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A regional model of E- and F-layer critical frequencies
0273-1177(95)00107-7
Asfv.SpaceJtes. Vol. 16, No. 1, pp. (1)115~1}1~8.1995 copyright bs)1995 CasPAR Printed in Great Britain. All . hts mewed. 0273-I 1&%9.50 + 0.00
A REGIONAL MODEL OF E- AND F-LAYER CRITICAL ~QUEN~~~ C. A. Zherebtsov, 0. M. Pig
and 0.
I. Razuvaev
Ittstituteof Solar-Terrestrial Physics, P.O. Box 4026, Irkutsk 664033, Russia
ABSTRACT
Realistic regional models are in~s~~~le at practical implementation in radio ~~~~tion and space na~~tion and therefore of particular interest in current research. Presented here is an analytic regional model for critical frequencies of the highlatitude ionosphe~c E- and F-regions based on data Tom a meridional chain of ionosondes. Estimates are made of the variance of observed characteristic frequencies in both regions. INPUT DATA AND PROCESSING TECHNIQUE Data obtained during the ~~-l~~de
lotion
“T~~-82“
from fonr sta~ons located
along the meridian (L - 90’ ; tDL = 56’ -70’ ) have been process& Critical frequencies of the E- and F-regions, covering a three-month observing interval, were averaged over two-hour intervals. A relation to magnetic activity was searched by the indices Kp and AE. Mean values obtained by this strategy were used to specify an appropriate regression formula (given low). The expression for diurnal variation takes account of diurnal and semidinrnal harmonics. A third order polynomial is admitted for the latitudinal variation and the linear dependence on maguetic activity. The regression equation contained 31 independent coefficients is resolved in one procedure.
(1)
i=1,2
(I)1 I5
(22)
G. A. Zherebtsov
(0116
there f
etal.
@’ - invariant latitude, T - local time in angular degrees,
- critical frequency,
and K - geomagnetic index., ao,Co,Cik - independent
coefficients.
RESULTS The regression formula represents reasonably adequately the characteristic of the empirical data. For the F2-layer, the proportion of the variation accounted for by the regression is 89% with Kp and 90% with AE; for the E-layer it is 82% in both cases. A regression model differs from an empirical model by a smoother dependence on model parameters: latitude, local time, and activity index. Since the regression formula is computed from the basic data in only one procedure it and takes into account the interrelation of values from neighboring averaging meshes, and is felt to be statistically superior to an empirical model built upon the same data. A mathematically expressed model is not only more convenient for practical purposes but also more reliable than a model in tabulated or graphic form. The assumption of linear dependence on the index of magnetic activity is not always legitimate. A second order polynomial might be preferable. An independent verification of the regression formula was carried out against with data from Dioxin for January 1983. Best correlation between empirical data and data obtained with the regression formula is achieved with two-hour averaging. computed and observed data are compared in Figures 1 and 2, their statistics is shown in Tables 1 and 2.
4 68
65
62
I
9
5
t
cp’
43
17
21 LT
I
68
65
62
I
I
I
Fig. 1. Maps of foF2 contours in invariant latitude - local time coordinates, (top observed, bottom - model.) for moderately disturbed conditions. (2 ,< K I 3).
Regioaal Modd of E- and F-Layer
i3
17
2t
oi
(I)117
05
09
LT
l”ABLE I. Mean critical~equencies/MH~of the FZ-layer (Subscripts:f observed,m - modet), with r con-elationcoefficientsand p - root-meansquare errors/MHz.
(1)118
G. A. Zherebtsov et al.
TABLE 2
I II
Same but for the Es-layer.
hours
K
5-7
r
( Em,
KP AE
1 f@rl. 3.2 3.2
3.1 3.2
0.46 0.49
P 0.8 0.8
11-13
AE Kp
1.7
2.6
0.63 0.71
1.1 1.0
17-19 23-01
AEZ Kp KP AEZ
2.4 3.3
2.8 2.6 3.3 3.5
0.58 0.56 0.35 0.34
0.8 1.0 1.1 1.0
1
1
J
As expected the formula represents the F-layer critical frequency (Table 1) to greater accuracy then those of E-layer (in which the Es phenomenon is included, see Table 2). If the AE-index is used to specify the magnetic activity then, depending on the hour the correlation coefficient is 0.66 to 0.69. Values found with the Kp-index, the correlation coefficient are between 0.63 (17 to 19h) and 0.78 (11 to 13h). The mean-root-square error lies in the range 0.8-l. 1 MHz thus about. Less good results were obtained for the Eregion. While, for the dayside E-layer, the correlation coefficient still reaches 0.6 to 0.7, it goes down to 0.4 at night (with data uniquely from Es-layers, see Table 2). CONCLUSION The regression formula introduced in this paper may be useful for estimating critical frequencies of the high-latitude ionospheric E- and F-layers and their dependence on magnetic activity. The formula holds good for the F-region and daytime E. Less good were the results for the nightside E-region and Es-layers.
Asfv.SpaceJtes. Vol. 16, No. 1, pp. (1)115~1}1~8.1995 copyright bs)1995 CasPAR Printed in Great Britain. All . hts mewed. 0273-I 1&%9.50 + 0.00
A REGIONAL MODEL OF E- AND F-LAYER CRITICAL ~QUEN~~~ C. A. Zherebtsov, 0. M. Pig
and 0.
I. Razuvaev
Ittstituteof Solar-Terrestrial Physics, P.O. Box 4026, Irkutsk 664033, Russia
ABSTRACT
Realistic regional models are in~s~~~le at practical implementation in radio ~~~~tion and space na~~tion and therefore of particular interest in current research. Presented here is an analytic regional model for critical frequencies of the highlatitude ionosphe~c E- and F-regions based on data Tom a meridional chain of ionosondes. Estimates are made of the variance of observed characteristic frequencies in both regions. INPUT DATA AND PROCESSING TECHNIQUE Data obtained during the ~~-l~~de
lotion
“T~~-82“
from fonr sta~ons located
along the meridian (L - 90’ ; tDL = 56’ -70’ ) have been process& Critical frequencies of the E- and F-regions, covering a three-month observing interval, were averaged over two-hour intervals. A relation to magnetic activity was searched by the indices Kp and AE. Mean values obtained by this strategy were used to specify an appropriate regression formula (given low). The expression for diurnal variation takes account of diurnal and semidinrnal harmonics. A third order polynomial is admitted for the latitudinal variation and the linear dependence on maguetic activity. The regression equation contained 31 independent coefficients is resolved in one procedure.
(1)
i=1,2
(I)1 I5
(22)
G. A. Zherebtsov
(0116
there f
etal.
@’ - invariant latitude, T - local time in angular degrees,
- critical frequency,
and K - geomagnetic index., ao,Co,Cik - independent
coefficients.
RESULTS The regression formula represents reasonably adequately the characteristic of the empirical data. For the F2-layer, the proportion of the variation accounted for by the regression is 89% with Kp and 90% with AE; for the E-layer it is 82% in both cases. A regression model differs from an empirical model by a smoother dependence on model parameters: latitude, local time, and activity index. Since the regression formula is computed from the basic data in only one procedure it and takes into account the interrelation of values from neighboring averaging meshes, and is felt to be statistically superior to an empirical model built upon the same data. A mathematically expressed model is not only more convenient for practical purposes but also more reliable than a model in tabulated or graphic form. The assumption of linear dependence on the index of magnetic activity is not always legitimate. A second order polynomial might be preferable. An independent verification of the regression formula was carried out against with data from Dioxin for January 1983. Best correlation between empirical data and data obtained with the regression formula is achieved with two-hour averaging. computed and observed data are compared in Figures 1 and 2, their statistics is shown in Tables 1 and 2.
4 68
65
62
I
9
5
t
cp’
43
17
21 LT
I
68
65
62
I
I
I
Fig. 1. Maps of foF2 contours in invariant latitude - local time coordinates, (top observed, bottom - model.) for moderately disturbed conditions. (2 ,< K I 3).
Regioaal Modd of E- and F-Layer
i3
17
2t
oi
(I)117
05
09
LT
l”ABLE I. Mean critical~equencies/MH~of the FZ-layer (Subscripts:f observed,m - modet), with r con-elationcoefficientsand p - root-meansquare errors/MHz.
(1)118
G. A. Zherebtsov et al.
TABLE 2
I II
Same but for the Es-layer.
hours
K
5-7
r
( Em,
KP AE
1 f@rl. 3.2 3.2
3.1 3.2
0.46 0.49
P 0.8 0.8
11-13
AE Kp
1.7
2.6
0.63 0.71
1.1 1.0
17-19 23-01
AEZ Kp KP AEZ
2.4 3.3
2.8 2.6 3.3 3.5
0.58 0.56 0.35 0.34
0.8 1.0 1.1 1.0
1
1
J
As expected the formula represents the F-layer critical frequency (Table 1) to greater accuracy then those of E-layer (in which the Es phenomenon is included, see Table 2). If the AE-index is used to specify the magnetic activity then, depending on the hour the correlation coefficient is 0.66 to 0.69. Values found with the Kp-index, the correlation coefficient are between 0.63 (17 to 19h) and 0.78 (11 to 13h). The mean-root-square error lies in the range 0.8-l. 1 MHz thus about. Less good results were obtained for the Eregion. While, for the dayside E-layer, the correlation coefficient still reaches 0.6 to 0.7, it goes down to 0.4 at night (with data uniquely from Es-layers, see Table 2). CONCLUSION The regression formula introduced in this paper may be useful for estimating critical frequencies of the high-latitude ionospheric E- and F-layers and their dependence on magnetic activity. The formula holds good for the F-region and daytime E. Less good were the results for the nightside E-region and Es-layers.