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A relationship between the life of M-regions and the rate of change of solar activity
Jonmalof~t~mxphericmc1TerrestrialPhysics,11160, Vol. 17,pp. 3 15to 319.PcrgnmonPressLtd. Printedin NorthernIrelan~l
A relationship between the life of M-regions and the rate of change of solar activity D. 1’1’.c:.
&ISPPELL Ikxninion Physicrtl Laboratory, Lower Hutt, New Zealand (Receiretl 28 Jdy
1039)
Abstract-To test the hypothesis that the observed lnclr of success in forecasting disturbances to radio propng~~tion by using the recurrence p&tern during the 1053P1!)64 sunspot minimum period is due to the high rate of decng of the 1047-195J cycle of solar :tetivity, rnwgnetic ch,zmeter figures for the period 1890&-l%O were examined. A nurnericd de&&ion of “persistence of recurrence” s gircn and ELlinear r&tionship is obt,nined between the l~~~~jn~~ll~~ v&xo of this qusntit.y at sunspot 1I~ini~nurnand the rate of decay of solur wtivity to tti;lt minimum. The extremely low v&~e of this quant.ity predicted by this reintionship for the I%& sunspot minimum I)(ariod is consi(tt*red to provide confirmatorg evidcncc for the initkl hypothesis.
‘I‘tix ( ‘1_I.~EJIAS-~EJ~RARO (193 l-l 933) t#heory of ionospheric and magnetic st’orms 1)ostrrlstcs that they result from t’he int’eraction between the ionosphere and a neuCra,l stjream of charged particles emanating from the 81111. Two \vell-defined types of emission have been recognized, an inipulsh-e t,ype which results from the solar ertiptions associat,ed witah large, a&\-e sunspots and causes large, noIi-recurrent storllls wiih P&den colllrllellcenleilt,s; and a steady type, whose soufee is not clearly ~~~~derst~~)oc~, which causes small, r~~c~~rrelltand slogs-starti~lg storms. As wc61ld be expected the former type is prevalent in sunspot lna~il~l~~iil years and ihe latter in sunspot minimum years. To explain Giis second type of emission, BIRTELS (1932) has postulated the esistener of especially active areas on the sun (called Z-regions) which emit particles continuously t’hroughout their lifetime. As the sun rotates with a mean ngnotlic period of 272 days, these particles form a rotst’ing spiral in space which nil1 overtake ‘the earth once in each solar rotation resultiq in the observed recurrence of t,he associated storms. ,4 number of tentative hypotheses have been proposed to explain the physical nature of these X-regions (infer nlia ‘C~_~LDMEIER, llir16; ALLES, 1044; and BABCOCK and BABCOCK, l&X), but none has so far achieved general acceptance. As long distance radio ~ro~agatio~~ depends for its success on the ionosphere, an ionospheric storm will result in a radio propagational disturbance. Such dist-urbances were forecast with considerable success during the sunspot minimum period of 1943-1045, but this success was not repeated during the 1954 sunspot minimum period. This observation could well be the result of the high rate of decay of the 10471954 cycle of solar activity, for it could be expected that the higher t,he rate of change of solar activity the shorter will be the life of any solar phenomenon, in particular N-regions. This investigation was undertaken to discover whether there is any evidence to support this hypothesis.
315
D. W. G. CHAPPELL DATA As M-regions are not directly observable, a study of their life must devolve into a study of the tendency to recur of one of their terrestrial manifestations (inter alia ionospheric storms, magnetic storms, radio propagational disturbances). Of these, magnetic storms provide the most promising avenue of enquiry for they alone have been observed for more than about 15 years and furthermore only these data are available in a form directly suitable for analysis. Each of the world-wide chain of magnetic observatories (some 50 in 1890 and some 100 in 1940, CHAPMANand BARTELS, 1940), inspects its records of the diurnal variation of the magnetic elements and places the day into one of three categories; 0 if the records represent a quiet day, 1 if a moderately disturbed day, or 2 if a determines the mean value of considerably disturbed day. Zurich Observatory these figures to one place of decimals and publishes it as the International Magnetic Character Figure for the day (C-figures). These C-figures are undoubtedly subjective but, being the mean value of over fifty independent judgements, could be expected to exhibit most of the properties of objective data: however, there will be systematic differences between C-figures recorded at times separated by many years, but reasonable homogeneity should be obtained over a period of 3 years which is all that is required by the analysis. By the choice of a suitable threshold value, these figures can be used to classify days into two groups-quiet and storm days. The value chosen for this purpose was C = 0.7 for two reasons; firstly, it is the intermediate value chosen by BARTELS (1932) to separate his red and black symbols, and secondly, this value results in a relatively large number of storm days enabling the analysis to be carried out using large numbers, thereby reducing the influence of random variations. Thus a day will be considered a storm day if its C-figure exceeds 0.7. DEFINITION OF PERSISTENCE If in any period of N days we have n, storm days and of these n2 have storm days 27 days later, we wish to combine these three numbers in such a way that the resultant figure will represent the tendency of storms to recur during the period. More generally, let there be a non-reciprocal law associating every day with some other day and in a period of N days there are n1 days exhibiting a given character and n2 pairs of associated days, both of which exhibit this character. If there is no relationship between the chosen law of association and the given character, then it can be shown by an argument precisely similar to that used by MOOD (1940) in his theory of random runs that, neglecting end effects, the expected value of the ratio: -nz nl
is
nl N’
If, on the other hand, there is a tendency for days exhibiting the given character to be associated by the chosen law, then the ratio n&r will exceed n,/N by a greater or less extent as the tendency to be associated is greater or less. In this case the character is “being a storm day” and the law is “that the day 316
-4 relationshipbetween the life of U-regions and the rate of ch;tngeof solar activity
associated wit,h day D is day IJ -+- 27”: so we can define the recurrence for the period or persistanee (P), as it will be called, by
tendency
where iV is the number of days if hhe period, ‘)&Iis the number of storm days, and v.~ t,he number of pairs of storm days separated by 27 days contained therein. METHOD
(a) Ikterneination
of the persistence
oti’
AXALYSIS
of ~ecwfence
The period 1890-19.57 was di-vided int,o running 3 year periods and, for each, t,he values of X, 1~~and 1~~mere counted and P calculated. ‘The diagram given by tfrixr~~s(1932) was used for the period 1907-1929, similar diagrams were constructed for the rest, of t,he period. (b)
netcrnzi?lcctift?e
of
the
mte
of
decay of solar actioit?f
It has been est’ablished for many years that the time variation of t’he running mean of t’he sunspot number is closely related to t,hat of solar activity. As in the A 60 5
50
02 z zti: 0
90 3O’
C
. 11
2; %Z
20
ys -id
10 20
D I 1904
I905
1906
007
1906
lw9
1910
B l911
1912
19l3
L 1914
YEAR
Fig. I.
drt,erlninat’io-11 of the values for persist*ence of recurrence a 3 year period was used ,a similar period was taken for the calculation of these running mean values. At first glance it would seem t,hat an acceptable value for the rat,e of decay of solar acti\?ty would be the slope of the line joining pointzs representing the maximum arjti ~~~i~li~ll~~~~l values (Fig. 1, points ‘-1 and B). Howere;*, t,his value is seriously af%ct~ed by curvature near t0he critical points of t’he curre; the points C and D would appear to give a more acceptable value for the rate of decay of sola,r activity. Tn this \vork the t,ime interraIs AC, BD are one-quartSer that, of SB.
The t’ime variation of P and sunspot number are shown in Fig. 2 and, as expecIn Fig. 3 are related the maximum tetl, they are approximately in antiphase. wlues of the P curve and the rate of decay of solar act’ivity towards the appropriate minimum. It will be seen that, in spite of the arbitrary nature of the definitions of these quantities, the points lie remarkably close to a straight line. This being so 317
D. W. G.
CHAPPELL
it can be inferred that there is a tendency for the maximum value of the persistence of recurrence of magnetic storms over a sunspot minimum period to vary in an inverse manner with the rate of decay of solar activity to that minimum and further that the length of life of M-regions will likewise vary inversely with that rate of decay. This result provides confirmatory evidence of the initial hypothesis that the observed lack of success in forecasting radio propagational disturbances using the -
11
12
Sunspot
l3
14 RATE
15
number.
16
OF DECAY
17 OF
16
SOLAR
19 ACTIVITY
20
21
22
23
24
25
UNITS/YEAR
Fig. 3.
27 day pattern during the 1954 minimum period was the result of the phenomenally high m&e of decay of the preceding cycle of solar activity. CoNCLUsroN
By studying the recurrence of magnetic storms for the period 1890-1957 it is shown that the maximum value of persistence of recurrence of magnetic storms during the sunspot minimum period varies in an inverse manner with the rate of It can be inferred that the lives of decay of solar activity to that minimum. M-regions vary inversely as the rate of change of solar activity and that the 318
A rel~~tionshipbetween the life of N-repions and the rate of vh~np of solar wtivit>
observed lack of success in the forecasting of radio propagational disturbances during the lW2 sunspot minimum period is a consequence of the high rat,e of decay of the present sunspot cycle. dcln~Ec:trdg~rrl~l~.~~-~he writer expresses his appreciation of the help he has received from his colleagues at Dominion physical Laboratory, in particular Messrs. W. H. W.4m and N. F. BARBER.
CHAPMAN MOOD
S.
itntl ?&~RTELS J.
A.M.
WALD~WEIER
ICI.
19.40
Geonra~r~etism~~ol. II, Table a, p. ‘rl.
1910 1946
don Press, Oxford. Bnn. Xath. Stat. 11,367. Terr. Xngn. Atnaos. Elect. 51, 537.
3 I!4
C’IH~IWI-
A relationship between the life of M-regions and the rate of change of solar activity D. 1’1’.c:.
&ISPPELL Ikxninion Physicrtl Laboratory, Lower Hutt, New Zealand (Receiretl 28 Jdy
1039)
Abstract-To test the hypothesis that the observed lnclr of success in forecasting disturbances to radio propng~~tion by using the recurrence p&tern during the 1053P1!)64 sunspot minimum period is due to the high rate of decng of the 1047-195J cycle of solar :tetivity, rnwgnetic ch,zmeter figures for the period 1890&-l%O were examined. A nurnericd de&&ion of “persistence of recurrence” s gircn and ELlinear r&tionship is obt,nined between the l~~~~jn~~ll~~ v&xo of this qusntit.y at sunspot 1I~ini~nurnand the rate of decay of solur wtivity to tti;lt minimum. The extremely low v&~e of this quant.ity predicted by this reintionship for the I%& sunspot minimum I)(ariod is consi(tt*red to provide confirmatorg evidcncc for the initkl hypothesis.
‘I‘tix ( ‘1_I.~EJIAS-~EJ~RARO (193 l-l 933) t#heory of ionospheric and magnetic st’orms 1)ostrrlstcs that they result from t’he int’eraction between the ionosphere and a neuCra,l stjream of charged particles emanating from the 81111. Two \vell-defined types of emission have been recognized, an inipulsh-e t,ype which results from the solar ertiptions associat,ed witah large, a&\-e sunspots and causes large, noIi-recurrent storllls wiih P&den colllrllellcenleilt,s; and a steady type, whose soufee is not clearly ~~~~derst~~)oc~, which causes small, r~~c~~rrelltand slogs-starti~lg storms. As wc61ld be expected the former type is prevalent in sunspot lna~il~l~~iil years and ihe latter in sunspot minimum years. To explain Giis second type of emission, BIRTELS (1932) has postulated the esistener of especially active areas on the sun (called Z-regions) which emit particles continuously t’hroughout their lifetime. As the sun rotates with a mean ngnotlic period of 272 days, these particles form a rotst’ing spiral in space which nil1 overtake ‘the earth once in each solar rotation resultiq in the observed recurrence of t,he associated storms. ,4 number of tentative hypotheses have been proposed to explain the physical nature of these X-regions (infer nlia ‘C~_~LDMEIER, llir16; ALLES, 1044; and BABCOCK and BABCOCK, l&X), but none has so far achieved general acceptance. As long distance radio ~ro~agatio~~ depends for its success on the ionosphere, an ionospheric storm will result in a radio propagational disturbance. Such dist-urbances were forecast with considerable success during the sunspot minimum period of 1943-1045, but this success was not repeated during the 1954 sunspot minimum period. This observation could well be the result of the high rate of decay of the 10471954 cycle of solar activity, for it could be expected that the higher t,he rate of change of solar activity the shorter will be the life of any solar phenomenon, in particular N-regions. This investigation was undertaken to discover whether there is any evidence to support this hypothesis.
315
D. W. G. CHAPPELL DATA As M-regions are not directly observable, a study of their life must devolve into a study of the tendency to recur of one of their terrestrial manifestations (inter alia ionospheric storms, magnetic storms, radio propagational disturbances). Of these, magnetic storms provide the most promising avenue of enquiry for they alone have been observed for more than about 15 years and furthermore only these data are available in a form directly suitable for analysis. Each of the world-wide chain of magnetic observatories (some 50 in 1890 and some 100 in 1940, CHAPMANand BARTELS, 1940), inspects its records of the diurnal variation of the magnetic elements and places the day into one of three categories; 0 if the records represent a quiet day, 1 if a moderately disturbed day, or 2 if a determines the mean value of considerably disturbed day. Zurich Observatory these figures to one place of decimals and publishes it as the International Magnetic Character Figure for the day (C-figures). These C-figures are undoubtedly subjective but, being the mean value of over fifty independent judgements, could be expected to exhibit most of the properties of objective data: however, there will be systematic differences between C-figures recorded at times separated by many years, but reasonable homogeneity should be obtained over a period of 3 years which is all that is required by the analysis. By the choice of a suitable threshold value, these figures can be used to classify days into two groups-quiet and storm days. The value chosen for this purpose was C = 0.7 for two reasons; firstly, it is the intermediate value chosen by BARTELS (1932) to separate his red and black symbols, and secondly, this value results in a relatively large number of storm days enabling the analysis to be carried out using large numbers, thereby reducing the influence of random variations. Thus a day will be considered a storm day if its C-figure exceeds 0.7. DEFINITION OF PERSISTENCE If in any period of N days we have n, storm days and of these n2 have storm days 27 days later, we wish to combine these three numbers in such a way that the resultant figure will represent the tendency of storms to recur during the period. More generally, let there be a non-reciprocal law associating every day with some other day and in a period of N days there are n1 days exhibiting a given character and n2 pairs of associated days, both of which exhibit this character. If there is no relationship between the chosen law of association and the given character, then it can be shown by an argument precisely similar to that used by MOOD (1940) in his theory of random runs that, neglecting end effects, the expected value of the ratio: -nz nl
is
nl N’
If, on the other hand, there is a tendency for days exhibiting the given character to be associated by the chosen law, then the ratio n&r will exceed n,/N by a greater or less extent as the tendency to be associated is greater or less. In this case the character is “being a storm day” and the law is “that the day 316
-4 relationshipbetween the life of U-regions and the rate of ch;tngeof solar activity
associated wit,h day D is day IJ -+- 27”: so we can define the recurrence for the period or persistanee (P), as it will be called, by
tendency
where iV is the number of days if hhe period, ‘)&Iis the number of storm days, and v.~ t,he number of pairs of storm days separated by 27 days contained therein. METHOD
(a) Ikterneination
of the persistence
oti’
AXALYSIS
of ~ecwfence
The period 1890-19.57 was di-vided int,o running 3 year periods and, for each, t,he values of X, 1~~and 1~~mere counted and P calculated. ‘The diagram given by tfrixr~~s(1932) was used for the period 1907-1929, similar diagrams were constructed for the rest, of t,he period. (b)
netcrnzi?lcctift?e
of
the
mte
of
decay of solar actioit?f
It has been est’ablished for many years that the time variation of t’he running mean of t’he sunspot number is closely related to t,hat of solar activity. As in the A 60 5
50
02 z zti: 0
90 3O’
C
. 11
2; %Z
20
ys -id
10 20
D I 1904
I905
1906
007
1906
lw9
1910
B l911
1912
19l3
L 1914
YEAR
Fig. I.
drt,erlninat’io-11 of the values for persist*ence of recurrence a 3 year period was used ,a similar period was taken for the calculation of these running mean values. At first glance it would seem t,hat an acceptable value for the rat,e of decay of solar acti\?ty would be the slope of the line joining pointzs representing the maximum arjti ~~~i~li~ll~~~~l values (Fig. 1, points ‘-1 and B). Howere;*, t,his value is seriously af%ct~ed by curvature near t0he critical points of t’he curre; the points C and D would appear to give a more acceptable value for the rate of decay of sola,r activity. Tn this \vork the t,ime interraIs AC, BD are one-quartSer that, of SB.
The t’ime variation of P and sunspot number are shown in Fig. 2 and, as expecIn Fig. 3 are related the maximum tetl, they are approximately in antiphase. wlues of the P curve and the rate of decay of solar act’ivity towards the appropriate minimum. It will be seen that, in spite of the arbitrary nature of the definitions of these quantities, the points lie remarkably close to a straight line. This being so 317
D. W. G.
CHAPPELL
it can be inferred that there is a tendency for the maximum value of the persistence of recurrence of magnetic storms over a sunspot minimum period to vary in an inverse manner with the rate of decay of solar activity to that minimum and further that the length of life of M-regions will likewise vary inversely with that rate of decay. This result provides confirmatory evidence of the initial hypothesis that the observed lack of success in forecasting radio propagational disturbances using the -
11
12
Sunspot
l3
14 RATE
15
number.
16
OF DECAY
17 OF
16
SOLAR
19 ACTIVITY
20
21
22
23
24
25
UNITS/YEAR
Fig. 3.
27 day pattern during the 1954 minimum period was the result of the phenomenally high m&e of decay of the preceding cycle of solar activity. CoNCLUsroN
By studying the recurrence of magnetic storms for the period 1890-1957 it is shown that the maximum value of persistence of recurrence of magnetic storms during the sunspot minimum period varies in an inverse manner with the rate of It can be inferred that the lives of decay of solar activity to that minimum. M-regions vary inversely as the rate of change of solar activity and that the 318
A rel~~tionshipbetween the life of N-repions and the rate of vh~np of solar wtivit>
observed lack of success in the forecasting of radio propagational disturbances during the lW2 sunspot minimum period is a consequence of the high rat,e of decay of the present sunspot cycle. dcln~Ec:trdg~rrl~l~.~~-~he writer expresses his appreciation of the help he has received from his colleagues at Dominion physical Laboratory, in particular Messrs. W. H. W.4m and N. F. BARBER.
CHAPMAN MOOD
S.
itntl ?&~RTELS J.
A.M.
WALD~WEIER
ICI.
19.40
Geonra~r~etism~~ol. II, Table a, p. ‘rl.
1910 1946
don Press, Oxford. Bnn. Xath. Stat. 11,367. Terr. Xngn. Atnaos. Elect. 51, 537.
3 I!4
C’IH~IWI-