New Approaches to Data Assimilation and Transport Processes as Hybrid of Eulerian and Lagrangian Methods.

摘要

Long Term Goal. My long term goal is to make substantial contributions to enhancement of forecast skills concerning the oceans and atmosphere, by deepening our knowledge for the nature of predictability. I place my emphasis on transition mechanism between dynamical regimes of planetary flows and coherent structures from both Eulerian and Lagrangian points of view. OBJECTIVES. I wish to develop theoretical frameworks for enhancement of predictability based on dynamical systems theory. To help enhance predictability of sudden and severe events, I wish to investigate transition mechanisms between dynamical regimes. I also wish to throw a bridge between Eulerian and Lagrangian viewpoints and explore impact of severe events on large-scale transport in planetary flows. Knowledge obtained by these predictability studies will lead to a design of comprehensive ensemble forecast systems and data-adaptive observing systems. APPROACH. To achieve my goals, I plan to develop new theories and improve already existing methodologies so that they can be combined systematically. I start from assessing and extending individual elements of the theoretical framework, and develop new theories to fill the gaps between them as necessary. My approach involves: identification and detection of the predictability elements, Eulerian and Lagrangian descriptions of the probability density function evolution, treatment of nonlinearity as well as additive and multiplicative stochasity in data assimilation systems. To improve forecast skills for severe and sudden events, I investigate role played by stochastic noises. Severe events can be viewed as rare extreme bursts and therefore may be related to stochastic noises whose probability distribution has heavy tail. I construct a new innovative methodology for data assimilation systems subject to dynamical and observational noises with heavy-tail distributions.