AMPERE Polar Cap Boundaries

. The high latitude atmosphere is a dynamic region with processes that respond to forcing from the Sun, magnetosphere, neutral atmosphere, and ionosphere. Historically, the dominance of magnetosphere-ionosphere interactions has moti-vated upper atmospheric studies to use magnetic coordinates when examining magnetosphere-ionosphere-thermosphere coupling processes. However, there are signiﬁcant differences between the dominant interactions within the polar cap, auroral oval, and equatorward of the auroral oval. Organising data relative to these boundaries has been shown to improve climatological 5 and statistical studies, but the process of doing so is complicated by the shifting nature of the auroral oval and the difﬁculty in measuring its poleward and equatorward boundaries. This study presents a new set of open-closed magnetic ﬁeld line boundaries (OCBs) obtained from Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) magnetic perturbation data. AMPERE observations of ﬁeld aligned currents (FACs) are used to determine the location of the boundary between the Region 1 (R1) and Region 2 (R2) FAC 10 systems. This current boundary is thought to typically lie a few degrees equatorward of the OCB, making it a good candidate for obtaining OCB locations. The AMPERE R1/R2 boundaries are compared to the Defense Meteorological Satellites Program Special Sensor J (DMSP SSJ) electron energy ﬂux boundaries to test this hypothesis and determine the best estimate of the systematic offset between the R1/R2 boundary and the OCB as a function of magnetic local time. These calibrated boundaries, as well as OCBs obtained from Magnetopause-to-Aurora Global Exploration (IMAGE) observations, are validated using si- 15 multaneous observations of the convection reversal boundary measured by DMSP. The validation shows that the OCBs from IMAGE and AMPERE may be used together in statistical studies, providing the basis of a long-term data set that can be used to separate observations originating inside and outside of the polar cap. line boundary (OCB) are sparse. Long-term and large-scale studies would 20 beneﬁt from speciﬁcations of the OCB in both hemispheres and all magnetic local times (MLTs) every 15 min or less (Cowley and Lockwood, 1992). Models that have the ability to distinguish between regions with open and closed ﬁeld lines would also beneﬁt from adaptive, high-latitude coordinates (Zhu et al., 2019). This study presents a new set of OCBs obtained from the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) magnetic perturbation observations. AMPERE measurements of FACs make it possible to estimate 25 the location where Region 1 (R1) and Region 2 (R2) FAC systems meet (the R1/R2 boundary). Because the location of the Birkeland current system is tied to the OCB, it seems logical to hypothesize that a dependable relationship between the R1/R2 boundary and the OCB exists. This study investigates the relationship between the AMPERE R1/R2 boundary and the OCB measured by the Defense Meteorological Satellites Program Special Sensor J (DMSP SSJ) electron energy ﬂux boundaries. Section 2 presents the details of both data sets. Section 3 explores the relationship between the different boundaries and 30 presents the calibration process that allows the AMPERE R1/R2 boundary to be used as a proxy for the OCB. This calibration, as well as the previous Magnetopause-to-Aurora Global Exploration (IMAGE) calibration performed by Chisham (2017b), is validated in section 4 by comparing calibrated OCBs with the convection reversal boundaries (CRBs) from DMSP plasma drift measurements and summarized in section 5.


Introduction
The high latitude atmosphere is a dynamic region driven by solar and magnetospheric forcing. The dominant coupling occurs between the ionosphere and magnetosphere, which drives plasma motions in the auroral oval and polar cap through the Dungey cycle (Dungey, 1961). These motions differ based on whether the ionospheric plasma lies on open or closed geomagnetic field lines, where open field lines are those that reach out from the Earth to connect with the Interplanetary Magnetic Field 5 (IMF) and closed field lines connect back to the Earth in the opposite hemisphere. In the simplest case, convective drifts within the polar cap ionosphere travel along approximately straight, antisunward paths (from magnetic local noon to midnight) and convective drifts in the auroral oval travel in curved, sunward paths. The auroral and polar cap regions also experience different types of magnetosphere-ionosphere-thermosphere (MIT) coupling. For example, field-aligned currents (FACs) flow between the ionosphere and the magnetosphere at auroral latitudes (Coxon et al., 2018, and references therein). In the polar cap, 10 the antisunward ionospheric convection flow driven by magnetic reconnection on the Earth's dayside magnetopause causes a highly structured polar ionosphere as the dense dayside ionospheric plasma is transported to the nightside where recombination processes destroy plasma that is not returned to sunlit regions quickly enough (e.g., Spiro et al., 1978). Focusing on the auroral oval, the high rate of particle precipitation in this region leads to additional Joule heating in the thermosphere (e.g., Vasyliūnas and Song, 2005). 15 Due to the differences in ionospheric and thermospheric behavior in the auroral oval and the polar cap, it is desirable to have a coordinate system that indicates in which region measurements were taken. This type of adaptive, high-latitude gridding has been performed with various data sets (Redmon et al., 2010;Chisham, 2017b;Kilcommons et al., 2017). These studies have demonstrated improved statistical and climatological results when using adaptive, high-latitude coordinates. Unfortunately, observations of the open-closed magnetic field line boundary (OCB) are sparse. Long-term and large-scale studies would 20 benefit from specifications of the OCB in both hemispheres and all magnetic local times (MLTs) every 15 min or less (Cowley and Lockwood, 1992). Models that have the ability to distinguish between regions with open and closed field lines would also benefit from adaptive, high-latitude coordinates (Zhu et al., 2019).
This study presents a new set of OCBs obtained from the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) magnetic perturbation observations. AMPERE measurements of FACs make it possible to estimate 25 the location where Region 1 (R1) and Region 2 (R2) FAC systems meet (the R1/R2 boundary). Because the location of the Birkeland current system is tied to the OCB, it seems logical to hypothesize that a dependable relationship between the R1/R2 boundary and the OCB exists. This study investigates the relationship between the AMPERE R1/R2 boundary and the OCB measured by the Defense Meteorological Satellites Program Special Sensor J (DMSP SSJ) electron energy flux boundaries.
Section 2 presents the details of both data sets. Section 3 explores the relationship between the different boundaries and 30 presents the calibration process that allows the AMPERE R1/R2 boundary to be used as a proxy for the OCB. This calibration, as well as the previous Magnetopause-to-Aurora Global Exploration (IMAGE) calibration performed by Chisham (2017b), is validated in section 4 by comparing calibrated OCBs with the convection reversal boundaries (CRBs) from DMSP plasma drift measurements and summarized in section 5.

Instrumentation
The data sets used in this study have a long and ongoing history of observations. The primary data set, AMPERE, is described in section 2.1. Two instruments from DMSP are used, one for calibration of the boundaries and another for validation. Both DMSP data sets are described in section 2.2. The IMAGE far ultraviolet (FUV) data set used in the validation is described in section 2.3. 5 2.1 AMPERE AMPERE assimilates measurements from the approximately 70 polar-orbiting spacecraft of the Iridium telecommunications constellation to deduce the high-latitude distribution of horizontal magnetic field perturbations produced by the FACs responsible for magnetosphere-ionosphere coupling (Anderson et al., 2000(Anderson et al., , 2002Waters et al., 2001;Coxon et al., 2018). The FAC pattern in both hemispheres is calculated from 10-minute averages at a 2 min cadence on a magnetic latitude and MLT grid (1 • ×1 h resolution); this study employs observations from 2010-2012.

DMSP
The DMSP OCB locations are obtained from energetic electron fluxes measured by three DMSP spacecraft (F16-F18) that were operational and have updated ephemera  during the period of time when AMPERE R1/R2 boundaries were available. The DMSP satellites were located in sun-synchronous polar orbits at an altitude of about 830 km, with an 15 orbital period of approximately 101 min. The geographic locations of the DMSP SSJ/5 equatorward and poleward boundaries were determined using ssj_auroral_boundary (Kilcommons and Burrell, 2019), which implements the technique described in Kilcommons et al. (2017). A clean set of OCBs were obtained by selecting the poleward boundaries with figures of merit greater than 3.0 and calculating the AACGM-v2 coordinates at each location (Shepherd, 2014;Burrell et al., 2018b).
The same DMSP spacecraft also carry an Ion Velocity Meter (IVM) that measures the three dimensional ion velocity (Heelis 20 and Hanson, 1998). Because the convective plasma drifts are strongly tied to the motion and state of the magnetic field lines, the CRB is typically located at or just equatorward of the OCB (Newell et al., 2004;Drake et al., 2009) except for regions of the dayside and nightside ionosphere that map to regions of ongoing magnetic reconnection. The CRB is the location where plasma drifts change from moving sunward to antisunward, or vice versa.
In this paper, CRBs obtained by Chen et al. (2015) are used to validate the AMPERE OCB locations within an hour of dawn 25 (06:00 MLT) and dusk (18:00 MLT). Other MLTs were not considered for several reasons. Most importantly: 1. Near magnetic noon and midnight the flows tend to be mostly sunward or antisunward, meaning there is no clear reversal in the convection as a function of magnetic latitude.
2. The IMF orientation will shift the MLT location of these sunward or antisunward flows, meaning more local times than just noon and midnight are affected. 3. Near midnight, the Harang reversal can give the appearance of multiple convection reversals at different latitudes.
The Chen et al. (2015) algorithm is optimized to identify the CRB in a two-cell convection pattern. If the plasma convection has a complex pattern with more than four reversals, or the plasma flows are weak and noisy, the program will not identify any CRB location. For symmetric, multi-cell patterns (such as those observed when the IMF is dominated by a positive B Z component), the program will identify the most equatorward reversal boundary. Otherwise, the most poleward reversal boundary will be selected as the CRB location. The algorithm typically performs better in the summer, since the DMSP IVM performs 5 better when the plasma density is higher (Chen et al., 2015;Chen and Heelis, 2018).

IMAGE FUV
Chisham (2017b)  During this time, the spacecraft was located in an elliptical orbit with a 90 • inclination, an apogee of 7 R E , a perigee of 1000 10 km, and an orbital period of ∼13.5 h.
This study uses data from the two FUV spectographic imagers, SI12 and SI13 (Mende et al., 2000). The SI13 imager measured oxygen emissions at 135.6 nm, resulting from energetic electron precipitation. The SI12 imager measured Dopplershifted Lyman-α emissions at 121.8 nm, resulting from proton precipitation. Both imagers provided data at a 2 min resolution, when the northern hemisphere is visible. The OCB was identified in the individual FUV images and fit across all magnetic 15 local times using the techniques described by Longden et al. (2010) and Chisham (2017b).

Relationship between the R1/R2 boundary and OCB
This study follows the process outlined in Boakes et al. (2008), which determined the offset between the IMAGE FUV poleward auroral boundaries and DMSP OCBs, to obtain a correction between the AMPERE R1/R2 boundary and the DMSP SSJ OCBs.
The five steps of this process are enumerated below. 4. Find a functional fit that describes the offset between the DMSP SSJ OCBs and the AMPERE R1/R2 boundaries. 5. Use the functional fit to correct the AMPERE R1/R2 boundary locations, creating an AMPERE OCB proxy.

25
The basis of the R1/R2 boundary identification is a fitting technique described by Milan et al. (2015). This technique aims to determine the centre and radius of the circle that best describes the boundary between the R1 and R2 FACs that were first identified by Iijima and Potemra (1976) without fitting to individual MLT bins. By avoiding this common method of defining a high-latitude boundary, this R1/R2 boundary identification is more robust in the event of sparse or weak currents and less influenced by the poorly defined current structures near local magnetic noon and midnight. The following procedure is applied to each AMPERE FAC grid. In this description, positive and negative values represent upward and downward currents, respectively. The R1 currents flow upwards at dusk and downwards at dawn, while the R2 currents have the opposite polarity and lie equatorward of the R1 current system. To distinguish between these two FAC systems, the first step is to multiply all FAC magnitudes on the dawn side (00:00 ≤ MLT < 12:00) by -1. This redefines the current signs such that R1 FACs are positive and R2 FACs are negative at all MLTs. Then a center point (x 0 , y 0 ) is assumed, 5 where x 0 is the dawnward distance from the noon-midnight meridian and y 0 is the sunward distance from the dawn-dusk meridian. A range of centres are tested, with x 0 varying between ±4 • and y 0 varying between -6 • and 0 • latitude. Additionally, a range of radii are tested at each centre point; varying the radius by 1 • latitude (111 km were compared. The hourly boundary offsets in each hemisphere and both hemispheres combined, all calculated using the magnetic co-latitude, are presented in Table 1. Table 1 were calculated by finding the typical difference between the DMSP SSJ OCB and the AMPERE R1/R2 boundary location in AACGM-v2 magnetic latitude in one hour MLT bins. The typical boundary latitude 30 difference (∆φ, which equals the DMPS SSJ OCB co-latitude minus the AMPERE R1/R2 boundary co-latitude) is represented by two values, the median of the boundary latitude differences and the peak of a Gaussian distribution (S.G. peak), fitted to a smoothed histogram (as in Boakes et al., 2008). The histograms have 1 • bins, and were smoothed using a 4 • running average.

The boundary offsets in
The smoothed histogram was then fit with a Gaussian function, allowing the S.G. peak and standard deviation to be calculated.    Figure 2. There is about a 0.49 • difference between the median and S.G. peak values. This 5 difference is very small compared to the width of the ∆φ distributions, and provides a measure of uncertainty for the resulting boundary correction. Unfortunately, the differences between the boundary fitting methodology used by Chisham (2017b) and Milan et al. (2015) mean that it is not reasonable to use a harmonic function to describe the offset between the DMSP SSJ OCBs and the AMPERE R1/R2 boundaries, as done in prior auroral boundary fitting studies (R.H. Holzworth, 1975;Carbary et al., 2003;Boakes et al., 2008). Because the R1/R2 boundary fitting method used by Milan et al. (2015) does not fit a series of MLT bins, the boundary correction cannot be applied prior to circle fitting and will determine the final shape of the OCB proxy. Thus, this study uses a 5 generalised ellipse (equation 1) rather than a harmonic function to avoid overfitting the MLT dependence of the offset between the DMSP SSJ OCBs and the AMPERE R1/R2 boundaries.
In equation 1, λ is the MLT in radians, a is the semi-major axis in degrees, e is the eccentricity (a unitless quantity), and τ is the angular offset of the ellipse's centre in radians. These four constants allow the ellipse to adjust its centre and axes. They As shown in Figure 3, the AMPERE R1/R2 boundary lies about 2 • equatorward of the OCB at magnetic midnight, about 4 • equatorward of the OCB at magnetic noon, and further out at dawn and dusk. The elliptical fit follows the central values very closely between 00:00 and 10:00 MLT, and smooths through the maxima and minima at 12:00, 16:00, and 22:00 MLT. 20 Even where the differences are greatest, though, the elliptical fit does not differ from the central value by more than 2 . This behaviour is consistent whether the median or S.G. peak is used in the fitting process. Indeed, the semi-major axis differs by less than the typical difference between the median and S.G. peak values and the eccentricity and angular offset are even more similar. The consistency of the elliptical fit for both central values, as well as its success at capturing the major features of ∆φ given the functional constraints, make it a good candidate for correcting the R1/R2 boundary to provide an OCB estimate.
The Gaussian nature of the hourly bins (shown in Figure 2) suggests that differences between the R1/R2 boundary and DMSP SSJ OCB are randomly distributed, confirming the conclusion that it is appropriate to use K to correct the R1/R2 boundary to obtain an AMPERE OCB estimate.

4 Validation
The appropriateness of using K to transform the AMPERE R1/R2 boundary into an AMPERE OCB is tested by comparing the AMPERE OCBs to the DMSP CRBs within an hour of dawn and dusk. To ensure that the performance of the AMPERE OCBs are on par with previous OCB calculations, this validation is also performed for the IMAGE OCBs. Unfortunately, it is impossible to directly compare the AMPERE and IMAGE OCBs because there is no temporal overlap between the two data 10 sets. This validation effort paired OCBs with DMSP CRBs that were identified within 10 min of one another. The location of the DMSP CRB relative to the OCB was then determined. In this adaptive coordinate system, the OCB is set at a co-latitude of 74 • (a latitude chosen to represent the OCB in adaptive, high-latitude coordinates based on the typical size of the polar cap).
CRBs that occur poleward or equatorward of the OCB will have co-latitudes greater than or less than 74 • , respectively. This adaptive gridding was performed using the Python package, ocbpy (Burrell and Chisham, 2018;Burrell et al., 2018a).
15 Figure 5. Histograms showing the differences between DMSP CRB and IMAGE or AMPERE OCB using paired boundaries that occur within 1 hr of 06:00 MLT or 18:00 MLT. Figure 4 shows the distribution of CRB observations for the different DMSP satellites, OCB sources, and hemispheres.
As was done with the DMSP SSJ observations, two years of CRBs and OCBs were paired in time after removing unreliable boundaries (as discussed in section 2). Note that both IMAGE and both AMPERE hemispheres show a similar spread of CRBs at different magnetic local times, with larger spreads near magnetic noon and midnight.

Conclusions
This study modified traditional auroral boundary fitting methods to establish an MLT dependent relationship between the OCB and the R1/R2 boundary. This was performed by determining the first moment of the distribution of differences between the 15 R1/R2 boundary and the OCB (as measured by the DMSP SSJ instrument) for 1 hr MLT bins. These moments (which included the median and the peak of a smoothed Gaussian) were then used to define the parameters of an elliptical function. This function specifies the distance between the OCB and R1/R2 boundary as a function of MLT.
The validity of this OCB, as well as previously determined IMAGE OCBs, were tested against the dawn and dusk measurements of the CRB (as measured by several DMSP IVM instruments). These boundaries were found to typically differ by less than a degree.

5
As mentioned in the introduction, modeling and statistical studies in polar regions should avoid mixing measurements taken in the auroral oval and the polar cap. In combination, the AMPERE and IMAGE OCBs form the basis of a multi-solar cycle data set that could be used to improve high latitude statistical studies and climatological models. The data sets and software tools presented in this paper allow researchers to begin using adaptive, high latitude coordinates in their investigations.
Code and data availability. AMPERE data are available from the John Hopkins University Applied Physics Laboratory at http://ampere.jhuapl.edu/.
We thank the AMPERE team and the AMPERE Science Center for providing the Iridium-derived data products. AMPERE boundaries can be requested from Steve Milan (steve.milan@leicester.ac.uk).
The IMAGE FUV data are provided courtesy of the instrument PI Stephen Mende (University of California, Berkeley). We thank the PI, the IMAGE mission, and the IMAGE FUV team for data usage and processing tools. The raw IMAGE data, and software, are available from http://sprg.ssl.berkeley.edu/image/. The auroral boundary data set, and the methodology used to create it, can be found at