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Abstract
Data Assimilation (DA) methods provide a means of combining model output with observations based on their respective uncertainties. They are considered an invaluable tool in a wide variety of disciplines, particularly in hydrologic and meteorological forecasting. There is significant potential to improve existing DA methods, which have predominantly been developed in an ad-hoc manner to enhance their applicability to complex real world problems. In particular, relatively little attention has been devoted to one of the most fundamental aspects of DA: Model uncertainty quantification. This thesis aims to develop improved DA based methods for highly non-Gaussian/non-linear systems, with a particular focus on hydrologic and atmospheric systems. It also examines how DA methods can be enhanced to solve problems outside of their traditional application domain. Specifically, two overarching aims are investigated: 1) the development of DA based methods for estimating time varying model parameters, with the ultimate goal of improving hydrologic predictions in dynamic catchments; and 2) the development of objective model uncertainty quantification techniques for use in state-estimation DA. Firstly, a DA based method for sequentially estimating time varying model parameters is investigated. Two new methods for proposing prior parameter distributions are developed, which can be utilised depending on the amount of a priori information available regarding the form of temporal variations in model parameters. The methods are verified against synthetic data and applied to a number of real catchments with land use change, without relying on prior information of such changes. This approach represents a promising modelling paradigm for hydrologists faced with providing predictions in rapidly changing catchments. In addressing the second objective, two model uncertainty quantification methods are developed for DA in partially observed systems with highly non-Gaussian uncertainties. The methods proposed in this thesis address some of the major shortcomings in existing methods related to objectivity and ability to characterise non-Gaussian errors. Their efficacy is demonstrated through application to flood forecasting problems, and also for state estimation in a partially observed multi-scale atmospheric toy model. In all cases, the proposed methods are shown to provide improved forecasts and updates compared to standard approaches.