Impacts of wave spreading and multidirectional waves on estimating Stokes drift

• Wave spreading and multidirectional wave effects are investigated in Stokes drift.
• An improved 1D spectral approximation is defined to incorporate wave spreading.
• The new approximation is used to differentiate between the aforementioned effects.
• Wave spreading and multidirectional effects are uncorrelated among data examined.
• Quantified differences are useful for reconciling 1D and 2D spectral calculations.

The Stokes drift, and its leading-order approximation, for a random sea depend upon the interaction of different wave groups and the process of wave spreading. Here Stokes drift direction and magnitude from prescribed spectra, local observational buoy data, and global model WAVEWATCH III output are used to analyze approximations of Stokes drift for directional random seas in deep water. To facilitate analysis, a new approximation is defined to incorporate the systematic effects of wave spreading. Stokes drift is typically overestimated by ignoring these effects or by ignoring directional differences in swell and wind seas. These two errors are differentiated and found to be largely uncorrelated. These errors depend strongly on depth, with deeper Stokes drift favoring narrow-banded swell and shallower Stokes drift favoring wind seas. Results are consistent among the data examined. Mean Stokes drift magnitude reductions from wave spreading and multidirectional wave effects alone are 14–20% and 7–23% respectively, giving a combined reduction of 20–40% versus unidirectional waves, depending on wave age and depth. Approximations that do not include these reductions however, will on average overestimate Stokes drift by 16–26%, 26–43%, and 45–71% respectively. In addition to magnitude, the direction of Stokes drift is also affected and multidirectional waves generate a directional veer with depth: the 30/60/90% confidence intervals are bounded (approximately) by ± 0.12/0.28/0.84 radians ( ± 7/16/48 deg) at the surface, with smaller intervals at depth. Complementary depth-integrated approximations are also investigated and directional effects are similar with depth-dependent subsurface results. Furthermore, an optimized directional spread correction for the surface is nearly identical for global simulations and a buoy located at Ocean Weather Station P (50°N 145°W), and does not require directional wave spectrum data.