# Effects of Wave-Induced Processes in a Coupled Wave-Ocean Model on Particle Transport Simulations
## 1 Introduction  
A rapid increase in marine litter in the ocean has recently been recognized as a serious environmental problem. The role of the physical factors contributing to it (e.g., atmosphere-ocean-wave interaction processes) has been not yet fully understood. Lagrangian analyses represent the natural approach to studying oceanic transport based on model simulations and observational data [1, 2]. The transport and accumulation of floating marine debris and the assessment of different scenarios of marine plastic distribution, along with a comprehensive synopsis of the tools currently available for tracking virtual particles. A detailed review of the Lagrangian ocean analysis, associated problems, sources of errors and validation issues was presented in [2, 3]. Still, an improved understanding of the physical processes influencing the transport of particles is required [2]. The Lagrangian simulation can be assessed by performing a time-evolving analysis of the separation distance betweenthe real track and the simulated ones. A skill score, based on the separation distance normalized by the length of the trajectory, has recently been proposed [4]. The separation distance between model simulations and observed trajectories has been estimated, showing that one day after initialization the distance was about 15-25 km, and five days later this increased to about 60-180 km. It was found that the root-mean-square error (RMSE) 13 days after the start of the integration was about 5 km [5]. A separation distance from model simulations versus observed trajectories in the first days after initialization of about 15 km was found [6]. Sea-state dependent processes affect the ocean circulation and thus also the results from Lagrangian transport models. A considerably enhanced momentum transfer from the atmosphere to the wave field is found [7] during growing sea state (young sea). Recently, a wind stress formulation depending on wind stress and wind-wave momentum released to the ocean was proposed [8]. Swell waves can even cause momentum transfer from the ocean to the atmosphere [9]. In growing sea states, waves extract momentum from the atmosphere, so that the ocean receives less momentum from the atmosphere than if waves were not considered [10]. Using stand-alone ocean or atmosphere models, the surface waves that represent the air-sea interface are not taken into account. This can cause biases in the upper ocean due to insufficient or, in some cases, too strong mixing [11], or because the momentum transfer is shifted in time and space compared to how the fluxes would behave in the presence of waves. Several parameterizations were recently proposed for momentum flux that is sea state-dependent, e.g., [12; 13]. Recently, the role of the Stokes drift and wave-induced transport of floating marine litter was studied in [14], showing that accounting for the wave-induced Eulerian-mean flow significantly alters predictions of transport of floating marine litter by waves. The skill scores between the model and observations were improved by adding the Stokes drift in [15], postulating that for Lagrangian simulations, the Stokes drift's contribution can be at the same order or even higher than the accuracy of the Eulerian circulation. However, the accuracy of Lagrangian simulations also depends on the hydrodynamic and Lagrangian model, demonstrating the need to tune Lagrangian models for the specific setup [16]. In a large and complex system such as the North Sea (Figure 1), minor perturbations may displace particles to very different drift regimes, causing strongly divergent particle trajectories [17]. Therefore, the particle distribution analysis is not intended to fully reproduce or explain the observations (the latter are extremely limited, particularly during extreme weather conditions). Instead, we aim to indicate the differences that can be due to wave-induced forcing processes.