CALS10k.1: A geomagnetic field model spanning 10~kyr

We present and evaluate CALS10k.1 and CALS10k.1b, time-varying geomagnetic field models spanning the past 10~kyrs. The CALS10k.1 reconstruction follows the strategy used in earlier millennial scale geomagnetic models forming a spherical harmonic representation to degree and order 10, and cubic spline temporal parametrization with knots at 40 year intervals. Quadratic regularization under the diffusion norm suppresses unnecessary spatial structure, and a penalty on the second temporal derivative provides a corresponding restraint in the time domain. The gufm1 model provides additional constraints over the time interval when direct directional (1590-1990 AD) and intensity (1840-1990 AD) observations were made. Although there are 12007 archeomagnetic data contributing to the 10 kyr model, it is heavily reliant on the additional 79181 sedimentary observations to provide adequate global coverage, and relative paleointensity observations have been iteratively re-calibrated, using local predictions from a sequence of improving models. Iterative data rejection is used to eliminate extreme outliers. The impact of uncertainties in the data is assessed by a bootstrap resampling scheme using suitable statistical models for the assigned ages and estimated data errors. CALS10k.1b is the average of 2000 bootstrap models constructed in this way and provides a more conservative estimate of geomagnetic variations over the 0--10~ka interval. We compare the model's dipole moment to other reconstructions and discuss the uncertainties. Further characteristic field features like motion of the dipole axis and changes in field morphology at the core-mantle boundary are discussed. It is now clear that even though they are visible in the 10~kyr average, flux lobes like those seen at the core mantle boundary for the historical time period are quite mobile over the 10~kyr time interval and that dynamical evolution of reverse flux features like the South Atlantic Magnetic Anomaly also occur in other areas over time.