  State of the art numerical models of the Geodynamo are still performed in a
parameter regime extremely remote from the values relevant to the physics of
the Earth's core. In order to establish a connection between dynamo modeling
and the geophysical motivation, {it is necessary to use} scaling laws. Such
scaling laws establish the dependence of essential quantities (such as the
magnetic field strength) on measured or controlled quantities. They allow for a
direct confrontation of advanced models with geophysical {constraints}.
  (...)
  We show that previous empirical scaling laws for the magnetic field strength
essentially reflect the statistical balance between energy production and
dissipation for saturated dynamos. Such power based scaling laws are thus
necessarily valid for any dynamo in statistical equilibrium and applicable to
any numerical model, irrespectively of the dynamo mechanism.
  We show that direct numerical fits can provide contradictory results owing to
biases in the parameters space covered in the numerics and to the role of a
priori hypothesis on the fraction of ohmic dissipation.
  We introduce predictive scaling laws, i.e. relations involving input
parameters of the governing equations only. We guide our reasoning on physical
considerations. We show that our predictive scaling laws can properly describe
the numerical database and reflect the dominant forces balance at work in these
numerical simulations. We highlight the dependence of the magnetic field
strength on the rotation rate. Finally, our results stress that available
numerical models operate in a viscous dynamical regime, which is not relevant
to the Earth's core.
