An Efficient and Statistically Accurate Lagrangian Data Assimilation Algorithm with Applications to Discrete Element Sea Ice Models
Abstract
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient datadriven statistically accurate reducedorder modeling algorithm is developed that significantly accelerates the computational efficiency of Lagrangian data assimilation. The algorithm starts with a Fourier transform of the highdimensional flow field, which is followed by an effective model reduction that retains only a small subset of the Fourier coefficients corresponding to the energetic modes. Then a linear stochastic model is developed to approximate the nonlinear dynamics of each Fourier coefficient. Effective additive and multiplicative noise processes are incorporated to characterize the modes that exhibit Gaussian and nonGaussian statistics, respectively. All the parameters in the reduced order system, including the multiplicative noise coefficients, are determined systematically via closed analytic formulae. These linear stochastic models succeed in forecasting the uncertainty and facilitate an extremely rapid data assimilation scheme. The new Lagrangian data assimilation is then applied to observations of sea ice floe trajectories that are driven by atmospheric winds and turbulent ocean currents. It is shown that observing only about $30$ noninteracting floes in a $200$km$\times200$km domain is sufficient to recover the key multiscale features of the ocean currents. The additional observations of the floe angular displacements are found to be suitable supplements to the centerofmass positions for improving the data assimilation skill. In addition, the observed large and small floes are more useful in recovering the large and smallscale features of the ocean, respectively. The Fourier domain data assimilation also succeeds in recovering the ocean features in the areas where cloud cover obscures the observations.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2108.00855
 Bibcode:
 2021arXiv210800855C
 Keywords:

 Physics  Atmospheric and Oceanic Physics;
 Mathematics  Numerical Analysis;
 Physics  Fluid Dynamics