Ensembles of low degree archeomagnetic field models for the past three millennia

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We introduce ensembles of time-varying archeomagnetic field models, consisting of a reference model, a mean model and a thousand individual models. We present a set of three such ensembles, built from archeomagnetic, volcanic and sedimentary data sets, that cover the past three millennia. These ensembles can be used to describe the field at any location from the core surface to the magnetosphere, and assess the way uncertainties due to the limited distribution and quality of the data affect any of its component or parameter, such as individual Gauss coefficients. They provide alternative - and, we argue, more complete - descriptions of the archeomagnetic field to those provided by previously published archeomagnetic field models, being better suited to existing and emerging needs, such as those of geomagnetic data assimilation. We present the data sets we rely on - essentially the same as those used by other recent archeomagnetic field models - and describe how errors affecting the data, and errors due to non-modelled small spatial scales of the field, are taken into account. We next explain our modeling strategy and motivation for building low degree spherical harmonic degree ensembles of models. We carry on a number of end-to-end simulations to both illustrate the usefulness of such ensembles and point at the type of errors one should expect. Practical illustrations of what can be done with these three ensembles of models, with examples of geomagnetic inferences, are also described. Northern high-latitude flux patches, for instance, appear to be the most robust features of all. These patches tend to fluctuate, but clearly have some favored locations, resulting in the same clear signature with three tongues (over Northern America, Europe and Asia) in the time-averaged field at the core-mantle boundary, similar to what had been found in earlier models. Inferences about the field behavior in the Southern hemisphere are more difficult to draw. Still, some suggestions that the well-known present South Atlantic reversed patch could have arisen as early as in 1500 A.D. are found in some of the ensembles. We otherwise confirm that most of the current archeomagnetic field model limitations are related to a number of sediment cores, identified as producing frequent outliers in the modeling process. We provide evidence that such cores are likely affected by timing errors and timing delays between magnetization lock-in and sediment deposition, that future more advanced treatment should be able to handle. All source files for the three ensembles of models, together with appropriate Matlab applications can be downloaded from http://geomagdpgp.fr/download/ARCHEO_FM.zip. (C) 2013 Elsevier B.V. All rights reserved.