ACCURACY AND STABILITY OF FILTERS FOR DATA ASSIMILATION
Abstract
The overarching goal of this work is to develop theoretical foundations for the study and development of algorithms to estimate properties of the atmosphere and the ocean. Detailed knowledge of the ocean state in specific regions is of paramount importance in many areas of science and technology, and in particular for a range of applications of interest to the US Navy. An example concerns the study of sea ice in the Arctics, a subject of fundamental importance in the study of climate change, and also of commercial importance in the determination of shipping routes. Geophysicists and oceanographers use a variety of instruments to aquire data pertinent to addressing these questions.Eulerian instruments include satellite observers which make measurements of the Earth~s properties such as velocity, temperature or height of an ice sheet. In contrast Lagrangian instruments are wholly, or partially, advected by the ocean flow and give implicit information about its Eulerian properties. For example the study of sea ice is being revolutionized by the use gliders: instruments which combine pre-set mission plans with oceanographic drift to locate themselves, potentially optimally, for the acquisition of data. Data assimilation provides a methodology for blending the data obtained by these instruments with our knowledge ofthe physics of the oceans, and of objects transported within them. In mathematical terms this corresponds to merging observed data with imperfect differential equation models of the physics which produce the data. Whilst there are numerous innovative algorithms for carrying this out, those employed in practical oceanography do not come equipped with an underpinning theory which justifies their use, in terms of robustness and accuracy of predictions. The purposeof this work is to provide a theory of robustness and accuracy, and to use it to develop more effective algorithms.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 04, 2017
- Source ID
- N000141712079
Entities
People
- Andrew M. Stuart
Organizations
- California Institute of Technology
- Office of Naval Research
- United States Navy