Stochastic Models of Geodynamo Simulations

The Earth's magnetic field originates primarily in the interior of the planet, and represents one of the few signals through which processes of the deep Earth are expressed at the surface. Observations and paleomagnetic measurements of the geomagnetic field therefore provide a valuable means of investigating the state and dynamics of the Earth's core. Fluctuations in the geomagnetic field occur on a wide range of timescales; however, the inaccessibility of the deep Earth means that these fluctuations are poorly understood. To investigate how external magnetic field variability relates to processes in the core, recent studies have constructed stochastic models from direct numerical simulations of the geodynamo. If these stochastic models reflect the underlying dynamics, then they may be used to characterize the paleomagnetic record and investigate the state of the Earth's core. In this thesis, I use geodynamo simulations in conjunction with stochastic models to investigate the expression of internal core processes on external field fluctuations. I examine how changes in the style and vigor of convection are reflected in stochastic models of axial dipole field variability. I find that the magnitude of variability is linked to dipole field generation, whereas the average regression to the mean is associated with turbulently enhanced magnetic diffusion. I also construct a stochastic model from a reversing geodynamo simulation, and find that stochastic models can approximately reproduce the statistics of polarity reversals. Finally, I develop a set of statistical techniques to fit stochastic processes to irregularly sampled time-series data, which are common in paleomagnetic measurements. The overall goal is to investigate the use of stochastic models as a means to relate external magnetic field variability to internal mechanisms in planetary dynamos