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For oceanographic applications, probabilistic forecasts typically have todeal with i) high-dimensional complex models, and ii) very sparse spatialobservations. In search-and-rescue operations at sea, for instance, theshort-term predictions of drift trajectories are essential to efficientlydefine search areas, but in-situ buoy observations provide only very sparsepoint measurements, while the mission is ongoing. Statistically optimalforecasts, including consistent uncertainty statements, rely on Bayesianmethods for data assimilation to make the best out of both the complexmathematical modeling and the sparse spatial data. To identify suitableapproaches for data assimilation in this context, we discuss localisationstrategies and compare two state-of-the-art ensemble-based methods forapplications with spatially sparse observations. The first method is a versionof the ensemble-transform Kalman filter, where we tailor a localisation schemefor sparse point data. The second method is the implicit equal-weights particlefilter which has recently been tested for related oceanographic applications.First, we study a linear spatio-temporal model for contaminant advection anddiffusion, where the analytical Kalman filter provides a reference. Next, weconsider a simplified ocean model for sea currents, where we conduct stateestimation and predict drift. Insight is gained by comparing ensemble-basedmethods on a number of skill scores including prediction bias and accuracy,distribution coverage, rank histograms, spatial connectivity and drifttrajectory forecasts.

Comparison of Ensemble-Based Data Assimilation Methods for Sparse Oceanographic Data