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Statistical properties of variability of the quiet ionosphere F2-layer maximum parameters over Irkutsk under low solar activity
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Advances in Space Research 51 (2013) 702–711 www.elsevier.com/locate/asr
Statistical properties of variability of the quiet ionosphere F2-layer maximum parameters over Irkutsk under low solar activity M.G. Deminov a,⇑, G.F. Deminova a, G.A. Zherebtsov b, N.M. Polekh b b
a IZMIRAN, 142190 Troitsk, Moscow Region, Russia Institute of Solar-Terrestrial Physics, SB RAS, P.O. Box 291, 664033 Irkutsk, Russia
Received 19 July 2012; received in revised form 25 September 2012; accepted 26 September 2012 Available online 5 October 2012
Abstract The statistical analysis of the quiet ionosphere F2-layer maximum parameters variability (deviations of NmF2 and hmF2 from the quiet medians, dn and Dh) under solar minimum at day (10–16 LT) and night (22–04 LT) hours based on data of Irkutsk station for 2007–2010 is presented. It is found that the experimental distribution (histogram) of dn can be approximated by a mixture of two normal distributions. The first and second components of the mixture characterize, mainly, relatively weak and strong fluctuations of dn which are presumably associated with the ionospheric effects of the atmospheric gravity waves and of the planetary waves and tides correspondingly. Deviation of the dn histogram from a single normal distribution is most considerable at night hours in winter and equinoxes. For these conditions the weak fluctuations of dn are mainly negative and the strong ones are mainly positive. The Dh histogram is a normal distribution except day hours in winter and equinoxes when a weak deviation of the histogram from the normal distribution occurs. Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Quiet ionosphere; F2-layer maximum parameters; Variability; Mixture of two normal distributions
1. Introduction Variability of the F2-layer maximum parameters and primarily of NmF2 (or the critical frequency, foF2) within one hour and day-to-day was investigated in many works (Zevakina et al., 1990; Gulyaeva et al., 1998; Forbes et al., 2000; Kouris et al., 2000, 2006; Rishbeth and Mendillo, 2001; Kouris and Fotiadis, 2002; Mendillo et al., 2002; Mizrahi et al., 2002; Pancheva et al., 2002; Lastovicka et al., 2003; Rawer et al., 2003; Liu et al., 2004; Mikhailov et al., 2004; Araujo-Pradere et al., 2005; Fotiadis and Kouris, 2006; Adeniyi et al., 2007; Altadill, 2007; Gordienko et al., 2007; Mitic and Cander, 2008; Zhang and Holt, 2008; Deminov et al., 2009; Rishbeth et al., 2009; Liu et al., 2010; Deminov et al., 2011; Pirog et al., 2011; Zolotukhina et al., 2011). It is believed that the day-to-day variability of the ionosphere is caused both by fluctuations of the solar ⇑ Corresponding author. Fax: +7 4967 510124.
E-mail address: [email protected] (M.G. Deminov).
and geomagnetic activity and by internal processes in the atmosphere (internal gravity waves, planetary waves and tides) (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Lastovicka, 2006). Exclusion of data corresponding to magnetically disturbed conditions from consideration makes it possible to estimate variability of the quiet ionosphere (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Deminov et al., 2011), which is important for analysis of ionospheric disturbances of any nature. Exclusion of geomagnetic activity effects in the ionosphere from consideration is a separate problem, as on average geomagnetic activity is not low and periods of prolonged low geomagnetic activity occur rather seldom. For example, in the interval 1932–2010 the average value of the 3 h index ap is near 14 nT. Usually by the quiet ionosphere is meant the ionosphere at periods of relatively low geomagnetic activity, but different authors use different criteria of a threshold level of this activity (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Mikhailov et al., 2004; Deminov et al., 2011).
0273-1177/$36.00 Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.asr.2012.09.037
M.G. Deminov et al. / Advances in Space Research 51 (2013) 702–711
Usually geomagnetic activity is lower under low solar activity. This makes it possible to establish properties of variability of the quiet ionosphere at low solar activity under sufficiently rigid restrictions on the threshold level of the geomagnetic activity. Such rigid restrictions were used by Deminov et al. (2011) who analyzed the F2-layer maximum parameters (foF2 and hmF2) variability on the basis of Irkutsk station (52.5 °N, 104 °E) data for the period of very low solar and geomagnetic activity of 2007–2008. It was obtained by Deminov et al. (2011) that properties of weak (|dfoF2| < 10%) and strong (30% > |dfoF2| > 10%) deviations of foF2 are essentially different. It can be assumed that approximation of dNmF2 (or dfoF2) by a mixture of two normal distributions will describe adequately this property of the ionosphere variability. A check of the validity of such approximation for dNmF2 and DhmF2 on the basis of Irkutsk station data for 2007–2010 is the main goal of this paper. This interval was chosen because the average level of the solar and geomagnetic activity in 2007–2010 was very low: average value of F10.7 was near 73 and average value of ap-index was near 6 nT, in 2009 the average value of ap was near 4 nT being the lowest for all years of regular measurements of this index. 2. Data The data set of NmF2 and hmF2 from Irkutsk station (52.5 °N, 104 °E) digital ionosounder for 01.01 2007– 12.31.2010 with a step of 15 min was initial for the analysis. In order to get the data array of nm = NmF2 and hm = hmF2 corresponding to the quiet ionosphere, the data which do not satisfy at least one of the conditions apðsÞ 7;
apmax 9;
AEmax < 400
ð1Þ
were excluded from the initial data set. Here ap(s) is the mean weighted value of the ap-index of the geomagnetic activity (Wrenn, 1987):
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These conditions seem to be an optimal compromise between the wish to exclude all magneto-disturbed periods from consideration and to save a sufficiently large data array of the F2-layer maximum parameters in order to obtain plausible statistical estimates of variability of these parameters. In the considered data set near 68% of all initial NmF2 and hmF2 data correspond to quiet conditions. Usually the time variations of NmF2 and hmF2 can be presented as consisting of high-frequency (within 1–2 h in UT) and low-frequency (day-to-day) parts (Kouris et al., 2000, 2006; Deminov et al., 2011). In order to separate these parts of nm and hm variations, the arrays of naver and haver were constructed, naver and haver being the average over 2 h (to be more exact, over 2.25 h = 9 15 min) in UT values of nm and hm with the center at a given UT. From naver and haver data the medians of naver and haver over 15 days for a given UT with the center at a given date, nmed and hmed, were built. Values of nmed and hmed are the smoothed medians of nm and hm from which the highfrequency part of nm and hm variations is excluded. As an example, in Fig. 1 the variations of nm, hm, naver, haver, nmed and hmed on 27–31 January, 2010, vs. UT are shown. As longitude of Irkutsk is 104 °E, its local time differs from UT almost by 7 h, so that the first part of a day in UT corresponds approximately to day hours and the second part to night hours. It is seen in this figure that naver and haver satisfy the criterion of separation: they reflect the major features of nm and hm day-to-day variations and do not contain the high-frequency part of these variations. The 2 h interval of averaging was chosen just on the basis of this criterion. Note that the 15 day interval for calculating the quiet medians of NmF2 and hmF2 was chosen in order to take correctly into account the annual NmF2 variations which are most strong in equinoxes (Mikhailov and Schlegel, 2001; Rishbeth and Mendillo, 2001; Deminov et al., 2009). The data arrays of nm, hm, nmed, hmed, naver and haver correspond to the quiet ionosphere and have the 15 min step in time. From these data the values of
apðsÞ ¼ ð1 sÞðap0 þ ap1 s þ ap2 s2 þ Þ
dn ¼ ðnm =nmed 1Þ100;
with the characteristic time T = 11 h or s = exp(3/ T) 0.76; ap0, ap1,. . . are the ap values at a given, preceding, etc. 3 h intervals; apmax is the maximal ap value for a given and preceding 3 h intervals; AE is the average over 15 min value of the AE-index; AEmax is the maximal value of AE for the preceding 6 h relative to a given universal time. These indices were calculated using 3 h ap-indices and 1 min AE-indices taken from Internet (http://wdc.kugi.kyoto-u.ac.jp). Note that the first condition excludes periods of storms in the ionosphere from consideration (Wrenn, 1987; Wrenn and Rodger, 1989), the second and third ones exclude periods of intense substorms in the ionosphere which are usually related to effects of the atmospheric gravity waves generated in the auroral ionosphere (e.g., Hunsucker, 1982; Jacobson et al., 1995; Hocke and Schlegel, 1996; Deminova et al., 1998).
dn0 ¼ ðnm =naver 1Þ100; dn1 ¼ ðnaver =nmed 1Þ100;
Dh ¼ ðhm hmed Þ; Dh0 ¼ ðhm haver Þ;
ð2Þ
Dh1 ¼ ðhaver hmed Þ
were obtained where dn and Dh are the full deviations of the F2-layer maximum parameters, i.e. the deviations of the measured values of the parameters from their medians; dn0, Dh0 and dn1, Dh1 are the high-frequency (within two hours) and low-frequency (day-to-day) components of dn and Dh. As a result, the data array was obtained in which six elements (dn, Dh, dn0, Dh0, dn1, Dh1) correspond to a given UT on a given date. The data in which at least one of these elements was absent (e.g., Dh) were excluded from the array. The data array of the F2-layer maximum parameters (dn, Dh, dn0, Dh0, dn1, Dh1) obtained in such a way was used for analysis of variability of the quiet ionosphere over Irkutsk under low solar activity (2007–2010).
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Fig. 1. Parameters of the F2-layer maximum (NmF2 and hmF2) over Irkutsk on January, 27–31, 2010 in UT: experimental data, nm and hm (points), averaged over 2.25 h values of these data, naver and haver (thin lines), and the quiet medians, nmed and hmed (thick lines).
In what follows the results of this analysis are presented for the day (10–16 LT) and night (22–04 LT) hours. To be more exact, for the 9:56–15:56 LT and 21:56–03:56 LT intervals as the Irkutsk station data are presented in UT and the longitude of this station is 104 °E. 3. Sample standard deviations Sample standard (or mean root square) deviations s of the F2-layer maximum parameters dn, Dh, dn0, Dh0, dn1, and Dh1 defined by Eq. (2) are used as characteristics of the quiet ionosphere F2-layer maximum parameters variability. These deviations and the ranges R of dn, Dh, dn0, Dh0, dn1, and Dh1 changes are given in Table 1 for winter (November, December, January, February), equinoxes (March, April, September, October), summer (May, June, July, August), and the whole year for day (10–16 LT) and night (22–04 LT) hours. The number N of measurements of the F2-layer maximum parameters for 2007– 2010 used for calculation of s and R for every season and the whole year are also given in Table 1. Table 1 shows that in every season the full variability of dn at night is almost twice as by day, and on average s(dn) is equal to 23.7% and 12.7% at night and by day correspondingly. Variability of dn in winter is greater than in summer. The range R of dn variations in winter is also greater than in summer and is maximal at night hours in winter (61% 6 R(dn) 6 174%). Hence, even under quiet conditions NmF2 can exceed the median more than by 2.7 times. This range is shifted to positive values of dn. E.g., in winter at night hours all large values of dn(|dn| > 61%) are positive (dn > 0). The total variability of Dh by day is smaller than that at night in all seasons, and on average s(Dh) is equal to 11.5 and 13.8 km by day and at night correspondingly. The dependence of s(Dh) on season is not distinct.
On average the high-frequency (within two hours) variability of dn0 by day is greater than at night. This tendency is most clear in winter when s(dn0) is equal to 11.3% and 6.6% by day and at night correspondingly. In summer the situation is opposite and variability of dn0 at night is greater than by day. Variability of Dh0 is rather high. It is almost the same by day and at night, and on average s(Dh0) 9–10 km. The dependence of s(Dh0) on season is not distinct. These statistical properties of the ionosphere can be seen in Fig. 1, namely, higher levels of the high-frequency variability of NmF2 at day hours and relatively high variability of hmF2 both by day and at night. It is seen from Table 1 that in all seasons both at day and night hours 2
2
2
sðdnÞ sðdn0 Þ þ sðdn1 Þ ;
2
2
2
sðDhÞ sðDh0 Þ þ sðDh1 Þ :
At night hours s(dn)2 is much greater than s(dn0)2 and the low-frequency (day-to-day) variability, dn1, is weakly different from the total variability, dn. For example, at night hours in winter s(dn1) = 27.9% and s(dn) = 29.5%. At day hours the contribution of the high-frequency variability, dn0, into the total variability, dn, is more considerable, and in winter s(dn1) = 9.1% and s(dn) = 15.8%. At night hours the high- and low-frequency variabilities of hmF2 contribute into the total variability of hmF2 almost equally and on average s(Dh) = 13.8%, s(Dh0) = 9.4%, s(Dh1) = 9.0%. At day hours the high-frequency variability prevails and on average s(Dh) = 11.5%, s(Dh0) = 9.9%, s(Dh1) = 4.9%. Additional analysis shows that in every season at day hours the value of dn correlates with Dh and on average the correlation coefficient K(dn, Dh) is equal to 0.17, K(dn0, Dh0) = 0.14, and K(dn1, Dh1) = 0.22. At night hours anticorrelation between these values is typical and on average K(dn, Dh) = 0.22, K(dn0, Dh0) = 0.05, and K(dn1, Dh1) = 0.32. These values of K(dn, Dh) and K(dn1, Dh1)
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Table 1 Sample standard deviations s of the F2-layer maximum parameters of the quiet ionosphere over Irkutsk and intervals R of variations of these parameters at daytime (10–16 LT) and nighttime (22–04 LT) hours in different seasons and for the whole year. Values dn0, Dh0 and dn1, Dh1 are the high-frequency (within two hours) and low-frequency (day-to-day) components of dn and Dh (see Eq. (1)). N is the number of measurements of the F2-layer maximum parameters for 2007–2010 used in computing of s and R. LT
10–16 22–04
10–16 22–04
10–16 22–04 10–16 22–04
s/R
Winter
Equinox
All year
Dh, km
dn, %
Dh, km
dn, %
Dh, km
dn, %
Dh, km
s R s R
15.8 4281 29.5 61174
11.7 3158 14.5 5148
11.9 3358 21.3 5694
9 3141 12.8 3939
8.6 2935 17.8 5173
13.5 3958 14 4361
12.7 4281 23.7 61174
11.5 3958 13.8 5161
s R s R
dn0, % 11.3 3553 6.6 2528
Dh0, km 10.6 3053 9.4 3245
dn0, % 6.8 2232 5 2417
Dh0, km 7.5 3039 8.6 3131
dn0, % 4.9 1718 7.5 3623
Dh0, km 11.1 3745 10.2 3443
dn0, % 8.4 3553 6.4 3628
Dh0, km 9.9 3753 9.4 3445
dn1, % 9.1 3153 27.9 60149 8296 8252
Dh1, km 4 1617 10.1 4131
dn1, % 8.2 2736 20.3 5385 6224 6884
Dh1, km 4 1616 8.6 2429
dn1, % 6.4 2625 15.6 4274 4644 7796
Dh1, km 6.3 3024 8.3 2924
dn1, % 8 3153 22 60149 19164 22932
Dh1, km 4.9 3024 9 4131
s R s R N
are significant at least at the 95% confidence level, according to the Fisher criterion. Fig. 1 illustrates the anti-phase changes of the density and height of the F2-layer maximum at night hours in January, 2010: on January 28 a marked increase of NmF2 relative the median occurred which was accompanied by a lowering of hmF2, on January 29 the pattern was opposite. On January 30 a strong increase of NmF2 occurred again but it was not accompanied by a distinct change in hmF2. So, the anti-phase changes of hmF2 and NmF2 at night are only a tendency, and a relatively low value of K(dn1, Dh1) confirms this qualitative conclusion. 4. Histograms More detailed properties of the F2-layer maximum parameters variability can be derived from histograms, e.g. from the histogram of dn, i.e. the number n of dn falling into a certain interval of values relative to a total number of measurements, N, where dn is defined by Eq. (2) and the N values are given in Table 1. Such histograms for night and day hours are shown in Fig. 2 for the whole year, i.e. without separation into seasons. In Fig. 2 also there is shown the approximation of every histogram by a mixture of two normal distributions characterized by probability density function (see, e.g., Hahn and Shapiro, 1967; Johnson and Leone, 1977): f ðx; l; rÞ ¼ f1 ðx; l1 ; r1 Þ þ f2 ðx; l2 ; r2 Þ f1 ðx; l1 ; r1 Þ ¼ c1 ð2pr21 Þ
1=2
ð3Þ 2
expððx l1 Þ =2r21 Þ
f2 ðx; l2 ; r2 Þ ¼ c2 ð2pr22 Þ1=2 expððx l2 Þ2 =2r22 Þ c1 þ c2 ¼ 1
Summer
dn, %
l ¼ c1 l1 þ c2 l2 2
r2 ¼ c1 r21 þ c2 r22 þ c1 ðl1 lÞ þ c2 ðl2 lÞ
2
where l and r2 are the mean value and variance of the mixture, l1, r12, and l2, r22 are the mean value and variance of the first and second components of the mixture. In this case x = dn. The coefficients of the Eq. (3) for every season and the whole year are given in Table 2. Some of these coefficients are shown in Fig. 2. The coefficients of Eq. (3) are chosen in such a way that the function f(x, l, and r) is close to the histogram. Quality of the approximation was estimated by the value of the correlation coefficient K between the cumulative distribution functions F(x) of the mixture and of the histogram, i.e. between the integral f(x, l, r) and the sum of n/N from 1 to x (e.g., Ramachandran and Tsokos, 2009) . These cumulative functions and the coefficients K are shown in Fig. 2, for this case K 1. Note that K > 0.999 for all cases below. It is seen from Fig. 2 that the first (f1) and second (f2) components of the mixture of two normal distributions are characteristics of relatively weak and strong fluctuations of dn correspondingly. Both at day and night hours r2 is approximately twice as r1, i.e. the variance of the strong fluctuations of dn is much greater than the variance of its weak fluctuations. At day hours the first component of the mixture is predominant (c1 = 0.72, c2 = 0.28), and the standard deviation of the mixture, r, is weakly different from r1. At night hours the second component of the mixture becomes significant (c1 = 0.44, c2 = 0.56), and r is near twice as r1. Both at day and night hours the standard deviation of the mixture weakly differs from the sample standard deviation: r = 12.5%, s = 12.7% at day hours and r = 21.8%, s = 23.7% at night hours (see Table 2).
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Fig. 2. Histograms of deviations of the measured NmF2 values from the quiet median (dn) for the daytime (10–16 LT) and nighttime (22–04 LT) hours under quiet conditions for the whole dataset, i.e. without separation into seasons. Approximation of the histograms by the mixture of two normal distributions of dn (thick lines), the first (1) and second (2) components of the mixture (thin lines), and the coefficients of these approximations (see Table 2). Cumulative distribution functions F of the histogram (dots) and the mixture (lines), and the correlation coefficient K between these functions.
Table 2 Coefficients of the Eq. (3) for the mixture of two normal distributions of dn, dn0, and dn1 for every season (Win, Equ, Sum) and for the whole year (All) for the day (10–16 LT) and night (22–04 LT) hours. Values of s are the sample standard deviations taken from Table 1. x
ssn
LT
c1
l1, %
r1, %
c2
l2, %
r2, %
l, %
r, %
s,%
dn
Win
10–16 22–04 10–16 22–04 10–16 22–04 10–16 22–04 10–16 10–16 10–16 10–16 22–04 10–16 22–04 10–16 22–04 10–16 22–04 10–16 22–04
0.6 0.33 0.7 0.5 1 0.6 0.72 0.44 0.64 1 1 0.87 1 0.63 0.39 0.72 0.5 1 0.6 0.75 0.45
1 5 0 5 0 4 1 4 0.5 1 0.5 0.5 1 1 5 0 3 0 2.5 0 2.5
11 12 8.5 11 8.6 12 8.5 11 8 6.7 4.9 6.4 6.4 6 11 5.5 10 6 10 6 10
0.4 0.67 0.3 0.5 0 0.4 0.28 0.56 0.36 0 0 0.13 0 0.37 0.61 0.28 0.5 0 0.4 0.25 0.55
6 6 6 7 – 1 7 4 5 – – 7 – 2.5 7 2.5 5 – 2.5 2.5 4
20 32 15 27 – 22 18 27 16 – – 16 – 12 32 12 26 – 22 12 28
1.8 2.4 1.8 1 0 2 1.2 0.5 2.1 1 0.5 1.3 1 0.3 2.3 0.7 1 0 0.5 0.6 1.1
15.6 27.6 11.2 21.5 8.6 16.9 12.5 21.8 11.7 6.7 4.9 8.6 6.4 8.9 26.6 8 20.1 6 16.1 8 22.1
15.8 29.5 11.9 21.3 8.6 17.8 12.7 23.7 11.3 6.8 4.9 8.4 6.4 9.1 27.9 8.2 20.3 6.4 15.6 8 22
Equ Sum All dn0
Win Equ Sum All
dn1
Win Equ Sum All
The condition s r is true for all conditions presented in Table 2, and this reflects the quality of the approximation. The weak fluctuations of dn are more often negative: l1 is equal to 1% at day hours and 4% at night hours (see Table 2). The strong fluctuations of dn are more often positive: l2 = 7% b 4% at day and night hours. The value of Dl21 = l2l1 is the shift between the components of the mixture. In the considered case Dl21 = 8% both for day and night hours. The shift between the mixture components results in that the borders of predominance of the
weak fluctuations are non-symmetrical: the condition f1 P f2 is valid for 21.8% 6 dn 6 15.2% at day hours and for 20.0% 6 dn 6 8.8% at night hours (see Fig. 2). Fig. 3 shows seasonal features of the dn histograms and of the mixtures of two normal distributions (see also Table 2). Both at day and night hours the relative contribution of the first component, f1, of the mixture in summer is greater than in winter. At day hours in summer this component of the mixture even becomes the only (c1 = 1, c2 = 0). The contribution of the second component, f2, of the
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Fig. 3. Histograms of deviations of the measured NmF2 values from the quiet median (dn) for the daytime (upper panel) and nighttime (lower panel) hours in every season. Approximations of the histograms by the mixture of two normal distributions of dn (thick lines), the components of the mixture (thin lines), and the coefficients c1 and c2 of these approximations (see Table 2).
mixture is maximal at night hours in winter (c1 = 0.33, c2 = 0.67) when the variances of this component, r22, and of the mixture, r2, are also maximal (r2 = 32%, r = 27.1%). At night hours in all seasons l1 < 0 and l2 > 0, i.e. the dn weak fluctuations are mainly negative and its strong fluctuations are more often positive. At day hours the dn weak fluctuations are almost symmetrical (|l1| 6 1%), the strong fluctuations are positive (l2 > 0) in winter and equinoxes. Analysis shows that the dn0 histogram which characterizes the high-frequency (within two hours) part of the NmF2 variability for night hours in all seasons corresponds to the normal distribution and r(dn0) s(dn0) at these hours. Therefore the values of s(dn0) for night hours presented in Table 1 are characteristics of the normal distribution of dn0. At day hours the dn0 histogram differs from the normal distribution only in winter (see Fig. 4 and Table 2). For the whole year, i.e. without separation into seasons, this feature results in a weak deviation of the dn0 histogram from the normal distribution: c1 = 0.87, c2 = 0.13 (see Table 2). Fig. 5 shows season features of the dn1 histogram and of the mixture of two normal distributions which are characteristics of the NmF2 day-to-day variability. These features are close to those shown in Fig. 3 for dn: both at day and night hours the relative contribution of the first component, f1, of the mixture in summer is greater than in winter; in summer at day hours this component of the mixture becomes even the only one. The day-to-day variability of NmF2 differs from its full variability mainly in that r1(dn1) < r1(dn) and r(dn1) < r(dn) in all seasons at day hours (see Table 2).
Fig. 6 shows distributions of Dh, Dh0, and Dh1 for the whole year, i.e. without separation into seasons (see also Table 3). The data in Fig. 6 evidence that the distributions of Dh and Dh0 at night hours and of Dh1 at day and night hours correspond to the normal distributions. Analysis showed that this feature of the ionosphere is kept in all seasons. Therefore in Table 3 the coefficients of Eq. (3) are given only for Dh and Dh0 at day hours. It is seen from Table 3 that c1(Dh) c1(Dh0) for every season, i.e. the relative contribution of the first and second components of the mixture of two normal distributions is almost equal for Dh and Dh0. Consequently, the deviation of the Dh distribution from the normal distribution is related mainly with the high-frequency (within two hours) variability of hmF2, Dh0. The hmF2 day-to-day variability, Dh1, does not contain Dh0, therefore the Dh1 corresponds to the normal distribution (see Table 3 and Fig. 6). Note that r(Dh) s(Dh), r(Dh0) s(Dh0), and r(Dh1) s(Dh1) for all conditions presented in Table 3. 5. Discussion The presented statistical properties of the NmF2 variability for quiet conditions under low solar activity agree in general with the results obtained earlier for other geophysical conditions: relatively low level of this variability at times less than 1 to 2 h (Zevakina et al., 1990; Kouris et al., 2000, 2006; Deminov et al., 2011), greater variability of NmF2 (or foF2) at night hours than at day hours (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Araujo-Pradere et al., 2005; Fotiadis and Kouris, 2006; Altadill, 2007; Deminov et al., 2009), deviations of the NmF2
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Fig. 4. Histograms of the high-frequency (within two hours) part of NmF2 fluctuations of the quiet ionosphere (dn0) for daytime (10–16 LT) hours in every season. Approximations of the histograms by the mixture of two normal distributions (thick lines), the components (1 and 2) of the mixture (thin lines) in winter, and the coefficients c1 and c2 of these approximations (see Table 2).
Fig. 5. Histograms of low-frequency (day-to-day) part of NmF2 fluctuations of the quiet ionosphere (dn1) for the daytime (upper panel) and nighttime (lower panel) hours in every season. Approximations of the histograms by the mixture of two normal distributions (thick lines), the components of the mixture (thin lines), and the coefficients c1 and c2 of these approximations (see Table 2).
fluctuations from the normal distribution at night hours (Adeniyi et al., 2007). But the possibility of approximation of the dNmF2 histogram by the mixture of two normal distributions seems to be evidenced for the first time. Comparison of the day-to-day variability of NmF2 of the quiet ionosphere with other estimates shows that at day hours there is a tendency to increase of this variability with growth of solar activity: s(dn) = 12.7% over Irkutsk under low solar activity (see Table 1), s(dn) 2s(dfoF2) 15% over Irkutsk under medium solar activity (1958–1992) (Deminov et al., 2009), s(dn) 15% over Slough under medium solar activity (F10.7 140) (Rishbeth and Mendillo, 2001). At night hours this tendency is not distinct: s(dn) = 23.7% over Irkutsk under
low solar activity (see Table 1), and s(dn) is near 21% and 24% over Irkutsk and Slough correspondingly at midnight under medium solar activity (Deminov et al., 2009). The high-frequency part of the NmF2 and hmF2 variability is believed to be associated mainly with the ionospheric effect of short-period (15–60 min) atmospheric gravity waves (AGWs) which are generated below the thermosphere and exist practically always (e.g., Hocke and Schlegel, 1996; Oliver et al., 1997; Miyoshi and Fujiwara, 2008). Weak magnetospheric substorms (AEmax < 300– 400 nT) occur almost every day even under geomagnetically quiet conditions (Eq. (2)). At periods of such weak substorms large-scale AGWs can be generated in the auroral region which propagate equatorwards and have
M.G. Deminov et al. / Advances in Space Research 51 (2013) 702–711
709
Fig. 6. Histograms of fluctuations of the F2-layer maximum height, Dh, Dh0 and Dh1, for the daytime (upper panel) and nighttime (lower panel) hours under quiet conditions for the whole dataset, i.e. without separation into seasons. Approximations of the histograms by the mixture of two normal distributions (thick lines), the components of the mixture (thin lines), and the coefficients c1 and c2 of these approximations (see Table 3).
Table 3 Coefficients of the Eq. (3) for the mixture of two normal distributions of Dh, Dh0, and Dh1 for every season (Win, Equ, Sum) for the day hours (10–16 LT) and for the whole year (All) for the day (10–16 LT) and night (22–04 LT) hours. Values of s are the sample standard deviations taken from Table 1. x
ssn
LT
c1
l1, km
r1, km
c2
l2, km
r2, km
l, km
r, km
s, km
Dh
Win Equ Sum All
Dh0
Win Equ Sum All
Dh1
All
10–16 10–16 10–16 10–16 22–04 10–16 10–16 10–16 10–16 22–04 10–16 22–04
0.78 0.82 0.67 0.81 1 0.72 0.87 0.68 0.77 1 1 1
3 0 0.5 2 0.5 2 0 0 1 1 0 0
8 7 9.5 9 13.5 7 6 8 7 9.4 4.8 8.5
0.22 0.18 0.33 0.19 0 0.28 0.13 0.32 0.23 0 0 0
7 1 0 4 – 5 1 0 1 – – –
19 15 19 18 – 16 14 15.5 16 – – –
0.8 0.2 0.3 0.9 0.5 0 0.1 0 0.5 1 0 0
12.1 9 13.4 11.5 13.5 10.8 7.5 11 9.9 9.4 4.8 8.5
11.7 9 13.5 11.5 13.8 10.6 7.5 11.1 9.9 9.4 4.9 9
horizontal wavelengths larger than 1000 km and periods in the range of 30 min–3 h, and they can cause NmF2 and hmF2 fluctuations (e.g., Hocke and Schlegel, 1996; Fujiwara and Miyoshi, 2006). Typical features of the ionospheric effects of the large-scale AGWs at day hours are hmF2 rise and the consequent increase of NmF2 (see e.g. Prolss and Ocko, 2000). At night hours these effects are characterized by a distinct rise of hmF2 and rather a weak decrease of NmF2 (Deminova et al., 1998). Relatively weak changes of NmF2 at night hours are, obviously, typical also for short-period AGWs. Therefore rather high values of s(Dh0) both at day and night hours and of s(dn0) only at day hours are the additional evidences that the highfrequency part of the ionospheric variability is related to short-period AGWs (see Fig. 1 and Table 1). The first component (f1) of the mixture of two normal distributions can also be associated to the ionospheric effects of AGWs: at night hours the changes dn, dn0 and dn1 related to the first component (f1) of the mixture are
more often negative (l1 < 0); at day hours these changes are almost symmetrical (see Table 2), and just these features are characteristic for ionospheric effects of AGWs. The first component of the mixture is predominant for the weak NmF2 fluctuations which are most often the high-frequency part of the ionospheric variability related to short-period AGWs (see Tables 1 and 2). The second component (f2) of the mixture of two normal distributions can be apparently associated to the planetary waves and tides in the atmosphere as an important cause of the day-to-day variability of the quiet ionosphere (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Lastovicka, 2006). Note that, although the quasi-stationary planetary wave does not propagate deep into the ionosphere due to the presence of critical layers and strong molecular dissipation, the planetary wave and tidal interaction lead to large changes in tides, which can impact the ionosphere at all latitudes (e.g., Lastovicka, 2006; Liu et al., 2010). Quasitwo-day variations of the ionospheric parameters are an
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example of contribution of these processes into the ionospheric variability (e.g., Apostolov et al., 1995; Forbes and Zhang, 1997). The second component of the mixture prevails for the strong NmF2 fluctuations which are mainly positive both at day and night hours: l2 > 0 for all conditions presented in Table 2. At night hours in winter and equinoxes this tendency is most clear. The data presented in Fig. 1 reflect also this feature of the ionosphere: in quasi-two-day variations of NmF2 there are seen distinct increases of NmF2 at night hours on 28 and 30 January, 2010 and much weaker decrease of NmF2 at night hours on 29 January. Distinct difference in the features of the ionospheric effects of AGWs and of the planetary waves and tides at night hours in winter and equinoxes (l1 < 0, l2 > 0, r1 < r2) is the principal cause of a considerable deviation of the NmF2 distribution from the normal distribution for these conditions (see Table 2 and Fig. 3). In Fig. 1 it is seen also that the amplitude of the quasi-two-day variations of hmF2 is not greater than the amplitude of the hmF2 fluctuations within two hours: s(Dh0) > s(Dh1) at day hours and s(Dh0) s(Dh1) at night hours (see Table 1). This is the cause of that the DhmF2 distributions are the normal distributions or weakly different from them (see Table 2 and Fig. 6). Very strong fluctuations of NmF2 are mainly positive. For example, for night hours in winter all values of |dn| > 61% are positive (see Table 1). Stronger asymmetry of the dn histogram at high values of |dn| is not sufficiently reflected by the mixture of two normal distributions. Weak deviations of r(dn) from s(dn) can be related to this cause (see Table 2). Strong deviations of the quiet ionosphere F2-layer maximum density from the usual median calculated over 27 days (|dNmF2| > 40%) were named Q-disturbances (Mikhailov et al., 2004). From data of 29 ionospheric stations located at high to low latitudes it was obtained that at all latitudes and under any level of solar activity positive Q-disturbances occur more often than negative ones (Mikhailov et al., 2004). Strong and very strong deviations of NmF2 from the quiet median over Irkutsk under low solar activity are also presumably positive (see Table 1 and Figs. 2 and 3). Qualitative agreement of this feature of the quiet ionosphere variability with the characteristic property of the Q-disturbance is, obviously, caused by the fact that prolonged periods of low solar activity correspond to relatively low geomagnetic activity, when the usual median is weakly different from the quiet median. Establishing of properties of the quiet ionosphere variability (with regard to the quiet median) for periods of high solar activity needs a separate study. Deviations of the dNmF2 distribution from the normal distribution are asymmetrical for all considered conditions. Therefore, e.g., the difference between the upper and lower quartiles of the dNmF2 distribution can give information about properties of the mixture of two normal distributions
of dNmF2, but a special study is needed in order to clear up this possibility. 6. Conclusions The analysis of statistical properties of the quiet ionosphere F-layer maximum parameters variability (deviations of NmF2 and hmF2 from the quiet median, dn b Dh) under low solar activity at day (10–16 LT) and night (22–04 LT) hours on the basis of Irkutsk station data for 2007–2010 made it possible to draw the following conclusions. 1. The experimental distribution (histogram) of dn can be approximated by a mixture of two normal distributions. The first and second components of the mixture are mainly characteristics of relatively weak and strong fluctuations of dn. Such approximation is most adequate for night hours in winter and equinoxes when the dn histogram is distinctly different from the normal distribution. For these conditions the dn weak fluctuations are mainly negative and its strong fluctuations are mainly positive. The Dh histogram is mainly the normal distribution. A weak deviation of the Dh histogram from the normal distribution occurs only at day hours in winter and equinoxes. 1. The weak and strong fluctuations of dn b Dh are principally associated with high-frequency (within two hours) and low-frequency (day-to-day) parts of changes of these parameters correspondingly. At night hours the low-frequency part of the dn variability prevails, at day hours the both parts of this variability are essential. The high- and low-frequency parts of the Dh variability are comparable at night hours, the high-frequency part becomes predominant at day hours. 2. The weak fluctuations of dn b Dh are obviously caused by ionospheric effects of medium-scale and large-scale atmospheric gravity waves (AGWs). The strong fluctuations are apparently associated, mainly, with planetary waves and tides. The different causes of the weak and strong fluctuations of the F2-layer maximum parameters are the main reason of the distinctly different features of these fluctuations.
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Advances in Space Research 51 (2013) 702–711 www.elsevier.com/locate/asr
Statistical properties of variability of the quiet ionosphere F2-layer maximum parameters over Irkutsk under low solar activity M.G. Deminov a,⇑, G.F. Deminova a, G.A. Zherebtsov b, N.M. Polekh b b
a IZMIRAN, 142190 Troitsk, Moscow Region, Russia Institute of Solar-Terrestrial Physics, SB RAS, P.O. Box 291, 664033 Irkutsk, Russia
Received 19 July 2012; received in revised form 25 September 2012; accepted 26 September 2012 Available online 5 October 2012
Abstract The statistical analysis of the quiet ionosphere F2-layer maximum parameters variability (deviations of NmF2 and hmF2 from the quiet medians, dn and Dh) under solar minimum at day (10–16 LT) and night (22–04 LT) hours based on data of Irkutsk station for 2007–2010 is presented. It is found that the experimental distribution (histogram) of dn can be approximated by a mixture of two normal distributions. The first and second components of the mixture characterize, mainly, relatively weak and strong fluctuations of dn which are presumably associated with the ionospheric effects of the atmospheric gravity waves and of the planetary waves and tides correspondingly. Deviation of the dn histogram from a single normal distribution is most considerable at night hours in winter and equinoxes. For these conditions the weak fluctuations of dn are mainly negative and the strong ones are mainly positive. The Dh histogram is a normal distribution except day hours in winter and equinoxes when a weak deviation of the histogram from the normal distribution occurs. Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Quiet ionosphere; F2-layer maximum parameters; Variability; Mixture of two normal distributions
1. Introduction Variability of the F2-layer maximum parameters and primarily of NmF2 (or the critical frequency, foF2) within one hour and day-to-day was investigated in many works (Zevakina et al., 1990; Gulyaeva et al., 1998; Forbes et al., 2000; Kouris et al., 2000, 2006; Rishbeth and Mendillo, 2001; Kouris and Fotiadis, 2002; Mendillo et al., 2002; Mizrahi et al., 2002; Pancheva et al., 2002; Lastovicka et al., 2003; Rawer et al., 2003; Liu et al., 2004; Mikhailov et al., 2004; Araujo-Pradere et al., 2005; Fotiadis and Kouris, 2006; Adeniyi et al., 2007; Altadill, 2007; Gordienko et al., 2007; Mitic and Cander, 2008; Zhang and Holt, 2008; Deminov et al., 2009; Rishbeth et al., 2009; Liu et al., 2010; Deminov et al., 2011; Pirog et al., 2011; Zolotukhina et al., 2011). It is believed that the day-to-day variability of the ionosphere is caused both by fluctuations of the solar ⇑ Corresponding author. Fax: +7 4967 510124.
E-mail address: [email protected] (M.G. Deminov).
and geomagnetic activity and by internal processes in the atmosphere (internal gravity waves, planetary waves and tides) (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Lastovicka, 2006). Exclusion of data corresponding to magnetically disturbed conditions from consideration makes it possible to estimate variability of the quiet ionosphere (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Deminov et al., 2011), which is important for analysis of ionospheric disturbances of any nature. Exclusion of geomagnetic activity effects in the ionosphere from consideration is a separate problem, as on average geomagnetic activity is not low and periods of prolonged low geomagnetic activity occur rather seldom. For example, in the interval 1932–2010 the average value of the 3 h index ap is near 14 nT. Usually by the quiet ionosphere is meant the ionosphere at periods of relatively low geomagnetic activity, but different authors use different criteria of a threshold level of this activity (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Mikhailov et al., 2004; Deminov et al., 2011).
0273-1177/$36.00 Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.asr.2012.09.037
M.G. Deminov et al. / Advances in Space Research 51 (2013) 702–711
Usually geomagnetic activity is lower under low solar activity. This makes it possible to establish properties of variability of the quiet ionosphere at low solar activity under sufficiently rigid restrictions on the threshold level of the geomagnetic activity. Such rigid restrictions were used by Deminov et al. (2011) who analyzed the F2-layer maximum parameters (foF2 and hmF2) variability on the basis of Irkutsk station (52.5 °N, 104 °E) data for the period of very low solar and geomagnetic activity of 2007–2008. It was obtained by Deminov et al. (2011) that properties of weak (|dfoF2| < 10%) and strong (30% > |dfoF2| > 10%) deviations of foF2 are essentially different. It can be assumed that approximation of dNmF2 (or dfoF2) by a mixture of two normal distributions will describe adequately this property of the ionosphere variability. A check of the validity of such approximation for dNmF2 and DhmF2 on the basis of Irkutsk station data for 2007–2010 is the main goal of this paper. This interval was chosen because the average level of the solar and geomagnetic activity in 2007–2010 was very low: average value of F10.7 was near 73 and average value of ap-index was near 6 nT, in 2009 the average value of ap was near 4 nT being the lowest for all years of regular measurements of this index. 2. Data The data set of NmF2 and hmF2 from Irkutsk station (52.5 °N, 104 °E) digital ionosounder for 01.01 2007– 12.31.2010 with a step of 15 min was initial for the analysis. In order to get the data array of nm = NmF2 and hm = hmF2 corresponding to the quiet ionosphere, the data which do not satisfy at least one of the conditions apðsÞ 7;
apmax 9;
AEmax < 400
ð1Þ
were excluded from the initial data set. Here ap(s) is the mean weighted value of the ap-index of the geomagnetic activity (Wrenn, 1987):
703
These conditions seem to be an optimal compromise between the wish to exclude all magneto-disturbed periods from consideration and to save a sufficiently large data array of the F2-layer maximum parameters in order to obtain plausible statistical estimates of variability of these parameters. In the considered data set near 68% of all initial NmF2 and hmF2 data correspond to quiet conditions. Usually the time variations of NmF2 and hmF2 can be presented as consisting of high-frequency (within 1–2 h in UT) and low-frequency (day-to-day) parts (Kouris et al., 2000, 2006; Deminov et al., 2011). In order to separate these parts of nm and hm variations, the arrays of naver and haver were constructed, naver and haver being the average over 2 h (to be more exact, over 2.25 h = 9 15 min) in UT values of nm and hm with the center at a given UT. From naver and haver data the medians of naver and haver over 15 days for a given UT with the center at a given date, nmed and hmed, were built. Values of nmed and hmed are the smoothed medians of nm and hm from which the highfrequency part of nm and hm variations is excluded. As an example, in Fig. 1 the variations of nm, hm, naver, haver, nmed and hmed on 27–31 January, 2010, vs. UT are shown. As longitude of Irkutsk is 104 °E, its local time differs from UT almost by 7 h, so that the first part of a day in UT corresponds approximately to day hours and the second part to night hours. It is seen in this figure that naver and haver satisfy the criterion of separation: they reflect the major features of nm and hm day-to-day variations and do not contain the high-frequency part of these variations. The 2 h interval of averaging was chosen just on the basis of this criterion. Note that the 15 day interval for calculating the quiet medians of NmF2 and hmF2 was chosen in order to take correctly into account the annual NmF2 variations which are most strong in equinoxes (Mikhailov and Schlegel, 2001; Rishbeth and Mendillo, 2001; Deminov et al., 2009). The data arrays of nm, hm, nmed, hmed, naver and haver correspond to the quiet ionosphere and have the 15 min step in time. From these data the values of
apðsÞ ¼ ð1 sÞðap0 þ ap1 s þ ap2 s2 þ Þ
dn ¼ ðnm =nmed 1Þ100;
with the characteristic time T = 11 h or s = exp(3/ T) 0.76; ap0, ap1,. . . are the ap values at a given, preceding, etc. 3 h intervals; apmax is the maximal ap value for a given and preceding 3 h intervals; AE is the average over 15 min value of the AE-index; AEmax is the maximal value of AE for the preceding 6 h relative to a given universal time. These indices were calculated using 3 h ap-indices and 1 min AE-indices taken from Internet (http://wdc.kugi.kyoto-u.ac.jp). Note that the first condition excludes periods of storms in the ionosphere from consideration (Wrenn, 1987; Wrenn and Rodger, 1989), the second and third ones exclude periods of intense substorms in the ionosphere which are usually related to effects of the atmospheric gravity waves generated in the auroral ionosphere (e.g., Hunsucker, 1982; Jacobson et al., 1995; Hocke and Schlegel, 1996; Deminova et al., 1998).
dn0 ¼ ðnm =naver 1Þ100; dn1 ¼ ðnaver =nmed 1Þ100;
Dh ¼ ðhm hmed Þ; Dh0 ¼ ðhm haver Þ;
ð2Þ
Dh1 ¼ ðhaver hmed Þ
were obtained where dn and Dh are the full deviations of the F2-layer maximum parameters, i.e. the deviations of the measured values of the parameters from their medians; dn0, Dh0 and dn1, Dh1 are the high-frequency (within two hours) and low-frequency (day-to-day) components of dn and Dh. As a result, the data array was obtained in which six elements (dn, Dh, dn0, Dh0, dn1, Dh1) correspond to a given UT on a given date. The data in which at least one of these elements was absent (e.g., Dh) were excluded from the array. The data array of the F2-layer maximum parameters (dn, Dh, dn0, Dh0, dn1, Dh1) obtained in such a way was used for analysis of variability of the quiet ionosphere over Irkutsk under low solar activity (2007–2010).
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Fig. 1. Parameters of the F2-layer maximum (NmF2 and hmF2) over Irkutsk on January, 27–31, 2010 in UT: experimental data, nm and hm (points), averaged over 2.25 h values of these data, naver and haver (thin lines), and the quiet medians, nmed and hmed (thick lines).
In what follows the results of this analysis are presented for the day (10–16 LT) and night (22–04 LT) hours. To be more exact, for the 9:56–15:56 LT and 21:56–03:56 LT intervals as the Irkutsk station data are presented in UT and the longitude of this station is 104 °E. 3. Sample standard deviations Sample standard (or mean root square) deviations s of the F2-layer maximum parameters dn, Dh, dn0, Dh0, dn1, and Dh1 defined by Eq. (2) are used as characteristics of the quiet ionosphere F2-layer maximum parameters variability. These deviations and the ranges R of dn, Dh, dn0, Dh0, dn1, and Dh1 changes are given in Table 1 for winter (November, December, January, February), equinoxes (March, April, September, October), summer (May, June, July, August), and the whole year for day (10–16 LT) and night (22–04 LT) hours. The number N of measurements of the F2-layer maximum parameters for 2007– 2010 used for calculation of s and R for every season and the whole year are also given in Table 1. Table 1 shows that in every season the full variability of dn at night is almost twice as by day, and on average s(dn) is equal to 23.7% and 12.7% at night and by day correspondingly. Variability of dn in winter is greater than in summer. The range R of dn variations in winter is also greater than in summer and is maximal at night hours in winter (61% 6 R(dn) 6 174%). Hence, even under quiet conditions NmF2 can exceed the median more than by 2.7 times. This range is shifted to positive values of dn. E.g., in winter at night hours all large values of dn(|dn| > 61%) are positive (dn > 0). The total variability of Dh by day is smaller than that at night in all seasons, and on average s(Dh) is equal to 11.5 and 13.8 km by day and at night correspondingly. The dependence of s(Dh) on season is not distinct.
On average the high-frequency (within two hours) variability of dn0 by day is greater than at night. This tendency is most clear in winter when s(dn0) is equal to 11.3% and 6.6% by day and at night correspondingly. In summer the situation is opposite and variability of dn0 at night is greater than by day. Variability of Dh0 is rather high. It is almost the same by day and at night, and on average s(Dh0) 9–10 km. The dependence of s(Dh0) on season is not distinct. These statistical properties of the ionosphere can be seen in Fig. 1, namely, higher levels of the high-frequency variability of NmF2 at day hours and relatively high variability of hmF2 both by day and at night. It is seen from Table 1 that in all seasons both at day and night hours 2
2
2
sðdnÞ sðdn0 Þ þ sðdn1 Þ ;
2
2
2
sðDhÞ sðDh0 Þ þ sðDh1 Þ :
At night hours s(dn)2 is much greater than s(dn0)2 and the low-frequency (day-to-day) variability, dn1, is weakly different from the total variability, dn. For example, at night hours in winter s(dn1) = 27.9% and s(dn) = 29.5%. At day hours the contribution of the high-frequency variability, dn0, into the total variability, dn, is more considerable, and in winter s(dn1) = 9.1% and s(dn) = 15.8%. At night hours the high- and low-frequency variabilities of hmF2 contribute into the total variability of hmF2 almost equally and on average s(Dh) = 13.8%, s(Dh0) = 9.4%, s(Dh1) = 9.0%. At day hours the high-frequency variability prevails and on average s(Dh) = 11.5%, s(Dh0) = 9.9%, s(Dh1) = 4.9%. Additional analysis shows that in every season at day hours the value of dn correlates with Dh and on average the correlation coefficient K(dn, Dh) is equal to 0.17, K(dn0, Dh0) = 0.14, and K(dn1, Dh1) = 0.22. At night hours anticorrelation between these values is typical and on average K(dn, Dh) = 0.22, K(dn0, Dh0) = 0.05, and K(dn1, Dh1) = 0.32. These values of K(dn, Dh) and K(dn1, Dh1)
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Table 1 Sample standard deviations s of the F2-layer maximum parameters of the quiet ionosphere over Irkutsk and intervals R of variations of these parameters at daytime (10–16 LT) and nighttime (22–04 LT) hours in different seasons and for the whole year. Values dn0, Dh0 and dn1, Dh1 are the high-frequency (within two hours) and low-frequency (day-to-day) components of dn and Dh (see Eq. (1)). N is the number of measurements of the F2-layer maximum parameters for 2007–2010 used in computing of s and R. LT
10–16 22–04
10–16 22–04
10–16 22–04 10–16 22–04
s/R
Winter
Equinox
All year
Dh, km
dn, %
Dh, km
dn, %
Dh, km
dn, %
Dh, km
s R s R
15.8 4281 29.5 61174
11.7 3158 14.5 5148
11.9 3358 21.3 5694
9 3141 12.8 3939
8.6 2935 17.8 5173
13.5 3958 14 4361
12.7 4281 23.7 61174
11.5 3958 13.8 5161
s R s R
dn0, % 11.3 3553 6.6 2528
Dh0, km 10.6 3053 9.4 3245
dn0, % 6.8 2232 5 2417
Dh0, km 7.5 3039 8.6 3131
dn0, % 4.9 1718 7.5 3623
Dh0, km 11.1 3745 10.2 3443
dn0, % 8.4 3553 6.4 3628
Dh0, km 9.9 3753 9.4 3445
dn1, % 9.1 3153 27.9 60149 8296 8252
Dh1, km 4 1617 10.1 4131
dn1, % 8.2 2736 20.3 5385 6224 6884
Dh1, km 4 1616 8.6 2429
dn1, % 6.4 2625 15.6 4274 4644 7796
Dh1, km 6.3 3024 8.3 2924
dn1, % 8 3153 22 60149 19164 22932
Dh1, km 4.9 3024 9 4131
s R s R N
are significant at least at the 95% confidence level, according to the Fisher criterion. Fig. 1 illustrates the anti-phase changes of the density and height of the F2-layer maximum at night hours in January, 2010: on January 28 a marked increase of NmF2 relative the median occurred which was accompanied by a lowering of hmF2, on January 29 the pattern was opposite. On January 30 a strong increase of NmF2 occurred again but it was not accompanied by a distinct change in hmF2. So, the anti-phase changes of hmF2 and NmF2 at night are only a tendency, and a relatively low value of K(dn1, Dh1) confirms this qualitative conclusion. 4. Histograms More detailed properties of the F2-layer maximum parameters variability can be derived from histograms, e.g. from the histogram of dn, i.e. the number n of dn falling into a certain interval of values relative to a total number of measurements, N, where dn is defined by Eq. (2) and the N values are given in Table 1. Such histograms for night and day hours are shown in Fig. 2 for the whole year, i.e. without separation into seasons. In Fig. 2 also there is shown the approximation of every histogram by a mixture of two normal distributions characterized by probability density function (see, e.g., Hahn and Shapiro, 1967; Johnson and Leone, 1977): f ðx; l; rÞ ¼ f1 ðx; l1 ; r1 Þ þ f2 ðx; l2 ; r2 Þ f1 ðx; l1 ; r1 Þ ¼ c1 ð2pr21 Þ
1=2
ð3Þ 2
expððx l1 Þ =2r21 Þ
f2 ðx; l2 ; r2 Þ ¼ c2 ð2pr22 Þ1=2 expððx l2 Þ2 =2r22 Þ c1 þ c2 ¼ 1
Summer
dn, %
l ¼ c1 l1 þ c2 l2 2
r2 ¼ c1 r21 þ c2 r22 þ c1 ðl1 lÞ þ c2 ðl2 lÞ
2
where l and r2 are the mean value and variance of the mixture, l1, r12, and l2, r22 are the mean value and variance of the first and second components of the mixture. In this case x = dn. The coefficients of the Eq. (3) for every season and the whole year are given in Table 2. Some of these coefficients are shown in Fig. 2. The coefficients of Eq. (3) are chosen in such a way that the function f(x, l, and r) is close to the histogram. Quality of the approximation was estimated by the value of the correlation coefficient K between the cumulative distribution functions F(x) of the mixture and of the histogram, i.e. between the integral f(x, l, r) and the sum of n/N from 1 to x (e.g., Ramachandran and Tsokos, 2009) . These cumulative functions and the coefficients K are shown in Fig. 2, for this case K 1. Note that K > 0.999 for all cases below. It is seen from Fig. 2 that the first (f1) and second (f2) components of the mixture of two normal distributions are characteristics of relatively weak and strong fluctuations of dn correspondingly. Both at day and night hours r2 is approximately twice as r1, i.e. the variance of the strong fluctuations of dn is much greater than the variance of its weak fluctuations. At day hours the first component of the mixture is predominant (c1 = 0.72, c2 = 0.28), and the standard deviation of the mixture, r, is weakly different from r1. At night hours the second component of the mixture becomes significant (c1 = 0.44, c2 = 0.56), and r is near twice as r1. Both at day and night hours the standard deviation of the mixture weakly differs from the sample standard deviation: r = 12.5%, s = 12.7% at day hours and r = 21.8%, s = 23.7% at night hours (see Table 2).
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Fig. 2. Histograms of deviations of the measured NmF2 values from the quiet median (dn) for the daytime (10–16 LT) and nighttime (22–04 LT) hours under quiet conditions for the whole dataset, i.e. without separation into seasons. Approximation of the histograms by the mixture of two normal distributions of dn (thick lines), the first (1) and second (2) components of the mixture (thin lines), and the coefficients of these approximations (see Table 2). Cumulative distribution functions F of the histogram (dots) and the mixture (lines), and the correlation coefficient K between these functions.
Table 2 Coefficients of the Eq. (3) for the mixture of two normal distributions of dn, dn0, and dn1 for every season (Win, Equ, Sum) and for the whole year (All) for the day (10–16 LT) and night (22–04 LT) hours. Values of s are the sample standard deviations taken from Table 1. x
ssn
LT
c1
l1, %
r1, %
c2
l2, %
r2, %
l, %
r, %
s,%
dn
Win
10–16 22–04 10–16 22–04 10–16 22–04 10–16 22–04 10–16 10–16 10–16 10–16 22–04 10–16 22–04 10–16 22–04 10–16 22–04 10–16 22–04
0.6 0.33 0.7 0.5 1 0.6 0.72 0.44 0.64 1 1 0.87 1 0.63 0.39 0.72 0.5 1 0.6 0.75 0.45
1 5 0 5 0 4 1 4 0.5 1 0.5 0.5 1 1 5 0 3 0 2.5 0 2.5
11 12 8.5 11 8.6 12 8.5 11 8 6.7 4.9 6.4 6.4 6 11 5.5 10 6 10 6 10
0.4 0.67 0.3 0.5 0 0.4 0.28 0.56 0.36 0 0 0.13 0 0.37 0.61 0.28 0.5 0 0.4 0.25 0.55
6 6 6 7 – 1 7 4 5 – – 7 – 2.5 7 2.5 5 – 2.5 2.5 4
20 32 15 27 – 22 18 27 16 – – 16 – 12 32 12 26 – 22 12 28
1.8 2.4 1.8 1 0 2 1.2 0.5 2.1 1 0.5 1.3 1 0.3 2.3 0.7 1 0 0.5 0.6 1.1
15.6 27.6 11.2 21.5 8.6 16.9 12.5 21.8 11.7 6.7 4.9 8.6 6.4 8.9 26.6 8 20.1 6 16.1 8 22.1
15.8 29.5 11.9 21.3 8.6 17.8 12.7 23.7 11.3 6.8 4.9 8.4 6.4 9.1 27.9 8.2 20.3 6.4 15.6 8 22
Equ Sum All dn0
Win Equ Sum All
dn1
Win Equ Sum All
The condition s r is true for all conditions presented in Table 2, and this reflects the quality of the approximation. The weak fluctuations of dn are more often negative: l1 is equal to 1% at day hours and 4% at night hours (see Table 2). The strong fluctuations of dn are more often positive: l2 = 7% b 4% at day and night hours. The value of Dl21 = l2l1 is the shift between the components of the mixture. In the considered case Dl21 = 8% both for day and night hours. The shift between the mixture components results in that the borders of predominance of the
weak fluctuations are non-symmetrical: the condition f1 P f2 is valid for 21.8% 6 dn 6 15.2% at day hours and for 20.0% 6 dn 6 8.8% at night hours (see Fig. 2). Fig. 3 shows seasonal features of the dn histograms and of the mixtures of two normal distributions (see also Table 2). Both at day and night hours the relative contribution of the first component, f1, of the mixture in summer is greater than in winter. At day hours in summer this component of the mixture even becomes the only (c1 = 1, c2 = 0). The contribution of the second component, f2, of the
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Fig. 3. Histograms of deviations of the measured NmF2 values from the quiet median (dn) for the daytime (upper panel) and nighttime (lower panel) hours in every season. Approximations of the histograms by the mixture of two normal distributions of dn (thick lines), the components of the mixture (thin lines), and the coefficients c1 and c2 of these approximations (see Table 2).
mixture is maximal at night hours in winter (c1 = 0.33, c2 = 0.67) when the variances of this component, r22, and of the mixture, r2, are also maximal (r2 = 32%, r = 27.1%). At night hours in all seasons l1 < 0 and l2 > 0, i.e. the dn weak fluctuations are mainly negative and its strong fluctuations are more often positive. At day hours the dn weak fluctuations are almost symmetrical (|l1| 6 1%), the strong fluctuations are positive (l2 > 0) in winter and equinoxes. Analysis shows that the dn0 histogram which characterizes the high-frequency (within two hours) part of the NmF2 variability for night hours in all seasons corresponds to the normal distribution and r(dn0) s(dn0) at these hours. Therefore the values of s(dn0) for night hours presented in Table 1 are characteristics of the normal distribution of dn0. At day hours the dn0 histogram differs from the normal distribution only in winter (see Fig. 4 and Table 2). For the whole year, i.e. without separation into seasons, this feature results in a weak deviation of the dn0 histogram from the normal distribution: c1 = 0.87, c2 = 0.13 (see Table 2). Fig. 5 shows season features of the dn1 histogram and of the mixture of two normal distributions which are characteristics of the NmF2 day-to-day variability. These features are close to those shown in Fig. 3 for dn: both at day and night hours the relative contribution of the first component, f1, of the mixture in summer is greater than in winter; in summer at day hours this component of the mixture becomes even the only one. The day-to-day variability of NmF2 differs from its full variability mainly in that r1(dn1) < r1(dn) and r(dn1) < r(dn) in all seasons at day hours (see Table 2).
Fig. 6 shows distributions of Dh, Dh0, and Dh1 for the whole year, i.e. without separation into seasons (see also Table 3). The data in Fig. 6 evidence that the distributions of Dh and Dh0 at night hours and of Dh1 at day and night hours correspond to the normal distributions. Analysis showed that this feature of the ionosphere is kept in all seasons. Therefore in Table 3 the coefficients of Eq. (3) are given only for Dh and Dh0 at day hours. It is seen from Table 3 that c1(Dh) c1(Dh0) for every season, i.e. the relative contribution of the first and second components of the mixture of two normal distributions is almost equal for Dh and Dh0. Consequently, the deviation of the Dh distribution from the normal distribution is related mainly with the high-frequency (within two hours) variability of hmF2, Dh0. The hmF2 day-to-day variability, Dh1, does not contain Dh0, therefore the Dh1 corresponds to the normal distribution (see Table 3 and Fig. 6). Note that r(Dh) s(Dh), r(Dh0) s(Dh0), and r(Dh1) s(Dh1) for all conditions presented in Table 3. 5. Discussion The presented statistical properties of the NmF2 variability for quiet conditions under low solar activity agree in general with the results obtained earlier for other geophysical conditions: relatively low level of this variability at times less than 1 to 2 h (Zevakina et al., 1990; Kouris et al., 2000, 2006; Deminov et al., 2011), greater variability of NmF2 (or foF2) at night hours than at day hours (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Araujo-Pradere et al., 2005; Fotiadis and Kouris, 2006; Altadill, 2007; Deminov et al., 2009), deviations of the NmF2
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Fig. 4. Histograms of the high-frequency (within two hours) part of NmF2 fluctuations of the quiet ionosphere (dn0) for daytime (10–16 LT) hours in every season. Approximations of the histograms by the mixture of two normal distributions (thick lines), the components (1 and 2) of the mixture (thin lines) in winter, and the coefficients c1 and c2 of these approximations (see Table 2).
Fig. 5. Histograms of low-frequency (day-to-day) part of NmF2 fluctuations of the quiet ionosphere (dn1) for the daytime (upper panel) and nighttime (lower panel) hours in every season. Approximations of the histograms by the mixture of two normal distributions (thick lines), the components of the mixture (thin lines), and the coefficients c1 and c2 of these approximations (see Table 2).
fluctuations from the normal distribution at night hours (Adeniyi et al., 2007). But the possibility of approximation of the dNmF2 histogram by the mixture of two normal distributions seems to be evidenced for the first time. Comparison of the day-to-day variability of NmF2 of the quiet ionosphere with other estimates shows that at day hours there is a tendency to increase of this variability with growth of solar activity: s(dn) = 12.7% over Irkutsk under low solar activity (see Table 1), s(dn) 2s(dfoF2) 15% over Irkutsk under medium solar activity (1958–1992) (Deminov et al., 2009), s(dn) 15% over Slough under medium solar activity (F10.7 140) (Rishbeth and Mendillo, 2001). At night hours this tendency is not distinct: s(dn) = 23.7% over Irkutsk under
low solar activity (see Table 1), and s(dn) is near 21% and 24% over Irkutsk and Slough correspondingly at midnight under medium solar activity (Deminov et al., 2009). The high-frequency part of the NmF2 and hmF2 variability is believed to be associated mainly with the ionospheric effect of short-period (15–60 min) atmospheric gravity waves (AGWs) which are generated below the thermosphere and exist practically always (e.g., Hocke and Schlegel, 1996; Oliver et al., 1997; Miyoshi and Fujiwara, 2008). Weak magnetospheric substorms (AEmax < 300– 400 nT) occur almost every day even under geomagnetically quiet conditions (Eq. (2)). At periods of such weak substorms large-scale AGWs can be generated in the auroral region which propagate equatorwards and have
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Fig. 6. Histograms of fluctuations of the F2-layer maximum height, Dh, Dh0 and Dh1, for the daytime (upper panel) and nighttime (lower panel) hours under quiet conditions for the whole dataset, i.e. without separation into seasons. Approximations of the histograms by the mixture of two normal distributions (thick lines), the components of the mixture (thin lines), and the coefficients c1 and c2 of these approximations (see Table 3).
Table 3 Coefficients of the Eq. (3) for the mixture of two normal distributions of Dh, Dh0, and Dh1 for every season (Win, Equ, Sum) for the day hours (10–16 LT) and for the whole year (All) for the day (10–16 LT) and night (22–04 LT) hours. Values of s are the sample standard deviations taken from Table 1. x
ssn
LT
c1
l1, km
r1, km
c2
l2, km
r2, km
l, km
r, km
s, km
Dh
Win Equ Sum All
Dh0
Win Equ Sum All
Dh1
All
10–16 10–16 10–16 10–16 22–04 10–16 10–16 10–16 10–16 22–04 10–16 22–04
0.78 0.82 0.67 0.81 1 0.72 0.87 0.68 0.77 1 1 1
3 0 0.5 2 0.5 2 0 0 1 1 0 0
8 7 9.5 9 13.5 7 6 8 7 9.4 4.8 8.5
0.22 0.18 0.33 0.19 0 0.28 0.13 0.32 0.23 0 0 0
7 1 0 4 – 5 1 0 1 – – –
19 15 19 18 – 16 14 15.5 16 – – –
0.8 0.2 0.3 0.9 0.5 0 0.1 0 0.5 1 0 0
12.1 9 13.4 11.5 13.5 10.8 7.5 11 9.9 9.4 4.8 8.5
11.7 9 13.5 11.5 13.8 10.6 7.5 11.1 9.9 9.4 4.9 9
horizontal wavelengths larger than 1000 km and periods in the range of 30 min–3 h, and they can cause NmF2 and hmF2 fluctuations (e.g., Hocke and Schlegel, 1996; Fujiwara and Miyoshi, 2006). Typical features of the ionospheric effects of the large-scale AGWs at day hours are hmF2 rise and the consequent increase of NmF2 (see e.g. Prolss and Ocko, 2000). At night hours these effects are characterized by a distinct rise of hmF2 and rather a weak decrease of NmF2 (Deminova et al., 1998). Relatively weak changes of NmF2 at night hours are, obviously, typical also for short-period AGWs. Therefore rather high values of s(Dh0) both at day and night hours and of s(dn0) only at day hours are the additional evidences that the highfrequency part of the ionospheric variability is related to short-period AGWs (see Fig. 1 and Table 1). The first component (f1) of the mixture of two normal distributions can also be associated to the ionospheric effects of AGWs: at night hours the changes dn, dn0 and dn1 related to the first component (f1) of the mixture are
more often negative (l1 < 0); at day hours these changes are almost symmetrical (see Table 2), and just these features are characteristic for ionospheric effects of AGWs. The first component of the mixture is predominant for the weak NmF2 fluctuations which are most often the high-frequency part of the ionospheric variability related to short-period AGWs (see Tables 1 and 2). The second component (f2) of the mixture of two normal distributions can be apparently associated to the planetary waves and tides in the atmosphere as an important cause of the day-to-day variability of the quiet ionosphere (Forbes et al., 2000; Rishbeth and Mendillo, 2001; Lastovicka, 2006). Note that, although the quasi-stationary planetary wave does not propagate deep into the ionosphere due to the presence of critical layers and strong molecular dissipation, the planetary wave and tidal interaction lead to large changes in tides, which can impact the ionosphere at all latitudes (e.g., Lastovicka, 2006; Liu et al., 2010). Quasitwo-day variations of the ionospheric parameters are an
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example of contribution of these processes into the ionospheric variability (e.g., Apostolov et al., 1995; Forbes and Zhang, 1997). The second component of the mixture prevails for the strong NmF2 fluctuations which are mainly positive both at day and night hours: l2 > 0 for all conditions presented in Table 2. At night hours in winter and equinoxes this tendency is most clear. The data presented in Fig. 1 reflect also this feature of the ionosphere: in quasi-two-day variations of NmF2 there are seen distinct increases of NmF2 at night hours on 28 and 30 January, 2010 and much weaker decrease of NmF2 at night hours on 29 January. Distinct difference in the features of the ionospheric effects of AGWs and of the planetary waves and tides at night hours in winter and equinoxes (l1 < 0, l2 > 0, r1 < r2) is the principal cause of a considerable deviation of the NmF2 distribution from the normal distribution for these conditions (see Table 2 and Fig. 3). In Fig. 1 it is seen also that the amplitude of the quasi-two-day variations of hmF2 is not greater than the amplitude of the hmF2 fluctuations within two hours: s(Dh0) > s(Dh1) at day hours and s(Dh0) s(Dh1) at night hours (see Table 1). This is the cause of that the DhmF2 distributions are the normal distributions or weakly different from them (see Table 2 and Fig. 6). Very strong fluctuations of NmF2 are mainly positive. For example, for night hours in winter all values of |dn| > 61% are positive (see Table 1). Stronger asymmetry of the dn histogram at high values of |dn| is not sufficiently reflected by the mixture of two normal distributions. Weak deviations of r(dn) from s(dn) can be related to this cause (see Table 2). Strong deviations of the quiet ionosphere F2-layer maximum density from the usual median calculated over 27 days (|dNmF2| > 40%) were named Q-disturbances (Mikhailov et al., 2004). From data of 29 ionospheric stations located at high to low latitudes it was obtained that at all latitudes and under any level of solar activity positive Q-disturbances occur more often than negative ones (Mikhailov et al., 2004). Strong and very strong deviations of NmF2 from the quiet median over Irkutsk under low solar activity are also presumably positive (see Table 1 and Figs. 2 and 3). Qualitative agreement of this feature of the quiet ionosphere variability with the characteristic property of the Q-disturbance is, obviously, caused by the fact that prolonged periods of low solar activity correspond to relatively low geomagnetic activity, when the usual median is weakly different from the quiet median. Establishing of properties of the quiet ionosphere variability (with regard to the quiet median) for periods of high solar activity needs a separate study. Deviations of the dNmF2 distribution from the normal distribution are asymmetrical for all considered conditions. Therefore, e.g., the difference between the upper and lower quartiles of the dNmF2 distribution can give information about properties of the mixture of two normal distributions
of dNmF2, but a special study is needed in order to clear up this possibility. 6. Conclusions The analysis of statistical properties of the quiet ionosphere F-layer maximum parameters variability (deviations of NmF2 and hmF2 from the quiet median, dn b Dh) under low solar activity at day (10–16 LT) and night (22–04 LT) hours on the basis of Irkutsk station data for 2007–2010 made it possible to draw the following conclusions. 1. The experimental distribution (histogram) of dn can be approximated by a mixture of two normal distributions. The first and second components of the mixture are mainly characteristics of relatively weak and strong fluctuations of dn. Such approximation is most adequate for night hours in winter and equinoxes when the dn histogram is distinctly different from the normal distribution. For these conditions the dn weak fluctuations are mainly negative and its strong fluctuations are mainly positive. The Dh histogram is mainly the normal distribution. A weak deviation of the Dh histogram from the normal distribution occurs only at day hours in winter and equinoxes. 1. The weak and strong fluctuations of dn b Dh are principally associated with high-frequency (within two hours) and low-frequency (day-to-day) parts of changes of these parameters correspondingly. At night hours the low-frequency part of the dn variability prevails, at day hours the both parts of this variability are essential. The high- and low-frequency parts of the Dh variability are comparable at night hours, the high-frequency part becomes predominant at day hours. 2. The weak fluctuations of dn b Dh are obviously caused by ionospheric effects of medium-scale and large-scale atmospheric gravity waves (AGWs). The strong fluctuations are apparently associated, mainly, with planetary waves and tides. The different causes of the weak and strong fluctuations of the F2-layer maximum parameters are the main reason of the distinctly different features of these fluctuations.
Acknowledgements This work was supported by the Russian Foundation for Basic Research (Project codes 11-05-00200 and 11-0500908) and by the RAS Presidium Program No. 22. References Adeniyi, J.O., Oladipo, O.A., Radicella, S.M. Variability of foF2 for an equatorial station and comparison with the foF2 maps in IRI model. J. Atmos. Solar-Terr. Phys. 69, 721–773, 2007.
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