During the Lagrangian submesoscale experiment (LASER), 1,000 drifters were launched to sample the surface ocean flow in the northern Gulf of Mexico. Due to half a dozen strong winter storms, about 40% of the drifters lost their drogue. This unintended situation facilitated documentation of both near‐surface (5 cm) and deeper (60 cm) flows. These depths are relevant to transport of oil spills, as well as marine debris, such as microplastics, a rapidly growing environmental problem. Here, we improve the surface Lagrangian current prediction by combining a state‐of‐the‐art ocean forecast model with wind and wave data. The ocean surface velocities are obtained from the Navy Coordinate Ocean Model at 1‐km horizontal resolution, while the wind and wave fields are from the Unified Wave INterface Coupled Model coupled atmosphere‐wave‐ocean model. Two Lagrangian parameterizations are tested: one is based on Ekman dynamics, and the other directly on the surface winds. LASER data set is then used to assess the performance of these formulations, as a function of wind/wave conditions, as well as geographic region. It is found that incorporation of wind and wave data into the ocean circulation model can lead to major prediction improvement, by reducing the average 2‐day separation from the modeled and real LASER trajectories by a factor ranging from 1.4 to 4.9. This is a significant improvement for applications, where a rapid deployment of assets is needed, such as oil spill response, or other tracking problems.