Bayesian statisical estimation for nonlinear dynamic systems in the marine environmental sciences

Mathematical models for the marine environmental sciences embody theoretical notions of how these systems operate. Models are well established for ocean currents, and are emerging for ocean biology. These mathematical models are typically large and complex, and generally solved numerically on a computer. Technological advances have led to a measurement revolution for marine systems in the form of new sensors for physical, biological and chemical variables, as well as new observing platforms such as satellites, automated ocean observatories, and underwater autonomous vehicles. The environmental data coming from these instruments is complex. A major challenge is how to effectively use the information coming from both model predictions and observations to optimally determine the state of the ocean (a problem that has come to be known as data assimilation).This research program is concerned with applying advanced statistical methods to the data assimilation problem. Mathematical modeling and measurement technology have far outstripped the development of statistical methods for combining models and data. This proposed research program intends to address this knowledge gap through the development and application of advanced statistical methods that fuse these different sources of information. These approaches rely on computational Monte Carlo methods and Bayesian reasoning. They provide a new class of general statistical methods for addressing the data assimilation problem for marine environmental systems, and ultimately contribute towards improved marine environmental prediction.