  In this paper, a rapid approximation method is introduced to estimate the sea
surface velocity field based on scattered measurements. The method uses a
simplified two-dimensional flow model as a surrogate model, which mimics the
real submesoscale flow. The proposed approach treats the interpolation of the
flow velocities as an optimization problem, aiming to fit the flow model to the
scattered measurements. To ensure consistency between the simulated velocity
field and the measured values, the boundary conditions in the numerical
simulations are adjusted during the optimization process. Additionally, the
relevance of quantity and quality of the scattered measurements is assessed,
emphasizing the importance of the measurement locations within the domain as
well as explaining how these measurements contribute to the accuracy and
reliability of the sea surface velocity field approximation. The proposed
methodology has been successfully tested in both synthetic and real-world
scenarios, leveraging measurements obtained from Global Positioning System
(GPS) drifters and high-frequency (HF) radar systems. The adaptability of this
approach for different domains, measurement types, and conditions implies that
it is suitable for real-world submesoscale scenarios where only an
approximation of the sea surface velocity field is sufficient.
