<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "journalpub-oasis3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" dtd-version="3.0">
  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">ANGEO</journal-id>
<journal-title-group>
<journal-title>Annales Geophysicae</journal-title>
<abbrev-journal-title abbrev-type="publisher">ANGEO</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Ann. Geophys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1432-0576</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/angeo-33-1443-2015</article-id><title-group><article-title>A critical note on the IAGA-endorsed Polar Cap index procedure: effects
of solar wind sector structure and reverse polar convection</article-title>
      </title-group><?xmltex \runningtitle{A critical note on the IAGA-endorsed Polar Cap index procedure}?><?xmltex \runningauthor{P.~Stauning}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Stauning</surname><given-names>P.</given-names></name>
          <email>pst@dmi.dk</email>
        </contrib>
        <aff id="aff1"><institution>Danish Meteorological Institute, Lyngbyvej 100, 2100
Copenhagen, Denmark</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">P. Stauning (pst@dmi.dk)</corresp></author-notes><pub-date><day>30</day><month>November</month><year>2015</year></pub-date>
      
      <volume>33</volume>
      <issue>11</issue>
      <fpage>1443</fpage><lpage>1455</lpage>
      <history>
        <date date-type="received"><day>12</day><month>February</month><year>2015</year></date>
           <date date-type="rev-recd"><day>2</day><month>November</month><year>2015</year></date>
           <date date-type="accepted"><day>4</day><month>November</month><year>2015</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015.html">This article is available from https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015.html</self-uri>
<self-uri xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015.pdf">The full text article is available as a PDF file from https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015.pdf</self-uri>


      <abstract>
    <p>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 (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) of the interplanetary magnetic field (IMF).
The added IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related terms may introduce unjustified
contributions to the PC index of more than 2 index units (mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).
Furthermore, cases of reverse convection during strong northward IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (NBZ)
conditions included in the database for calculation of index
coefficients can cause unjustified index enhancements of 0.5–1 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> during
calm conditions, reduction of index values by more than 20 % during
disturbed conditions, and inconsistencies between index coefficients and
index values for the northern and southern polar caps. The aim here is to
specify these adverse features and quantify their effects, and to suggest
alternative steps for future modifications of the index procedure.</p>
  </abstract>
      <kwd-group>
        <kwd>Interplanetary physics (interplanetary magnetic fields) – magnetosphere physics (polar cap phenomena; solar wind–magnetosphere interactions)</kwd>
      </kwd-group>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>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.</p>
      <p>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).</p>
      <p>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 <uri>http://pc-index.org</uri> is
supplied jointly by Arctic and Antarctic Research Institute (AARI), Russia,
and DTU Space, Denmark. However, a comprehensive description of the PC index
derivation procedure is not yet available. At the pc-index.org website
reference is made to the note “Polar Cap (PC) Index” which, however, was written several years
ago to describe a former PC index version developed at AARI. Thus, this
description is not adequate now. In the documentation PC_index_description_main_document.pdf found at the Space
DTU (2014) ftp site <uri>ftp://ftp.space.dtu.dk/WDC/indices/pcn/PC_index_IAGA_endorsement_documentation/</uri>, reference is
made to the following sources for more extended descriptions of the PC index
procedures: Troshichev et al. (2006); Janzhura and Troshichev (2008, 2011); Troshichev and Janzhura (2012). However, these references
also describe previous PC index versions, which in some respects deviate
substantially from the present IAGA-endorsed procedure. Further PC index
documentation is found in the file PC_index_description_Appendix_A.pdf (hereinafter Appendix_AD), while a partial
transcript of the MatLab program and some of the data files used to
calculate PC index coefficients and index values are found in the directory:
PC_index_description_AppendixA___file_archive (hereinafter Appendix_AF) at the above DTU Space ftp site.</p>
      <p>The present note describes and quantifies adverse features in the
IAGA-endorsed PC index procedure related to IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> effects on the QDC values
used for the derivation of actual PC index values, and to the effects on the
PC index scaling coefficients (slope and intercept) from including reverse
convection events related to strong northward IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (NBZ) conditions in the
database used for the parameter derivation. The goal is to document the
effects of these problems in order to make them known to possible users of
the IAGA-endorsed PC index values. Alternative steps in the index procedure
are suggested for future modifications of the IAGA-endorsed
procedure.<?xmltex \hack{\vspace{-3mm}}?></p>
</sec>
<sec id="Ch1.S2">
  <title>Polar convection modes and PC index basics</title>
<sec id="Ch1.S2.SS1">
  <title>Convection modes</title>
      <p>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.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p>Sketches of ionospheric and field-aligned currents related to
DP1 (substorm), DP2 (forward), DP3 (reverse), and DP4 (DPY) polar convection
systems.</p></caption>
          <?xmltex \igopts{width=207.705118pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f01.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS2">
  <title>PC index definition</title>
      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the “geo-effective” (or “merging”) electric
field in the solar wind encountering the Earth, and <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the polar cap horizontal magnetic variation (at ground)
projected to the so-called “optimum direction”.</p>
      <p>The linear relation is
            <disp-formula id="Ch1.E1" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The optimum direction is perpendicular to the average DP2 transpolar
equivalent current direction (see Fig. 1) and makes an angle <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> to
the dawn–dusk direction. The projection enhances the coupling of the PC
index to the dominant DP2 forward convection mode.</p>
      <p>The “geo-effective” (or “merging”) electric field (Kan and Lee, 1979) is defined
through
            <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">SW</mml:mi></mml:msub><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:msup><mml:mi mathvariant="normal">sin</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>(</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">SW</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the solar wind velocity, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the transverse component
of the interplanetary magnetic field (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mo>(</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mi>y</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mi>z</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:msqrt><mml:mo>,</mml:mo></mml:mrow></mml:math></inline-formula> while <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> is the polar angle between the
<inline-formula><mml:math display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula> axis of the geocentric solar-magnetospheric (GSM) coordinate system and
the transverse IMF component.</p>
      <p>Equation (1) is now inverted to give a definition of the PC index by
equivalence with the merging electric field measured in mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>:
            <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">PC</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>(</mml:mo><mml:mo>∼</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The scaling parameters comprise the optimum direction angle, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>,
derived to give optimum correlation between the solar wind intensities and
the projected magnetic variations, while the coefficients, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> (slope)
and <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> (intercept), are found from Eq. (1) through regression analyses
based on an ensemble of concurrent values of the merging electric field,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and the polar cap horizontal magnetic variation vector,
<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:mi mathvariant="bold-italic">F</mml:mi></mml:mrow></mml:math></inline-formula>, counted from the quiet level, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">QL</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <title>Initial QDC procedure</title>
      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>D</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>H</mml:mi></mml:mrow></mml:math></inline-formula> 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.”</p>
      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related solar wind sector (SS) term derived from the
daily median of all data, quiet as well as disturbed, to the basic QDC
derived from quiet data samples only.</p>
      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> component, is
lost. This is seen clearly in Fig. 4 of JT2008 where the displayed variations in
QDC amplitudes through November months during all years 1998–2002 are almost
perfectly linear to indicate slow seasonal changes only.<?xmltex \hack{\vspace{-3mm}}?></p>
</sec>
</sec>
<sec id="Ch1.S3">
  <?xmltex \opttitle{IMF $B_{y}$-related solar wind sector effects in the IAGA-endorsed QDC
procedure}?><title>IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related solar wind sector effects in the IAGA-endorsed QDC
procedure</title>
<sec id="Ch1.S3.SS1">
  <?xmltex \opttitle{Derivation of the IMF $B_{y}$-related solar wind sector term}?><title>Derivation of the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related solar wind sector term</title>
      <p>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).</p>
      <p>The “Note on calculation 2 (sector structure)” reads:</p>
      <p>“The sector structure is determined for each minute by a two-step smoothing process from the THL (Thule) <inline-formula><mml:math display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mi>Y</mml:mi></mml:math></inline-formula> component daily median values,
respectively. In the first step, a 7-day running mean is produced, which in the
next step is again smoothed by a 7-day “Robust Loess” (quadratic
fit).”</p>
      <p>The solar wind sector (SS) contributions, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, determined from
the daily median values of the <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-components, are presented in Fig. 6a, b of
Janzhura and Troshichev, 2011 (hereinafter JT2011) for June 1996 and 2001. Examples of smoothing and
processing over various intervals are shown in the figures. The variations
in the final <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> term through any single day are generally
small (here less than <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>5 nT) compared to the amplitude of the total
variation (<inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>35 to <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>65 nT) through June 2001.</p>
      <p>A similar presentation could be made for the geomagnetic <inline-formula><mml:math display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>-component.
Examples of the solar wind sector terms for the <inline-formula><mml:math display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>-component are provided in
JT2011. Note, however, that there are inconsistencies between the scaling of the
SS effects in Figs. 3, 6, and 7 vs. Figs. 4 and 8 in JT2011 to be discussed in
Sect. 5.2 below.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Solar wind sector effects on the “basic” QDC derivation</title>
      <p>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 <uri>http://pc-index.org</uri>, but found only by analysing the computer procedure
“qday_db.m“ in Appendix_AF that reads
<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
<monospace>% Calculate COMP-SS<?xmltex \hack{\newline}?>
    by_x <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">=</mml:mo></mml:math></inline-formula> var_x <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">-</mml:mo></mml:math></inline-formula> ss_x;<?xmltex \hack{\newline}?>
    by_y <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">=</mml:mo></mml:math></inline-formula> var_y <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">-</mml:mo></mml:math></inline-formula> ss_y;<?xmltex \hack{\newline}?>
% Calculate QDC for every component</monospace><?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
The effects of this modification of the data basis for QDC calculations
depend on the relative position of quiet intervals with respect to the IMF
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> phase. They are possibly small but uncertain, which stresses (again) the
need for a comprehensive and updated description of the IAGA-endorsed PC
index procedure. Moreover, the files holding the solar sector terms
(ss_x, ss_y) and the derived QDC values (qdc_x, qdc_y) are not available in
Appendix_AF for independent examination.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <title>The “effective” QDC in the IAGA-endorsed PC index procedure</title>
      <p>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 <inline-formula><mml:math display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> and THL <inline-formula><mml:math display="inline"><mml:mi>Y</mml:mi></mml:math></inline-formula> and make 5 min averages”.
The corresponding computer procedure “dist5m.m” found in
Appendix_AF reads
<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
<monospace>% substract SS and QDC variations<?xmltex \hack{\newline}?>
    dist_xs <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">=</mml:mo></mml:math></inline-formula> x <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">-</mml:mo></mml:math></inline-formula> ss_x <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">-</mml:mo></mml:math></inline-formula> qdc_x;<?xmltex \hack{\newline}?>
    dist_ys <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">=</mml:mo></mml:math></inline-formula> y <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">-</mml:mo></mml:math></inline-formula> ss_y <inline-formula><mml:math display="inline"><mml:mo mathvariant="normal">-</mml:mo></mml:math></inline-formula> qdc_y;</monospace><?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Thus, an “effective” quiet day level is composed of a “basic” QDC
(TJS2006; JT2008) with an added solar wind sector (SS) contribution as explained in
JT2011. It is important to note that all elements of the basic QDC are derived
from quiet samples recorded at corresponding times of the day while the
added SS term is based on daily median values of all data whether quiet or
disturbed. The main problem for the “effective” QDC now defined in the
IAGA-endorsed procedure relates to the solar wind sector contributions as
pointed out in the critical commentary by Stauning (2013a).</p>
      <p>Here, we resolve the horizontal geomagnetic terms in orthogonal
(<italic>H,D</italic>) components in order to use the examples of the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related vector,
<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, provided in JT2011. The
“effective” QDC values for the geomagnetic <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component are produced by
adding IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related terms, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (presented for June 2001 in
Fig. 6b of JT2011) to the initial basic QDCs determined (approximately) by the
method described in JT2008. The result is presented in Fig. 1 of JT2011 for days 145
through 245 of the summer of 2001 with the QDC curve in black superimposed
on the magnetic variation data in faint grey or
in Fig. 4.10 (in colour, more readable) of Troshichev and Janzhura (2012) (hereinafter TJ2012).</p>
      <p>When adding the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> terms to the smoothly varying basic QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>
values, the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> variation patterns are transferred to
become modulations of the “effective” QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> component patterns as seen
most easily in the upper envelope corresponding to night values, and in the
lower envelope for midday values of the QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> curves shown in Fig. 1 of
JT2011 (or in Fig. 4.10 of TJ2012) The QDC-<inline-formula><mml:math display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> component including a <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> term
is handled correspondingly.</p>
      <p>Note from these figures that the upper and lower envelopes of the
“effective” QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> traces are almost congruent such that the in-between
daily range of the “effective” QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> series only shows slow seasonal
variations with maximum amplitude at midsummer. When <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> varies
monotonically (with constant slope), the modulation patterns of the
upper and lower envelopes are identical apart from half a day's phase shift.
When the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> slope changes, then small differences between the
upper and lower envelopes may result. The display in Fig. 1 of JT2011 (Fig. 4.10
of TJ2012) presents these characteristics.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><caption><p>Mean daily variation in the <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component at Thule during summer
2001 derived for three gradations of the IMF azimuthal component:
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &gt; 3 nT (red line), <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2 &lt; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &lt; 2 nT (blue line),
and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &lt; <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>3 nT (green line) (cf. Fig. 5b of JT2011).</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f02.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p>Data 2002. Thule <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-comp – QDC(AARI) in blue line for: <bold>(a)</bold> all
hours, <bold>(b)</bold> daytime, <bold>(c)</bold> night-time hours. Smoothed median values in red
line. IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in magenta line (scale to the right).</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f03.png"/>

        </fig>

      <p>There are two improper features in the “effective” QDCs presented in these
figures:
<list list-type="custom"><list-item><label>A.</label><p>The top of the QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> traces present calculated night values of the quiet
magnetic field, but the real night values are not significantly affected by the
IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-variations (cf. Figs. 2 and 3c here). Hence, the upper envelope of
the “effective” QDC should be rather flat and not strongly modulated by
IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> variations.</p></list-item><list-item><label>B.</label><p>The amplitude ranges between the upper and lower envelopes of the
presented QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> traces are not affected by the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> variations, but the real daily
variation ranges in the magnetic field are significantly different for
positive and negative IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> cases (see Fig. 2).</p></list-item></list></p>
</sec>
</sec>
<sec id="Ch1.S4">
  <?xmltex \opttitle{IMF $B_{y}$ modulation of the horizontal polar geomagnetic field
components}?><title>IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> modulation of the horizontal polar geomagnetic field
components</title>
<sec id="Ch1.S4.SS1">
  <?xmltex \opttitle{Statistics for IMF $B_{y}$ modulation of polar magnetic fields}?><title>Statistics for IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> modulation of polar magnetic fields</title>
      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are quite different and, therefore,
could not be compensated for by just adding a slowly varying daily term.
Statistically, the difference between IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> effects at day and night is
easily seen in Fig. 2 (cf. Fig. 5 of JT2011), which displays the mean daily
variation in the <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component recorded at Thule during the summer months for
three gradations of the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>: <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &lt; <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>3 nT, <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2 &lt; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &lt; 2 nT,
and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &gt; 3 nT. With magnetic local time (MLT) noon located at
15:00 UT and local time (LT) noon at 16:00 UT it is easy to see that there is
hardly any IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related difference between the three gradations through
local night (<inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 00:00–12:00 UT) while there are substantial
differences at local daytime (<inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 12:00–24:00 UT).</p>
      <p>Note also from Fig. 2 that the amplitude range in the mean daily variation
varies with the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> parameter. For summer 2001, from midnight
(<inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 04:00 UT) to noon (<inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 16:00 UT) the amplitudes in
the daily variation for the three cases are <inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 70, 120
and 230 nT for positive, near-zero, and negative IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> gradations,
respectively. Corresponding large variations should appear in the daily
amplitudes of the “effective” QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> component displayed for the same
period in Fig. 1 of JT2011 (or Fig. 4.10 of TJ2012) but are not seen.</p>
      <p>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-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> series the (almost) same <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> shift at night
and at day is not in agreement with the statistics presented in Fig. 2. It
could be noted from Fig. 1 of JT2011 (or Fig. 4.10 of TJ2012) that the amplitude of the
variations in both the upper and lower envelope of the “effective” QDCs
through June (days 152–181) are <inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 nT, which corresponds to
the range in the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> variation (<inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>35 to <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>65 nT) through June
2001 shown by the magenta line in Fig. 6b of JT2011.</p>
      <p>These objections were published in <italic>Ann. Geophys</italic>. in a commentary, Stauning (2013a), to the paper
JT2011. The commentary paper was submitted in 2012 and forwarded at that time to
the authors of JT2011, but no reply has been published yet.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <?xmltex \opttitle{IMF $B_{y}$ modulations of Thule magnetic data at~daytime and at
night-time}?><title>IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> modulations of Thule magnetic data at daytime and at
night-time</title>
      <p>Magnetic data from Thule have been examined for a closer inspection of the
different day and night response in the <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>- and <inline-formula><mml:math display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>-components to IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
variations. Plots were made to present summer data from mid-May to
mid-August (days 135 to 235). For each year the component data have been
divided into all-hour (00:00–24:00 UT), daytime (13:00–23:00 UT), and night-time
(01:00–11:00 UT) groups. The <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component data from these groups are displayed in separate
plots in the example for 2002 in Fig. 3.</p>
      <p>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 <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-components the daily median values have been derived. With a
weighted smoothing over 5 days these median values are shown in heavy red
line. For comparison, the related IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values (smoothed over 7 days) are
presented in magenta line in the lower part of the diagrams with their scale
values indicated to the right.</p>
      <p>From Fig. 3 it is seen that the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> variations displayed by the magenta
line in the bottom of each field are reproduced to some extent in the
all-hour plot of the <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component in Fig. 3a. However, it is clear that the
strong IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related variations are only reflected in the daytime values
displayed in Fig. 3b. For the night-time values of the <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component displayed
in Fig. 3c there is no correspondence between the variations in the
<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component and the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> changes. Corresponding results appear in similar
diagrams for further years (1997–2009) looked at.</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <title>Effects of the IAGA-endorsed “effective” QDC procedure on PC index
values</title>
<sec id="Ch1.S5.SS1">
  <title>Calculation of the effects of the solar wind sector term</title>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Sector-related contributions to PCN index on 22 June 2001
according to index parameters from <uri>http://pc-index.org</uri> and
<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values from JT2011.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:tbody>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Hour (UT)</oasis:entry>  
         <oasis:entry colname="col2">Opt angle (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">Slope (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">proj</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">SS</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">proj</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">00.00</oasis:entry>  
         <oasis:entry colname="col2">55.22<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">40.21</oasis:entry>  
         <oasis:entry colname="col4">48.66<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">22.38 nT</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.56</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">06.00</oasis:entry>  
         <oasis:entry colname="col2">43.44<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">31.61</oasis:entry>  
         <oasis:entry colname="col4">126.88<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">76.00 nT</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.40</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">12.00</oasis:entry>  
         <oasis:entry colname="col2">18.46<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">45.22</oasis:entry>  
         <oasis:entry colname="col4">191.90<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">25.74 nT</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.57</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">15.00 (noon)</oasis:entry>  
         <oasis:entry colname="col2">18.09<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">65.17</oasis:entry>  
         <oasis:entry colname="col4">236.53<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>32.16 nT</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>0.49</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">18.00</oasis:entry>  
         <oasis:entry colname="col2">40.48<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">54.54</oasis:entry>  
         <oasis:entry colname="col4">303.92<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>76.26 nT</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>1.40</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>To derive PC index values, the magnetic variation vector, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:mi mathvariant="bold-italic">F</mml:mi></mml:mrow></mml:math></inline-formula>, corrected for the “effective” QDC
(QDCeff) should be projected to the optimum direction characterized by the angle,
<inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula>. Then the intercept value, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>, should be subtracted, and
the result should be divided by the slope, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>. Thus, for the magnetic
variation vector:
            <disp-formula id="Ch1.E4" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">RAW</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">QDCeff</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">RAW</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">QDC</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi mathvariant="bold">Δ</mml:mi><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Here, for Thule (77.47 N, 290.77 E), with declination (year 2001) <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 297.33<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, the optimum angle and slope values presented at
<uri>http://pc-index.org</uri> have been used in combination with <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> vectors comprising the
components <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> presented in JT2011
(SS(<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">THL</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and SS(<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">THL</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. For the projection of the SS contributions to
the optimum direction we have used
            <disp-formula id="Ch1.E5" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">SS</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">PROJ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mi mathvariant="normal">sin</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mi mathvariant="normal">cos</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where
            <disp-formula id="Ch1.E6" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="normal">longitude</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="normal">declination</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">UThr</mml:mi><mml:mo>×</mml:mo><mml:msup><mml:mn>15</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Using the relation in Eq. (3) the SS-related contribution to the PC index is
then
            <disp-formula id="Ch1.E7" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi mathvariant="normal">SS</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">PROJ</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The optimal direction at noon is close to perpendicular to the IMF
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related contributions. Hence the projection of the SS vector, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, to the optimum direction is small at noon. At other local hours
the projection angle changes and the projected values of the (almost
constant) SS vector become more significant in magnitude and shift sign
twice. The diminished slope values, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula>, away from midday cause
further enhancement (cf. Eq. 7) of the effects from the SS contribution to
the PC index values during local night and morning hours.</p>
</sec>
<sec id="Ch1.S5.SS2">
  <title>Example case for 22 June 2001</title>
      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related currents (DP4
convection mode, cf. Fig. 1) in and around the daytime Cusp region at
latitudes equatorward of Thule, the current direction being related to the
sign of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. This current system is located at and close to local noon and
its effects on magnetic recordings from Thule are very clear for the daytime
sector in the data plots in Fig. 3b as well as in the statistical daytime
values presented in Fig. 2. It should be noted that since the solar wind
sector-related disturbance vectors, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="bold">Δ</mml:mi><mml:msub><mml:mi mathvariant="bold-italic">F</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, are derived from smoothed daily medians, they keep an
almost constant value and direction in the local (rotating) reference frame
through day and night and from one day to the next.</p>
      <p>Since we need both the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> terms to
calculate <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, example values could have been extracted from
Fig. 4b in JT2011, where the peak values seen on 22 June 2001 are also the peak
values in the displays in their Fig. 8. There is a problem, however. The example
values, counted from the levels at IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0, would then be <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 150 nT , <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 90 nT. Control calculations of
the 5-day sliding averages of the median <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
terms for June 2001 agree with the concept that the values in Fig. 6b of JT2011 are correct while the values presented in their Figs. 4 (with the
scale factor 10) and in Fig. 8 are around twice the correct values. Hence,
for calculations of the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> modulation of the PCN index we use here:

                <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>65</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">nT</mml:mi><mml:mo>;</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>40</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">nT</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E8"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">on</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mn>22</mml:mn><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi mathvariant="normal">June</mml:mi><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mn>2001</mml:mn><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi mathvariant="normal">at</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi mathvariant="normal">IMF</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>∼</mml:mo><mml:mn> 4</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">nT</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            Using these values for the present case from 22 June 2001 where IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
<inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 4 nT, the solar wind sector (SS) related changes, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, in the index values have been calculated and are displayed in
Fig. 4. The contributions, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, related to the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> terms, which change little during the day
or from day to day (see Fig. 6b of JT2011), come on top of the PCN values
calculated from the actual magnetic variations corrected for the basic QDC.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p>IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related solar wind sector (SS) contributions to the
PCN index values derived according to the “effective QDC” procedure
defined in JT2011 with the excursions <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 65 nT defined in their
Fig. 6b and <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 40 nT. Index coefficients are from
<uri>http://pc-index.org</uri>.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f04.png"/>

        </fig>

      <p>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 <uri>http://pc-index.org</uri>.</p>
      <p>Thus, although the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related variations in the polar cap magnetic
fields maximize at noon, the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values at this local
time are quite small due to the projection to the optimum direction in
combination with the high slope values. The real IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related variations
in the polar cap magnetic fields are almost absent during the night and
morning hours as seen clearly in Fig. 3c as well as in the statistical
values in Fig. 2. Hence, it is not appropriate that the unjustified solar
wind sector-related <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values are so large in the night and
morning hours, here almost 2.5 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in the index values through 03:00–09:00 UT,
for a case with IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 4 nT, which is a moderate and common
value.<?xmltex \hack{\newpage}?></p>
</sec>
<sec id="Ch1.S5.SS3">
  <title>Comparisons PCN-IAGA and Em-OMNI data</title>
      <p>For comparison of specific data sets, OMNI solar wind data referred to the
magnetospheric nose have been downloaded from the omniweb site (<uri>ftp://omniweb.gsfc.nasa.gov/omni/</uri>) while PCN index values derived
according to the new IAGA-adopted PC index procedure have been downloaded
from the <uri>http://pc-index.org</uri> (2014) website.</p>
      <p>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 (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) shifted in time to apply to the polar cap have been contrasted in
plots of which some examples are shown here. Both quantities have
fluctuations. Hence, for a fair comparison some averaging is needed.</p>
      <p>From the diagram in Fig. 6b of JT2011 a period of positive excursion in the
<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> term could be the interval from 18 to 25 June 2001 with
peak value on 22 June, the date used for Fig. 4 here. For this interval the
series of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as well as PCN values have been averaged over corresponding times
through the 8 days. The 8-day mean values are displayed in Fig. 5a. From
Fig. 6b of JT2011 a corresponding interval for negative excursions in <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> could be from 3 to 10 June, 2001. The 8-day average values for
this interval are presented in Fig. 5b.</p>
      <p>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<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, than the
corresponding <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values (in mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). This agrees well with the values of the
anticipated depression, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi mathvariant="normal">PCN</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, seen within this time interval
in Fig. 4 bearing in mind that the values on 22 June represent the peak
excursion with <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 65 nT in Fig. 6b of
JT2011. The <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values also needed for calculation of PCN index
values vary similarly to <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as seen in Fig. 4 of JT2011.</p>
      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Now, the average PCN values are larger than the
corresponding <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values by 0.5 to 1.0 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Considering that the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values range from <inline-formula><mml:math display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>20 to <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>35 nT during this
interval and that the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values are also lower than in the
foregoing interval there is again agreement with the expectations provided
by Fig. 4.</p>
      <p>There are also some systematic differences in the relations between PCN and
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> during daytime in the two cases (cf. Fig. 12 in Sect. 7.3 on reverse
convection). The important point here is the documentation that during night
hours the handling of the solar wind sector terms (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> used in the “effective” QDC derivation in new
IAGA-endorsed procedure has adverse consequences. The solar wind sector
terms, which give small contributions at the dayside, may give quite substantial, but unjustified changes in the PC index values when used at the night
side.<?xmltex \hack{\newpage}?></p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><caption><p>Display of 8-day averages of PCN-IAGA indices
and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-OMNI values. <bold>(a)</bold> 18–25 June 2001 for positive <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.
<bold>(b)</bold> 3–10 June 2001 for negative <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mi mathvariant="normal">SS</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f05.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S6">
  <title>Alternative QDC procedure</title>
      <p>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.</p>
      <p>The QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> values derived by this “Solar Rotation Weighted” (SRW) procedure (Stauning, 2011) are displayed by
the red line in Fig. 6 superposed on the <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component values in blue line
corresponding to the signature used in Fig. 4.10 of TJ2012 (Fig. 1 of JT2008). At the
bottom of Fig. 6 the smoothed IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values are displayed in magenta line
relating to the scale shown to the right.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><caption><p>Thule <inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula>-component in blue line with the “solar rotation
weighted” (SRW) QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> component superposed in red. (derived by the
procedure described in Stauning, 2011).</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f06.png"/>

      </fig>

      <p>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 <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values displayed at the bottom of Fig. 6 could
also be used for judging the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> excursions. Comparing the
QDC values in Fig. 1 of JT2011 (or Fig. 4.10 of TJ2012) and Fig. 6, note the two proper
features of the QDCs presented in Fig. 6 (in contrast to the corresponding
features in Fig. 1 of JT2011 (or Fig. 4.10 of TJ2012):
<list list-type="custom"><list-item><label>A.</label><p>The rather constant top levels of the QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> traces in Fig. 6
represent night values of the quiet magnetic field not significantly
affected by the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-variations (cf. Figs. 2 and 3c).</p></list-item><list-item><label>B.</label><p>The amplitudes in the daily range of the QDC-<inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> traces seen in Fig. 6 are quite strongly affected by the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> variations since the real daily
variation in the magnetic field are significantly different for positive and
negative IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> cases (see Figs. 2 and 3).</p></list-item></list>
This QDC procedure may not be perfect but it provides considerable
improvements compared to the IAGA-endorsed “effective” QDC procedure,
particularly for the night-time QDC levels.</p>
</sec>
<sec id="Ch1.S7">
  <title>The reverse convection problem for PC index coefficients and index
values</title>
      <p>During cases of strong northward interplanetary magnetic fields (IMF
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> &gt;&gt; 0) the transpolar ionospheric convection (DP3
mode, cf. Fig. 1) and the associated magnetic variations are often opposite
(reverse) of the usual forward (DP2) convection and could be quite strong.
The proportionality between the magnetic variations projected to the optimum
direction and the geo-effective (or “merging”) solar wind electric field,
which is assumed in the definition of a polar cap index (cf. Eq. 3), breaks
down. The (negative) projected magnetic variations could be quite large,
numerically, while the geo-effective electric field (cf. Eq. 2) approaches
zero for purely northward IMF regardless of its magnitude.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7"><caption><p>Strong reverse convection cases illustrated by the monthly
sums of intensity times duration ([nT <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> h]) for strongly negative
values (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (QDCcorr) &lt; <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>50 nT) of the projected
horizontal deviations for Thule (blue line) and Vostok (red). (Note: no
Vostok data in 2003).</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f07.png"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><caption><p>Forward convection cases illustrated by the monthly sums of
intensity times duration [nT <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> h]) for strongly positive values
(<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (QDCcorr) &gt; <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>50 nT) of the projected
horizontal variation for Thule (blue line) and Vostok (red). (Note: no
Vostok data in 2003).</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f08.png"/>

      </fig>

<sec id="Ch1.S7.SS1">
  <title>Forward and reverse convection intensities at Thule and
Vostok</title>
      <p>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, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, is more than 50 nT below
the projected quiet level. The figure presents the monthly sums (smoothed
over 2 months) of the product of the QDC-corrected and projected field
values and their duration [nT <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> h] for Thule (blue line) and
Vostok (red line).</p>
      <p>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 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> duration value at Thule (<inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>221 369 nT <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> h)
compared to Vostok (<inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>73 955 nT <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> h).</p>
      <p>For comparison, Fig. 8 presents the corresponding display for strong forward
convection cases (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> more than 50 nT above the projected quiet
level) and for the same span of years (1997–2009). From Fig. 8 it is seen
that the intensities of forward convection cases are about the same for
Thule and Vostok. The summations over the entire span of years (excluding
year 2003) give an intensity <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> duration value at Thule of
2 486 796 nT <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> h slightly less than that for Vostok of 2 627 511 nT <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> h.<?xmltex \hack{\newpage}?></p>
</sec>
<sec id="Ch1.S7.SS2">
  <title>Comparison of PCN and PCS regression coefficients</title>
      <p>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.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><caption><p>Slopes (upper field) and intercepts (bottom field) from PCN
derivation provided in <uri>http://pc-index.org</uri> (IAGA endorsed) (red
lines), derived by Troshichev et al. (2006) (green lines), and derived by DMI (blue lines).
Each field has 12 columns to display monthly means of the variations 00:00 to
24:00 UT.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f09.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10"><caption><p>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
<uri>http://pc-index.org</uri>, 2014).</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f10.png"/>

        </fig>

      <p>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 <uri>http://pc-index.org</uri>) in red line is based on data from 1997 to 2009. The
AARI#3 version in green line is based on data from 1998 to 2001
(TJS2006). Both versions include reverse convection cases. The DMI version in blue
line is based on data from 1997 to 2009 excluding strong reverse convection
events. A similar figure without the IAGA-endorsed parameters and using a different epoch for the DMI coefficients is provided in Stauning (2013b).<?xmltex \hack{\newpage}?></p>
      <p>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.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11"><caption><p>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.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f11.png"/>

        </fig>

<?xmltex \hack{\newpage}?><?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p>Ratio of strong reverse to forward convection intensities
and extreme values of slope (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and intercept (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
coefficients for various index versions and epochs.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="center"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:tbody>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Version</oasis:entry>  
         <oasis:entry colname="col2">Index</oasis:entry>  
         <oasis:entry colname="col3">Epoch</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula>Rev/Fwd</oasis:entry>  
         <oasis:entry colname="col5"><inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> [nT/mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> [nT]</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">AARI#3 (2006)</oasis:entry>  
         <oasis:entry colname="col2">PCN</oasis:entry>  
         <oasis:entry colname="col3">1998–2001</oasis:entry>  
         <oasis:entry colname="col4">40.1 %</oasis:entry>  
         <oasis:entry colname="col5">96.4</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>117.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">pc-index.org</oasis:entry>  
         <oasis:entry colname="col2">PCN</oasis:entry>  
         <oasis:entry colname="col3">1997–2009</oasis:entry>  
         <oasis:entry colname="col4">31.0 %</oasis:entry>  
         <oasis:entry colname="col5">66.0</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>41.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">pc-index.org</oasis:entry>  
         <oasis:entry colname="col2">PCS</oasis:entry>  
         <oasis:entry colname="col3">1997–2009</oasis:entry>  
         <oasis:entry colname="col4">4.7 %</oasis:entry>  
         <oasis:entry colname="col5">48.0</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>15.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Dmi (2015)</oasis:entry>  
         <oasis:entry colname="col2">PCN</oasis:entry>  
         <oasis:entry colname="col3">1997–2009</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula>0 %</oasis:entry>  
         <oasis:entry colname="col5">53.2</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.6</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Dmi (2015)</oasis:entry>  
         <oasis:entry colname="col2">PCS</oasis:entry>  
         <oasis:entry colname="col3">1997–2009</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula>0 %</oasis:entry>  
         <oasis:entry colname="col5">47.2</oasis:entry>  
         <oasis:entry colname="col6"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>10.7</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> Forward and reverse convection intensities are calculated for Thule:
June–July, 12:00–20:00 UT; and for Vostok: December–January, 04:00–12:00 UT. Projected
deviations &gt; 100 nT from QDC.<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula> For these two versions the strong reverse convection events are screened
away in the regression.</p></table-wrap-foot></table-wrap>

      <p><?xmltex \hack{\newpage}?>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 (<uri>http://pc-index.org</uri>).
For easy comparison, the regression parameters have now been plotted vs.
local solar time by advancing the PCN coefficients by 4 h and delaying
the PCS coefficients by 7 h corresponding to the different longitudes of
the two stations. Furthermore, the seasonal axis for the PCS index (in red)
has been shifted by 6 months to make the seasonal variations in the PCS
traces correspond to the equivalent variations in the PCN traces. It is now
easy to see that the correspondence between PCN and PCS coefficients is not
good.</p>
      <p>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).</p>
      <p>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.</p>
      <p>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 (<uri>http://pc-index.org</uri>) version
(epoch 1997–2009) the ratios of strong reverse to strong forward convection
intensities have been calculated from events with projected deviation from
QDC in the horizontal component exceeding 100 nT. The events were extracted
within local summer months (June–July for Thule, December–January for Vostok) and
within local midday hours (12:00–20:00 UT for Thule, 04:00–12:00 UT for Vostok). For the
DMI version for epoch 1997–2009, the strong reverse convection cases have
been screened away in the regression procedure.</p>
      <p>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.</p>
      <p>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, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">PROJ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, is
small, an increased negative intercept value gives larger PC index values.
With the present IAGA-endorsed regression coefficients, the large intercept
values for Thule give PCN index values that on the average are around 0.5–1.0 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> too large compared to the related geoeffective electric field values during quiet summer daytime conditions.</p>
</sec>
<sec id="Ch1.S7.SS3">
  <title>Example case of unjustified PC index enhancement during quiet
conditions</title>
      <p>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 <uri>http://pc-index.org</uri>. The two quantities should, on the
average, be equal according to the definition of the PC index. During midday
hours (12:00–22:00 UT) the average PCN index values are up to 1 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> larger than
the corresponding electric field values. The increased PCN level is not
justified in the magnetic variations, which are very small at this time, but
just the result of the large negative intercept regression parameter that was derived
with the inclusion of strong reverse convection cases.</p>
      <p>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 <uri>http://pc-index.org</uri> are <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn>65.61</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>40.89 (cf.
Fig. 10). Hence, the addition to the PC index coming just from the
coefficients, notably the large (negative) intercept value, is <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula> PC <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi mathvariant="italic">β</mml:mi></mml:mrow></mml:math></inline-formula>/<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.62 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
which is in agreement with the display in Fig. 12.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12"><caption><p>Display of 8-day averages of PCN-IAGA indices (red line)
and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-OMNI values (blue line) for the quiet interval 17–24 June 2008.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/33/1443/2015/angeo-33-1443-2015-f12.png"/>

        </fig>

<?xmltex \hack{\newpage}?>
</sec>
</sec>
<sec id="Ch1.S8">
  <title>Discussions</title>
      <p>It was shown (cf. Sect. 5.2) that the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related solar sector (SS)
term added to the basic QDC can produce up to 2.4 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> unjustified changes
in the PC index values (cf. Fig. 4 and Table 1) during night and morning
hours, where the real IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> effects are negligible (cf. Figs. 2 and 3c).
Furthermore, the pre-processing step where the SS term is subtracted from
the component data used in the basic QDC procedure (cf. Sect. 3.2) is
problematic. If the quiet samples are clustered in either the positive or
the negative phase of the IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> variations over the 30-day interval then
the SS effect on the basic QDC may further reduce or enhance the resulting
SS contribution to the PC indices.</p>
      <p>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 <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>30 to <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>373 nT,
started when the PC index and, correspondingly, the <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">M</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> field firmly exceeded the
threshold &gt; 2 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.” Thus, unjustified changes in the PC index of magnitude
up to 2.4 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (or possibly more), which could go both ways, might hide the
start of geomagnetic storms or, conversely, could indicate storm development
during completely calm conditions. And there is no guarantee that the
presented examples have found the most extreme cases.</p>
      <p>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.</p>
      <p>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 (<uri>http://pc-index.org</uri>),
and in a further step omitting the strong reverse
convection events (cf. Fig. 9). The peak slope (at noon in summer) is
reduced from 96 through 66 to 53 nT/mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> while the intercept is reduced from
<inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>117 through <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>41 to <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6 nT (cf. Table 2). The latter set of parameters is in
concordance with the corresponding parameters for the PCS index.</p>
      <p>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<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> during
midday hours in the summer months (cf. Table 2 and Fig. 12). With the
IAGA-endorsed coefficients for Vostok the “quiet” PCS values are close to
zero throughout the day and year.</p>
      <p>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 <uri>http://pc-index.org</uri>) ranges from 1.95 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
during a solar max year (2003) to 0.99 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> during a solar min year (2008).</p>
</sec>
<sec id="Ch1.S9" sec-type="conclusions">
  <title>Conclusions</title>
      <p>The use of IMF <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-related solar wind sector (SS) terms derived from the
daily median component values in the IAGA-adopted PC index procedure is
based on the erroneous concept that the IMF-<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> effects are the same through
day and night. The adverse consequences are
<list list-type="bullet"><list-item><p>uncertain IMF-<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> effects in the derivation of basic QDC values</p></list-item><list-item><p>unjustified positive or negative contributions to the PC indices of up to
more than 2 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (2.4 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in example case).</p></list-item></list>
The inclusion of NBZ-related strong reverse convection cases in the data
base used to calculate PC index coefficients (slope and intercept) has some
adverse consequences particularly for the PCN index:
<list list-type="bullet"><list-item><p>the coefficients for PCN depend critically on the amount of solar maximum or
solar minimum intervals included in the data base</p></list-item><list-item><p>reduction by up to 24 % in PCN index values during strong disturbances</p></list-item><list-item><p>unjustified contributions of 0.5–1.0 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to daytime PCN index values during
quiet conditions</p></list-item><list-item><p>imbalance between PCN and PCS index coefficients and index values.</p></list-item></list>
It is acknowledged that no index is perfect and also that having an
internationally agreed PC index is a valuable asset. However, noting that
index average values range from 1 to 2, and that magnetic storms generally
start at PC index values exceeding 2 mV m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, the
adverse effects related to the QDC derivation and to the handling of reverse
convection events seriously devaluate the present IAGA-endorsed PC indices
and make them less useful for space weather monitoring as well as for
scientific analyses of solar wind–magnetosphere interactions.</p>
      <p>Previously published alternative procedures for handling of the QDC and
reverse convection problems to avoid the adverse effects are outlined here.</p>
<sec id="Ch1.S9.SSx1" specific-use="unnumbered">
  <title>Data availability</title>
      <p>Live PC index values and PCN and PCS index series are now made available
through the new web site: <uri>http://pc-index.org</uri>. Furthermore, it
holds PCN and PCS index coefficients derived by the IAGA-endorsed procedure.
QDC values are not included. The web site includes the document “Polar Cap
(PC) Index” written by O. A. Troshichev.</p>
      <p>The Space-DTU (2014) ftp web site for PC indices: <uri>ftp://ftp.space.dtu.dk/WDC/indices/pcn/PC_index_IAGA_endorsement_documentation/</uri> includes the documents:
PC_index_description_main_document.pdf and PC_index_description_Appendix_A.pdf, and a directory, PC_index_description_Appendix_A___file_archive, with program transcripts and data files (neither
including QDC values nor solar wind sector terms).</p>
</sec>
</sec>

      
      </body>
    <back><ack><title>Acknowledgements</title><p>The observatories in Qaanaaq and Vostok and their
supporting institutes are gratefully acknowledged for providing high-quality
geomagnetic data for this study.
<?xmltex \hack{\newline}?><?xmltex \hack{\hspace*{4mm}}?> The topical editor G. Balasis thanks three anonymous referees for help in evaluating this paper.</p></ack><ref-list>
    <title>References</title>

      <ref id="bib1.bib1"><label>1</label><mixed-citation>Chun, F. K., Knipp, D. J., McHarg, M. G., Lu, G., Emery, B. A.,
Vennerstrøm, S., and Troshichev, O. A.: Polar cap index as a proxy
for hemispheric Joule heating, Geophys. Res. Lett., 26 , 1101–1104,
<ext-link xlink:href="http://dx.doi.org/10.1029/1999GL900196" ext-link-type="DOI">10.1029/1999GL900196</ext-link>, 1999.</mixed-citation></ref>
      <ref id="bib1.bib2"><label>2</label><mixed-citation>Chun, F. K., Knipp, D. J., McHarg, M. G., Lacey, J. R., Lu, G., and Emery, B.
A.: Joule heating patterns as a function of polar cap index, J. Geophys. Res., 107,
SIA 8-1–SIA 8-9, <ext-link xlink:href="http://dx.doi.org/10.1029/2001JA000246" ext-link-type="DOI">10.1029/2001JA000246</ext-link>, 2002.</mixed-citation></ref>
      <ref id="bib1.bib3"><label>3</label><mixed-citation>Fiori, R. A. D., Koustov, A. V., Boteler, D., and Makarevich R. A.: PCN
magnetic index and average convection velocity in the polar cap inferred
from SuperDARN radar measurements, J. Geophys. Res., 114, A07225,
<ext-link xlink:href="http://dx.doi.org/10.1029/2008JA013964" ext-link-type="DOI">10.1029/2008JA013964</ext-link>, 2009.</mixed-citation></ref>
      <ref id="bib1.bib4"><label>4</label><mixed-citation>Gao, Y., Kivelson, M. G., Ridley, A. J., Weygand, J. M., and Walker, R. J.: Utilizing the polar cap index to explore strong driving of polar cap
dynamics, J. Geophys. Res., 117, A07213,
<ext-link xlink:href="http://dx.doi.org/10.1029/2011JA017087" ext-link-type="DOI">10.1029/2011JA017087</ext-link>, 2012.</mixed-citation></ref>
      <ref id="bib1.bib5"><label>5</label><mixed-citation>Huang, C.-S.: Variations of polar cap index in response to solar wind
changes and magnetospheric substorms, J. Geophys. Res., 110, A01203,
<ext-link xlink:href="http://dx.doi.org/10.1029/2004JA010616" ext-link-type="DOI">10.1029/2004JA010616</ext-link>, 2005.</mixed-citation></ref>
      <ref id="bib1.bib6"><label>6</label><mixed-citation>Janzhura, A. S. and Troshichev, O. A.: Determination of the running
quiet daily geomagnetic variation, J. Atmos. Sol.-Terr. Phy., 70,
962–972, <ext-link xlink:href="http://dx.doi.org/10.1016/j.jastp.2007.11.004" ext-link-type="DOI">10.1016/j.jastp.2007.11.004</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bib7"><label>7</label><mixed-citation>Janzhura, A. S. and Troshichev, O. A.: Identification of the IMF sector
structure in near-real time by ground magnetic data, Ann. Geophys., 29,
1491–1500, <ext-link xlink:href="http://dx.doi.org/10.5194/angeo-29-1491-2011" ext-link-type="DOI">10.5194/angeo-29-1491-2011</ext-link>, 2011.</mixed-citation></ref>
      <ref id="bib1.bib8"><label>8</label><mixed-citation>Janzhura A., Troshichev, O. A., and Stauning, P.: Unified PC indices:
Relation to the isolated magnetic substorms, J. Geophys. Res., 112, A09207,
<ext-link xlink:href="http://dx.doi.org/10.1029/2006JA012132" ext-link-type="DOI">10.1029/2006JA012132</ext-link>, 2007.</mixed-citation></ref>
      <ref id="bib1.bib9"><label>9</label><mixed-citation>Kan, J. R. and Lee, L. C.: Energy coupling function and solar
wind-magnetosphere dynamo, Geophys. Res. Lett., 6, 577–580,
<ext-link xlink:href="http://dx.doi.org/10.1029/GL006i007p00577" ext-link-type="DOI">10.1029/GL006i007p00577</ext-link>, 1979.</mixed-citation></ref>
      <ref id="bib1.bib10"><label>10</label><mixed-citation>Liou, K., Carbary, J. F., Newell, P. T., Meng, C.-I., and Rasmussen, O.:
Correlation of auroral power with the polar cap index, J. Geophys. Res., 108, 1108,
<ext-link xlink:href="http://dx.doi.org/10.1029/2002JA009556" ext-link-type="DOI">10.1029/2002JA009556</ext-link>, 2003.</mixed-citation></ref>
      <ref id="bib1.bib11"><label>11</label><mixed-citation>Lukianova, R.: Magnetospheric response to sudden changes in solar
wind dynamic pressure inferred from polar cap index, J. Geophys. Res., 108, 1428, <ext-link xlink:href="http://dx.doi.org/10.1029/2002JA009790" ext-link-type="DOI">10.1029/2002JA009790</ext-link>, 2003.</mixed-citation></ref>
      <ref id="bib1.bib12"><label>12</label><mixed-citation>Ridley A. J. and Kihn, E. A.: Polar cap index comparisons with AMIE
cross polar cap potential, electric field, and polar cap area, Geophys. Res. Lett., 31, L07801,
<ext-link xlink:href="http://dx.doi.org/10.1029/2003GL019113" ext-link-type="DOI">10.1029/2003GL019113</ext-link>, 2004.</mixed-citation></ref>
      <ref id="bib1.bib13"><label>13</label><mixed-citation>Stauning, P.: Determination of the quiet daily geomagnetic variations
for polar regions, J. Atmos. Sol.-Terr. Phy., 73, 2314–2330,
<ext-link xlink:href="http://dx.doi.org/10.1016/j.jastp.2011.07.004" ext-link-type="DOI">10.1016/j.jastp.2011.07.004</ext-link>, 2011.</mixed-citation></ref>
      <ref id="bib1.bib14"><label>14</label><mixed-citation>Stauning, P.: Comments on quiet daily variation derivation in “Identification
of the IMF sector structure in near-real time by ground magnetic data” by
Janzhura and Troshichev (2011), Ann. Geophys., 31, 1221–1225,
<ext-link xlink:href="http://dx.doi.org/10.5194/angeo-31-1221-2013" ext-link-type="DOI">10.5194/angeo-31-1221-2013</ext-link>, 2013a.</mixed-citation></ref>
      <ref id="bib1.bib15"><label>15</label><mixed-citation>Stauning, P.: The Polar Cap index: A critical review of methods and
a new approach, J. Geophys. Res.-Space, 118, 5021–5038, <ext-link xlink:href="http://dx.doi.org/10.1002/jgra.50462" ext-link-type="DOI">10.1002/jgra.50462</ext-link>,
2013b.</mixed-citation></ref>
      <ref id="bib1.bib16"><label>16</label><mixed-citation>Stauning, P.: Power grid disturbances and polar cap index during
geomagnetic storms, J. Space Weather Space Clim. 3, A22,
<ext-link xlink:href="http://dx.doi.org/10.1051/swsc/2013044" ext-link-type="DOI">10.1051/swsc/2013044</ext-link>,
2013c.</mixed-citation></ref>
      <ref id="bib1.bib17"><label>17</label><mixed-citation>Stauning, P., Troshichev, O. A., and Janzhura, A.: The Polar Cap (PC)
indices. Relations to solar wind parameters and global magnetic activity, J.
Atmos. Sol.-Terr. Phy., 70, 18, 2246–2261, <ext-link xlink:href="http://dx.doi.org/10.1016/j.jastp.2008.09.028" ext-link-type="DOI">10.1016/j.jastp.2008.09.028</ext-link>, 2008.</mixed-citation></ref>
      <ref id="bib1.bib18"><label>18</label><mixed-citation>Takalo, J. and Timonen, J.: Neural network prediction of the AE index
from the PC index, Phys. Chem. Earth. Pt. C, 24,
89–92, <ext-link xlink:href="http://dx.doi.org/10.1016/S1464-1917(98)00013-0" ext-link-type="DOI">10.1016/S1464-1917(98)00013-0</ext-link>, 1999.</mixed-citation></ref>
      <ref id="bib1.bib19"><label>19</label><mixed-citation>
Troshichev, O. A. and Andrezen, V. G.: The relationship between
interplanetary quantities and magnetic activity in the southern polar cap,
Planet. Space Sci., 33, 415–419, 1985.</mixed-citation></ref>
      <ref id="bib1.bib20"><label>20</label><mixed-citation>Troshichev, O. A. and Janzhura, A.: Relationship between the PC and AL
indices during repetitive bay-like magnetic disturbances in the auroral
zone. J. Atmos. Sol.-Terr. Phy.., 71, 1340–1352, <ext-link xlink:href="http://dx.doi.org/10.1016/j.jastp.2009.05.017" ext-link-type="DOI">10.1016/j.jastp.2009.05.017</ext-link>,
2009.</mixed-citation></ref>
      <ref id="bib1.bib21"><label>21</label><mixed-citation>Troshichev, O. A. and Janzhura, A.: Space Weather monitoring by
ground-based means, Springer Praxis Books, Springer-Verlag Berlin Heidelberg, Germany, 287 pp., <ext-link xlink:href="http://dx.doi.org/10.1007/978-3-642-16803-1" ext-link-type="DOI">10.1007/978-3-642-16803-1</ext-link>,
2012.</mixed-citation></ref>
      <ref id="bib1.bib22"><label>22</label><mixed-citation>
Troshichev, O. A., Andrezen, V. G., Vennerstrøm, S., and
Friis-Christensen, E.: Magnetic activity in the polar cap – A new index,
Planet. Space Sci., 36, 1095–1102, 1988.</mixed-citation></ref>
      <ref id="bib1.bib23"><label>23</label><mixed-citation>Troshichev, O. A., Hayakawa, H., Matsuoka, A., Mukai, T., and Tsuruda, K.: Cross polar cap diameter and voltage as a function of PC index and
interplanetary quantities, J. Geophys. Res., 101, 13429–13435, <ext-link xlink:href="http://dx.doi.org/10.1029/95JA03672" ext-link-type="DOI">10.1029/95JA03672</ext-link>, 1996.</mixed-citation></ref>
      <ref id="bib1.bib24"><label>24</label><mixed-citation>Troshichev, O. A., Lukianova, R. Y., Papitashvili, V. O., Rich, F. J., and
Rasmussen, O.: Polar Cap index (PC) as a proxy for ionospheric electric
field in the near-pole region, Geophys. Res. Lett., 27, 3809–3812,
<ext-link xlink:href="http://dx.doi.org/10.1029/2000GL003756" ext-link-type="DOI">10.1029/2000GL003756</ext-link>, 2000.</mixed-citation></ref><?xmltex \hack{\newpage}?>
      <ref id="bib1.bib25"><label>25</label><mixed-citation>Troshichev, O. A., Janzhura, A., and Stauning, P.: Unified PCN and
PCS indices: method of calculation, physical sense and dependence on the IMF
azimuthal and northward components, J. Geophys. Res., 111, A05208,
<ext-link xlink:href="http://dx.doi.org/10.1029/2005JA011402" ext-link-type="DOI">10.1029/2005JA011402</ext-link>,  2006.</mixed-citation></ref>
      <ref id="bib1.bib26"><label>26</label><mixed-citation>Troshichev, O. A., Podorozhkina, N. A., and Janzhura, A. S.: Invariability of relationship
between the polar cap magnetic activity and geoeffective interplanetary electric
field, Ann. Geophys., 29, 1479–1489, <ext-link xlink:href="http://dx.doi.org/10.5194/angeo-29-1479-2011" ext-link-type="DOI">10.5194/angeo-29-1479-2011</ext-link>, 2011a.</mixed-citation></ref>
      <ref id="bib1.bib27"><label>27</label><mixed-citation>Troshichev, O. A., Somarkov, D., and Janzhura, A.: Relation of PC index
to the geomagnetic storm Dst variation, J. Atmos. Sol.-Terr. Phy.., 73,
611–622, <ext-link xlink:href="http://dx.doi.org/10.1016/j.jastp.2010.12.015" ext-link-type="DOI">10.1016/j.jastp.2010.12.015</ext-link>, 2011b.</mixed-citation></ref>
      <ref id="bib1.bib28"><label>28</label><mixed-citation>Troshichev, O., Sormakov, D.,
and Janzhura, A.: Sawtooth substorms generated under conditions of the
steadily high solar wind energy input into the magnetosphere: Relationship
between PC, AL and ASYM indices, Adv. Space Res., 49, 872–882,
<ext-link xlink:href="http://dx.doi.org/10.1016/j.asr.2011.12.011" ext-link-type="DOI">10.1016/j.asr.2011.12.011</ext-link>, 2012.</mixed-citation></ref>
      <ref id="bib1.bib29"><label>29</label><mixed-citation>Vassiliadis, D., Angelopoulos, V., Baker, D. N., and Klimas, A. J.: The
relation between the northern polar cap and auroral electrojet geomagnetic
indices in the wintertime, Geophys. Res. Lett., 23, 2781–2784,
<ext-link xlink:href="http://dx.doi.org/10.1029/96GL02575" ext-link-type="DOI">10.1029/96GL02575</ext-link>, 1996.</mixed-citation></ref>
      <ref id="bib1.bib30"><label>30</label><mixed-citation>Vennerstrøm, S., Friis-Christensen, E., Troshichev, O. A., and Andrezen, V.
G.: Comparison between the polar cap index PC and the auroral electrojet
indices AE, AL and AU, J. Geophys. Res., 96, 101–113,
<ext-link xlink:href="http://dx.doi.org/10.1029/90JA01975" ext-link-type="DOI">10.1029/90JA01975</ext-link>, 1991.</mixed-citation></ref>

  </ref-list><app-group content-type="float"><app><title/>

    </app></app-group></back>
    <!--<article-title-html>A critical note on the IAGA-endorsed Polar Cap index procedure: effects
of solar wind sector structure and reverse polar convection</article-title-html>
<abstract-html><h6 xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg">Abstract. </h6><p xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="p">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 (<m:math display="inline"><m:mrow><m:mi mathvariant="italic">B</m:mi><m:msub level="3"><m:mi/><m:mi mathvariant="italic">y</m:mi></m:msub></m:mrow></m:math>) of the interplanetary magnetic field (IMF).
The added IMF <m:math display="inline"><m:mrow><m:mi mathvariant="italic">B</m:mi><m:msub level="3"><m:mi/><m:mi mathvariant="italic">y</m:mi></m:msub></m:mrow></m:math>-related terms may introduce unjustified
contributions to the PC index of more than 2 index units (mV m<m:math display="inline"><m:msup level="3"><m:mi/><m:mrow><m:mo>-</m:mo><m:mn mathvariant="normal">1</m:mn></m:mrow></m:msup></m:math>).
Furthermore, cases of reverse convection during strong northward IMF <m:math display="inline"><m:mrow><m:mi mathvariant="italic">B</m:mi><m:msub level="3"><m:mi/><m:mi mathvariant="italic">z</m:mi></m:msub></m:mrow></m:math> (NBZ)
conditions included in the database for calculation of index
coefficients can cause unjustified index enhancements of 0.5–1 mV m<m:math display="inline"><m:msup level="3"><m:mi/><m:mrow><m:mo>-</m:mo><m:mn mathvariant="normal">1</m:mn></m:mrow></m:msup></m:math> during
calm conditions, reduction of index values by more than 20 % during
disturbed conditions, and inconsistencies between index coefficients and
index values for the northern and southern polar caps. The aim here is to
specify these adverse features and quantify their effects, and to suggest
alternative steps for future modifications of the index procedure.</p></abstract-html>
<ref-html id="bib1.bib1"><label>1</label><mixed-citation>
Chun, F. K., Knipp, D. J., McHarg, M. G., Lu, G., Emery, B. A.,
Vennerstrøm, S., and Troshichev, O. A.: Polar cap index as a proxy
for hemispheric Joule heating, Geophys. Res. Lett., 26 , 1101–1104,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/1999GL900196" title="" class="ref">10.1029/1999GL900196</a>, 1999.
</mixed-citation></ref-html>
<ref-html id="bib1.bib2"><label>2</label><mixed-citation>
Chun, F. K., Knipp, D. J., McHarg, M. G., Lacey, J. R., Lu, G., and Emery, B.
A.: Joule heating patterns as a function of polar cap index, J. Geophys. Res., 107,
SIA 8-1–SIA 8-9, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2001JA000246" title="" class="ref">10.1029/2001JA000246</a>, 2002.
</mixed-citation></ref-html>
<ref-html id="bib1.bib3"><label>3</label><mixed-citation>
Fiori, R. A. D., Koustov, A. V., Boteler, D., and Makarevich R. A.: PCN
magnetic index and average convection velocity in the polar cap inferred
from SuperDARN radar measurements, J. Geophys. Res., 114, A07225,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2008JA013964" title="" class="ref">10.1029/2008JA013964</a>, 2009.
</mixed-citation></ref-html>
<ref-html id="bib1.bib4"><label>4</label><mixed-citation>
Gao, Y., Kivelson, M. G., Ridley, A. J., Weygand, J. M., and Walker, R. J.: Utilizing the polar cap index to explore strong driving of polar cap
dynamics, J. Geophys. Res., 117, A07213,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2011JA017087" title="" class="ref">10.1029/2011JA017087</a>, 2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib5"><label>5</label><mixed-citation>
Huang, C.-S.: Variations of polar cap index in response to solar wind
changes and magnetospheric substorms, J. Geophys. Res., 110, A01203,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2004JA010616" title="" class="ref">10.1029/2004JA010616</a>, 2005.
</mixed-citation></ref-html>
<ref-html id="bib1.bib6"><label>6</label><mixed-citation>
Janzhura, A. S. and Troshichev, O. A.: Determination of the running
quiet daily geomagnetic variation, J. Atmos. Sol.-Terr. Phy., 70,
962–972, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1016/j.jastp.2007.11.004" title="" class="ref">10.1016/j.jastp.2007.11.004</a>, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib7"><label>7</label><mixed-citation>
Janzhura, A. S. and Troshichev, O. A.: Identification of the IMF sector
structure in near-real time by ground magnetic data, Ann. Geophys., 29,
1491–1500, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.5194/angeo-29-1491-2011" title="" class="ref">10.5194/angeo-29-1491-2011</a>, 2011.
</mixed-citation></ref-html>
<ref-html id="bib1.bib8"><label>8</label><mixed-citation>
Janzhura A., Troshichev, O. A., and Stauning, P.: Unified PC indices:
Relation to the isolated magnetic substorms, J. Geophys. Res., 112, A09207,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2006JA012132" title="" class="ref">10.1029/2006JA012132</a>, 2007.
</mixed-citation></ref-html>
<ref-html id="bib1.bib9"><label>9</label><mixed-citation>
Kan, J. R. and Lee, L. C.: Energy coupling function and solar
wind-magnetosphere dynamo, Geophys. Res. Lett., 6, 577–580,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/GL006i007p00577" title="" class="ref">10.1029/GL006i007p00577</a>, 1979.
</mixed-citation></ref-html>
<ref-html id="bib1.bib10"><label>10</label><mixed-citation>
Liou, K., Carbary, J. F., Newell, P. T., Meng, C.-I., and Rasmussen, O.:
Correlation of auroral power with the polar cap index, J. Geophys. Res., 108, 1108,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2002JA009556" title="" class="ref">10.1029/2002JA009556</a>, 2003.
</mixed-citation></ref-html>
<ref-html id="bib1.bib11"><label>11</label><mixed-citation>
Lukianova, R.: Magnetospheric response to sudden changes in solar
wind dynamic pressure inferred from polar cap index, J. Geophys. Res., 108, 1428, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2002JA009790" title="" class="ref">10.1029/2002JA009790</a>, 2003.
</mixed-citation></ref-html>
<ref-html id="bib1.bib12"><label>12</label><mixed-citation>
Ridley A. J. and Kihn, E. A.: Polar cap index comparisons with AMIE
cross polar cap potential, electric field, and polar cap area, Geophys. Res. Lett., 31, L07801,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2003GL019113" title="" class="ref">10.1029/2003GL019113</a>, 2004.
</mixed-citation></ref-html>
<ref-html id="bib1.bib13"><label>13</label><mixed-citation>
Stauning, P.: Determination of the quiet daily geomagnetic variations
for polar regions, J. Atmos. Sol.-Terr. Phy., 73, 2314–2330,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1016/j.jastp.2011.07.004" title="" class="ref">10.1016/j.jastp.2011.07.004</a>, 2011.
</mixed-citation></ref-html>
<ref-html id="bib1.bib14"><label>14</label><mixed-citation>
Stauning, P.: Comments on quiet daily variation derivation in “Identification
of the IMF sector structure in near-real time by ground magnetic data” by
Janzhura and Troshichev (2011), Ann. Geophys., 31, 1221–1225,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.5194/angeo-31-1221-2013" title="" class="ref">10.5194/angeo-31-1221-2013</a>, 2013a.
</mixed-citation></ref-html>
<ref-html id="bib1.bib15"><label>15</label><mixed-citation>
Stauning, P.: The Polar Cap index: A critical review of methods and
a new approach, J. Geophys. Res.-Space, 118, 5021–5038, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1002/jgra.50462" title="" class="ref">10.1002/jgra.50462</a>,
2013b.
</mixed-citation></ref-html>
<ref-html id="bib1.bib16"><label>16</label><mixed-citation>
Stauning, P.: Power grid disturbances and polar cap index during
geomagnetic storms, J. Space Weather Space Clim. 3, A22,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1051/swsc/2013044" title="" class="ref">10.1051/swsc/2013044</a>,
2013c.
</mixed-citation></ref-html>
<ref-html id="bib1.bib17"><label>17</label><mixed-citation>
Stauning, P., Troshichev, O. A., and Janzhura, A.: The Polar Cap (PC)
indices. Relations to solar wind parameters and global magnetic activity, J.
Atmos. Sol.-Terr. Phy., 70, 18, 2246–2261, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1016/j.jastp.2008.09.028" title="" class="ref">10.1016/j.jastp.2008.09.028</a>, 2008.
</mixed-citation></ref-html>
<ref-html id="bib1.bib18"><label>18</label><mixed-citation>
Takalo, J. and Timonen, J.: Neural network prediction of the AE index
from the PC index, Phys. Chem. Earth. Pt. C, 24,
89–92, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1016/S1464-1917(98)00013-0" title="" class="ref">10.1016/S1464-1917(98)00013-0</a>, 1999.
</mixed-citation></ref-html>
<ref-html id="bib1.bib19"><label>19</label><mixed-citation>
Troshichev, O. A. and Andrezen, V. G.: The relationship between
interplanetary quantities and magnetic activity in the southern polar cap,
Planet. Space Sci., 33, 415–419, 1985.
</mixed-citation></ref-html>
<ref-html id="bib1.bib20"><label>20</label><mixed-citation>
Troshichev, O. A. and Janzhura, A.: Relationship between the PC and AL
indices during repetitive bay-like magnetic disturbances in the auroral
zone. J. Atmos. Sol.-Terr. Phy.., 71, 1340–1352, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1016/j.jastp.2009.05.017" title="" class="ref">10.1016/j.jastp.2009.05.017</a>,
2009.
</mixed-citation></ref-html>
<ref-html id="bib1.bib21"><label>21</label><mixed-citation>
Troshichev, O. A. and Janzhura, A.: Space Weather monitoring by
ground-based means, Springer Praxis Books, Springer-Verlag Berlin Heidelberg, Germany, 287 pp., <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1007/978-3-642-16803-1" title="" class="ref">10.1007/978-3-642-16803-1</a>,
2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib22"><label>22</label><mixed-citation>
Troshichev, O. A., Andrezen, V. G., Vennerstrøm, S., and
Friis-Christensen, E.: Magnetic activity in the polar cap – A new index,
Planet. Space Sci., 36, 1095–1102, 1988.
</mixed-citation></ref-html>
<ref-html id="bib1.bib23"><label>23</label><mixed-citation>
Troshichev, O. A., Hayakawa, H., Matsuoka, A., Mukai, T., and Tsuruda, K.: Cross polar cap diameter and voltage as a function of PC index and
interplanetary quantities, J. Geophys. Res., 101, 13429–13435, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/95JA03672" title="" class="ref">10.1029/95JA03672</a>, 1996.
</mixed-citation></ref-html>
<ref-html id="bib1.bib24"><label>24</label><mixed-citation>
Troshichev, O. A., Lukianova, R. Y., Papitashvili, V. O., Rich, F. J., and
Rasmussen, O.: Polar Cap index (PC) as a proxy for ionospheric electric
field in the near-pole region, Geophys. Res. Lett., 27, 3809–3812,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2000GL003756" title="" class="ref">10.1029/2000GL003756</a>, 2000.
</mixed-citation></ref-html>
<ref-html id="bib1.bib25"><label>25</label><mixed-citation>
Troshichev, O. A., Janzhura, A., and Stauning, P.: Unified PCN and
PCS indices: method of calculation, physical sense and dependence on the IMF
azimuthal and northward components, J. Geophys. Res., 111, A05208,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/2005JA011402" title="" class="ref">10.1029/2005JA011402</a>,  2006.
</mixed-citation></ref-html>
<ref-html id="bib1.bib26"><label>26</label><mixed-citation>
Troshichev, O. A., Podorozhkina, N. A., and Janzhura, A. S.: Invariability of relationship
between the polar cap magnetic activity and geoeffective interplanetary electric
field, Ann. Geophys., 29, 1479–1489, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.5194/angeo-29-1479-2011" title="" class="ref">10.5194/angeo-29-1479-2011</a>, 2011a.
</mixed-citation></ref-html>
<ref-html id="bib1.bib27"><label>27</label><mixed-citation>
Troshichev, O. A., Somarkov, D., and Janzhura, A.: Relation of PC index
to the geomagnetic storm Dst variation, J. Atmos. Sol.-Terr. Phy.., 73,
611–622, <a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1016/j.jastp.2010.12.015" title="" class="ref">10.1016/j.jastp.2010.12.015</a>, 2011b.
</mixed-citation></ref-html>
<ref-html id="bib1.bib28"><label>28</label><mixed-citation>
Troshichev, O., Sormakov, D.,
and Janzhura, A.: Sawtooth substorms generated under conditions of the
steadily high solar wind energy input into the magnetosphere: Relationship
between PC, AL and ASYM indices, Adv. Space Res., 49, 872–882,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1016/j.asr.2011.12.011" title="" class="ref">10.1016/j.asr.2011.12.011</a>, 2012.
</mixed-citation></ref-html>
<ref-html id="bib1.bib29"><label>29</label><mixed-citation>
Vassiliadis, D., Angelopoulos, V., Baker, D. N., and Klimas, A. J.: The
relation between the northern polar cap and auroral electrojet geomagnetic
indices in the wintertime, Geophys. Res. Lett., 23, 2781–2784,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/96GL02575" title="" class="ref">10.1029/96GL02575</a>, 1996.
</mixed-citation></ref-html>
<ref-html id="bib1.bib30"><label>30</label><mixed-citation>
Vennerstrøm, S., Friis-Christensen, E., Troshichev, O. A., and Andrezen, V.
G.: Comparison between the polar cap index PC and the auroral electrojet
indices AE, AL and AU, J. Geophys. Res., 96, 101–113,
<a xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" href="http://dx.doi.org/10.1029/90JA01975" title="" class="ref">10.1029/90JA01975</a>, 1991.
</mixed-citation></ref-html>--></article>
