Error subspace data assimilation methods for ocean field estimation: Theory, validation and applications

General basic properties and heuristic characteristics of ocean measurements and models are utilized to obtain efficient assimilation schemes for real ocean field estimation. The nonlinear data assimilation methods derived are based on an evolving Error Subspace of variable size that spans and tracks the scales and processes where the dominant, most energetic, errors occur. Perceiving data assimilation as the acknowledgement of the uncertain ocean field experiments, focusing on the most energetic errors is sensible. The continuous organization of the most energetic errors also facilitates understanding.; Common data assimilation methods are intercompared and issues specific to coastal ocean assimilation addressed. A comprehensive, versatile and portable data assimilation system via Error Subspace Statistical Estimation is developed and implemented. The subspace approach is utilized to address ocean stochastic models. Relations with recent progress made in weather forecasting and turbulent studies are drawn. Model Error Optimals and Data Optimals are defined. A stochastic error model is added to the Primitive Equation model of the Harvard Ocean Prediction System. Objective analyses are employed to exemplify the sensitivity to the Error Subspace size. Efficient systems for continuous minimum error variance filtering via adaptive Error Subspace Statistical Estimation are obtained. Error Subspace hybrid smoothing schemes are also derived.; The Error Subspace approach is validated for use in three applications. Identical twin experiments consisting of nonlinear evolutions of idealized Mid-Atlantic Bight shelfbreak front simulations demonstrate the properties of the Error Subspace method in the ideal exact model situation. Quantitative intercomparisons with an Optimal Interpolation scheme are made. The adaptive assimilation system is applied in real-time to NATO naval operations in the Strait of Sicily. Real-time field and error estimates are quantitatively verified and several components of the variability in the Strait decomposed. Finally, the spreading of the Levantine Intermediate Water is investigated and the predominant dispersal mechanism hypothesized. These applications demonstrate that the developed assimilation system improves the Optimal Interpolation scheme, captures model nonlinearities, estimates the dominant uncertainty of the forecast, facilitate understanding of errors and allows assimilation in real time, adaptive filtering and parameter estimation.