The quiet reference level for the horizontal magnetic field vector, F_QL, (H_QL, D_QL) or (X_QL, Y_QL), could be considered built from the secularly varying base level, F_BL, adding the daily variation, F_QDC, observed during quiet days (quiet day curve, QDC).

For illustration, Fig. 1 presents the H component of magnetic data (blue line) measured at Qaanaaq (Thule). The interval of data, days 135–235 of year 2001, is much the same as that used in Fig. 1 of J&T2011. The base level, H_BL, is marked by the solid horizontal line. The excursions from the base level relate to the combination of quiet day variations to be omitted and magnetic disturbances to be included at PC index calculations. The varying transverse component, IMF B_Y, of the interplanetary magnetic field (IMF) displayed in a smoothed version (the magenta line) at the bottom of Fig. 1 appears to impose systematic variations on the recorded level.

Figure 2Qaanaaq (Thule) H-component data averaged through the 10 quietest hours of the summer months in 2000–2002 for groups of data with −5 < IMF B_Y < −3 nT (green dotted line), −2 < IMF B_Y < +2 nT (solid blue line), and +3 < IMF B_Y < +5 nT (red dashed line), respectively. H_QL,SS for 22 June 2001 in “final” (solid magenta line) and “real-time” (magenta line with dots) versions (see text). Local solar and magnetic noon are at around 16 UT.

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The H-component daily median values have been Gaussian smoothed through 7 days (e-folding period = 2 days). The resulting median values presented by the wavy curve (the red line) in Fig. 1 are modulated much like the smoothed IMF B_Y values, which have a dominant period at or close to the 27 days solar rotation period. The systematic modulation of the IMF B_Y patterns relates to shifts between sustained away and toward solar magnetic field directions within solar wind sectors (e.g. Svalgaard, 1973). The effects on the magnetic data are caused by IMF B_Y-related changes in the polar plasma convection patterns particularly close to the dayside cusp region located near noon in magnetic local time (MLT). The IMF B_Y-related effects are enhanced by high ionospheric conductivities at local time (LT) noon, in the summer season, and at solar maximum (e.g. Friis-Christensen et al., 1985).

Figure 1 conveys the impression that the recorded H-component level varies systematically, both day and night, by a slowly varying amount related to IMF B_Y. In an attempt to compensate for such level changes, Troshichev (2011) introduced a solar wind sector (SS) term, which for each component of the recorded magnetic field is the difference between the long term average (horizontal line in Fig. 1) and the daily median value with adequate smoothing (superimposed wavy curve in Fig. 1). For the resulting reference QL, it is stated in J&T2011 (p. 1499) that “this level of reference can be derived if the SS effect is taken into account prior to the QDC derivation”.

A comprehensive description of the derivation of the QL reference level, from which the disturbances are counted, is not available. The computer program description (function pc_db in Appendix A, 2014) in the PC index documentation supplied to IAGA shows that the solar wind sector term is added as a specific contribution to the quiet level as well as taken into account in the QDC derivation. Thus, in the IAGA-endorsed version, the quiet reference level, F_QL,SS, could be considered built from the secularly varying base level, F_BL, the quiet daily variation, F_QDC,SS, and a solar wind sector term, F_SS, according to Eq. (2):

The IAGA-endorsed QDC procedure (function qday_db in Appendix A, 2014) is described in Janzhura and Troshichev (2008, hereafter J&T2008). An initial QDC for each component is calculated by superposition of samples of quiet data collected through an interval of 30 days to determine the daily variation for one day at a time. Depending on the distribution of quiet samples, this day is usually positioned at the middle of the interval. A series of initial QDCs is calculated by shifting the 30-day period by 10 days at a time. The final QDCs for all days are now found by smoothing interpolation through the series of initial QDCs

To provide an illustration of the quiet daily variation, Fig. 2 presents QDCs made from hourly averages of the H component of the magnetic field measured at Qaanaaq during the 10 quietest hours of each month of the summer periods (May–August) of 2000–2002. The data are grouped according to the IMF B_Y level. Data for the interval −5 < IMF B_Y < −3 nT are represented by the green dotted curve, −2 < IMF B_Y < +2 nT by the solid blue curve, and +3 < IMF B_Y < +5 nT by the dashed red curve.

Figure 3(a) Calculation of H_SS from 3-day median values (green curve), based on data available up to and including 13 June (from Fig. 6b of J&T2011), using cubic spline interpolation (black line) on 3-day medians between 6 and 12 June (dots on green curve) and extrapolation to define H_SS=91 nT on 14 June (large black dot). Resulting H_SS values for June (so far) are displaced 60 nT downward and connected by a dashed line using the lower right scale. (b) cubic spline interpolation on 3-day median samples between 9 and 15 June to define H_SS=21 nT on 17 June. (c) cubic spline interpolation on samples between 14 and 20 June to define H_SS=112 nT on 22 June. (d) Cubic spline interpolation between 19 and 25 June to define $H_{\mathrm{SS}}=-\mathrm{70}$ nT on 27 June. Smoothed IMF B_Y values are displayed at the top of the diagrams using the upper right scale.

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These three curves in Fig. 2 represent the expected daily variation, H_QDC, with sustained IMF B_Y levels within the defined limits and for the epoch considered. Local (LT and MLT) noon at Qaanaaq is at around 16 UT. The night H_QDC values (00–08 UT) are not changed much with differing IMF B_Y, while the daytime H_QDC values (12–20 UT), and thus the amplitude in the daily variation, change considerably with the varying IMF B_Y level. For the three cases, the IMF B_Z conditions are about the same with average values ranging between −0.1 and +0.1 nT.

For the J&T2008 QDC procedure, the contributions from the IMF B_Y-related positive and negative level shifts over the 30-day interval considered at a time tend to balance each other (cf. Fig. 1). For the examined interval, days 135–235 of 2001, as an example, the average IMF B_Y over any 30-day subsections range between −0.7 and 1.2 nT. Thus, the quiet daily variation for the SS-corrected data, H_QDC,SS, is most likely close to the result obtained for the case −2 < IMF B_Y < +2 nT (the solid blue curve in Fig. 2). Consequently, the sector effect on the QL is mainly provided by the addition of the slowly varying term, H_SS, (cf. Eq. 2) to the daily course found at IMF B_Y≈0. The addition will change the daytime and the nighttime parts of the QLs by similar amounts without changing the amplitude in the daily variation.

This is illustrated in Fig. 2 by the solid magenta curve where, as an example, the H_SS term (64 nT) in the final version from J&T2011 for day 173 (22 June) of 2001 has been added to the H_QDC for IMF B_Y≈0 (blue solid line) to provide the H_QL,SS variations for the day according to Eq. (2). On this day, IMF B_Y (smoothed) ≈4 nT (see Fig. 1). The expected QL based on quiet samples only is represented by the H_QDC curve for 3 < IMF B_Y < 5 nT (red dashed curve) in Fig. 2. It is seen that the H_QL,SS resulting from Eq. (2) matches the expected H_QDC level at daytime, while large differences appear at night causing PC index changes that may not be justified by the actual magnetic variations. In order to ease comparisons of real-time and post-event QL methods, the curve marked by dots (in magenta) in Fig. 2 displays the H_QL,SS variations on 22 June obtained by addition of the real-time H_SS=112 nT for this day (cf. Fig. 3c) to the H_QDC for IMF B_Y≈0.

The QL derivation for archival (post-event) data in the IAGA-endorsed procedure is discussed in Stauning (2013b, 2015). The main problem for the procedure is the incorrect assumption that the IMF B_Y-related level changes are the same day and night. As seen in Fig. 2 for the quiet samples, in Fig. 5 of J&T2011 for all data samples, or by separate displays of the daytime and nighttime data (Stauning, 2015), the IMF B_Y-related effects on the H components are strong during daytime only. The addition of the same term, H_SS, to daytime as well as nighttime QLs causes the nighttime reference levels to step up or down with IMF B_Y instead of remaining steady. The problem is aggravated by the still larger H_SS amplitudes found by using the real-time QL version.

Figure 4Calculation of H_SS=21 nT for 30 June from 3-day medians from 22, 24, 26, and 28 June. The 3-day median values (from Fig. 6b of J&T2011) are shown in green line. The H_SS values from Fig. 6b of J&T2011 are shown by the smooth solid magenta line on the scale to the right, while the H_SS values calculated here by cubic spline extrapolation are shown on the same scale by dots connected by the dashed magenta line.

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The derivation of the reference QL in real time poses further challenges. As indicated in Eq. (2), the QL (IAGA-endorsed version) comprises a QDC and an additional solar wind sector (SS) term. The QDC procedures described in J&T2008 comprise a real-time option, where the most recent completed QDCs are projected forward in time by using the seasonal trend obtained from stored QDCs derived at corresponding times in past year(s). It is not clear how to derive the proper trend if past QDCs are based on data corrected for the SS effects, which could not be taken to repeat a year later. This issue, left unresolved, is considered a minor problem compared to the derivation of the SS term in real time.

The J&T2011 publication describes the SS-related contribution to the reference quiet level (cf. Eq. 2), from which the magnetic variations used in the derivation of PC index values are counted. The SS term relies on median values of the recorded data. The daily medians display large fluctuations from day to day. In the post-event processing, these fluctuations are reduced according to J&T2011 by smoothing the daily medians over 7 days centred at the day in question. Such smoothing is not possible at real time applications where, in addition to missing the median value for the present day (which may not have ended), median values for 3 future days are lacking. The procedure for deriving the real-time SS terms, as defined in J&T2011 (1496–1497), is quoted below.

“Keeping in mind this specification, the 3-day smoothing averages of the median values were subjected to the interpolation procedure including the following steps:

1. median values for magnetic components H and D are derived for 4 intervals of preceding days with the exception of the current day (n=0):

   • r1=F[for interval from n−3 day to n−1 day]

   • r2=F[for interval from n−5 day to n−3 day]

   • r3=F[for interval from n−7 day to n−5 day]

   • r4=F[for interval from n−9 day to n−7 day];

2. piecewise polynomial form of the cubic spline interpolant for r1, r2, r3, and r4 segments is determined;

3. termination of this form related to day n=0 is examined as representative of the SS effect for the current day, even if this day is disturbed.

The procedure is repeated each subsequent day. Results of the procedure, the variation of the reconstructed magnetic H component, are presented by the magenta line in the same Fig. 6, the reconstructed H-component curve being shifted by 50 nT to a lower position.”

However, there must be an error in the presentation by J&T2011 of the procedure and its results. As will be shown, the smooth H_SS variation represented by the magenta line in their Fig. 6b (reproduced by the smooth magenta curve in Fig. 5 here) could not have been derived by using the above real-time procedure. In order to demonstrate the correct result, the 3-day median values were read from Fig. 6b of J&T2011 (shown in Appendix A here) to provide a series of values for June 2001. These values were processed strictly according to steps 1–3 of the quoted procedure.

In J&T2011 and in the following sections here, the median values are presented by their deviations from the base level. Representative results are displayed in Figs. 3 and 4. In these figures, the green curve using the left scale reproduces the 3-day median values shown by the green curve in Fig. 6b of J&T2011. Calculations of H_SS start here with the value on 9 June in order to have enough prior 3-day median values available for the cubic spline construction. Figure 3a presents an example of the cubic spline function (the black line) defined from the four 3-day median values (shown by black dots) for days 6 (spanning days 5–7), 8 (7–9), 10 (9–11), and 12 (11–13) of June 2001. The extrapolation from 12 to 14 June defines the resulting H_SS value, marked by a large dot at 91 nT on the left scale, for 14 June.

For clarity and to store the results, the H_SS values (including the 14 June value) are subsequently shifted downward by 60 nT (shown by a downward arrow) and displayed by dots connected by the dashed line using the lower right scale. Figure 3b, c, d display corresponding constructions of further H_SS values by similar cubic spline inter- and extrapolations. All H_SS values have been derived from data in the past relative to their own time as illustrated in the figures. For information on the solar wind sector conditions, smoothed IMF B_Y values are displayed at the top of the diagrams using the upper right scale.

Figure 4 presents the corresponding calculations to define the solar sector term H_SS=21 nT for 30 June 2001 by cubic spline extrapolation based on 3-day medians from 22 (21–23), 24 (23–25), 26 (25–27), and 28 (27–29) June. The diagram presents available data up to and including 29 June.

In Fig. 4, the H_SS values read from the magenta line in Fig. 6b of J&T2011 are shown by the smooth solid magenta line on the scale to the right. Their values range between −35 nT (5 June) and +64 nT (22 June). These values could also be deduced from Fig. 1 by the differences between the median values (red wavy line) and the base level (horizontal line) on the appropriate days.

The cubic spline construction operating on four points leaves no room for smoothing. The H_SS values calculated by following the procedure defined in J&T2011 to the letter are shown (on the same scale as the smoothed values) by the dots connected by the dashed magenta line. With their large excursions, these values are not reproducing the smooth “reconstructed H component presented by the magenta line” as claimed in the above procedure quoted from J&T2011. The H_SS values calculated by the real-time cubic spline extrapolation procedure range between −70 nT (on 27 June) and 112 nT (on 22 June). The differences, ΔH_SS, between the real-time and the final H_SS values range between −70 nT (on 27 June) and +72 nT (on 14 June).

The magenta curve marked by dots in Fig. 2 presents the H_QL values for 22 June 2001 using H_SS=112 nT (cf. Fig. 3c) determined by the real-time method quoted from J&T2011. This curve aggravates the differences, seen particularly at night (00–08 UT), between the H_QL,SS level derived by using H_SS=64 nT (from Fig. 6 of J&T2011 on 22 June) and the H_QL (quiet) values defined for the same IMF B_Y level (≈4 nT) and corresponding seasonal conditions (summer, solar max), but from quiet samples only (red dashed line in Fig. 2).

Figure 5From top: solar wind electric field (blue line, left scale) and IMF B_Y component (red line, right scale), PCS (prompt), PCS (final), and (in bottom panel) differences between final and prompt PCS values. Average, rms, and peak differences are noted. The presented values are 5 min averages of 1 min data.

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Figure 6PCS indices for 7 to 11 November 2014 from downloads on 11 November 2014 (red line) and 25 October 2017 (blue line). The prompt values shown by the red curve terminate in the real-time PCS value at the time of download. The displayed values are 5 min averages of the 1 min data.

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In Eq. (2) the SS term, F_SS, added to derive the quiet level, from which the projected variations, ΔF_PROJ, are counted, is a vector comprising the H component (shown in Figs. 1–4) as well as the D component (not presented in J&T2011). With specification of the quiet level defined in Eq. (2), the expression for the PC index in Eq. (1) could be written as

The projection angle varies through 360^∘ each day. Hence, the projected term, F_SS,PROJ, equals the H_SS component in magnitude two times a day (at night and in the day). Thus, the effect on the PC index value can be derived for these two cases (whether real-time or final values) through

The H_SS term is derived once a day. With typical daily variations in the slope, α, the ΔPC values at night would be around twice the corresponding values at daytime although the real SS effects are much smaller at night than in daytime (see Fig. 2). Typical values for the slope in June are α=32 nT (mV m⁻¹)⁻¹ at night and α=65 nT (mV m⁻¹)⁻¹ in the day (see http://pcindex.org). Accordingly, the changes in PC index values for differences of 70 nT between the real-time and the final H_SS values range between 1.1 mV m⁻¹ in the day and 2.2 mV m⁻¹ with opposite sign at night. Corresponding deviations between real-time and final values of D_SS could only increase (not reduce) the amplitudes in the daily oscillations (like those seen in Figs. 5 and 6) of the differences between real-time and final PC index values.

It should be noted that the 3-day median values displayed in Fig. 6b of J&T2011 are possibly smoothed by the authors. At true real-time conditions, the smoothing is not possible for the most recent 3-day median values. Hence, the potential fluctuations might generate still larger excursions in the H_SS values and in the derived real-time QL and PC index values than demonstrated here.

Apparently, the real-time PC index values exist only at the time of their presentation at http://pcindex.org. It seems that they are not kept for further analyses of their validity. Hence the only available examples are those recorded at occasional downloads of PC index values. Figure 5 presents an example based on the download of PC indices on 11 November 2014 at 09:41 UT. The data define the prompt PCS index values extending up to the real-time value provided at the time of the download. On the provision that the magnetic data are not changed from their real-time values, the current recalculations with added data turn the prompt PC index data into final values in 1–2 months. The download of final values of PCS for 2014 used here took place on 25 October 2017.

The last value of the PCS (prompt) data in the second panel from the top of Fig. 5 is the real-time value at the time of the download (11 November 2014, 09:41 UT). Further data in this panel are “prompt” values that include the “near-real-time” values. The average, rms, and peak differences between the final and the prompt values for the span of data displayed in Fig. 5 are noted in the bottom panel. It is seen that the prompt values deviate from the final values by up to 3.67 mV m⁻¹ in this example.

Figure 6 holds a more detailed display through the days 7 to 11 November 2014 of the PCS prompt (near-real-time) values (from download 11 November 2014) in the red line and final values (from download 25 October 2017) in the blue line. Note in Fig. 6 that the differences between the final and the prompt PCS values vary between (mostly) positive values at local daytime (local MLT noon at Vostok is at around 13 UT) and negative values at night at twice the amplitude.

The differences between real-time and final values need not be that large. Figure 7 presents PCS values based on the same Vostok magnetic data as those used for the PCS indices displayed in Figs. 5 and 6, but processed according to the methods suggested in Stauning (2016). The quiet reference levels (QLs) for the prompt values from a simulated download on 11 November 2014 were calculated using the “solar rotation weighted” (SRW) QDC method (Stauning, 2011) on Vostok data extending up to the date and time of the download of the PCS values presented in Figs. 5 and 6.

With the SRW method, the QL is constructed by weighted superposition of quiet samples for corresponding times of the day from an interval of ±40 days from the day in question. In the superposition, the samples are weighted to give preference to dates close to (and including) the day in question and to dates with the same view of the sun in its 27-day rotation. In real-time calculations of PC indices, the QL estimates use data recorded 40 days prior to the date and time in question. In post-event calculations, the QL estimates are gradually improved as samples from up to 40 days past the day in question become available. In contrast to the IAGA-endorsed QL method, the SRW method provides adequate QL values at night and preserves the IMF B_Y-related differences in daytime QL amplitudes (cf. Fig. 2). For QL calculations in real-time applications, the SRW method is inherently more robust to data gaps and other irregularities in the stream of incoming magnetic data than the cubic-spline-based extrapolation method.

Figure 7Prompt and final PCS index values based on Vostok data for the dates and in the format of Fig. 5. The E_M and IMF B_Y data in the top panel are the same as those presented in Fig. 5. The PCS prompt and final indices have been processed from Vostok data by using the “DMI” methods (Stauning, 2016).

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For the case presented in Fig. 7, the maximum difference between prompt and final values is just 0.43 mV m⁻¹. At the start of the interval presented in Fig. 7, the date (15 October) is 27 days from the date (11 November) of simulated download. Thus, just a small part (13/80) of the total amount of samples from the usual ±40 days interval are missing at the start and their weights are low. The derived QDC is now close to its final value. As the date for PC index calculations approaches the simulated download date, more samples ahead of the day in question are missing such that the QDCs may differ more and more from their final values.

The example of large differences between prompt (real-time) and final PC index values presented here in Figs. 5 and 6 agree with the indications presented in Figs. 3 and 4 of the possible effects (large excursions) of using the real-time cubic spline extrapolation to derive the (daily) solar wind sector (SS) term, F_SS. In the IAGA-endorsed procedure (Appendix A, 2014), the SS term is part of the quiet reference level, (F_QL,SS), from which the magnetic variations included in the PC index calculations are counted (cf. Eq. 2). F_QL,SS, furthermore, includes the quiet daily variation, F_QDC,SS, calculated around one month earlier and projected forward to the actual date by using past year(s) seasonal trend (J&T2008). The validity of this process is difficult to assess when operating on data corrected for the SS term. The SS effects may not repeat in successive years. However, it is assumed that possible differences between real-time and final F_QDC,SS values are relatively small compared to variations in the F_SS term.

It should be noted that the example presented in Figs. 5 and 6 just represents one occasional download of PC indices including the real-time value at the time of the download. Further cases not recorded may display still larger deviations between the real-time index values supplied at download times and the final values downloaded at later times and considered to represent the best possible values. The cubic spline extrapolation method to estimate the solar wind sector term for the real-time QLs is vulnerable to the configuration of the four involved 3-day median values, as evident in Figs. 3a–d and 4, and probably also highly sensitive to irregularities in the supply of magnetic data.

The magnitude of the peak differences between prompt and final values found here, ΔPC(max) = 3.67 mV m⁻¹, corresponds to the anticipated PC index levels at strong substorms since PC index values above 2 mV m⁻¹ usually indicate magnetic storm and substorm activity (e.g. Troshichev et al., 2014). Thus, in a real-time monitoring application, the distorted PC index values may indicate ongoing substorm activity during calm conditions or indicate quiet conditions hiding an actual magnetic storm or substorm event.

Near-real-time PC index values and PCN and PCS index series derived by the IAGA-endorsed procedure are available through the web site: http://pcindex.org. The web site, furthermore, holds PCN and PCS index coefficients. QDC values are not included. The web site includes the document “Polar Cap (PC) Index” (Troshichev, 2011). Prompt and final PCS data used in the present paper are provided in the Supplement.

Geomagnetic data from Qaanaaq and Vostok were supplied from the INTERMAGNET data service center at http://intermagnet.org.

Solar wind OMNI BSN data from combined ACE, WIND, IMP8, and Geotail interplanetary satellite measurements were provided from the OMNIweb data service at the Goddard Space Flight Center, NASA, at http://omniweb.gsfc.nasa.gov

The “DMI” PC index version is documented in the report SR-16-22 (Stauning, 2016) available at the DMI web site: http://www.dmi.dk/fileadmin/user_upload/Rapporter/TR/2016/SR-16-22-PCindex.pdf. Prompt and final PCS values for October–November 2014 calculated by the DMI method are available in the Supplement.

Appendix A (2014): The web site ftp://ftp.space.dtu.dk/WDC/indices/pcn/ includes documentation forwarded to IAGA for endorsement of the PC indices, among others 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. The documents referred to in the present work are available in the Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/angeo-36-621-2018-supplement.

The author declares that he has no conflict of interest.