Application of Quasi-Uniform B-Spline Surfaces with Different Degrees to Mesoscale Eddy Fitting

Satellite altimetry technology provides along-track sea level anomaly (SLA) data for studying mesoscale eddies. However, accurately reconstructing their spatial structures from discrete and non-uniform along-track observations remains a significant challenge. This study systematically evaluates the performance of bi-quadratic, bi-cubic, and bi-quartic quasi-uniform B-spline surface fitting methods for mesoscale eddy reconstruction in the South Indian Ocean (60°S–30°S, 75°E–105°E). By combining idealized experiments with real satellite data, a comprehensive comparison is conducted across several dimensions, including fitting accuracy, computational efficiency, parameter robustness, error distribution, and the physical plausibility of derived vorticity fields. For SLA surface fitting, all three methods achieve comparable accuracy, but the bi-quadratic B-spline demonstrates marked advantages in computational efficiency. Its single-fit time is only 53% and 27% of that of the bi-cubic and bi-quartic methods, respectively, and it shows insensitivity to node configuration, highlighting its practicality. In contrast, vorticity field inversion, which relies on the second derivative of the fitted surface, requires higher-order continuity. Only the bi-quartic B-spline, with C3 continuity, produces physically credible and smooth vorticity fields, whereas lower-degree methods result in discontinuous or non-smooth fields. Based on these findings, this study proposes an application-oriented selection principle: the bi-quadratic B-spline is recommended for efficiency-focused tasks, such as eddy detection, while the bi-quartic B-spline is necessary for dynamic analyses involving vorticity.