Related papers: An Efficient and Statistically Accurate Lagrangian…
Modeling and understanding sea ice dynamics in marginal ice zones relies on acquiring Lagrangian ice floe measurements. However, optical satellite images are susceptible to atmospheric noise, leading to gaps in the retrieved time series of…
Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact…
Sea ice dynamics are crucial to the global climate system, yet traditional continuum (e.g., viscous-plastic) models often fail to represent the discrete floe interactions that dominate in the marginal ice zone. Lagrangian discrete element…
We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional…
The discrete element method (DEM) is providing a new modeling approach for describing sea ice dynamics. It exploits particle-based methods to characterize the physical quantities of each sea ice floe along its trajectory under Lagrangian…
State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…
Lagrangian trajectories are widely used as observations for recovering the underlying flow field via Lagrangian data assimilation (DA). However, the strong nonlinearity in the observational process and the high dimensionality of the…
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…
Reconstructing ocean dynamics from observational data is fundamentally limited by the sparse, irregular, and Lagrangian nature of spatial sampling, particularly in subsurface and remote regions. This sparsity poses significant challenges…
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data…
Lagrangian data assimilation aims to recover hidden Eulerian flow fields from sparse, indirect observations of moving tracers. This problem is challenging because tracer trajectories are nonlinearly coupled with the underlying flow, making…
Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it…
This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
We propose a defiltering method of turbulent flow fields for Lagrangian particle tracking using machine learning techniques. Numerical simulation of Lagrangian particle tracking is commonly used in various fields. In general, practical…
Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past…
This study presents a novel approach to applying data assimilation techniques for particle-based simulations using the Ensemble Kalman Filter. While data assimilation methods have been effectively applied to Eulerian simulations, their…
Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is…
Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…
This work is about low dimensional reduction for a slow-fast data assimilation system with non-Gaussian $\alpha-$stable L\'evy noise via stochastic averaging. When the observations are only available for slow components, we show that the…