Envisioning Data Assimilation for Adaptive Mesh Computational Models and Intermittency
Abstract
The use of adaptive meshing techniques for data assimilation (DA) presents both challenges and opportunities. The focus of the proposed research will be on the development of a flexible framework for adaptive mesh DA (AMDA) based on the combination of metric tensors associatedwith different factors. Among the factors considered will be the accuracy of ensemble solutions, the location of observations, detection and increased resolution of intermittent extreme events, tracking of coherent structures, as well as incorporating adjoint sensitivity analysis into the development ofadaptive meshes for DA.The techniques developed will be applicable adaptively in time. Many of the factors being employed (accuracy and conditioning of ensemble forecasts, observation locations, Lagrangian flow, intermittent extreme events, adjoint sensitivities, etc.) to determine enhanced meshes areoften time dependent. A primary goal is to identify and weight different factors that will be used to generate the forecast and analysis meshes in ways that enhance the DA skill. There is a tradeoff between the gains in accuracy (of both the forecasts and the analysis) and efficiency from adaptive meshing and the loss of accuracy and efficiency from interpolating between meshes. As a result, we will further develop meshes (typicallyrequiring greater computational resources) that performeffectively over larger ranges of time and/or solution behavior.A second focus of the research planned will be on intermittency. Apparently unpredictable changes in a system can occur on irregular time intervals. These changes are flips between different stable states of the system that are not triggered by internal dynamics but rather external noise.The set-up for intermittent behavior will be a stochastic differential equation in which the system shift is a noise-induced transition. The case of vanishingly small noise is well studied under the banner of Large Deviation Theory. The level of noisepresent in environmental systems while smallis likely to be of sufficient magnitude that this theory is limited in its applicability. Another issue is that slower background changes may also impact the system and its susceptibility to a rapid shift. Moreover, theresponse of the system may be to the rate at which the background is changing as opposed to the magnitude of that change.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 15, 2024
- Source ID
- N000142412198
Entities
People
- Christopher K. R. T. Jones
Organizations
- George Mason University
- Office of Naval Research
- United States Navy