Swarm SCARF equatorial electric field inversion chain
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB 2013
Received: 19 March 2013
Accepted: 10 September 2013
Published: 22 November 2013
The day-time eastward equatorial electric field (EEF) in the ionospheric E-region plays a crucial role in equatorial ionospheric dynamics. It is responsible for driving the equatorial electrojet (EEJ) current system, equatorial vertical ion drifts, and the equatorial ionization anomaly (EIA). Due to its importance, there is much interest in accurately measuring and modeling the EEF for both climatological and near real-time studies. The Swarm satellite mission offers a unique opportunity to estimate the equatorial electric field from measurements of the geomagnetic field. Due to the near-polar orbits of each satellite, the on-board magnetometers record a full profile in latitude of the ionospheric current signatures at satellite altitude. These latitudinal magnetic profiles are then modeled using a first principles approach with empirical climatological inputs specifying the state of the ionosphere. Since the EEF is the primary driver of the low-latitude ionospheric current system, the observed magnetic measurements can then be inverted for the EEF. This paper details the algorithm for recovering the EEF from Swarm geomagnetic field measurements. The equatorial electric field estimates are an official Swarm level-2 product developed within the Swarm SCARF (Satellite Constellation Application Research Facility). They will be made freely available by ESA after the commissioning phase.
Electromagnetic fields in the Earth’s ionosphere are responsible for driving many interesting phenomena. At low and mid latitudes, neutral winds combine with ionospheric electric fields to drive the equatorial electrojet (EEJ) and solar-quiet (Sq) current systems (Sugiura and Poros, 1969; Richmond, 1973) which produce significant magnetic signatures both on the ground and at low Earth orbiting (LEO) satellite altitude. Equatorial electric fields are also responsible for driving the equatorial plasma fountain, which lifts plasma to the upper regions of the ionosphere, where it then diffuses downward and poleward to form enhanced density regions near ±15° magnetic latitude, known as the equatorial ionization anomaly (EIA) (Anderson, 1981). In recent decades, direct measurements of ionospheric electric fields have been restricted to a small number of ground-based radar systems (Hysell et al., 1997; Chau and Woodman, 2004; Chau and Kudeki, 2006) and a few satellite missions (Fejer et al., 2008; de la Beaujardière and the C/NOFS Science Definition Team, 2004). Due to the sparse availability of ionospheric electric field measurements, techniques have been developed over the past decade to indirectly infer electric field values from other sources, in particular at low-latitudes. Anderson et al. (2004) developed a method to infer equatorial vertical ion drift velocities from ground-based magnetometer measurements in Peru using an observatory close to the magnetic equator and another several degrees higher in latitude. Their method relies on training a neural network with horizontal magnetic field inputs ΔH and known electric field outputs which were provided by the Jicamarca radar near Lima, Peru. Without a global set of electric field measurements it is difficult to extend this technique to other longitudes.
Alken and Maus (2010a) developed a technique to estimate the equatorial electric field (EEF) from a latitudinal profile of the EEJ current as the CHAMP satellite crossed the magnetic equator, building upon the earlier work of Lühr et al. (2004). Alken et al. (2013) then extended this work to derive EEF estimates in real-time using ΔH measurements from ground-based magnetometers at any longitude. This method will be used to produce EEF estimates in near real-time each time a Swarm satellite crosses the magnetic equator. While parts of this algorithm have been published before in the previously mentioned papers, the detailed algorithm has never been published in its entirety. The purpose of this paper is to detail the whole algorithm. This so-called “Swarm SCARF equatorial electric field inversion chain” is one of more than a dozen processing chains developed by the Swarm SCARF (Satellite Constellation Application Research Facility) to be operated during the mission (see Olsen et al., 2013), to which IPGP and NOAA will further contribute via the Swarm SCARF dedicated ionospheric and lithospheric chains (see Chulliat et al. (2013) and Thébault et al. (2013)). General information about the Swarm mission can otherwise be found in Friis-Christensen et al. (2006), (2009).
2. Satellite Data
The primary input to the equatorial electric field chain will come from the Swarm absolute scalar magnetometer (ASM) instrument on-board all three satellites (Leger et al., 2009). The Swarm ASM is expected to provide 1 Hz scalar magnetic field measurements with an accuracy better than 0.3 nT (Friis-Christensen et al., 2006). While the ASM is also capable of measuring the vector field, only the scalar field data is used for the EEF chain, since the EEJ signature is clearly observable in scalar field measurements and the EEF modeling procedure is considerably simpler with scalar data.
Many of the algorithms in the EEF inversion chain were developed during the CHAMP satellite mission (Reigber et al., 2003). The CHAMP satellite (2000–2010) flew in a near polar orbit (87.3° inclination) with an initial altitude of 454 km which decayed to about 250 km by the end of its mission. CHAMP carried both a scalar Overhauser and a vector fluxgate magnetometer. Many CHAMP-based studies of ionospheric electromagnetic fields and currents led to the development of the algorithms used in the Swarm EEF inversion chain (Lühr et al., 2004; Alken et al., 2008; Alken and Maus, 2010a). The CHAMP database also served as the primary source of input data during the development of the Swarm EEF processor for the Level 2 processing facility.
3. Coordinate Systems
The Swarm scalar magnetic measurements will contain contributions from the Earth’s core, lithospheric, ionospheric, and magnetospheric fields. An important step in the processing is to compute scalar magnetic residuals which represent the ionospheric equatorial electrojet, eliminating as many other sources of the geomagnetic field as possible. While this is described in detail in the following section, here we will discuss the various coordinate systems used during this analysis. During the data processing, we fit a model of the Sq (solar-quiet) mid-latitude ionospheric current system to the scalar residuals in order to eliminate its magnetic signature. This model is a standard spherical harmonic expansion in three dimensions, however we replace the geocentric colatitude θ with quasi-dipole colatitude, denoted θ q (Richmond, 1995). Quasi-dipole coordinates are a generalization of simple dipole coordinates to a general geomagnetic field. Quasi-dipole latitude is a coordinate which varies along the geomagnetic field B, but changes only slightly with altitude. These coordinates are used because the ionospheric current systems (both Sq and EEJ) are organized with respect to the geomagnetic field, and using a coordinate system which exploits this fact reduces the number of spherical harmonic coefficients needed to model the Sq magnetic field. Throughout the paper, when we refer to the “magnetic equator”, we mean the quasi-dipole equator where the quasi-dipole latitude is 0. The spherical harmonic model used to filter out Sq is also designed to filter out fields originating in the magnetosphere. We represent this part of the model in solar magnetic (SM) coordinates (Russell, 1971). In solar magnetic coordinates, the Z axis is chosen parallel to the Earth’s magnetic dipole and positive toward north. The Y axis is chosen perpendicular to the Earth-Sun line and positive toward dusk. The X axis completes the right-handed basis set and is positive toward the Sun. Since most of the magnetospheric field contribution is driven by solar forcing, using SM coordinates exploits this geometry to reduce the number of external field coefficients needed to sufficiently model these effects. Now that we have defined the relevant coordinate systems for our analysis, we will discuss the processing of the scalar magnetic data in detail.
The first step in the data processing involves detection of day-side equatorial crossings. Because the EEJ signal vanishes during the night, or is too weak to perform a meaningful inversion, we restrict our analysis to crossings of the magnetic equator between 06:00 and 18:00 local time. When such a dayside orbit is detected, it is analyzed from −65 to +65 degrees quasi-dipole magnetic latitude. This latitude range is designed to ensure the magnetic signal of both the ionospheric Sq and EEJ current systems are captured. Although we are mainly interested in the EEJ signal, the effect of Sq needs to be carefully separated from the total signal, since Sq effects can be significant at low latitudes where the EEJ is flowing. This is further discussed in the next section.
5. Sq Removal
6. Current Inversion
7. Electrodynamic Modeling
The PDE in Eq. (24) is solved on a 2D grid in the (r, θ) plane, holding ϕ fixed at the longitude of the satellite crossing of the magnetic equator. The grid ranges from 65 to 500 km altitude in steps of 2.175 km, and −25 to 25 degrees latitude in steps of 0.25 degrees. The boundary conditions imposed on the PDE are that the current vanishes at the lower and upper boundaries (ψ = 0 at r = rmin and rmax), and there is no radial current flow at the northern and southern boundaries ( at and ). We solve the PDE using finite differencing on the 2D grid with a 9-cell stencil.
8. EEF Inversion
9. Validation of EEF Estimates
In this paper we have presented in detail the algorithm for the Swarm Level 2 Equatorial Electric Field inversion chain. The main inputs to the algorithm are the scalar magnetic field measurements from the absolute scalar magnetometer (ASM) instrument on-board each Swarm satellite. The chain then subtracts internal and magnetospheric field models, filters out the mid-latitude Sq current system, inverts the resulting magnetic profile for the E-region height-integrated current density, and then models this current density with a combination of first-principles and empirical modeling to recover the driving zonal electric field at the time of the satellite crossing of the magnetic equator. This algorithm has been thoroughly tested against the CHAMP database, and the resulting EEF estimates have been validated against independent measurements from the JULIA radar, with a correlation of 0.80 between the two, a best fit line with a slope of nearly 1, and a bias close to 0. Validation against JULIA measurements will be carried out periodically throughout the Swarm mission to ensure the algorithm continues to produce reliable EEF estimates.
The operational support of the CHAMP mission by the German Aerospace Center (DLR) is gratefully acknowledged. The Jicamarca Radio Observatory is a facility of the Instituto Geofisico del Peru operated with support from the NSF through Cornell University. The authors gratefully acknowledge support from the Centre National d’Études Spatiales (CNES) within the context of the “Travaux préparatoires et exploitation de la mission SWARM” project, and from the European Space Agency (ESA) through ESTEC contract number 4000102140/10/NL/JA “Development of the Swarm Level 2 Algorithms and Associated Level 2 Processing Facility.” We also thank two anonymous reviewers for their comments on an earlier version of the manuscript. This is IPGP contribution number 3446.
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