The Swarm mission was selected as the 5th mission in ESA's Earth Explorer Programme in 2004. The mission will provide the best ever survey of the geomagnetic field and its temporal evolution that will lead to new insights into the Earth system by improving our understanding of the Earth's interior and its effect on Geospace, the vast region around the Earth where electrodynamic processes are influenced by the Earth's magnetic field. Scheduled for launch in 2010, the mission will comprise a constellation of three satellites, with two spacecraft flying sideby-side at lower altitude (450 km initial altitude), thereby measuring the East-West gradient of the magnetic field, and the third one flying at higher altitude (530 km). High-precision and high-resolution measurements of the strength, direction and variation of the magnetic field, complemented by precise navigation, accelerometer and electric field measurements, will provide the necessary observations that are required to separate and model the various sources of the geomagnetic field. This results in a unique “view” inside the Earth from space to study the composition and processes of its interior. It also allows analysing the Sun's influence within the Earth system. In addition practical applications in many different areas, such as space weather, radiation hazards, navigation and resource management, will benefit from the Swarm concept.

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Swarm, a satellite constellation to measure Earth's magnetic field with unpreceded accuracy, has been selected by ESA for launch in 2009. The mission will provide the best ever survey of the geomagnetic field and its temporal evolution, in order to gain new insights into the Earth system by improving our understanding of the Earth's interior and climate. An End-to-End mission performance simulation was carried out during Phase A of the mission, with the aim of analyzing the key system requirements, particularly with respect to the number of Swarm satellites and their orbits related to the science objectives of Swarm. In order to be able to use realistic parameters of the Earth's environment, the mission simulation starts at January 1, 1997 and lasts until re-entry of the lower satellites five years later. Synthetic magnetic field values were generated for all relevant contributions to Earth's magnetic field: core and lithospheric fields, fields due to currents in the ionosphere and magnetosphere, due to their secondary, induced, currents in the oceans, lithosphere and mantle, and fields due to currents coupling the ionosphere and magnetosphere. Several independent methods were applied to the synthetic data to analyze various aspects of field recovery in relation to different number of satellites, different constellations and realistic noise sources. This paper gives an overview of the study activities, describes the generation of the synthetic data, and assesses the obtained results.

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This paper reports on the findings of a simulation study designed to test various satellite configurations suggested for the upcoming Swarm magnetic mapping mission. The test is to see whether the mission objectives of recovering small-scale core secular variation (SV) and lithospheric magnetic signals, as well as information about mantle conductivity structure, can be met. The recovery method used in this paper is known as comprehensive inversion (CI) and involves the parameterization of all major fields followed by a co-estimation of these parameters in a least-squares sense in order to achieve proper signal separation. The advantage of coestimation over serial estimation of parameters is demonstrated by example. Synthetic data were calculated for a pool of six Swarm satellites from a model based heavily on the CM4 comprehensive model, but which has more small-scale lithospheric structure, a more complicated magnetospheric field, and an induced field reflecting a 3-D conductivity model. These data also included realistic magnetic noise from spacecraft and payload. Though the parameterization for the CI is based upon that of CM4, modifications have been made to accommodate these new magnetospheric and induced fields, in particular with orthogonality constraints defined so as to avoid covariance between slowly varying induced fields and SV. The use of these constraints is made feasible through an efficient numerical implementation. Constellations of 4, 3, 2, and 1 satellites were considered; that with 3 was able to meet the mission objectives, consistently resolving the SV to about spherical harmonic (SH) degree n = 15 and the lithosphere to a limited n < 90 due to external field leakage, while those with 2 and 1 were not; 4 was an improvement over 3, but was much less than the improvement from 2 to 3. The resolution of the magnetospheric and induced SH time-series from the 3 satellite configuration was sufficient enough to allow the detection of 3-D mantle conductivity structure in a companion study.

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A primary objective of the Swarm constellation mission is to resolve the lithospheric magnetic field with the best achievable accuracy in order to bridge the spectral gap between satellite and airborne/marine magnetic surveys. In a series of end-to-end simulations, the possibilities of high degree field recovery were investigated. The proposed constellation consists of a higher and a lower pair of satellites. It was soon found that a constellation as such does not yet guarantee improved high degree field recovery. Of crucial importance is the orbit constellation of the lower pair of satellites. If the lower satellites follow each other, as investigated in Constellation 1, the gain of a constellation turns out to be marginal, compared to a single satellite. For Constellation 2, the lower satellites were separated in the E/W direction. In this setup, one can use the instantaneous E/W magnetic field gradient between the satellites, as well as the N/S along track gradients. Incorporating this vector gradient information results in significantly improved field resolution. Indeed, the final simulation suggests that the envisaged Swarm constellation will enable the recovery of the lithospheric field to beyond spherical harmonic degree 130.

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We investigate how well the core field component of the underlying model used in the Swarm End-to-End simulator can be recovered when relatively simple geomagnetic field models are fitted to synthetic Swarm satellite and observatory data. In particular we demonstrate the potential benefits of Swarm by deriving models without these data. From two years of observatory data, the underlying secular variation model is recovered up to about spherical harmonic degree 8. This maximum degree is higher than was expected but increases to 10 when satellite data are also used. The constant part of the geomagnetic field model is recovered to at least degree 17. These results improve when a better statistical treatment of the data errors is made, a slightly more complex field model is fitted, or when five years of data are used.

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An approach is presented to detect deep-seated regional conductivity anomalies by analysis of magnetic observations taken by low-Earth-orbiting satellites. The approach deals with recovery of C-responses on a regular grid and starts with a determination of time series of external and internal coefficients of the magnetic potential. From the coefficients, time series of the magnetic vertical component and of the horizontal divergence of the horizontal components are synthesized on the grid and the C-responses are determined by means of signal processing of the corresponding time series. For validation of the approach, 3 years of realistic synthetic data at simulated orbits of the forthcoming Swarm constellation of 3 satellites have been used. To obtain the synthetic data for a given 3-D conductivity Earth's model a time-domain scheme has been applied which relies on a Fourier transformation of the inducing field, and on a frequency domain forward modelling. The conductivity model consists of a thin surface layer of realistic conductance and a 3-D mantle that incorporates a hypothetic deep regional anomaly beneath the Pacific Ocean plate. To establish the ability of the approach to capture the geometry of the mantle heterogeneities used in the forward approach, numerical experiments have been undertaken using various satellite combinations, sampling periods of the resulting time series, and numbers of internal coefficients. The possibility of the approach to map anomalies in the mantle using satellite data that contain contributions from the core and lithosphere, from the magnetosphere and ionosphere (and their Earth-induced counterparts), as well as payload noise has been investigated. The model studies have shown that C-responses obtained on a regular grid might be used to map regional deep-seated conductivity anomalies. Moreover, it has been demonstrated that these C-responses are successfully recovered from magnetic data collected by the proposed Swarm constellation of 3 satellites.

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Conducting ocean water, as it flows through the Earth's magnetic field, generates secondary electric and magnetic fields. An assessment of the ocean-generated magnetic fields and their detectability may be of importance for geomagnetism and oceanography. Motivated by the clear identification of ocean tidal signatures in the CHAMP magnetic field data we estimate the ocean magnetic signals of steady flow using a global 3-D EM numerical solution. The required velocity data are from the ECCO ocean circulation experiment and alternatively from the OCCAM model for higher resolution. We assume an Earth's conductivity model with a surface thin shell of variable conductance with a realistic 1D mantle underneath. Simulations using both models predict an amplitude range of ±2 nT at Swarm altitude (430 km). However at sea level, the higher resolution simulation predicts a higher strength of the magnetic field, as compared to the ECCO simulation. Besides the expected signatures of the global circulation patterns, we find significant seasonal variability of ocean magnetic signals in the Indian and Western Pacific Oceans. Compared to seasonal variation, interannual variations produce weaker signals.

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We have used a global model of the solar wind magnetosphere interaction to model the high latitude part of the external contributions to the geomagnetic field near the Earth. The model also provides corresponding values for the electric field. Geomagnetic quiet conditions were modeled to provide simulated external contributions relevant for internal field modeling. These have proven very valuable for the design and planning of the upcoming multi-satellite Swarm mission. In addition, a real event simulation was carried out for a moderately active time interval when observations from the Ørsted and CHAMP sattelites were available. Comparisons between the simulation results and the satellite observations for this event demonstrate the current level of validity of the global model. We find that the model reproduces quite well the region 1 current system and nightside region 2 currents whereas it consistently underestimates the dayside region 2 currents and overestimates the horizontal ionospheric closure currents in the dayside polar cap. Furthermore, with this example we illustrate the great benefit of utilizing the global model for the interpretation of Swarm external field observations and, likewise, the potential of using Swarm measuremnets to test and improve the global model.

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Solar wind generated magnetic disturbances are currently one of the major obstacles for improving the accuracy in the determination of the magnetic field due to sources internal to the Earth. In the present study a global MHD model of solar wind magnetosphere interaction is used to obtain a physically consistent, divergence-free model of ionospheric, field-aligned and magnetospheric currents in a realistic magnetospheric geometry. The magnetic field near the Earth due to these currents is analyzed by estimating and comparing the contributions from the various parts of the system, with the aim of identifying the most important aspects of the solar wind disturbances in an internal field modeling context. The contribution from the distant magnetospheric currents is found to consist of two, mainly opposing, contributions from respectively the dayside magnetopause currents and the cross-tail current. At high latitudes the field-aligned component is of partidular interest in connection with internal field-modelling. In the altitude regime of 400-800 km (typical for low Earth orbit satellites) the ionospheric currents are found to contribute significantly to the disturbancance, and account for more than 90% of the field-aligned disturbance. The magnetic disturbance field from field-aligned currents (FACs) is basically transverse to the main field, and they therefore contribute with less than 2% to the disturbance in total field intensity. Inhomogeneity in ionospheric conductance is identified as the main cause of main-field disturbance in the field-aligned direction. These disturbances are associated with the ionospheric Pedersen currents, and may introduce systematic errors in internal field models.

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The constellation of the Swarm satellites provides for the first time the opportunity to determine field-aligned currents in the ionosphere uniquely. This is achieved by employing the curl-B relation of Ampere's law directly to measurements of a satellite pair flying side-by-side. The new technique is applied to a set of consistent magnetic field and current data generated by a global magnetospheric model. Using a realistic Swarm constellation the current distribution is determined along the orbit from the synthetic magnetic field data. The resulting currents are tested against the input currents. The agreement between input model and recovered field-aligned currents is excellent and much improved compared to the single-satellite estimates. Due to the spatial separation of the sampling points, only the distribution of large-scale field-aligned currents can be determined. These investigations demonstrate one important aspect of the broad capabilities provided by the upcoming space mission.

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A set of functions is defined that can be used for modelling the internal part of the geomagnetic field. These functions are represented in term of spherical harmonics of a given maximum degree L and are centred at specific latitudes and longitudes. The number of functions needed and the positions of their centres are such that any potential field of maximum spherical harmonic degree L can be modelled. Formulae are obtained to transform between the potential field representation using these functions and a classic spherical harmonic representation. The shape of these functions can be optimized to make them reasonably localized, and from there it is shown how a localized constraint can be applied to an internal geomagnetic field model. The technique is demonstrated by means of models built from a few months of the Swarm mission synthetic data set.

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Present lithospheric field models, like the MF4 and CM4, are produced by least squares estimation using spherical harmonic basis functions with global support. Accounting for the different properties of magnetic data at low and high latitudes, a method that can take regional differences into account is proposed. Using four years of CHAMP satellite data, a detailed lithospheric magnetic field snapshot is obtained at 400 km altitude over the entire sphere by stitching together a dense coverage of regional models. The individual forward models computed on a quasi-regular grid over the Earth are then transformed to spherical harmonics by direct integration. Despite the stitching procedure, the long wavelength lithospheric features are correctly reproduced and small scale features are well resolved. Without regularization, the resulting model is stable to spherical harmonic degree 56. In addition to accounting for regionally varying noise levels, the proposed technique is also well suited to deal with incomplete data coverage issues when combining satellite with near surface data. The method could therefore make an important contribution to one of the main goals of the Swarm mission: to close the spectral gap between satellite and near-surface magnetic surveys.

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