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A global optimal solution (GOS) provides surface velocities from Advanced Very High Resolution Radiometer (AVHRR) remote image sequences using bilinear interpolation algorithms. Although an accurate velocity field can be estimated by GOS from a sequence of infrared images, the field has only first-order continuity. Because an actual coastal ocean has a complex irregular coastland and some ocean studies need vorticity and divergence analysis, which must be extracted from the velocity field, the development of generic GOS algorithms with higher order continuity and smoothed cutouts around these edges is very important. This paper addresses the issues of higher order continuity and smoothed cutouts around coastland edges for using GOS to estimate surface velocities. GOS bilinear polynomials, previously applied to square tiles with first-order continuity, are replaced by surface B-spline functions. The new GOS algorithms can be applied to AVHRR images containing complicated coastal land boundaries, even clouds, to yield smooth velocity fields next to land and higher order continuity velocity fields. The velocity fields obtained through the applications of the first- and higher order GOS techniques to a sequence of two National Oceanic Atmospheric Administration AVHRR images, which were taken from the New York Bight fields, are compared with those measured with the CODAR array. The retrieved velocity fields are used directly to calculate the surface divergence and vorticity. It is found that the angular and magnitude errors of the velocity by the first- and third-order GOSs are quite close for both numerical model data and AVHRR image sequences, and the velocity field estimated by the third-order GOS is globally smoothed.