Annales Geophysicae Anomalous variations of Nm F 2 over the Argentine Islands : a statistical study

We present a statistical study of variations in the F2-layer peak electron density, NmF2, and altitude,hmF2, over the Argentine Islands ionosonde. The critical frequencies,foF2, and,foE, of the F2 and E-layers, and the propagation factor,M(3000)F2, measured by the ionosonde during the 1957–1959 and 1962–1995 time periods were used in the statistical analysis to determine the values of NmF2 and hmF2. The probabilities to observe maximum and minimum values ofNmF2 andhmF2 in a diurnal variation of the electron density are calculated. Our study shows that the main part of the maximum diurnal values of NmF2 is observed in a time sector close to midnight in November, December, January, and February exhibiting the anomalous diurnal variations of NmF2. Another anomalous feature of the diurnal variations ofNmF2 exhibited during November, December, and January when the minimum diurnal value of NmF2 is mainly located close to the noon sector. These anomalous diurnal variations ofNmF2 are found to be during both geomagnetically quiet and disturbed conditions. Anomalous features are not found in the diurnal variations of hmF2. The statistical study of theNmF2 winter anomaly phenomena over the Argentine Islands ionosonde was carried out. The variations in a maximum daytime value, R, of a ratio of a geomagnetically quiet daytime winter NmF2 to a geomagnetically quiet daytime summer NmF2 taken at a given UT and for approximately the same level of solar activity were studied. The conditional probability of the occurrence of R in an interval ofR, the most frequent value of R, the mean expected value of R, and the conditional probability to observe the F2-region winter anomaly during a daytime period were calculated for low, moderate, and high solar activity. The calCorrespondence to: A. V. Pavlov (pavlov@izmiran.ru) culations show that the mean expected value of R and the occurrence frequency of the F2-region winter anomaly increase with increasing solar activity.


Introduction
The Argentine Islands ionosonde station (65.2 • S, 295.7 • E) has a high geographic latitude, but due to the offset of the geographic and geomagnetic poles and the difference between the geomagnetic field center and the Earth's center, it is a geomagnetically mid-latitude station in terms of its geomagnetic coordinates (see Wrenn et al., 1987, and Sect. 2 of this paper).As a result, the ionosphere over the Argentine Islands ionosonde station exhibits certain high-latitude characteristics (near 24 h daylight during local summer months) and certain mid-latitude characteristics (Sojka et al., 1988;Pavlov et al., 2008a, b).This creates an extreme set of physical conditions and resulting anomalous diurnal variations of the F2-layer peak electron density, NmF2, when a maximum value of NmF2 is displaced from the expected mid-latitude noon sector to a sector close to midnight (Wrenn et al., 1987;Sojka et al., 1988;Pavlov et al., 2008a, b).It should be noted that such anomalous diurnal variations of NmF2 are observed not only by the Argentine Islands ionosonde station.This unusual phenomenon observed in the Southern Hemisphere is known as the Weddell Sea Anomaly in NmF2 (see Horvath, 2007, and references therein).
As far as the authors know, there are no published studies of statistical relationships of these anomalous diurnal variations of NmF2 with season and geomagnetic activity levels.The first purpose of this work is to study, for the first time, these statistical relationships in terms of occurrence probabilities using the critical frequency, foF2, of the F2layer measured by the Argentine Islands ionosonde station and provided by the Ionospheric Digital Database of the National Geophysical Data Center in Boulder, Colorado.Such a study presented in our work is important to identify potential mechanisms for these anomalous diurnal variations of NmF2.
The F2-region winter anomaly is a well-known phenomenon when the F2-layer peak electron density is greater in winter than that in summer at the same point in time over the same Earth's surface point for geomagnetically quiet daytime conditions, despite the reduced solar insolation in winter in comparison with that in summer (e.g.Croom et al., 1960;King, 1961;Torr and Torr, 1973;Millward et al., 1996;Zou et al., 2000;Rishbeth et al., 2000;Tao Yu et al., 2000;Pavlov andPavlova, 2005, 2008a, b).The winter/summer variations in the foF2 monthly noon medians were studied by Torr and Torr (1973) using the data of 140 ionosondes in 1958, 1964, and 1969.It follows from this study that the winter anomaly phenomenon in the foF2 monthly noon medians is more pronounced in the Northern Hemisphere than in the Southern Hemisphere and the region of existence and magnitude of the winter anomaly decrease with decreasing solar activity.The mechanisms of formation of the winter-summer variations in NmF2 over the Millstone Hill radar and Argentine Island ionosonde, whose locations are approximately magnetically conjugate, were studied for the geomagnetically quiet daytime conditions of 2-3 June 1979 and 5-6 January 1980 at high solar activity, and 15-17 January 1985 and 10-13 July 1986 at low solar activity (Pavlov and Pavlova, 2005a, b).They found that the phenomenon of NmF2 winter anomaly is observed by the Millstone Hill radar, whereas this event is not observed by the Argentine Islands ionosonde, except of one instant of time (close to noon) in the comparison of the 2 June 1979 and 5 January 1980 diurnal variations of foF2 measured by the Argentine Islands ionosonde.The second purpose of this work is to carry out the first statistical study of the NmF2 winter anomaly over Argentine Islands using the Argentine Islands ionosonde measurements of foF2 to find, for the first time, a probability to observe the winter anomaly in NmF2 and an average amplitude of the NmF2 winter anomaly at solar minimum, at moderate solar activity, and at solar maximum.

Data
Our analysis is based on hourly foF2 data measured by the Argentine Islands station (65.2 • S, 295.7 • E) during the 1957-1959 and 1962-1995 time periods (month median foF2 are not used in this work).The foF2 data are available by Internet from the Ionospheric Digital Database of the National Geophysical Data Center, Boulder, Colorado.It should be noted that the value of NmF2 is related to foF2 as where the unit of NmF2 is m −3 , the unit of foF2 is MHz.
To determine the ionosonde value of the F2-layer peak altitude, hmF2, the relation between hmF2 and the values of foF2, the dimensionless ionospheric propagation factor, M(3000)F2, and the critical frequency, foE, of the E-layer recommended by Dudeney (1983) is used as where M=0.253/(foF2/foE−1.215)−0.012, the unit of hmF2 is km, and the units of foF2 and foE are the same.
If there are no foE data then it is suggested that M=0, i.e. the hmF2 formula of Shimazaki (1955) is used.
When the thermosphere is disturbed, the time it takes to relax back to its initial state, this thermosphere relaxation determines the time for the disturbed ionosphere to relax back to the quiet state, and the values of NmF2 and hmF2 at given UT with 3-h geomagnetic index, K p ≤3, cannot always be considered as geomagnetically quiet NmF2 and hmF2.The characteristic time of the neutral composition recovery after a storm impulse event ranges from 7 to 12 h on average (Hedin, 1987), while it may need 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 believe that the values of NmF2 and hmF2 at given UT are the geomagnetically quiet ionospheric parameters if K p ≤3 at UT under consideration and for 24-h time period prior to given UT.
We use an eccentric tilted dipole approximation for the geomagnetic field (Fraser-Smith, 1987;Deminov and Fishchuk, 2000) to calculate the geomagnetic latitude and longitude of the ionosonde station which values depend on a year.The limits of the geomagnetic latitude and longitude year changes are calculated to be (−51.70±0.27)• and (7.76±0.83)• , respectively, and the McIlwain parameter, L, is changed from 2.677 to 2.786.

Statistical study of NmF2 and hmF2 diurnal variations: results and discussion
The value of NmF2 reaches its minimum, NmF2 min , and maximum, NmF2 max , values, and the F2-layer peak altitude is changed between its minimum, hmF2 min , and maximum, hmF2 max , values for each time period from 00:00 UT to 24:00 UT where UT is the universal time.The solar local time is related with UT as where λ is the geographic longitude, the unit of measurements of λ is degree, SLT and UT come in units of hours.The differences of locations in SLT of the maximum and minimum values of NmF2 and hmF2 determine differences between mid-latitude diurnal variations of NmF2 and hmF2.We calculate a probability to observe each value of Y=NmF2 min , NmF2 max , hmF2 min , hmF2 max in 2 intervals of a maximum 3-h geomagnetic index K p for 24-h time period prior to and including SLT where the value of Y under study is observed: K max p ≤3 (it is labeled as "geomagnatically quiet conditions") and K max p >3 (it is labeled as "geomagnetically disturbed conditions").Each value of NmF2 min , NmF2 max , hmF2 min , and hmF2 max is tested individually for each time period from 00:00 UT to 24:00 UT to label it as a geomagnetically quiet or geomagnetically disturbed value.
For each specified values of K max p and SLT, we determine a number, N min (M, K max p , SLT), of the NmF2 min observations and a number, N max (M, K max p , SLT), of NmF2 max observations in a given month of M provided the value of K max p was located within the interval specified (K max p >3 or K max p ≤3).The probability, N , to observe NmF2 max and the probability, P N , to observe NmF2 min at given SLT during a diurnal time period (from 00:00 UT to 24:00 UT) in a chosen month of M during geomagnetically quiet or geomagnetically disturbed conditions, are determined as where N (M, K max p ) is a number of days in a chosen month of M when the ionosonde measurements of NmF2 were carried out provided the value of K max p is located within the interval specified (K max p >3 or K max p ≤3).The F2-layer peak altitude is changed between its minimum, hmF2 min , and maximum, hmF2 max , values for each time period from 00:00 UT to 24:00 UT.For a given month in a year, we calculate a number, H min (M, K max p ,SLT), of the hmF2 min observations and a number, H max (M, K max p ,SLT), of the hmF2 max observations in a given month of M provided the value of K max p is located within the interval specified (K max p >3 or K max p ≤3).The probability, h , to observe hmF2 max and the probability, P h , to observe hmF2 min at given SLT during a diurnal time period (from 00:00 UT to 24:00 UT) in a chosen month of M during geomagnetically quiet or geomagnetically disturbed conditions, are determined as where H (M, K max p ) is a number of days in a chosen month of M when the ionosonde measurements of M(3000)F2 were carried out provided the value of K max p was located within the interval specified (K max p ≤3 or K max p >3).The results of calculations of N and P N are shown in Figs. 1 and 2, respectively, for each month in a year.In each panel of Figs.1-2, solid and dashed lines correspond to quiet (K max p ≤3) and disturbed (K max p >3) conditions, respectively.We consider that mid-latitude diurnal variations of NmF2 are anomalous for a month in a year if the F2-layer peak electron density reaches its minimum value close to the noon sector, or the F2-layer peak electron density maximum is located in a time sector close to midnight.On the bases of these features, we conclude from Figs. 1 and 2 that, in the main, NmF2 does not exhibit anomalous diurnal variations in April, May, June, July, August, and September.As the model calculations show, during these months the maximum value of NmF2 is mainly located in the sector close to the minimum value of the solar zenith angle, χ, and a main peak of P N is displaced from a peak of N to larger solar zenith angles (to calculate the solar zenith angle we use the Fortran subroutine soco taken from the IRI2007 model at ftp: //nssdcftp.gsfc.nasa.gov/models/ionospheric/iri/iri2007/).In November, December, January, and February, the maximum value of NmF2 is not primarily observed in a time sector close to noon.Furthermore, the minimum value of the F2layer peak electron density is observed mainly close to the noon sector during November, December, and January (see Fig. 2).We conclude that the diurnal variations of NmF2 are anomalous in November, December and January and these diurnal variations are partially anomalous in February.The changeover from the November and February diurnal variations of NmF2 to those in April and September occurs in March and October, respectively.The difference between the quiet and disturbed values of N (see solid and dashed lines in Fig. 1) and the difference between P N for K max p ≤3 and that for K max p >3 (see solid and dashed lines in Fig. 2) can be produced by the difference in the wind-induced plasma drift and neutral densities between quiet and disturbed conditions.
Figure 3 shows the calculated values of P h (solid lines and squares) and h (dashed and dotted lines) at SLT for K max p ≤3 (solid lines and squares) and K max p >3 (dashed and dotted lines) for each month in a year.As Fig. 3 shows, the diurnal variations of hmF2 over the Argentine Islands correspond to the normal diurnal variations of hmF2 observed at middle latitudes.The F2-layer peak altitude is mainly lowest close to midday because the thermospheric wind blows poleward and forces ions and electrons down the field lines.Conversely, close to midnight the thermospheric wind blows away from the pole to the equator forcing the ionospheric plasma up the field lines and consequently increasing hmF2.

May June
July August September  variations in the production rates of O + ions during the main part of a daytime period, and the main part of these diurnal variations of NmF2 is caused by changes in the neutral wind-induced plasma drift along magnetic field lines and by neutral densities variations.A poleward neutral wind causes a lowering of the F2-region height and a resulting reduction of NmF2 due to an increase in the loss rate of O + ( 4 S) ions in the chemical reactions of these ions with unexcited and vibrationally excited N 2 and O 2 , whereas a wind, which is equatorwards, tends to increase the value of NmF2 by transporting the plasma up along field lines to regions of lower chemical loss of O + ( 4 S) ions.It follows from Fig. 3 that, close to the noon sector, the F2-layer is lowered into an altitude region of higher recombination rates of O + ( 4 S) ions leading to lower NmF2 values.Close to the midnight sector, the F2-layer is raised and maintained by this plasma drift.As the ionosphere is sunlit during the long summer day in January and December, the value of NmF2 is increased leading to the observed higher anomalous NmF2 values close to midnight.This mechanism of the formation of the anomalous diurnal variations of NmF2 over the Argentine Islands is supported by the model simulations of the monthly diurnal Fig. 2. A probability, P N , of the minimum NmF2 value occurrence at SLT for K max p ≤3 (solid lines) and K max p >3 (dashed lines) in diurnal variations of NmF2 measured at the Argentine Islands ionosonde station for January, February, and March, April, May, June, July, September, October, November, and December.variations for the geomagnetically quiet conditions at several levels of solar cycle (Sojka et al., 1988) and by the comparison between the measured and modeled NmF2 during the 5-6 January 1980 and 15-17 January1985 geomagnetically quiet time periods at solar maximum and minimum (Pavlov et al., 2008a, b).
The maximum value of N is located close to midnight in February and in November while t d =14:16-17:30 in February and t d =16:28-19:57 in November.It appears reasonable to assume that this daytime duration is large enough to provide the mechanism of the February and November anomalous diurnal variations of NmF2 described above for January and December.It should be noted that, contrary to January, November, and December, the majority of the minimum values of P N is not observed close to the noon sector in February (see Fig. 2).The difference between the February and November diurnal variations of N and P N is an evidence in favour of a difference between February and November thermospheric circulations during geomagnetically quiet conditions.
Month averages of NmF2 min , hmF2 min , NmF2 max , and hmF2 max are the observed characteristic of the anomalous diurnal variations of NmF2.
Fig. 3.A probability, P h , of the minimum hmF2 value occurrence (solid lines and squares) and a probability, h , of the maximum hmF2 value occurrence (dashed and dotted lines) at SLT for K max p ≤3 (solid lines and squares) and K max p >3 (dashed and dotted lines) in diurnal variations of hmF2 measured at the Argentine Islands ionosonde station for January, February, and March, April, May, June, July, September, October, November, and December.conditions taking into consideration three different F10.7 solar activity index relative labels: "low, moderate, and high solar activity", for which we use F10.7<100, 100≤F10.7≤170, and F10.7>170, respectively.Average values of NmF2 min and NmF2 max for a given value of M, quiet and disturbed conditions, and low, moderate, and high solar activity levels are determines as where N (M, K max p ,F10.7) is a number of days in a chosen month in a year when the ionosonde measurements of NmF2 were carried out provided the values of K max p and F10.7 were located within the intervals specified, SN min (M, K max p ,F10.7) and SN max (M, K max p ,F10.7) are sums of NmF2 min and NmF2 max , respectively, for chosen values of M, K max p , and F10.7.We determine average values of hmF2 min and hmF2 max for a given month in a year, 2 intervals of K max p , and 3 intervals of F10.7 as Table 1.The month averages of NmF2 min , hmF2 min (first numbers), and NmF2 max , hmF2 max (second numbers) found from the measurements of the Argentine Island ionosonde station during the geomagnetically quiet and disturbed conditions for low, moderate, and high solar activity in January, February, November, and December.
where H (M, K max p ,F10.7) is a number of days in a chosen month in a year when the ionosonde measurements of M(3000)F2 were carried out provided the values of K max p and F10.7 were located within the intervals specified, SH min (M, K max p ,F10.7) and SH max (M, K max p ,F10.7) are sums of hmF2 min and hmF2 max , respectively, for chosen values of M, K max p , and F10.7.Table 1 shows the calculated values of <NmF2 min >, <NmF2 max >, <hmF2 min >, <hmF2 max >, for January, February, November, and December when the anomalous diurnal variations of NmF2 are observed.As Table 1 shows, during the geomagnetically quiet conditions the <NmF2 max >/<NmF2 min > ratio is equal to 2.7-2.9,1.8-2.3,2.1-2.5, 2.8-3.1 in January, February, November, and December, respectively, and an increase in solar activity leads only to a weak decrease in the <NmF2 max >/<NmF2 min > ratio in February, November, and December, while this ratio is approximately the same in January for moderate and high solar activity.It is seen from Table 1 that the average geomagnetic storm and substorm response is negative in <NmF2 min > and <NmF2 max >, except of February and November for low solar activity and February for moderate solar activity when a change of the geomagnetic activity level from K max p ≥3 to K max p <3 causes a reduction in <NmF2 max >.The differences in the wind-induced plasma drift and neutral densities between quiet and disturbed conditions are responsible for the difference between the quiet and disturbed values of <NmF2 min > and <NmF2 max >.As it was shown above, the diurnal variations of hmF2 are not anomalous.It is only worth noting that the value of <hmF2 max > for K max p ≥3 is greater than that for K max p <3.This increase in <hmF2 max > can be interpreted as a result of an increase in the strength of the average wind-induced plasma drift.
Soft particle precipitation can be suggested as a mechanism in changing the diurnal variations of NmF2 under investigation.The bombardment of the atmosphere by low energy electrons causes diffuse aurora which is located in the region near the equatorward edge of the auroral oval (Feldstein and Galperin, 1985;Horwitz et al., 1986).However, only a part of the low energy electrons with energies less than or equal to about 2-5 eV is mainly effective for producing ionization at F-region altitudes (Rees, 1964).Nevertheless, it is possible to suggest that this low energy electron participation produces additional ionization in the F2-region over the Argentine Islands and a part of the studied diurnal variations of N and P N .Soft electrons, with energy greater than 1.97 eV, excite the atomic oxygen to the D level by collisional impact at F2region altitudes (where atomic oxygen is the dominant neutral gas constituent) leading to an increase in the intensity of the 630 nm atomic oxygen emission.As far as the authors know, there are no published papers where this optical manifestation of such bombardment of the atmosphere at the F2-region altitudes for geomagnetically quiet conditions would discussed.Therefore, an argument against ionization of neutral species by soft electrons as a part of a source of the geomagnetically quiet diurnal variations of N and P N is that such ionization would be accompanied by strong airglow emissions at 630 nm.
It follows from the DE 1 and 2 spacecraft measurements that the most probable equatorial boundary location of low energy electrons (100 eV) of diffuse aurora corresponds to the McIlwain parameter L=L eq =8.02, 7.18, 6.34, 5.50 for K p =0, 1, 2, 3, respectively, in the 15:00-24:00 MLT sector (Horwitz et al., 1986).The value of L eq >3.16 for K p ≤3.75 during all the DE 1 and 2 spacecraft measurements, and, L eq ≥3.34 for K p ≤4.75, except of only two measurements with L eq ≈3.16 (see Fig. 6 of Horwitz et al., 1986).Thus, the Argentine Islands ionosonde cannot be located in a region of low energy electron precipitation during geomagnetically quiet conditions for K p ≤3.The electron bombardment of the atmosphere cannot be invoked to account for the studied diurnal variations of N and P N for K max p ≤3.
Precipitation of low energy electrons (∼1-2 keV) was recorded by instruments on board the Aureol-1, 2 satellites.The empirical model produces the equatorward boundary of this precipitation region at L=3.78-9.90 for K p =00:00-03:00 and 00:00-07:00 MLT, and these results agree with the data from the DMSP satellites (Galperin et al., 1997).It should be noted that low energy electron fluxes measured by the instruments on board the Aureol-1, 2 satellites in the region of the main ionospheric trough of the subauroral ionosphere in the sector of 18:00-24:00 MLT were very weak, and, there were no significant resulting additional ionization of the F2-region (Lissakov et al., 1985).Therefore, not all low energy electron precipitations can produce noticeable variations of the F2-region electron density even if these low energy electron precipitations exist.If there are measurements of soft electron precipitations or increases in the 630 nm emission caused by these precipitations during geomagnetically disturbed conditions at middle geomagnetic latitudes, then it is necessary to study the relative role of these electrons as a possible source of variations in NmF2 in each case.

Statistical study of the NmF2 winter anomaly: results and discussion
In the Southern Hemisphere, the December and June solstices are usually considered to be centre points of the local summer and winter seasons, respectively.Therefore, we compare NmF2 measured during December and June while January NmF2 measurements are compared with those measured during July to reach 6 month difference between summer and winter months.The study of the F2-region winter anomaly carried out in this work, is based on the comparison of geomagnetically quiet daytime values of NmF2 (see Sect. 2) at given UT when χ<90 • .To reach approximately the same level of the solar activity for summer and winter days, the difference between the winter and summer daily F10.7 solar activity indexes is taken to be less or equal to 20 in the statistical analysis.On the other hand, the value of NmF2 is a function of production and loss rate of unexcited and electronically excited O + ions (see, e.g., Pavlov and Pavlova, 2005).As a result, the F2-layer peak electron density depends on the neutral temperature and densities whose values are functions of F10.7 solar activity index for a previous day (Hedin, 1987).Hence, we find a difference between F10.7 solar activity indexes for days preceding the winter and summer days examined.If this difference is less or equal to 20, then these winter and summer days are taken into consideration.The F2-region winter anomaly is determined by the ratio r = NmF2(W, UT, F10.7)/NmF2(S, UT, F10.7), ( 8) where NmF2(W ,UT,F10.7) and NmF2(S,UT,F10.7) are geomagnetically quiet daytime winter and summer values of NmF2, respectively, described above.
If there are several values of NmF2(S,UT,F10.7) arranged in order of increasing a number of a day in a month for a given value of NmF2(W ,UT,F10.7),then only the first one is used in the statistical analysis.
It should be noted that the mid-latitude ionosphere exhibits considerable day-to-day variability in NmF2 during geomagnetically quiet conditions under similar solar activity conditions at all local times for each month (Forbes et al., 2000;Rishbeth and Mendillo, 2001).The origins of this ionospheric variability are discussed in detail by Forbes et al. (2000) and Rishbeth and Mendillo (2001).This day-today variability of NmF2 results in a variability of r, and the statistical methods are required to be used in the study of the NmF2 winter anomaly.
A dependence of r on UT has a maximum value R=r max during each daytime period under consideration at some value of UT.The F2-region winter anomaly occurs during a daytime period for given F10.7 and chosen winter and summer months if R>1.The statistical study of this phenomena is carried out taking into consideration three different daily F10.7 solar activity index relative labels: "low, moderate, and high solar activity", for which we use F10.7<100, 100≤F10.7≤170, and F10.7>170, respectively.To determine these solar activity intervals, we employ F10.7 index corresponding to a winter day.A difference between F10.7 indexes for summer and winter days used in each calculation of r is taken to be less or equal to 20.
To study the distribution of R in amplitude, we split the range of R into intervals of the same length, R=0.2.The conditional probability, Q(R), of the occurrence of R in an interval of R is determined as a ration of a number of R with amplitudes in a given range to a number of R including all amplitudes of R provided the value of F10.7 was located within the interval specified.Figure 4 shows the calculated value of Q(R) for high (solid lines), moderate (dashed lines), and low (dotted lines) solar activity on the base of the December and June foF2 data set (left panel) and the January and July foF2 data set (right panel).It is seen from Fig. 4 that the solid, dashed, and dotted lines of each panel do not differ greatly in appearance.The most frequent value, R MF , of R is an amplitude where the maximum of Q(R) is achieved.As Fig. 4 shows this maximum of Q(R) is sharply pronounced.The value of R MF is the same for low, moderate, and high solar activity if the December and June foF2 data set is used (see Fig. 4 and Table 2).The use of the January and July foF2 data set leads us to conclude that the most frequent value of R at low solar activity coincides with that at high solar activity and is slightly less than that at middle solar activity (see Fig. 4 and Table 2).The mean value of expectation of R (the average) is defined by where R k =(k−0.5)R.
The results of calculations presented in Table 2 show that the magnitude of <R> decreases with decreasing solar activity.It follows from Table 2 that the value of <R> exceeds the value of R MF .Nevertheless, this difference is not very large because the conditional probability distribution Q(R) is not strongly skewed (see Fig. 4).It follows from Table 2 that the value of <R> is less than 1 for low and moderate solar activity when the probability to observe the NmF2 winter anomaly is changed between 8.4% and 35.4%.We conclude that a comparison of the winter/summer values of <R> cannot be a criterion of the absence of the NmF2 winter anomaly.
The conditional probability, Q(R>1), to observe the F2region winter anomaly during a daytime period can be determined as a ratio of the number of R>1 to the number of R including all amplitudes of R provided the value of F10.7 Table 2.The conditional probability, Q(R>1), to observe the F2region winter anomaly during a daytime period, the most frequent value, R MF , of R, and the expected value, <R>, of R found from the measurements of the Argentine Island ionosonde station during the geomagnetically quiet conditions for low, moderate, and high solar activity.

December and June
January and July We use the hourly foF2 data measured by the Argentine Islands station during the 1957-1959 and 1962-1995 time periods, and we consider that the seasonal anomaly in NmF2 exists in the ionosphere if the ratio r given by Eq. ( 8) exceeds 1.We calculate a number, S, of daytime periods when the seasonal anomaly in NmF2 is observed for given solar activity if the December and June foF2 or January and July data set is used.Among these anomalous events, we find numbers, S 1 and S 2 , of the seasonal anomaly events when r>1 only at one instant of time for S 1 and only at two instants of time for S 2 during a daytime period under consideration.We determine G 1 =S 1 /S and G 2 =S 2 /S and express these calculated values in percentage terms.It follows from the calculations that G 1 =86, 53, and 40% and G 2 =14, 24, and 28% at low, moderate, and high solar activity, respectively, if the December and June foF2 data are used.The calculated values of G 1 =85, 53, and 56% and G 2 =15, 24, and 25% correspond to the low, moderate, and high solar activity levels if the January and July measurements of foF2 are used.We conclude that the hourly foF2 measured by the Argentine Islands inosonde exhibit the winter anomaly mainly at one instant of time by day at low solar activity.On average, the winter anomaly duration is less at low solar activity than that at moderate solar activity or at high solar activity.
The NmF2 winter anomaly is often explained by the winter/summer changes in the [O]/[N 2 ] ratio (e.g.Millward et al., 1996;Zou et al., 2000;Rishbeth et al., 2000;Tao Yu et al., 2000).On the other hand, Zou et al. (2000) compared the coupled thermosphere-ionosphere-plasmasphere model (CTIP) results with ionosonde data from mid-latitudes for geomagnetically quiet conditions.Observed variations of the mid-latitude winter anomaly of NmF2 at solar maximum and the fact of the matter that the winter anomaly of NmF2 is stronger at solar maximum than at solar minimum are not successfully explained by the CTIP model (see pages 927 and 942 of Zou et al., 2000).Zou et al. (2000) concluded that these disagreements may be a consequence of the increase of F2-layer loss rate in summer in comparison with that in winter by vibrationally excited N 2 which is not included in the CTIP model.
Unexcited O + ( 4 S) ions that predominate at F2-region altitudes are lost in the reactions of O + ( 4 S) ions with vibrationally unexcited and vibrationally excited N 2 and O 2 .The fundamental laboratory measurements (Schmeltekopf et al., 1968;Hierl et al., 1997) show that vibrationally excited N 2 and O 2 react much more strongly with O + ( 4 S) ions than vibrationally unexcited N 2 and O 2 .The daytime mid-latitude electron density of the F2-region is decreased up to a factor of 2-3 due to vibrationally excited N 2 and O 2 (Pavlov, 1998;Pavlov et al., 1999;Pavlov and Foster, 2001;Prolss and Werner, 2002).As a result, a part of the mid-latitude F2layer winter anomaly can be attributed to the seasonal difference of the increase in the loss rate of O + ( 4 S) ions due to vibrationally excited N 2 and O 2 (Torr et al., 1980;Pavlov and Pavlova, 2005;Pavlov et al., 2008a, b).
Using the photoionization cross-section for atomic oxygen compiled by Richards et al. (1994) and the EUVAC solar flux model (Richards et al., 1994), we conclude that, during atomic oxygen photoionization, a part of oxygen ions, which is created in electronically excited states, is larger than that forming electronically unexcited O + ( 4 S) ions with the production rate, P EUV .These electronically excited oxygen ions are converted to N + 2 and O + 2 ions, and O + ( 4 S) ions in chemical reactions constituting a large daytime source, P ex , of O + ( 4 S) ions through chemical reactions (see, e.g., Pavlov and Pavlova, 2005).Neglect of electronically excited oxygen ions in model simulations, leads to inaccurate values of NmF2 while a difference between seasonal variations of P EUV +P ex and P EUV can lead to disagreements between values of r (see Eq. 8) found from ionosonde observations and model simulations.
The model simulations (Torr et al., 1980;Pavlov and Pavlova, 2005;Pavlov et al., 2008a, b) provide evidence that the mid-latitude winter/summer anomalous difference in NmF2 is produced, not only by seasonal changes in the [O]/[N 2 ] and [O]/[O 2 ] ratios, but also by seasonal variations in the N 2 and O 2 vibrational temperatures, and by an increase in the production rate of O + ( 4 S) ions in winter in comparison with that in summer due to chemical reactions of electronically excited O + ions as a source of O + ( 4 S) ions.A part of the mid-latitude F2-layer winter anomaly which can be attributed to seasonal variations of the vibrationally excited N 2 and O 2 temperatures and the production rate of O + ( 4 S) ions from electronically excited O + ions is decreased with declining solar activity from solar maximum to solar minimum (Pavlov et al., 2008a, b).This decrease in the relative role of these two sources of the NmF2 winter anomaly can be responsible for the decrease of Q(R>1) with decreasing solar activity over the Argentine Islands (see Table 2).At solar minimum, the mid-latitude winter anomaly of NmF2 is practically not produced by seasonal variations of the vibrationally excited N 2 and O 2 temperatures, and the role of electronically excited oxygen ions in producing the mid-latitude winter/summer anomalous difference in NmF2 is less than that caused by seasonal variations of neutral number densities (Pavlov et al., 2008b).We conclude that seasonal neutral composition variations are mainly responsible for the very low probability to observe the winter anomaly of NmF2 over the Argentine Islands at solar minimum shown in Table 2.
A statistical median of a set of numbers is one of statistical parameters used in statistical studies (e.g.Johnson and Leone, 1977).As a particular case of a general definition of a statistical median, a definition of a monthly median value, foF2(med), of foF2 at given UT measured by an ionosonde is presented by the URSI handbook of ionogram interpretation and reduction (1978).The values of foF2 measured during a month at given UT are sorted in such a way that their magnitude is increased from lowest value to highest value.An odd number of foF2 values under investigation leads us to determine foF2(med) as the middle value.The average of the  Torr andTorr, 1973, andZou et al., 2000).
Table 3 shows the arithmetical mean, <foF2(med)>, of the median values of foF2 at 16:00 UT (11:43 SLT) for January, June, July, and December calculated from the Argentine Island ionosonde foF2 data for low, moderate, and high solar activity during the 1957-1959 and 1962-1995 time periods.It follows from Table 3 that the winter anomaly of NmF2 is not observed over the Argentine Islands from the point of view of the winter/summer arithmetical mean median comparison.This wrong conclusion, which is in contradiction with our statistical study, shows the shortcomings of the median approach.As was pointed out above, even the winter/summer comparison of <R> cannot be used to prove the absence of the NmF2 winter anomaly.The statistical analysis carried out in this work leads us to find find the conditional probability to observe the F2-region winter anomaly during a daytime period.
The percentage, P q (med), of the geomagnetically quiet median values of foF2 at 16:00 UT presented in Table 3 is determined as a ratio of a sum of foF2(med) corresponding to geomagnetically quiet conditions to a sum of foF2(med) corresponding to geomagnetically quiet and disturbed conditions in a month for given solar activity.In agreement with our definition of a geomagnetically quiet value of an ionospheric parameter given in Sect.2, a value of foF2(med) determined as the middle value is considered as a geomagnetically quiet value if K p ≤3 for 24-h time period prior to and including UT (16:00 UT for the results of Table 3) where foF2(med) is taken.A value of foF2(med) calculated as the average of the two middle value is taken into consideration as a geomagnetically quiet value if K p ≤3 for each 24-h time period prior to and including UT for two middle values of foF2 used in calculations of foF2(med).The results of the calculations presented in Table 3 show that only a part of foF2(med) corresponds to geomagnetically quiet conditions, and the percentage of foF2(med) which does not correspond to geomagnetically quiet conditions is large enough.It is an argument against the use of foF2(med) in ionospheric studies instead of geomagnetically quiet foF2 without an examination if foF2(med) could be considered as a geomagnetically quiet value.

Conclusions
A statistical study of the diurnal variations of NmF2 and hmF2 over the Argentine Islands was carried out to reveal anomalous features in these variations and to study statistical relationships of the found anomalous diurnal variations with season and geomagnetic activity levels.The ionosonde measurements of foF2, M(3000), and foE during the 1957-1959 and 1962-1995 time periods were used in the statistical analysis.Probabilities to observe maximum and minimum values of NmF2 and hmF2 in a diurnal variation of the electron density are calculated.Diurnal variations of NmF2 are considered to be anomalous for a month in a year if the F2-layer peak electron density reaches its minimum value close to the noon sector, or the maximum in diurnal variations of NmF2 is located in a time sector close to midnight.It is found that, in the main, NmF2 do not exhibit anomalous diurnal variations in April, May, June, July, August, and September.Our calculations do not show anomalous features in the diurnal variations of hmF2 during each month in a year.
It is shown that, in November, December, January, and February, the main part of the maximum diurnal values of NmF2 is observed in a time sector close to midnight, while the minimum diurnal values of NmF2 are observed mainly close to the noon sector only during November, December, and January.It follows from the statistical study that these anomalous diurnal variations of NmF2 are observed during both geomagnetically quiet and disturbed conditions.Geomagnetic disturbance effects in the month averages of NmF2 max and NmF2 min are found to be negative in November, December, January, and February, except for February and November for low solar activity and February for moderate solar activity when these effects are positive.
Statistical data processing has been performed to study statistical characteristics of the F2-region winter anomaly phenomena over the Argentine Islands inosonde.We compare NmF2 measured during January (local summer) and July (local winter), and December NmF2 measurements (local summer) with those during June (local winter).Changes in a maximum daytime value R of a ratio of a geomagnetically quiet daytime winter NmF2 to a geomagnetically quiet daytime summer NmF2 taken at a given UT and for approximately the same level of solar activity were studied.The conditional probability of the occurrence of R in an interval of R, the most frequent value R MF of R, the mean expected value <R> of R, and the conditional probability Q(R>1) to observe the F2-region winter anomaly during a daytime period were calculated for low, moderate, and high solar activity.The calculations show that R MF =0.7-0.9, <R>=0.67-1.09,and Q(R>1)=8.4-41.7%.The data sets provide evidence that the mean expected value of R and the occurrence frequency of the F2-region winter anomaly increase with increasing solar activity.We found that the hourly foF2 measured by the Argentine Islands ionosonde exhibit the NmF2 winter anomaly mainly at one instant of time by day at low solar activity, and the probability to observe this anomaly at two moments in time by day is found to be negligible at low solar activity.The hourly Argentine Islands ionosonde measurements of foF2 show that there is only a relatively small chance to observe this phenomenon at two moments in time by day at moderate solar activity.

Fig. 1 .
Fig.1.A probability, N , of the maximum NmF2 value occurrence at SLT for K max p ≤3 (solid lines) and K max p >3 (dashed lines) in diurnal variations of NmF2 measured at the Argentine Islands ionosonde station for January, February, and March, April, May, June, July, September, October, November, and December. Fig.2 Fig.4

Fig. 4 .
Fig. 4. The conditional probability, Q(R), of the occurrence of R in an interval of R for high (solid lines), moderate (dashed lines), and low (dotted lines) solar activity calculated by the use of the December and June foF2 data set (left panel) and the January and July foF2 data set (right panel).

Table 3 .
The arithmetical mean, <foF2(med)>, of the median values of foF2 at 16:00 UT (11:43 SLT) and the percentage, P q (med), of the geomagnetically quiet median values of foF2 at 16:00 UT for January, June, July, and December calculated from the Argentine Island ionosonde foF2 data for low, moderate, and high solar activity.