Extracting scaling laws from numerical dynamo models

Earth's magnetic field is generated by processes in the electrically conducting, liquid outer core, subsumed under the term 'geodynamo'. In the last decades, great effort has been put into the numerical simulation of core dynamics following from the magnetohydrodynamic equations. However, the numerical simulations are far from Earth's core in terms of several control parameters. Different scaling analyses found simple scaling laws for quantities like heat transport, flow velocity, magnetic field strength and magnetic dissipation time. We use an extensive data set of 116 numerical dynamo models compiled by Christensen and co-workers to analyse these scalings from a rigorous model selection point of view. Our method of choice is leave-one-out cross-validation which rates models according to their predictive abilities. In contrast to earlier results, we find that diffusive processes are not negligible for the flow velocity and magnetic field strength in the numerical dynamos. Also the scaling of the magnetic dissipation time turns out to be more complex than previously suggested. Assuming that the processes relevant in the numerical models are the same as in Earth's core, we use this scaling to estimate an Ohmic dissipation of 3-8 TW for the core. This appears to be consistent with recent high core mantle boundary heat flux scenarios.