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

2025-09-17

AI Summary

Oceanic eddy reconstruction in aperiodic systems—such as Arctic sea-ice drifter trajectories—remains challenging due to the limitations of conventional Fourier-based data assimilation methods, which rely on periodic boundary conditions and lack locality-aware, time-adaptive modeling capability. Method: This work introduces the first physical-domain implementation of Lagrangian–Eulerian multiscale data assimilation (LEMDA), integrating a conditional Gaussian nonlinear system (CGNS) within a two-layer quasi-geostrophic model to perform multiscale assimilation directly in physical space. Evaluation employs normalized root-mean-square error (NRMSE) and pattern correlation coefficient. Contribution/Results: The posterior mean significantly improves eddy recovery accuracy—achieving high pattern correlation and low NRMSE—demonstrating the efficacy of physical-domain LEMDA. Furthermore, a neural-network-accelerated optimization pathway is proposed, enabling efficient, real-time assimilation for complex, nonstationary ocean dynamics. This establishes a novel paradigm for operational oceanographic data assimilation in aperiodic domains.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Search and Optimization: Mixed Discrete/Continuous Search
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data

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.

Problem

• Develops Lagrangian-Eulerian multiscale data assimilation in physical domain
• Replaces Fourier space to handle non-periodic systems and localized phenomena
• Uses sea ice trajectories to recover Arctic ocean eddies

Innovation

• Physical domain data assimilation replacing Fourier space
• Conditional Gaussian Nonlinear System for nonlinear solutions
• Two-layer Quasi-geostrophic model for ocean eddies