PCN magnetic index and average convection velocity in the … · PCN magnetic index and average convection velocity in the polar cap inferred from SuperDARN radar measurements R

PCN magnetic index and average convection velocity in the polar cap

inferred from SuperDARN radar measurements

R. A. D. Fiori,1,2 A. V. Koustov,1 D. Boteler,2 and R. A. Makarevich3

Received 4 December 2008; revised 29 April 2009; accepted 12 May 2009; published 31 July 2009.

[1] The relationship between the polar cap north (PCN) magnetic index and the averageconvection velocity of the plasma flow across the polar cap is investigated using data fromboth the Rankin Inlet (RKN) polar cap Super Dual Auroral Radar Network (SuperDARN)radar and the entire SuperDARN network. Correlation between the PCN index andthe average velocity, determined from the median RKN line of sight (LOS) velocity,maximizes near magnetic noon and midnight when the radar field of view is roughlyaligned with the noon-midnight meridian. For observations between 1000 and 1100 MLT,a roughly linear increase of the average velocity was found for a PCN index between 0 and2, but the rate of increase is �2 times faster than in previous publications in which theaverage velocity was estimated from DMSP ion drift measurements. Comparisonsbetween the PCN index with the cross-polar cap velocity estimated from (1) SuperDARNconvection maps and (2) median RKN LOS velocities show similar trends. Both theaverage cross-polar cap velocity (estimated by two methods) and the cross-polar cappotential show a tendency for saturation at PCN > 2. No significant seasonal change in thenature of the relationships was found.

Citation: Fiori, R. A. D., A. V. Koustov, D. Boteler, and R. A. Makarevich (2009), PCN magnetic index and average convection

velocity in the polar cap inferred from SuperDARN radar measurements, J. Geophys. Res., 114, A07225, doi:10.1029/2008JA013964.

1. Introduction

[2] The polar cap (PC) magnetic index was initiallyintroduced to characterize magnetic activity in the polarcap and the merging electric field [Troshichev and Andrezen,1988; Troshichev et al., 2006]. Subsequent investigationsshowed a high correlation of the PC index with the cross-polar cap potential (CPCP) and the average antisunwardconvection velocity within the polar cap [Troshichev et al.,1996, 2000; Lukianova et al., 2002]. These results imply thatthe index characterizes ionospheric convection. Researchover the last several years indicates a considerable interestin assessing the significance of the PC index [e.g., Liou etal., 2003; Troshichev et al., 2006, 2007a; Stauning andTroshichev, 2008].[3] The PC index was first produced for the Southern

Hemisphere based on data from the Vostok magnetometer(MLAT = �83.4�), and later for the Northern Hemisphereusing data from the Thule magnetometer (MLAT = 85.4�).Indices for the Southern and Northern Hemispheres aretermed PCS and PCN, respectively, and are available inboth 1 min and 15 min resolutions. Although the PCN andPCS indices were expected to be very similar, detailed

analysis revealed some differences [Troshichev et al.,2006]. Currently, reasons for the discrepancies are underinvestigation [Troshichev et al., 2006, 2007b; Lukianova,2007], and a new unified polar cap index is being developed[Stauning, 2007].[4] The present study is aimed at further investigation of

the relationship between the PCN magnetic index and theaverage cross-polar cap convection velocity (CPCV) and theCPCP. This is to extend earlier comparisons by Troshichevet al. [1996, 2000] and Lukianova et al. [2002] whichinvolved limited E � B drift data sets obtained from theExos D and DMSP satellites. We note that although thesestudies demonstrated clear relationships between the CPCVand PC index, the quantitative conclusions drawn did notagree. For example, in both studies the average velocity isshown to relate to the PCN/PCS indices through a quadraticfunction, but the fitting coefficients differ by a factor of�2 inthe quadratic terms and 1.3 for the linear terms (Troshichev etal. [2000] equation (4) versus equation in the work ofLukianova et al. [2002]). More recently, Ridley and Kihn[2004] compared the PCN index and the polar cap electricfield inferred from magnetometer data by applying theassimilative mapping of ionospheric electrodynamics(AMIE) technique. These authors observed a linear rela-tionship between the PCN index and electric field and foundvery different fitting coefficients from earlier findings byTroshichev et al. [2000] and Lukianova et al. [2002]. Inaddition, Ridley and Kihn [2004] separated summer andwinter data and discovered a significant seasonal change inthe fitting coefficients. Ridley and Kihn [2004] hypothe-sized that the seasonal effect could be at least partially due

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1ISAS, University of Saskatchewan, Saskatoon, Saskatchewan, Canada.2Geomagnetic Laboratory, Natural Resources Canada, Ottawa, Ontario,

Canada.3Department of Physics, La Trobe University, Melbourne, Victoria,

Australia.

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to uncertainty in the ionospheric conductance in their AMIEderivations and suggested making a more thorough com-parison of the PCN index with electric field data collectedusing a ‘‘conductance independent source,’’ for exampleby considering the Super Dual Auroral Radar Network(SuperDARN) radar data.[5] All accumulated SuperDARN data can be used to

estimate the CPCP and average CPCV. However, becausethe radars were originally positioned to monitor flowswithin the auroral oval, direct measurements in the polarcap were very limited. Recently (July 2006), the Universityof Saskatchewan installed a new SuperDARN radar atRankin Inlet (Nunavut, Canada) at a magnetic latitude of�73.4�. This radar is the first in a pair called PolarDARN.The second paired PolarDARN radar began taking observa-tions at Inuvik (NorthWest Territories, Canada) in November2007. The Rankin Inlet (RKN) radar has proved to be aninvaluable tool for studying the cross-polar cap convectionhaving accumulated a large database of direct convectionmeasurements from the polar cap region with high echooccurrence rates compared to other SuperDARN radars,which motivated us to pursue a comparison with the PCNindex.[6] In this paper, the cross-polar cap convection velocity

measured directly with the Rankin Inlet PolarDARN radarand convection velocity estimates derived from all NorthernHemisphere SuperDARN radars using standard techniquesare compared to the PCN index (http://web.dmi.dk/projects/wdcc1/pcn/pcn.html). An additional comparison is madebetween the CPCP and the PCN index. Observations are

divided into summer and winter periods to examine theseasonal dependence of the results.

2. Geometry of Observations and Radar DataHandling

[7] The Rankin Inlet PolarDARN radar is very similar tothe rest of the SuperDARN radars [Greenwald et al., 1995].The radars operate in the high-frequency (HF) radio band,typically at 8–20 MHz, and observe echoes from iono-spheric plasma irregularities. The radar sequentially scansthrough 16 beam positions over 1 or 2 min measuring echopower, Doppler velocity, and spectral width in 75 rangegates. The nominal beam separation is 3.24� and the rangegates are separated by 45 km, starting at a range of 180 km.The RKN velocity data are used in combination with datafrom other SuperDARN radars to produce global-scaleconvection maps and to estimate the cross-polar cap potentialby applying the FIT technique developed by Ruohoniemiand Baker [1998].[8] Figure 1 shows the field of view of the Rankin Inlet

radar located at a geographic latitude and longitude of62.82�N and 93.11�W, respectively. The radar central beamsare oriented toward the magnetic pole making it convenientto monitor the cross-polar cap convection in the noon andmidnight sectors for which the flows are predominantlymeridional. In this paper we concentrate on observations inthe noon sector where the conductance is more uniform andnot strongly affected by injections of energetic particlesfrom the magnetotail.

Figure 1. Location and field of view of the Rankin Inlet HF radar (light shading) and Thulemagnetometer. The dark shading shows the beam/gates of the radar data used in this study as described inthe text. Heavy lines represent geomagnetic latitudes of 60�, 70�, and 80�.

A07225 FIORI ET AL.: PCN INDEX COMPARISONS WITH SUPERDARN

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[9] Also shown in Figure 1 is the location of the Thulemagnetic observatory (77.47�N, 69.33�W). The observatoryzenith corresponds to beam 11 and gate 39 of the Rankinradar. RKN observations over Thule are of primary interestin the first part of this study as it is natural to compare radarand magnetometer data collected from the same location.Unfortunately, as we discuss below, insufficient radar datahave been accumulated over Thule. For this reason, weconsider Rankin data not only for the beams overlookingThule (beams 10–12, range gates 34–42) but also for thecentral region (beams 6–9, range gates 20–50). Bothregions are indicated in Figure 1 by the darker shading.We represent the RKN velocity within the region of interestby the median value of the top 50% of all velocity values foreach radar scan. Such a limitation helps to eliminate low-velocity magnitudes caused by both ground scattered echoesand cross-polar cap flows with significant azimuthal com-ponents. Since the radar measures the line of sight (LOS)component of the plasma convection velocity, this estimaterepresents the lower limit on the plasma convection intensity.[10] Figures 2a and 2b show the echo occurrence rates for

each RKN beam and range gate to provide a quantitativeassessment of the radar performance and to indicate thelevel of difficulty in making the radar-magnetometer com-parison over Thule. The occurrence rates were computed asthe ratio of the number of ionospheric echoes observed tothe total number of possible echoes. Observations areshown separately for summer (June 2007; July 2006,2007; August 2006, 2007) and winter (January 2007;November 2006, 2007; December 2006, 2007). A quickexamination of the diagram indicates that the occurrence

rates are highest between range gates 8 and 15 during winter(>40%). Occurrence rate decreases with increasing rangegate, reaching �10% in both summer and winter months byrange gate 39, the range of the Thule magnetometer(indicated by a black and white horizontal line). Occurrencerates are higher for the central beam region (beams 6–9)than for the Thule region (beams 10–12). It should be notedthat in addition to the RKN radar, the field of view of radarslocated at Goose Bay, Kapuskasing, and Saskatoon alsooverlap with the Thule magnetometer. However, these over-laps occur at range gates >55. The phenomenon of de-creased occurrence with increasing range gate is commonfor all radars. Therefore the RKN radar, in addition tohaving a higher echo occurrence rate compared to otherradars, is best situated to make observations over Thule.[11] In Figures 2c and 2d we present a histogram distri-

bution of all velocities observed in the central beams/gatesduring the summer and winter months at 1000–1100magnetic local time MLT (prenoon). Here we have definedpositive flow as being directed antisunward with respect tothe noon-midnight meridian. The size of the data set isconsiderable with 66,649 and 190,013 points in the summerand winter months, respectively. During summer, the ve-locity is mostly positive (antisunward flow) and the distri-bution has a major peak at �700 m/s. The distribution dropsoff strongly at larger velocities so that very few points areavailable for velocities of �1000 m/s. There are a number ofpoints with negative velocity. For winter, the velocitydistribution is smoother and peaks at �300 m/s which is amuch smaller velocity as compared to the summer obser-vations. However, the tail of large velocities is strongerhere.[12] We should emphasize that Figures 2c and 2d include

velocity data for all IMF conditions. This is a very impor-tant circumstance. During periods of southward IMF, theconvection pattern consists of two cells with antisunwardflow over the polar cap region. The size and shape of thecells depend on the IMF By and Bz components. Figure 3shows the IMF-dependent model convection pattern accord-ing to the empirical model of Ruohoniemi and Greenwald[2005] for low IMF By, Bz < 0, and 4 < BT < 6, where BT

represents the IMF magnitude in nT. The field of view ofthe Rankin radar and the two regions of data averaging areindicated by light and dark shading for two instances of theradar location at (1) 1000 MLT and (2) 2300 MLT. Nearthese periods, the regions of data averaging align well withantisunward convection in the noon and midnight sectors.For most of the time, however, the convection flow is tiltedwith respect to the radar beam directions, and only thecosine component of the total velocity is expected to bemeasured.[13] The second comparison that we perform in this paper

is between the cross-polar cap velocity, estimated from theCPCP, and the PCN index (see section 3.2). In this ap-proach, the average convection velocity over the polar capis estimated by dividing the CPCP by the distance along aspherical shell between the foci of the convection cells.Contributions from the RKN radar help to close the gap indata coverage over the polar cap typical for SuperDARNobservations in the past. This approach, however, has itsown difficulties, namely the overall SuperDARN echooccurrence rates are not great for the entire period of the

Figure 2. Echo occurrence rate for the Rankin radar forbeams 0–15 and range gates 0–74 for the (a) summer (June2007; July 2006, 2007; August 2006, 2007) and (b) winter(January 2007, November 2006, 2007; December 2006,2007) months. Solid black and white horizontal lineindicates the range gate of the Thule magnetometer.Also shown are the Doppler velocity distributions for the(c) summer and (d) winter months.


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RKN operation so that individual convection maps havelimited numbers of points. For example, occasions with>300 points on a single convection map are quite rare. Toselect data with the best possible coverage, the SuperDARNdatabase for 2006–2008 was manually searched to locateperiods when at least 200 points were available, the pointswere reasonably spread over the throat region, the two-cellconvection pattern was obviously in effect, and the locationof the convection foci seemed to be reliably determined.

3. Results

[14] We begin by comparing the PCN index with RKNaverage velocities obtained for two separate regions, overThule and in the central beam/gate region.

3.1. PCN and RKN Velocity

[15] Figure 4 is an example of the RKN average velocityand PCN index variations for 11 January 2007 for the twoselected areas: for observations over Thule (Figure 4a) andfor the central region (Figure 4b). Blue (red) coloredvelocity corresponds to the antisunward (sunward) flow in

the prenoon, noon, and afternoon sectors of observations.Velocity is smoothed using a box car method of width 3.The thick vertical line just before 1900 universal time (UT)indicates magnetic noon at the radar location.[16] In Figures 4a and 4b one can see relatively smooth

variations of the PCN index between 0 and 2 and somewhatmore ragged changes of the RKN velocity. A good corre-lation between PCN and the velocity variations can beseen near 1800 UT (Figure 4b). As one goes away from the1200 MLT line, the magnitude of the velocity decreases andthe correlation with the PCN variations is not easily identi-fiable. Both effects are expected, as explained above. Inter-estingly enough, the red colored velocities observed�70minbefore and �20 min after 1200 MLT (sunward convection)when the radar is approximately aligned with the throatregion, correspond to near zero or negative PCNs, in agree-ment with the notion that negative PCNs often correspondwith periods of reverse convection [Troshichev et al., 2006].For observations over Thule (Figure 4a) the data set isconsiderably reduced, and one may only identify occasionalcorrelations between changes in the PCN index and RKNvelocity.

Figure 3. Model convection pattern determined using the Super Dual Auroral Radar Network(SuperDARN) radar software toolkit for periods of IMF By � 0 nT, Bz < 0 nT, and 4 < BT < 6 nT, plottedin terms of Altitude Adjusted Corrected Geomagnetic magnetic latitude and magnetic local time (MLT).Solid (dashed) lines indicate negative (positive) potential contours. The location of the minimum(maximum) potential is indicated by the cross (plus sign). Light shading indicates the field of view of theRankin SuperDARN radar when the radar is located at (a) 1000 MLT and (b) 2300 MLT. Two regions ofinterest are indicated by dark shading.

Figure 4. Line plot of the PCN index (black) against universal time for 11 January 2007 for the (a) Thuleand (b) central beam/gate regions of interest. Velocity magnitude is overplotted for positive (red) andnegative (blue) line of sight (LOS) velocities. Magnetic noon is indicated by the heavy vertical line.


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[17] There is no doubt that deterioration of the PCN-RKNvelocity positive correlation for observations away fromnoon occurs partially due to the fact that the radar measuresonly the component of the flow along a selected beam. Tojustify our selection of the period for comparison, twoanalyses have been performed. First, we simply identifiedperiods of the best correlation between the radar data andPCN index by considering the Spearman’s rank correlationcoefficients R for each MLT sector and for each of the tworegions of interest. Figure 5 shows the correlation coeffi-cients obtained for observations over the Thule (Figure 5a)and central (Figure 5b) beam regions. Observations withPCN > 0 were used to calculate the correlation coefficients.For both regions, and for both the summer and wintermonths, the correlation peaks once a few hours before noon,and again near midnight. This is consistent with the expec-tation that the radar beams would align with the cross-polarcap flow during these periods, as indicated in Figure 3. Ingeneral, correlation is better for the noon peak than for themidnight peak, for the winter months than for the summermonths, and for the central region than for the region overThule.[18] Figure 5 indicates that the best correlation occurs in

the hours before noon. To determine the prenoon MLTsector in which the radar beam in both the Thule and centralbeam regions best aligns with the cross-polar cap convec-tion flow, the convection direction was compared with theradar beam azimuth in each region. Convection maps weregenerated using observations of all SuperDARN radars andapplying the FIT technique for all 2-min intervals of wintermonths. Then, the azimuth of the convection vector locatedin the Thule region (beam 11, gate 39) and the central region(average of beam 7,8, gate 35) was compared with theazimuth of the radar look direction. To maintain reliability,only convection maps with >250 points were considered.

[19] Figure 6 shows histograms of the difference betweenthe azimuth of the convection flow direction and the radarlook-direction when RKN was located in the 0900 MLT(bottom), 1000 MLT (middle) and 1100 MLT (top) for theThule (Figure 6a) and central (Figure 6b) region of interest.For observations over Thule, the distribution at 0900, 1000,and 1100 MLT show similar peaks at �50�. This suggeststhat at Thule, the flow is primarily directed along the Lshells whereas the radar looks in the meridional direction.Therefore the full flow vector is not observed at thislocation. In the central beam region, the distribution isdouble peaked for the 0900 and 1100 MLT sectors. Peaksat the 0900 and 1100 MLT sector occur once near 0�, with asecond peak at �60� and �30�, respectively. This suggeststhat in the 0900 and 1100 MLT sectors a portion of the flowis observed along the radar line of sight, but for a significantperiod of the time, the flow is also observed to be L shellaligned. The distribution in the 1000 MLT sector is singlepeaked with a maximum near 0�, suggesting the radar lineof sight is aligned with the convection flow and the radarobserves the full convection vector. For this reason, furtheranalysis will be performed on RKN data collected between1000 and 1100 MLT.[20] Figure 7 shows a scatterplot of the PCN index versus

Rankin Inlet LOS velocity for summer (Figures 7a and 7c)

Figure 5. Correlation coefficients between the PCN 1 minindex and the Rankin median LOS velocity for the summer(white) and winter (black) months for the (a) Thule and(b) central beam/gate regions of interest.

Figure 6. Distribution of the difference in azimuthbetween the convection vector and the radar line of sightfor observation over the (a) Thule (beam 11, gate 39) and(b) central (average of beam 7,8, gate 35) regions of interestin the (bottom) 0900, (middle) 1000, and (top) 1100 MLTsectors.


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and winter (Figures 7b and 7d) months (1000–1100 MLT)for observations over Thule (Figures 7a and 7b) and incentral (Figures 7c and 7d) beams. RKN observations wereavailable at a 1-min resolution allowing a direct comparisonwith PCN values. Owing to the low geomagnetic activityduring the period studied (near solar minimum) PCNindices >4 were seldom observed, particularly during thesummer months. Over Thule, �1800 (�4000) points wereavailable for the summer (winter) months. The correlationcoefficient is quite poor for summer (R = 0.13) and muchbetter (0.45) for winter. For the central beam region, �1.5times more points are available for both summer and winter.The correlation coefficients are much better for both thesummer (R = 0.58) and winter (R = 0.66) months. With theexception of the summer plot for observations over Thule(Figure 7a), there is a visible relationship between PCN and

RKN velocity. The relationship is more pronounced for thewinter months and for the central beam region.[21] Scatterplots in Figure 7 show that for small PCNs,

the velocity can be both positive and negative. There areseveral factors leading to this result. One effect is that thetwo-cell convection pattern is changed/distorted under spe-cific IMF conditions. For example, for IMF Bz > 0 lobe cellsdevelop in the dayside convection pattern with sunwardflow directed over the polar cap. Another effect is theformation of strongly asymmetric cells under a dominatingIMF By component. Since the magnetic latitudes of the RKNobservations are not extremely high, local flow rotationsmay have occasional sunward components even for near-noon observations. For these reasons, further analysis hasbeen performed by restricting the data according to the IMF.More specifically, to limit the observations to patterns

Figure 7. Scatterplot of the LOS velocity and PCN 1 min index for the (a and b) Thule and (c and d)central beam/gate regions of interest at 1000 MLT. Observations are divided for the (Figures 7a and 7c)summer and (Figures 7b and 7d) winter months.

Figure 8. Scatterplot of the LOS velocity and PCN 1 min index for the (a and b) Thule and (c and d)central beam/gate regions of interest at 1000 MLT where Bz < �1, jByj < 2, and jBzj > jByj. Observationsare divided for the (Figures 8a and 8c) summer and (Figures 8b and 8d) winter months.


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similar to the one shown in Figure 3 the following con-ditions were applied to the original data set:Bz <�1 nT, jByj <2 nT, and jByj < jBzj. Observations of the IMF were takenfrom the ACE satellite, and the propagation delay from thesatellite to the Earth was calculated as described by Weimeret al. [2003] and Weimer [2004].[22] Figure 8 shows a scatterplot of the RKN velocity

versus PCN for the restricted data set. The number ofavailable points has dropped to �180 in the summerand �260 in the winter months over Thule, with roughly1.5 times as many points in the central beam region. Forsummer observations over Thule, a clear trend is still notdiscernible. Over the central region in the summer months,correlation improved to R = 0.72. The correlation did notchange much in winter either over Thule (R = 0.40 versus0.45 in Figure 7b) or in the central region (R = 0.63 versus0.66 in Figure 7d).[23] To emphasize the trends in the relationship between

PCN and RKN velocity, the data in Figure 8 were binnedaccording to PCN bins of width 0.33. For each bin, theaverage RKN velocity and its standard deviation weredetermined, provided there were at least 10 measurementswithin the bin. These averages are represented by the redcircles and bars plotted over the scatter points. The redcircles in Figures 8b and 8c indicate there is a linearrelationship between the RKN velocity and the PCN indexfor the PCN between 0 and 2 for the central region. The rateof increase appears to decrease in the winter months forPCN > 2, but it is not clear if this is a saturation effect or if itis due to the reduced data set for larger PCN. The slope of

the relationship seems to be the same for the winter andsummer months for PCN < 2. To assess the trends in a morequantitative way, we produced the best linear fits to thebinned values for PCN < 2 shown in Figure 8. Theparameters of the fit are presented in Table 1.3.2. PCN, CPCP, and Average Velocity Inferred FromSuperDARN Convection Maps

[24] We next consider the CPCP data. For observations in2006 and 2007, 1170 two-minute maps of satisfactoryquality were identified for the summer (June–August) andwinter (November–January) months. For each 2-min inter-val the average PCN index was compared to the CPCP andCPCV.[25] Figures 9a and 9b show scatterplots of the CPCP

versus PCN for summer (515 points) and winter (655 points)measurements, respectively, There is a general tendency forthe potential to increase with PCN. The correlation coeffi-cient between the CPCP and PCN is 0.50 and 0.61 for thesummer and winter months, respectively. To show trendsmore clearly, the CPCPs were binned over PCN bins of0.33; these are shown in Figures 9a and 9b in blue, alongwith the standard deviation. The binned values clearly showthat the CPCP increases and then saturates for PCN > 1.5–2.A linear fit was made to the first five points in Figures 9a and9b and the coefficients of the fits are presented in Table 2.[26] Figures 9c and 9d show scatterplots of the average

CPCV (calculated as described in section 2) versus PCN forsummer and winter months, respectively. The correlationcoefficients drop to 0.40 and 0.23, respectively, as comparedto the data presented in Figures 8c and 8d. Summer obser-

Table 1. Coefficients of the Fits for the Relationship V = a + b � (PCN) + c � (PCN)2

Source

Summer Winter

a b c a b c

Figure 8 (Thule) - - - �185.4 296.1 -Figure 8 (central region) 26.29 335.27 - �19.04 386.75 -Figure 9 (CPCV) 138.51 194.73 - 336.50 45.53 -Troshichev et al. [2000] 306 153 �0.578 306 153 �0.578Lukianova et al. [2002] 204 102 �2.04 204 102 �2.04Ridley and Kihn [2004] 970.4 104 - 593.8 115.8 -

Figure 9. Scatterplot of the (a and b) cross-polar cap potential and (c and d) velocity versus PCN 1 minindex for (Figures 9a and 9c) summer and (Figures 9b and 9d) winter months.


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vations indicate a linear increase for PCN between 0 and 1.5and a saturation for larger values. Data for the winter monthsshow a much slower rate of velocity increase and a muchlarger velocity at PCN�0. The coefficients of a linear fit tothe first four binned points are also given in Table 1.

4. Discussion

[27] Previous studies showed that the PC index correlateswell with the average dawn-dusk electric field across thepolar cap and therefore the CPCV [Troshichev et al., 2000;Lukianova et al., 2002; Ridley and Kihn, 2004]. Thedependence was described in terms of a quadratic function.However, the fitting coefficients reported vary depending onthe period selected and the method of convection velocitymeasurement. This inconsistency prompted the presentinvestigation.[28] In this study, we used direct observations to charac-

terize the PCN-CPCVrelationship by involving SuperDARNradar measurements of the average plasma flow velocity.Using the SuperDARN radars allowed us to significantlyincrease the data statistics over previous studies. Twoapproaches were implemented: we considered the RankinInlet radar measurements alone (over Thule and the centralbeam region) and velocity estimates from the SuperDARNconvection maps built by combining measurements from theentire SuperDARN network. The disadvantage of the first

method is that only a component of the velocity, along theselected radar beams, is considered. Our presentation wasfocused on observations in the central beams that are roughlyoriented along the magnetic meridian. We should note thatthis is not a very serious limitation. Our data for observationsover Thule (beams 10–12) are fairly consistent with the datain the central beams 6–8 (Figures 7 and 8).[29] In the second approach, convection maps with indi-

vidual vectors of the plasma flow were considered. In thiscase, the estimated velocities very likely reflect the trueaverage plasma flow through the polar cap as maps wereselected for which the patterns were strongly driven by thedata with a prominent contribution from the high-latitudeRKN radar. In addition, observations where the RKN radarwas near noon were selected and the maps used wererestricted to those with reasonable coverage.[30] It is important to realize that average velocity derived

by the two independent methods (LOS observations andconvection maps) agree, although not entirely, for PCN valuesbetween 1 and 3, as will be shown below in Figures 10c and10d. This is important, especially considering that theapproaches did not necessarily include the same events/periods. We should note that more significant differences inthe typical velocities, obtained by the two methods, werefound for small PCN values of less than �1. To explainthese differences, we have to point out that although weexpect that the RKN radar averaging areas are positionedwith respect to the two-cell convection pattern as shown inFigure 3, this is not quite true all the time. For small PCNvalues, the merging electric field is small and the conditionsin the ionosphere are weakly disturbed. For such conditions,the convection cells shrink in size, and the RKN radar mightmonitor flows with significant azimuthal components, notstretched along the magnetic meridian. In this case, evensunward polarity of the flow can be detected for IMF Bz < 0,

Table 2. Coefficients of the Fits for the Relationship CPCP =

a + b � (PCN)

Source

Summer Winter

a b a b

Figure 9 26.58 20.42 34.21 12.91Troshichev et al. [1996] 8.78 19.35 8.78 19.35Ridley and Kihn [2004] 38.20 16.22 27.12 15.50

Figure 10. Relationship between the cross-polar cap potential and PCN 1 min index in the (a) summerand (b) winter months as derived by Troshichev et al. [1996] (black line), Ridley and Kihn [2004] (dashedline), Khachikjan et al. [2008] (black squares), and as shown in Figure 9 (blue circles). Relationshipbetween the flow across the polar cap and PCN 1 min index in the (c) summer and (d) winter months asderived by Troshichev et al. [2000] (heavy black line), Lukianova et al. [2002] (thin black line), andRidley and Kihn [2004] (dashed line), and the SuperDARN-derived velocity shown in Figure 8 (redcircles) and Figure 9 (green circles).


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especially if the By component is large. We believe this isthe main reason for the appearance of points with negativePCN values and positive RKN velocity in Figures 7 and 8.[31] To show how the previously reported relationships

between average CPCV or CPCP and PCN compare to ourresults, in Figure 10 we plot appropriate empirical depen-dencies from Troshichev et al. [1996, 2000], Lukianova etal. [2002], and Ridley and Kihn [2004]. To present theresults of the above papers in terms of the velocity, and notthe electric field, a constant magnetic field value of 0.5 �10�4 T was applied. Note that no data separation accordingto season was performed by Troshichev et al. [1996] andLukianova et al. [2002]. We also present in Figures 10a and10b the subset of the Khachikjan et al.’s [2008] measure-ments of the CPCP (black squares and bars) collected forthe period of 31 January to 10 February 2002.[32] For both summer and winter months, our observa-

tions of the CPCP (blue filled circles from Figure 9) areclose to those reported by Khachikjan et al. [2008] (blacksquares), within experimental errors. Predictions of theCPCP by Ridley and Kihn [2004] for both seasons alsoagree with the SuperDARN measurements with perhapslarger differences during the summer months for PCN > 2.The line by Troshichev et al. [1996] lies somewhat below theSuperDARN points for small PCNs but agrees with them atlarge PCNs.[33] Figures 10c and 10d more clearly show that our

observations of the average CPCV by the two independentmethods applied agree reasonably well for PCN valuesbetween 1 and �3. The points diverge at small PCN of<1 but this might be explained by detection of flows withsignificant azimuthal component as explained above.[34] The empirical lines by Troshichev et al. [2000] and

Lukianova et al. [2002] for the average CPCV lie somewhataway from both SuperDARN sets of points but within thestandard deviations of the SuperDARN data. The empiricallines by Ridley and Kihn [2004] are significantly aboveboth the SuperDARN measurements and the trends fromTroshichev et al. [2000] and Lukianova et al. [2002]. Forboth the summer and winter months, SuperDARN showsbest agreement with observations of Lukianova et al.[2002].[35] In attempting to understand reasons for disagreement

in Figures 10c and 10d, one should keep the followingcircumstances in mind. Observations with drift meters onsatellites [Troshichev et al., 2000; Lukianova et al., 2002]are limited as high-quality data are not readily available.The statistics referenced here include 200–300 points. Forthese measurements, only the cross-track component of theion drift was considered for satellites passing approximatelyperpendicular to the noon-midnight meridian. SuperDARNobservations show that flows can deviate significantly froma well-defined two-cell convection pattern with strictlyantisunward flow over the central polar cap. Estimates ofthe transpolar flow velocities using the AMIE techniquealso have limitations, largely based on the reliability of theionospheric conductance model applied. In particular, sub-storm periods are very difficult to handle properly using thismethod.[36] We should also say that although our data statistics

are significantly larger than for any previous studies, ourRKN data for observations over Thule are limited, espe-

cially during the summer months. Low data statistics is themain reason why data for the central RKN beams arediscussed in more depth in this study. It is unfortunate thatlarge PCN values did not occur often over the last 2 years sothat only relatively low values of PCN < 4 were available.This restricts our study to only the initial part of the CPCVversus PCN curve.[37] Year-round observations by the RKN radar and the

entire SuperDARN network allowed us to address thequestion on the seasonal variation of the CPCV-PCNrelationship. We showed that the slopes of the best linearfit lines for the RKN data in the central beams were aboutthe same for the winter and summer observations. Similarslopes were also inferred from the CPCV data for the summerobservations (see red versus green circles in Figure 10c forPCN > 0.5). The CPCV data for the winter observations(Figure 9d) showed much larger intercept of the fit line andsmaller slope. We note that in data set for the summerobservations in Figure 9c, very few points are used toconstruct the binned value for small PCN < 1, but this valuesignificantly influences the slope and intercept of the best fitline. We expect that for larger data statistics, summer obser-vations would be more consistent with winter observations,i.e., would show smaller slope and larger intercept. Accu-mulation of more SuperDARN/RKN summer data is neededto confirm this expectation.[38] Despite some summer-winter differences, our data do

not show significant seasonal changes in the coefficients offits. This implies that the AMIE modeling by Ridley andKihn [2004] are noticeably affected by the choice of theconductance model. We would like to add that statistics forthe actual RKN velocities presented in Figures 2c and 2dindicate that velocity magnitudes >1000 m/s seldom occur,while Ridley and Kihn [2004] expected velocity magnitudesabove 1000 m/s for all PCN in the summer and for PCN > 3in the winter. On the other hand, the velocity distribution inFigures 2c and 2d indicate that overall velocities peak atlarger values during the summer season. It is known thatSuperDARN data show stronger CPCPs during summermonths [Shepherd, 2007], and our data of Figures 9a and 9bare consistent with this result. Faster flows during thesummer months imply conductance is a factor in establish-ing stronger dawn-dusk electric field as discussed byVennerstrøm and Friis-Christensen [1991].[39] At this point we would like to mention that in this

study we accepted a linear fit to the data, whereas otherstudies used a quadratic fit, see Table 1. If we compare thelinear coefficients for the fit (coefficients ‘‘b’’ in Table 1),we notice a difference by a factor of �2 between thecoefficients for our data and the data previously reportedby others. In general, this alone is not indicative of significantdifference in the data trends. It is more appropriate toexamine the actual lines plotted with the same scale alonghorizontal and vertical axes. For the quadratic fits reportedby both Troshichev et al. [2000] and Lukianova et al.[2002], the nonlinear terms are not significant for PCNsbetween 0 and 4, and the factor of 2 can be judged as asignificant difference. However, trends in Figures 10c and10d give a rather mixed impression as our data are spread inbetween the lines by Troshichev et al. [2000] and Lukianovaet al. [2002]. For a more accurate comparison, one needs to


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have joint, and even simultaneous, radar, DMSP, and PCNindex data which is a future possibility.[40] Data presented in Figures 10a–10d allow us to touch

upon whether or not CPCP and CPCV saturate for largePCN values. One can see that as the PC index increases,both the CPCP-PCN and CPCV-PCN dependences showsigns of saturation for PCN > 2, and the correlation betweendata sets could have been described in terms of the quadraticfunction. We have not pursued this kind of assessmentbecause data for large PCN index are needed to properlyconstrain the quadratic fitting. Our data are in contrast withTroshichev et al. [1996] who did not find any saturationeffect in the CPCP data obtained from satellite measure-

ments of the ion drift. Our data in Figures 9a and 9b areconsistent with those obtained by Khachikjan et al. [2008].[41] Another interesting question deals with the nature of

negative PCN indices. Our data clearly indicate that, formany PCN < 0 occasions, the CPCV polarity correspondsto the sunward (reversed) flow. Our Figures 7–8 show thatthere are significantly more periods with PCN < 0 duringthe summer months as compared to the winter months. Thisis a well-known result [Troshichev et al., 2006]. It isgenerally accepted that the major cause of a negative PCindex is formation of a reverse current flow in the summerionosphere during periods of northward IMF [Vennerstrømand Friis-Christensen, 1991; Lukianova et al., 2002; Liou etal., 2003; Troshichev et al., 2006]. Thus, for the first timeour direct observations have confirmed the expectations ofprevious studies.[42] The predominance of negative PC values during the

summer months is thought to be related to larger conduc-tance of the summer ionosphere, which allows closure ofthe field-aligned currents associated with northward IMFand the setting up of the reverse current system [Lukianovaet al., 2002]. Ionospheric conductivity is higher in the polarcap in the summer months due to solar radiation but mayalso become high enough during the winter months due tothe injection of energetic particles into the polar cap duringpolar cap absorption events [Lukianova et al., 2002], whichmay explain several points of PCN < 0 in our winterdiagrams (Figures 7 and 8).[43] To reduce the possible effects of the reverse current

system,we restricted data in Figure 7 by requiringBz <�1 nT.However, imposing such a data limitation did not eliminateoccurrences of negative PC and reversed velocity polarity(Figure 8). Figure 11a shows an example data setcorresponding to negative PCN and sunward flow duringa period of negative Bz. The diagram shows the NorthernHemisphere with the RKN field of view and the Thule andcentral regions overplotted as in Figure 1. Contours indicatethe electrostatic contours determined using the SuperDARNFIT technique. Vectors for the RKN radar line of sightobservations are shown in black (sunward flow) and darkgray (antisunward flow). The locations of observations fromother radars are indicated by light gray filled circles. Duringthis period the IMF is weakly negative. The convection cellsare shrunken with a protrusion on the dusk cell in the�0900 MLT sector causing the observation of antisunwardflow over the central beam region. Figure 11b shows anexample where the IMF was also weakly southward. In thiscase, the PCN index was positive, but the RKN radarobserved a patch of antisunward flow in both the centraland Thule regions of interest. Both events occurred forperiods of somewhat oscillating IMF. As an illustrativeexample, Figure 11c shows a period where the IMF wasstrongly northward, the PCN was negative, and the RKNradar observed sunward flow. Such cases were filtered increating Figure 8.[44] Troshichev and Lukianova [2002] noted that the

correlation between the PC index and the merging electricfield breaks down when there is sufficient oscillation in theIMF Bz. In this respect, we should note that the PC index isderived by assuming that magnetic disturbances at Thule (orVostok) are produced by the horizontal Hall currents. Thisassumption might be violated, for example on the nightside

Figure 11. Sample convection patterns for the 2 min periodon (a) 14 August 2007 at 1656–1658, (b) 3 December 2006at 1702–1704, and (c) 26 July at 2007 1732–1734 forperiods of PCN < 0, Bz <�1 (Figure 11a); PCN > 0, Bz <�1(Figure 11b); and PCN < 0, Bz > 0 (Figure 11c). Contoursindicate the electrostatic potential. Vectors observed by theRKN radar are overplotted in black (sunward flow) and darkgray (antisunward flow), and the location of observationsfrom other Northern Hemisphere radars are indicated bylight gray circles.


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where there are strong conductance inhomegeneities due toparticle precipitation and uncompensated strong field-aligned currents that are set up during substorms or duringstrongly variable IMF conditions. Comparison of theSuperDARN convection direction and equivalent convec-tion (assumption of the Hall current effect) for observationsin the auroral zone showed that, statistically speaking,reasonable agreement occurs only in roughly 50% of cases[Benkevitch et al., 2006]. In the past, Vennerstrøm andFriis-Christensen [1991] reported difficulties relating PCNvariations and global scale plasma flows for substormperiods. During such periods, the PC index may notaccurately describe the merging electric field.[45] Our observations demonstrated better correlation

between CPCV and PCN on the dayside as compared tothe nightside (Figure 5). This is not surprising as iono-spheric conductivity is much higher and more uniform onthe dayside than on the nightside. Changes to the conduc-tivity caused, for example, by particle precipitation, wouldtherefore have a greater effect on magnetometer records onthe nightside. Also, flows are more erratic on the nightsideespecially during substorm periods, making it difficult tocharacterize them with a set resolution or integration time.[46] Finally, we would like to comment on the observa-

tions reported over Thule for summer months. No clearcorrelation or tendencies between the average velocity andthe PCN index were found (Figure 7a). The situation did notimprove after restricting the data according to the IMFconditions (Figure 8a). We believe these results are notrelated to the high-latitude electrodynamics but simplyreflect some technical problems with the RKN velocitymeasurements at these specific ranges. A significant numberof points in Figures 7 and 8 have velocity magnitudes below�100–150 m/s. The SuperDARN standard software iden-tified these echoes as ionospheric, but these echoes wellmight be strongly contaminated by ground scatter. Detec-tion of ground scattered echoes over Thule (actually, forRKN ranges above �1500 km) during summer is a verytypical phenomenon. To confirm our explanation for lowcorrelation of PCNs and RKN velocities over Thule duringsummer, more validation work on RKN should be conducted.

5. Conclusions

[47] In this study we tested the use of the PCN index asan indicator of ionospheric convection across the polar capby comparing it with convection measurements made usingthe SuperDARN radars. We concentrated on observationsfrom the recently installed high-latitude Rankin Inlet radar.For PCN < 4 we showed the following:[48] 1. The velocity estimated from the Rankin Inlet line

of sight Doppler measurements increases with the PCNindex. The correlation coefficient between the velocity andPCN index depends on the magnetic local time of measure-ment, maximizing to �0.6–0.7 in the midnight and noonsectors when the radar field of view is roughly orientedalong the noon-midnight meridian. In the 1000 MLT sectorthe dependence is approximately linear for PCN < 2, but therate of velocity increase slows as the PCN index increasesabove 2, possibly indicating the onset of saturation.[49] 2. The slope for the linear part of the average

velocity-PCN dependence was found to be �2 times larger

as compared to the previous publications by Troshichev et al.[2000], Lukianova et al. [2002], and Ridley and Kihn [2004].However, if the RKN data for PCNs < 1 are not considered(observations for low PCNs are expected to occur duringperiods of antisunward flows with significant azimuthalflow components) than the slopes for the RKN data becomecomparable to those from previous publications.[50] 3. The cross-polar cap average velocity estimated

from the cross-polar cap potential divided by the distancebetween the two-cell convection foci shows a linear increasewith the PCN index for values between 0 and �2. The slopeof the best fit line agrees with previous publications,particularly during the summer months for the centralregion.[51] 4. The observed relationships between the PCN

index and the cross-polar cap velocity derived from bothline of sight observations and from the cross-polar cappotential did not show significant differences betweensummer and winter months.[52] 5. The cross-polar cap potential determined from

1170 convection maps (involving polar cap Rankin Inletradar data) also increases with the PCN magnetic index. Thedependence can be approximated by a linear function forPCN < 2. For larger PCNs, the rate of increase slows downand the onset of the saturation effect is evident.[53] To better characterize the average velocity-PCN

dependence, observations during periods with PCN > 4 arehighly desirable. These data will be collected in the comingyears as solar activity picks up.

[54] Acknowledgments. We acknowledge the support of the nationalfunding agencies that made possible continuous operation of the SuperDARNradars considered in this study. This work has been supported by a NSERC(Canada) grant to A.V.K. We thank the Danish Meteorological Institute forproviding observations of the polar cap magnetic activity index. Constructivecritical comments of both reviewers are greatly appreciated.[55] Zuyin Pu thanks Renata Lukianova and another reviewer for their

assistance in evaluating this paper.

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��D. Boteler and R. A. D. Fiori, Geomagnetic Laboratory, Natural

Resources Canada, Ottawa, ON K1A 0E8, Canada. ([email protected])A. V. Koustov, ISAS, University of Saskatchewan, 116 Science Place,

Saskatoon, SK S7N 5E2, Canada.R. A. Makarevich, Department of Physics, La Trobe University,

Melbourne, Vic 3086, Australia.


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PCN magnetic index and average convection velocity in the … · PCN magnetic index and average convection velocity in the polar cap inferred from SuperDARN radar measurements R