) (10 “arcsin.d
from analyses
._..-_. _-_
Huancayo (1923-1947) ____-12.11 f 1.76 45.88*3.56 16.54i3.30 -26.521t2.07 1.11 zt2.07 1.55 *2.85
-- 19.38 -40.40 - 16.74 15.81 5 .os 4.17
_-_.__.-3.32 X.h7 5.23 0.57 --0.69 -2.24
-_-.
Huancayo
4.67 * 0.68 64.21 zt0.79 40.91 iO.56 -- 12.OOk 0.68 6.75 f 0.X0 -9.54* 1.01
--.
_._..__
(1948-19613
__A B A B A B
S, S, L,
-3.67 -9.48 -3.45 4.05 1.70 1.31
-24.32 + 3.07 -4.16k3.53 19.0753.28 20.21* 3.51 7.26 k 2.94 X.49 i 2.46 --___--____
---21.52 -53.72 -21.2X 18.80 5.42 4.3 1
San Juan
17.29 f 8.45 -4.59zk 9.29 12.2116.17 --0.2217.25 5.15i5.88 X.26*6.1 1 -._
3.54* 1.99 19.81*2.(11 14.2Xrt2.70 - 5.731 1.40 0.04 + 1 .xu --3.70i2.17 -1.55 .__ .___--..__
-4.55 6.11 3.77 1.58 -0.27
(1929-1964) --
%
A B A B A B
S, L*
--Il.92 6.82 10.11 6.40 2.02 -1.92
X.12+0.62 3.OlzkO.64 -5.53kO.82 -6.46 L+C 0.39 --3.50* 1.07 0.60 * 0.89
-1.55 --I.67 0.99 2.29 --0.91 0.X4
4. DISCUSSION
shall examine whether the solar daily variation is more closely tied to a local magnetic or geographic coordinate system. For this purpose we use the results from San Juan, where D, the angle between local magnetic north and geographic north, changed by over 3” between 1929 and 1964. Since we have taken linear fits to the secular changes in the daily variations we shall also take a linear fit to D, and this gives a change of -2.97”* 0.03” from 1929.5 to 1964.5. Figure 3 illustrates how D and the direction of a harmonic component of the daily variation are related at different epochs, tl and t2. We see that First
we
1.23ztO.47 -0.42*0.X2 0.981 1.06 -2.87~tO.87 1.2Xi 0.49 1.65kO.84
3.2X 4.65 0.71 -3.09 -0.01 -0.80
-0.2 1 + 0.40 0.58*0.31 - 1 .Ol i 0.23 0.53 * 0.35 -1.10*0.2x -0.11*0.31
the direction of the horizontal component of the main field (denoted H) changes from Dt, to % relative to the geographic axis between the epochs. The position and magnitude of a harmonic component of the daily variation are represented by the vectors V,, and V,,. The directions of these components relative to the magnetic north are denoted by @,,, and @,2 respectively, where @ =: tan.-’ {A,(D)/A,(H)j for the in-phase component, and Cp= tan-’ {B,(D)/B,(H)} for the quadrature component; the letter in parenthesis indicates the appropriate element. If the direction of V remains fixed relative to the local magnetic north, then a,, --a,, = /3 = 0; alternatively. if V is fixed relative
693
Secular trends in daily geomagnetic variations
Table 3. The angles through which the in-phase and quadrature components of S1 and St at San Juan move with respect to magnetic north (fi) and geographic north (0) between 1929.5 and 1964.5
-
Fig. 3. The relationship between the horizontal component of the main field and the in-phase component of the nth harmonic of the daily variation at two epochs tl and 12. to geographic
coordinates,
a,, -a,,
t D,, - D,2 =
8=0.
Values of A, and B, have been synthesized for 19292 and 1964.5 from equations (2), assuming R = R and used to determine the values of p and 6 given Table 3. Clearly the values of /3 are smaller than those of 8, favouring the hypothesis that the solar daily variation is tied to local magnetic coordinates. Two of the quantities which exert a direct influence on S, namely the tensor ionospheric conductivity and the horizontal electric field in the ionosphere, depend on the magnitude and direction of the Earth’s main field. The above result implies that these are of greater importance in determining
Coefficient
P(“)
A, B, ‘4, B,
1.51kO.32 0.52* 1.55 1.35* 1.47 -0.89* 1.64
different epochs San Juan Coefficient ‘4, BI A2
J%
C 1964.5
5
(nT) 8.31kO.07 4.89 f 0.05 1.21*0.11 3.98 f 0.08
4.48 f 3.49* 4.32* 2.08*
0.32 1.55 1.47 1.64
the morphology of S than the wind pattern, which remains fixed relative to the geographic coordinate system. Next we shall consider the temporal changes in the amplitudes of the first two solar harmonics. The tensor ionospheric conductivity is dependent on F, the total intensity of the main field, while in midlatitudes the horizontal electric field depends on Z. Hence we may reasonably expect to see significant secular changes in the magnitudes of the harmonic components of S at stations where F and IZI show large temporal variations. At San Juan, where changes in H have been small, IZl has decreased by over 6% between 1929 and 1964. At Hermanus, decreases of about 24% and 13% have occurred in H and ]ZI respectively between 1941 and 1976. The results from Huancayo will be discussed later. The magnitude of the in-phase component of the nth harmonic is given by C= {[A,,(H)]‘t [A,(Z)]2}“2; for the quadrature component the A’s are replaced by B’s. The values of C for 1929.5 and 1964.5 at San Juan and for 1941.5 and 1976.5 at Hermanus have been synthesized at R = R using equations (2), and are presented in Table 4. At San Juan, only the B2 term shows a significant change. The change in this term is consistent with a 6% decrease, corresponding to that in Z. A 6% change in A2 would not be significant, whereas such a change would be detectable in A, and B, but is not seen. At Hermanus ail the changes are significant, and all except the smallest term (B,) change in the same sense as H and JZ(. However
Table 4. The amplitudes of the in-phase and quadrature components of S, and S, at
C 1929
W)
8.17rtO.07 4.99 f 0.05 1.23zt0.12 3.72ztO.08
Hermanus C 1941.5 C 1976S (n7-I 6.OlztO.11 12.20*0.10 6.62kO.11 2.92hO.13
5.53zto.11 11.75*0.10 5.83iz0.12 4.02ztO.13
R %L.I.Ph
694
there is no obvious quantitative reiation between these changes and those in H and IZ/. At Huancayo, most of the daily variation 1s a direct result of currents flowing in the equatorial electrojet, so we would expect any secular changes in S and L to be the result of either changes in the magnitude of these currents or movements of the electrojet. From the N-S gradient of Z. we infer that an increase of 1 nT corresponds to a 1 15 m movement of the geomagnetic equator (and hence the electrojet) in the N-S direction towards Huancayo. Using the observed values of Z, and representing the electrojet by an E-W current at a height of 110 km and showing no secular change of amplitude, we deduce that AH and AZ (the amplitudes of the daily variations in H and Z) should vary as shown in Fig. 4. The main points to note are a decrease in AH and an increase in AZ between 1923 and 1947, and very little change between 1948 and 1961. Precisely these changes are seen in the values of AH and AZ for S, and S, given in Table 5, suggesting that secular changes in S at Huancayo are closely related to movements of the electrojet. These values were synthesized from the data of Table 2 via equations (2), again assuming R = R and taking AH = {[A,(H)]2+[B,(H)]*}1’2 and AZ = {[A,(Z)]Z+[B,(Z)]2}“2 5. CONCLUSIONS Significant secular trends have been detected in both the solar and lunar daily geomagnetic variations. The statistical evidence of secular change in S seems conclusive and the reality of the effect is confirmed by its qualitative agreement with the predictions of simple theory. The results for L have less statistical weight and might possibly be improved in the future by the analyses of longer series of data. The secular changes in the solar daily variations
r [
!
“l
-c/ I
J\- - - - ___. - - - _. _
I
i-
:
:
1
,’
L__
__,_____-~-. - ----__.
--- - AZ AH , 1930
I
1 ,
1940
,950
1 i
are more closely related to local magnetic
coordinates than to geographic coordinates. Thus, for the analysis of long series of data it is more appropriate to use D and H rather than X and Y. The secular changes in S and L appear to result from changes in the main geomagnetic field, although possible long term variations in other parameters may also contribute to these effects. If similar studies were made for a wider distribution of observatories, each with its characteristic pattern of main field secular change, it should be possible to establish an empirical relation betweeen secular changes in main field elements and the daily variations. This would lead to a better understanding of physical processes in the dynamo region of the ionosphere. Acknowledgements-The author wishes to thank Dr S. R. C. MALIN, who provided the initial stimulus for the work, for his invaluable guidance and advice. Thanks are also due to Dr D. M. SCHLAPPfor many helpful comments, Dr C. A. GREEN for his assistance with the computation, and Miss S. A. JEFFERYwho helped with the preparation of the paper. The author is funded by a Science Research Council grant.
1947.5
1948.5
(nV 46.86kO.32 24.31 kO.26 6.84 f 0.08 3.60 f 0.05
t
1960
Fig. 4. The variations of AH and AZ at Huancayo as predicted from N-S movements of the equatorial electrojet. The arrow marks the temporal division of the two data sets.
different epochs
AH@,) AHW AZ@,) AZ&)
_I
Year
Table 5. The amplitudes of AH and AZ at Huancayo for S, and S2 at 1923.5
--‘.‘-T”.-~
1961.5 (nT)
42.78 f 0.32 21.67zt0.26 1190~0.08 7.02*0.05
57.90*0.46 28.63 f 0.36 7.30*oo.09 3.84kO.11
57.80 f 0.46 28.19kO.36 7.95 f 0.09 4.35*0.12
Secular trends in daily geomagnetic variations
hLDREDOEL. R. FOREIUSHS. E. and CASAVERDEM. GUPTA J. C. and CHAPMAN S.
B. R.,
LEATON MALIN
MALIN
S.
R. C. and FINCH H. F.
S.R. C. and SCHL,QP D. M.
MATSUSHITA
MCNISH
S. and CAMPBELLW. H.
1973 1961 1970
1963 1980 1967
1936
695
I.A.G.A. Bull. 35, 105. Carnegie Inst. Wash. Publ., 620. Manual of the coefficients of rhe first four harmonics of the solar and lunar daily geomagnetic uariations computed from IGY/C and certain other data. National Centre for Atmospheric Research, Boulder, Colorado. R. Obs Bulls. 63 Geophys. .I. R. astr. Sot. 60,409. Physics of Geomagnetic Phenomena. Vol. 1, pp. 381-388, Academic Press, New York and London. I.U.G.G. Bull. 10,271.