Bridging Gaps in the Climate Observation Network: A Physics-Based Nonlinear Dynamical Interpolation of Lagrangian Ice Floe Measurements via Data-Driven Stochastic Models

Modeling and understanding sea ice dynamics in marginal ice zones rely on measurements of sea ice. Lagrangian observations of ice floes provide insight into the dynamics of sea ice, the ocean, and the atmosphere. However, optical satellite images are susceptible to atmospheric noise, leading to gaps in the retrieved time series of floe positions. This paper presents an efficient and statistically accurate nonlinear dynamical interpolation framework for recovering missing floe observations. It exploits a balanced physics-based and data-driven construction to address the challenges posed by the high-dimensional and nonlinear nature of the coupled atmosphere-ice-ocean system, where effective reduced-order stochastic models, nonlinear data assimilation, and simultaneous parameter estimation are systematically integrated. The new method succeeds in recovering the locations, curvatures, angular displacements, and the associated strong non-Gaussian distributions of the missing floes in the Beaufort Sea. It also accurately estimates floe thickness and recovers the unobserved underlying ocean field with an appropriate uncertainty quantification, advancing our understanding of Arctic climate. Plain Language Summary Tracking individual ice floes is a unique measurement of areas of the Arctic where the ice cover interacts with the open ocean. Unfortunately, optical satellite images of these areas are frequently obscured by clouds, leading to missing observations of the ice floes. Traditional methods of filling in these gaps in the data set have issues. Linear interpolation, which averages between available observations to fill in missing ones, fails to recover the curvature of the floes. Dynamical interpolation methods, which take into account the physical properties of the ice floes, are very computationally expensive. This paper presents a nonlinear dynamical interpolation framework for recovering missing floe observations, which is both computationally efficient and statistically accurate. The framework incorporates a model of the atmosphere, ocean, and sea ice and systematically develops data-driven reduced-order stochastic models, which significantly accelerate the dynamical interpolation while retaining accuracy. In addition, the framework estimates key physical parameters, such the floe thickness. This new method succeeds in recovering the locations, curvatures, angular displacements, and strong non-Gaussian statistics of the missing floes in a data set of ice floes in the Beaufort Sea. These results can provide complete data sets that advance our understanding of Arctic climate.