Parametric wave spectrum models for prediction of Stokes drift profiles

Abstract

In this report, 15 variants of nine parametric models for non-directional ocean wave spectra are reviewed. They are compared against observation-based spectra created by taking spectra measured by moored buoys, binning by wind speed, and averaging. Surface Stokes drift (SSD) and Stokes drift profiles are computed using the model and observation-based spectra, and these are compared. This 'parametric wave model' strategy for estimating Stokes drift is contrasted with other methods for estimating Stokes drift, such as using spectra from a dynamical wave model. Advantages and shortcomings are reviewed. One practical application for Stokes drift profiles is in ocean circulation modeling. Here, the information is used to compute wave-enhanced mixing ('Langmuir turbulence'). We present examples of such cases, in the context of a global ocean model, tested in two modes (coupled and uncoupled) and with two types of forcing (Stokes drift approximated using wind speed and Stokes drift computed using a full ocean wave model). A more comprehensive review of the uncoupled tests with the full ocean wave model can be found in a separate report, Fan et al. (2026). We evaluate simple Stokes drift models that use wind speed and/or wind stress but do not require a dynamical wave model. We find some are sufficiently accurate for routine prediction of SSD. A subset of these models can also predict Stokes drift profiles (via parametric spectra), but none are accurate in this role. The SSD values computed from a very large drifting buoy dataset are compared with the total drift calculated using positional change of the same buoys. The SSD is roughly 25% of the total drift, consistent with expectations based on 'rules of thumb'. However, the scatter is large, indicating that such rules have predictive skill only in the mean sense.