Lagrangian-Eulerian Multiscale Data Assimilation in Physical Domain based on Conditional Gaussian Nonlinear System

Abstract: This research aims to further investigate the process of Lagrangian-Eulerian Multiscale Data Assimilation (LEMDA) by replacing the Fourier space with the physical domain. Such change in the perspective of domain introduces the advantages of being able to deal in non-periodic system and more intuitive representation of localised phenomena or time-dependent problems. The context of the domain for this paper was set as sea ice floe trajectories to recover the ocean eddies in the Arctic regions, which led the model to be derived from two-layer Quasi geostrophic (QG) model. The numerical solution to this model utilises the Conditional Gaussian Nonlinear System (CGNS) to accommodate the inherent non-linearity in analytical and continuous manner. The normalised root mean square error (RMSE) and pattern correlation (Corr) are used to evaluate the performance of the posterior mean of the model. The results corroborate the effectiveness of exploiting the two-layer QG model in physical domain. Nonetheless, the paper still discusses opportunities of improvement, such as deploying neural network (NN) to accelerate the recovery of local particle of Lagrangian DA for the fine scale.