A southern Africa harmonic spline core field model derived from CHAMP satellite data
Introduction
The CHAMP satellite mission provided very high quality vector measurements of the Earth's magnetic field which has enabled many studies about its external and internal sources. The majority of the magnetic field measured at the Earth's surface is due to a geodynamo mechanism operating in the liquid, metallic, outer core. It is generated in the fluid outer core by the self-exciting dynamo process. Electrical currents flowing in the slowly moving molten iron core generate this magnetic field known as the main or core field (Olsen and Mandea, 2007). It exhibits long-term changes which occur at irregular and unpredictable rates. In addition to this dominant contribution of the Earth's magnetic field, the lithospheric field arising from the magnetisation carried by rocks in the crust and upper mantle must also be considered. Another significant contribution is that of external sources which originate in the ionosphere and magnetosphere. In this study, the focus is put on the core field. The understanding of its time variations can shed light on the processes that drive them inside the liquid outer core.
The Earth's main magnetic field is not constant but changes non-uniformly with time. This phenomenon is known as secular variation, while sudden changes in the linear secular variation trend are known as geomagnetic jerks or secular variation impulses (Mandea et al., 2010). Torsional oscillations in the fluid outer core have been used to explain the occurrence of geomagnetic jerks (Bloxam et al., 2002) on a decadal timescale. No direct information, however, is available for timescales of less than a couple of years (Mandea and Olsen, 2009). It has been shown that changes in the magnetic field occurring over only few months, as well as the fluid flow at the top of the core that is believed to generate them, can be resolved (Olsen and Mandea, 2008). These changes involving rapid variations over timescale of few months have been called rapid secular variation fluctuations, or, in short, rapid fluctuations by Mandea and Olsen (2009). Chulliat et al. (2010), using the annual differences of monthly means of the Y and Z components from 1997 to 2009 at five INTERMAGNET magnetic observatories (Ascension, Kourou, MBour, Tamanrasset and Tsumeb), showed the occurrence of a 2007 jerk in Y and Z components. Kotzé (2011) used ground data collected at Hermanus observatory (HER) to show a 2007 jerk in X, Y and Z. The polynomial modelling of CHAMP satellite data measured between 2001 and 2005 over southern Africa identified rapid secular variation fluctuations during 2003 and 2004 in all components – X, Y and Z (Nahayo and Kotzé, 2012)
The considered area of study, southern Africa, is located in a region where the rapid decrease of magnetic field intensity is observed at the Earth's surface stretching across southern Africa and the south Atlantic Ocean (Lesur et al., 2008). This coincides with a region known as the South Atlantic Anomaly where the field is already very weak by approximately 30% compared to other locations at similar latitudes. In this region, the ground recording stations are limited and the use of high quality satellite data is needed for studies where spatial and temporal resolution data is required.
An attempt to study the time variation of the geomagnetic field in this region using the harmonic splines technique was done previously using only ground-based data (Geese et al., 2009). In this paper, the results of the use of harmonic splines technique on CHAMP satellite data recorded between 2001 and 2010 were compared with ground-based data recorded in the same period at Hermanus and Tsumeb magnetic observatories and the global GRIMM-2 model (Lesur et al., 2010).
Section snippets
Method
Our aim is to derive a core field regional model over southern Africa using harmonic splines. The harmonic splines were first introduced by Shure et al. (1982) for global magnetic field modelling, but it is also suitable for regional modelling. Modelling magnetic data by harmonic splines requires solving a square system of equations with dimension equal to the number of data points (Shure et al., 1982). The harmonic spline functions satisfy Laplace's equations, therefore allowing a potential
Satellite data
The data selection was performed on CHAMP satellite data that was recorded between roughly 300 km and 480 km of altitude. The quiet night data recorded between 2001 and 2010 were selected over the southern Africa region covering the area between 10°S and 38°S in latitude and 10°E and 38°E in longitude. Only quiet time data corresponding to a Dst index between −20 and 0 nT measured during local night times between 19:00 and 06:00 were considered. The choice of the time interval for data selection
Data modelling, data analysis and results
The SARM model is based on harmonic spline fitting of vector satellite data recorded between 2001 and 2010. The root mean square (rms) values of the difference between observed and model values were 12.6 nT, 6.9 nT and 6.5 nT for X, Y and Z components, respectively.
Secular variation values for each of X, Y and Z components in the analysis of derived data values from the 2 models (SARM and GRIMM-2) and ground data at 2 permanent observatories (HER and TSU) were calculated from monthly values as
Discussion and conclusions
The SARM model shows a general agreement in mapping the temporal and spatial characteristics of magnetic features with GRIMM-2 model, which was derived by fitting a vector data consisting of CHAMP satellite and observatory data. Table 4 presents the rms values of differences between these two models for epoch 2006.5 at 400 km altitude. For the main field models, the rms values are 25.7 nT, 9.2 nT and 8.5 nT for the X, Y and Z components, respectively. The rms values for the secular variation models
Acknowledgments
The support of the CHAMP mission by the German Aerospace Center (DLR) and the Federal Ministry of Education and Research is gratefully acknowledged. We thank Vincent Lesur and Anne Geese for the harmonic spline technique source code and two anonymous reviewers for their constructive comments.
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