Abstract
Drifter observations can provide high-resolution surface velocity data (Lagrangian data), commonly used to reconstruct Eulerian velocity fields. Gaussian Process Regression (GPR), a machine learning method based on Gaussian probability distributions, has been widely applied for velocity field interpolation due to its ability to provide interpolation error estimates and handle separations between particles. However, its evaluation has primarily relied on cross-validation, which approximates temporal and spatial correlations but does not fully capture their dependencies, limiting the comprehensiveness of performance assessment. Moreover, GPR has not been rigorously tested on model datasets with reference velocity fields to evaluate its overall accuracy and the reliability of the error estimate. This study addresses these gaps by (1) assessing the accuracy of GPR-reconstructed fields and their error estimates, (2) evaluating GPR performance across temporal and spatial dimensions, and (3) analyzing the relationship between training data density and prediction accuracy. Using six metrics, GPR predictions are evaluated on a double-gyre model and a Navy Coastal Ocean Model (NCOM). Results show that GPR achieves high accuracy, contingent on sampling density and velocity magnitude, while validating the posterior covariance matrix as a reliable error predictor. These findings provide critical insights into the strengths and limitations of GPR in oceanographic applications.