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.