Investigation in the Variations of Ionospheric f 0 F 2 due to Sunspot Numbers over Wakkanai using EDA Technique

In this research article, the authors have implemented the Exploratory Data Analysis (EDA) techniques to examine the deviation of the monthly median noon and midnight values of the critical frequency of F2 layer ionosphere (i.e. f0F2) at the Wakkanai station (45.39°N, 141.68°E), Japan, during sunspot cycle 21 (1976-1986) and 23 (19962008). Primarily, univariate analysis has been done, which shows the variations in f0F2 at different local times, seasons and in the range of sunspot numbers (SSN), in which winter and semi-annual anomalies are detected in the months of December and March respectively. Secondly, the regression analysis is being used as a bivariate data analysis. The results proved a significantly nonlinear relationship exists between f0F2 and SSN. In both solar cycles, saturation effects are seen in the month of March during the noontime period and immensely in June during the midnight time. The behavior of the ionosphere has been studied for different latitudes, seasonal effects and sunspot dynamic conditions, in which this paper plays an essential role in it.


INTRODUCTION
The upper part of the Earth's atmosphere begins around from 50 to 600 kilometers, where the neutral components coexist with ionized particles and it is called the Ionosphere.This region has been affected by the intense solar natural radiation, such as Extreme Ultraviolet (EUV) rays, X-rays, gamma rays, cosmic rays and supernovae emissions that are responsible for the establishment of the ionosphere.Due to fluctuation in the ionosphere constituents i.e., temperature, density and average kinetic energy; the nature has divided this portion of the atmosphere into four layers such as D, E, F 1 and F 2 .The F 2 layer is a prominent one because it persists all the time in any kind of solar or terrestrial conditions and responsible for long haul communication [1].It is our motive to study ionospheric characteristics and processes under different conditions of solar activity.But it is not always possible to direct measured EUV radiations coming from the Sun, that is the main source of ionization in the region of the ionosphere.So researchers have to depend on solar proxies, in this scenario the Sun's most evident temporary features, i.e., sunspot numbers, which are one of the best representation of solar activity [2][3][4], also the other advantages of sunspot numbers are the longest available data and easy to measure.*Address correspondence to this author at the Institute of Space and Planetary Astrophysics (ISPA), University of Karachi, Karachi-75270, Pakistan; Tel: +4915217141800; E-mail: mushtaq@stud.uni-heidelberg.de The variability of the solar activity causes enormous variations in the density of particles, temperature, neutral winds, electric fields and other parameters in the ionosphere [5,6].The solar activity reliance on the F 2 layer's critical frequency of the Ionosphere (f 0 F 2 ) or peak electron density (NmF2) have been considered for a long time [7][8][9].The relationship involving the peak electron density (NmF2) and solar 10.7 cm radio flux (F10.7) or sunspot numbers (SSN) was depicted to be linear by earlier works.A nonlinear dependence of the ionospheric parameters on solar proxies was revealed in latter learning [10][11][12].Then further investigations confirmed that the solar activity has an effect on the ionosphere which can be well represented by a quadratic pattern [13].A higher-order polynomial does not effectively improve the fitting among solar activity and ionospheric parameters [14].
In our univariate analysis, we used some descriptive statistics and the graphical techniques such that the histogram and box plots were analyzed on the parameter of monthly median hourly f 0 F 2 values.The bivariate data were also analyzed by using the regression plots between sunspot numbers and f 0 F 2 parameters.In this paper, primarily, we show the effect of the different range of sunspot numbers on the noontime f 0 F 2 , secondly, observing the seasonal effects on f 0 F 2 .Finally, analyzed the effect of the sunspot numbers on the noon and midnight values of f 0 F 2 in the months of March, June, September and December.These months are crucial when the solar zenith angle is taken into account.As we know that, solar zenith angle is same at the equinoxes (i.e., March and September) while the maximum and minimum in winter (December) and summer (June) respectively.From the literature survey, we have found that ionospheric parameters over Wakkanai in 45° N latitude are not fully explored for relating sunspot dynamics with f 0 F 2 .

METHODOLOGY
The data on the relative sunspot number are given by the Royal Observatory of Belgium acquired from Solar Influence Data Center [15] Chen et al., (2000) [11] and Yadav et al., (2010) [16].The hourly data of f 0 F 2 observed in the Japanese standard time (JST) (JST = Universal Time + 9 hours).We have used Spyder (Python 2.7) and Minitab 16 for data analyses.

Exploratory Data Analysis
Exploratory data analysis is an approach for data analysis which utilizes the variety of techniques, mostly based on graphs, for deep understanding a data set, extract important variables, detect outliers and develop models.EDA is a perspective that how we divide a data set, what important points we should look for, how we can examine it, and how we deduce the data.For analyzing, the data can be split into two components: quantitative and graphical.A set of statistical dealings that yield numeric or tabular output are called quantitative techniques, secondly the graphical method are techniques to analyze the data through graphs.Most EDA techniques are graphical in nature which explains the structure of a data set in further detail and reveals the data's secret pattern, than the quantitative techniques [17].

Univariate Analyses
Histograms of monthly median noontime f 0 F 2 of twelve months are shown in Figure 1a Figure 1a, b is further divided into three panels and each panel represents the corresponding f 0 F 2 at different sunspot number range (i.e., when sunspot numbers are less than 20, while sunspot numbers are greater than 20 but lesser than 100, whilst sunspot numbers are larger than 100) [18,19].These figures illustrate that how much different ranges of sunspot numbers affect the f 0 F 2 .The f 0 F 2 data are near to symmetric at high sunspot numbers while much asymmetric is seen at moderate sunspot numbers during both solar cycles.
The statistical evaluation of parametric values is mentioned in the Table 1.In both solar cycles, it can be observed that if sunspot numbers are low, then the f 0 F 2 is much confined (i.e., the mean of the coefficient of variation is around 13.5%) into smaller values, i.e., the mean value is around 6 MHz, while if sunspots are moderate in numbers, the values of f 0 F 2 scattered more (i.e., mean of the coefficient of variation is about 24.4%) but the mean value is in the region of 8 MHz and beyond this, the f 0 F 2 is restricted into some extent, i.e., the approximate mean of 10.5 MHz.Whilst also the minimum and maximum values of f 0 F 2 showing some similarities in both solar cycles.The major source of photo-ionization process in F 2 layer is solar EUV radiations [1].The variability in the Solar radiation emission is due to the strong magnetic field nearer to the sunspots on the Sun which dominates the emission in the high energy range of the solar spectrum, i.e., ultraviolet and X-rays [20].
In Table 1, Positive skewness or Right skewed can be found in f 0 F 2 when SSN are low and moderate, where higher values of skewness in moderate SSN show that the few values of f 0 F 2 reached to higher level i.e., over 12 MHz.While the Negative skewness or Left skewed found when SSN are greater, which indicates that only few f 0 F 2 values contacted with a smaller range   i.e., at around 6 MHz.Finally, for all SSN ranges, kurtosis shows negative values (i.e., platykurtic distribution), which demonstrate that f 0 F 2 have flatness to the peak, and has slight tails.The more flattening in f 0 F 2 can be seen when SSN is greater.
Further exploration and information can be extracted by using box plots as seen in Figure 2a, b.Box plots can be used to illustrate the quartiles information and outlier detection of the data.The variation in f 0 F 2 can be evidently seen at different local times and in seasons i.e., different months.
The Figure 2a  Winter anomaly is those where electron densities (or f 0 F 2 ) is higher in winter i.e., December, than in the summer i.e., June, at daytime, whereas semi-annual anomaly are those in which f 0 F 2 is larger in equinoxes than in solstice, which can be seen in the box plots of December and March.
The reason of semi-annual anomaly is the asymmetric hemispheric heating of the atmosphere in the period of solstices, which stimulates the global scale interhemispheric thermospheric circulation [21,22].In this condition heavy molecular gases are moved up and their density amplifies in the F region, which decrease in the atomic oxygen and molecular nitrogen ratio (i.e., O/N 2 ), during the summer solstice in midlatitude.The solar heating is symmetric in equinoxes and the stormy mixing is relatively weaker as compared to summer solstice.As a result, the O/N 2 ratio is greater during equinox than during the summer solstice and creates the semi-annual anomaly in thermospheric neutral composition [21].
The winter anomaly is known to be linked with the seasons and variations in thermospheric neutral composition [23][24][25].The summer-to-winter wind circulation, stimulates different thermospheric neutral compositions between summer and winter.In summer, molecular gases raises in the F region, which increases the reaction of O + with molecular gases, resulting decrease in the density of plasma.The reverse process takes place in winter, resulting increase in the density of plasma.
However box plots for midnight time as illustrated in Figure 2b which shows that for both solar cycles, box plot is highest in level in the month of June which illustrate the opposite behavior from noontime.Second and third highest level of box plots are in March and September respectively, while December has lowest in level.Around the same information are for the maximum, minimum, median and inter-quartile range (IQR) values of f 0 F 2 at midnight time for both solar cycles.
Comparison between noon and midnight f 0 F 2 clearly shows that values of f 0 F 2 are towering in noontime due to the solar EUV radiations shown in Figure 2a, although at midnight time all given months showing low values except for the month of June where the values of f 0 F 2 around similar as shown in Figure 2b, this is due to the effect called Mid-latitude Summer Nighttime Anomaly (MSNA).This is the combined phenomena of neutral wind and the geomagnetic configuration in which during daytime (around noon) the electron density are low and fluctuate slightly but at premidnight (~22:00 LT) electron density enhance and decline at post-midnight (~04:00 LT).Because at nighttime, the upward wind lifted the ionosphere up to regions of lower recombination rate, although during daytime strong downward wind tends the ionosphere up to regions of high recombination rate [9,26].

Bivariate Data Analyses
In order to find out the dependence of ionization of F 2 layer on the sunspots, regression analysis have been executed between f 0 F 2 and the sunspot numbers.Previously done researches show that the saturation effect could not be explained by linear fitting, so quadratic fitting were used instead [27][28][29].
Where, a 0 , a 1 and a 2 are the coefficients of the quadratic regression fit.The term a 2 has its importance, when a 2 < 0, indicates that f 0 F 2 declines with increasing sunspot numbers which represents the saturation effect.Whilst a 2 > 0 signify that f 0 F 2 increases with the number of spots increases.
Δf 0 F 2max parameter is used to determine the effect of the different magnitude of solar cycles on f 0 F 2 .Δf 0 F 2max has been calculated by deducting the highest values of f 0 F 2 acquired from the two solar cycles [16].  2 could attribute that the different magnitude of solar activity affects less in March where the semi-annual anomaly play a main role for ionization.While in September, different magnitude of solar activity affects noticeable on both the noon and midnight time f 0 F 2 values.However, in December at noontime, the negative value is due to the saturation effect on high sunspot numbers and in June at midnight, the strong influence of the magnitude of solar activity on f 0 F 2 values clearly seen.Pearson correlation (CC) in noon time is higher in the 21 st solar cycle for each given month, while it is slightly lower in the 23 rd solar cycle.And for all given months in noon and at midnight the correlation coefficients are strongly positive for both the solar cycles except in the month of December at midnight for the 23 rd solar cycle in which the relationship between sunspot number and f 0 F 2 is less strongly positive.
The saturation effect is especially the result of the changing in neutral O/N 2 concentration ratio.N 2 is a major constituents taking part in the recombination process in the ionosphere [30].The ratio of O/N 2 depends on the solar zenith angle, the immense aspect about this ratio is the huge decrease with solar activity for winter, when the solar zenith angle is maximized at 45° latitude [31].It is due to non-uniform expansion of atmospheric constituents in response of absorption of EUV radiation [32].The scale height of N 2 increases appreciably than atomic oxygen scale height as the sunspot number approaches to their maximum.The recombination process increases due to increases in the scale height of N 2 .This anomalous role of N 2 enhances the recombination process, appear as a saturation effect.

CONCLUSION
Ionospheric investigation is being done for numerous years to understanding the behavior of ionosphere for different solar and seasonal circumstances.The univariate analysis shows that the range of sunspot numbers changing f 0 F 2 data, which are near to symmetric at high sunspot numbers (i.e., SSN>100), while much asymmetry is found in moderate sunspot numbers (20<SSN<100) where the data of f 0 F 2 are scattered more.Box plot analysis shows that, firstly, box plots are higher in noontime as compared to the midnight time.Secondly, at a noontime box plot is highest in height in the month of March.Second and third elevated box plots are in the months of December and September respectively, while the lowest height is in the month of June.Winter and semi-annual anomaly can be observed in December and March respectively because of their high values.However box plots for midnight time is highest in level in the month of June which is opposite from noontime.
Regression plots used as a bivariate data analysis explained that f 0 F 2 is not linearly dependent on sunspot numbers, however the quadratic fit is better for explaining relationship instead, which represent the saturation effect accurately.The phenomenon of saturation depends on local time, seasons (different months) and on the magnitude of solar activity.The different magnitude of solar activity affects largely in the month of September while, minimum influence on March.The Correlation coefficient illustrates positive, strong relationships between f 0 F 2 and SSN at noon and at midnight time, except for the month of December at midnight time during the 23 rd solar cycle, which shows moderate high positive relation.
The study demonstrates the modulation of ionosphere, relative to diurnal, seasonal and sunspot numbers, which improved the understanding of the ionospheric structure and its evolution for the researchers, Space agencies and Radio communication organizations.

Figure 1 :
Figure 1: (a): Histogram of monthly median noontime f0F2 at different Sunspots range of the 21 st solar cycle.(b): Histogram of monthly median noontime f0F2 at different Sunspots range of the 23 rd solar cycle.

Figure 2 :
Figure 2: (a): Box plots of monthly median noontime values of f0F2 for given months for the 21 st and 23 rd solar cycles.(b): Box plots of monthly median midnight time values of f0F2 for given months for the 21 st and 23 rd solar cycles.
for 21 st solar cycle) -f 0 F 2max (for 23 rd solar cycle) The maximum noontime value of f 0 F 2 is around 8-14 MHz for 21 st solar cycle while it is about 8-13 MHz for the 23 rd solar cycle.During the midnight time, the maximum f 0 F 2 values are in the region of 3-8 MHz for the solar cycle 21 st whilst around 4-7 MHz for the 23 rd solar cycle.Result of Table

Figure 3 :
Figure 3: (a): Regression plots between f0F2 and SSN at midnight time period during the 21 st and 23 rd solar cycles.(b): Regression plots between f0F2 and SSN at noontime period during the 21 st and 23 rd solar cycles.

Table 1 : Statistics of Noon Time f0F2 (MHz) at Different Sunspot Ranges
shows the monthly median noon time values of f 0 F 2 during the months of March, June, March.Second and third highest box plots are in the months of December and September respectively, while the lowest height in the month of June.The same interpretations are for the maximum, minimum, median and inter-quartile range (IQR) values of f 0 F 2 at noon time for both solar cycles.Seasonal behavior of f 0 F 2 that deviate from solar zenith angle dependence, are categorized into winter and semi-annual anomalies.