Modelling decadal secular variation with only magnetic diffusion

Secular variation (SV) of Earth's internal magnetic field is the sum of two contributions, one resulting from core fluid flow and the other from magnetic diffusion. Based on the millenial diffusive timescale of global-scale structures, magnetic diffusion is widely perceived to be too weak to significantly contribute to decadal SV, and indeed is entirely neglected in the commonly adopted end-member of frozen-flux. Such an argument however lacks consideration of radially fine-scaled magnetic structures in the outermost part of the liquid core, whose diffusive timescale is much shorter. Here we consider the opposite end-member model to frozen flux, that of purely diffusive evolution associated with the total absence of fluid flow. Our work is based on a variational formulation, where we seek an optimized full-sphere initial magnetic field structure whose diffusive evolution best fits, over various time windows, a time-dependent magnetic field model. We present models that are regularized based on their magnetic energy, and consider how well they can fit the COV-OBS.x1 ensemble mean using a global error bound based on the standard deviation of the ensemble. With these regularized models, over time periods of up to 30 yr, it is possible to fit COV-OBS.x1 within one standard deviation at all times. For time windows up to 102 yr we show that our models can fit COV-OBS.x1 when adopting a time-averaged global uncertainty. Our modelling is sensitive only to magnetic structures in approximately the top 10 per cent of the liquid core, and show an increased surface area of reversed flux at depth. The diffusive models recover fundamental characteristics of field evolution including the historical westward drift, the recent acceleration of the North Magnetic Pole and reversed-flux emergence. Based on a global time-averaged residual, our diffusive models fit the evolution of the geomagnetic field comparably, and sometimes better than, frozen-flux models within short time windows.