V.: G condition in the F2 region peak electron density: a statistical study

Abstract. We present a study of statistical relationships between the G condition, F1-layer and NmF2 negative disturbance occurrence probabilities and geomagnetic and solar activity indices Kp and F10.7, season, and geomagnetic latitude, busing experimental data acquired by the Ionospheric Digital Database of the National Geophysical Data Center, Boulder, Colorado from 1957 to 1990. It is shown that the dependence of the G condition occurrence probability, y G, on Kp is mainly determined by processes that control the behaviour of the F2 layer with Kp changes. We found that the relationship for log y G versus Kp is very close to the linear one. The G condition occurrence probability decreases from 0.55% to 0.17% as the value of  F10.7 increases from low to middle values, reaches its minimum at the middle solar activity level of F10.7 = 144 – 170, increasing from the minimum value of 0.17% to 0.49% when the F10.7 index increases from the middle solar activity level to F10.7 = 248 – 274. Interhemispheric asymmetry is found for the G condition occurrence probability in the ionosphere, with a stronger enhancement seen in the magnetic latitude range close to the northern magnetic pole and a deep minimum of the G condition occurrence probability in the low magnetic latitude range from – 30° to 30°. The measured magnetic latitude variation of the F1-layer occurrence probability is also asymmetrical relative to the geomagnetic equator. Our results provide additional evidence the F1-layer is more likely to be formed in summer than in winter. The Northern Hemisphere peak F1-layer occurrence probability is found to exceed that in the Southern Hemisphere. The G condition occurrence probability has maximum values of 0.91 and 0.75% in summer, and minimum values of 0.01 and 0.05% in winter for the Northern and Southern Hemisphere, respectively. Key words. Ionosphere; ion chemistry and composition; ionosphere-atmosphere interactions; ionospheric disturbances


Introduction
The Ionospheric Digital Database of the National Geophysical Data Center, Boulder, Colorado, provides the routine sounding ground-based station measurements of the critical frequencies and virtual heights of different ionospheric layers extracted from ionograms; in particular, the critical frequencies fof1 and f of2 of the F1 and F2 layers that are analyzed in this study.This Database is formed using the rules of the URSI standard (URSI handbook of ionogram interpretation and reduction, 1978).In addition to numerical values of ionospheric parameters, the qualifying and descriptive letters A-Z are used in this Database.The descriptive letter G means that a measurement is influenced, or impossible, because the ionization density of the layer is too small to enable it to be made accurately; this case is described as a G condition in the F-region of the ionosphere when f of2 ≤ fof1 (URSI handbook of ionogram interpretation and reduction, 1978).If the layer is not seen from ionograms due to other reasons, then other letters are used.For example, the letter R is used if the layer is influenced by, or is not seen from ionograms due to, attenuation of radio waves.The aim of this paper is to carry out a statistical study of a G condition using the Digital Database f of2 measurements, i.e. the groundbased ionosonde measurements of the F2-region peak electron densities, NmF2.
The G condition arises in the ionosphere when the critical frequency of the F2-layer drops below that of the F1-layer, i.e. when the peak density, N mF1, of the F1-layer, which is composed mostly of the molecular ions NO + and O 2 + , is larger than that of the F2-layer, which is dominated by O + ions (King, 1962).As a result, a very low main peak altitude, hmax, value (below 200 km) is observed in ionograms, so that no information is obtainable above this height from ground-based ionosonde data.As far as the authors know, the first altitude distribution of the electron density with NmF2 ≤ N mF1 (G condition) was deduced by Norton (1969) from ionograms recorded by the Alouette I satellite ionosonde and the St. John's ground-based ionosonde during the severe negative ionospheric storm on 18 April 1985.
The physics of this phenomenon has been studied by Buonsanto (1990) using ionosonde data from two midlatitude stations, Boulder and Wallops Island, by Oliver (1990) using Millstone Hill incoherent scatter radar (ISR) data, and by Fukao et al. (1991) using data from the middle and upper atmosphere radar in Japan.Pavlov and Buonsanto (1998), Pavlov (1998), Pavlov et al. (1999), and Schlesier and Buonsanto (1999) studied the G condition formation for quiet and disturbed mid-latitude ionosphere during periods of low, moderate, and high solar activity using the Millstone Hill ISR data.Model results also show that O + can become a minor ion in the F-region creating G condition during disturbed conditions at high latitudes (Banks et al., 1974;Schunk et al., 1975); observations at EISCAT confirm this conclusion (e.g., Häggström and Collis, 1990).These papers provide evidence that changes in [O], [N 2 ], [O 2 ] and the plasma drift velocity, the effect of the perpendicular (with respect to the geomagnetic field) component of the electric field on the electron density (through changes in the rate coefficients of chemical reactions of ions), and the effects of vibrationally excited N 2 and O 2 on the electron density are important factors that control the G condition formation in the ionosphere.This means that the probability of G condition occurrence depends on the daily solar activity index, F10.7, the 3-h geomagnetic index, K p , the number, n d , of a given day in a year and the geomagnetic latitude, ϕ.As far as the authors know, although the anomalous structure of the ionosphere has been observed on ionograms and by ISR for many years, there are no published studies of the statistical relationship of G condition occurrences with K p , F10.7, ϕ and n d .The main purpose of this work is to study, for the first time, these statistical relationships and to evaluate the probability of the G condition occurrence.
During N mF2 disturbances, believed to be caused by geomagnetic storms and substorms, N mF2 decreases (N mF2 negative disturbances) lead to increases in the G condition occurrence probability if the F1-layer exists.On the other hand, the G condition cannot exist in the ionosphere if there is no the F1-layer.In our analysis we study a possible relationship of the probability of the G condition occurrence with the probabilities of the F1-layer occurrence and the N mF2 negative disturbance occurrence.

The formation of the F1-and F2-layers in the ionosphere
The F-region is located in the altitude range above 140-160 km.Within the F-region are the F1 and F2-layers with peak altitudes hmF1< 190-200 km and hmF2> 200-210 km.The major F1-and F2-layer ions are O + ( 4 S), O 2 + , and NO + ions.The F-region behaviour is controlled by physical processes described in many review articles and books on the formation of the ionosphere (e.g.Ratcliffe, 1972;Rishbeth and Garriot, 1969;Brunelli and Namgaladze, 1988;Rees, 1989;Fejer, 1997).The present section is not intended to be a comprehensive review.Its purpose is to point out the main physical processes that form the F1-and F2-layers in the ionosphere by a balance between production, chemical loss, and transport of electrons and ions.+ and O + ions.At high latitudes, there is a source of ionization in the auroral oval which exists in both the Northern and Southern hemispheres above about 60 • geomagnetic latitude.Auroral electrons come from the magnetosphere and spiral down the magnetic field lines of the Earth, producing N 2 + , O 2 + and O + ions by ionization of the main neutral species N 2 , O 2 and O. Auroral charged particle precipitation is characterized by long-term unpredictability and highly variable strength and spatial inhomogeneity (Rees, 1989).
At the F2 peak altitude, the atomic species dominate, with O + ( 4 S) and O being the major ion and neutral species, respectively.Following Richards et al. (1994), we conclude that about 60% of the oxygen ions are created in electronically excited states 2 D, 2 P, 4 P and 2 P * during atomic oxygen photoionization.As the radiation flux penetrates into the atmosphere it is attenuated owing to absorption.The results of many theoretical studies (see Ratcliffe, 1972;Rishbeth and Garriot, 1969;Brunelli and Namgaladze, 1988, and references therein) provide sufficient evidence to neglect the effects of this absorption on production rates of oxygen ions at the daytime F2 peak altitudes.Therefore, the production rate, P( 4 S) of unexcited oxygen ions and the production rates, P( 2 D), P( 2 P), P( 4 P), and P( 2 P * ) of excited oxygen ions by photoionization and by photoelectrons are proportional to [O] and the P( 4 S)/[O], P( 2 D)/[O], P( 2 P)/[O] and P( 2 P * )/[O] ratios do not depend on neutral number densities during daytime conditions.
The excited oxygen ions are converted to unexcited O + ( 4 S) ions and N 2 + and O 2 + ions by chemical reactions that are included in current models of the ionosphere and plasmasphere (e.g.Torr et al., 1990;Pavlov, 1997).As a result, the total production rate, P(O + ), of O + ( 4 S) ions (that is the sum of P( 4 S) and the production rate of O + ( 4 S) ions from excited oxygen ions by chemical reactions) is proportional to [O] and there is some dependence of the P(O + )/[O] ratio on [O], [N 2 ] and [O 2 ] at the daytime F2 peak altitudes (for more details see Eq. (A3) of Pavlov and Buonsanto, 1997).It should be noted that near sunrise and sunset the optical depths become large for the important radiations in the F2layer and the production rate of O + ions by photoionization depends strongly on the (O)/[N 2 ] ratio (Rishbeth and Garriot, 1969).

Loss rate of O
with the loss rate where v = 0,1,... is the number of the vibrational level of N 2 or O 2 .The effective rate coefficients of reactions ( 1) and ( 2) are determined as (Pavlov, 1998) where β v is the recombination rate coefficient of O + ( 4 S) ions with N 2 (v), γ v is the recombination rate coefficient of O + ( 4 S) ions with O 2 (v) and the total N 2 and O 2 number densities are determined as and are the number densities of N 2 and O 2 at the v-th vibrational level.
The model of the Boltzmann distribution determines the number densities of vibrationally excited N 2 (v) and O 2 (v) as where E 1 = 3353 K is the energy of the first level of N 2 given by Radzig and Smirnov (1985), E 1 = 2239 K is the energy of the first level of O 2 given by Radzig and Smirnov (1985).
It follows from Eq. ( 5) that Schmeltekopf et al. (1968) measured the dependence of β on the N 2 vibrational temperature, T N2v , over the vibrational temperature range 300-6000 K when the neutral and ion temperatures, T n and T i , are fixed at 300 K.The values of β v for the vibrational levels v = 1 -11 were extracted by Schmeltekopf et al. (1968) from the measured dependence of β on T N2v .As a result, the β v /β 0 ratios for T n = T i = 300 K can be determined for the vibrational levels v = 1-5 that are usually included in the model calculations (Pavlov, 1998;Pavlov et al., 1999) as The measurements of β were presented by Hierl et al. (1997) over the temperature range 300-1600 K for T n = T i = T N2v .The fundamental results of Hierl et al. (1997) confirm the observations of Schmeltekopf et al. (1968), and show for the first time that the translation temperature dependencies of β v are similar to β 0 .This means that the β v /β 0 ratios given by Eq. ( 7) are valid for T n = T i = 300-1600 K and that these β v /β 0 ratios can be used to model the F-region of the ionosphere.Hierl et al. (1997) determined the dependence of γ on the O 2 vibrational temperature, T O2v , over the temperature range 300-1800 for T O2v = T n = T i .The flowing afterglow measurements of γ given by Hierl et al. (1997) were used by Hierl et al. (1997) and Pavlov (1998) to invert the data to find the rate coefficient γ v , for the various vibrational levels of O 2 (v>0) as The thermal rate coefficients β 0 and γ 0 depend on T n , T i , and a relative drift velocity, V d , between ions and molecules (which is a function of the perpendicular component, E ⊥ , of the electric field with respect to the geomagnetic field) only by means of an effective temperature (St.-Maurice and Torr, 1978) where k is the Boltzmann constant, m i and m n denote the masses of the ion and neutral reactants, respectively.As a result, we conclude that the loss rate of O + ( 4 S) ions is a function of [N 2 ], [O 2 ], T n , T i , E ⊥ , T N2v and T O2v .
The excitation of N 2 and O 2 by thermal electrons provides the main contribution to the values of N 2 and O 2 vibrational excitations if the electron temperature, T e , is higher than about 1600-1800 K at F-region altitudes; the values of T N2v and T O2v are close to T n for T e <1600-1800 K and the values of T N2V − T n and T O2V − T n increase with increasing the electron temperature (Pavlov, 1988(Pavlov, , 1994(Pavlov, , 1997(Pavlov, , 1998;;Pavlov and Namgaladze, 1988;Pavlov and Buonsanto, 1997;Pavlov and Oyama, 2000;Pavlov et al., 2000Pavlov et al., , 2001)).This means that the loss rate of O + ( 4 S) ions is a function of (N 2 ), (O 2 ), T n , T i , E ⊥ and T e .Our calculations show that an increase in the effective temperature results in an increase of β for T eff > 920 K and in an increase of γ for T eff > 850 K if T eff = T N2V = T O2V .The variation of β is less than 20% in the effective temperature range of 620 K -1170 K and the variation of γ is less than 20% in the effective temperature range of 550 K -1240 K if T eff = T N2V = T O2V .

Transport of electrons and ions
In the F2-layer, both neutral wind induced and field-aligned diffusion of O + ( 4 S) ions and electrons are important in addition to chemical reactions.Electric fields of magnetospheric origin are mapped along geomagnetic field lines to the high latitude ionosphere.These electric fields are perpendicular to the geomagnetic field and cause the high latitude ionosphere to move approximately horizontally across the polar region at F-region altitudes.The geomagnetic field lines at high latitudes are not completely vertical and the electric fieldinduced plasma motion has a vertical component which has an effect on both N mF2 and hmF2.There are also electric fields associated with neutral wind induced ionospheric currents.In the daytime equatorial F2-layer, electrons and ions are lifted to great heights by the eastward electric fields (the electromagnetic drift of plasma), that exist in low latitudes by day, and then diffuse downward along field lines.The result of this plasma transport is that the daytime latitude distribution of NmF2 has a minimum value (the equatorial trough in N mF2) in the vicinity of the geomagnetic equator and two peaks on each side of the magnetic equator.At the geomagnetic equator, hmF2 is largely controlled by the electromagnetic drift which is directed upward by day and downward at night.

Formation of the ionospheric F2-layer
The characteristic time for the decay of [O + ( 4 S)] by the chemical reactions (1) and ( 2) is obtained as τ c = L −1 .The characteristic diffusion time of O + ( 4 S) ions can be determined at middle and high latitudes as τ D = H p 2 D a −1 , where D a = sin 2 I (T e + T i ) k (m i ν i ) −1 is the ambipolar diffusion coefficient, I is the magnetic dip angle, m i is the ion mass, ν i is the collisional frequency of O + ( 4 S) ions with oxygen atoms, H p = k (T e + T i ) (m i g) −1 is the characteristic scale length and g is the acceleration due to gravity.
In the F1-layer, the value of τ c is much less than the value of τ D .Therefore, the photochemistry dominates in the F1layer and the steady state daytime F1-layer number density of O + ( 4 S) ions is directly proportional to the [O]/L ratio, i.e. the value of [O + ( 4 S)] increases with altitude.The value of D a increases exponentially with altitude owing to its dependence on [O] (D a ∼ [O] −1 ) and, hence at high altitudes, diffusion dominates.As a result, if the plasma drift effect on hmF2 is unimportant, the height of the middle and high latitude F2 peak is located approximately at the altitude level where the characteristic times for diffusion and chemistry are equal (Strobel and McElroy, 1970;Ratcliffe, 1972;Rishbeth and Garriot, 1969;Brunelli and Namgaladze, 1988).The F2 peak altitude is lowered by the action of a windinduced downward plasma drift, due to a poleward wind, and a wind-induced upward plasma drift, caused by an equatorward wind, acts to raise the F2 peak altitude (Strobel and McElroy, 1970;Ratcliffe, 1972;Rishbeth and Garriot, 1969;Brunelli and Namgaladze, 1988).
In order to find the analytical solution of the steady state continuity equation for O + ions during quiet days for midlatitudes, Badin and Deminov (1982) and Badin (1989) assumed that the optical depth of the atmosphere goes to zero, the drift velocity of the plasma in the vertical direction does not depend on the altitude, T i ≈ const, T n ≈ const, and T e ≈ const.As a consequence of this analytical approach, N mF2 (Badin, 1989;Pavlov and Buonsanto, 1997).
The relationship between NmF2 and the [O]/L ratio is complicated by effects of plasma drifts due to electric fields and neutral winds (see Sect. 2.3) on NmF2 and by some dependence of the P ratio measured by satellites (e.g. by the ESRO 4 satellite) and the F2 peak density measured by ionosonde stations are similar (Prolss, 1980(Prolss, , 1995) ) and it is usually supposed that the value of NmF2 is approximately directly proportional to the [O]/L ratio at hmF2 during daytime conditions (Rishbeth and Garriot, 1969;Brunelli and Namgaladze, 1988;Rishbeth and Muller-Wodarg, 1999;Rishbeth et al., 2000).Therefore, this assumption is used in our study in discussions of NmF2 variation sources.

Formation of the ionospheric F1-layer
The role of the ion transport is less than the role of chemical reactions of ions with electrons and neutral components of the upper atmosphere at the F1-layer altitudes, and production and loss rates of electron and ions determine the F1-layer formation.
As is well known, the major molecular ions are O 2 + and NO + ions in the F-region of the ionosphere.The chemistry of NO + ions in the F-region of the ionosphere is comparatively simple, with the NO + production via reactions of O + ( 4 S) ions with N 2 (v = 0 −5) given by Eq. ( 1), O 2 + ions with NO and N and N 2 + ions with O, and loss through dissociative recombination (for more details see Rishbeth and Garriot, 1969;Brunelli and Namgaladze, 1988;Rees, 1989;Torr et al. 1990;Pavlov, 1997).The O 2 photoionization, the O 2 ionization by photoelectrons and auroral electrons, the chemical reactions of O + ( 4 S) ions with unexcited and vibrationally excited O 2 is given by Eq. ( 2), and N 2 + with O 2 are the sources of O 2 + ions in the F-region of the ionosphere while the sinks of O 2 + ions are dissociative recombination of O 2 + and the chemical reactions of O 2 + with N and O 2 + with NO (for more details see Rishbeth and Garriot, 1969;Brunelli and Namgaladze, 1988;Rees, 1989;Torr et al., 1990;Pavlov, 1997).
To study the formation of the F1-layer, Ratcliffe (1972) assumed that the main source of NO + ions is the chemical reaction of O + with N 2 and that there are only NO + and O + ions.Ratcliffe (1972) found that the peak of the F1-layer exists in the ionosphere if the peak altitude, h 0 , of the total production rate of thermal electrons is less than the altitude, h t , that is determined from the condition of where α is the rate coefficient of the dissociative recombination of NO + ions.Ratcliffe (1972) concluded that the value of h t -h 0 is decreased with the solar activity level increase and the value of h t -h 0 has a maximum value close to midday.As a result, the F1 peak is more clearly in evidence at solar minimum than at solar maximum and the F1 peak is more commonly formed near midday and in summer (Ratcliffe, 1972).

Data and method of data analysis
Ionograms produced by ionosondes are records that show variations of virtual height of radio wave reflection from the ionosphere as a function of the radio frequency, h (f), within the frequency band range 1 MHz-20 MHz that is normally used (URSI handbook of ionogram interpretation and reduction, 1978).The radio wave that is reflected from the ionosphere level of ionization is split into two waves of different polarization by the Earth's magnetic field thereby leading to two sorts of observed h (f) curves.These waves are called the ordinary wave (o-mode) and the extraordinary wave (xmode).There are also z-mode traces on some ionograms, generated by radio waves which have been propagated along the magnetic field lines.The mode traces can be identified by the frequency separation and by other indications presented in URSI handbook of ionogram interpretation and reduction (1978).A simple approach is used to find peak electron densities of the ionosphere from observations of h (f) curves, i.e. when the level of the peak electron density in the layer is reached, the value of h (f) becomes effectively infinite df dh → 0 .
The frequency at which this occurs is determined as the critical frequency of the ionospheric layer.The values of N mF2 and NmF1 are related to the critical frequencies f of2 and f of1 extracted from the h (f) curve of the ordinary wave as N mF2 = 1.24•10 10 f of2 2 and NmF1=1.24• 10 10 f of1 2 , where the unit of NmF2 and N mF1 is m −3 and the unit of f of2 and f of1 is MHz (URSI handbook of ionogram interpretation and reduction, 1978).Our analysis is based on 34 years of hourly f of2 and f of1 data from 1957 to 1990 from stations on the Ionospheric Digital Database of the National Geophysical Data Center, Boulder, Colorado.The total probabilities of the G condition and F1-layer occurrences can be determined as the ratio of total G condition observations to the total number of studied observations and as the ratio of total F1-layer observations to the total number of observations, respectively.We study the dependence of the probabilities of G condition and F1-layer occurrences on F10.7, K p , n d and ϕ.A sum, S G , of G condition observations and a sum, S F1 , of F1-layer observations over 3 parameters from these 4 parameters are functions of a fourth parameter, X.The G condition probability function, G (X), of this fourth parameter has been introduced as a ratio of S G to the total number of studied observations, and the F1-layer probability function, F1 (X), of the same parameter has been introduced as a ratio of S F1 to the total number of studied observations.To investigate G (X) and F1 (X) dependencies, we split the range of X into twelve intervals of the same length and calculate the G (X) and F1 (X) variations.The following investigation seeks to find these probability function variations.
The electron density can either decrease or increase during geomagnetically disturbed conditions, and these changes in the electron density are denoted as negative and positive ionospheric disturbances, respectively.To test the effects of geomagnetic activity, we use two different K p labels: "disturbed", for which we take K p > 3 and use the peak density, NmF2(d) and critical frequency, f of2(d), of the F2-layer observed during the time periods with K p > 3, and "quiet", for which we take K p ≤ 3. The determination of the quiet peak density, NmF2(q) and critical frequency, f of2(q), of the F2-layer, is crucial for studies of negative and positive ionospheric disturbances.When the thermosphere is disturbed, the time it takes to relax back to its initial state and this thermosphere relaxation determines the time for the disturbed ionosphere to relax back to the quiet state.This means that not every f of2 observed during the day with K p ≤ 3 can be considered as f of2(q).The characteristic time of the neutral composition recovery after a storm impulse event ranges from 7 h to 12 h on average (Hedin, 1987) while it is may need up to days for all altitudes down to 120 km in the atmosphere to recover completely back to the undisturbed state of the atmosphere (Richmond and Lu, 2000).Therefore, we determine the quiet reference day with f of2(q) by the choice of the quiet day with K p ≤ 3 from 00:00 UT to 24:00 UT if the previous day was the day with K p ≤ 3 from 00:00 UT to 24:00 UT.Furthermore, we use only quiet days with uninterrupted f of2 measurements from 00:00 UT to 24:00 UT; the comparison between f of2(d) and f of2(q) measured at the chosen station is carried out if the time difference between f of2(d) and f of2(q) measurements is less than or equal to 30 days.We use the nearest quiet day to the studied disturbed time period, and determine the relative deviation, δ, of f of2 observed at the given station from f of2(q) as Negative and positive values of δ correspond to negative and positive disturbances in NmF2, respectively.We study the dependence of the probabilities of negative and positive disturbance occurrences in NmF2 on K p , n d , ϕ and F10.7.The sum, S δ<0 , of negative disturbance observations and the sum, S δ>0 , of positive disturbance observations, over 3 parameters from these 4 parameters, are functions of a fourth parameter, X.The negative disturbance probability function, δ<0 (X), of this fourth parameter has been introduced as a ratio of S δ<0 to the total number of studied disturbed observations, and the positive disturbance probability function, δ>0 (X), of the same parameter has been introduced as a ratio of S δ>0 to a total number of studied disturbed observations.To investigate δ<0 (X) and δ>0 (X) dependencies, we split the range of X into twelve intervals of the same length and calculate the δ<0 (X) and δ>0 (X) variations.
Our analysis is carried out by sorting the data versus one independent parameter (K p , n d , ϕ and F10.7), i.e. singleparameter statistics is used.This approach can be considered as the first step in our studies of the N mF2 negative disturbance, G condition and F1-layer occurrence probabilities; we plan to use multiple-parameter statistics in our future studies of these probabilities.
4.1 Magnetic activity trends in the F1-layer, G condition and NmF2 negative disturbance occurrence probabilities Figure 1 shows the probability F1 (K p ) of F1-layer occurrence (bottom panel), the probability G (K p ) of the G condition occurrence (middle panel), and the probability δ<0 (K p ) of the negative disturbance occurrence in NmF2 (top panel) as functions of K p .Circles displayed in Fig. 2 shows log G versus K p that is clearly very close to linear.We found that this dependence can be approximated as  where the coefficients A = −6.94± 0.03, B = 0.426 ± 0.012 are found by the method of least squares.This linear dependence is shown by the solid line in Fig. 2. In contrast to Fig. 1, the values of G (K p ) presented by Eq. ( 11) and Fig. 2 are not multiplied by a factor of 100 (the unit of G (K p ) is not percentage).
It can be seen from Fig. 1 that G (K p ) and δ<0 (K p ) reveal the increase with geomagnetic activity, whereas F1 (K p ) does change with the K p variations that could be responsible for the G (K p ) changes.This means that the dependence of the probability of the G condition occurrence on K p is mainly determined by processes that control the behaviour of the F2-layer with K p changes and G (K p ) has no significant relation to F1 (K p ).This result seems to be quite natural because a G condition in the geomagnetically disturbed ionosphere is associated with a significant negative ionospheric storm in NmF2.
The value of δ<0 (K p ) includes all negative ionospheric disturbances with δ < 0. Figure 3 shows the probabilities δ≤−0.1 (K p ) (top panel), δ≤−0.3 (K p ) (middle panel), and δ≤−0.5 (K p ) (bottom panel) of the N mF2 negative disturbance occurrence as functions of K p .We found that the values of δ<0 (K p ), δ≤−0.1 (K p ), δ≤−0.3 (K p ), and δ≤−0.5 (K p ) have minimum values of 54.9%, 22.3%, 2.5% and 0.2% and maximum values of 80.2%, 70.6%, 52.0% and 24.6%, respectively.We conclude that the ratio of the maximum value of δ≤δ0 (K p ) to the minimum value of δ≤δ0 (K p ) is increased with the increase of the minimum absolute value of the N mF2 negative disturbance amplitude, i.e. the δ≤δ0 (K p ) dependence shows a stronger positive K p tendency with the increase in |δ0|.
Previous F2-layer negative ionospheric disturbance studies (Mednikova, 1980;Zevakina and Kiseleva, 1985;Wrenn et al., 1987;Brunelli and Namgaladze, 1988), based on limited data sets, show that the value of K p can be used as a rough indicator of the minimum value of δ and the increase in K p results in the decrease in this minimum value of δ.
To check this hypothesis, we calculate the probability density function, ρ(K p , δ), of negative disturbance occurrences in NmF2.The relationship between δ<0 (K p ) and ρ(K p , δ) is To estimate the probability density function, we split the range of δ into ten intervals of the same length.
Lines 1, 2, 3, 4, and 5 of Fig. 4 show the calculated values of ρ(K p , δ) for K p = 1, 3, 5, 7 and 9, respectively.It follows from Fig. 4 that there is some small amount of strong NmF2 negative disturbance amplitudes for low values of K p = 1 and 3.This means that these NmF2 negative disturbances are the result of the previous history of geomagnetic activity.We found that there is a difference in the dependence of the probability density function on δ for K p ≤ 5 and K p ≥ 7.For K p ≤ 5, the probability density function is decreased with the decrease in δ in the all of the studied range of δ from  0 to 1 while for K p = 7 and 9, the value of ρ(K p , δ) is decreased with the decrease in δ only for δ < −0.3 and −0.5, respectively.The maximum values of the probability density function (15.2% and 15.5%) appear for K p = 7 and 9 close to δ = −0.25 and −0.45, respectively.On the other hand, the middle panel of Fig. 1 shows that the increase in K p leads to the enhancement in the G condition occurrence probability.As a result, the G condition occurrence is associated with large values of |δ|.
The Joule heating of the thermosphere can be viewed as the frictional heating produced in the thermosphere as the rapidly convecting ions collide with neutral molecules; the most part of the Joule heating is deposited in the 115-150 km altitude region, although some extends to higher altitudes (Richmond and Lu, 2000).The geomagnetic storm Joule heating of the thermosphere is considerably more effective than the energy of the auroral electrons in affecting the thermospheric circulation and the increase of the neutral temperature (Richmond and Lu, 2000).Joule heating from the dissipation of ionospheric currents raises the neutral temperature of the upper thermosphere and ion drag drives highvelocity neutral winds during geomagnetic storms at high latitudes (Prolss, 1980(Prolss, , 1995;;Fuller-Rowell et al., 1996, 2000).This leads to generation of a disturbed composition zone of the high latitude neutral atmosphere with an increase in the heavier gases and a decrease in the lighter gases, i.e. with  As a result, thermospheric altitude distribution of neutral species at middle and low latitudes is influenced by a global large scale wind circulation of the neutral atmosphere which is produced by geomagnetic storm energy input at high latitudes (theoretical and observational studies of thermospheric composition responses to the transport of neutral species from auroral regions to middle latitudes during geomagnetic storms are reviewed by Prolss, 1980Prolss, , 1995)).The increase in the [N 2 ]/[O] ratio maximizes in a region that is roughly located within the auroral oval; this [N 2 ]/[O] increase intensifies and can expand to middle magnetic latitudes with the K p increase (Brunelli and Namgaladze, 1988;Prolss, 1980Prolss, , 1995;;Zuzic et al., 1997).The high latitude geomagnetic storm upwelling brings air rich in the heavy species N 2 and O 2 to high altitudes and the geomagnetic storm circulation carries this N 2 and O 2 -rich air to midlatitudes at lower latitudes, the downwelling leads to the opposite effect; air with low values of [N 2 ] and [O 2 ] is carried downward, reducing their concentrations at all altitudes (e.g.Fuller-Rowell et al., 1996;Field et al., 1998;Richmond and Lu, 2000).Thus, the values of the [N 2 ]/[O] and the [O 2 ]/[O] ratios are enhanced at higher latitudes and depleted at lower latitudes, contributing to high latitude N mF2 decreases and low latitude NmF2 increases during daytime conditions.The G condition is observed mainly during daytime conditions at middle and high latitudes (Polyakov et al., 1968;Ratcliffe, 1972;see also Sect. 4.3).Until now, the prediction of geomagnetic storm thermospheric variations and perturbations in empirical models have been keyed to geophysical indices like K p and A p which are taken to represent the geophysical processes.Thus, the N 2 and O 2 depletion is stronger for high K p at high and middle latitude; the boundary between N 2 and O 2 enrichment and N 2 and O 2 depletion penetrates to more low latitudes with the increase in K p .
The MSIS-86 model (Hedin, 1987) simulations show that the neutral temperature is increased with the increase in A p .This means that the K p increase can produce the increase of vibrational temperatures of N 2 and O 2 (see Sect. 2.2), leading to some additional increase in the loss rate of the O + ( 4 S) ions given by Eq. ( 3).
As a result, the dependence of N mF2 on [O]/L leads to the increases in the NmF2 negative disturbance and G condition occurrence probabilities with the K p increase that are shown in Figs. 1 and 3.However, it remains to be answered why the G (K p ) dependence is exponential.

Dependence of the F1-layer, G condition and N mF2
negative disturbance occurrence probabilities on solar activity The histograms of the dependence of the F1-layer, G condition and N mF2 negative disturbance(with δ < 0) percentage occurrences on the daily solar activity index F10.7 are shown in the bottom, middle, and top panels of Fig. 5, respectively.It can be seen from the bottom panel of Fig. 5 that the value of F1 (F10.7) is decreased with the solar activity index increase.This result agrees with well known conclusions from previous F1-layer studies (for more details see, for example, Polyakov et al., 1968;Ratcliffe, 1972), based on a more limited data set, that the probability to observe the F1-layer is lower at solar maximum then that at solar minimum.
A prominent feature of the G condition occurrence probability, shown in the middle panel of Fig. 5 is that G (F10.7) reaches its minimum at middle solar activity conditions  The conditional probability of K p occurrence for F10.7 ≤ 100 (solid line), 100 < F10.7 < 170 (dashed line), and F10.7 ≥ 170 (dotted line).
The bottom panel of Fig. 5 shows that there are fewer F1layers at solar maximum; the middle panel of Fig. 5 shows that there are more occasions when the F1-layer is stronger than the F2-layer at solar maximum.The value of G (F10.7) is increased from 0.17% to 0.49% when the F10.7 index increases from F10.7 = 144-170 to F10.7 = 248-274.The latter occurrence must be due to an increase in occasions at solar maximum when the F2 peak density is depressed below the F1 peak density.
The middle and bottom panels of Fig. 6 show that at high solar activity, the F10.7 trend in the probability of strong and very strong NmF2 negative disturbances has the higher influence on G (F10.7) compared with the F10.7 trend in the F1-layer occurrence probability.However, the F10.7 trend in the probability of strong and very strong NmF2 negative disturbances can result from a possible relationship between K p and F10.7 indices and the K p trend in the probability of N mF2 negative disturbances shown in Fig. 3. To investigate this relationship between K p and F10.7 indices for the studied time period, we divide the F10.7 range into three intervals F10.7 ≤ 100, 100 < F10.7 < 170, and F10.7 ≥ 170, which correspond approximately to low, moderate, and high solar activity, respectively.We then estimate conditional probabilities, F10.7≤100 (K p ), 100<F10.7<170(K p ), and F10.7≥170 (K p ) for different values of K p to occur, pro- vided the index F10.7 is within the intervals specified by the subscripts.The calculated values of F10.7≤100 (K p ), 100<F10.7<170(K p ) and F10.7≥170 (K p ) are shown in Fig. 7 by solid, dashed, and dotted lines, respectively.It can be seen from Fig. 7 that the conditional probability for low values of K p (approximately below 2 0 −2 + ) to occur is decreased as the solar activity increases while the high values of K p (approximately above 2 + −3 0 ) become more probable.These results are in agreement with the well-known fact that magnetic storms are more frequent on average at solar maximum than at solar minimum (Field et al., 1998).Thus, at least in part, the F10.7 trends in the probabilities of strong and very strong NmF2 negative disturbances can arise from the K p trends in the probabilities of these N mF2 negative disturbances shown in Fig. 3.
The middle panel of Fig. 5 shows that the G condition probability has oscillations above F10.7 = 274 that can be explained by oscillations in δ≤−0.3 (F10.7) and δ≤−0.5 (F10.7).We did not find any physical explanation of these oscillations in δ≤−0.3 (F10.7) and δ≤−0.5 (F10.7);further work is required to express this result in physical processes that determine the value of f of2. ) and Southern (ϕ < 90 • ) Hemispheres separately.The first thing to note is that the F1-layer occurrence probability has a minimum value of 2.1-6.4% in the magnetic latitude range from -15 • to 15 • , close to the magnetic equator.
The value of F1(ϕ) reaches 15.4-15.8% at the magnetic latitudes 30-75 • in the Northern Hemisphere and 9.4-11.8% in the magnetic latitude range from −30 to −75 • in the Southern Hemisphere.We found the Northern Hemisphere F1(ϕ) peak value of 8.5% at the magnetic latitudes 75-90 • and the Southern Hemisphere F1(ϕ) peak value of 21.2% in the magnetic latitude range from −75 • to −90 • .It is necessary to point out that the trend in F1(ϕ) is in agreement with the previous F1-layer studies (Cummack, 1961;Polyakov et al., 1968;Ratcliffe, 1972) based on a more limited data set.At the same time, as far as the authors know, we found for the first time that the magnetic latitude variation of the F1-layer occurrence probability is asymmetrical relative to the geomagnetic equator.The probabilities δ≤−0.1 (ϕ), δ≤−0.3 (ϕ), and δ≤−0.5 (ϕ) of the NmF2 negative disturbance occurrence are shown in the top, middle, and bottom panels of Fig. 9, respectively.The top panels of Fig. 8 and 9 show that the NmF2 negative disturbance occurrence probabilities δ<0 (ϕ) and δ≤−0.1 (ϕ) have minimum values of 46.9-47.0%and 19.8-21.6%,respectively, in the same low latitude range from −15 • to 15 • and their dependence on the geomagnetic latitude is approximately symmetric with respect to the magnetic equator.Our results clearly show the latitude dependence of δ≤δ0 (ϕ), reproducing the tendency for decreased δ≤δ0 (ϕ) at low latitudes and increased δ≤δ0 (ϕ) at high latitudes.The middle panel of Fig. 8 shows an interhemispheric asymmetry, calculated for the G condition occurrence probability in the ionosphere, with a stronger enhancement seen in the magnetic latitude range of 75-90 • close to the northern magnetic pole.We see a sharp increase in G (ϕ) in the Northern Hemisphere as one goes from middle to high latitudes with G (ϕ) = 1.75% at magnetic latitudes 75-90 • whereas we compute G (ϕ) = 0.67-0.72%from −45 • to −90 • in the Southern Hemisphere.We can also see a deep minimum of the G condition occurrence probability in the low magnetic latitude range from −30 • to 30 • .Comparison of G (ϕ) and F1 shows that the G condition pattern is more symmetrical about the geomagnetic equator than the F1-layer pattern.
This G condition occurrence probability variation is caused by the F1-layer occurrence probability variation and the geomagnetic latitude trend in δ<0 (ϕ) shown in the bottom and top panels of Fig. 8, respectively.The fact that the G condition occurrence is more probable at middle and high magnetic latitudes than at low magnetic latitudes is in agreement with a similar feature of the F1-layer occurrence, and the fact that geomagnetic storm reduction in N mF2, with respect to estimated quiet-time values, is greatest at high geomagnetic latitudes as shown in Fig. 9 and the top panel of Fig. 8 and discussed in previous studies by Zevakina and Kiseleva (1985), Wrenn et al. (1987), andBrunelli andNamgaladze (1988).As the F1-layer occurrence probability variation is asymmetrical, relative to the geomagnetic equator, it appears reasonable to assume that the G condition occurrence probability interhemispheric asymmetry can be due to the F1 (ϕ) asymmetry found in this paper.Comparison of the top and bottom panels of Fig. 10 shows that the F1-layer occurrence probability has a maximum value of 32.4 and 20.3% in the Northern and Southern Hemisphere, respectively, which occurs in summer in the N d range from 152 to 183.The maximum reduction in F1 occurs in winter when the F1-layer occurrence probability reaches the minimum value of 1.5 and 3.9% in the Northern and Southern Hemisphere, respectively.
We can sum the observations in both hemispheres for the same values of N d .The resulting seasonal dependence of the occurrence of the G condition (top panel) and F1-layer (bot-  In previous F1-layer studies (Polyakov et al., 1968;Ratcliffe, 1972;Shchepkin et al., 1984), based on a limited data set, it was demonstrated that the chance that the F1-layer will be formed is greater in summer than in winter; our results provide additional evidence of this phenomenon, giving a more detailed picture of the F1-layer seasonal behaviour.At the same time, as far as the authors know, we found for the first time that the Northern Hemisphere peak F1-layer occurrence probability shown in the top panel of Fig. 10   We now examine the G condition occurrence probability shown in Fig. 11 and find a G (N d ) maximum value of 0.91 (top panel of Fig. 11) and 0.75% (bottom panel of Fig. 11) in the Northern and Southern Hemispheres, respectively; this occurs in summer in the N d range from 183 to 213.The value of G (N d ) reaches its hemisphere minimum value of 0.01 (top panel of Fig. 11) and 0.05% (bottom panel of Fig. 11) in winter in the Northern and Southern Hemisphere, respectively.
Figure 12 presents the calculated values of F1 (N d ) (bottom panel) and G (N d ) (top panel) that take into account the seasonal variations of the F1-layer and G condition occurrence probabilities in both hemispheres.One can see that this averaging leads to the G condition occurrence probability maximum value of 0.87% in summer in the N d range from 183 to 213.The minimum of G (N d ) is located in winter in the N d interval 332-366.
Ionosonde f of2 measurements from the Argentine Islands ionozonde station for 1971-1981 were analyzed by Wrenn et al. (1987).Wrenn et al. (1987) distinguished geomagnetic activity levels as very quiet, quiet, normal, disturbed and very disturbed conditions; they found that the large negative ionospheric storm effect in NmF2 during very geomagnetically disturbed conditions, is usually observed in summer.The dominance of NmF2 negative storm effects in summer compared to winter was shown by Putz et al. (1990) for three European stations.At Stanford, USA, in summer, the negative effects were much larger than the positive ones (Titheridge and Buonsanto, 1988) and, in winter, positive effects dominate (Putz et al., 1990;Titheridge and Buonsanto, 1988).A decrease in the [O]/[N 2 ] and [O]/[O 2 ] thermospheric ratios at high and middle latitudes during geomagnetic storms has been suggested as the cause of the negative phase for many years; this has been demonstrated clearly with satellite data (Prolss, 1995).As is well known (for more details see Sect.4.1), this ratio decrease is caused by magnetic storm equatorward winds from high latitudes to the geomagnetic equator; this mechanism is especially effective in the summer hemisphere where the quiet mid-latitude circulation is already equatorward (Fuller-Rowell et al., 1996).The boundary between N 2 and O 2 geomagnetic storm enrichment and N 2 and O 2 geomagnetic storm depletion is sharper and lies at higher latitude in winter as compared with summer (Prolss, 1995;Richmond and Lu, 2000).
During daytime, N mF2 is approximately proportional to [O]/L and the [O]/[N 2 ] and [O]/[O 2 ] ratio decreases determine decreases in N mF2.As a result, the seasonal behaviour of the G condition occurrence probability is found to be related to the seasonal behaviour of the F1-layer and the N mF2 negative disturbance occurrence probability.

Conclusions
The primary goal of the present work is to find the statistical relationships of the G condition occurrence probability with geomagnetic and solar activity indices K p and F10.7, season and geomagnetic latitude, using experimental data acquired by the Ionospheric Digital Database of the National Geophysical Data Center, Boulder, Colorado, from 1957 to 1990.The F1-layer is included in our analysis because the G condition cannot exist in the ionosphere if there is no the F1layer.During ionospheric disturbances, the N mF2 decrease leads to an increase in the G condition occurrence probability if the F1-layer exist, and, as a result, relationships exist between the G condition and N mF2 negative disturbance occurrence probabilities; these are studied in this paper.
We found that the G condition occurrence probability reveals a strong increase with the increase of K p whereas variations in the F1-layer occurrence probability do not show significant changes with the K p variations.It is shown that the dependence of the G condition occurrence probability on K p is mainly determined by processes that control the behaviour of the F2-layer with K p changes.The relationship for log G (K p ) versus K p fit well to a straight line.We found that increase of the minimum absolute value of the NmF2 negative disturbance amplitude leads to a decrease in the maximum and minimum values of the N mF2 negative disturbance occurrence probability and to an increase in the ratio of the maximum value of this probability to its minimum value, i.e. the N mF2 negative disturbance occurrence probability dependence shows the stronger positive K p tendency with the increase in the maximum absolute value of the NmF2 negative disturbance amplitude.
The decrease in the probability of observing the F1-layer occurs with the change from solar minimum to solar maximum.As far as the authors know, we found for the first time a positive tendency in the NmF2 negative disturbance occurrence probability dependencies on F10.7 for strong and very strong negative NmF2 disturbances, while the weak and normal NmF2 negative disturbances do not show any dependence of their occurrence probabilities on F10.7.The very interesting feature of the G condition is that the G condition occurrence probability is decreased as the value of F10.7 increases from low to middle values, reaches its minimum at the middle solar activity level of F10.7 = 144-170, followed by an increase when the F10.7 index increases from the middle solar activity level to F10.7 = 248-274.The dependence of the G condition occurrence probability on F10.7 contains contributions from two sources, the F1 and F2-layers.The main source that contributes to the dependence of the G condition occurrence probability on F10.7, at low solar activity, is the dependence of the F1-layer occurrence probability on F10.7, while at high solar activity, the dependence of the NmF2 negative disturbance occurrence probability on F10.7 for strong and very strong negative NmF2 disturbances is found to be more efficient in maintaining the G condition against the F1-layer F10.7 trend that tends to decrease the G condition occurrence probability.We found that, at least in part, the F10.7 trends in the probabilities of strong and very strong NmF2 negative disturbances can arise from the K p trends in the probabilities of these NmF2 negative disturbances.
Our results clearly show latitude dependence in the weak, normal, strong and very strong NmF2 negative disturbance occurrence probabilities, reproducing the tendency for decreased probabilities at low latitudes and increased probabilities at high latitudes.It is found that the F1-layer occurrence probability has a minimum value of 2.1-6.4% in the magnetic latitude range from −15 • to 15 • , close to the magnetic equator.The value of the F1-layer occurrence probability reaches 15.4-15.8% at magnetic latitudes 30-75 • in the Northern Hemisphere and 9.4-11.8% in the magnetic latitude range from −30 to −75 • in the Southern Hemisphere.
The magnetic latitude trend in the F1-layer occurrence probability is found to be in agreement with previous F1-layer studies (Cummack, 1961;Polyakov et al., 1968;Ratcliffe, 1972) based on a more limited data set.However, as far as the authors know, we found for the first time that the F1-layer occurrence probability has asymmetrical variation relative to the geomagnetic equator.
Our calculations show an increase in the G condition occurrence probability in the both hemispheres as one goes from middle to high latitudes and a deep minimum of the G condition occurrence probability in the low magnetic latitude range from −30 • to 30 • .Interhemispheric asymmetry is found for the G condition occurrence probability in the ionosphere, with stronger enhancement in the magnetic latitude range close to the Northern magnetic pole.
In agreement with the previous F1-layer studies (Polyakov et al., 1968;Ratcliffe, 1972;Shchepkin et al., 1984) based on a limited data set, our results provide additional evidence that the probability that the F1-layer will be formed is greater in summer than in winter.However, as far as the authors know, we found for the first time that the Northern Hemisphere peak F1-layer occurrence probability exceeds that in the Southern Hemisphere.
We found that the G condition occurrence probability maximum value of 0.91 and 0.75% in the Northern and Southern Hemispheres, respectively, occurs in summer.It is shown that the G condition occurrence probability reaches its hemisphere minimum value of 0.01 and 0.05% in winter in the Northern and Southern Hemisphere, respectively. Fig.1

Fig. 1 .
Fig. 1.The dependence of the F1-layer (bottom panel), G condition (middle panel) and NmF2 negative disturbance (top panel) probability functions on the 3-h geomagnetic activity index K p . Fig.2

Fig. 2 .
Fig. 2. The statistical relationship (circles) and linear approximation (solid line) for log G (K p ) versus K p . Fig.3

Fig. 3 .
Fig. 3.The dependence of the N mF2 negative disturbance probability functions on the 3-h geomagnetic activity index K p for the values of the N mF2 negative disturbance amplitude δ ≤ −0.1 (top panel), δ ≤ −0.3 (middle panel) and δ ≤ −0.5 (bottom panel).

Fig. 5 .
Fig. 5.The dependence of the F1-layer (bottom panel), G condition (middle panel) and NmF2 negative disturbance (top panel) probability functions on the daily solar activity index F10.7. Fig.6

4. 3
Figure8displays the histograms of the dependence of the F1-layer (bottom panel), the G condition (middle panel) and NmF2 negative disturbance (top panel) percentage occurrence on the geomagnetic latitude for the Northern (ϕ > 90 • ) and Southern (ϕ < 90 • ) Hemispheres separately.The first thing to note is that the F1-layer occurrence probability has a minimum value of 2.1-6.4% in the magnetic latitude range from -15 • to 15 • , close to the magnetic equator.The value of F1(ϕ) reaches 15.4-15.8% at the magnetic latitudes 30-75 • in the Northern Hemisphere and 9.4-11.8% in the magnetic latitude range from −30 to −75 • in the Southern Hemisphere.We found the Northern Hemisphere F1(ϕ) peak value of 8.5% at the magnetic latitudes 75-90 • and the Southern Hemisphere F1(ϕ) peak value of 21.2% in the magnetic latitude range from −75 • to −90 • .It is necessary to point out that the trend in F1(ϕ) is in agreement with the previous F1-layer studies(Cummack, 1961;Polyakov et al., 1968;Ratcliffe, 1972) based on a more limited data set.At the same time, as far as the authors know, we found for the first time that the magnetic latitude variation of the F1-layer occurrence probability is asymmetrical relative to the geomagnetic equator.The probabilities δ≤−0.1 (ϕ), δ≤−0.3 (ϕ), and δ≤−0.5 (ϕ) of the NmF2 negative disturbance occurrence are shown in the top, middle, and bottom panels of Fig.9, respectively.The top panels of Fig.8 and 9show that the NmF2 negative disturbance occurrence probabilities δ<0 (ϕ) and δ≤−0.1 (ϕ) have minimum values of 46.9-47.0%and 19.8-21.6%,respectively, in the same low latitude range from −15 • to 15 • and their dependence on the geomagnetic latitude is approximately symmetric with respect to the magnetic equator.Our results clearly show the latitude dependence of δ≤δ0 (ϕ), reproducing the tendency for decreased δ≤δ0 (ϕ) at low latitudes and increased

4. 4
Figures 10 and 11 show histograms of the seasonal dependence of the F1-layer and G condition percentage occurrence for the Northern (top panels) and Southern (middle and bottom panels) Hemispheres, respectively, where n d is the number of a given day in a year.Comparison of the top and middle panels of Figs. 10 and 11 shows that the seasonal components of each hemisphere are about 6 months out of phase.

Fig. 10 .
Fig. 10.The dependence of the F1-layer probability function on a number, n d , of a given day of year for the Northern (top panel) and Southern (middle panel) Hemispheres.The seasonal components of each hemisphere are about 6 months out of phase.As a result, to compare the F1-layer probability function seasonal effects in the Northern (top panel) and Southern (middle panel) Hemispheres we compare the dependence of the F1-layer probability function on N d in both hemispheres, where the value of N d is calculated as N d = n d +183 for 0 ≤ n d ≤ 183 and N d = n d −183 for n d >183 in the Southern Hemisphere.The bottom panel shows the resulting dependence of the F1-layer probability function on N d for the Southern Hemisphere.In the Northern Hemisphere, the value of N d is the same as n d , i.e.F1 (N d ) = F1 (n d ). Fig.11

Fig. 11 .
Fig. 11.The dependence of the G condition probability function on a number, n d , of a given day in a year for the Northern (top panel) and Southern (middle panel) Hemispheres.The seasonal components of each hemisphere are about 6 months out of phase.As a result, to compare the G condition probability function seasonal effects in the Northern (top panel) and Southern (middle panel) Hemispheres we compare the dependence of the G condition probability function on N d in both hemispheres, where the value of N d is calculated as N d = n d + 183 for 0 ≤ n d ≤ 183 and N d = n d −183 for n d > 183 in the Southern Hemisphere.The bottom panel shows the found dependence of the G condition probability function on N d for the Southern Hemisphere.In the Northern Hemisphere, the value of N d is the same as n d , i.e.G (N d ) = G (n d ). Fig.12

Fig. 12 .
Fig. 12.The seasonal dependence of the F1-layer (bottom panel), and G condition (top panel) probability functions in both hemispheres.