# Effects of Wave-Induced Processes in a Coupled Wave-Ocean Model on Particle Transport Simulations
## 4 Model Trajectories
### Particle Trajectories of the Albatros Drifters  
The trajectory of drifter 5 in the REF experiment deviated in a northwesterly direction. (Figure 10a) The trajectories obtained by the CPL experiments correctly reproduced the drifter direction and were in good agreement with observations. By north and northwest-erly winds on 10 June and the anticyclonic circulation [27], the CPL experiments reproduced the windage of drifter 5 well. CPL-TAUOC separation distance was on the order of the model grid resolution (Figure 6). The low _dd_ values remained until 29 June. The trajectory of WD-CPL_10 (Figure 10b) made a higher loop towards the north and northeast, deviating from the observations. By a 0.5% contribution of windage, the drifter was unrealistically transported towards the east and was beached. The trajectory of WD-CPL with 0.1% started deviating for 2.3 days after starting the simulation. WD-REF with 0.5% leeway showed a smaller separation distance (Figure 8), and the trajectory remained closer than that of WD-CPL with 0.5%. By adding 1.0% leeway, the simulated trajectories of WD-CPL and WD-REF can be considered as wrong. Skill scores and STDs for all experiments and during the deployment period of the drifters are given in Tables S1 and S2. specific objects [33], backtracking [60], larval drift [61] and marine plastics [62; 63] to the connectivity between different marine protected areas [16]. Accurate measures can potentially have a strong impact on biodiversity risk assessments (e.g., connected to marine litter or oil spills). In [16], several models of the North Sea were compared to study the variability and resulting uncertainty and differences between the models. In our study, Eulerian currents from a coupled ocean-wave model were used to perform CPL and WD-CPL experiments. In this way, additional tuning of the contributing factors of the Stokes drift by the drifter model can be excluded in CPL experiments. Our results are in line with the study of [56]. The latter concluded that implementing the Stokes drift as a simple additive component of drift velocity, parameterized in terms of wind forcing, can be inconsistent (a violation of momentum and energy conservation) if Eulerian currents were simulated without taking into account the reservoir of wave momentum and energy. Our results indicate the relevance of the role of waves for redistribution of momentum, especially in periods of changing wind direction (Figures 6-8). The Eulerian currents in most of the Lagrangian transport models, e.g., for search and rescue operations, are taken from, for example, operational model output. The wind stress is parameterized to drive the dynamics of the upper ocean directly if the wave model is not included. However, part of the wind stress is supported by the flux of momentum from wind to waves. These processes were considered in our CPL-TAUOC and CPL-TAUST experiments to simulate the Eulerian velocity needed for OpenDrift. Due to the non-linearity of wave-current interactions, the individual effect of the wave-induced coupled STCOR and TAUOC processes are not superimposed on TAUST [18]. This result shows that the Eulerian currents by the coupled run provided the best fit to the observed particle trajectories. The worsening of the Lagrangian model skill, especially at the beginning of the drifter simulation, can have an impact on applications like search and rescue, in which skilled Lagrangian transport forecasts are needed at the very beginning of the operation. In summary, the use of additional wind corrections cannot be justified in WD-CPL experiments, since neither of the additional windage correction experiments demonstrated an improvement compared with the CPL experiments. Displacements of the more offshore drifters, 5 and 6, were observed on 3-6 June [27], and the models turned out to be largely overestimated, concluding that neither simulated currents, windage fields nor Stokes drift by their Lagrangian model were able to reproduce the spatial gradients.