This paper describes the implementation of a coupling between a three-dimensional ocean
general circulation model (NEMO) and a wave model (WW3) to represent
the interactions of upper-oceanic flow dynamics with surface waves. The focus is on the impact
of such coupling on upper-ocean properties (temperature and currents) and mixed layer depth (MLD)
at global eddying scales. A generic coupling interface has been developed, and the NEMO
governing equations and boundary conditions have been adapted to include wave-induced terms following
the approach of

An accurate representation of ocean surface waves has long been recognized as essential
for a wide range of applications from marine meteorology to ocean and coastal
engineering. Waves also play an important role in the short-term forecasting of extratropical
and tropical cyclones by regulating sea surface roughness

Besides affecting the air–sea fluxes, waves define the mixing in the oceanic surface boundary
layer (OSBL) via breaking and Langmuir turbulence. For example,

Most previous studies of the impact of ocean–wave interactions at the global scale have
used an offline one-way coupling and included only parts of the wave-induced terms in
the oceanic model governing equations

To go into the details of those different steps, the paper is organized as follows. The modifications
brought to the oceanic model primitive equations, their boundary conditions, and the subgrid-scale
physics to account for wave–ocean interactions are described in Sect.

In order to set the necessary notations, we start by introducing the classical primitive equations
solved by the NEMO ocean model. Note that between the two possible options to
formulate the momentum equations, namely the so-called “vector-invariant” and “flux” forms,
we present the first one here, which will be used for the numerical simulations in Sect.

Here,

Asymptotic expansions of the wave effects based on Eulerian velocities

In the notations of

In the notations of

Reconstructing the full Stokes drift profile

As illustrated in Fig.

Under the assumption of horizontal homogeneity generally retained in general circulation models,
the contribution from Stokes drift to the turbulent kinetic energy (TKE) prognostic equation arises
from the vortex force vertical term

In addition to the modification of the shear production term in the TKE equation, the wave will affect the
surface boundary condition for

The length scales

Langmuir mixing is parameterized following the approach of

Annual average of the surface Stokes drift module

While the

Our coupled model is based on the NEMO oceanic model, the WW3 wave model, and the OASIS library for data exchange and synchronization between the two components.

NEMO is a state-of-the-art primitive-equation, split–explicit, free-surface oceanic model
whose equations are formulated both in the vector-invariant and flux forms (see Eq.

The NEMO ocean model has been coupled to the WW3 wave model.
In numerical models, waves are generally described using several phase and amplitude parameters.
We provide only the details sufficient to understand the coupling of waves with the oceanic
model here, and an exhaustive description of WW3 is given by

The practical coupling between NEMO and WW3 has been implemented using
the OASIS-MCT

Surface waves affect the momentum exchange between the ocean and the atmosphere in two different ways.
First, the modification of surface roughness acts on the incoming atmospheric momentum flux

The 10 m wind

In our coupling strategy two different values of the atmospheric wind stress and the wave-to-ocean wind stress
are computed with two different bulk formulations. This strategy is not fully satisfactory since it breaks the momentum conservation.
However, it was necessary in practice since the WW3 results were very sensitive to the bulk formulation, and at the same
time it was not conceivable to use the WW3 bulk formulation to force the ocean model because the latter ignores the
effect of stratification in the atmospheric surface layer. Previous implementations in NEMO

In Table

Variables exchanged between NEMO (O) and WW3 (W) via the OASIS-MCT coupler.
The

The wave hindcasts presented here are all based on the WW3 model in its version 6.02
configured with a single grid at

For the oceanic component, we use a global ORCA025 configuration at a

The atmospheric fields used to force both ocean and wave models are based on the ECMWF (European Centre for
Medium-Range Weather Forecasts) ERA-Interim reanalysis

Sensitivity experiments have been conducted to check the proper implementation of various
components of the present coupled modeling system. For the sake of clarity, our developments are split
into four components: (i) the modification of the wind stress by waves through the Charnock
parameter and the inclusion of wave-supported stress, (ii) the modifications of the NEMO
governing equations through the Stokes–Coriolis, vortex force, and wave-induced surface pressure terms,
(iii) the addition of a Langmuir turbulence parameterization, and (iv) the
modifications to the TKE scheme. As summarized in Table

In

Various model configurations analyzed in Sect.

The wave distribution being inhomogeneous on the globe, it is expected that with the wave-modified wind stress
parameterization the stress should follow the wave patterns more closely.
In Fig.

To isolate the effect of the Charnock parameter we compare the results obtained
in the No_CPL and WS_CPL experiments. Those two experiments
show relatively similar sea surface temperature patterns, meaning that the modification
of the wind stress

Figure

Wind stress difference

As described in Sect.

Seasonal difference of 1 m depth turbulent kinetic energy (m

It shows an almost homogeneous increase in the TKE (up to more than 100 %) in the extratropical areas.
While low seasonal variability in the extratropical areas is visible in Fig.

Spatially averaged turbulent kinetic energy (m

In this section, we evaluate the wave effect on vertical mixing using the mixed layer depth (MLD)
as a relevant metric.
Figure

To assess whether the overall deepening of the mixed layer is realistic, we make a comparison with available observations. Available observations for 2014 were extracted following an updated dataset from

Spatially averaged MLD for

From January to July, the deepening of the MLD induced by the wave coupling significantly reduces the bias
between the model and ARGO data. From July to December, results in the coupled case show an overestimation
of MLDs, which were already too deep in the uncoupled case, thereby increasing the bias between the data and model.
Since mesoscale activity makes direct comparisons to data unreliable for such a short period of time,
we compare the normalized distribution of MLD between the different simulations and available ARGO data.
Results are presented in Fig.

Mixed layer depth probability density function for

To better understand which components of the wave–ocean coupling are responsible for this improvement,
the summer PDF in the Southern Hemisphere has been computed for each of the experiments described
in Table

Mixed layer depth probability density function in the Southern Hemisphere during summer months. The details of each experiment can be found in Table

Since the near-surface mixing is strengthened by the coupling, we can expect an impact on sea surface temperature (SST).
Figure

Time series of the spatially averaged sea surface temperature (

To better characterize the wave impact on the SST, we show in Fig.

As already noticed by

Hovmöller diagram of the longitudinally averaged sea surface temperature (

Time series of the spatially averaged surface kinetic energy (m

The last aspect of our solutions we would like to evaluate is the impact of the surface waves
on surface currents and kinetic energy (KE). To do so, we show in Fig.

Zonally averaged zonal

In this paper we have described the implementation of an online coupling between the oceanic
model NEMO and the wave model WW3. The impact of such coupling
on the model solutions has been assessed from the oceanic point of view for a global configuration.
In particular, the following steps to set up the coupled model have been discussed in detail:
(i) the inclusion of all wave-induced terms in NEMO primitive equations, only
neglecting the terms relevant for the surf zone, which is outside the scope of the NEMO community;
(ii) modification of the subgrid-scale vertical physics (including the bulk formulation) to
include wave effects and a parameterization of Langmuir turbulence; (iii) development of a
coupling interface based on the OASIS-MCT software for the exchange of data between
the two models; and (iv) tests of our developments on a realistic global configuration
at

Following

The development of a coupling infrastructure based on OASIS-MCT has several advantages
as it allows for an efficient data exchange (including the treatment of nonconformities between the
computational grids) but also for versatility in the inclusion of a wave model in existing ocean–atmosphere
or ocean-only models. At a practical level, the OASIS interface we have implemented in
NEMO is similar to other interfaces (e.g., toward atmospheric models) existing in the code,
which is important for maintenance and for further developments. It paves the way for a seamless and
more systematic inclusion of the coupling with waves for NEMO users. Unlike most previous studies of wave–ocean coupling using NEMO, we have shown that satisfactory
results can be obtained from the TKE vertical turbulent closure scheme without activating the ad hoc
parameterization for the mixing induced by near-inertial waves, surface waves, and swell (known as the ETAU parameterization).
This parameterization that allows users to empirically propagate the surface TKE at depth using a prescribed shape function
is a pragmatic way to cure the shallow mixed layer depths in the Southern Ocean found in simulations ignoring wave effects.
Previous studies of wave–ocean coupling by

The numerical experiments based on the ORCA25 configuration discussed in Sect.

Since the magnitude of the vertical mixing is increased by the coupling with waves we expect an impact on
sea surface temperature and currents. Indeed, the summer deepening of the mixed layer in the Southern
Hemisphere leads to colder sea surface temperatures, resulting in better agreement with the OSTIA SST analysis.
More generally, although the global SST biases are not totally compensated for, they tend to be reduced when
considering the effect of waves (see Sect.

In this Appendix we describe the necessary changes when a flux formulation for advective terms
in the momentum equations is preferred to the vector-invariant form presented in Eqs. (

Here,

Single-column experiments based on

Solution obtained for the

The changes to the NEMO code have been made on the standard NEMO
code (nemo_v3_6_STABLE). The code can be downloaded
from the NEMO website (

XC prepared and carried out all the numerical experiments, investigated the results, and wrote the paper with the help of all the coauthors. GM, FL, RB, and XC made the changes in the NEMO code to include the wave–ocean interactions. GS helped to prepare the necessary datasets for the numerical experiments and analyze the model outputs. FA and JR helped to investigate the results and to formalize the necessary wave-induced terms in both the primitive equations and the TKE closure.

The authors declare that they have no conflict of interest.

We thank George Nurser and Oyvind Breivik, whose efforts helped to improve earlier versions of this paper, as well as Qiang Wang and Svenja Langer.
We also thank Knut Klingbeil, Patrick Marchesiello, and Patrick Marsaleix for useful discussions.
Xavier Couvelard, Florian Lemarié, and Jean-Luc Redelsperger
acknowledge support by Mercator-Ocean and the Copernicus Marine
Environment Monitoring Service (CMEMS) through contract
22-GLO-HR – Lot 2 (High-resolution ocean, waves, atmosphere interaction).
Numerical simulations were performed on Ifremer HPC facilities DATARMOR of
“P

This paper was edited by Qiang Wang and reviewed by A. J. George Nurser and Oyvind Breivik.

^{®}Development Group: User manual and system documentation of WAVEWATCH III

^{®}version 5.16, Tech. Note 329, NOAA/NWS/NCEP/MMAB, College Park, MD, USA, 326 pp. + Appendices, 2016.