Optimal Model State Correction That Preserves Feature Information

Monday, November 18, 2013 - 3:30pm - 3:50pm
Lind 305
W. Steven Rosenthal (University of Arizona)
Data assimilation algorithms predict the true model state by minimizing uncertainty due to errors from multiple sources, typically between forecast models and physical measurements of the state variables. The accuracy of state predictions is affected by how model error is parameterized, and taking care to preserve model physics in statistical estimators can improve performance. A popular assimilation framework in geoscience applications is the Kalman filter, which is a weighted average that can blur important features such as fronts and extrema. These optimal estimates predict features with reduced intensity and obscured locality; moreover, the statistics of the estimator describe the intensity of feature information, but not its position. This may be detrimental to understanding the trajectories of large scale features. One possible remedy is parameterizing model error in terms of positional shifts of coherent model features over time. Physical constraints can be built into the prediction of the most likely coordinate system supporting the true state, so that its uncertainty can be reduced with much less impact on the intensity and geometry of dominant features. A modified extended Kalman filter is developed to track Lagrangian and Eulerian solutions to a vorticity advection model. A basis for canonical transformations ensures the area of each solution contour is preserved throughout assimilation, and a Tikhonov regularization is proposed to facilitate the change of measure of model state uncertainty into the canonical basis. Passive tracers are considered for an observing system as an indirect measurement of vorticity, and due to their availability and recent attention in ocean transport research. Twin experiments show that this assimilation methodology successfully tracks a simulated truth in the presence of noisy perturbations to the coordinate system and tracers.

This is joint work with Juan Restrepo and Shankar Venkataramani (Univ. of Ariz.), and Arthur Mariano (Univ. of Miami, RSMAS).