Temporal Cross-Covariance Lagrangian Data Assimilation for Drifter Observations with Long Observation Intervals

Drifter displacements are commonly converted into interval-mean velocity observations for Eulerian data assimilation (EUDA), but this temporal compression can lose information about flow evolution when observations are widely separated in time. We propose temporal cross-covariance Lagrangian data assimilation (Tc-LaDA), which represents velocity states at multiple times within an observation interval and couples terminal-position innovations with intermediate-time velocity states through ensemble-estimated temporal cross-covariances. Tc-LaDA requires neither explicit tangent-linear nor adjoint models, reducing model-specific implementation requirements. Identical-twin double-gyre experiments show that Tc-LaDA generally yields lower velocity-vector RMSE and mean angular error than EUDA at 2-, 5-, and 10-day intervals, whereas EUDA remains competitive at the 1-day interval and performs better in some dynamical regimes depending on the verification metric. Ablation experiments indicate that within the tested cases, off-diagonal temporal cross-covariances provide additional benefits beyond the multi-time control-vector formulation. These results demonstrate the potential of Tc-LaDA for assimilating sparsely sampled drifter positions.