1 Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark4 Department of Applied Mathematics and Computer Science, Technical University of Denmark
This thesis consists of six research papers published or submitted for publication in the period 2006-2009 together with a summary report. The main topics of this thesis are nonlinear data assimilation techniques and estimation in dynamical models. The focus has been on the nonlinear filtering techniques for large scale geophysical numerical models and making them feasible to work with in the data assimilation framework. The filtering techniques investigated are all Monte Carlo simulation based. Some very nice features that can be exploited in the Monte Carlo based data assimilation framework from a computational point of view, e.g. low storage cost, no linearizations of the numerical models, etc. However, this also gives rise to many unforeseen difficulties, e.g. the curse of dimensionality, huge computational costs, etc. The challenge faced in this thesis was finding filters that could handle the nonlinearities encountered in data assimilation and at the same time are robust and reliable enough given the constraints and difficulties that can arise. These problems were addressed in the papers A, E and D. The other topic of this thesis is estimation in dynamical geophysical numerical models. The challenge of estimating model parameters for well establish geophysical dynamical systems is that these models are not formulated in a way that incorporates the necessary stochastic assumptions that make estimation possible in a maximum likelihood sense. The maximum likelihood approach is selected due to its unique performance in data rich situations. The estimations are often based on output from the model and the raw observations which lead to suboptimal estimates. The challenge is to give a meaningful description of the model errors through diffusion processes that can be identified and incorporated into the existing maximum likelihood framework. These issues are discussed in paper B. The third part of the thesis falls a bit out of the above context is work published in papers C, F. In the first paper, a simple data assimilation scheme was investigated to examine the potential benefits of incorporating a data assimilation concept into an atmospheric chemical transport model. This paper deals with the results and conclusions obtained through some of the first experiments with the Optimal Interpolation filter in a geophysical model. The second paper F, deals with the construction of a finite element solver for the Fokker-Planck equation on a 2 dimensional flexible mesh system. The report details the construction of the finite element solver and investigates the potential benefits of a parallel FORTRAN implementation through a series of experiments.