Coupling hydrodynamic and wave models: first step and sensitivity experiments in the Mediterranean Sea
 947 Downloads
 3 Citations
Abstract
This work describes the first step towards a fully coupled modelling system composed of an ocean circulation and a wind wave model. Sensitivity experiments are presented for the Mediterranean Sea where the hydrodynamic model NEMO is coupled with the thirdgeneration wave model WaveWatchIII (WW3). Both models are implemented at 1/16° horizontal resolution and are forced by ECMWF 1/4° horizontal resolution atmospheric fields. The models are twoway coupled at hourly intervals exchanging the following fields: sea surface currents and temperature are transferred from NEMO to WW3 by modifying the mean momentum transfer of waves and the wind speed stability parameter, respectively. The neutral drag coefficient computed by WW3 is then passed to NEMO, which computes the surface stress. Fiveyear (2009–2013) numerical experiments were carried out in both uncoupled and coupled mode. In order to validate the modelling system, numerical results were compared with coastal and drifting buoys and remote sensing data. The results show that the coupling of currents with waves improves the representation of the wave spectrum. However, the waveinduced drag coefficient shows only minor improvements in NEMO circulation fields, such as temperature, salinity, and currents.
Keywords
Mediterranean Sea Hydrodynamics Waves Numerical modelling NEMO WaveWatch31 Introduction
Windwavecurrent coupling is of growing interest since it has long been recognized that these interactions control the momentum and energy exchange between the atmosphere and the ocean, and need to be better understood and resolved. The currents are driven by surface wind stresses that in turn are a function of the sea state. On the other hand, the sea state depends on the wind stress and the currents. These are complicated feedback mechanisms which can be modelled by coupling hydrodynamic and wave models which to date have been developed separately.
Model coupling can be achieved at various levels of complexity. A complete review of windwavecurrent interactions processes can be found in Jonsson (1990) and more recently in Cavaleri et al. (2012). The present work focuses on wave and current modifications due to interactions of waves with surface currents, and the wind speed correction due to a stability parameter that depends on airsea temperature differences (Tolman 2002), and to the surface drag coefficient for currents which takes into account the wave effects.
The difference between sea surface temperature (SST) and air temperature affects the stability of the lower atmosphere and thus the wind velocity structure. Tolman (2002) formulated a stability correction by replacing the wind speed with an effective wind speed so that the wave growth reproduces Kahma and Calkoen (1992) stable and unstable wave growth curves.
In this first step approach to couple wind waves and currents, all three abovementioned processes, consisting in feeding the wave model with sea surface temperature and surface currents computed by the hydrodynamic model and returning a neutral wind drag coefficient to the latter, were selected in order to develop the model coupling between a hydrodynamic model and a wave model forced by winds from an atmospheric analysis and forecasting model. The paper concentrates on the process of momentum exchange between wind waves and currents in the Mediterranean Sea. For a full coupling between waves and currents, the hydrodynamic equations should make use of Stokes Drift velocities, seastatedependent momentum flux, a parameterization of waveinduced vertical mixing, and include coastal radiation stresses or vortex force term in the hydrodynamic model equations (Mellor 2003, 2008, 2011; McWilliams et al. 2004; Rascle 2007; Ardhuin et al. 2008; Bennis et al. 2011; Uchiyama et al. 2010; Kumar et al. 2012; Michaud et al. 2012; Breivik et al. 2014, 2015, Alari et al. 2016, Staneva et al. 2017); however, this is out of the scope of the development of the present work. By excluding these processes, surface wave effects are not accounted in the ocean model primitive equations; moreover, breaking waves effect in enhancing turbulence is not performed nor wave absorbed (or released) stress is directly accounted.
The effect of wavedependent drag coefficient was analyzed in Mastenbroek et al. (1993) showing improvements by modelling surge heights in the North Sea when the wavedependent drag is taken into account instead of a standard Smith and Banke (1975) stress relation. Other works in the Baltic Sea (Alari et al. 2016) and the North Sea (Staneva et al. 2017) show a coupling approach previously implemented by Breivik et al. (2014, 2015) consisting in coupling the wave model to the circulation model modified in order to include the StokesCoriolis effect and both the seastatedependent momentum and energy fluxes. These works show a pronounced effect due to wave coupling on the vertical temperature distribution and on mesoscale events as well as an improved skill in the predicted sea level and currents during storm events. Moreover, in the Mediterranean basin, Lionello et al. (2003) investigated the importance to couple the wave and ocean models with an atmospheric model analyzing airsea interface fields on a short time scale range for regional meteorological prediction.
The performance of the wave model in the present work is evaluated by comparing numerical results with buoy measurements and altimeter data for satellite significant wave height, mean, and peak wave periods. The performance of the hydrodynamic model is assessed by comparing sea surface currents with coastal buoy observations, model SST with satellite estimates, and vertical temperature and salinity model profiles with ARGO float observations.
The paper is organized as follows. Section 2 presents the model system and the coupling strategy. Section 3 illustrates the numerical experiment design and setup. Section 4 shows the numerical model results and comparison with observations, and in Sect. 5, the conclusions are given.
2 The model system
The model system presented in this work is a twoway coupled hydrodynamic circulation model with a thirdgeneration spectral wind wave model as described in the following sections.
2.1 The atmospheric forcing fields
ECMWF 6hourly operational analysis fields were used to force both wave and hydrodynamic models for the 5year experimental time period 2009–2013. The ECMWF system that produced the atmospheric forcing fields is the IFS (Integrated Forecast System, http://www.ecmwf.int/en/forecasts/documentationandsupport/changesecmwfmodel) at 1/4° horizontal resolution and 91 vertical levels.
The meteorological fields of interest were as follows: meridional and zonal components of the velocity field at a 10m height, air temperature at 2 m, dew point temperature at 2 m, mean sea level atmospheric pressure, and cloud cover. All fields were linearly interpolated to the hydrodynamic and wave model time steps of 600 s.
2.2 The wave model: WaveWatchIII (WW3)
Equation 3 describes the evolution, in a slowly varying depth domain, of a 2D ocean wave spectrum where individual spectral components satisfy the linear wave theory locally.
In our application, WW3 was implemented following WAM Cycle4 model physics (Gunther et al. 1993). Wind input and dissipation terms are based on Janssen’s quasilinear theory of windwave generation (Janssen 1989, 1991): the surface waves extract momentum from the air flow and therefore the stress in the surface layer depends both on the wind speed and the waveinduced stress. The dissipation source term was based on Hasselmann’s (1974) whitecapping theory according to Komen et al. (1984). The nonlinear wavewave interaction was modelled using the discrete interaction approximation (DIA, Hasselmann et al. 1985, Hasselmann and Hasselmann 1985).
The wave model was implemented in the Mediterranean Sea (Fig. 1) considering closed boundaries in the Atlantic Sea, which is a fairly good approximation for the Mediterranean Sea. This is because the occasional propagation of Atlantic swell through the Gibraltar Straits only affects the western part of the Alboran Sea.
2.3 The hydrodynamic model: NEMO
The NEMO model version 3.4 (Nucleus for European Modelling of the Ocean, Madec 2008) was used as the hydrodynamic component of our coupled system. The NEMO code solves the primitive equations (derived assuming the hydrostatic and the incompressible approximations), and here, we used the linear free surface formulation solved by the timesplitting technique; thus, the external gravity waves are explicitly resolved. Additionally, the atmospheric pressure effect was introduced in the model dynamics (Oddo et al. (2014) describes the NEMO implementation with timesplitting and atmospheric pressure effect in the Mediterranean Sea). Figure 1 shows the bathymetry, the river positions (red circles), and the model domain, which extends into the Atlantic Ocean. Lateral boundary conditions in the Atlantic are open and nested into the monthly mean climatological fields computed from 10year daily output of the 1/4° global model (Drevillon et al. 2008); the nesting details are given in Oddo et al. (2009). Seven rivers are considered as volume inputs: Ebro, Rhone, Po, Vjose, Seman, Bojana, and Nile, and the Dardanelles Strait is closed but is considered as net volume input through a riverlike parameterization.
The NEMO configuration parameters can be found in Appendix 2. The advection scheme for active tracers, temperature and salinity, is a mixed upstream/MUSCL (Monotonic Upwind Scheme for Conservation Laws, Van Leer 1979), originally implemented by Estubier and Lévy (2000) and modified by Oddo et al. (2009). The vertical diffusion and viscosity terms are a function of the Richardson number as parameterized by Pacanowsky and Philander (1981).
The model interactively computes airsurface fluxes of momentum, mass, and heat. The bulk formulae implemented are described in Pettenuzzo et al. (2010) and are currently used in the Mediterranean operational system (Tonani et al. 2015). A detailed description of other specific features of the model implementation can be found in Oddo et al. (2009, 2014).
2.4 Model coupling
In the first part of the coupling, the effects of surface currents on waves are taken into account as specified in Eqs. 5–7.
3 Numerical experiment design and validation data sets

EXP1: WW3 uncoupled. The wave model is a standalone model that does not use sea surface currents and temperature derived from the circulation model. This means that no wavecurrent interactions (refraction of waves due to currents) take place, and no wind correction due to airsea temperature differences is included.

EXP2: NEMO uncoupled. The hydrodynamic model is uncoupled, and the turbulent drag coefficient is calculated using the Hellerman and Rosenstein (1983) formulation.

EXP3: WW3NEMO coupled. The two models are twoway coupled by hourly exchanging parameters as described in Sect. 2.4 and depicted in Fig. 2.

EXP4: WW3NEMO coupled as in EXP3 but WW3 does not receive airsea temperature difference fields from NEMO, which means that no wind correction is performed.
List of numerical experiments carried out and simulation period
Experiment  Description  Simulation period 

EXP1  WW3 standalone (not coupled with NEMO)  2009–2013 
EXP2  NEMO standalone (not coupled with WW3)  2009–2013 
EXP3  WW3 and NEMO coupled every hour as detailed in Sect. 2.4  2009–2013 
EXP4  WW3 and NEMO coupled every hour as in EXP3 but without exchanging airsea temperature difference fields  2010 
3.1 Observational data sets for validation
The first source of data consists of daily averages of in situ observations derived from a fixed buoy network (http://calval.bo.ingv.it/). Figure 3 shows the spatial buoy locations, and their name, position, and corresponding networks are listed in Table 9 (Appendix 1).
The second set of data is composed of satellite altimeterderived wave heights from OSTM/Jason2. The recommended calibrated significant wave height data (with corrections applied to the altimeter 1 Hz estimated values) were used.
The satellite sea surface temperature daily gapfree maps (L4) are used at 1/16° horizontal resolution over the Mediterranean Sea (Buongiorno Nardelli et al. 2013). These data were made available through the CMEMS (Copernicus Marine Environment Monitoring Service) catalogue (http://marine.copernicus.eu/web/69interactivecatalogue.php).
The fourth dataset is composed of vertical profiles of temperature and salinity measured by ARGO profiling floats integrated by the CMEMS In Situ Thematic Assembly Group (CMEMS INSITUTAC), quality checked, and made available through the CMEMS catalogue.
4 Results and discussion
In order to compare statistics for different experiments, bootstrap 95% confidence intervals (CI) were evaluated for the Mean, Bias, and RMSE metrics, being this approach applicable to any sample distribution.
This section is organized into three parts. The first describes the wave model comparison with buoys and altimeter data, highlighting the impact of the coupled system on waves. The second part shows the circulation model comparison with buoys, satellite, and ARGO measurements in order to assess the model performance in both uncoupled and coupled modes. The third one presents the effects of coupling on both waves and currents considering a short time scale analysis.
4.1 Impact of the coupled system on waves
Results of WW3 uncoupled (EXP1) and coupled (EXP3) experiments are compared to buoy measurements by daily averaged wave fields for the entire experimental period (2009–2013).
The comparison of significant wave heights (Fig. 4a, b) shows that there is a relatively good agreement between measurements and the model output. In particular, the coupled model significant wave heights (Fig. 4a) correlate better with in situ observations than the uncoupled model estimates (Fig. 4b). In general, the model results underestimate the data from the buoys, particularly the largest wave heights, and similar outcomes have already been highlighted by Ardhuin et al. (2007) and Korres et al. (2011). In the period considered, the maximum daily average wave height was always lower than 6 m, and 95% of wave heights came between 0.2 and 2 m for both measured and modelled data, with an average value of 0.8 m for measurements and 0.7 m for model results. These results are in agreement with other works carried out in the Mediterranean Sea for different periods and using different wave models by Cavaleri and Bertotti (2003) and Korres et al. (2011).
The comparison of mean and peak wave periods is represented in Fig. 4c, d and e, f, respectively, showing a larger scatter with respect to the significant wave height data. Coupled model values correlate slightly more with observations than the uncoupled model. As already found by Korres et al. (2011) for uncoupled model simulations, the predicted mean period is lower than the measured one and presents a lower performance compared to the significant wave height. Mean period values are included between 2 and 10 s with an average value of 4.1 s for the model and 4.3 s for the measurements. Peak period values range between 2 and 12 s and the simulated values, characterized by an average value of 5 s, underestimate the measured average value of 5.5 s.
Statistics evaluated by comparing buoy measurements and model results in terms of wave height (HS), mean period (TM), and peak period (TP) for uncoupled (EXP1) and coupled (EXP3) wave models
Metric  HS [m] EXP1  HS [m] EXP3  TM [s] EXP1  TM [s] EXP3  TP [s] EXP1  TP [s] EXP3 

Mean  0.695  0.723  4.131  4.157  5.143  5.149 
CI  +0.006 −0.006  +0.006 −0.007  +0.015 −0.014  +0.013 −0.014  +0.022 −0.022  +0.023 −0.021 
Bias  −0.152  −0.124  −0.207  −0.172  −0.454  −0.435 
CI  +0.002 −0.002  +0.002 −0.002  +0.011 −0.011  +0.011 −0.011  +0.014 −0.013  +0.013 −0.015 
RMSE  0.256  0.236  0.901  0.887  1.047  1.023 
CI  +0.004 −0.004  +0.004 −0.003  +0.009 −0.010  +0.009 −0.010  +0.018 −0.018  +0.018 −0.017 
STDN  0.896  0.931  1.38  1.38  1.15  1.14 
R  0.95  0.95  0.76  0.77  0.84  0.84 
Statistics evaluated by comparing satellite significant wave height (HS) with uncoupled model results (EXP1) for years 2010 to 2013
Uncoupled EXP1 HS [m]  Year 2010  Year2011  Year 2012  Year 2013 

Mean  1.203  1.001  1.119  1.119 
CI  +0.015 −0.014  +0.004 −0.004  +0.005 −0.005  +0.006 −0.005 
Bias  −0.213  −0.236  −0.208  −0.195 
CI  +0.007 −0.007  +0.002 −0.002  +0.002 −0.002  +0.002 −0.003 
RMSE  0.479  0.417  0.429  0.439 
CI  +0.015 −0.014  +0.005 −0.004  +0.007 −0.07  +0.018 −0.015 
STDN  0.870  0.868  0.861  0.872 
R  0.906  0.909  0.925  0.916 
Statistics evaluated by comparing satellite significant wave height (HS) with coupled model results (EXP3) for years 2010 to 2013 and coupled model results without Tolman (2002) wind correction (EXP4) for year 2010
Coupled HS [m]  EXP3  EXP4  

Year2010  Year2011  Year2012  Year2013  Year 2010  
Mean  1.304  1.047  1.166  1.143  1.271 
CI  +0.015 −0.016  +0.004 −0.004  +0.005 −0.005  +0.006 −0.006  +0.016 −0.016 
Bias  −0.112  −0.190  −0.162  −0.170  −0.253 
CI  +0.007 −0.007  +0.002 −0.002  +0.002 −0.002  +0.002 −0.003  +0.007 −0.007 
RMSE  0.439  0.390  0.405  0.389  0.454 
CI  +0.018 −0.015  +0.004 −0.004  +0.009 −0.007  +0.004 −0.005  +0.014 −0.013 
STDN  0.941  0.901  0.902  0.888  0.856 
R  0.908  0.91  0.925  0.918  0.934 
Figure 7a–h shows how the model results fit the altimeter data from 2010 to 2013. For all the years, the coupled model performs better than the uncoupled WW3. The main statistics for EXP1 and EXP3 are listed in Tables 3 and 4, respectively, and show that the coupled model decreases the Bias by about 25%.
The impact of wavecurrent interaction without considering wind speed correction was also evaluated by performing a 1year (2010) integration of the system where the Tolman (2002) correction in Eq. 9 was not used (EXP4). Thus, only the exchange of currents and wind drag between NEMO to WW3 was kept. Model results were compared to satellite altimeter significant wave height and are summarized in Table 4 (last column) showing that this simple currentwave interaction coupling slightly improves the RMSE but worsens the Bias. This result is in agreement with previous studies by Galanis et al. (2012) probably due to the still coarse resolution of the models and the winds used in both studies. In a semienclosed basin like the Mediterranean Sea, where the windsea strongly determines the shape of the wave spectrum, better improvements in the wave field predictions could be achieved by using higher resolution winds. This is evidenced by Ardhuin et al. (2007) who demonstrate that different forcing winds produce larger wave differences than using different wave models.
4.2 Impact of the coupled system on the hydrodynamic fields
In order to evaluate the impact of the coupled system on the circulation model, we compared model surface currents with coastal buoy measurements; the sea surface temperature was validated using satellite data, and vertical profiles of temperature and salinity were compared to ARGO floating measurements.
Statistics evaluated by comparing current amplitude measurements from buoy and model results in the uncoupled (EXP2) and coupled (EXP3) circulation model
Metric  Surface currents EXP2  Surface currents EXP3 

Mean [m/s]  0.130 ± 0.002  0.133 ± 0.002 
Bias [m/s]  −0.046 ± 0.003  −0.042 ± 0.003 
RMSE [m/s]  0.160 ± 0.003  0.156 ± 0.003 
STDN  0.87  0.88 
Buoy no.  Mean [m/s]  Bias [m/s]  RMSE [m/s]  

EXP2  EXP3  EXP2  EXP3  EXP2  EXP3  
Zonal velocity  
2  0.017  0.020  −0.135  −0.132  0.294  0.293 
CI  +0.010 −0.011  +0.010 −0.010  +0.014 −0.014  +0.014 −0.013  +0.009 −0.010  +0.010 −0.010 
3  −0.043  −0.034  −0.095  −0.086  0.228  0.224 
CI  +0.004 −0.005  +0.005 −0.005  +0.010 −0.010  +0.010 −0.010  +0.012 −0.012  +0.010 −0.011 
4  0.034  −0.051  0.006  0.023  0.126  0.126 
CI  +0.004 −0.003  +0.004 −0.04  +0.006 −0.006  +0.006 −0.005  +0.005 −0.005  +0.004 −0.004 
6  0.013  0.017  0.059  0.064  0.124  0.133 
CI  +0.003 −0.003  +0.003 −0.003  +0.006 −0.005  +0.006 −0.005  +0.005 −0.005  +0.005 −0.05 
7  0.09  0.00  0.020  0.011  0.091  0.086 
CI  +0.003 −0.003  +0.003 −0.003  +0.004 −0.004  +0.004 −0.004  +0.003 −0.003  +0.003 −0.003 
21  0.001  −0.017  0.043  0.026  0.106  0.096 
CI  +0.010 −0.011  +0.009 −0.009  +0.016 −0.015  +0.015 −0.015  +0.012 −0.012  +0.012 −0.012 
22  −0.055  −0.054  0.005  0.004  0.120  0.117 
CI  +0.004 −0.005  +0.004 −0.004  +0.007 −0.007  +0.007 −0.007  +0.006 −0.006  +0.007 −0.006 
25  −0.045  −0.038  0.017  0.024  0.197  0.203 
CI  +0.0052 −0.0052  +0.005 −0.005  +0.011 −0.011  +0.012 −0.012  +0.010 −0.011  +0.011 −0.011 
28  −0.019  −0.012  −0.002  0.004  0.170  0.163 
CI  +0.005 −0.005  +0.005 −0.005  +0.010 −0.010  +0.010 −0.010  +0.011 −0.010  +0.011 −0.011 
Buoy no.  Mean [m/s]  Bias [m/s]  RMSE [m/s]  

EXP2  EXP3  EXP2  EXP3  EXP2  EXP3  
Meridional velocity  
2  0.020  0.043  −0.014  0.009  0.143  0.155 
CI  +0.005 −0.005  +0.005 −0.005  +0.007 −0.007  +0.008 −0.007  +0.005 −0.006  +0.006 −0.006 
3  0.054  0.063  −0.009  0.001  0.189  0.203 
CI  +0.006 −0.005  +0.005 −0.005  +0.009 −0.009  +0.009 −0.009  +0.007 −0.007  +0.007 −0.007 
4  0.100  0.131  −0.06  0.025  0.161  0.171 
CI  +0.006 −0.006  +0.007 −0.007  +0.008 −0.007  +0.008 −0.008  +0.006 −0.006  +0.008 −0.007 
6  −0.055  −0.043  0.077  0.090  0.174  0.178 
CI  +0.006 −0.006  +0.006 −0.006  +0.007 −0.008  +0.008 −0.008  +0.006 −0.005  +0.005 −0.005 
7  0.018  0.012  0.026  0.020  0.095  0.085 
CI  +0.004 −0.004  +0.003 −0.003  +0.004 −0.004  +0.004 −0.004  +0.004 −0.003  +0.003 −0.003 
21  −0.023  −0.025  −0.023  −0.025  0.099  0.096 
CI  +0.009 −0.009  +0.008 −0.009  +0.015 −0.015  +0.015 −0.015  +0.012 −0.012  +0.012 −0.012 
22  −0.053  −0.055  0.001  0.003  0.117  0.111 
CI  +0.004 −0.005  +0.005 −0.005  +0.007 −0.007  +0.007 −0.007  +0.006 −0.006  +0.006 −0.006 
25  0.016  0.010  0.012  0.006  0.174  0.175 
CI  +0.004 −0.004  +0.004 −0.004  +0.011 −0.010  +0.011 −0.010  +0.009 −0.011  +0.010 −0.010 
28  −0.007  −0.010  0.017  0.014  0.158  0.158 
CI  +0.004 −0.004  +0.004 −0.004  +0.010 −0.009  +0.010 −0.010  +0.011 −0.011  +0.010 −0.010 
Statistics evaluated by comparing temperature and salinity vertical profile measurements and model results from uncoupled (EXP2) and coupled (EXP3) circulation models
Metric  Temperature EXP2 [^{o}C]  Temperature EXP3 [^{o}C]  Salinity EXP2 [PSU]  Salinity EXP3 [PSU] 

Mean  15.872  15.873  38.423  38.436 
CI  +0.576 −0.550  +0.568 −0.505  +0.068 −0.062  +0.066 −0.064 
Bias  −0.051  −0.051  −0.149  −0.136 
CI  +0.013 −0.012  +0.017 −0.016  +0.018 −0.019  +0.017 −0.018 
RMSE  0.069  0.079  0.165  0.152 
CI  +0.010 −0.011  +0.014 −0.016  +0.016 −0.016  +0.013 −0.017 
R  1  1  0.988  0.992 
We conclude that the effects of the different waveinduced turbulent wind drag coefficients have a small, if nonexistent, impact on the quality of the simulated current, temperature, and salinity fields when considering space or time averaged fields. Possible impacts on restricted area at short time scale are presented in the following section.
4.3 Wavecurrent coupling at short time scale
The modelled significant wave height, surface temperature, and currents have been compared to in situ observations at the Tarragona and Dragonera buoys (buoy nos. 6 and 4 in Table 9 and Fig. 3) for 1 week: from the 24^{th} December 2010 (2 days before the selected event) to the 30^{th} December 2010 (4 days after the event).
The comparison of the modelled surface temperature against daily observations at the Tarragona buoy is presented in Fig. 11c where the coupled model shows a good agreement with the measurements with respect to the uncoupled one, which overestimates the buoy surface temperature. Figure 11d illustrates the surface temperature at the Dragonera buoy showing that the uncoupled model underestimates the observations, while the coupled one provides more reliable predictions of the measurements especially in correspondence of the storm event.
Figure 11e, f shows that the coupled model overestimates the measured surface currents at the Tarragona and Dragonera buoys, but it better represents the evolution of the measured velocity after the extreme event with respect to the uncoupled model, which is less affected by the increased wind speed.
The short time scale analysis for the selected event demonstrates that both wave and hydrodynamic fields are affected by the coupling, resulting in an enhanced skill, particularly of the modelled significant wave heights and, to a lesser extent, of the surface temperature and current fields.
5 Conclusions
A coupled wavecurrent numerical model system was developed and validated against observations for a 5year period between 2009 and 2013. The coupled model was implemented in the Mediterranean Sea using NEMO and WW3 model codes. Fields were exchanged hourly between the two components while atmospheric forcing fields from ECMWF were interpolated to the single model time steps.
The coupling consists of feeding the wave model with sea surface temperature and surface currents computed by the hydrodynamic model and returning a neutral wind drag coefficient to the latter, which then computes a turbulent wind drag coefficient used in the momentum surface boundary condition.
One major conclusion drawn from the various results presented in the work is that the wave model is impacted by this kind of wind wave–hydrodynamic model coupling, while the hydrodynamics changes are negligible at large space and time scales becoming more evident when considering the coupling impacts during storm events.
Both the uncoupled and coupled wave models perform well in reproducing in situ as well as satellite measured wave parameters, and the coupled system improves the significant wave height simulation values with respect to the uncoupled system. The results also highlight that the enhanced performance of the coupled model is mainly achieved by better representing effect of airsea temperature differences impacting the wave growth, while surface currents lead to only a minor improvement. This might be due to the low resolution of the hydrodynamic and wave models and in particular to the scarce resolution of the coastal areas geometry and bathymetry.
The waveinduced turbulent wind drag correction and the traditional Hellerman and Rosenstein (1983) formulations differ significantly only in the coastal areas and even there only by 10–20%. The impact of the coupling on the simulated hydrodynamic fields is thus much lower, and most of the time is negligible. Evidence of the effect of wave dependent surface stress on the computation of coastal currents and temperature is shown on a short time scale analysis, while, on the typical time scale of ocean circulation, the main effect is expected because of a wavedependent ocean mixing, which is not included in this study.
We probably need to wait for a stronger coupling between waves and currents before an improvement in the hydrodynamics will be evident. Future work in fact will consider the wave dissipated energy (as provided by the wave model) in the vertical mixing of the water column and will add the Stokes drift velocity in the momentum and tracer equations.
The present work suggests that a twoway coupled model could improve the prediction of wave characteristics, in particular the significant wave height, for both open ocean and coastal areas.
Notes
Acknowledgements
This work was supported by the CMEMS MedMFC (Copernicus Marine Environment Monitoring Service–Mediterranean Marine Forecasting Centre), Mercator Ocean Service Contract and RITMARE Flagship Project (National Research Programmes), Italian Ministry of University and Research contract.
We would like to thank Dr. Enrique AlvarezFanijul and Dr. Marta de Alfonso (Puertos de l’Estado, ES), Dr. Joaquin Tintoré (CSIC, ES), Mr. Leonidas Perivoliotis (HCMR, GR), and Dr. Gabriele Nardone (ISPRA, IT).
References
 Alari V, Staneva J, Breivik Ø, Bidlot JR, Mogensen K, Janssen P (2016) Surface wave effects on water temperature in the Baltic Sea: simulations with the coupled NEMOWAM model. Ocean Dyn 66(8):917–930CrossRefGoogle Scholar
 Ardhuin F, Rascle N, Belibassakis KA (2008) Explicit waveaveraged primitive equations using a generalized Lagrangian mean. Ocean Model 20:235–264CrossRefGoogle Scholar
 Ardhuin F, Bertotti L, Bidlot JR, Cavaleri L, Filipetto V, Lefevre JM, Wittmann P (2007) Comparison of wind and wave measurements and models in the western Mediterranean Sea. Ocean Eng 34:526–541CrossRefGoogle Scholar
 Bennis A, Ardhuin F, Dumas F (2011) On the coupling of wave and threedimensional circulation models: Choice of theoretical framework, practical implementation and adiabatic tests. Ocean Model 40:260–277CrossRefGoogle Scholar
 Breivik Ø, Mogensen K, Bidlot JR, Balmaseda MA, Janssen PA (2015) Surface wave effects in the NEMO ocean model: forced and coupled experiments. J Geophys Res, Oceans 120:2973–2992CrossRefGoogle Scholar
 Breivik Ø, Janssen P, Bidlot J (2014) Approximate stokes drift profiles in deep water. J Phys Oceanogr 44(9):2433–2445. doi: 10.1175/JPOD140020.1 CrossRefGoogle Scholar
 Brodeau L (2007) Contribution à l’Amélioration de la Fonction de Forcage des Modéles de Circulation Générale Océanique. Université JosephFourier, DissertationGoogle Scholar
 Buongiorno Nardelli B, Tronconi C, Pisano A, Santoleri R (2013) High and ultrahigh resolution processing of satellite sea surface temperature data over southern European seas in the framework of MyOcean project. Remote Sens Environ 129:1–16CrossRefGoogle Scholar
 Cavaleri L, Bertotti L (2003) The characteristics of wind and wave fields modelled with different resolutions. Q J R Meteorol Soc 129:1647–1662CrossRefGoogle Scholar
 Cavaleri L, FoxKemper B, Hemer M (2012) Wind waves in the coupled climate system. Bull Amer Meteor Soc 93:1651–1661CrossRefGoogle Scholar
 Drevillon M, BourdalleBadie R, Derval C et al (2008) The GODAE/MercatorOcean global ocean forecasting system: results, applications and prospects. J Operational Oceanography 1:51–57CrossRefGoogle Scholar
 Estubier A, Levy M (2000) Quel schema numerique pour le transport d’organismes biologiques par la circulation oceanique. Note Techniques du Pole de modelisation, Institut PierreSimon Laplace, p 81Google Scholar
 Galanis G, Hayes D, Zodiatis G, Chu PC, Kuo YH, Kallos G (2012) Wave height characteristics in the Mediterranean Sea by means of numerical modeling, satellite data, statistical and geometrical techniques. Mar Geophys Res 33:1–15CrossRefGoogle Scholar
 Gunther H., Hasselmann H, Janssen PAEM (1993) The WAM model cycle 4. DKRZ report n.4Google Scholar
 Hasselmann K (1974) On the characterization of ocean waves due to white capping. BoundLayer Meteorol 6:107–127CrossRefGoogle Scholar
 Hasselmann S, Hasselmann K (1985) Computations and parameterizations of the nonlinear energy transfer in a gravity wave spectrum. Part I: a new method for efficient computations of the exact nonlinear transfer integral. J Phys Oceanogr 15:13691377Google Scholar
 Hasselmann S, Hasselmann K, Allender JH, Barnett TP (1985) Computations and parameterizations of the nonlinear energy transfer in a gravity wave spectrum. Part II: parameterizations of the nonlinear energy transfer for application in wave models. J Phys Oceanogr 15:1378–1391CrossRefGoogle Scholar
 Hellerman S, Rosenstein M (1983) Normal monthly wind stress over the world ocean with error estimates. J Phys Oceanogr 13:93–104CrossRefGoogle Scholar
 Janssen PAEM (1991) Quasilinear theory of wind wave generation applied to wave forecasting. J Phys Oceanogr 21:1631–1642CrossRefGoogle Scholar
 Janssen PAEM (1989) Wave induced stress and the drag of air flow over sea wave. J Phys Oceanogr 19:745–754CrossRefGoogle Scholar
 Jonsson IG (1990) Wavecurrent interactions. In: Le Mehaute B, Hanes DM (eds) The sea. Ocean Engineering Science, Wiley, New York, pp 65–120Google Scholar
 Kahma KK, Calkoen CJ (1992) Reconciling discrepancies in the observed growth of windgenerated waves. J Phys Oceanogr 22:1389–1405CrossRefGoogle Scholar
 Komen GJ, Hasselmann S, Hasselmann K (1984) On the existence of a fully developed windsea spectrum. J Phys Oceanogr 14:1271–1285CrossRefGoogle Scholar
 Korres G, Papadopoulos A, Katsafados P, Ballas D, Perivoliotis L, Nittis K (2011) A 2year intercomparison of the WAMCYCLE4 and the WAVEWATCHIII wave models implemented within the Mediterranean Sea. Mediterr Mar Sci 12(1):129–152CrossRefGoogle Scholar
 Kumar N, Voulgaris G, Warner JC, Olabarriet M (2012) Implementation of the vortex force formalism in the coupled oceanatmospherewavesediment transport (COAWST) modeling system for inner shelf and surf zone applications. Ocean Model 47:65–95CrossRefGoogle Scholar
 Large W, Yeager S (2004) Diurnal to decadal global forcing for ocean and seaice models: the data sets and flux climatologies. CGD NCAR Technical Note: TN460+STR, pp 111Google Scholar
 Large W (2006) Surface fluxes for practitioners of global ocean data assimilation. In: Chassignet E and Verron J (ed) Ocean weather and forecasting, Springer, pp 229270Google Scholar
 Lionello P, Martucci G, Zampieri M (2003) Implementation of a coupled atmospherewaveocean model in the Mediterranean Sea: sensitivity of the short time scale evolution to the airsea coupling mechanisms. Global Atmos Ocean Syst 9(1–2):65–95CrossRefGoogle Scholar
 Madec G (2008) NEMO ocean engine. Note du Pole de modélisation, Institut PierreSimon Laplace (IPSL), France, Note 27 ISSN 12881619, pp 209Google Scholar
 Madec G, Delecluse P, Imbard M, Levy C (1998) OPA version 8.1 ocean general circulation model reference manual. Technical Report, LODYC/IPSL, Note 11, pp 91Google Scholar
 Mastenbroek C, Burgers GJH, Janssen PAEM (1993) The dynamical coupling of a wave model and a storm surge model through the atmospheric boundary layer. J Phys Oceanogr 23:1856–1866CrossRefGoogle Scholar
 McWilliams JC, Restrepo JM, Lane EM (2004) An asymptotic theory for the interaction of waves and currents in coastal waters. J Fluid Mech 511:135–178CrossRefGoogle Scholar
 Mellor GL (2011) Wave radiation stress. Ocean Dyn. doi: 10.1007/s1023601003592
 Mellor GL (2008) The depthdependent current and wave interaction equations: a revision. J Phys Oceanogr 38:2587–2596CrossRefGoogle Scholar
 Mellor GL (2003) The threedimensional current and surface wave equations. J Phys Oceanogr 33:1978–1989CrossRefGoogle Scholar
 Michaud H, Marsaleix P, Leredde Y, Estournel C, Bourrin F, Lyard F, Mayet C, Ardhuin F (2012) Three dimensional modelling of waveinduced current from the surf zone to the inner shelf. Ocean Sci 8:657–681CrossRefGoogle Scholar
 Miles JW (1957) On the generation of surface waves by shear flows. J Fluid Mech 3:185–204CrossRefGoogle Scholar
 Oddo P, Adani M, Pinardi N, Fratianni C, Tonani M, Pettenuzzo D (2009) A nested AtlanticMediterranean Sea general circulation model for operational forecasting. Ocean Sci 5:461–447CrossRefGoogle Scholar
 Oddo P, Bonaduce A, Pinardi N, Guarnieri A (2014) Sensitivity of the Mediterranean sea level to atmospheric pressure and free surface elevation numerical formulation in NEMO. Geosci Model Dev 7:3001–3015CrossRefGoogle Scholar
 Pacanowsky RC, Philander SGH (1981) Parameterization of vertical mixing in numerical models of tropical oceans. J Phys Oceanogr 11:1443–1451CrossRefGoogle Scholar
 Pettenuzzo D, Large WG, Pinardi N (2010) On the corrections of ERA40 surface flux products consistent with the Mediterranean heat and water budgets and the connection between basin surface total heat flux and NAO. J Geophys Res 115:C06022. doi: 10.1029/2009JC005631 CrossRefGoogle Scholar
 Phillips OM (1977) The dynamics of the upper ocean. Cambridge Univ Press, p 336Google Scholar
 Rascle N (2007) Impact of waves on the ocean circulation (impact des vagues sur la circulation océanique). Université de Bretagne Occidentale, Dissertation http://tel.archivesouvertes.fr/tel00182250 Google Scholar
 Smith SD, Banke EG (1975) Variation of the sea surface drag coefficient with wind speed. Quart J Roy Meteorol Soc 101:665–673CrossRefGoogle Scholar
 Staneva J, Alari V, Breivik Ø, Bidlot JR, Mogensen K (2017) Effects of waveinduced forcing on a circulation model of the North Sea. Ocean Dyn 67(1):81–101CrossRefGoogle Scholar
 Tolman HL (2009) User manual and system documentation of WAVEWATCH III™ version 3.14. NOAA/NWS/NCEP/MMAB Tech. Note 276, pp 194Google Scholar
 Tolman HL (2002) Validation of WAVEWATCH III version 1.15 for a global domain. NOAA/NWS/NCEP/OMB Technical Note 213, pp 33Google Scholar
 Tonani M, Balmaseda M, Bertino L, Blockley E, BrassingtonG DF, Drillet Y, Hogan P, Kuragano T, Lee T, Mehra A, Paranathara F, Tanajura CAS, Wang H (2015) Status and future of global and regional ocean prediction systems. J Operational Oceanography 8:201–220. doi: 10.1080/1755876X.2015.1049892 CrossRefGoogle Scholar
 Uchiyama Y, McWilliams JC, Shchepetkin AF (2010) Wavecurrent interaction in an oceanic circulation model with a vortexforce formalism: Application to the surf zone. Ocean Model 34:16–35CrossRefGoogle Scholar
 Van Leer B (1979) Towards the ultimate conservative difference scheme. V A Second Order Sequel to Godunov’s Method J Comp Phys 32:101–136Google Scholar
 Wu J (1982) Windstress coefficients over sea surface from breeze to hurricane. J Geophys Res 87:9704–9706CrossRefGoogle Scholar
 Wu J (1980) Windstress coefficients over sea surface near neutral conditions: a revisit. J Phys Oceanogr 10:727–740CrossRefGoogle Scholar
Copyright information
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.