High-latitude plasma convection from Cluster EDI: variances and solar wind correlations

Transcription

1 Ann. Geophys., 25, , 27 European Geosciences Union 27 Annales Geophysicae High-latitude plasma convection from Cluster EDI: variances and solar wind correlations M. Förster 1, G. Paschmann 2, S. E. Haaland 2,3, J. M. Quinn 4, R. B. Torbert 5, H. Vaith 2, and C. A. Kletzing 6 1 GeoForschungsZentrum Potsdam, Potsdam, Germany 2 Max-Planck-Institut für extraterrestrische Physik, Garching, Germany 3 Department of Physics, University of Bergen, Norway 4 Boston University, Boston, MA 2215, USA 5 University of New Hampshire, Durham, NH 3824, USA 6 University of Iowa, Iowa City, IA 52242, USA Received: 14 March 27 Revised: 21 June 27 Accepted: 16 July 27 Published: 3 July 27 Abstract. Based on drift velocity measurements of EDI instruments on Cluster during years 21 26, we have constructed a database of high-latitude ionospheric convection velocities and associated solar wind and magnetospheric activity parameters. In an earlier paper (Haaland et al., 27), we have described method, consisting of an improved technique calculating propagation delay between chosen solar wind monitor (ACE) and Earth s magnetosphere, filtering data periods of sufficiently stable IMF orientations, and mapping EDI measurements from ir high-altitude positions to ionospheric altitudes. The present paper extends this study, by looking at spatial pattern of variances of convection velocities as a function of IMF orientation, and by perming sortings of data according to IMF magnitude in GSM y-z plane, Byz IMF, estimated reconnection electric field, E r,sw, solar wind dynamic pressure, P dyn, season, and indices characterizing ring current (D st ) and tail activity (ASYM-H). The variability of high-latitude convection shows characteristic spatial patterns, which are mirror symmetric between Norrn and Sourn Hemispheres with respect to IMF B y component. The latitude range of highest variability zone varies with IMF B z similar to auroral oval extent. The magnitude of convection standard deviations is of same order as, or even larger than, convection magnitude itself. Positive correlations of polar cap activity are found with Byz IMF and with E r,sw, in particular. The strict linear increase small magnitudes of E r,sw starts to deviate toward a flattened increase above about 2 mv/m. There is also a weak positive correlation with P dyn. At very small values of P dyn, a secondary maximum appears, which is even Correspondence to: M. Förster (mfo@gfz-potsdam.de) more pronounced correlation with solar wind proton density. Evidence enhanced nightside convection during high nightside activity is presented. Keywords. Ionosphere (Plasma convection) Magnetospheric physics (Magnetospheric configuration and dynamics; Solar wind-magnetosphere interactions) 1 Introduction Large spatial and temporal variability is a fundamental property of magnetospheric convection. This is mainly caused by variations in driving solar wind and interplanetary magnetic field (IMF) conditions toger with complexity of coupled system. Competing time-dependent processes are acting with various characteristic time scales such that steady-state conditions ree rarely exist and any response to changes in various interplanetary conditions any given moment in time depend furr on prior state of system (Rostoker et al., 1988). The major part of transfer of energy and momentum from solar wind to Earth s magnetosphere and basic high-latitude convection patterns are now known to be caused by reconnection between IMF and Earth s geomagnetic field (Dungey, 1961) and to a minor extent by quasi-viscous interaction processes at magnetopause (Axd and Hines, 1961). During periods when IMF has a sourly component, reconnection takes place on dayside magnetopause. The newly reconnected field lines and plasma attached to m are swept across polar caps into magnetotail where y eventually reconnect again. Both of se two basic timedependent components of magnetospheric convection cycle can be reasonably parametrized in terms of concurrent Published by Copernicus Publications on behalf of European Geosciences Union.

2 1692 M. Förster et al.: Cluster EDI measurements: variances and correlations Pdyn [npa] Dst [nt] ASYM_H [nt] B IMF yz [nt] V sw [km/s] log E r sw [mv/m] clock angle [deg] (magnetic latitudes >58 olar wind and Fig. geomagnetic 1. Solar parameter wind and distribution geomagnetic parameter time interval distribution of EDI observations ) ionospheric convection as a function of IMF clock angle, deduced from measurements time interval of EDI observations All data points used points used analysis, i.e., i.e., after after filtering filtering stable stable IMF IMF conditions, conditions, are drawn are as green by lines; Electron Drift Instruments (EDI) onboard Clus- filtering. satellites The during years 21 26, was presented. nes illustrate drawn contrasting green data lines; set ofpurple all those lines data illustrate points that contrasting were removed databy ter set of all those data points that were removed by filtering. The Paper 1 describes method, consisting of an improved om top to bottom show dynamic pressure of solar wind protons, P dyn, at magnetopause, panels from top to bottom show dynamic pressure of solar wind geomagnetic protons, Pactivity dyn, at of magnetopause, ring current, ASYM-H D st index index char- which is solar usedwind here asmonitor, Advanced Composition Explorer technique calculating propagation delay between ndex characterizing of AE index acterizing of auroral geomagnetic activity activity, of magnitude ring current, of IMF ASYM-H vector components (ACE), inand Earth s magnetosphere, filtering data pe- electric of field, sufficiently stable IMF orientations, and mapping -plane, Byz IMF index which is used here as a proxy of AE index of auroral geomagnetic activity, magnitude of IMF vector components in, magnitude of solar wind velocity, V s.w., solar wind reconnectionriods e Eq. 3), and finally GSMy-z-plane, IMF clock B angle. yz IMF EDI measurements from ir high-altitude positions to iono-, The magnitude vertical lines ofinsolar eachwind panelvelocity, indicate quartiles of on corresponding V s.w., solar parameter. wind reconnection electric field, E r,sw (see Eq. 3), and finally IMF clock angle. The vertical lines in each panel indicate quartiles of distribution corresponding parameter. near-earth interplanetary conditions, although with different response times (Cowley and Lockwood, 1992). For northward IMF, reconnection takes place at high latitudes between IMF and Earth s lobe field (see, e.g., Burke et al., 1979; Reiff and Burch, 1985; Reiff and Heelis, 1994). The result of se processes is a large scale circulation of plasma in Earth s magnetosphere. Since geomagnetic field lines are nearly equipotentials, 23 and large scale circulation map to high magnetic latitudes, this plasma circulation and its variability is also manifested in high latitude ionosphere. In addition, ionosphere itself and rmosphere where it is embedded play a role. Sunlight and particle precipitation enhances ionospheric conductivity leading to an attenuation of electric field, and ionosphere, being tightly coupled to rmosphere, acts as a drag on convection (Cole, 1963; Hill, 1976). The highlatitude convection and its variability in particular also play a major role in Joule heating of ionosphere and rmosphere. Joule heating is generated due to relative motions of neutral gas and ionized components, being proportional to square of velocity difference. The contribution of irregular part of convection has been shown to be comparable to or in certain regions even larger than Joule heating of averaged or background convection. It is as an essential contributor of rmospheric energy at high latitudes (Codrescu et al., 1995, 2; Crowley and Hackert, 21). The inertia of rmospheric neutral winds can help to maintain ionospheric convection independently of magnetospheric driver processes and is known as fly-wheel effect (Banks, 1972; Coroniti and Kennel, 1973). Taken toger, convection patterns are thus caused by combined effect of several processes rar than a single elementary process (Tanaka, 21). Statistical dependencies of solar wind drivers such as IMF and solar wind dynamic pressure, have been studied extensively several decades (e.g., Reiff et al., 1981; Heppner and Maynard, 1987; Boyle et al., 1997). In an earlier paper (Haaland et al., 27), henceth referred to as Paper 1, statistical pattern of high-latitude spheric altitudes. In Paper 1 we sorted data according to IMF orientation, averaged data, and generated maps of potential distribution. In present paper we use same comprehensive data set to investigate dependencies of high-latitude convection on various or solar wind and magnetospheric activity parameters. We also discuss spatial pattern of variances of convection velocities. 2 Data set characteristics In order to characterize data set, Fig. 1 shows distributions of selected solar wind parameters over time-span of our data set: clock angle θ, magnitude of IMF in GSM (y,z)-plane Byz IMF (sometimes called B T or transverse IMF magnitude ), solar wind speed V s.w., magnitude of solar wind electric field projected along reconnection line at dayside magnetopause, E r,sw, and dynamic Ann. Geophys., 25, , 27

3 M. Förster et al.: Cluster EDI measurements: variances and correlations 1693 pressure P dyn of solar wind protons (including heavier ions like alpha particle gives on average about 2% higher values). The parameters were derived from measurements at ACE as described in Paper 1. Figure 1 also shows distribution of two geomagnetic indices (D st and ASYM-H) assembled toger with solar wind and IMF parameters with same 1-min resolution. The solar wind parameters have been shifted arrival time at magnetopause (assumed to be located at X GSE =1 R E ). The method described in Paper 1 used a bias vector filtering to select relatively stable IMF conditions well-defined magnetospheric convection response patterns as a function of IMF clock angle in eight discrete sectors with 45 width each. IMF sector is purely northward (IMF B z +) directed, or sectors follow clockwise in IMF y-z plane, so that IMF sectors 2 and 6 correspond to B y + and B y, respectively, and sector 4 is close to strict southward direction (IMF B z ). This selection process resulted in a filtered data set which comprises nearly half full data set originally available. However, IMF stability filtering of distributions. might have biased characteristic solar wind conditions in a systematic manner. To check this, we plotted in Fig. 1 not only distributions of data set with stable IMF conditions used our study (green lines), but also complementary ones, i.e., distributions all rejected data points (purple lines). The vertical lines indicate quartiles of distribution. Differences between two data sets are clearly seen in solar wind parameter P dyn, IMF magnitude Byz IMF, and solar wind velocity V s.w.. The discarded data points are characterized by larger average solar wind speed and ree larger mean P dyn values while proton density distribution (not shown) is generally not influenced. The D st index becomes more concentrated within range 1 nt to 35 nt under disturbed IMF conditions while partial ring current activity index ASYM-H as well as average clock angle distribution of IMF vectors do not show any significant difference. The parameters we have chosen our secondary sortings are not independent of IMF clock angle that we used to sort data in Paper 1, and y are also somewhat dependent on each or. This is illustrated by Table 1. For a significance test of correlation coefficients we used Student s t-distribution. Due to large number of data points, all correlation coefficients estimated can be regarded as statistically reliable. Their significance in a pure statistical sense is already gained values above.1. The quality of correlation, on or hand, is given by correlation coefficient itself with its range from 1. to +1.; larger magnitudes indicate stronger correlations. To guide reader, we highlighted in Table 1 all coefficients with magnitudes >.5. The clear anticorrelation between Bz IMF and absolute value of clock angle θ results simply from its definition as function of By IMF and Bz IMF. A furr clear anticorrelation Number of records North Hemisphere South Hemisphere solar zenith angle [deg] Fig. 2. Solar zenith angle distributions at ionospheric footpoint Fig. 2. Solar zenith angle distributions at ionospheric footpoint location of mapped EDI drift location of mapped EDI drift vectors in ionosphere North ionosphere North (blue) and South (red) Hemisphere separately. The vertical lines indicate indicate quartiles of distributions. exists between geomagnetic indices D st and ASYM-H; declining ring current values of disturbed periods are related to a rising auroral activity. All or high correlation values concern reconnection electric field parameter of solar wind E r,sw, except its relation to P dyn and V s.w.. There are also some smaller, but noticeable correlations of ASYM- H with Bz IMF and Byz IMF. All or pairs of parameters are uncorrelated. The line of apsides of Cluster orbit, originally equatorial, is tilting furr and furr southward with time. In our data set, re is ree an asymmetry in North- South coverage within high magnetic latitudes regions. This manifests itself, example, in different seasonal coverages at Norrn and Sourn Hemisphere (see Fig. 5 in Paper 1, middle and bottom panels). Also, Sourn Hemisphere data are on average obtained at higher altitudes (9 R E versus 7 R E Norrn Hemisphere). However, Sourn Hemisphere data contain a larger fraction of observations taken during sunlit conditions. This is probably due to a clear difference in offsets between geographic and geomagnetic poles at North and South Hemisphere. Based on International Geomagnetic Reference Field (IGRF) model, 25 location of north magnetic pole is N and W and south magnetic pole is S and E. The larger displacement at Sourn Hemisphere leads to a larger diurnal wobbling of polar cap area with respect to geographic coordinates. Figure 2 shows number of observations Norrn (blue lines) and Sourn (red lines) Hemisphere versus solar zenith angle. Zenith angles below approximately 1 corresponds to a sunlit polar cap ionosphere and thus enhanced ionization and subsequent attenuation of electric field. As already pointed out by Cole (1963) and Hill (1976), a higher Ann. 24 Geophys., 25, , 27

4 1694 M. Förster et al.: Cluster EDI measurements: variances and correlations Table 1. Correlations between various driver parameters (using all bias-filtered data). V s.w. B IMF z Driver parameter B IMF yz E r,sw P dyn D st ASYM-H θ V s.w. 1 Bz IMF.2 1 Byz IMF E r,sw P dyn D st ASYM-H θ absolute values of clock angle used. ionospheric conductivity will retard convection due to drag ce caused by ion-neutral collisions. Since magnetic field lines are nearly equipotentials, effect of this drag is also observed at Cluster altitudes. Due to asymmetry, average convection velocities obtained within Sourn polar cap are slightly lower ( 7%) than those from Norrn Hemisphere. This difference is smaller within very central part of polar cap, where mapped EDI drift data have best coverage. 3 Convection variability In Paper 1, we have presented average convection patterns as a function of IMF direction without any considerations of variability. But as noted earlier, convection pattern is known to be highly variable on different timescales. Variations on timescales of minutes are known even relatively stable IMF conditions (Bristow et al., 24). To characterize variability of convection in our statistical study of EDI drift measurements, we used two different variances. Normalized to average drift magnitude, y are defined as follows: σtotal 2 = v 2 v 2 v 2 σmag 2 = v 2 v 2 v 2 where... denotes average over time and v is velocity vector. The first variance, σtotal 2, is normalized variance (equivalent to sum over component variances) of total velocity vector. It represents variability of full vector, with a steady pointing direction yielding zero variance. The second variance, σmag 2, is normalized variance of velocity magnitude, and gives average deviation of velocity magnitude from its local average value. Both variances range from to 1. (1) (2) The normalized total drift velocity variance, σtotal 2, is shown in Figs. 3 and 4 Norrn and Sourn Hemisphere, respectively. The eight panels are different clock angle ranges (corresponding to those in Paper 1) and reveal a systematic pattern of drift variance over whole polar cap as a function of IMF clock angle. The variability approaches 1 over large areas in a systematic way. For three sectors of northward IMF (upper row), this enhanced variability fills nearly whole polar cap region, while southward IMF (bottom panels), variance is small within polar cap. The By IMF dominated sectors (2 and 6) show a dawn-dusk asymmetry in maximum intensities of normalized variance. The normalized variance at Norrn Hemisphere (Fig. 3) shows high values at dusk (dawn) side positive (negative) By IMF values. The dayside quadrant at dusk (dawn) side is completely covered while this enhanced normalized variance is confined to about 2: MLT (3: MLT) on nightside. Note that regions inside polar cap with normalized variances close to 1 have lower average convection velocities. They correspond to roundshaped convection cells areas with wider spaced potential contours (see Figs. 7 and 8 in Paper 1). For northward IMF, somewhat broader regions of more enhanced variability are seen on dayside as, e.g., in sector 1 of Fig. 3 and sector 7 of Fig. 4. Inside polar cap region, re is a region of more structured flow (smaller normalized variances and more bundled convection stream lines) which broadens furr southward turning of IMF as seen in lower row (sectors 3 5). For purely southward IMF (Sector 4), well-organized transpolar flow covers entire polar cap region down to nearly 7. Furr equatorward, in convection reversal zone and return flow, variance is higher than in central polar cap again. The diameter of low-variance region in central polar cap becomes smaller northward turning IMF. Ann. Geophys., 25, , 27

5 M. Fo rster et al.: Cluster EDI measurements: variances and correlations 1695 Fig. 3. Total normalized of EDI drift vectors mapped Norrn ionosphere time interval Fig. 3. variance Total normalized variance of EDI drift to vectors mapped high to latitude Norrn high latitude ionosphere from February 21 to March 26. The outer circle of each panel represents 6 magnetic latitude and numbers indicate magnetic local time (MLT). time interval from Febvariability; 21 to Mar The outer circleare of confined each paneltorepresents 6 between magnetic latitude The color bar shows intensity of 26. normalized values an interval and 1. The variance is numbers indicate magnetic bar within shows bin. intensity of variability; calculated eachand bin individually, based on at least local three time valid(mlt). mappedthe driftcolor vectors normalized values are confined to an interval between and 1. The variance is calculated each bin individually, based on at least three valid mapped drift vectors within bin. Comparing Sourn Hemisphere (Fig. 4) with Figures 3 and 4 were normalized variances. To emnorrn (Fig. 3), patterns are mirror symmetric with rephasize absolute variations, Fig. 5 shows standard despect to ByIMF dependence, that is, re are high values viation of full vector Norrn Hemisphere, withof normalized variance at dawn (dusk) side positive out any normalization. (negative) ByIMF values, respectively. All or differences are The auroral oval (convection reversal zone) and its diaminor as, e.g., an apparently broader ring of enhanced varimeter change with varying BzIMF values is clearly reflected ability at auroral and subauroral latitudes on nightside in se patterns. For sector (purely northward IMF), this southward IMF. 2 oval has its smallest radial extent and region of enhanced The or normalized variance, σmagn (not shown here), standard deviation values is nearly closed throughout poreveals similar patterns of variability with same IMF lar cap. This oval gradually extends or sectors with By dependence, but on a much lower level of amplitudes. a maximum diameter low values (more ordered convection) Its maximum magnitudes reach only about half of those of 25 within polar cap sectors 3 5 under southward IMF total variance. conditions. The absolute values within auroral oval are of order of average drift velocity and are marked by Ann. Geophys., 25, , 27

6 1696 M. Fo rster et al.: Cluster EDI measurements: variances and correlations Fig. 4. As in Fig. 3,Fig. but4. Sourn As in Fig. 3, but Hemisphere. Sourn Hemisphere. range of colour scale chosen (about 7 m s 1 ). Within auroral oval inside central polar cap standard deviations have about half of this magnitude (around 35 m s 1 ). The ByIMF dependence that was apparent in normalized variances is not seen here in standard deviation plot. On nightside, re is a tendency enhanced values in evening to midnight magnetic local times, in particular southward IMF, extending toward early morning hours ( 2: MLT) as can be seen in sector 5 (this cannot be confirmed sectors 3 and 4 due to scarcity of mapped EDI drift vectors in this area). This might be due to enhanced substorm activity. four different main IMF directions corresponding to four 9-deg quadrants of IMF clock angle. Particular striking is that re is a large variability down to very short time scales, in particular northward IMF (quadrant top panel), but also IMF directions in ecliptic plane (quadrants 1 and 3). For southward IMF (quadrant 2) variability is much lower, and comparable to or even smaller than average drift vector magnitude (see red lines in Fig. 6). Table 2 lists additionally mean values and standard deviations of boxcar averages shown in Fig. 6. Note also that re are no long-term trends of averages. While Figs. 3 5 characterize variability in terms of 4 Solar wind dependencies normalized variances and unnormalized standard deviations, 26 Fig. 6 shows time series of XSM component of all availto investigate influence on convection of various soable EDI velocity data that are mapped into central polar lar wind and IMF quantities, such as solar wind dynamic cap region poleward of 8 magnetic latitude, divided into pressure Pdyn, solar wind electric field Er,sw, IMF Ann. Geophys., 25, , 27

7 M. Fo rster et al.: Cluster EDI measurements: variances and correlations 1697 Fig. 5. Standard Fig. deviation of deviation total vector variation [m s 1 ] of EDI to Norrn high latitudehigh ionosphere 5. Standard of total vector variation [mdrift s 1 ]vectors of EDImapped drift vectors mapped to Norrn time interval from Feb 21 to Mar 26. As in Figs. 3 and 4, each circular panel shows magnetic local time (MLT) versus magnetic latitude latitude ionosphere interval Feb 21 to Mar 26.deviation, As in Figs. 3 andis 4, each circular panelbin individually, with 6 at outer border. The color bartime indicates from magnitude of standard which calculated each magnetic localdrift timevectors (MLT) within versus magnetic based on at least shows three valid mapped bin. latitude with 6 at outer border. The color bar indicates magnitude of standard deviation, which is calculated each bin individually, based on at least three valid bin. IMF magnitude Byz, mapped and drift Dstvectors index,within we bin our data set In following, we use magnitude of average veinto a number of subsets each of se parameters. The locity components hvx i and hvy i as measures magbinning is a compromise between adequate resolution and netospheric convection velocity across center polar cap sufficient data coverage. A good and homogeneous coveras well as hv i, which represents average of velocage is particularly important construction of poity magnitudes. Vx, Vy and Vz are mapped EDI drift tential patterns. Large gaps in longitudinal or latitudinal velocity components at ionospheric level (4 km) in Solar coverage cause problems with Legendre polynomial exmagnetic (SM) coordinates (Vz is usually very small in pansion, which can lead to artifacts in potential distribuhigh-latitude ionosphere). Note that antisolar velocity is tion (see Sect. 3.5 in Paper 1). For this reason, we calculate plotted with an inverted sign (h Vx i) in following figures average convection velocity within central polar cap of this section better comparison with hv i dependencies. (magnetic latitude φm >8 ) each subset. Note that this 4.1 IMF direction selected area typically does not include low latitude regions of convection return flow. 27 Figure 7 shows cross-polar cap potential (upper panel) as well as average velocities defined above versus clock Ann. Geophys., 25, , 27

8 1698 M. Fo rster et al.: Cluster EDI measurements: variances and correlations Both hemispheres Quadrant MLAT > 8 deg 2 4 Potentials versus clock angle (deg) North hemisphere South hemisphere Vx_SM (km/s) 1 Cross-polar potential U (kv) Vx_SM (km/s) 4 Quadrant Vx_SM (km/s) 4 Quadrant Quadrant 3 clock angle (deg) 9 18 Convection versus clock angle MLAT > 8 deg 6 < V > Vx_SM (km/s) Fig months of mapped EDI drift measurements in X 62 months of mapped EDI drift measurements in XSM direction within SM central polar cap region direction within central polar cap region (magnetic latitude tic latitude φ φ > 8 ), plotted as condensed time series four different m m >8 ), plotted as condensed time series four differentquadrants of IMF quadrants of IMF anglecircle distribution. indicated withpanel, quadrant of clock ngle distribution. As indicated withclock small inlet As each respective small circle inlet each respective panel, quadrant of clock angle 1 stribution comprises ± 45comprises centered ±45 around clockaround angle, quadrant 1 same centered clock angle, distribution quad-angular width centered rant Boxcar 1 same angular widthcentered centeredwindow) around are 9 shown, and so 9, and so th. averages (6 month as th. red lines and ir8standard Boxcar averages (6 month centered window) are shown as red lines 6 ns are indicated by dashed red lines. and ir standard deviations are indicated by dashed red lines. 4 Table 2. Average values of sliding boxcar mean values 62 months of mapped EDI drift measurements in XSM direction (red lines in Fig. 6) and ir average standard deviations each quadrant of IMF clock angle distribution individually. max # : 9146 max # : clock angle (deg) 9 18 Fig. 7. Top: Polar cap potentials as a function of clock angle (blue) Sourn (red) Hemisphere. clock (blue) angle and Sour Fig. 7. Top: Polar capnorrn potentials as aand function of clock angle The Norrn Quadrant IMF Mean value STDDEV range is divided in 16 steps of equal width (22.5 ). The potentials Hemisphere. The clock angle range is divided in 16 steps of equal width (22.5 ). The potentials in thi direction m/s m/s in this panel are derived from full high-latitude (>58 ) convecare derived from fulltion high-latitude 58 bin, ) convection pattern each bin, as explained pattern (> each as explained in Paper 1. Middle: The av- in Paper-I. M Bz convection hv i, within x i, and hv y i (dashed) 1 By The average convectionerage velocities hv i, velocities h Vx i, and hvh V within central polar cap at m y i (dashed) central polar cap at magnetic latitudes φm >8 as function 2 Bz latitudes φm > 8 as of clock angle, usingcolour same colour andwidths bin-step widths as offunction clock angle, using same coding andcoding bin-step 3 By as above. Bottom: characteristics lines, each bin individubottom: coverage characteristics each coverage bin individually. The solid which refer to middle ally. The solid lines, which refer to middle panel, show relashow relative number of data points within high-latitude circle (> 8 ) each bin, as perc tive number of data points within high-latitude circle (>8 ) angle in 16 steps of 22.5 each (middle panel) corre- number of and maximum noted panel. The dashed lines refer to upper each bin, within as percentage of maximum number noted within panel, indicat sponding spatial coverage (lower panel). Thispercentage figure complepanel. The dashed lines refer to upper panel, indicating perof valid grid points of full area of polar cap potential pattern construction. ments Figs. 7 and 8 in Paper 1, but has twice resolution in centage of valid grid points of full area of polar cap potential pattern construction. clockangle. The cross-polar cap potential is derived from po- 28 tential pattern that were constructed with all data points of Ann. Geophys., 25, ,

9 M. Förster et al.: Cluster EDI measurements: variances and correlations 1699 bin-step interval as explained in Sect. 3.5 of Paper 1. The potential difference between maximum and minimum value of potential pattern is used curves in upper panel. In most cases, this co-incides with cross-polar cap potential difference between main cells, positive focus of dawn cell and negative of dusk cell. The figure confirms rough mirror symmetry between North and South as well as remaining minor hemispheric differences. There are different minimum positions of potentials North and South close to zero degree clock angle (Bz IMF +) in upper panel. The Norrn Hemisphere shows a smooth broad minimum slightly shifted toward negative clock angles while at Sourn Hemisphere this minimum near clock angle is less clear and seems rar shifted toward positive values. At sourly clock angles two curves of V and two curves V x in middle panel of Fig. 7 are close, which means that velocity directions are rar steady in antisolar direction over central polar cap. This indicates that contribution of V y (dashed), being approximately mirror symmetric between North and South with respect to clock angle, is negligible. By contrast, at norrly clockangles V and V x curves are quite far apart and V y is comparable to V x, indicating that directions are less steady: averaging magnitudes n gives a large value V, while variable directions causes partial compensation in individual components. V x even becomes positive on average values near clock angle (northward IMF). This is due to appearance of lobe cells with sunward convection at high latitudes. The minimum value of V x is slightly shifted toward negative clock angles both Norrn and Sourn Hemisphere. This behaviour is similar to potential variation in upper panel resulting in steeper variation in range of negative clock angles compared to positive half-sphere. The averaged convection velocity (middle panel of Fig. 7) reveals some North-South asymmetry, particularly in V and V x (when mirrored sourn curve at clock angle). This is presumably partially a result of conductivity differences discussed in Sect. 2, but mainly result of Cross-polar potential U (kv) Potentials versus B yz IMF (nt) B IMF yz (nt) mirror-symmetric action of By IMF dependence. Deviations of geomagnetic field configuration from symmetry, yz IMF pattern each bin as a fu Fig. 8. Top: Polar cap potentials derived from full high-latitude Fig. 8. Top : Polar capconvection potentials derived patternfrom eachfull bin high-latitude as a function convection of B in particular at ionospheric altitudes, will probably of Balso yz IMF affect Norrn Norrn (blue) (blue) and and Sourn Sourn Hemisphere Hemisphere (red). (red). Middle Middle panel panel: : Average veloc Average velocities as a function of IMF magnitude B results (see also discussion later in Sect. a function 4.5). of IMF magnitude B IMF yz IMF within central yz polar within capatcentral magnetic polar latitudes cap magnetic φ m >8 latitudes only. φ m > Effect of IMF magnitude Byz IMF Lower panel : coverage Lower each panel: bin as coverage explained in each Fig. bin 7, except as explained that weinnow Fig. used 7, except variable bin widths that we now used variable bin widths so that amount of data amount of data points are about equal in each bin-step. points are about equal in each bin-step. In a recent paper, Ruohoniemi and Greenwald (25), examined influence of IMF magnitude in GSM y- z plane ( Byz IMF ) on convection patterns. They divided in 5 1 nt range, y also found signatures of sunward IMF magnitude Byz IMF into three bins: 3 nt, 3 5 nt convection and emergence of lobe cells in high latitude dayside polar cap. Byz IMF is one of parameters that and 5 1 nt, and found that higher values of Byz IMF correspond to higher polar cap potentials. The only exception was determines solar wind electric field and is thus expected found pure northward IMF, where polar cap potential to influence cross polar cap potential. remained fairly low and stable. For northward IMF values North hemisphere South hemisphere Convection versus B yz IMF MLAT > 8 deg max # : 6145 max # : B IMF yz (nt) All points > Ann. Geophys., 25, , 27

10 17 M. Förster et al.: Cluster EDI measurements: variances and correlations yz To perm a similar analysis, we have combined all IMF directions, but divided parameter range into more bins. These bin-steps were chosen such that y contain about same amount of data steps are ree not equidistant in contrast to previous figure. The number of steps was chosen such that number of data points in each bin is sufficient velocity averages, and guarantees at same time a good grid point coverage polar cap potential pattern, which results in 15 non-equal steps. The resulting coverage is illustrated in bottom panel of Fig. 8. The full lines show relative number of data points in each bin as percentage of maximum number Norrn and Sourn Hemispheres separately. The deviations from maximum number and varying relative coverage between North and South is due to small hemispheric differences. The dashed lines show percentage of valid grid points within full area polar cap potential pattern construction (see Paper 1, Sect. 3.5) which is used upper panel. The upper panel of Fig. 8 shows derived cross-polar cap potential as a function of Byz IMF both Norrn (blue line) and Sourn Hemisphere (red line). They show same positive trend, although re are some non-regular variations in middle range from about 3 nt to 7 nt. For small magnitudes of B IMF < 3 nt, cross-polar cap potential has a minimum value between about 2 kv to 25 kv. Up to about 1 nt, re is a positive correlation, in agreement with Ruohoniemi and Greenwald (25). For B IMF yz values above range shown in Fig. 8, potential construction suffers from poor spatial coverage. The last step, marked with grey shading, contains ree all data points above 1.8 nt. The middle panel of Fig. 8 shows dependence on Byz IMF of convection velocities V, V x, and V y. As already mentioned above, se averages are derived with data points from central polar cap area (at φ m >8 ). The binning of whole parameter range is same as potential pattern in upper panel. The velocities in middle panel, particularly V x, show approximately same dependence on Byz IMF as cross-polar cap potential in upper panel, including minor variations in middle range. It can ree be regarded to some extent as Fig. 9. Top: Cross-polar cap potentials as function of solar wind Fig. 9. Top: Cross-polar reconnection cap potentials electric as function field, Eof a proxy cross-polar cap potential. This will be utilized furr in subsequent sections. The proxy North character (blue) and is South r,sw, solar both wind North reconnection (blue) andelectric South field, E r,sw, (red) (red) high-latitude high-latitude convection convection pattern, pattern, derived derived each each bin bin separately (cf. Paper 1). Here, again we use variable step widths as separately (cf. not surprising given that v=e B/B 2 and BHere, is essentially again we use variable in Fig. step 8. Middle: widths as Central in Fig. polar 8. Middle: cap convection Central velocities polar cap convection velocitie constant within auroral oval. While V x represents same variable bin steps same as above, variable butbin averaged steps as within above, but central averaged polar cap within at magnetic central latitudes at φ m localized dawn-dusk electric field strength within central polar cap at magnetic latitudes at φ m >8 only. The bottom panel polar cap, polar cap potential stands only. larger-scale, The bottom panel shows shows coverage coverage characteristics characteristics each each bin bin like like in in Fig. Fig integrating effect of solar wind magnetosphere coupling. Starting from a level of 2 m s lowermost bins, V x rises up to a level of about 4 m s 1 highest bins. At that end, averages start to fluctuate about this level. This can be interpreted as an indication saturation 4.3 Dependence on solar wind electric field at Byz IMF > 11 nt. Cross-polar potential U (kv) Potentials versus E r sw (mv/m) North hemisphere South hemisphere E r sw (mv/m) Convection versus E r,sw MLAT > 8 deg max # : 5571 max # : E r,sw (mv/m) Figure 9 shows cross polar cap potential estimations (upper panel), average convection velocities V x and V y (>8 ), and convection magnitude V (middle panel) as function of solar wind electric field, projected along 31 All points > 3.42 Ann. Geophys., 25, , 27

11 M. Förster et al.: Cluster EDI measurements: variances and correlations 171 Convection versus Pdyn a Convection versus s.w. proton density b Convection versus V_sw c Both hemispheres MLAT > 8 deg max # : Both hemispheres MLAT > 8 deg max # : Both hemispheres MLAT > 8 deg max # : Pdyn (npa) s.w. proton density (cm -3 ) V_sw (km/s) Fig. 1. (a):the polar cap convection velocity shown as function of solar wind dynamic pressure P dyn ; (b, c): corresponding dependencies of Fig. 1. solar (a):the wind polar protoncap density convection n velocity shown as function of solar wind dynamic pressure P dyn ; p and velocity V s.w.. Data points from both hemispheres have been combined analysis. The bottom (b,c): panels corresponding indicate dependencies spatial coverage of characteristics solar wind proton eachdensity bin within n p and high-latitude velocity V s.w.. area Data ( φ m points >8 ). from both hemispheres have been combined analysis. The bottom panels indicate spatial coverage characteristics each bin within high-latitude area ( φ m > 8 ). dayside reconnection X-line according to method by Sonnerup (1974): E r,sw = E yz,sw sin 2 (θ/2) = V x,sw B IMF yz,sw sin2 (θ/2) (3) that last bin, which collects all E r,sw values above approximately 3.4 mv m 1, still shows a significant increase. This issue of potential saturation has been addressed by Siscoe et al. (e.g. 22); Hairston et al. (e.g. 25). where E yz,sw is solar wind electric field, V x,sw is X- 4.4 Dependence on solar wind dynamic pressure component of solar wind velocity, Byz IMF is interplanetary magnetic field in GSM yz-plane, and θ is IMF As mentioned, due to nature of statistical studies, we are clock angle. As seen from Eq. (3), this parameter strongly not able to investigate direct response to time variances depends on direction of IMF. The electric field E r,sw such as pressure pulses or sudden reductions in dynamic serves as an indicator of reconnection rate at frontside pressure. But we can draw conclusion about statistical magnetopause (dayside reconnection), or, a fixed length behaviour of a large data set. of reconnection line, of cross-polar cap potential drop. Figures 1a c show solar wind dynamic pressure P dyn As expected, re is a clear correlation between antisolar (left panel) toger with parameters it is constructed convection velocity V x and E r,sw. Higher recon- from, namely solar wind proton density n p (middle nection rates at magnetopause cause faster transport of panel) and solar wind velocity V s.w. (right panel). They flux across polar cap. As noted in Paper 1, convection are related according to P dyn =m p n p Vs.w. 2 p is between main cells is slow, but still antisunward over proton mass. No significant North-South asymmetries were central polar cap, low values of E r,sw (which typically indicate found convection velocities. Theree we are comdividually a northward directed IMF). Closer inspection of inbining measurements from both hemispheres in this plot. averaged components V x and V y show, that at This is done by folding Sourn data points into low values of E r,sw sunward convection, which is taking Norrn by inverting By IMF dependence. The bottom panels indicate spatial coverage characteristics each bin place within lobe cells, and usual antisunward convection cancel each or within high-latitude circle at magnetic within high-latitude area ( φ m >8 ). latitudes >8, so that V x shows straight linear The drift velocity averages show a weak positive correla- behaviour, starting at zero. In contrast, potential curves tion with P dyn (upper panel of Fig. 1a). Even more interestingly, have a finite magnitude of 15 kv vanishing E r,sw as y at very low pressures re seems to be a significant result from remaining main convection cells. The V y peak, that is, low P dyn are related to higher convection velocities. component increases slowly with increasing values of E r,sw, The reason this is not clear, but data coverage starting close to zero and raising up to 5 1 m s 1 over is good, so effect seems to be real and it is related to range shown in Fig. 9. While re is linear correlation solar wind density, which reveals this peak at very low densities (upper panel of Fig. 1b). The furr variation with values of E r,sw (up to almost 2 mv m 1 ), curve n flattens out, but does not saturate, as demonstrated by fact 32 proton density is quite flat, except of a secondary small peak Ann. Geophys., 25, , 27

12 172 M. Förster et al.: Cluster EDI measurements: variances and correlations Convection versus DOY Convection versus DOY 6 North hemisphere South hemisphere a 6 North hemisphere South hemisphere b MLAT > 8 deg max # : 9364 max # : MLAT > 8 deg max # : 7745 max # : DOY (days) DOY (days) Fig. 11. Average convection velocity variations versus Day of Year (DOY) (or seasonal dependencies) Norrn (blue curves) and Sourn Hemisphere Fig. 11. Average (red). Left convection (a): using velocity all datavariations points of our versus dataday set. of Right (b): Year using (DOY) a filtered (or seasonal data setdependencies) with D st > 3 nt only (quiet conditions). The bottom panels illustrate data coverage of 12 equally sized steps corresponding to approximately monthly resolution. Norrn (blue curves) and Sourn Hemisphere (red). Left (a): using all data points of our data set. Right (b): using a filtered data set with Dst > -3 nt only (quiet conditions). The bottom panels illustrate data In Fig. 11 we tried to estimate possible seasonal variations that could be revealed from our data set. Due to orbital constraints, as explained in Paper 1, Sect. 3.4, only very central part of polar cap can be considered as equally covered with data points throughout whole year, though mapped drift vectors might originate from different spatial volumes of magnetosphere. Several studies in past investigated seasonal dependencies of large-scale high-latitude convection pattern, but many studies (e.g., De La Beaujardiere et al., 1991; Rich and Hairston, 1994; Weimer, 1995; Ruohoniemi and Greenwald, 1995; Milan et al., 21) came to different or even con- in range coverage of 7 8 of cm The equally slow sized rise ofsteps convection corresponding ve-tlocities with increasing P dyn is explained by a corresponding found that seasonal effect is similar to that of sign approximately tradictory results. monthly Ruohoniemi resolution. and Greenwald (1995, 25) rise in solar wind speed, shown in Fig. 1c. of By IMF. They state that combination of B y +/summer Equating velocity variations with cross-polar cap potential variations, we expect that re should be an increased (B y /winter) reinces tendency of By IMF sign factor potential at very low P dyn values which is due primarily to a solar wind density effect. The amplitude of this effect is up to about 25% relative to level at mean solar wind dynamic pressure. 4.5 Seasonal variations to sculpt dusk and dawn cells into more round/crescent shapes and to shift crescent cell across midnight MLT meridian while lowering total cross polar cap potentials. The non-reincing combinations, on or hand, produce elevated cross-polar potentials, especially B y /summer conditions and y found an overall tendency cross polar cap potential to increase from winter to summer. These conclusions of Ruohoniemi and Greenwald (25) study are based on Norrn Hemisphere observations of SuperDARN network. The upper pair of curves in upper panel of Fig. 11a, showing seasonal variation of averages of drift magnitudes, V, reveal generally higher level of Norrn Hemisphere velocity. On average, this amounts to about 7% whole area of our high-latitude grids, as already mentioned in Sect. 1, and it is slightly smaller but still visible within 8 circle shown here. The relative seasonal variations of this parameter are very small, i.e., less than 1% at Norrn Hemisphere and somewhat larger (up to 2%) Ann. Geophys., 25, ,

13 M. Förster et al.: Cluster EDI measurements: variances and correlations 173 at Sourn. The weak trend shows slight maxima (if ever) during winter months of respective Hemisphere. The velocity averages V x in Fig. 11a show a somewhat different behaviour. The relative seasonal variations and variations from month to month are larger and annual variation seem to be more-or-less in phase with upper curves in case of Sourn Hemisphere, while it seems to be in opposite phase at Norrn. After filtering time series geomagnetically undisturbed conditions, as is done in Fig. 11b D st >3 nt, a clear semiannual variation becomes evident with larger convection values during solstices both hemispheres. The July maximum (Norrn summer) seems to be more pronounced than that of December/January. It is well known that geomagnetic storms are more frequent during equinoxes. This was discovered by analyzing time series of geomagnetic indices. The semiannual variation (and to a minor degree also a diurnal variation) has been explained by Russell-McPherron (R-M) effect (Russell and McPherron, 1973) as being due to geometrical relationship between Earth s dipole axis and Parker spiral plane. Additionally, semiannual effect has recently be shown to originate also from periodical change of solar wind magnetosphere ionosphere (SMI) coupling efficiency (e.g., Cliver et al., 24; Nagatsuma, 26) which leads to more frequent and stronger geomagnetic storms near equinoxes. During quiet-time conditions, on or hand, we observe on average enhanced and more ordered indicated. convection during solstice periods, as shown in Fig. 11b. The reason this is not yet clear, but can probably be related to rmosphere ionosphere influences on magnetospheric convection. This should be analyzed in more detail in a future study. The relative variations unfiltered data (Fig. 11a) are generally larger at Sourn Hemisphere. Seasonal variations are likely to be related to different illumination conditions (cf. Fig. 2) and ree different ionospheric conductances. The larger relative variations in Sourn Hemisphere might also partially be caused by differences in geomagnetic field configuration. Whereas Norrn Hemisphere IGRF field poleward of 58 is fairly homogeneous, Sourn Hemisphere contains many crustal anomalies, causing a larger spatial variation in magnetic field. Values of IGRF magnetic field at 4 km altitude in Norrn Hemisphere 58 range from 42.9 to 49.9 µt, with an average of 47.4 µt. For Sourn Hemisphere, corresponding spatial variation is between 3.8 to 54.7 µt, with an average of 49.7 µt. Time variations of IGRF field in period from February 21 to March 26 are slow and insignificant in this connection. The data coverage, shown in bottom panel of Fig. 11, is largest around September equinox both hemispheres with Sourn maximum being larger than Norrn. During this time of year, Cluster satellites have ir apogee in tail magnetosphere and spend relatively long Both hemispheres MLAT > 8 deg Convection versus Dst max # : Dst (nt) Fig. 12. Top: Dependence of average convection velocities on Fig. 12. Top: Dependence D st of index, average with data convection from bothvelocities hemispheres on combined. Dst index, Bottom: with data from both spheres combined. Bottom: number of number data points of data with points equally with sized equally steps, sized in percentage steps, in percentage of of max maximum indicated. time intervals re. As mentioned earlier, due to southward tilt of line of apsides of Cluster orbit, satellites spend more time below neutral sheet on magnetospheric tailside which maps to Sourn Hemisphere nightside ionosphere. Generally, seasonal effect is minor with maximum amplitudes of 1% to 3% at most in cross-polar potential as deduced from locally confined average velocity estimations of V x within central polar cap. According to same reasoning, an overall tendency a semiannual variation of cross polar cap potential during geomagnetically undisturbed conditions is likely with on average larger potentials during solstices. 4.6 Dependence on D st index Figure 12 shows correlation with Disturbed Storm Time (D st ) index. The D st index is a measure of horizontal magnetic deflection on Earth at equatorial latitudes. Negative deflections in D st are mainly controlled by Earth s ring current, though solar wind pressure also contributes (e.g., Siscoe et al., 1968; Burton et al., 1975; O Brien and McPherron, 2). Positive 34 deflections are usually caused by pressure enhancements in solar wind which cause a displacement of magnetospheric drift shells. Ann. Geophys., 25, , 27