  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 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.
