The International Association of Geomagnetism and Aeronomy (IAGA) has
recently endorsed a new Polar Cap (PC) index version to supersede
the previous seven different versions of the PCN (North) index and the five
different PCS (South) index versions. However, the new PC index has some
adverse features which should be known and taken into account by users of
the index. It uses in its derivation procedure an “effective” quiet day
level (QDC) composed of a “basic” QDC and an added solar wind sector term
related to the azimuthal component (

The Polar Cap (PC) index concept was suggested by Troshichev and Andrezen (1985) and developed roughly into its present form by Troshichev et al. (1988, 2006). The index has become an important parameter for solar–terrestrial relations and associated geomagnetic disturbances. PC index values are primarily derived from the intensity of magnetic variations associated with the ionospheric forward two-cell convection patterns in the polar cap and scaled with respect to the driving interplanetary geoeffective electric field to make the index independent of local daily and seasonal variations. The PCN (North) index is based on geomagnetic variation data from Qaanaaq (Thule) in Greenland while the PCS (South) index is based on data from Vostok in Antarctica.

The PC indices have been used to derive interplanetary geoeffective electric fields (e.g. Troshichev et al., 2006), solar wind pressure pulses (Lukianova, 2003; Huang, 2005), cross polar cap voltage and polar cap diameter (Troshichev et al., 1996, 2000; Ridley and Kihn, 2004), ionospheric Joule heating (Chun et al., 1999, 2002), and general polar cap dynamics (Stauning et al., 2008; Fiori et al., 2009; Gao et al., 2012). The PC indices were also used to predict auroral electrojet intensities (Vennerstrøm et al., 1991; Vassiliadis et al., 1996; Takalo and Timonen, 1999), global auroral power (Liou et al., 2003), and ring current intensities (Stauning et al., 2008, Troshichev et al., 2011b, 2012). For specific space weather purposes the PC indices can be used to predict substorm development (Janzhura et al., 2007; Troshichev and Janzhura, 2009), and power line disturbances in the subauroral regions (Stauning, 2013c).

In the past there have been seven different versions of the PCN index and
five versions of the PCS index (see Stauning, 2013b). The new PC index version endorsed
by IAGA in 2013 and published at

The present note describes and quantifies adverse features in the
IAGA-endorsed PC index procedure related to IMF

Polar magnetic variations beyond the quiet daily variations (QDC) are predominantly caused by the horizontal and field-aligned currents related to the convection systems sketched in Fig. 1. The horizontal currents are equivalent to oppositely directed ionospheric drift motions. The DP2 (forward) and DP3 (reverse) convection modes could be considered the basic modes for the transpolar convection and currents while DP1 (substorm) and DP4 (DPY) convection modes may generate perturbations of the two basic transpolar convection systems.

Sketches of ionospheric and field-aligned currents related to DP1 (substorm), DP2 (forward), DP3 (reverse), and DP4 (DPY) polar convection systems.

The basic definition of the Polar Cap (PC) index could be found in
Troshichev et al. (2006). In summary (cf. Stauning, 2013b), the PC index is based on an assumed
linear relation between

The linear relation is

The “geo-effective” (or “merging”) electric field (Kan and Lee, 1979) is defined
through

Equation (1) is now inverted to give a definition of the PC index by
equivalence with the merging electric field measured in mV m

The initial concept of the reference quiet day curve (QDC) for Polar Cap (PC)
index calculations was defined in Troshichev et al. (2006) (hereinafter TJS2006) by the
sentence: “Magnetic deviations

The initial QDC procedure described in Janzhura and Troshichev (2008) (hereinafter JT2008) is based on
the above principle. Each element of the two components of an initial QDC
value is derived from quiet data values recorded at the same time of day
within an interval of 30 days. The date for the calculated QDC is found as
the weighted average of all dates with quiet segments. Successive
displacements of the 30-day interval provide a series of QDC data sets from
which non-linear interpolation provides QDC values for each day. The
selection relies on quiescence criteria based on limits regarding the
variability and the gradient of the respective component data within 20 min
intervals. The concept from TJS2006 is violated in the new index procedure by the
addition of an IMF

In the initial (JT2008) QDC procedure the separations within the 30-day interval
between the dates of the quiet samples and the actual QDC date are not
considered. Thus, the possible modulation of the basic QDC values with the
phase of the solar 27-day rotation cycle, in particular with the solar wind
sector-related phase of systematic variations in the IMF

The IAGA-endorsed QDC procedure, which includes a solar wind sector (SS) contribution, is described briefly in the notes found in the PC index documentation (Appendix_AD).

The “Note on calculation 2 (sector structure)” reads:

“The sector structure is determined for each minute by a two-step smoothing process from the THL (Thule)

The solar wind sector (SS) contributions,

A similar presentation could be made for the geomagnetic

A quite new feature in the IAGA-endorsed QDC derivation procedure is the
subtraction of the SS terms from the measured component data values thereby
changing the data base used to derive the “basic” QDC. This feature is
included neither in JT2011 nor in the “Polar Cap (PC) index” documentation
available at

The IAGA-endorsed “effective” QDC is defined in “Note on calculation 5
(geomagnetic disturbances in observatory data)” found in
Appendix_AD: “Subtract sector structure and QDC from THL

Here, we resolve the horizontal geomagnetic terms in orthogonal
(

When adding the

Note from these figures that the upper and lower envelopes of the
“effective” QDC-

Mean daily variation in the

Data 2002. Thule

There are two improper features in the “effective” QDCs presented in these
figures:

The top of the QDC-

The amplitude ranges between the upper and lower envelopes of the
presented QDC-

The addition of the solar wind sector term to the basic QDC in the new
IAGA-endorsed PC-procedure is not justified since the day and night changes
in the magnetic components with IMF

Note also from Fig. 2 that the amplitude range in the mean daily variation
varies with the IMF

The display in Fig. 2 relates to all conditions and not just the quiet
cases, but the trends are the same for just the quiet cases. Thus, imposing
on the basic QDC-

These objections were published in

Magnetic data from Thule have been examined for a closer inspection of the
different day and night response in the

In order to reduce the ordinary daily variations, the regular quiet day
variations have been suppressed by subtracting the basic QDC values from the
recorded data using QDC files (without the solar wind sector contributions)
calculated by the JT2008 procedure and supplied from AARI. Furthermore, from the
displayed

From Fig. 3 it is seen that the IMF

Sector-related contributions to PCN index on 22 June 2001
according to index parameters from

To derive PC index values, the magnetic variation vector,

The next question is now: what are the consequences of using the
“effective” QDC procedure (Appendix_AF) for the PC index calculations? Here, we use
the data published by the authors of the procedure to derive the additions
to the PCN index values from the solar wind sector terms. The solar wind
sector effects are mainly associated with IMF

Since we need both the

IMF

Table 1 displays the SS contributions to the PCN index from the solar wind
sector terms given in Eq. (8) for some selected times through the day. Like
for Fig. 4, the coefficients, optimum angle and slope values are taken from
the IAGA-endorsed files of coefficients provided at the web site

Thus, although the IMF

For comparison of specific data sets, OMNI solar wind data referred to the
magnetospheric nose have been downloaded from the omniweb site (

In order to get a clear view of the effects of the solar wind sector terms,
values of the northern Polar Cap (PCN) index and the geo-effective electric
field (

From the diagram in Fig. 6b of JT2011 a period of positive excursion in the

In Fig. 5a it is seen that between 03:00 and 09:00 UT (local night at Thule) the
PCN index values are much lower, by around 1.0 to 1.5 mV m

For the night hours of the second interval, 3–10 June 2001, the data
displayed in Fig. 5b indicate the opposite trend compared to Fig. 5a for the
relation between PCN and

There are also some systematic differences in the relations between PCN and

Display of 8-day averages of PCN-IAGA indices
and

A different QDC derivation procedure built from the principles described in TJS2006 and JT2008 is outlined in Stauning (2011). From TJS2006 the principle of using the quietest data values, like those quoted in Sect. 2.3, is implemented. From JT2008 the variability and gradients in the data are considered to be useful parameters for the selection of quiet samples. In addition, the quiet samples are weighted to give preference to cases where the same face of the sun is in view.

The QDC-

Thule

The range in dates from day 145 to 245 is the same as in Fig. 1 of JT2011 (or Fig. 4.10 of TJ2012).
Hence the IMF

The rather constant top levels of the QDC-

The amplitudes in the daily range of the QDC-

During cases of strong northward interplanetary magnetic fields (IMF

Strong reverse convection cases illustrated by the monthly
sums of intensity times duration ([nT

Forward convection cases illustrated by the monthly sums of
intensity times duration [nT

Figure 7 presents the statistics for the occurrence frequencies and strengths
of strong reverse convection cases through the data interval from 1997 to
2009 used in the recent IAGA-endorsed PC index procedure. Here, the strong
reverse convection cases are defined as those where the (negative) value of the
horizontal magnetic term projected to the optimum direction,

For Thule and for Vostok the occurrence frequency of reverse convection
cases peaks in the local summer months. Furthermore, from Fig. 7 it is clear
that the occurrence frequency and intensity of reverse convection cases are
much larger at Thule compared to Vostok. The summations over the entire span
of years (excluding year 2003, no data from Vostok) give 3 times the
intensity

For comparison, Fig. 8 presents the corresponding display for strong forward
convection cases (

Including reverse convection cases adds to the “noise level” in the calculations of the optimum angle determined by the bulk of forward convection cases but the changes in angles are small. For the regression coefficients, however, including reverse convection events gives substantial increases in the slope values and negative increases in the intercept values. The effects from reverse convection events on the regression are illustrated in Fig. 11a and b of Stauning (2013b). The effects are particularly strong at daytime in the summer season and much larger for Thule than for Vostok due to the larger frequency and strength of reverse convection events in the northern polar cap compared to the southern. In addition to the direct consequences, in particular for the PCN index values, including the reverse convection cases causes strong imbalance between PCN and PCS coefficients and values.

Slopes (upper field) and intercepts (bottom field) from PCN
derivation provided in

Slope and regression coefficients for PCN (blue) and PCS (red
line) from the IAGA-endorsed PC index procedure. Data from Thule, Vostok and
OMNI 1997–2009. Reverse convection cases included (Index coefficients from

The effects of including reverse convection cases in the data base for the
regression calculations are illustrated in Fig. 9. In each of the fields for
slopes (upper field) and intercepts (bottom field) the diagram holds a
section for each of the 12 months of a year. The curves within 1 monthly
section define the coefficient values through the 24 h of a day averaged
over the month in question. They are shown in different line colours for the
three versions. The IAGA-endorsed version (from

The extended data base interval for the IAGA version compared to the AARI#3 version now includes the less active years 1997 and 2002–2009. Referring to Fig. 7 it is easy to see that the abundance of reverse convection cases is much smaller in these years than in the very active years from 1998 to 2001. Hence, the relative importance of reverse convection cases is reduced from the AARI#3 (green lines) to the IAGA version (red lines) in Fig. 9, and the consequences are reduced slopes and less negative intercept values particularly at midday in the summer months. These changes are in strong contrast to the general conclusion in Troshichev et al. (2011a) on the invariability of PC index coefficients regardless of epoch. The PCS coefficients may remain about the same but the PCN coefficients change substantially with changing data epoch.

Slope and regression coefficients for PCN (blue) and PCS (red line) derived with DMI procedure. Data from Thule, Vostok, and OMNI 1997–2009 (ex. 2003). Strong reverse convection cases excluded.

Ratio of strong reverse to forward convection intensities
and extreme values of slope (

For illustration of the inter-hemispherical balance, Fig. 10 presents the PCN
and PCS regression parameters, slopes and intercepts, derived from the
present IAGA-endorsed coefficient files (

Figure 11 presents the corresponding diagrams for the PCN and PCS coefficients derived by the DMI procedure omitting strong reverse convection events, but using the same span of years (1997–2009, ex. 2003), the same geomagnetic data from Thule and Vostok, respectively, and the same OMNI data as those used in the IAGA-endorsed procedure. The traces are again plotted vs. local time and season like in Fig. 10. A similar diagram based on data from the epoch 1995–2005 was published in Stauning (2013b).

From a comparison between the plots in Figs. 10 and 11, two features emerge. Firstly, the DMI procedure provides much better agreement between PCN and PCS index coefficients than the IAGA-endorsed procedure. Secondly, the sets of PCS coefficients agree fairly well between the IAGA-endorsed version and the DMI version, whereas there are large differences between the two sets of slope and intercept coefficients for the PCN index. The main reason for this discrepancy is the inclusion of strong reverse convection cases in the IAGA-endorsed procedure in combination with the much larger frequency and intensity of strong reverse convection events at Thule compared to Vostok.

Table 2 provides a summary of the effects from strong reverse convection on
the peak values of the slope and intercept coefficients. For the AARI#3 version (epoch
1998–2001) and the IAGA-endorsed (

Note the strong decrease in the peak slope parameter with the decreasing relative amount of reverse convection events and the corresponding decrease in the numerical value of the (negative) intercept parameter. Also note the improved match between slope and intercept parameters for the northern (PCN) and southern (PCS) indices obtained by omitting the strong reverse convection cases in the DMI version.

Referring to the defining equation (Eq. 3) for the PC index, a larger slope
gives reduced PC index values for the strong events where the intercept
contribution is relatively small compared to the disturbance. Conversely,
for weak events, where the projected disturbance,

An example of unjustified PC index enhancements for a quiet interval (17–24
June 2008) is presented in Fig. 12. The blue line indicates the (weak)
average geoeffective electric field through 24 h determined from OMNI
data while the red line presents the mean IAGA-endorsed PCN values taken
from

At the date and time at the middle of the interval of enhanced index values
(20 June, 16:00 UT) the IAGA-endorsed coefficients according to

Display of 8-day averages of PCN-IAGA indices (red line)
and

It was shown (cf. Sect. 5.2) that the IMF

To judge the importance of SS-related index modifications, note from
Troshichev et al. (2011b): “It has been found that all examined storms, lying in (Dst) range from

Concerning the NBZ-related reverse convection issue, the PC indices are meant to scale the forward transpolar (DP2) convection in response to the solar wind forcing by using the projection of magnetic variations to the forward convection-dominated “optimum direction” (cf. Troshichev et al., 1988, 2006). The large negative values of the projected variations during strong reverse convection events associated with northward IMF conditions disturb the least squares regression of magnetic variations against the non-negative solar wind merging electric field in the derivation of index coefficients.

It is documented here that strong reverse convection events are much more
frequent at Thule (PCN index) than at Vostok (PCS index) (cf. Fig. 7).
Furthermore, it is shown how the PCN index coefficients respond to a
reduction in the relative abundance of reverse convection events going from
solar maximum epoch 1998–2001 (Troshichev et al., 2006) to epoch 1997–2009 (

The effects from such major coefficient changes could be assessed from the
formula provided in Eq. (3). With the new IAGA-endorsed coefficients for
Thule, the calculated PCN index values could be reduced by up to 24 %
during disturbed conditions due to the inclusion of strong reverse
convection events in the regression procedure, while index values during
calm conditions may be given unjustified values of 0.5 to 1 mV m

To judge the importance of such systematic coefficient-based index changes,
for instance, in conjugate studies, note that the yearly average of positive
PCN values (from

The use of IMF

uncertain IMF-

unjustified positive or negative contributions to the PC indices of up to
more than 2 mV m

the coefficients for PCN depend critically on the amount of solar maximum or solar minimum intervals included in the data base

reduction by up to 24 % in PCN index values during strong disturbances

unjustified contributions of 0.5–1.0 mV m

imbalance between PCN and PCS index coefficients and index values.

Previously published alternative procedures for handling of the QDC and reverse convection problems to avoid the adverse effects are outlined here.

Live PC index values and PCN and PCS index series are now made available
through the new web site:

The Space-DTU (2014) ftp web site for PC indices:

The observatories in Qaanaaq and Vostok and their supporting institutes are gratefully acknowledged for providing high-quality geomagnetic data for this study. The topical editor G. Balasis thanks three anonymous referees for help in evaluating this paper.