Geomagnetic data assimilation using ensemble methods to estimate forecast error covariance

Data assimilation is the methodology to assimilate observational data with numerical models for better estimation of the true physical states. This research focuses on application of ensemble estimation of error covariance to assimilate surface geomagnetic data into a numerical geodynamo model, aiming at better understanding the dynamical processes in the Earth's core, and predicting geomagnetic secular variation on decadal time scales and longer.; Geomagnetic data assimilation faces problems associated with sparsity of the observations and heavy computation. Surface geomagnetic observation history is very short compared to typical time scales of the core dynamics, and only a small subset of the state variables are observable. It is important therefore to understand whether such sparse observation could impose a sufficiently strong constraint to make the numerical model output closer to the truth. Since, in the ensemble method of data assimilation, large ensembles of experiments need to be carried out with time-dependent covariance to obtain optimal and statistically significant forecast results, the computing load will be at least two orders of magnitude (102) more than that for regular numerical dynamo simulation. Therefore selection of a cost-effective algorithm is necessary for a working geomagnetic data assimilation framework. This research directly address these issues.; This research can be divided into two parts: (i) Demonstrating a working ensemble estimated multivariate error covariance with a simplified magnetohydrodynamics (MHD) system (to get the first-hand knowledge necessary for the full geodynamo system), and (ii) assimilating synthetic data to the full geodynamo model through a series of Observing System Simulation Experiments (OSSE's). In particular, through this research, we wish to understand how the full dynamo state (from numerical model) is affected (or corrected) by limited surface observations, and whether a fixed (in time) covariance could be sufficient to bring forecast closer to the truth. The latter is in particular important for geomagnetic data assimilation: the computational needs could be reduced by one order of magnitude (101), if it is sufficient.; Research results from the current work suggest that (i) sparse observation could produce a significant constraint on the numerical model to make the forecast closer to the true physical states; (ii) observed physical variables correlate strongly with unobservable fields in the dynamo process, and implementation of the cross-correlation could improve the assimilation system; (iii) dynamo solutions can converge to the surface observations in a very short time period (compared to the magnetic free-decay time), but the convergence of the dynamo solutions in the deep interior requires much longer time periods.