# Unified PCN and PCS indices: Method of calculation, physical sense, and dependence on the IMF azimuthal and northward components

## Abstract

[1] The PC index estimates the polar cap magnetic activity generated by the solar wind and its embedded magnetic field. It shows a high degree of correlation with geophysical disturbance parameters characterizing the state of magnetosphere. After transition to 1-min PC index values, significant differences were revealed between the PCN and PCS indices, derived on the basis of magnetic data from Thule and Vostok stations, respectively. Differences in values of the 1-min PCN and PCS indices may give rise to discrepancy in results of various analyses and to quite erroneous physical conclusions. To eliminate any influence of the calculation technique on scientific results a unified method for derivation of the PC index was elaborated in the Arctic and Antarctic Research Institute (St. Petersburg) and Danish Meteorological Institute (Copenhagen), and new sets of the unified PCN and PCS indices were calculated. Under conditions of southward IMF the unified positive PCS and PCN indices are well consistent with one another in their value and behavior and linearly correlate with the solar wind merging electric field (MEF), irrespective of season. The IMF B_{Y} component is responsible for occurrence of the electric field MEF (and positive PC index) under conditions B_{Z} > 0. Being proportional to MEF the PC index would be regarded as a measure of the interplanetary merging (geoeffective) electric field with the appropriate dimensionality of mV/m.

## 1. Introduction

[2] The PC index was introduced [*Troshichev and Andrezen*,1985; *Troshichev et al.*, 1988] to characterize magnetic activity in the polar caps generated by the solar wind coupling with the magnetosphere. The concept of the antisunward convection within the polar cap, controlled by the solar wind parameters, served as a basis for the method of the index calculation [*Troshichev*, 1982]. In consequence, the PC index was derived as a dimensionless quantity parameterized by season, UT, and hemisphere, and calibrated for the merging (geoeffective) interplanetary electric field (MEF). It implies that the PC index would be well related to the merging electric field MEF as well as to those magnetospheric parameters that are controlled by the coupling between MEF and the magnetosphere.

[3] Two polar cap magnetic stations are used to monitor the PC index: station Thule in Greenland (at 85.4° corrected geomagnetic latitude) and station Vostok in Antarctica (at −83.4°). Initially the 15-min PC indices were calculated [*Vennerstroem et al.*, 1994], while calculation of 1-min PC index values was started in 1999–2000. Results of the statistical analyses, carried out with use of the published PC index sets, have shown that the PC index has a high degree of correlation with such geophysical parameters as auroral electrojet intensity (AE index) [*Vennerstrøm et al.*, 1991; *Vassiliadis et al.*, 1996; *Takalo and Timonen*, 1998], the cross polar cap voltage and polar cap diameter [*Troshichev et al.*, 1996; *Ridley and Kihn*, 2004], the ionospheric electric field in the near-pole region [*Troshichev et al.*, 2000; *Ridley and Kihn*, 2004], ionospheric Joule heat production [*Chun et al.*, 1999, 2002], and global auroral power [*Liou et al.*, 2003]. Thus the results of the various statistical analyses suggest that the PC index can be regarded as a measure of coupling between the solar wind and its embedded magnetic field and the magnetosphere.

[4] After transition to the 1-min PC index significant differences were revealed between the PCN index, calculated in the Danish Meteorological Institute (DMI), and the PCS index, calculated in the Arctic and Antarctic Research Institute (AARI) [*Lukianova et al.*, 2002]. Part of the reason for these differences is some difference in the procedures for derivation of the 1-min index, applied in AARI and DMI, respectively. The difference concerns the level of reference for magnetic disturbances in the polar cap and technique for derivation of coefficients determining the relationship between the interplanetary electric field and the polar cap magnetic activity.

[5] Differences in values of the 1-min PCN and PCS indices give rise to discrepancy in results of various analyses and to quite dissimilar physical conclusions. Different frequency of occurrence of negative PC index values in the northern and southern hemispheres was found by B. Emery (private communication, 2001). The PCN and PCS indices have quite different relationship with the electric field. According to *Troshichev et al.* [2000] there is “effect of the electric field saturation,” while according to *Nagatsuma* [2002] “effect of PC index saturation” takes place. The PCS and PCN indices respond in different manner to pulses in the solar wind dynamic pressure [*Lukianova*, 2003; *Huang*, 2005]. Relations between the PC and AE indices turned out to be also different for the northern and southern hemispheres: increase of AE index follows after growth of the PCS index [*Troshichev and Lukianova*, 2002], while PCN and AE indices start to increase synchronously [*Huang*, 2005].

[6] It is evident that PCN and PCS indices derived by a unified method are required to eliminate any influence of the technique of calculation on results of the analysis and physical conclusions. The unified PCN and PCS indices would not report exactly the same value because there will always be differences due to location of magnetometers, ionospheric conditions and asymmetry in the IMF effects for the northern and southern polar caps. Our goal is to derive the PC index that adequately accounts for the interplanetary merging electric field making allowance for location of station, UT and season. Such a work was successfully fulfilled in the Arctic and Antarctic Research Institute (St. Petersburg) and Danish Meteorological Institute (Copenhagen). This paper presents the initial results of the work showing that the research community can confidently use the unified PC index to estimate the merging electric field MEF. Further we plan to replace the existing sets of the 1-min PC indices (1993–2005) for the unified PCN and PCS indices and to use this new database to revise the PCN/PCS relationship with the solar wind dynamic pressure and auroral substorms.

## 2. Method for Calculation of the PC Index

*Troshichev et al.*[1988] was applied in the analysis. First, a scalar parameter, δF, for the magnetic disturbances was determined using the magnetic observations from a near-pole station

_{m}= V

_{SW}(B

_{Z}

^{2}+B

_{Y}

^{2})

^{1/2}sin

^{2}(Θ/2) [

*Kan and Lee*, 1979] is calculated for each month and UT hour. Here V

_{SW}is velocity of the solar wind, B

_{Z}and B

_{Y}are the components of the interplanetary magnetic field (IMF), and Θ is angle between the IMF transverse component and the geomagnetic dipole.

_{m}were used for calculation of the PC index

_{m}, and parameterized by season, UT and hemisphere.

[9] In our analysis the data sets of IMF and solar wind values derived from ACE satellite data for 4 years free of gaps, 1998–2001, and the appropriate δF values were used as the basis for elaboration of the method. The unified procedure for calculations of the PCN and PCS indices included (1) determination of the level of reference (quiet level) for estimation of the magnetic disturbance value δF; (2) calculation of the 5-min values δF at Thule and Vostok stations according to formula (1); (3) determination of the optimal angle ϕ from the comparison of δF at each station with the appropriate 5-min value E_{m} observed at ACE spacecraft and reduced to the magnetopause, with allowance for an additional 15-min delay [see *Troshichev and Andrezen*, 1985]; and (4) calculation of coefficients α and β needed to convert the δF value to the PC index.

### 2.1. Determination of the Quiet Level in Evaluating of the Magnetic Deviations δD and δH

[10] Magnetic deviations δD and δH are calculated from a certain level, “curve of quiet day,” which presents the daily magnetic variation, observed at the particular station during extremely quiescent days. The quiet daily variation looks like sine curve, whose amplitude and phase is defined by the regular currents flowing in the ionosphere during the quiet periods. The magnetic field induced by these regular currents is added to the main geomagnetic field according to position of station with respect to the current pattern, as a result the quiet magnetic field varies with the local time LT. The intensity of the quiet current system is influenced by the ionospheric conductance and, therefore, changes from winter to summer, showing the early course. Moreover, the quiet current pattern changes from year to year referring to the appropriate modification of the ionospheric currents during the solar cycle. Thus the parameters of the quiet daily variation are unique for each particular station being connected with the geographical and geomagnetic coordinates of the point and dependent on season and the solar activity cycle.

[11] The quiet daily variation is modified, to a greater or lesser extent, by the irregular magnetic disturbances produced by persistent changes in the solar wind coupling with the magnetosphere. These disturbances do not significantly influence the phase of daily variation but can considerably increase its magnitude (Figure 1). This feature substantially complicates definition of the daily quiet variation, since criteria for quiet day turn out to be dependent on the level of magnetic activity and phase of the solar cycle. The choice of the quietest 5 days for each month is the commonly accepted method for construction of the quiet daily variation. However, this method has severe shortcomings. First, the length of magnetic quiescence is quite arbitrary and does not coincide with the astronomical day. Secondly, even long periods of magnetic quiescence can include the short intervals with magnetic disturbances. Thirdly, in years of solar maximum it is very difficult to find 5 really quiet days for each month, almost all of them contain some disturbed intervals. It means that concept of “quiet day” is fairly conventional, and another technique must be used for construction of the quiet daily variation.

[12] Below we describe a new method of automatic construction of daily quiet variation, which is free from the mentioned disadvantages. The method is based on use of all quiet intervals (for 30 day period), with duration more than 1 hour, irrespective of day and time of magnetic quiescence within this period. To separate the quiet intervals the parameterization of the magnetic field variations is performed on the principle that the variability of the magnetic field is higher for larger magnetic disturbances. The variability is estimated by two parameters: the gradient of magnetic field components on scale of adjacent 1-min samples, and dispersion of separate samples relative to mean value for definite, sufficiently short time lapse (1 hour). The successive iterations are used to choose the quietest intervals. The most severe conditions for steadiness of geomagnetic field are examined first: the temporal gradient would be not more than 5 nT/min, and mean dispersion of all samples for 20-min interval would not exceed 10 nT from the running mean for this period. These criteria are weakened with each of successive iteration. The set of data obtained in course of the first iteration presents the most quiescent field, but often it is statistically insufficient to restore the quiet daily variation for all 24 hours of day. In such a case the second (and, if required, successive) iteration starts. The values of the field component derived just in course of the first iteration are regarded as the most plausible. The successive iterations fill the missed intervals, the certain field steadiness index being assigned to each of successive iterations. The iterations are executed until each hour in the daily interval will be derived from a sufficient number of samples (N = 120). The quiet daily variation is calculated by the superposition epoch method, the 1-min averaged values of the quiet daily variation being obtained for each 30 days. To exclude undesirable outliers the nonlinear median filtering is used.

[13] The entire procedure is repeated each new day. As a result, the running 30-day mean quiet daily variation is derived, which makes allowance for estimations of the gradual day-to-day changes of the quiet magnetic field and its modulation within the solar cycle. As an example, Figure 2 shows features of the quiet daily variations in D and H components at stations Thule and Vostok during 1998–2002, *x* and *y* coordinates being taken for days of year and hours of day, respectively. One can see that daily variation in both components is minimal during local winter (November–February at Thule and May–August at Vostok) and maximal during local summer. This daily variation in geomagnetic components has been taken as level of reference in calculation of magnetic deviations δD and δH.

### 2.2. Technique of Derivation for Parameters α, β and ϕ

[14] At first these 5 min parameters were averaged for each sequential 10 days during 1998–2001. To eliminate the random oscillations these averaged 5-min values were subjected to the 6-point running “lowess smoothing” (taken from MATLAB) that is resistant to outliers. Then the 6-point smoothed values were averaged for all 4 years. As a result, the averaged yearly courses of the parameters were derived, which made it possible to obtain the averaged 1-min parameters α, β and ϕ. On such basis the calibration of the PC index at Thule and Vostok stations for merging electric field E_{m} has been realized with allowance for season and UT. It has been mainly the unified smoothing procedure which has led to similarity of the newly unified PCN and PCS indices. Indeed, when deriving the former 1-min PC indices, too high of a smoothing was applied in case of the PCN index, and extremely weak of a smoothing was applied in case of the PCS index. As a result, the amplitudes of the former PCN index turned out to be underestimated, whereas the former PCS index was overestimated.

[15] Finally, the parameters α, β and ϕ based on data for 1998–2001 were compared with the appropriate parameters derived independently from data for 2002. The results of comparison demonstrated that coefficients α, β and angle ϕ derived from two different samplings are closely related. This test can be regarded as verification of the technique used in our analysis.

[16] Figure 3 shows the smoothed contour lines for parameters α, β and ϕ obtained in this manner for Thule and Vostok stations. The behavior of the coefficients α and β is clearly seen from Figure 3. At both stations they are of the greatest value during the summer months, when the geomagnetic effect of MEF is maximal, and of the least value during the winter months, when the effect of MEF is minimal. The maximum positive values at Thule are observed near MLT noon (∼1400 UT), the maximum (negative) values at Vostok are observed before and after MLT noon (coming at about ∼1200 UT here), and the coefficients variation at Thule is much more pronounced that at Vostok. These peculiarities are explained by the lesser geomagnetic latitude of Vostok, which has the consequence that Vostok intersects the converging, but separated, prenoon and postnoon, streams of the antisunward convection controlled by the southward IMF, whereas Thule meets at noon the just united powerful polar cap convection stream.

## 3. Relationship Between the Unified PCN and PCS Indices

[17] Figure 4 shows as an example the run of the PCN and PCS indices during 1998–2001. One can see the remarkable agreement in behavior of the positive PC indices in the northern and southern hemispheres, with the index reaching as large value as 20 at both the Thule and Vostok stations. As for the negative PC indices, their occurrence is typical of the local summer in both hemispheres. This regularity is determined by the physical sense of the PC index as a signature of intensity of the sunward electric currents in the near-pole region (or antisunward convection), which are common phenomena for both, summer and winter, polar caps. The reversed (antisunward) currents within the polar cap (and, correspondingly, the negative PC index) occur only under influence of strong northward IMF.

[18] Figure 5 shows the statistical relationship between the PCN (PCS) index and the IMF B_{Z} for three seasons, local summer, local winter and equinox. If we examine the relationship as a linear function, the correlation coefficients turn out to be not too large, about 0.5, which is a result of the IMF B_{Y} component effect and inclusion of the negative PC indices in the statistics. The negative PC indices are observed in relation to the northward B_{Z} in summer and equinox seasons, but are practically unavailable in winter season. There is no evident relationship between values of the negative PC and positive B_{Z}. According to *Lukianova et al.* [2002] the negative PC indices in the winter polar cap were observed in the course of Bastille storm (15–16 July 2000), when the polar cap was bombarded by intense flux of the solar flare-accelerated protons. These results imply that sufficiently high ionospheric conductivity is a necessary condition, along with the northward IMF, for development of the reversed current system, which is responsible for a negative PC index. The high ionospheric conductivity is common in the summer (and equinox) polar cap exposed to sunlight, but in the winter cap it can happen in association with the polar cap absorption (PCA) events.

[19] Taking into account that the PC index is designed to characterize the antisunward convection within the polar cap and only positive values of PC specify the intensity of the related current system, we shall examine whether or not the linear relation holds only for positive PCN and PCS indices. As Figure 6 (top) shows, the linear relationship, with coefficient of regression equal to 1, is valid for all seasons (May–August, November–February, and March/April, September/October). The best correlation between the unified PCN and PCS indices is observed for the equinox conditions (Rmean = 0.83). In other seasons the correlation between the PCN and PCS indices diminishes to 0.71–0.73 owing to small prevalence of the local summer PC index above the local winter PC index. This prevalence is explained by the increased role of the IMF B_{Y} component in the summer polar cap. Indeed, if we exclude from examination the intervals when the effect of the B_{Y} component becomes dominant over the southward IMF effect (i.e., intervals with 3∣B_{Y}∣ > ∣B_{Z<0}∣), the correlation between the positive PCN and PCS indices in seasons May–August and November–February improves up to 0.80 and 0.85, correspondingly (Figure 6, bottom).

[20] To illustrate the character of the IMF B_{Y} influence on the PC index we show in Figure 7 the behavior of the PCN and PCS indices responding to the appropriate run of the IMF B_{Y} and B_{Z} components on 13 December 1999. One can see that the southward IMF component gives a determining effect on behavior of the PCN and PCS indices. If influence of the southward component is dominant (interval from 00 to 0900 UT) the values of PCN and PCS are closely related and vary in similar manner. When B_{Z} component approaches to zero or reversed to northward (after 0900 UT), the effect of the B_{Y} component becomes to be the main driver and values of PCN and PCS start to differ from one another, the PC index in summer polar cap (PCS) being largest. The B_{Y} effect is reversed while changing the B_{Y} polarity (at 1515 and at 1730 UT), so the difference between the PC indices in summer and winter polar caps can be of positive or negative sign depending on the B_{Y} polarity. We shall return to effects of the IMF B_{Y} component below.

[21] Figure 8 shows the yearly variation of correlation between the unified PCN and PCS indices for all values of PC (dashed line) and only for positive values of PCN and PCS (solid line). Correlation reaches maximum (up to 0.88) in equinox seasons irrespective of sets of data. The minimal values of correlation are observed in the solstice periods: R = 0.70 for all PC and R = 0.74 in case of positive values of PCN and PCS. It means that incorporation of the negative PC indices in general statistics insignificantly impairs the results because their percentage is not essential in comparison with the positive PC indices.

[22] The statistical characteristics of the unified PCN and PCS indices obtained for 1996–2004 are presented in Figure 9. The left column shows the function of distribution for the PC index. One can see the large predominance of the number of positive PC indices above negative ones and evident of similarity in the occurrence of positive PC indices in both polar caps. As we mention above, this regularity follows from definition of the PC index. As for negative PC indices, their occurrence depends on season (May–August at Thule and November–February at Vostok, see Figure 4). As a result, the negative PC indices appear in different months in the northern and southern polar caps and their frequency, determined by the northward IMF frequency, can be quite different. The right column shows such statistical characteristics as the mean and median values of the PC index and its standard deviation (STD). A remarkable agreement is seen in value of these characteristic parameters at Thule and Vostok stations and in their variations in course of the solar cycle: the minimal PC values were observed in 1996, and maximal values took place in 2001. The appearance of the second maximum in 2003, reported by observations at Thule, unfortunately, cannot be verified by the Vostok data, since the station was inoperative in 2003.

## 4. Relationship Between the Unified PCN, PCS Indices and the Merging Electric Field

[24] It is remarkable that small values of the positive and negative PC indices can be observed for zero values of the electric field E_{m}. As for positive PC indices, their appearance is evidently connected with the magnetospheric currents caused by the quasi-viscous interrelation between the solar wind and magnetosphere. These currents generated irrespective of the IMF polarity have the same structure as DP-2 currents induced by the southward IMF [*Troshichev*, 1982]. They are responsible for the dawn-dusk voltage in the polar cap available even for conditions B_{Z} = B_{Y} = 0. As for negative PC indices typical of the local summer season, it is believed that they are related to the specific field-aligned current system NBZ stimulated within the polar cap by the northward IMF [*Iijima et al.*, 1984]. Polarity of the electric voltage within the polar cap depends on relation between these two independent field-aligned current systems. If the effect of the quasi-viscous interaction is prevailing, then the positive PC index is observed. If the effect of the NBZ system is dominant the negative PC index is observed. Analysis of the relationship between the PCN, PCS indices and E_{m} field under the condition B_{Z} > 2 nT shows (Figure 11) that the negative PC indices are compatible with insignificant values of the merging electric field (E_{m} < 2.5 mV/m). However, this peculiarity evidently results from effect of the field-aligned currents generated in the polar cap under influence of the IMF B_{Y} component [*Troshichev*, 1982].

[25] To demonstrate the role of the IMF B_{Y} component in generation of the merging electric field provided that IMF is northward we examined the relationship between the PC index and E_{m }under the condition of B_{Z} > 2 nT for different absolute values of B_{Y}. As Figure 12 shows, E_{m} grows as B_{Y} increases, and the relationship between the PC index and E_{m} approaches proportionality in spite of the northward IMF. Thus the merging electric field coupling with the magnetosphere is mainly related to B_{Z} component, when the IMF is southward, and to B_{Y} component, when the IMF is northward, as indicated by the expression of *Kan and Lee* [1979]. Being proportional to the value of E_{m}, the PC index follows these variations.

## 5. Discussion

[26] The relationship between the PCN and PCS indices calculated by the identical technique was examined earlier by *Lukianova et al.* [2002]. It should be noted that these “identical” PCN and PCS indices analyzed in [*Lukianova et al.*, 2002] and the unified PC indices presented in this paper are not the same indices. As mentioned above, the technique used by *Lukianova et al.* [2002] applies the extremely weak smoothing procedure resulting in large and sometimes arbitrary fluctuations of the coefficients α and β. Nevertheless, both analyses demonstrated that the relationship between the PCS and PCN indices, derived by the same technique, can be regarded as linear, with a coefficient of regression equal to 1. It implies that any unified technique would provide the similar values for PCN and PCS indices. If so, what criterion would be taken to select the proper technique for calculation of the unified PCN and PCS indices?

[27] It is reasonable to suppose that the relationship between the PCN/PCS indices and the MEF would be regarded as the criterion. Indeed, if we consider the PC index as a signature of the merging electric field, the ground index would closely follow changes in the extraterrestrial field. As analysis of *Nagatsuma* [2002] showed, the use of the former underestimated PCN index provides effect of “the PC index saturation,” when the MEF growth is not followed by the appropriate increase of the PC index. The analogous examination for the former overestimated PCS index was not performed, but effect of “the MEF saturation” is expected. The unified PC indices ensure the best linear correlation between δF and E_{m}. At the same time, the unified positive PCN and PCS indices turned out to be in linear relation to one another, with regression coefficient equal to one.

[28] It should be noted that parameters α, β and ϕ, ensuring the best correlation between δF and E_{m}, were derived for period of the maximum solar activity. We suppose that these parameters would be invariant during the entire solar cycle, since modification of the ionospheric currents in course of the solar cycle had been taken into account while calculating the quiet daily variation. Nevertheless, we shall verify our supposition by determining the parameters α, β and ϕ for years of the solar activity decay (2004–2005) and later on for years of the solar activity minimum (2007–2008). If the parameters derived from independent samplings turn out to be closely related, it will mean that relationship between the merging electric field E_{m} and PC index is held invariant irrespective of course of the solar cycle. Otherwise, the each phase of the solar cycle would be provided with proper coefficients α, β and angle ϕ.

## 6. Conclusions

[29] 1. The unified PCS, PCN indices are well consistent one with another in their value and behavior when influence of the IMF southward component is dominant.

[30] 2. Effect of the IMF B_{Y} component is manifested in magnifying the PC index in the summer polar cap and, correspondingly, in some dependence of the linear correlation between the PCN and PCS indices on season.

[31] 3. Under conditions of southward IMF the unified PCN, PCS indices linearly correlate with the merging electric field E_{m} irrespective of season.

[32] 4. The IMF B_{Y} component is responsible for occurrence of the merging electric field E_{m} (and positive PC index) under conditions B_{Z} > 0.

[33] 5. Being proportional to E_{m} the PC index would be regarded as a measure of the merging electric field, with the appropriate dimensionality of mV/m.

## Acknowledgments

[34] Arthur Richmond thanks Francis K. Chun and another reviewer for their assistance in evaluating this paper.