Data assimilation, as presented in this thesis, is the statistical merging of sparse observational data with computational models so as to optimally improve the probabilistic description of the field of interest, thereby reducing uncertainties. The centerpiece of this thesis is the introduction of a novel such scheme that overcomes prior shortcomings observed within the community. Adopting techniques prevalent in Machine Learning and Pattern Recognition, and building on the foundations of classical assimilation schemes, we introduce the GMM-DO filter: Data Assimilation with Gaussian mixture models using the Dynamically Orthogonal field equations.

We combine the use of Gaussian mixture models, the EM algorithm and the Bayesian Information Criterion to accurately approximate distributions based on Monte Carlo data in a framework that allows for efficient Bayesian inference. We give detailed descriptions of each of these techniques, supporting their application by recent literature. One novelty of the GMM-DO filter lies in coupling these concepts with an efficient representation of the evolving probabilistic description of the uncertain dynamical field: the Dynamically Orthogonal field equations. By limiting our attention to a dominant evolving stochastic subspace of the total state space, we bridge an important gap previously identified in the literature caused by the dimensionality of the state space.

We successfully apply the GMM-DO filter to two test cases: (1) the Double Well Diffusion Experiment and (2) the Sudden Expansion fluid flow. With the former, we prove the validity of utilizing Gaussian mixture models, the EM algorithm and the Bayesian Information Criterion in a dynamical systems setting. With the application of the GMM-DO filter to the two-dimensional Sudden Expansion fluid flow, we further show its applicability to realistic test cases of non-trivial dimensionality. The GMM-DO filter is shown to consistently capture and retain the far-from-Gaussian statistics that arise, both prior and posterior to the assimilation of data, resulting in its superior performance over contemporary filters. We present the GMM-DO filter as an efficient, data-driven assimilation scheme, focused on a dominant evolving stochastic subspace of the total state space, that respects nonlinear dynamics and captures non-Gaussian statistics, obviating the use of heuristic arguments.

Professor Allan R. Robinson was one of the founding fathers of geophysical fluid dynamics. His research interests and seminal contributions have encompassed the dynamics of rotating and stratified fluids, boundary-layer flows, thermocline dynamics, the dynamics and modeling of mesoscale ocean currents, and the influence of physical processes on ocean biology. He is recognized as one of the pioneers and leading experts in modern ocean prediction, and contributed significantly to the techniques for the assimilation of data into ocean forecasting models. In the late 1950s and 1960s, Prof. Robinson’s research focused on fundamental geophysical fluid dynamics, including major contributions to thermocline theory, the wind-driven ocean circulation, coastally trapped waves, inertial currents and boundary layers. In the early 1970s, Prof. Robinson initiated investigations on realistic flow fields focusing in particular on mesoscale dynamics and forecasting, with contributions to western boundary currents, mesoscale eddies and baroclinic instabilities. He pioneered “ocean weather forecasting science” at the beginning of the 1980s, especially the development of conceptual models for the assimilation of both in situ and satellite data, specializing in the 1990s in the coupling between the deep sea and the coastal ocean. Focusing on mesoscale dynamics and coastal interactions, he also contributed to the development of new coupled physical-biological-acoustical and optical models, and he developed theories on the effects of oceanic motions on biological dynamics. Professor Robinson was also the Founding Editor of Dynamics of Atmospheres and Oceans.

If you are interested by our group and its research, check with us from time to time as opportunities often arise. Contact us if you are interested.

A comprehensive data set from the ocean and atmosphere was obtained just north of the Monterey Bay as part of the Monterey Bay 2006 (MB06) field experiment. The wind stress, heat fluxes, and sea surface temperature were sampled by the Naval Postgraduate School’s Twin Otter research aircraft. In situ data were collected using ships, moorings, gliders and AUVs. Four data-assimilating numerical models were additionally run, including the Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS) model for the atmosphere and the Harvard Ocean Prediction System (HOPS), the Regional Ocean Modeling System (ROMS), and the Navy Coastal Ocean Model (NCOM) for the ocean. The scientific focus of the Adaptive Sampling and Prediction Experiment (ASAP) was on the upwelling/relaxation cycle and the resulting three-dimensional coastal circulation near a coastal promontory, in this case Point Ano Nuevo, CA. The emphasis of this study is on the circulation over the continental shelf as estimated from the wind forcing, two ADCP moorings, and model outputs. The wind stress during August 2006 consisted of 3-10 day upwelling favorable events separated by brief 1-3 day relaxations. During the first two weeks there was some correlation between local winds and currents and the three models’ capability to reproduce the events. During the last two weeks, largely equatorward surface wind stress forced the sea surface and barotropic poleward flow occurred over the shelf, reducing model skill at predicting the circulation. The poleward flow was apparently remotely forced by mesoscale eddies and alongshore pressure gradients, which were not well simulated by the models. The small, high-resolution model domains were highly reliant on correct open boundary conditions to drive these larger-scale poleward flows. Multiply-nested models were no more effective than well-initialized local models in this respect.

Over the past decade, the feature-oriented regional modeling methodology has been developed and applied in several ocean domains, including the western North Atlantic and tropical North Atlantic. This methodology is model-independent and can be utilized with or without satellite and/or in situ observations. Here we develop new feature-oriented models for the eastern North Pacific from 36 to 48? – essentially, most of the regional eastern boundary current. This is the first time feature-modeling has been applied to a complex eastern boundary current system. As a prerequisite to feature modeling, prevalent features that comprise the multiscale and complex circulation in the California Current system (CCS) are first overviewed. This description is based on contemporary understanding of the features and their dominant space and time scales of variability. A synergistic configuration of circulation features interacting with one another on multiple and sometimes overlapping space and time scales as a meander-eddy-upwelling system is presented. The second step is to define the feature-oriented regional modeling system (FORMS). The major multiscale circulation features include the mean flow and southeastward meandering jet(s) of the California Current (CC), the poleward flowing California Undercurrent (CUC), and six upwelling regions along the coastline. Next, the typical synoptic width, location, vertical extent, and core characteristics of these features and their dominant scales of variability are identified from past observational, theoretical and modeling studies. The parameterized features are then melded with the climatology, in situ and remotely sensed data, as available. The methodology is exemplified here for initialization of primitiveequation models. Dynamical simulations are run as nowcasts and short-term (4-6 weeks) forecasts using these feature models (FM) as initial fields and the Princeton Ocean Model (POM) for dynamics. The set of simulations over a 40-day period illustrate the applicability of FORMS to a transient eastern boundary current region such as the CCS. Comparisons are made with simulations initialized from climatology only. The FORMS approach increases skill in several factors, including the: (i) maintenance of the low-salinity pool in the core of the CC; (ii) representation of eddy activity inshore of the coastal transition zone; (iii) realistic eddy kinetic energy evolution; (iv) subsurface (intermediate depth) mesoscale feature evolution; and (v) deep poleward flow evolution.