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Day-to-day variations in the F2 critical frequency
JoumalofAtmospheric and TerrestrialPhysics,1966, Vol. 28, pp. 531-535. PergamonPrewLtd. Printedin NorthernIreland
SHORT PAPER
Day-to-day variations in the
F2
critical frequency
G. A. M. KING Geophysical Observatory, D.S.I.R., New Zealand (Received 7 October 1965) Abstract-From a comparisonof ionosphericchangesat Fl and F2 heights it is found that most of the variations in foF2 can be attributed to variations in the incident ionizing radiation and in the rate of electron recombination. The ionizing radiation follows fairly closely the 2800 MC/S solar radio flux. The recombination rate is affected by ionosphericstorms and travelling disturbances, and it also shows a steady drift over the period studied. 1.
INTRONJ~TI~N
critical frequency of the PZ-layer shows day-to-day variations. They could be due to changes in electron production, recombination, gas temperature, electron temperature or movements of ionization. This paper reports a study at a mid-latitude station during summer which puts some limits on the relative importance of the several factors. At the F2 peak the movement terms, diffusion and perhaps electrodynamic drift, are comparable with the others. However, with decreasing height they become less effective while production and recombination become much stronger. We assume that analysis at 3’1 heights can give the production and loss terms only, and they can be used to assess the changes in production and loss at 3’2. Any changes not accounted for in this way are attributed to the other factors. A forty-day period, 29 January-8 March, 1960 was selected at Campbell Island (53% 16S’E). It contained no major magnetic activity. Every suitable ionogram between 10h and 14h was scaled for the Fl parameters, In G, In (a/,x x lo-lo) and I’ (KING and LAWDEN, 1964) and for the F2 critical frequency, f. As usual, travelling disturbances spoilt many of the records so that only 652 were read from a total of 1168 in the period. In G and In q/a were combined to give In /?/afor each record. In b/a and In q/a were then reduced to a constant solar zenith angle corresponding to noon at the start of the period. For the reduction, a scale height gradient of O-3 was assumed. This value is much lower than the mean r actually read, but it should be remembered that I’ is merely a device to generate a scale height at the peak of the production function. The mean scale height, 49 km, was applied to CUMMACK’S(1961) tables to estimate a more realistic scale height gradient, which turned out to be a little less than 0.3. The daily means of In /?/a and In q/a, both corrected for solar zenith angle, and of lnf and I’ are called In /Y, In q’, lnf and r. Figure 1 shows I’, the 2800 MC/S solar flux 4, and In q’ over the period, while Fig. 2 shows In /?’ and In f THE
531
0. 9. 31. Krx 2. THE IONIZING
RADIATIOS
C’onsiderfirstly In q’ (Fig. 1). The bar on the lower left gives the reading error for single determination. On the average, each point plotted is the mean of sixteen determinations, so that the mean error is only about a quarter of the bar. However, on five days the count fell below eight because of the high incidence of travelling disturbances. Data for those days are distinguished by open circles, and it looks as though In q’ has been systematically depressed by the travelling disturbances. a
_____
CAMPBELL -.-____-.
.---
___I___L-I1
31 JAN
05
10
15 FEB
ISLAND . .--. .----..
20 1960
25
-- --
01
08 MAR
Fig. 1. The ‘gradient of scale height’ r (C~OSNS), the 2800 MC/S solar radio flux + (line) and the logarithm of the electron production rate at tied solar zenith angle In q’ (dots); open circles indicate less significant values.
Over the forty-day period, In q’ drops uniformly by O-69, i.e. q’ drops by a half. This trend parallels closely that shown by the 2800 MC/Sflux, even to the change in slope near 18 February. The fine details in the two curves do not go together as well, although some matching peaks and troughs stand out. The OS0 satellite (LINDSAY, 1964) has shown similar in-phase variations between the 2800 Mcjs flux and the strengths of the solar lines at 304, 284 and 335A-among the most important lines producing the P-region -so the present result is not unexpected. However, the relation could well not hold at the peak of a solar cycle (KING and LAWDEN,1962). Quantitatively, the sequences of In q’ and 4 in Fig. 1 correlate with a coefficient, 0.934. The ionizing radiation is the main heat source in the F-region. With the large variation in q’ over the period we should therefore expect that the scale height would change. Indeed, the data for I at the top of Fig. 1 show a steady trend such that the scale height has dropped from 51 to 47 km. Most of the variability in I’ is real, in particular the very high value on 9 Feb. (H = 54 km) and the very low value on 6 March (H = 41 km). However, the high value on 2 February results from the effects of travelling disturbances.
Day-to-day
variatioIle in the F.2 critical frequency
533
The incoming solar radiation is proportional to the product of q’ and H, which drops over the 40-day period to only 0*46 of its initial value. Of course, we have no information on changes in the solar spectrum. 3. ELECTRONRECOMBINATION Consider now Fig. 2. The scale of In /3’ has been inverted and compressed to aid the comparison with lnf There is an obvious short-term similarity plus a steady ISLAND
CAMPBELL
I
I
I
05
s
1
10
15 FEB
JAiY
I
I
25
01
I
20 1960
I
06 MAR
Fig. 2. The logarithm of the electron recombination rate at a fixed level in the atmosphere
ln p
(upper line;
inverted scale) and the logarithm (lower line).
of f,,FZ lnf
drift of one with respect to the other. To make a detailed correlation the dependence of the F2 critical frequency was written as follows: Inp = 4 In q’ + R In fi’ + constant + other factors
(1)
The factor, 4, with In q’ of course reflects the quadratic relation between the critical frequency and the electron density. It also assumes that the ionizing radiation at FZ heights is almost unattenuated; this is readily seen by putting E-” + l/10 in q = q. . E(l--e-cw-z)
(2)
Iffresulted from an equilibrium between production, recombination and diffusion, all varying exponentially with height, then R = -l/(k
+
1)
(3)
where k is the ratio of particle weights of the molecules and atoms (K.IxQ, 1964). However, as In /?’ and In q’ are measured at Fl heights, (3) requires complete diffusive equilibrium between FI and FL?. This may not always hold and therefore R might well be a larger negative number than -l/(k + 1). The ‘other factors’ include any non-linear dependence of q’ and 8’ on atmospheric scale height such as can arise in
q’ from the change in composition with height and in /Y through temperature-sensitive rate coefficients-the latter are unlikely to be important, as otherwise they would show clearly over the solar cycle. Notice that the linear changes of q’ and ,Y cancel and need not be considered, even though the fractional change in scale height is greater at the FZ peak than at the peak of electron production. (CUMMACK, 1961). ‘Other factors’ also include trends in the diffusion coefficient, the electron temperature and the electrodynamic forces. We now assume that the R for the shorter period changes (Fig. 2) is the same as for the steady trend in In p’. The best fitting line relating In p’ and (ln J - + In ry’) had a slope of -l/2.36. However, the function [lnf - -$In q’ f l/2*36 In B’] showed a steady decrease of 0.064 through the 40-day period. This drift was attributed to ‘other factors’ and was subtracted from (In f --. 4 In q’) to generate a new fun&ion, In f ‘. In /Y and In f’ correlate with a coefficient O-932. The best fitting line now ha,s a slope - lj2.56 and the regression of lnf’ on In fl’ is -l/2*61. The drift which we have attributed to “other factors” is only a fifth as important as the allowance which must be made for the change in In q’ . (4 A In q’ = $ x 0.69 in 40 days). One factor which may have both short and long term changes is electrodynamic movement, and we can assess the importance of the short term electrodynamic movement. It acts to degrade the correlation between In p’ and 1nJ” ; from t,he high coefficient obtained we can say that it less than a sixth as effective as recombina tion in altering hif The changes in 111/?’ can be resolved int,o a trend and short term changes. The trend amounts to -0.56 in In b’ over 40 days, i.e. fl’ drops to 0.57 of its initial value. Lacking a physical model, we resist the temptation to secure a good correlation between the trends of In @’ and In q’. There is no sign of a ‘step’ in In /3’ such as FRENCH (In press) and KING and LAWDEW (Submitted) have found during summer at this st’ation. In fact, shortly after this sequence. on 17 March, 1960. p’ did decrease abruptly to about a hnlf (KING, 1961). Present views on this particular step are that it is probably the autumnal seasonal change, the complement of the vernal one that BULI,EN (1964) found. If so, the trend between 29 January and 8 March may be a precursor of the abrupt seasonal change. The short term changes in In /l’ could be due to a variety of causes, a,nd the scope of this paper allows only brief mention of two. One is the continual passage of atmospheric waves which manifest themselves as travelling disturbances. The ionograms showed that much of the travelling disturbance activity took place in the lower F-region (KING, 1961). If this were wholly the case, then the region between FI and F2 would behave as though in complete diffusive equilibrium with a variable turbopause below Fl, and (KIXG, 1964) d lllf’/d
In p’ = -l/(1;
-j- I)>
(4)
with an effective k between l-75 and 2.0. This 40-day period yielded cl lnf’/d
In 8’ = -1j2.61
suggesting that some of the mixing was taking place between PI and F2.
(5)
Day-to-day variations in the P2 critical frequency
535
The second cause for the short period changes is the occurrence of ionospheric storms. It has been found previously that /l is raised following a storm (Kr~a, 1962). As a crude measure, therefore, the R-index sum for the previous 24 hr at Amberley was compared with In J . (1nJ”has the advantage over both In /?’ and lnf’ for this purpose in that by chance it was very little trend; we know already that its short period changes reflect mostly In j3’.) The correlation coefficient was 0.49-very significant within the 1 per cent confidence level. The minor storm activity during this period (K =p 5) has made an appreciable contribution to the changes in /?. 4. CoNCLUsIoNs
The results of this study can now be summarized. Nearly all the changes in the F2 critical frequency arise through changes in the incident ionizing radiation and in the recombination rate. The latter is affected, among other things, by ionospheric storms and travelling disturbances. A variety of other factors can contribute in a small way to the F2 critical frequency. As the storm-time effect of electrodynamic forces seems small it is unlikely that the steady electrodynamic forces play a major role. These conclusions apply to a sample from summer daytime at a mid-latitude station; they should not be generalized uncritically. work is part of the research programme of the Geophysical Observatory, D.S.I.R.; Superintendent, Mr. J. W. BEAQLEY. Mrs. V. MEHRTENS scaled the ionograms and carried out much of the numerical analysis. Acknowledgements-This
REFERENCES BULLEN J. M. CUMMACK C. H. FRENCH A. G. KING G. A. M. KING G. A. M. KING G. A. M. KING G. A. M. and LAWDEN M. D. KING G. A. M. and LAWDEN M. D. KING G. A. M. and LAWDEN M. D. LINDSAY J. C.
1964 1961 1966 1961 1962 1964 1962 1964 1966 1964
J. Atrnoaph. Terr. Phy8. 26, 559. J. Geophya. Rea. 88, 2751. J. Atmoaph. Terr. Phys. (In press). J. Geophys. Rea. 66, 4149. Planet. Space Sci. 9, 95. J. Atmoaph. Sci. 21, 231. J. Atmmph. Tern. Phys. 24, 565. J. Atwwaph. Terr. Phya. 26, 1273. J. Atmoaph. Terr. Phys. (Submitted). Planet. Space ~5%.12, 379.
SHORT PAPER
Day-to-day variations in the
F2
critical frequency
G. A. M. KING Geophysical Observatory, D.S.I.R., New Zealand (Received 7 October 1965) Abstract-From a comparisonof ionosphericchangesat Fl and F2 heights it is found that most of the variations in foF2 can be attributed to variations in the incident ionizing radiation and in the rate of electron recombination. The ionizing radiation follows fairly closely the 2800 MC/S solar radio flux. The recombination rate is affected by ionosphericstorms and travelling disturbances, and it also shows a steady drift over the period studied. 1.
INTRONJ~TI~N
critical frequency of the PZ-layer shows day-to-day variations. They could be due to changes in electron production, recombination, gas temperature, electron temperature or movements of ionization. This paper reports a study at a mid-latitude station during summer which puts some limits on the relative importance of the several factors. At the F2 peak the movement terms, diffusion and perhaps electrodynamic drift, are comparable with the others. However, with decreasing height they become less effective while production and recombination become much stronger. We assume that analysis at 3’1 heights can give the production and loss terms only, and they can be used to assess the changes in production and loss at 3’2. Any changes not accounted for in this way are attributed to the other factors. A forty-day period, 29 January-8 March, 1960 was selected at Campbell Island (53% 16S’E). It contained no major magnetic activity. Every suitable ionogram between 10h and 14h was scaled for the Fl parameters, In G, In (a/,x x lo-lo) and I’ (KING and LAWDEN, 1964) and for the F2 critical frequency, f. As usual, travelling disturbances spoilt many of the records so that only 652 were read from a total of 1168 in the period. In G and In q/a were combined to give In /?/afor each record. In b/a and In q/a were then reduced to a constant solar zenith angle corresponding to noon at the start of the period. For the reduction, a scale height gradient of O-3 was assumed. This value is much lower than the mean r actually read, but it should be remembered that I’ is merely a device to generate a scale height at the peak of the production function. The mean scale height, 49 km, was applied to CUMMACK’S(1961) tables to estimate a more realistic scale height gradient, which turned out to be a little less than 0.3. The daily means of In /?/a and In q/a, both corrected for solar zenith angle, and of lnf and I’ are called In /Y, In q’, lnf and r. Figure 1 shows I’, the 2800 MC/S solar flux 4, and In q’ over the period, while Fig. 2 shows In /?’ and In f THE
531
0. 9. 31. Krx 2. THE IONIZING
RADIATIOS
C’onsiderfirstly In q’ (Fig. 1). The bar on the lower left gives the reading error for single determination. On the average, each point plotted is the mean of sixteen determinations, so that the mean error is only about a quarter of the bar. However, on five days the count fell below eight because of the high incidence of travelling disturbances. Data for those days are distinguished by open circles, and it looks as though In q’ has been systematically depressed by the travelling disturbances. a
_____
CAMPBELL -.-____-.
.---
___I___L-I1
31 JAN
05
10
15 FEB
ISLAND . .--. .----..
20 1960
25
-- --
01
08 MAR
Fig. 1. The ‘gradient of scale height’ r (C~OSNS), the 2800 MC/S solar radio flux + (line) and the logarithm of the electron production rate at tied solar zenith angle In q’ (dots); open circles indicate less significant values.
Over the forty-day period, In q’ drops uniformly by O-69, i.e. q’ drops by a half. This trend parallels closely that shown by the 2800 MC/Sflux, even to the change in slope near 18 February. The fine details in the two curves do not go together as well, although some matching peaks and troughs stand out. The OS0 satellite (LINDSAY, 1964) has shown similar in-phase variations between the 2800 Mcjs flux and the strengths of the solar lines at 304, 284 and 335A-among the most important lines producing the P-region -so the present result is not unexpected. However, the relation could well not hold at the peak of a solar cycle (KING and LAWDEN,1962). Quantitatively, the sequences of In q’ and 4 in Fig. 1 correlate with a coefficient, 0.934. The ionizing radiation is the main heat source in the F-region. With the large variation in q’ over the period we should therefore expect that the scale height would change. Indeed, the data for I at the top of Fig. 1 show a steady trend such that the scale height has dropped from 51 to 47 km. Most of the variability in I’ is real, in particular the very high value on 9 Feb. (H = 54 km) and the very low value on 6 March (H = 41 km). However, the high value on 2 February results from the effects of travelling disturbances.
Day-to-day
variatioIle in the F.2 critical frequency
533
The incoming solar radiation is proportional to the product of q’ and H, which drops over the 40-day period to only 0*46 of its initial value. Of course, we have no information on changes in the solar spectrum. 3. ELECTRONRECOMBINATION Consider now Fig. 2. The scale of In /3’ has been inverted and compressed to aid the comparison with lnf There is an obvious short-term similarity plus a steady ISLAND
CAMPBELL
I
I
I
05
s
1
10
15 FEB
JAiY
I
I
25
01
I
20 1960
I
06 MAR
Fig. 2. The logarithm of the electron recombination rate at a fixed level in the atmosphere
ln p
(upper line;
inverted scale) and the logarithm (lower line).
of f,,FZ lnf
drift of one with respect to the other. To make a detailed correlation the dependence of the F2 critical frequency was written as follows: Inp = 4 In q’ + R In fi’ + constant + other factors
(1)
The factor, 4, with In q’ of course reflects the quadratic relation between the critical frequency and the electron density. It also assumes that the ionizing radiation at FZ heights is almost unattenuated; this is readily seen by putting E-” + l/10 in q = q. . E(l--e-cw-z)
(2)
Iffresulted from an equilibrium between production, recombination and diffusion, all varying exponentially with height, then R = -l/(k
+
1)
(3)
where k is the ratio of particle weights of the molecules and atoms (K.IxQ, 1964). However, as In /?’ and In q’ are measured at Fl heights, (3) requires complete diffusive equilibrium between FI and FL?. This may not always hold and therefore R might well be a larger negative number than -l/(k + 1). The ‘other factors’ include any non-linear dependence of q’ and 8’ on atmospheric scale height such as can arise in
q’ from the change in composition with height and in /Y through temperature-sensitive rate coefficients-the latter are unlikely to be important, as otherwise they would show clearly over the solar cycle. Notice that the linear changes of q’ and ,Y cancel and need not be considered, even though the fractional change in scale height is greater at the FZ peak than at the peak of electron production. (CUMMACK, 1961). ‘Other factors’ also include trends in the diffusion coefficient, the electron temperature and the electrodynamic forces. We now assume that the R for the shorter period changes (Fig. 2) is the same as for the steady trend in In p’. The best fitting line relating In p’ and (ln J - + In ry’) had a slope of -l/2.36. However, the function [lnf - -$In q’ f l/2*36 In B’] showed a steady decrease of 0.064 through the 40-day period. This drift was attributed to ‘other factors’ and was subtracted from (In f --. 4 In q’) to generate a new fun&ion, In f ‘. In /Y and In f’ correlate with a coefficient O-932. The best fitting line now ha,s a slope - lj2.56 and the regression of lnf’ on In fl’ is -l/2*61. The drift which we have attributed to “other factors” is only a fifth as important as the allowance which must be made for the change in In q’ . (4 A In q’ = $ x 0.69 in 40 days). One factor which may have both short and long term changes is electrodynamic movement, and we can assess the importance of the short term electrodynamic movement. It acts to degrade the correlation between In p’ and 1nJ” ; from t,he high coefficient obtained we can say that it less than a sixth as effective as recombina tion in altering hif The changes in 111/?’ can be resolved int,o a trend and short term changes. The trend amounts to -0.56 in In b’ over 40 days, i.e. fl’ drops to 0.57 of its initial value. Lacking a physical model, we resist the temptation to secure a good correlation between the trends of In @’ and In q’. There is no sign of a ‘step’ in In /3’ such as FRENCH (In press) and KING and LAWDEW (Submitted) have found during summer at this st’ation. In fact, shortly after this sequence. on 17 March, 1960. p’ did decrease abruptly to about a hnlf (KING, 1961). Present views on this particular step are that it is probably the autumnal seasonal change, the complement of the vernal one that BULI,EN (1964) found. If so, the trend between 29 January and 8 March may be a precursor of the abrupt seasonal change. The short term changes in In /l’ could be due to a variety of causes, a,nd the scope of this paper allows only brief mention of two. One is the continual passage of atmospheric waves which manifest themselves as travelling disturbances. The ionograms showed that much of the travelling disturbance activity took place in the lower F-region (KING, 1961). If this were wholly the case, then the region between FI and F2 would behave as though in complete diffusive equilibrium with a variable turbopause below Fl, and (KIXG, 1964) d lllf’/d
In p’ = -l/(1;
-j- I)>
(4)
with an effective k between l-75 and 2.0. This 40-day period yielded cl lnf’/d
In 8’ = -1j2.61
suggesting that some of the mixing was taking place between PI and F2.
(5)
Day-to-day variations in the P2 critical frequency
535
The second cause for the short period changes is the occurrence of ionospheric storms. It has been found previously that /l is raised following a storm (Kr~a, 1962). As a crude measure, therefore, the R-index sum for the previous 24 hr at Amberley was compared with In J . (1nJ”has the advantage over both In /?’ and lnf’ for this purpose in that by chance it was very little trend; we know already that its short period changes reflect mostly In j3’.) The correlation coefficient was 0.49-very significant within the 1 per cent confidence level. The minor storm activity during this period (K =p 5) has made an appreciable contribution to the changes in /?. 4. CoNCLUsIoNs
The results of this study can now be summarized. Nearly all the changes in the F2 critical frequency arise through changes in the incident ionizing radiation and in the recombination rate. The latter is affected, among other things, by ionospheric storms and travelling disturbances. A variety of other factors can contribute in a small way to the F2 critical frequency. As the storm-time effect of electrodynamic forces seems small it is unlikely that the steady electrodynamic forces play a major role. These conclusions apply to a sample from summer daytime at a mid-latitude station; they should not be generalized uncritically. work is part of the research programme of the Geophysical Observatory, D.S.I.R.; Superintendent, Mr. J. W. BEAQLEY. Mrs. V. MEHRTENS scaled the ionograms and carried out much of the numerical analysis. Acknowledgements-This
REFERENCES BULLEN J. M. CUMMACK C. H. FRENCH A. G. KING G. A. M. KING G. A. M. KING G. A. M. KING G. A. M. and LAWDEN M. D. KING G. A. M. and LAWDEN M. D. KING G. A. M. and LAWDEN M. D. LINDSAY J. C.
1964 1961 1966 1961 1962 1964 1962 1964 1966 1964
J. Atrnoaph. Terr. Phy8. 26, 559. J. Geophya. Rea. 88, 2751. J. Atmoaph. Terr. Phys. (In press). J. Geophys. Rea. 66, 4149. Planet. Space Sci. 9, 95. J. Atmoaph. Sci. 21, 231. J. Atmmph. Tern. Phys. 24, 565. J. Atwwaph. Terr. Phya. 26, 1273. J. Atmoaph. Terr. Phys. (Submitted). Planet. Space ~5%.12, 379.