Separation and Quantification of Ionospheric Convection Sources: 2. The Dipole Tilt Angle Influence on Reverse Convection Cells During Northward IMF
J. P. Reistad, K.M. Laundal, N. Østeward, A. Ohma, E.G. Thomas, S. Haaland, K. Oksavik, S.E. Milan
SSeparation and Quantification of Ionospheric ConvectionSources: 2. The Dipole Tilt Angle Influence on ReverseConvection Cells During Northward IMF
J. P. Reistad , K. M. Laundal , N. Østgaard , A. Ohma , E. G. Thomas ,S. Haaland , K. Oksavik , and S. E. Milan Birkeland Centre for Space Science, University of Bergen, Bergen, Norway, Thayer School of Engineering, DartmouthCollege, Hanover, NH, USA, Max Planck Institute for Solar System Research, Göttingen, Germany, Arctic Geophysics,University Centre in Svalbard, Longyearbyen, Norway, Department of Physics and Astronomy, University of Leicester,Leicester, UK
Abstract
This paper investigates the influence of Earth's dipole tilt angle on the reverse convectioncells (sometimes referred to as lobe cells) in the Northern Hemisphere ionosphere during northward IMF,which we relate to high-latitude reconnection. Super Dual Auroral Radar Network plasma driftobservations in 2010–2016 are used to quantify the ionospheric convection. A novel technique based onSpherical Elementary Convection Systems (SECS) that was presented in our companion paper (Reistadet al., 2019, https://doi.org/10.1029/2019JA026634) is used to isolate and quantify the reverse convectioncells. We find that the dipole tilt angle has a linear influence on the reverse cell potential. In the NorthernHemisphere the reverse cell potential is typically two times higher in summer than in winter. This changeis interpreted as the change in interplanetary magnetic field-lobe reconnection rate due to the orientationof the dipole tilt. Hence, the dipole tilt influence on reverse ionospheric convection can be a significantmodification of the more known influence from v sw B z . These results could be adopted by the scientificcommunity as key input parameters for lobe reconnection coupling functions.
1. Introduction
Magnetic reconnection allows energy from the solar wind and its embedded interplanetary magnetic field(IMF) to enter and be distributed within the magnetosphere system. In terms of energy transport in thesystem, the Dungey cycle (Dungey, 1961; opening of magnetic flux on the dayside and subsequent closureon the nightside) is of most importance. For this cycle, a strong degree of symmetry between the two polarregions is required by the Maxwell equation ∇ · ⃗ B = , requiring both polar caps to contain the same amountof open flux.However, reconnection can take place at other locations in the magnetosphere system, leading to plasmacirculations that are not necessarily restricted by the north-south symmetry constraints for the Dungey cycle(Wilder et al., 2013). This is the case during lobe reconnection, where the IMF reconnects with open fieldlines at the high-latitude magnetopause just tailward of the cusp, as schematically illustrated in Figure 1a.The lobe reconnection process is entirely independent in the two hemispheres. However, it is possible thatan IMF field line can simultaneously reconnect with the lobe in both hemispheres leading to closure of openflux (Imber et al., 2006), known as dual lobe reconnection. Based on analysis of global magnetospheric mag-netohydrodynamic modeling, Watanabe et al. (2005) and (Watanabe & Sofko, 2009a, 2009b) have pointedout additional possible reconnection geometries during northward IMF, all occurring on high latitudes,tailward of the cusps. Although the relative importance of these other reconnection geometries are stillunknown, we will discuss our results in light of this framework in section 4. Throughout the text we will usethe term “high-latitude reconnection” when discussing any of these possible reconnection processes asso-ciated with northward IMF. When using the term “lobe reconnection,” we specifically refer to the IMF-lobereconnection process as illustrated in Figure 1a.Although the energy transport related to lobe reconnection is usually much less than the one associatedwith the Dungey type reconnection, the region of influence is also much smaller, usually limited to above80 ◦ MLAT on the dayside (06–18 MLT) in the ionosphere. However, the redistribution of open flux during
RESEARCH ARTICLE
This article is a companion to Reistadet al. (2019), https://doi.org/10.1029/2019JA026634.
Key Points: • For purely northward IMF thereverse convection potentialdifference is typically two timeshigher in summer than in winter• The reverse convection potentialdifference has a linear dependenceon the Earth's dipole tilt angle• The Earth's dipole tilt angle is asecondary important controllingparameter of the lobe reconnectionrate
Correspondence to:
J. P. Reistad,[email protected]
Citation:
Reistad, J. P., Laundal, K. M.,Østgaard, N., Ohma, A.,Thomas, E. G., Haaland, S., et al.(2019). Separation and quantificationof ionospheric convection sources:2. The dipole tilt angle influence onreverse convection cells duringnorthward IMF.
Journal ofGeophysical Research: Space Physics , , 6182–6194. https://doi.org/10.1029/2019JA026641Received 20 FEB 2019Accepted 8 JUN 2019Accepted article online 4 JUL 2019Published online 22 JUL 2019©2019. The Authors.This is an open access article under theterms of the Creative CommonsAttribution-NonCommercial-NoDerivsLicense, which permits use anddistribution in any medium, providedthe original work is properly cited, theuse is non-commercial and nomodifications or adaptations are made. REISTAD ET AL. 6182 ournal of Geophysical Research: Space Physics
Figure 1. (a) A sketch of the lobe reconnection geometry at the Northern Hemisphere high-latitude magnetopausewhen the Earth's dipole (blue axis) is inclined toward the Sun (northern summer, positive tilt). (b and c) A conceptualview of the magnetosphere-ionosphere coupling in a steady state where the ionosphere is considered to respond only tothe magnetospheric forcing. The ionosphere is assumed to have a homogeneous conductivity, being low in panel(b) representing a dark ionosphere and higher in panel (c) representing a sunlit ionosphere. The same level ofmagnetospheric circulation is imposed in both panels (b) and (c), resulting in equal plasma circulation in theionosphere as illustrated with the red arrows. The higher conductivity levels in (c) will lead to a stronger shear in ⃗ B (blue lines) as a result of increased ionospheric friction, leading to a larger j || (large green arrow) in the sunlitionosphere. Panels (b) and (c) are reproduced from Paschmann et al. (2002) Figure 3.7. IMF = interplanetarymagnetic field. lobe reconnection has also been shown to introduce asymmetries on closed field lines (Tenfjord et al., 2018).Within the polar cap, strong disturbances due to the lobe reconnection process are observed (e.g., Burchet al., 1980; Friis-Christensen & Wilhjelm, 1975; Wilder et al., 2010). Furthermore, as the plasma circulationwithin the polar cap due to lobe reconnection is not bound by the same north-south symmetry constraints asthe flows initiated by the Dungey cycle, its dependence on IMF and solar wind parameters might be differentin the two hemispheres. One obvious geometric difference is the different inclination toward the Sun of thetwo polar regions, as quantified by the dipole tilt angle; see Figure 1a. The local conditions determiningthe reconnection rate are the shear angle between the two magnetic domains and the rate of flux transporttoward the reconnection line. Since the dipole tilt angle can change by almost 70 ◦ between its extreme valuesaround the solstices, this is a likely source of variability of the reconnection rate. The purpose of this paperis to give an estimate of the influence on the lobe reconnection rate due to variations of the dipole tilt angle.There are good physical reasons to relate observations of sunward ionospheric convection in the daysidepolar cap during northward IMF to lobe reconnection. The observation of strong sunward convection athigh latitudes was in fact the strongest argument for the existence of lobe reconnection. Although the exis-tence of lobe reconnection was proposed by Dungey (1963), direct observations at the magnetopause werenot presented until decades later (Gosling et al., 1991; Kessel et al., 1996). The reason why signatures ofsunward ionospheric convection in response to lobe reconnection was expected is due to the strong cou-pling between the magnetosphere and polar cap ionosphere. In a steady state description, one can directlyrelate the driver, for example, lobe reconnection initiating circulation of plasma in the lobes, to the iono-spheric response, namely, a corresponding circulation of plasma within the dayside polar cap. This situationis schematically illustrated in Figures 1b and 1c for two different ionospheric conditions: (b) local winterwhere the ionosphere has low and uniform conductivity and (c) local summer where the ionosphere hashigh and uniform conductivity. Figures 1b and 1c are adopted from Paschmann et al. (2002) Figure 3.7. Notethat the lobe reconnection rate is assumed to be the same in the two cases, hence the identical red arrowsof plasma circulation on the magnetospheric side. As the stresses from the twisting of the magnetic field atthe magnetospheric side will propagate toward the ionosphere, the F region ionospheric plasma will start torotate in response, leading to a ∇· ⃗ E within the rotating tube since ⃗ E = − ⃗ v × ⃗ B in the F region ionosphere andabove in this strong coupling scenario. In the steady state, strong coupling case (what is shown in Figures 1bREISTAD ET AL. 6183 ournal of Geophysical Research: Space Physics Figure 2.
Average Magnetic field and Polar current System (AMPS) model values of Birkeland currents during purelynorthward interplanetary magnetic field for three different values of the dipole tilt angle corresponding to northernwinter, equinox, and summer conditions. Model parameters are chosen to reflect the average conditions in Figure 3. and 1c), the ionospheric convection will be at a rate corresponding to a constant shear in ⃗ B , hence indepen-dent of ionospheric conductivity. The amount of shear in ⃗ B , proportional to j || (green arrow), is related to theforce needed to move the ionospheric footprints. During local winter (Figure 1b), the ionospheric conduc-tivity and hence the frictional force are low, leading to a small shear in ⃗ B . During local summer conditions(Figure 1c), the conductivity is higher. The increased friction lead to a larger shear in ⃗ B and hence j || toaccommodate the steady state during the same levels of magnetospheric circulation. In this discussion wehave assumed that a decoupling between the magnetosphere and ionosphere due to E || is negligible insidethe dayside polar cap. According to statistical studies of particle precipitation, E || associated precipitation ison average mainly confined to the duskside oval (Newell et al., 1996, 2009), enabling a ground-based inves-tigation of the origin of plasma convection in the magnetosphere. Despite being limited by assumptionsabout the coupling between the polar cap ionosphere and the magnetosphere, the ground-based nature ofthis study benefits from being able to observe the footprint of the entire magnetospheric region where theseinteractions take place.Birkeland currents mapping to the magnetospheric lobe circulation region cannot be directly used to inferthe strength of the lobe reconnection rate for different orientations of the dipole tilt angle, as the currents arehighly influenced by the ionospheric conductivity, which in turn depend strongly on the dipole tilt angle. Anexample of this, which will be used as reference for our results, is shown in Figure 2. Here, Birkeland cur-rents from the Average Magnetic field and Polar current System (AMPS) model (Laundal, Finlay, et al., 2018)are shown. AMPS is an empirical model of the perturbation magnetic field derived from low Earth orbitingsatellites, from which the full 3-D ionospheric current system can be calculated. The model is parameterizedby the external parameters v sw , IMF B y , IMF B z , dipole tilt angle, and F10.7 index and is designed to reflectthe influence of the solar wind-magnetosphere interactions taking place on the dayside. Figure 2 shows theBirkeland currents from the Northern Hemisphere during purely northward IMF for three different dipoletilt values corresponding to local winter, equinox, and summer conditions. The model parameter input isprinted on the figure and is chosen to reflect the average conditions of the statistics presented in Figure 3.The NBZ (northward B z ; Iijima, 1984) current system is clearly seen, located poleward of the dayside region1 currents, at 80–85 ◦ MLAT. These currents we attribute to high-latitude reconnection, and the maximumabsolute value within 80 ◦ MLAT is printed in each panel, corresponding to the location of the “+” symbol.Using this value as a proxy of the intensity of the current system associated with high-latitude reconnec-tion, it can be seen, as also qualitatively shown earlier (e.g., Green et al., 2009; Laundal, Finlay, et al., 2018;Weimer, 2001), that the NBZ currents increase by a factor of ∼ − ◦ to tilt = 21 ◦ . We willlater return to this average influence of dipole tilt on the NBZ currents, as our results will put constraintson how much of this variation we attribute to an increase in high-latitude reconnection and how much isrelated to the increased solar-induced conductivity.Earlier studies have found strong evidence that lobe reconnection is more efficient in the hemisphereinclined toward the Sun, that is, the local summer hemisphere (Crooker & Rich, 1993; Frey et al., 2004;Koustov et al., 2017; Østgaard et al., 2018; Wilder et al., 2010; Yakymenko et al., 2018), from observing thesunward ionospheric convection velocity in the dayside polar cap during northward IMF. However, moststudies have focused on the dependence on the solar wind electric field, E sw = v sw B T , where B T is the trans-REISTAD ET AL. 6184 ournal of Geophysical Research: Space Physics Figure 3.
Inferred reverse convection potential Φ RC from the Northern Hemisphere during northward interplanetarymagnetic field (IMF) for three different dipole tilt intervals based on Super Dual Auroral Radar Network line-of-sightmeasurements: (left column) winter (dipole tilt less than − ◦ ), (middle column) equinox (dipole tilt within ± ◦ ), and(right column) summer (dipole tilt > ◦ ). The upper row shows the inferred Δ n e from the Spherical ElementaryConvection Systems analysis, with reverse convection grid cells indicated with black dots. The middle row shows theelectric potential Φ . The bottom row shows the electric potential resulting from the selected reverse convection gridcells only. This potential is what we relate to the lobe reconnection rate and is printed below each panel. verse component of the IMF, B T = √ B 𝑦 + B z (Koustov et al., 2017; Sundberg et al., 2009; Wilder et al., 2009;2010; Yakymenko et al., 2018), likely to be the most important controlling factor on the lobe reconnectionrate during purely northward IMF. These studies all suggest a linear dependence of the ionospheric sun-ward convection speed in the dayside polar cap to E sw during northward IMF; however, a saturation effectis observed when E sw ≳ mV/m.A key difference of the present study compared to other studies on the seasonal differences of ionosphericconvection during northward IMF is the focus on the magnetic flux transport rate in the ionosphere, whichwe assume is directly related to the high-latitude reconnection rate due to the strong coupling between thetwo regions. Previous studies have mainly focused on the ionospheric sunward convection speed. However,the study by Chisham et al. (2004) is an exception, where the lobe reconnection rate is inferred from iono-spheric observations in a case study, also assuming the strong coupling between the ionosphere and thereconnection region. In order to arrive at a lobe reconnection coupling function, which is currently notexisting in literature to our knowledge, the ionospheric convection needs to be translated into a magneticflux transport rate; that is, the magnetic field strength and the distance where this convection exists must betaken into account. The present study aims to quantify the contribution from the dipole tilt angle to such aREISTAD ET AL. 6185 ournal of Geophysical Research: Space Physics coupling function. Our findings also suggest that the high-latitude reconnection rate depends linearly on thedipole tilt angle and is typically two times higher during summer versus winter for purely northward IMF.The present paper takes advantage of a novel technique described in our companion paper Separation andquantification of ionospheric convection sources: 1. A new technique , referred to as Paper I. In Paper I we showhow this technique can be used to separate the different sources of the ionospheric convection, enabling usin particular to estimate the magnetic flux transport rate (the potential) associated with the high-latitudereconnection processes. In the following section we describe the underlying convection data set that themethod in Paper I is applied to. Section 3 presents the results during northward IMF for different orientationsof the Earth's dipole axis. Sections 4 and 5 discuss and summarize the results.
2. Method
We here describe the underlying data used to make the convection maps, the selection of external drivingconditions, and finally a brief summary of the main steps of the Spherical Elementary Convection Systems(SECS) technique described in Paper I.
The ionospheric convection data set used in this study is from the Super Dual Aurora Radar Network (Super-DARN; Chisham et al., 2007; Greenwald et al., 1995). The LOS (line-of-sight) ionospheric plasma velocity isdeduced from the Doppler shift of the backscattered echo, caused by decameter-scale magnetic field-alignedirregularities in the electron density. Following the procedure of Thomas and Shepherd (2018), 7 years(2010–2016) of LOS velocity data from all available Northern Hemisphere SuperDARN radars are binnedonto an equal-area MLAT/MLT grid with spatial resolution of ∼
100 km and temporal resolution of 2 min(Ruohoniemi & Baker, 1998). Data from ranges less than 800 km are excluded to prevent contamination bylower-velocity E region echoes. We have also removed velocity data obtained from ranges further away than2,000 km to reduce the likelihood of geolocation inaccuracies associated with multihop HF radio propaga-tion. Finally, measurements collected during nonstandard radar operating modes are discarded. By doingthis, we ensure that only the highest-quality radar data are considered and also allowing for close com-parison and validation with the statistical results presented by Thomas and Shepherd (2018), as done inPaper I. Since we are interested in describing the ionospheric convection during northward IMF, it is important thatwe select data during periods when the IMF has been stable and northward for some time, to avoid con-tamination from flows initiated during southward IMF. We identify intervals of stable IMF using the biasfiltering technique (Haaland et al., 2007). With this technique, randomly oriented IMF vectors would leadto bias vector length of 0. For increasingly stable IMF, the length of the bias vector approaches 1. Similar toHaaland et al. (2007), we calculate the bias vector length at a given time based on a 30-min rolling intervalincluding the previous 20 min and the following 10 min using 1-min OMNI data (King & Papitashvili, 2005)and require the length of the bias vector to be > − ◦ , 30 ◦ ]. Note that when quantifying the IMF stability, only sta-bility in the YZ plane is considered. We also note that an inherent limitation of the data selection based onupstream solar wind and IMF is the effect of draping of the IMF through the magnetosheath (Sibeck et al.,1990). This will probably account for some of the large spread of the ionospheric convection observations.Only a dedicated in situ study of the lobe reconnection rate would be able to overcome this challenge.To reduce the known variability of lobe reconnection rate on the solar wind velocity and the magnitudeof the northward component of the IMF, we only consider SuperDARN observations when E sw = v sw B T is between 1 and 2 mV/m, where B T is the transverse magnitude of IMF. This corresponds to an intervalaround the peak occurrence of E sw and is satisfied 30% of the time.The last selection parameter is the dipole tilt angle, defined as the angle between the centered magneticdipole axis and the GSM Z axis, in the GSM XZ plane. By convention, positive values correspond to northernREISTAD ET AL. 6186 ournal of Geophysical Research: Space Physics summer. Since higher-order terms in the multipole expansion of the Earth's magnetic field decrease fasterthan the dipole term, the dipole tilt angle describes to a large extent the geometric north-south asymmetriesimposed from the earthward side of the solar wind-magnetosphere interactions. We have used the dipolecoefficients from the International Geomagnetic Reference Field model (Thébault et al., 2015) to determinethe dipole orientation that corresponds to the time of SuperDARN observations. This study focuses mainlyon three intervals of the dipole tilt angle corresponding to the three main regimes of solar illumination inthe Northern Hemisphere: winter (less than − ◦ ), equinox (within ± ◦ ), and summer ( > ◦ ). The methodology of the SECS description of the average ionospheric convection is described in Paper I. Herewe summarize the main steps of the technique to give a brief background. We describe the convection electricfield above 60 ◦ MLAT as a sum of the electric field contributions from 480 nodes distributed uniformly acrossthe MLT/MLAT domain at fixed locations. Each node has its own curl-free electric field associated with it,pointing away from or toward the node along the spherical surface (ionosphere). In vicinity of the node,the magnitude of the node electric field is approximately proportional to ∕ r , where r is the distance to thenode, and is scaled by an amplitude specific for that node. In this specific description, the convection electricfield is determined by the 480 node amplitudes, which are estimated by an inversion process based on theobserved LOS plasma velocities during the specific selection conditions.The input data to the SECS analysis are the LOS SuperDARN convection velocities as described in section2.1 selected during the conditions described in section 2.2. To relate the plasma velocities to an electric field,we also need the value of the magnetic field at each measurement location, found using the InternationalGeomagnetic Reference Field model. To overcome challenges due to an uneven spatial distribution of avery large number of observations, typically LOS observations, we have used an intermediate step in theinversion for the SECS amplitudes. Instead of the direct inversion of a ( ∼ , 480) size matrix, we computebinned average E fields from the LOS observations on a new grid. This intermediate step is described indetail in section 2.5 in Paper I.As shown in Paper I, it is the node amplitudes that describe the ionospheric convection in the SECS rep-resentation. Paper I presents how to calculate the convection electric field and potential directly from theamplitudes. More importantly, Paper I shows that the values and distribution of the node amplitudes containinformation about the magnetospheric sources of the ionospheric convection field, as the values of the nodeamplitudes reflect the local contributions to the ionospheric convection. Equation 14 in Paper I shows thatthe node amplitude is proportional to the divergence of the convection electric field. Hence, for a homoge-neous convection field, the amplitudes are ∼
0, while for a region with structure in the convection, indicatinga structure in the magnetospheric convection due to, for example, reconnection, the local node amplitudesincrease in absolute value.In our approach to determine ⃗ E SECS , we do not impose any constraints using statistical fill-in data from anempirical model, as is usually the case when instantaneous global convection patterns are derived. Thisis possible as our analysis is not used to describe a specific event or time interval, but rather the averagelarge scale plasma circulation during specific IMF clock angle, E sw , and dipole tilt interval ranges. The largedatabase of SuperDARN data from the years 2010–2016 has no need for fill-in data to calculate the binnedaverage ⃗ E in any grid cell. We use a weakly imposed boundary condition at our low-latitude boundary byincluding synthetic observations of zero electric field at 59 ◦ MLAT in the inversion for ⃗ E SECS ; see Paper I fordetails. This is similar to the use of the Heppner-Meynard boundary (Shepherd & Ruohoniemi, 2000) in theSuperDARN map potential technique (Ruohoniemi & Greenwald, 2005).
3. Seasonal Variation of the Lobe Cell Circulation
We here infer, using the technique described in Paper I, the reverse convection potential in the NorthernHemisphere during purely northward IMF for different values of the Earth's dipole tilt angle. As mentionedin section 2.2, we also keep E sw ∈ [ , ] mV/m, as it is known to be an important controlling parameter forthe lobe reconnection rate (Koustov et al., 2017; Sundberg et al., 2009; Wilder et al., 2009). This interval ischosen because of data coverage while still limiting the externally driven variations in the lobe reconnectionrate due to E sw .REISTAD ET AL. 6187 ournal of Geophysical Research: Space Physics Figure 4.
Statistics of the Super Dual Auroral Radar Network data used to produce Figure 3. The three columns referto the same dipole tilt intervals as in Figure 3. The upper row shows the magnitude of the binned average ⃗ E as colorand corresponding vectors as white pins from the center of the bin. The middle row is the magnitude of the estimatedcurl-free ⃗ E SECS and its associated vector shown as red pins. The bottom row is the data coverage shown as number ofunique hours of observations in each bin. SECS = Spherical Elementary Convection Systems.
Figure 3 shows the results for three different intervals of the dipole tilt angle. The three columns correspondto the dipole tilt intervals [ − ◦ , − ◦ ] (winter), [ − ◦ , 10 ◦ ] (equinox), and [10 ◦ , 35 ◦ ] (summer). The toprow shows Δ n e from the SECS analysis on the SECS node grid. Δ n e is the charge density expressed as thenumber of excess electrons per cubic meter, needed to maintain the electric field, found using Gauss law;see equation 14 in Paper I. We identify the grid cells associated with the reverse convection as done in PaperI, namely, using a threshold value of | Δ n e | > electrons per cubic meter inside the dayside polar cap (MLAT ⩾ ◦ , MLT ∈ [6, 18]). These identified grid cells are highlighted as black dots in the top and bottom rowsof Figure 3. The average E sw in the dayside polar cap of the underlying data is shown next to the polar plotat 09 MLT, indicating no significant bias in E sw between the different tilt angle intervals. The correspondingaverage dipole tilt angle is printed at 08 MLT. We also show the electric potential Φ in the second row andthe potential from the reverse convection nodes only, Φ RC , in the bottom row in Figure 3.As discussed in Paper I, we argue that the segmentation of the convection, where we express the potentialrelated to the reverse convection cells only (bottom row in Figure 3), is more directly addressing the source ofthe reverse convection circulation than the potential difference inferred from looking at Φ in the second rowof Figure 3, where the potential difference is calculated from the locations of the maximum and minimumREISTAD ET AL. 6188 ournal of Geophysical Research: Space Physics Figure 5.
A summary of the reverse convection potential difference ΔΦ RC versus dipole tilt angle. (Blue) The same analysis as presented in Figure 3but for smaller dipole tilt intervals, indicated by the horizontal bars at thebottom of the figure (blue/green). ΔΦ RC is found to respond linearly tochanges in the dipole tilt angle. The results for the extreme tilt angles areconsidered less reliable due to data coverage and are shown in transparentcolor. Due to a bias in E sw between the different dipole tilt intervals, wehave normalized ΔΦ RC to represent the situation when E sw = . mV/m,shown here in green. The results from Figure 3 are shown for referencein red. Φ in the region MLAT ≥ ◦ and MLT ∈ [06, 18], indicated with bold “+”symbols in the middle row in Figure 3. However, a significant increasein the inferred reverse convection potential is observed in both cases.Judging from the potentials inferred from the reverse convection nodesonly, the reverse convection potential increases from 9 kV for dipole tilt ∈ [ − ◦ , − ◦ ] to 15 kV for tilt ∈ [10 ◦ , 35 ◦ ].In Figure 4 we show the underlying statistics that was used to makeFigure 3. The three columns refer to the same tilt angle intervals as inFigure 3. The top row in Figure 4 shows the magnitude of the binnedaverage ⃗ E in color. ⃗ E is also shown as a vector in white color in the centerof each grid cell. Below each panel is also indicated the total number ofLOS vectors going into the analysis. The second row in Figure 4 shows themagnitude of the estimated ⃗ E SECS in color and the corresponding vectoras a red pin originating at the grid cell center. This is the same locationas the binned average ⃗ E , which is also shown in these panels for refer-ence. The SECS node locations are also shown as orange dots, located atthe same latitude but half way between the locations where we evaluate ⃗ E SECS . In the bottom panel we show the data coverage as the number ofunique hours of observation in each grid cell. The color scale used is suchthat the most blue bins have observations from less than 50 unique hours,and therefore, its corresponding binned average ⃗ E is down-weighted inthe inversion as described in Paper I. Hence, the influence of grid cellsshowing very large ⃗ E toward lower latitudes in the upper row is reduced,as is seen in the middle row in Figure 4.The upper and middle rows of Figure 4 show that ⃗ E SECS is less than thebinned average ⃗ E in most grid cells. This is likely one of the reasons whyour potentials are slightly lower (typically ∼ ⃗ E SECS approaches0 toward 60 ◦ MLAT in all MLT sectors.
4. Discussion
The most comprehensive investigations of seasonal variations in sunward convection velocities associatedwith lobe reconnection are the studies by Wilder et al. (2010) and Koustov et al. (2017). Both studies focusedon the sunward convection velocity inside the polar cap during purely northward IMF, in response to the E sw . Both studies found that on average, the summer hemisphere had stronger sunward convection veloc-ities than winter. However, Koustov et al. (2017) found a more prominent increase in sunward convectionvelocities with increasing E sw than Wilder et al. (2010). By making assumptions about the extent and thevelocity distribution across the sunward convection channel, one can approximate a measure of the asso-ciated potentials due to their observed sunward convection velocities within the E sw interval used in thisstudy. Based on our results in Figure 3, a typical width of the sunward convection channel is ∼ ΔΦ RC is linear, as we only show three rather wide dipole tilt intervals. We have made an attemptto more accurately describe the variation in ΔΦ RC versus dipole tilt angle by performing the same analysison smaller tilt angle intervals. A big challenge when reducing the tilt angle interval is to get enough datapoints to make a good determination of the binned average ⃗ E vectors. In Figure 4 one can see that in theregions having observations from >
50 unique hours, the binned averages of ⃗ E show systematic variationsREISTAD ET AL. 6189 ournal of Geophysical Research: Space Physics between neighboring grid cells, which indicates that the binned averages represent the typical vector for thegiven conditions. We were able to produce similarly robust binned average ⃗ E in 10 ◦ wide dipole tilt intervalsbetween − ◦ and 25 ◦ (five bins). For the edge intervals (tilt > |25 ◦ |) the fit was too poor to produce a reliableresult. We also increased the E sw interval by 0.5 mV/m in both directions to improve data coverage. The IMFclock angle interval and stability were kept the same. The results are summarized in Figure 5 as blue dotswith a corresponding fitted line. The less reliable results for the dipole tilt angles > |25 ◦ | are also shown butindicated with transparent blue color. A linear increase in ΔΦ RC is seen, except for the [25 ◦ , 35 ◦ ] interval,which has the poorest data coverage ( · LOS vectors). Although this value has a larger uncertainty thanthe the other data points in Figure 5, we cannot rule out the possibility that there could be some saturationof the dipole tilt influence on ΔΦ RC for very large dipole tilt angles.Using backscattered HF radio signals to measure the global ionospheric convection (as we do with Super-DARN) has intrinsic caveats and limitations. A successful observation depends both on the HF radiopropagation conditions as well as the existence of ionospheric decameter irregularities in the electron den-sity. Some of these issues can be seen in the statistics presented in this study and can influence the results.One example is that SuperDARN receives less backscatter echoes when the ionosphere is sunlit, reducingthe amount of data for increasing dipole tilt angle. This is usually interpreted as a consequence of the sunlitplasma having weaker decameter-scale irregularities than what is needed to produce a detectable backscat-tered echo (Ghezelbash et al., 2014; Ruohoniemi & Greenwald, 1997), but the HF propagation conditionsare also affected (Milan et al., 1997) leading to a different occurrence distribution of backscatter echoes asseen in the bottom row in Figure 4. However, due to the good radar coverage in the Northern Hemisphere,we are still able to reproduce ionospheric convection patterns during summer conditions, so this effect haslikely a minor influence on the results. In addition to sunlight, we have experienced that geomagnetic activ-ity has a similar influence on production of irregularities in the dayside polar cap. In our analysis, the dataobtained in the dayside polar cap during sunlit conditions are obtained from times that are slightly moredisturbed compared to the analysis when the same region is less illuminated. For the analysis in Figure 5,the mean E sw in the dayside polar cap increased from 1.2 to 1.7 mV/m from the lowest to highest tilt angleinterval. This effect is more pronounced compared to the analysis presented in Figure 3, and it likely affectsthe slope of the blue line in Figure 5. Based on the results from Sundberg et al. (2009), an increase in E sw of0.5 mV/m is associated with an increase of ∼ E sw = . mV/m still leads to a linear trend, as seen by the greendots and its fitted line in Figure 5. We also show the results from Figure 3 for reference as red dots and afitted line. We can see that the Sundberg et al. (2009) correction to the blue line places it close to the resultsfrom Figure 3 (red line) that did not have a significant bias in E sw .Chisham et al. (2004) presented a detailed examination of the ionospheric convection in the dayside polarcap from both hemispheres during an event when IMF was stable northward. Similar to this study, theyassumed a strong coupling between the ionosphere and the lobe reconnection site and related the iono-spheric convection to the lobe reconnection rate. From a low Earth orbiting satellite with a favorable orbitalconfiguration, they estimated the northern and southern reverse convection potential, interpreted as thelobe reconnection rate in the respective hemisphere, to be 13.5 and 19.7 kV, respectively. During these obser-vations, E sw = . mV/m and dipole tilt = − ◦ . This hemispheric difference represents an increase of 46 %from the local winter reconnection rate. From Figure 5, the reverse convection potential difference ΔΦ RC is 34 % larger for dipole tilt = +10 ◦ compared to dipole tilt = − ◦ when using the corrected values (greendots), and 50 % larger if considering the values with a slight bias in E sw (1.4 mV/m vs. 1.6 mV/m, blue dots).Although our statistical averages are similar to the event based values of the lobe reconnection rate as pre-sented by Chisham et al. (2004), deviations are expected when looking at single events, especially if the IMFdirection is varying.As illustrated in Figures 1b and 1c, we argue that when the magnetosphere and ionosphere are in equilib-rium, the average ionospheric convection is largely independent of the conductivity. By first principles, thetwo-cell flux transport is controlled by the dayside/nightside reconnection rates and should be equal in bothhemispheres. Hence, the two-cell convection pattern in the two hemispheres should on average be simi-lar in terms of magnetic flux transport. However, from observations, this interpretation can in some casesbe challenging to justify. Chisham et al. (2009) presented average maps of the vorticity of the ionosphericconvection deduced from SuperDARN measurements. They found a seasonal dependence of the vorticity,where stronger vorticity was found during summer compared to winter. This seems to contradict that theREISTAD ET AL. 6190 ournal of Geophysical Research: Space Physics two hemispheres are highly coupled and that the convection is to a large degree similar in the two hemi-spheres. However, as discussed earlier in this section, there are inherent limitations of the SuperDARNtechnique when comparing average convection from different seasons. From Figures 6 and 8 in Chishamet al. (2009) it is evident that the entire oval region is shifted to lower latitudes during the summer statistics,indicating that the underlying data are sampled during higher levels of activity making the summer/wintercomparison challenging. Also Pettigrew et al. (2010) found, using SuperDARN, a tendency of larger crosspolar cap potential in the summer hemisphere, also during southward IMF when no lobe reconnection isexpected to occur. Despite sorting the observations by B T (IMF magnitude in GSM YZ plane), the resultsfrom Pettigrew et al. (2010) are likely affected by the geomagnetic activity bias mention above, highlight-ing the difficulty to asses the conductivity influence on the ionospheric convection also in that study. In arecently developed model of the ionospheric convection using SuperDARN (Thomas & Shepherd, 2018),the Northern Hemisphere cross polar cap potential difference was found to vary little with season duringsouthward IMF. In that study, the underlying data were sorted by E sw in 0.5 mV/m intervals, likely furtherreducing the influence of the activity bias in SuperDARN compared to the study by Pettigrew et al. (2010).Furthermore, in a study of the nightside convection velocities focusing on the return flow (Reistad et al.,2018), no significant seasonal difference below 70 ◦ MLAT and away from the nightside convection throatcan be seen in the return flow when AL > − nT. We therefore conclude that the observed variations inionospheric convection with dipole tilt is mainly reflecting the changing levels of external driving, namely,the lobe reconnection rate when focusing on the dayside polar cap. Note that an underlying assumption forthis strong coupling is that there are no parallel electric field in this region.In Figure 2 we presented numbers reflecting the strength of the NBZ current system during northward IMFfrom the AMPS model, for three different values of the dipole tilt angle corresponding to the intervals usedin Figure 3. The AMPS model indicates that the average NBZ currents are approximately four times strongerin summer than in winter (dipole tilt angle 21 ◦ vs. − ◦ ). Since our results of the reverse convection above80 ◦ MLAT on the dayside is considered independent of the ionospheric conductivity, at least to the firstorder, we can make a quantitative estimate of how much this increase in field-aligned current is attributedto the increase in solar-induced ionospheric conductivity. To do so, we need to assume that the conductivityin this region (dayside polar cap) is uniform, simplifying the relation between the Birkeland current, thePedersen conductance, and Δ n e , as expressed in equation 16 in Paper I. Based on the minimum values of Δ n e from Figure 3 corresponding to the “+” location in Figure 2, we use equation 16 in Paper I to computethe Pedersen conductance. We obtain values of Σ P of 1.8, 3.1, and 4.6 S for winter, equinox, and summer,respectively, indicating an increase in Σ P of a factor of 2.6 when the field-aligned current increases by afactor of 3.8. Hence, the increase in NBZ currents with increasing dipole tilt angle is mostly an effect of theincreased ionospheric conductivity, highlighting the shortcoming of using currents alone to quantify themagnetospheric source process for this purpose. Comparing to Σ P estimated by the empirical model by Moenand Brekke (1993) using the F . solar flux and the solar zenith angle, we get 8.1 S during the summerconditions, 3.3 S during equinox, and 0 during winter as the model go to zero when the solar zenith anglereach 90 ◦ .Recently, Laundal, Reistad, et al. (2018) reported that when IMF was southward, the combination of IMF B x and dipole tilt angle could modify the dayside reconnection rate. For northward IMF, an IMF B x influencehas been speculated, but results are ambiguous (Østgaard et al., 2003; Yakymenko et al., 2018). We have alsolooked into the possible influence of the sign of the IMF B x component on the reverse convection potentialdifference, ΔΦ RC . When separating the analysis above into positive and negative IMF B x , ΔΦ RC was foundto be very similar to those presented in Figure 3. When using observations only during negative IMF B x ,we obtained values for ΔΦ RC of 10, 13, and 15 kV, while during positive IMF B x the corresponding ΔΦ RC was found to be 9, 11, and 14 kV. Hence, we conclude that the IMF B x influence on ΔΦ RC and thereforelobe reconnection rate is small compared to the dipole tilt influence. These results are consistent with thefindings of Yakymenko et al. (2018) that reported a similar response of the sunward convection speed inthe polar cap to E sw during both positive and negative IMF B x conditions. Despite being a small effect, thedifference in ΔΦ RC between positive and negative IMF B x conditions is in the expected direction (Østgaardet al., 2003) in each of the three dipole tilt angle intervals.This study aims to quantify the influence of the dipole tilt angle on the lobe reconnection rate. Other recon-nection geometries than the IMF-lobe reconnection scenario (Figure 1a) has been suggested to play a roleduring northward IMF (Watanabe et al., 2005; Watanabe & Sofko, 2009a, 2009b), possibly complicatingREISTAD ET AL. 6191 ournal of Geophysical Research: Space Physics the interpretation of ΔΦ RC as the lobe reconnection rate. In particular, the so-called “interchange cycle”(Watanabe & Sofko, 2009a) is expected to lead to reverse convection on closed field lines in the hemisphereopposite to where IMF-lobe reconnection takes place. It is therefore possible that our observations duringwinter are influenced by the flux transport being part of the interchange cycle due to lobe reconnection inthe opposite summer hemisphere, since we are not explicitly distinguishing between open and closed fieldlines in our analysis. However, our analysis indicates that the source region of the reverse convection also inthe winter is above 80 ◦ MLAT, usually interpreted as open field lines. Then, the inferred reverse convectionpotential difference ΔΦ RC can be interpreted as the lobe reconnection rate in the hemisphere we do the anal-ysis (assuming “reverse Dungey” type reconnection—Watanabe & Sofko, 2009b—is negligible). If this regionis in fact threaded by closed field lines, and lobe reconnection (or IMF-closed reconnection; Watanabe &Sofko, 2009b) is exclusively a summer phenomenon, as suggested by Watanabe and Sofko (2009b), our winterresults must be interpreted as the fraction of the IMF-lobe reconnection from the opposite hemisphere thatparticipate in the interchange (and/or reverse Dungey; Watanabe & Sofko, 2009b) cycle, while the summerresults is the IMF-lobe (and possibly reverse Dungey) reconnection rate in the summer hemisphere.Regardless of the importance of the additional high-latitude reconnection scenarios during northward IMF,the dipole tilt influence on the lobe reconnection rate is highly significant. In light of the above discussion,interpreting the observed reverse convection potential difference, ΔΦ RC as the lobe reconnection rate willplace a lower limit of the influence of dipole tilt on the lobe reconnection rate in the local hemisphere. Anycontribution from the interchange and/or reverse Dungey cycle reconnection (Watanabe & Sofko, 2009b)will lead to a stronger influence of dipole tilt on lobe reconnection rate in the Northern Hemisphere com-pared to the trend seen in Figure 5. Hence, the importance of the reconnection geometries during northwardIMF suggested by Watanabe et al. (2005) and (Watanabe & Sofko, 2009a, 2009b) needs further investigationsto more accurately address the lobe reconnection rate in each hemisphere separately.Our results suggest that the two main ingredients in a lobe reconnection coupling function during northwardIMF are most likely E sw and the dipole tilt angle. The implication of this significant dipole tilt dependenceis that the electrodynamics in the northern and southern polar cap regions can be severely different. Theseare important global differences that at the moment are not well quantified and understood. Deriving afirst-order global lobe reconnection coupling function will be a first step of quantifying this hemisphericdifference due to the hemispheric differences in the lobe reconnection rate. As demonstrated here, the SECStechnique is well suited for such further studies.
5. Conclusions
In this paper we have demonstrated the use of the SECS representation of the average ionospheric convectionelectric field, as described in Paper I. The new ability to separate and quantify the sources of the ionosphericconvection is shown to be highly applicable for a quantitative description of the reverse convection potentialduring northward IMF. The findings in this paper can be summarized as follows:• The dipole tilt angle is a secondary important controlling parameter of the lobe reconnection rate duringnorthward IMF, after v sw B z .• During northward IMF, the Northern Hemisphere typically has a reverse convection potential differenceduring summer that is two times that during winter, suggesting a strong hemispheric asymmetry. Thisinfluence can be considered as a lower bound of the dipole tilt influence on lobe reconnection rate in eachhemisphere during northward IMF.• The reverse convection potential difference depends linearly on the dipole tilt angle in the range [ − ◦ ,25 ◦ ].• The SECS representation of the ionospheric convection allows for a convenient separation of the inferredmagnetospheric sources of the convection, making it highly suited for further studies of the controllingparameters of lobe reconnection. References
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