Improving geomagnetic field reconstructions for 0–3 ka

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Abstract

Global geomagnetic field reconstructions on millennial time scales can be based on comprehensive paleomagnetic data compilations but, especially for older data, these still suffer from limitations in data quality and age controls as well as poor temporal and spatial coverage. Here we present updated global models for the time interval 0–3 ka where additions to the data basis mainly impact the South-East Asian, Alaskan, and Siberian regions. We summarize recent progress in millennial scale modelling, documenting the cumulative results from incremental modifications to the standard algorithms used to produce regularized time-varying spherical harmonic models spanning 1000 BC to 1990 AD: from 1590 to 1990 AD gauss coefficients from the historical gufm1 model supplement the paleomagnetic information; in addition to absolute paleointensities, calibrated relative paleointensity data from sediments are now routinely included; iterative data rejection and recalibration of relative intensity records from sediments ensure stable results; bootstrap experiments to generate uncertainty estimates for the model take account of uncertainties in both age and magnetic elements and additionally assess the impact of sampling in both time and space. Based on averaged results from bootstrap experiments, taking account of data and age uncertainties, we distinguish more conservative model estimates CALS3k.nb representing robust field structure at the core–mantle boundary from relatively high resolution models CALS3k.n for model versions n = 3 and 4. We assess the impact of newly available data and modifications to the modelling method by comparing the previous CALS3k.3, the new CALS3k.4, and the conservative new model, CALS3k.4b. We conclude that with presently available data it is not feasible to produce a model that is equally suitable for relatively high-resolution field predictions at Earth’s surface and robust reconstruction of field evolution, avoiding spurious structure, at the core–mantle boundary (CMB). We presently consider CALS3k.4 the best high resolution model and recommend the more conservative lower resolution version for studies of field evolution at the CMB.

Highlights

► New global geomagnetic field reconstruction (CALS3k.4) for 0–3 ka. ► Bootstrap average gives robust field evolution at core–mantle boundary. ► Higher resolution field description at Earth’s surface. ► Additions to global data basis for Holocene magnetic field models.

Introduction

Geomagnetic field changes are rather well documented since the advent of routine direct measurements several centuries ago, but this time frame is not sufficient for the larger goal of understanding the physical processes that control long term changes in the geodynamo in Earth’s core. Significant efforts have been made over recent years to reconstruct not only the axial dipole strength, but also the dipole tilt and further large scale regional field variations on millennial timescales (Johnson and Constable, 1998, Hongre et al., 1998, Constable et al., 2000, Korte and Constable, 2003, Korte and Constable, 2005, Valet et al., 2008, Korte et al., 2009, Nilsson et al., 2010). Global compilations from numerous publications of archeomagnetic data (Donadini et al., 2006, Genevey et al., 2008, Donadini et al., 2009) and paleomagnetic records from sediments with high accumulation rates (Korte et al., 2005, Korte and Constable, 2006, Donadini et al., 2009) are the basis for such global field models. The spherical harmonic models, CALS3K.1 (Korte and Constable, 2003) and CALS7K.2 (Korte and Constable, 2005), with the names standing for “Continuous model from Archeomagnetic and Lake Sediment data of the past 3/7 kyrs”, have been used in a broad suite of applications. These range across investigations of westward and eastward motions in the core (e.g. Dumberry and Bloxham, 2006, Dumberry and Finlay, 2007, Wardinski and Korte, 2008), field asymmetry related to archeomagnetic jerks (Gallet et al., 2009), geomagnetic shielding for cosmic rays and cosmogenic isotope production for various kinds of studies (e.g. Usoskin et al., 2006, Muscheler et al., 2007, Usoskin et al., 2008, Lifton et al., 2008), to data assimilation for geodynamo models (Kuang et al., 2008). Despite these successes, previous attempts to characterize the spatial and temporal resolution of these models (Korte and Constable, 2008) have highlighted a number of issues with the available data and limitations of the chosen modelling techniques that lead to significant uncertainties in millennial scale geomagnetic field reconstructions.

Archeomagnetic data in general have smaller experimental uncertainties than those derived from sediments and their dating is often more precise. However, the number of archeomagnetic results available for times prior to 1000 BC is too small to allow for global reconstructions based purely on this data type. Even for the most recent epochs such information comes mostly from the northern hemisphere, and particularly from Europe, resulting in regionally biased models from these limited sources (Korte et al., 2009). Sediment records have a better geographic distribution, and are thus essential for global modeling efforts, but they are also intrinsically noisier. In some cases depositional and post-depositional processes will smooth out rapid field variations and they may suffer from strong dating uncertainties related to magnetization lock-in depth or radiocarbon reservoir effects that can influence large parts of or even complete time series. Moreover, intensity variations obtained from sediments are only relative, and must be calibrated somehow for use in global geomagnetic modeling. In recent work, (Donadini et al., 2009) and (Korte et al., 2009) constructed a suite of models using various classes of data and were able to show that even those based exclusively on sedimentary records, comprising magnetic field directions and suitably calibrated intensities, provide reasonable if somewhat smoothed reconstruction of past field variations. It should, however, be noted that some of the contributing records appear inconsistent with one another so that individual data records may have a poor fit to the resulting model. For regional studies, it makes sense to consider only highest quality data which can provide more detailed information for a specific geographical area than is possible with a global model. For the global field evolution, however, (Korte et al., 2009) concluded that the best reconstructions were produced using a combination of all available information, including knowledge derived from direct field observations spanning the interval 1590–1990 AD.

In this work we investigate the influence of modifications to the modelling method and the data by comparing two new models spanning the past 3 kyrs to the immediate predecessor CALS3k.3 (Korte et al., 2009). Section 2 details some additions to our data set. Then we summarize the evolution of the basic modeling method and describe improvements regarding outlier rejection, calibration of relative intensity data and obtaining a more conservative model by a bootstrap average. We discuss aspects of robustness and sensitivity of the CALSxk type models to changes in modelling and to the addition of newly available data by comparing CALS3k.3, the new CALS3k.4 and the more conservative new model, CALS3k.4b.

Section snippets

An updated data set

The data set used here is based on and extended from earlier compilations by Korte et al., 2005, Genevey et al., 2008, Donadini et al., 2009. These span the time interval 10000 BC to 1990 AD to allow for a future 10 or 12 kyr model. The archeomagnetic data consist of all those included in the GEOMAGIA V.2 database (Korhonen et al., 2008, Donadini et al., 2009, http://geomagia.ucsd.edu/) by August 2009. There are 163 more archeomagnetic data than were used for CALS3k.3, consisting of 56

The modeling method

The regularized modeling method using an expansion in spherical harmonic basis functions in space and cubic B-splines in time is essentially the same as for our earlier models and has been described in detail elsewhere (Bloxham and Jackson, 1992, Jackson et al., 2000, Korte and Constable, 2003, Korte and Constable, 2008). The spherical harmonic basis is expanded to degree 10 and the knot-point spacing of the splines is chosen as 10 years here. The actual spatial and temporal resolution after

Results

An overview of the models and their parameters is given in Table 4 and Fig. 2, where using the terminology of all our previous models λ and τ are the spatial and temporal regularization factors, respectively. The value of the spatial norm, Ψ, is the lower bound of the integrated Ohmic dissipation of the field over the Earth (Gubbins, 1975) and a measure of spatial complexity. The temporal variability is measured by temporal norm Φ, the integral of the second derivative of the radial field

Discussion

There are important philosophical differences about how to obtain the most reliable field reconstructions for Holocene time scales, given the large uncertainties in the data. A major problem is that for a significant part of the global data set it is very difficult to get independent, realistic, and internally consistent estimates of the uncertainties. Significant differences in the techniques applied to obtain the data, very different levels of documentation, and the gradual evolution of

Conclusions

We have presented two updated versions of the CALS3k spherical harmonic field model for the past 3 kyr using all available archeomagnetic and sediment data. Approximately 5000 new data have been added. In addition to the CALS3k.4 model based on the individual data compilation, we created average models from bootstrap experiments using data and age uncertainty combined with data distribution for both the old and new versions of the model. This bootstrap averaging to produce CALS3k.3b and CALS3k.4b

Acknowledgements

We thank Ute Frank for alerting us to newly available sediment records and for useful discussion of paleomagnetic sedimentary data and Fabio Donadini for updating the Geomagia database. Richard Holme provided valuable discussions about the modeling strategy and methods. Two anonymous reviewers provide detailed comments and suggestions for improving the clarity of the manuscript. We wish to express our gratitude to all the colleagues who shared their data with us personally, by making them

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