Statistical Features of Polar Cap North and South Indices in Response to Interplanetary and Terrestrial Conditions: A Revisit

In this study, we investigate statistical features of polar cap north (PCN) and south (PCS) indices in response to various interplanetary conditions (interplanetary magnetic field [IMF] orientation in three‐dimensions) and terrestrial conditions (seasonal and magnetic local time [MLT] locations of the index stations). The concurrent PCN‐PCS pairs for 1998–2002 and 2004–2018 are divided based on their sign type (positive‐positive, negative‐negative, negative‐positive, and positive‐negative PCN‐PCS pairs) and time coverage (the times when both index stations are in the dawn/dusk MLT sector during northern summer/winter). Analyzing the IMF orientation dependence on the occurrence probabilities of concurrent indices and on the differences between the indices in various sign types for each time coverage reveals that the statistical features in PCN‐PCS pairs obtained in the dawn MLT sector can be largely explained by the effects of the three‐component IMF (related to the polar cap convection patterns) combined with season (related to the hemispheric asymmetry in solar illumination‐induced ionospheric conductance). However, those obtained in the dusk MLT sector are controlled dominantly by seasonal effects rather than IMF orientation effects. Our findings indicate that PCN‐PCS pair data provide local views about the solar wind‐magnetosphere‐ionosphere (SW‐M‐I) coupling system with different control efficiencies of IMF orientation and season depending on the MLT location of the stations. Therefore, introducing polar cap indices recorded simultaneously at various locations in both hemispheres and analyzing them are strongly required to infer global views of the coupled SW‐M‐I system in the open field regions with higher confidence.


Introduction
Polar caps are regions of open magnetic field lines connected directly to the interplanetary magnetic field (IMF) lines at latitudes poleward of the auroral oval in both the Northern and Southern Hemispheres.Because of this open magnetic topology, the direct solar wind-magnetosphere-ionosphere (SW-M-I) coupling and relevant global-scale ionospheric electrodynamics (such as ionospheric electric fields, currents, and magnetic perturbations) in these regions have received much attention hitherto (see Milan & Grocott, 2021;Milan et al., 2017, and references therein).In order to monitor the space weather in the polar cap ionosphere in terms of the level of SW-M-I coupling, O. A. Troshichev et al. (1988) introduced polar cap indices calculated using the magnetic field data from a single nearpole station at Qaanaaq (formerly Thule) in Greenland and those at Vostok in Antarctica, respectively.O. Troshichev et al. (2006) proposed the "unified" PC derivation method for elimination of any influences of the calculation technique on scientific results in these polar cap indices (hereinafter called PC indices, or PCN for polar cap north index and PCS for polar cap south index separately).According to O. Troshichev et al. (2006), each of the PC indices is designed to indicate the ionospheric electric field, which is responsible for ground magnetic perturbations projected onto the axis of the ground magnetic disturbance caused by merging electric field E KL = V SW B yz sin 2 (θ/2) (Kan & Lee, 1979).Here V SW is the solar wind speed, B yz is the IMF magnitude in the Geocentric Solar Magnetospheric (GSM) Y-Z plane, and θ is the IMF clock angle (the angle between geomagnetic north and the projection of the IMF vector onto the GSM Y-Z plane viewed from the Sun).The direction of the E KL -induced magnetic disturbance axis is statistically estimated by selecting the angle of the magnetic disturbance axis (φ), which gives the best correlation coefficient between E KL (in units of mV/m) and the magnetic perturbation values projected onto the corresponding axis (δF; in units of nT) in each UT hour and month bin through the years.This can be represented by the following equation: where the slope (α; in units of nT/(mV/m)) gives the coupling strength between E KL and δF and the y-intercept (β; in units of nT) is the background level of magnetic activity (at E KL = 0 mV/m), respectively, obtained with φ in δF.We note that φ is limited to a range of ±90°with respect to the dawn-dusk magnetic local time (MLT) meridian (from the axis pointing duskward in the Northern Hemisphere and from the axis pointing dawnward in the Southern Hemisphere) under the assumption that the E KL -induced ionospheric equivalent currents have sunward components in both hemispheres.Because the linear regression method is applied, the scaling parameters φ, α, and β for each index are provided as functions of UT hour and month.These scaling parameters remain nearly invariant (within 10% uncertainty) over years irrespective of solar activity (O. A. Troshichev et al., 2011).
Under the assumption that the coupling strength of δF with the ionospheric electric field is equal to that with E KL (i.e., a scale factor between each of PC indices and E KL is set to unity), the PC index at a given time t (PC t ; in units of mV/m) can be therefore represented by the following equation: where δF t , β t , and α t are the magnetic perturbation projected onto the E KL -induced ground magnetic disturbance axis, the background level of magnetic activity, and the coupling strength of δF t with PC, respectively, obtained by applying interpolation methods over time (as functions of UT hour and month) to φ in δF, β, and α.More detailed descriptions of the calculation method for PC indices are also provided in many literature (e.g., O. A. Troshichev, 2022;O. Troshichev & Janzhura, 2012a;Troshichev et al., 2006).
As mentioned above, the value of α t is estimated from α values with the positive correlation between E KL and δF (Equation 1).Therefore, the sign of the PC indices depends mainly upon the sign of δF t β t (Equation 2).This implies that the direction of background-adjusted magnetic perturbations (either parallel or antiparallel to the E KL -induced magnetic perturbation direction) can be inferred from their sign (O. A. Troshichev, 2022;O. Troshichev et al., 2006).
Previous studies pointed out from some cases that the discrepancy (in terms of not only the values but also the signs) between the PCN and PCS indices recorded simultaneously is a consequence of combined effects of the IMF clock angle orientation and ionospheric conductivity on the global-scale current/convection patterns in highlatitude ionospheres (e.g., Lukianova et al., 2002;O. Troshichev & Janzhura, 2012b;O. Troshichev et al., 2006).More recently, several studies have been conducted to statistically investigate the physical reasons that cause not only the occurrence of positive/negative values in PCN and PCS indices but also the difference in these indices (Lockwood, 2023a(Lockwood, , 2023b;;O. A. Troshichev, 2022;O. A. Troshichev et al., 2023).These studies have shown that the differences between these indices are results of the decoupling of solar wind and magnetospheric electric fields in association with the changes in the magnetosheath and magnetospheric magnetic fields (Lockwood, 2023a(Lockwood, , 2023b)).In this regard, the distortion of the E KL -induced ionospheric current/convection system under conditions of a nonzero dusk-dawn component of the IMF (IMF B y ) can result in the difference between PCN and PCS values (Lockwood, 2023a(Lockwood, , 2023b;;O. A. Troshichev, 2022;O. A. Troshichev et al., 2023).Besides, the differences in the ionospheric conductance between the northern and southern polar caps can be a possible candidate because of their effects on the hemispheric differences in the ionospheric current system (Lockwood, 2023a(Lockwood, , 2023b;;Lukianova et al., 2002;O. A. Troshichev, 2022;O. A. Troshichev et al., 2023).
In order to determine whether the discrepancy between the simultaneously recorded PC indices is directly affected by the IMF orientation, however, it is strongly required to investigate statistical features of PCN-PCS index pairs (in terms of the occurrence distribution of PCN-PCS index pairs and the difference in values between these index pairs, for each of data sets divided according to possible combinations in their sign types) in relation to all three components of the IMF.Examination of these concurrent PC indices for various seasons and MLT locations of the PC index stations also enables to extend the analyses in previous studies (e.g., Lockwood, 2023aLockwood, , 2023b;;O. A. Troshichev, 2022;O. A. Troshichev et al., 2023) in the context of the hemispheric difference in the ionospheric conductance produced by solar illumination as well as that in the global-scale current/convection patterns in high-latitude ionospheres.Based on this argument, we revisit the influences of the three-component IMF orientation on the statistical features of concurrent PCN and PCS indices for different seasons and MLT locations of the PC index stations, that is, the influences of interplanetary drivers (associated with IMF orientation) and terrestrial drivers (associated with Earth's revolution and rotation) on the ionospheric electric field (inferred from the ground-based magnetometer data) near the central polar caps.
The rest of this paper is organized as follows.In Section 2, we introduce the data set used in this study.The results showing the statistical features in the concurrent PCN and PCS indices in relation to the three components of the IMF for various seasons and MLT locations of the stations are in Section 3. We provide the discussion and conclusions of this study in Sections 4 and 5, respectively.

Data Set
For this study, we use both the Qaanaaq PCN and Vostok PCS indices for 20-year period 1998-2002 and 2004-2018.The data in 2003 are not used because of lack of the PCS index data during this period.These indices are calculated at 1-min cadence by the unified method (O.Troshichev et al., 2006) in the Space Institute of the Danish Technical University and Arctic and Antarctic Research Institute, respectively.In order to reduce any ambiguities in our results caused by timescale-dependent relationship between near-Earth interplanetary parameters and ground magnetic field perturbations (e.g., Laundal et al., 2020), these 1-min resolution data are resampled to 1-hr cadence using boxcar averages.If there are less than 45 data points available in a 1-hr boxcar window, the obtained value in the corresponding boxcar window is replaced with a missing value (not used in this study).The difference between concurrent PCN and PCS (∆PC) is then obtained using ∆PC = PCN PCS with the 1-hr averaged data.
Qaanaaq (77.5°, 290.8°) and Vostok ( 78.5°, 106.8°) stations are nearly antipodal to each other in geographic coordinates (latitude, longitude).Figures 1a and 1b show the averaged values of the solar zenith angles (SZAs) at Qaanaaq PCN and Vostok PCS index stations, respectively, during 1998-2002 and 2004-2018 in the twodimensional bins of UT and month (grid size of 1 hr × 1 month).The SZA is calculated using SZA = cos 1 (P x,PC ), where P x,PC is the X-GSM position (in R E ) of either Qaanaaq or Vostok station.The SZAs at the Qaanaaq station show the diurnal and seasonal variations with the minimum degree of about 50°at 16:00-17:00 UT in June and the maximum degree of about 120°at 04:00-05:00 UT in December.Since the Vostok station is situated close to the antipode of the Qaanaaq station, the diurnal and seasonal variations of the SZAs exhibited the opposite trends at this position (with the minimum degree of about 50°at 04:00-05:00 UT in December and the maximum degree of about 120°at 16:00-17:00 UT in June).Correspondingly, the SZA difference between these stations (i.e., ∆SZA = SZA at Qaanaaq station SZA at Vostok station) shows the significant variations with UT and month in the ∆SZA range of approximately 70°-70°, which can be seen in Figure 1c.It is also clear in Figure 1c that the zenith line at the Qaanaaq station is in general further tilted toward the Sun compared to that at the Vostok station (∆SZA < 0°) during northern summer and vice versa (∆SZA > 0°) during northern winter.
The near-Earth interplanetary data used in this study are the time-shifted (from a solar wind monitor to the Earth's bow shock nose) IMF data in GSM coordinates provided by the OMNI database (King & Papitashvili, 2005).In this study, we consider the time delay of the merging electric field to be transferred from the nominal bow shock nose to the polar caps (i.e., the time lag of ionospheric electric field-associated ground magnetic perturbations in response to E KL ) by shifting the OMNI IMF data in time to +20 min (O.Troshichev & Janzhura, 2012a).The time-shifted 1-min OMNI data are also resampled to 1-hr cadence using boxcar averages.In other words, we take 1-hr boxcar averages starting at each hour (e.g., 01:00-02:00 UT) for the PC indices and starting 20 min prior to the corresponding time (e.g., 00:40-01:40 UT) for the IMF data.In the same manner as the PC indices, we only use the averaged IMF components which are obtained with no less than 45 data points in a 1-hr boxcar window.
In this study, the IMF clock angle and the IMF cone angle (ψ) are used to examine the influences of the IMF orientation on the PC indices.The IMF clock angle is defined as θ = tan 1 (IMF B y /IMF B z ) covering the range between 180°and 180°.The IMF clock angles of 0°, 90°, ±180°, and 90°therefore correspond to purely northward, duskward, southward, and dawnward IMF orientations, respectively, in the GSM Y-Z plane.The IMF cone angle is defined as the angle of the IMF vector from the Sun-Earth line (starting from the sunward direction) and is calculated using ψ = cos 1 (IMF B x /IMF B), where IMF B x is the Sun-Earth IMF component and IMF B is the magnitude of the IMF.Accordingly, the IMF cone angle has the range from 0°(purely sunward direction) to 180°(purely earthward direction).

Results
The main objective of this study is to provide further statistical evidence for the similarity/difference between concurrent PCN and PCS indices in relation to the IMF orientation and the ionospheric conductivities induced by the solar illumination over the PC index stations (Lockwood, 2023a(Lockwood, , 2023b;;O. A. Troshichev, 2022;O. A. Troshichev et al., 2023).In the present study, the occurrence distribution of PCN-PCS pair data (Section 3.1) and the level of the differences between the paired values (Section 3.2) for various interplanetary and terrestrial conditions are examined after splitting the PCN-PCS pair data into four categories according to their values as follows: Sign  Troshichev, 2022;O. A. Troshichev et al., 2023).In the present study, we further divide the opposite-sign PCN-PCS category into two sign categories (Sign 3 and Sign 4 categories) and provide evidence that the current version of the PCN and PCS indices represents local views of SW-M-I coupling modes (associated with the ionospheric flow pattern) at the locations of the corresponding stations.It is clear from Figures 2a-2d that the positive-positive PCN-PCS pairs (Figure 2a) can be obtained more than half of the number of PCN-PCS pairs over the entire ranges in UT and month.The negative-negative PCN-PCS pairs (Figure 2b) can be obtained from premidnight to noon times (21:00-12:00 UT) over the months with a peak higher than 15% at postmidnight time (00:00-02:00 UT) in April and May.The negative-positive PCN-PCS pairs (Figure 2c) can be obtained mainly from postnoon to premidnight times (13:00-21:00 UT) between April and September with peaks higher than 25% at dusk time (16:00-19:00 UT).This tendency is consistent with the findings in Nagatsuma (2002) using the PCN index, although the examination of the PCS index was beyond the scope of his study.There are also minor peaks of approximately 20% from dawn to postnoon times (06:00-13:00 UT) between April and September and approximately 15% from predawn to prenoon times (04:00-10:00 UT) between October and March.Less than 10% of the number of data points are from prenoon to predawn times (10:00-04:00 UT) between October and March.On the other hand, the UT-month distribution of the probabilities of obtaining the positive-negative PCN-PCS pairs (Figure 2d) shows two clear peaks (∼20%) with one at postmidnight-to-prenoon time (02:00-10:00 UT) and the other one at noon-to-dusk time (12:00-18:00 UT) between November and February.

Distributions of Occurrence Probability
The results shown in Figure 2 indicate that for all sign categories, the probability of obtaining the corresponding PCN-PCS pairs significantly varies with time in UT and month.Therefore, we cannot rule out the possibility that the probabilities of obtaining the PCN-PCS pairs in each of the sign categories can also vary with time even for specific IMF orientation.Because of this reason, we distinguish the diurnal and seasonal effects from the IMF clock angle effect on signs in the PCN-PCS pairs by subdividing each of the sign categories into four different time coverages according to UT and month as follows: Time 1: At 04:00-12:00 UT in May-August (the time when both the PCN and PCS index stations are in the dawn MLT sector during the northern summer) Time 2: At 04:00-12:00 UT in November-February (the time when both the PCN and PCS index stations are in the dawn MLT sector during the northern winter) Time 3: At 16:00-24:00 UT in May-August (the time when both the PCN and PCS index stations are in the dusk MLT sector during the northern summer) Time 4: At 16:00-24:00 UT in November-February (the time when both the PCN and PCS index stations are in the dusk MLT sector during the northern winter)  and 90°and between 90°and 180°with peaks of greater than 90% at θ ∼ ±180°) irrespective of season and MLT location of the PC stations.The occurrence probability is down to approximately 25% when the IMF is northward (in θ bins between 90°and 90°).On the contrary, the probability of obtaining the negative-negative PCN-PCS pairs (Sign 2) reaches its peak (higher than 25%) under purely northward IMF conditions (in θ bins around 0°), regardless of season and MLT location of the stations.The occurrence probability becomes lower (down to a few percent) as the IMF clock angle changes from 0°to ±180°.
The panels in the third and fourth rows (Sign 3 and Sign 4) show that the occurrence probability of opposite-sign PCN-PCS pairs depends on the MLT location of the PC stations as well as the IMF B y orientation under positive IMF B z conditions.In the dawn MLT sectors (Time 1 and Time 2), the occurrence probabilities of the negativepositive PCN-PCS pairs (Sign 3) have a maximum in the IMF clock angle range of 90°to 0°(shifted dawnward from purely northward direction), while those of the positive-negative PCN-PCS pairs (Sign 4) have a maximum in the IMF clock angle range of 0°-90°(shifted duskward from purely northward direction).Oppositely, the probability distributions in the dusk MLT sectors (Time 3 and Time 4) are skewed duskward for the negativepositive PCN-PCS pairs and dawnward for the positive-negative PCN-PCS pairs, respectively.
In addition, it is clear that for Sign 3 category, the maximum occurrence probability among the IMF clock angle bins is higher in Time 1 (41%) and Time 3 (49%) coverages compared to Time 2 (29%) and Time 4 (9%) coverages, respectively.For Sign 4 category, on the other hand, the maximum value is higher in Time 2 (44%) and Time 4 (27%) coverages than in Time 1 (30%) and Time 3 (9%) coverages, respectively.The occurrence distributions of the opposite-sign PCN-PCS pairs also clearly show that in the case of northward IMF conditions (in 90°≤ θ < 90°bins), the occurrence probabilities of the negative-positive (positive-negative) PCN-PCS pairs are in general higher during northern winter (summer) than northern summer (winter) for both the dawn and dusk MLT sectors.These imply that there is a systematic change in the occurrence distribution of the opposite-sign PCN-PCS pairs with seasons.
Figure 4 shows the occurrence probabilities (displayed as a percentage) of the PCN-PCS pairs binned by IMF clock angle and cone angle (grid size of 30°× 30°) in various sign categories (first to fourth rows) for different time coverages (first to fourth columns).For each time coverage, these values are equivalent to the numbers of PCN-PCS pairs in the sign category divided by the total number of PCN-PCS pairs in all sign categories (fifth row).For all sign categories and time coverages, the occurrence peaks can be seen in the θ bins corresponding to the peaks in the IMF clock angle distribution of the occurrence probabilities of the PCN-PCS pairs shown in Figure 3.
The main feature shown in Figure 4 is the IMF cone angle dependence.The occurrence probabilities tend to reach either peaks or valleys (depending on the θ bins) at ψ ∼ 90°, indicating the IMF in the direction perpendicular to the Sun-Earth line.This implies that the existence of the strong IMF B x component can modulate the occurrence probabilities of PCN-PCS pairs for given IMF clock angle conditions regardless of season and MLT location of the PC index stations.
Another feature associated with the IMF B x component is the preferred orientations of the IMF in the occurrence of the opposite-sign PCN-PCS pairs (Sign 3 and Sign 4) under radially oriented IMF (IMF B x -dominated) conditions.This can be seen by comparing their occurrence probabilities between 0°≤ ψ < 30°bins and 150°≤ ψ ≤ 180°bins (also see Figure S1).In the dawn MLT sector (Time 1 and Time 2 coverages), the occurrence probabilities are higher in 150°≤ ψ ≤ 180°bins than in 0°≤ ψ < 30°bins for the negative-positive PCN-PCS pairs (Sign 3).The opposite trend can be clearly seen for the positive-negative PCN-PCS pairs (Sign 4) in such a way that their occurrence probabilities are higher in 0°≤ ψ < 30°bins than in 150°≤ ψ ≤ 180°bins.In the dusk MLT sector (Time 3 and Time 4 coverages), however, these features are not clear (i.e., the occurrence probabilities in 0°≤ ψ < 30°bins and in 150°≤ ψ ≤ 180°bins are comparable to each other) or even reversed (i.e., the occurrence probabilities are higher in 0°≤ ψ < 30°bins than in 150°≤ ψ ≤ 180°bins for the negative-positive PCN-PCS pairs and are higher in 150°≤ ψ ≤ 180°bins than in 0°≤ ψ < 30°bins for the positive-negative PCN-PCS pairs).bar only in the UT-month bins that contain greater than five PCN-PCS data pairs (otherwise, color-coded in gray).The number of paired data for any UT-month bin is equal to the occurrence probability multiplied by the total number of the available PCN-PCS pairs, which have been presented in Figure 2.

Difference Between Concurrent PCN and PCS
In Figure 5a, we can see that for the positive-positive PCN-PCS pairs, more than half of the data pairs during northern summer (winter) season have a larger (smaller) value in PCN compared to PCS irrespective of UT.By contrast, the opposite trend is visible in Figure 5b in such a way that for the negative-negative PCN-PCS pairs, PCN is generally lower (higher) than PCS over UTs during northern summer (winter) season.For the negativepositive PCN-PCS pairs (Figure 5c), the median values of ∆PC are relatively low (approximately ∆PC < 1 mV/ m) around dusk times (15:00-19:00 UT) during northern summer (May-July) compared to the other time intervals.The diurnal and seasonal variations in SZA at the PCN index station (Figure 1a) indicate that the median values of ∆PC is low during periods of low SZA at this location (SZA at Qaanaaq < 60°).A similar trend can be seen by comparing between ∆PC for the positive-negative PCN-PCS pairs (Figure 5d) and the SZAs at the PCS index station (Figure 1b).The median values of ∆PC are generally high (approximately ∆PC > 1 mV/m) during periods of low SZA at the location of the Vostok station (SZA at Vostok < 75°).
Figure 6 shows scatter plots of the differences between concurrent PCN and PCS versus the IMF clock angle, split according to the sign category (different rows) and time coverage (different columns).The circles and error bars overplotted onto the scattered data points indicate the medians and upper/lower quartiles of ∆PC values in θ bins (with 30°bin widths).The median and quartiles are calculated only in the θ bins that contain greater than five data points.
In Figure 6, we find distinctive features between the dawn and dusk MLT sectors in IMF clock angles variations of the difference in the positive-positive PCN-PCS pairs (first row panels).It is clear that in the dawn MLT sector (first and second panels), the distributions of the scattered data points and the medians follow sinusoidal variations along the IMF clock angles with lower ∆PC values at θ ∼ 90°bins and higher ∆PC values at θ ∼ 90°bins (∆PC < 0 mV/m and ∆PC > 0 mV/m, respectively, for more than half of the data points) regardless of the season.These sinusoidal variations display shifts toward more positive in northern summer (minimum of 0.26 mV/m at 120°≤ θ < 90°bin and maximum of 0.58 mV/m at 60°≤ θ < 90°bin for medians) and more negative in northern winter (minimum of 0.71 mV/m at 120°≤ θ < 90°bin and maximum of 0.26 mV/m at 90°≤ θ < 120°bin for medians).However, those in the dusk MLT sector (third and fourth panels) do not clearly show the sinusoidal response to the IMF clock angle variations.Instead, the scattered data tend to cover wider range of ∆PC values at θ ∼ ±90°bins than any other θ bins.Moreover, the median values indicate that more than half of the data points have ∆PC > 0 mV/m and ∆PC < 0 mV/m in northern summer and northern winter, respectively, for all θ bins.
For negative-negative PCN-PCS category (second row panels), the distributions of the scattered data points and the medians of ∆PC only show the seasonal differences, which can be also seen in Figure 5b (i.e., ∆PC < 0 mV/m during northern summer and ∆PC > 0 mV/m during northern winter in general).Moreover, the scattered data tend to cover wider range of ∆PC with either lower or higher values (depending on the season) in 90°≤ θ < 90°bins.A similar trend can be seen in the opposite-sign PCN-PCS categories (third and fourth row panels) in such a way that the scattered data cover wider range of ∆PC (with either lower or higher values depending on the sign category) at around θ bins where the occurrence peaks exist (see third and fourth row panels of Figure 3) except for the Time 4 coverage.Based on these results, we can rule out intuition that the occurrence probabilities of the PCN-PCS pairs in these sign categories (also see Figure 3) result mainly from the PC indices whose values are expected to be small (approaching ±0 mV/m with signs depending on the sign category) under northward IMF conditions with weak (near background level) plasma convection in both hemispheres.
Figure 7 shows median values of the differences between concurrent PCN and PCS in two-dimensional bins of the IMF clock angle and cone angle (grid size of 30°× 30°) for different sign categories (first to fourth rows) and time coverages (first to fourth columns).We note that the number of data points in each θ-ψ bin can be obtained by multiplying the occurrence probability by the total number of the available PCN-PCS pairs (shown in Figure 4), and the θ-ψ bins that contain less than or equal to five PCN-PCS data pairs are left gray.
In Figure 7, the panels in the first row show that for the positive-positive PCN-PCS category, median values of ∆PC in the dawn MLT sector (first and second panels) have the peaks in the magnitude (either positive or negative values) at ψ ∼ 90°and θ ∼ ±90°, with their sign reversal at θ ∼ 0°over the IMF cone angle ranges.The magnitudes in ∆PC are generally higher in θ ∼ 90°(with positive values) during northern summer (first panel) and in θ ∼ 90°(with negative values) during northern winter (second panel), which can be also seen in the corresponding panels of Figure 6.On the other hand, those in the dusk MLT sector (third and fourth panels) are in general positive in the northern summer and negative in the northern winter over the θ-ψ domain without sign reversal at θ ∼ 0°.The panels in the second row show the seasonal changes in the discrepancy in negative-negative PCN-PCS pairs with ∆PC < 0 mV/m in northern summer and ∆PC > 0 mV/m in northern winter over the θ-ψ domain.These imply that for the same-sign PCN-PCS categories, the variations in ∆PC are not significantly affected by the IMF orientation (especially, the IMF cone angle), in comparison to the season.
For the opposite-sign PCN-PCS categories (third and fourth row panels), the median values in ∆PC tend to have either peaks or valleys (depending on the sign category) at θ bins where the occurrence peaks (shown in the corresponding panels of Figure 4) exist.However, it is not clear whether the level of the difference between PCN and PCS are controlled by the existence of the strong IMF B x component (the cases that the median values of ∆PC in 90°≤ θ < 90°bins have peaks in the magnitude at either 0°≤ ψ < 30°bins or 150°≤ ψ ≤ 180°bins as shown in the first and second panels of the third row) or not (the cases they have peaks in the magnitude at 30°≤ ψ < 150°b ins as shown in the remaining panels).

Discussion
The magnetic field perturbations in the ionosphere observed by satellites provided evidence for the existence of field-aligned current (FAC) systems and their fundamental importance for the SW-M-I coupling (Armstrong & Zmuda, 1970;Iijima & Potemra, 1976a, 1976b;Zmuda & Armstrong, 1974).The high-latitude FACs are linked to the ionospheric convection with the same process in the magnetosphere-ionosphere coupling system (Juusola et al., 2014;Kamide & Troshichev, 1994; also see Milan et al., 2017, and references therein).In this section, we discuss the results presented in the previous section (in terms of the occurrence distributions of paired data for different sign types and the discrepancy between the indices) based on the relationship between the FAC system and the plasma convection pattern in the high-latitude ionosphere of both hemispheres for various IMF orientations-Note that the equivalent currents are assumed equal to the Hall currents whose direction is opposite to the plasma flow, although this can be satisfied under conditions of ionospheric conductance being uniform or varying in directions perpendicular to the convection streamlines (Laundal et al., 2015).
In Figures 3 and 4, we have shown that the occurrence distributions of the same-sign PCN-PCS pairs depend strongly on the IMF B z component regardless of the season and the MLT sector of both the PC index stations.More specifically, the occurrence distributions have peaks at due southward IMF (θ ∼ ±180°and ψ ∼ 90°) for positive-positive PCN-PCS pairs and at due northward IMF (θ ∼ 0°and ψ ∼ 90°) for negative-negative PCN-PCS pairs.These statistical features can be interpreted as results of well-known antisunward plasma flow poleward of the Region 1 FAC systems in the two-cell convection pattern and sunward plasma flow centered between northward IMF-induced FACs (hereinafter called the NBZ FAC system) with the additional reversed two-cell convection pattern in the polar caps (Juusola et al., 2014;Kamide & Troshichev, 1994), respectively, in both hemispheres.
The presence of the IMF B y component (whose magnitude is dominant over or comparable to the magnitude of IMF B z ) under positive IMF B z conditions becomes an important factor that causes opposite-sign PCN-PCS pairs, especially when the IMF B x component is minor in magnitude compared to the other two IMF components.Their occurrence distributions have peaks at either 90°≤ θ < 0°or 0°≤ θ < 90°bins with ψ ∼ 90°depending on the sign type and the MLT location of the PC index stations.Such sign type and MLT dependence can be explained by the contribution of the FACs distorted due to the presence of the IMF B y component (hereinafter called the BY FAC system).The ionospheric equivalent currents with BY FAC system cause the shift of the antisunward flowing portion of the NBZ FAC-associated equivalent currents in the ionosphere toward the dawnside/duskside (duskside/dawnside) in the Northern/Southern Hemisphere under negative (positive) IMF B y conditions, as a superposition between them (Friis-Christensen & Wilhjelm, 1975;Kuznetsov & Troshichev, 1977).From the perspective of the convection pattern, northward and dawnward IMF (in 90°≤ θ < 0°bins) can produce the sunward flowing portion in the reversed two-cell pattern shifted toward the dawnside in the Northern Hemisphere and the duskside in the Southern Hemisphere.Based on these geometric features, it is suggested that the negativepositive PCN-PCS pairs are preferred to be obtained in the dawn MLT sector, while the positive-negative PCN-PCS pairs are expected to be more frequently obtained in the dusk MLT sector.For northward and duskward IMF (in 0°≤ θ < 90°bins), on the other hand, the sunward flowing portion in the reversed two-cell pattern can be shifted to the dusk MLT sector in the Northern Hemisphere and dawn MLT sector in the Southern Hemisphere.Consequently, the negative-positive PCN-PCS pairs and the positive-negative PCN-PCS pairs are obtained predominantly in the dusk and dawn MLT sectors, respectively.
As mentioned above, the IMF clock angle dependence of the occurrence of the PCN-PCS pairs is more obvious when IMF B x is weak (i.e., in ψ ∼ 90°bins) for all sign categories and time coverages.For strong IMF B x cases (i.e., in 0°≤ ψ < 30°bins and 150°≤ ψ ≤ 180°bins), on the other hand, the occurrence of the opposite-sign PCN-PCS pairs tend to have the preferred IMF B x orientations depending on the sign type and the MLT location of the PC index stations (third and fourth row panels of Figure 4; also see Figure S1).Park et al. (2022) pointed out that the hemispheric asymmetry in the SW-M-I coupling in the polar cap induced by strong IMF B x can be responsible for the discrepancy between the concurrent PCN and PCS.According to them, under strong IMF B x conditions, dayside magnetopause reconnection can take place in one hemisphere where the IMF drapes southward along the magnetopause, while single-lobe reconnection can occur in the other hemisphere where the IMF drapes northward along the magnetopause (also documented in Pi et al. (2017)).Because the ionospheric footprints of the field lines caused by the single-lobe reconnection are placed in the same hemisphere, the reversed two-cell convection circulation in the polar cap can occur only in the corresponding hemisphere.This could make the occurrence probability of the negative-positive PCN-PCS pairs possible to be higher for earthward IMF cases than for sunward IMF cases.For the positive-negative PCN-PCS pairs, on the other hand, their occurrence probability could be higher for sunward IMF cases than for earthward IMF cases.Wang et al. (2014) also argued from their observational results that under conditions of strong IMF B x , north-south asymmetry in the lobe reconnection generates not only the FACs (whose directions are opposite to BY FACs) in the cusp region but also the sunward flow in the polar cap region of the corresponding hemisphere.The above scenario (on the topology of open field lines under strong IMF B x conditions and the resultant ionospheric convection patterns in each polar cap) is applicable to our statistical results for opposite-sign PCN-PCS pairs in the dawn MLT sector (Time 1 and Time 2 coverages).The occurrence probabilities of the positive-positive PCN-PCS pairs, which are higher for strong IMF B x than for weak IMF B x during positive IMF B z intervals regardless of the time coverage, also support the above scenario that the global two-cell convection with antisunward flow in the polar caps can occur in both hemispheres as a result of the dayside magnetopause reconnection even under strong IMF B x conditions.
For opposite-sign PCN-PCS pairs in the dusk MLT sector (Time 3 and Time 4 coverages), however, the overall tendency is not clear or even reversed compared to that in the dawn MLT sector at the corresponding sign categories.We speculate that the IMF orientation is less effective in controlling the global convection pattern in the dusk MLT sector than in the dawn MLT sector.This is supported by the results shown in Figures 6 and 7 that especially for positive-positive PCN-PCS pairs, the differences between concurrent PCN and PCS in the dawn MLT sector vary with IMF orientation (depending mainly on the conditions of nonzero IMF B y ) and season, while those in the dusk MLT sector vary with season in general.Using the Super Dual Auroral Radar Network (SuperDARN) measurements (Greenwald et al., 1995), previous studies have shown that there exist dawn-dusk asymmetries in the high-latitude ionospheric convection patterns, which depend not only on the interplanetary and geophysical factors (such as IMF orientation, season, and UT) (e.g., Pettigrew et al., 2010;Ruohoniemi & Greenwald, 2005) but also on the intrinsic factors (such as latitudinal gradient of the Hall conductance and the dayside-nightside conductivity gradient) (e.g., Grocott & Milan, 2014;Walach et al., 2022).Quantitative studies on dawn-dusk differences in the influences of the IMF orientation and season on the polar cap convection patterns (inferred, for example, from the SuperDARN observations) are needed in the future to investigate the difference in the control efficiencies of the interplanetary and terrestrial drivers on the SW-M-I coupling system between these MLT sectors (which we suggested in the present study).
The median values of the differences between the PC indices at 04:00-12:00 UT and 16:00-24:00 UT, respectively, binned by IMF clock angle and SZA difference (grid size of 30°× 15°) for all sign categories are shown in Figure 8 to provide further evidence for their seasonal variations in both the dawn and dusk MLT sectors.The panels in the first row clearly show that for the positive-positive PCN-PCS category, the median values of ∆PC in the dawn MLT sector vary with IMF clock angle and season (with the minimum of 1.01 mV/m at 120°≤ θ < 90°and 60°≤ ∆SZA <75°bin and the maximum of 0.75 mV/m at 90°≤ θ < 120°and 60°≤ ∆SZA < 45°bin).On the other hand, those in the dusk MLT sector vary with season (with the minimum of 0.54 mV/m at 150°≤ θ < 120°and 45°≤ ∆SZA <60°bin and the maximum of 0.99 mV/m at 90°≤ θ < 60°and 75°≤ ∆SZA < 60°bin) in general.The trends for the negative-negative PCN-PCS category (second row) are opposite to those for the positive-positive PCN-PCS category.The median values of ∆PC in the dawn MLT sector have the minimum of 1.22 mV/m at 30°≤ θ < 0°and 60°≤ ∆SZA < 45°bin and the maximum of 0.85 mV/m at 30°≤ θ < 60°and 60°≤ ∆SZA < 75°bin, while those in the dusk MLT sector have the minimum of 1.41 mV/m at 30°≤ θ < 60°and 75°≤ ∆SZA < 60°bin and the maximum of 0.42 mV/ m at 0°≤ θ < 30°and 30°≤ ∆SZA < 45°bin.These indicate that the magnitude of the summer PC index is generally larger than that of the winter PC index (i.e., |PCN| > |PCS| during northern summer and |PCN| < |PCS| during northern winter) regardless of the MLT location of the stations.
For the opposite-sign PCN-PCS categories (third and fourth rows), the magnitudes of the median value of ∆PC tend to be larger in the ∆SZA ranges far away from 0°compared to the ∆SZA ranges near 0°, except for ∆SZA ≥ 0°ranges in the dusk MLT sector.We note that in contrast to the same-sign PCN-PCS pairs, the opposite-sign PCN-PCS pairs do not provide direct evidence for the seasonal variation in contributions of PCN and PCS to ∆PC (i.e., either |PCN| > |PCS| or |PCN| < |PCS|).Therefore, we also provide θ-∆SZA distributions of the median values of PCN and PCS, respectively, in the opposite-sign PCN-PCS pairs at 04:00-12:00 UT and 16:00-24:00 UT in Figure 9 to investigate the seasonal variation in contribution of each index to the differences between these pairs.Comparing the variations between the median values of PCN and PCS with ∆SZA reveals that for both sign categories (top and bottom), the changes in the PCN index are more sensitive to the SZA difference in ∆SZA < 0°ranges (first and third panels).The magnitudes of the PCN index are also larger in the corresponding ∆SZA ranges.On the other hand, the changes in the PCS index are more sensitive to the SZA difference with their magnitudes being larger in ∆SZA ≥ 0°ranges (second and fourth panels).
The results shown in Figures 8 and 9 provide evidence that the solar illumination which can control the ionospheric conductance plays a significant role in the increase of the magnitude of the summer PC index (i.e., in the intensity enhancement in equivalent ionospheric currents regardless of the SW-M-I coupling mode).Previous studies pointed out that the summer PC index can be used as an indicator of the influences of the additional FAC systems (such as NBZ and BY FACs) on the polar cap magnetic perturbations, whereas the winter PC index can be used to estimate mainly the R1 FAC system in response to the geoeffective electric field (i.e., E KL ) (O. A. Troshichev, 2022;O. A. Troshichev et al., 2023).These are also consistent with our results shown in Figure 9 that the variation of the winter PC index is less sensitive to ∆SZA compared to that of the summer PC index due to the reduction in contribution of solar illumination to the generation/enhancement of various types of ionospheric currents (induced by the IMF orientation) in the polar caps.
In the above interpretations, we have neglected the role of α t and β t in influencing the PC indices (Equation 2).These scaling parameters for each index can contribute not only to the modulation of the occurrence probabilities of the PCN-PCS pairs between the sign categories (Figures 2-4), but also to the spread of the differences between the concurrent PCN and PCS values (Figures 5-8).Moreover, the PC indices are not proportional to the E KL -induced equivalent current in the ionosphere, because the background-adjusted magnetic perturbations are normalized by the (statistically estimated) coupling strength of δF with E KL (i.e., δF t β t normalized by α t as shown in Equation 2) to derive each of these indices.However, these effects would be minor in question because the basic tendencies of the global convection pattern for various IMF conditions (e.g., Reiff & Burch, 1985) are still applicable to the PCN-PCS pair data (obtained particularly in the dawn MLT sector if IMF B x effects are considered as well).Therefore, we can extend our interpretations in such a way that the PC indices can have both positive and negative values depending on the location of the station with respect to the ionospheric convection pattern for specified interplanetary and terrestrial conditions.Combining with the results in the IMF orientation dependence on the differences between the indices in various sign categories and time coverages reveals that the PCN-PCS pair data provide evidence for local views of the SW-M-I coupling modes at the observation points for the solar wind energy input to the magnetosphere with asymmetric control efficiency between the dawn and dusk MLT sectors.In order to investigate the global features of the SW-M-I coupling system (in terms of the patterns of ionospheric convection, electric field, and current) in the open field regions (rather than local features over the central polar caps) with high confidence using ground-based magnetometer data, therefore, one requires to provide the polar cap indices derived from magnetic field data measured at various stations in both hemispheres.The polar cap indices for various locations (in terms of MLAT and MLT) would compensate for the limitation of the single-station indices (i.e., PCN and PCS) to be used for solar-terrestrial sciences as well as for the applications of space weather monitoring, which are in agreement with the study of Stauning (2022).

Conclusions
The results shown in the present study indicate that the type of the SW-M-I coupling determined mainly from the interplanetary conditions (IMF orientation in three-dimensions) causes the sign types in PCN-PCS pairs, whereas not only the interplanetary conditions but also the terrestrial conditions (solar illumination-induced ionospheric conductivity) influence the level of the similarities/differences in the values between PCN and PCS.However, the control efficiencies of these interplanetary and terrestrial conditions are different between the dawn and dusk MLT sectors.Therefore, the current version of the PCN and PCS indices can be treated as proxies for the local view of SW-M-I coupling modes inferred from ground-based magnetometer data measured at the location of the corresponding stations in the polar caps.In this regard, deriving the polar cap indices from magnetic field data measured simultaneously at various locations (in terms of MLAT and MLT) in both hemispheres and analyzing them are proposed in order to infer the global views of the SW-M-I coupling system in open field regions with high confidence using ground-based magnetometer data.

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Combined effects of interplanetary magnetic field (IMF) orientation and ionospheric conductivity explain statistical features of polar cap northpolar cap south index pairs (PCN-PCS pairs) in the dawn magnetic local time (MLT) sector • For those in the dusk MLT sector, however, ionospheric conductivity effects are dominant over IMF orientation effects • PCN-PCS pairs provide local views about the SW-M-I coupling with different efficiencies depending on the MLT location of the stations Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.(a, b) Averaged values of the solar zenith angles (SZAs) at Qaanaaq polar cap north (PCN) index station and Vostok polar cap south (PCS) index station, respectively, in UT-month bins (grid size of 1 hr × 1 month).(c) The SZA difference between these stations (i.e., ∆SZA = SZA at Qaanaaq station SZA at Vostok station) in UT-month bins.SZA data at 1-hr cadence in 1998-2002 and in 2004-2018 are used.

Figures
Figures2a-2dshow UT-month distributions of the occurrence probability (P occ ) of the PCN-PCS pairs in various sign categories.The occurrence probability shown in these figures is equivalent to the ratio (displayed as a percentage) of the number of the PCN-PCS pairs in the corresponding sign category to the number of available PCN-PCS pairs (shown in Figure2e) within each UT-month bin (grid size of 1 hr × 1 month).All values in Figure2are color-coded according to the color bar on the bottom of each panel.

Figure 2 .
Figure 2. UT-month distributions of the occurrence probability (P occ ) for (a) positive-positive polar cap north-polar cap south index pairs (PCN-PCS pairs), (b) negativenegative PCN-PCS pairs, (c) negative-positive PCN-PCS pairs, and (d) positive-negative PCN-PCS pairs, respectively, in 1998-2002 and 2004-2018.The bin size is 1 hr × 1 month.(e) Distribution of the number of the PCN-PCS pairs with the same UT-month bins.

Figure 3
Figure3shows IMF clock angle variations (with bin widths of 30°) of the occurrence probabilities of the PCN-PCS pairs in various sign categories (first to fourth rows) for four different time coverages (first to fourth columns).The occurrence probability shown in this figure is calculated by dividing the number of PCN-PCS pairs in the corresponding sign category and time coverage by the number of PCN-PCS pairs available in the corresponding time coverage (shown in the fifth row) within each IMF clock angle bin (displayed as a percentage).In a particular IMF clock angle range for individual time coverages, therefore, the sum of the occurrence probabilities between the sign categories is 100%.The panels in the first and second rows (Sign 1 and Sign 2) clearly show that the occurrence probability for the same-sign PCN-PCS pairs depends strongly on the IMF B z orientation.The probabilities of obtaining the positivepositive PCN-PCS pairs (Sign 1) are greater than 70% under southward IMF conditions (in θ bins between 180°F

Figure 5
Figure5shows median values of the differences between concurrent PCN and PCS for all sign categories in twodimensional bins of UT and month (grid size of 1 hr × 1 month).The values are color-coded according to the color

Figure 5 .
Figure 5. UT-month distributions of the median values in the difference between polar cap north (PCN) and south (PCS) indices (∆PC = PCN PCS) for (a) positive-positive PCN-PCS pairs, (b) negative-negative PCN-PCS pairs, (c) negativepositive PCN-PCS pairs, and (d) positive-negative PCN-PCS pairs, respectively, in 1998-2002 and 2004-2018.The bin size is 1 hr × 1 month.The bins where the number of PCN-PCS pairs is less than or equal to five are color-coded in gray.

Figure 4 .
Figure 4.The occurrence probabilities (P occ ) of polar cap north-polar cap south index pairs (PCN-PCS pairs) binned by interplanetary magnetic field clock angle (θ) and cone angle (ψ) in various sign categories (first to fourth rows) for each of four different time coverages (first to fourth columns).The bin size is 30°× 30°.The numbers of PCN-PCS pairs available in θ-ψ bins in the corresponding time coverage are given in the fifth row.

Figure 6 .
Figure 6.Scatter plots of the difference between polar cap north (PCN) and south (PCS) indices (∆PC = PCN PCS) versus interplanetary magnetic field clock angle (θ) for various sign categories (first to fourth rows) and time coverages (first to fourth columns).The circles and error bars indicate the medians and upper/lower quartiles of the ∆PC values in θ bins (with bin widths of 30°) that contain greater than five data points.

Figure 7 .
Figure7.The median values of the differences between polar cap north (PCN) and south (PCS) indices (∆PC = PCN PCS) for various sign categories (first to fourth rows) and time coverages (first to fourth columns), binned by interplanetary magnetic field clock angle (θ) and cone angle (ψ).They are color-coded in θ-ψ bins with a grid size of 30°× 30°.The median values calculated using greater than five data points are displayed only in the bins (otherwise, color-coded in gray).

Figure 8 .
Figure 8.The median values of the differences between polar cap north (PCN) and south (PCS) indices (∆PC = PCN PCS) at 04:00-12:00 UT (first column) and 16:00-24:00 UT (second column) for various sign categories (first to fourth rows), binned by interplanetary magnetic field clock angle (θ) and solar zenith angle (SZA) difference between PCN and PCS index stations (∆SZA = SZA at Qaanaaq station SZA at Vostok station).They are color-coded in θ-∆SZA bins with a grid size of 30°× 15°.The median values in the θ-∆SZA bins that contain greater than five data points are displayed only (otherwise, color-coded in gray).

Figure 9 .
Figure 9.The median values of polar cap north (PCN) index and polar cap south (PCS) index, respectively, at 04:00-12:00 UT (first and second columns) and 16:00-24:00 UT (third and fourth columns) for the opposite-sign PCN-PCS categories (different rows), binned by interplanetary magnetic field clock angle (θ) and solar zenith angle (SZA) difference between PCN and PCS index stations (∆SZA = SZA at Qaanaaq station SZA at Vostok station).They are color-coded with a grid size of 30°× 15°in θ-∆SZA bins.The median values are displayed only in the θ-∆SZA bins with the data points greater than five (otherwise, color-coded in gray).