講演情報
[U02-10]A Mathematical Framework for Quantifying Nonlinear Uncertainty Propagation in Eddy Identification Criteria★Invited Papers
*Charlotte Moser1、Nan Chen1、Stephen Wiggins2 (1.University of Wisconsin Madison、2.US Naval Academy)
Ocean eddies are flow structures with strong influence on global ocean dynamics. The data and models used to track eddies naturally carry uncertainty, limiting eddy diagnostic accuracy. This uncertainty is challenging to quantify as eddy diagnostics inherently contain nonlinearity that interacts with and alters the uncertainty. Here, a highly efficient mathematical framework to explore the propagation of uncertainty from the flow field to the eddy criteria is developed, enabling rigorous uncertainty assessment through closed formulae and information theory. The framework addresses challenging questions about the nonlinear uncertainty propagation from two crucial angles: i) how the uncertainty interacts with the non-linearity in the eddy diagnostic, and ii) how the uncertainty reduction from observations changes once the diagnostic is applied. The framework employs a simple flow field model that captures realistic turbulent dynamics while facilitating theoretical study. Furthermore, it leverages a non-linear, but analytically tractable, data assimilation scheme to incorporate observations into the model simulation, reducing the uncertainty. Then, the framework utilizes information theory hand in hand with data assimilation to rigorously quantify the uncertainty reduction via additional observations in both the flow field and the eddy diagnostic. To demonstrate the framework’s utility, it is applied to the widely used eddy diagnostic, the OW parameter. The framework produces closed formulae for the OW statistics, exposing their explicit connection to flow field statistics, and revealing the dominant behavior of the uncertainty as the number of observations increases. Notably, the closed formulae uncover distinct spatial patterns in the uncertainty of the flow field and the OW parameter. In fact, there is a close link between the local minima of the OW parameter expectation - corresponding to eddy centers - and the local maxima of the uncertainty. Additionally, the framework quantifies a practical information barrier in the asymptotic behavior of the uncertainty reduction in the flow field and the OW parameter.