It is commonly accepted that there is a need for a better understanding of the factors that contribute to air–sea interactions and their feedbacks. In this context it is important to develop advanced numerical prediction systems that treat the atmosphere and the ocean as a unified system. The realistic description and understanding of the exchange processes near the ocean surface requires knowledge of the sea state and its evolution. This can be achieved by considering the sea surface and the atmosphere as a continuously cross-talking dynamic system. Following and adapting concepts already developed and implemented in large-scale numerical weather models and in hurricane simulations, this study aims to present the effort towards developing a new, high-resolution, two-way fully coupled atmosphere–ocean wave model in order to support both operational and research activities. A specific issue that is emphasized is the determination and parameterization of the air–sea momentum fluxes in conditions of extremely high and time-varying winds. Software considerations, data exchange as well as computational and scientific performance of the coupled system, the so-called WEW (worketa-wam), are also discussed. In a case study of a high-impact weather and sea-state event, the wind–wave parameterization scheme reduces the resulted wind speed and the significant wave height as a response to the increased aerodynamic drag over rough sea surfaces. Overall, WEW offers a more realistic representation of the momentum exchanges in the ocean wind–wave system and includes the effects of the resolved wave spectrum on the drag coefficient and its feedback on the momentum flux.
There is a need for a better understanding of the factors that contribute to air–sea interaction mechanisms, and for the development of corresponding advanced prediction systems that treat the atmosphere and the sea as a unified system. The lack of consistent skill in present forecasting systems may be partially attributed to inadequate surface and boundary-layer formulations, and the lack of full coupling to a dynamic ocean (Chen et al., 2007). Sea waves play a key role in the exchange of momentum, heat, and turbulent kinetic energy at the air–sea interface. Wind waves, while being generated by the wind, extract energy and momentum from the atmosphere and therefore the drag that is felt by the atmosphere over the oceans becomes sea-state dependent. Furthermore, ocean waves affect the mixing of heat and momentum in the upper ocean layers.
For a better description and understanding of the exchange processes near the ocean surface, an accurate forecast of the evolution of the sea state requires considering the coupled sea surface and atmosphere as a continuously cross-talking system. Generally, at shorter and even more at longer scales, reliable results can be obtained by considering the fluid layer surrounding Earth as a single system. This means to simulate the atmosphere and the ocean as a single fully coupled system and to construct multi-model, multi-scale integrated systems (Liu et al., 2011).
The development of fully coupled simulation systems between atmosphere and
ocean is the
Coupled atmosphere–ocean wave systems generally exchange near-surface wind velocity from the atmosphere to the surface wave and exchange friction velocity from the wave to the atmosphere. The modeling of the wave field allows for the introduction of a sea surface roughness feedback on the momentum flux (Lionello et al., 2003). Primarily, the change of the intensity of a storm or a cyclone due to the wave and the drag coefficient variability, under strong wind conditions is a critical field of study. More specifically, the hurricane force winds increase the drag coefficient magnitude of the sea surface that leads to a decrease of the wind speed and a change in the wind direction. Generally, the feedbacks ultimately create non-linear interactions between different components and make it difficult to assess the full impact on each specific model (Warner et al., 2010).
Various numerical experiments for 10 hurricane case studies in the western
Atlantic Ocean during 1998–2003 were performed with an atmosphere–wave model
(Moon et al., 2004), in which the drag coefficient used to approach the sea
surface friction at different wave evolution stages was based on the
relation proposed by Charnock (1955). As a result, in hurricane force wind
conditions (above 33 ms
Following the abovementioned research, a number of centers and institutes worldwide have employed coupled systems for their upgraded operational activities. The European Centre for Medium-Range Weather Forecasts (ECMWF) is the pioneer in the development and implementation of coupling systems. ECMWF developed a coupled atmospheric–ocean wave model in order to be able to have two-way interaction, based on the quasi-linear theory of Janssen (1989, 1991). The ocean wave model of ECMWF (ECMWF WAM (wave model) or ECWAM) is fully coupled to the integrated forecasting system (IFS), which is the operational global meteorological forecasting model of the ECMWF (IFS Documentation, 2013; Diamantakis and Flemming, 2014). The ECWAM model software has been developed over a period of 10 years (1992 to 2002) for operationally predicting over the whole globe (Janssen, 2004). The ECWAM code was originally written for global-scale applications; however, it was extended to also run on smaller domains and in shallower water.
The United States Geological Survey (USGS) operates the coupled ocean–atmosphere–wave–sediment transport (COAWST) modeling system, which is integrated by the model coupling toolkit to exchange data fields between the ocean model ROMS (regional ocean modeling system), the atmosphere model WRF (weather research and forecasting model), the wave model SWAN (simulating waves nearshore), and the sediment capabilities developed as part of the Community Sediment Transport Modeling Project (Warner et al., 2010). The Earth system model (CNRM-CM5, Centre National de Recherches M'etéorologiques Coupled Global Climate Model version 5) running operationally at Meteo-France consists of several existing models designed independently and coupled through the OASIS software (Redler et al., 2010). It includes the ARPEGE (Action de Recherche Petite Echelle Grande Echelle) model for the atmosphere, the NEMO (Nucleus for European Modelling of the Ocean) model for the ocean circulation, the GELATO (Global Experimental Leads and ice for ATmosphere and Ocean) model for sea-ice, the SURFEX (Surface Externalisée) model for land and the ocean–atmospheric fluxes, and the TRIP (total runoff integrating pathways) model to simulate river routing and water discharge from rivers to the ocean (Voldoire et al., 2012).
In a recent study three physical processes related to ocean surface waves, namely, the surface stress, the turbulent kinetic energy flux from breaking waves, and the Stokes–Coriolis force are incorporated in a general circulation ocean model (Breivik et al., 2015). Experiments are done with the NEMO model in ocean-only (forced) mode and coupled to the ECMWF atmospheric and wave models. Using ocean-only integrations and experiments with a coupled system consisting of the atmospheric model IFS, the wave model ECWAM, and NEMO, they demonstrated that the impact of the wave effects is particularly noticeable in the extratropics. Of the three processes, the modification of the sea-state-dependent turbulent kinetic energy has the largest impact.
In this context, this paper describes the strategy and approach adopted to develop a new, advanced, fully coupled atmosphere–ocean wave model for supporting the research and operational activities of the Hellenic Centre for Marine Research (HCMR) in the framework of the European Union (EU) funded MyWave project. A specific issue that is emphasized is the determination, parameterization, and the sensitivity of air–sea momentum fluxes in a case study involving extremely high and time-varying winds.
The coupled system consists of two components: the atmospheric and the ocean wave models of the POSEIDON system. The atmospheric component is based on the Workstation Eta non-hydrostatic limited area model (Papadopoulos et al., 2002; Janjic, 2001; Nickovic et al., 2001; Mesinger et al., 1988). The ocean wave component is based on the fourth generation OpenMP (OMP) version of the WAM model (Monbaliu et al., 2000; Korres et al., 2011) and the resulting name of the coupled system is WEW.
The atmospheric model is based on an advanced version of the SKIRON/Eta mesoscale meteorological model, which is a modified version of the Eta/NCEP (National Centers for Environmental Prediction) model (Kallos et al., 1997; Nickovic et al., 2001; Papadopoulos et al., 2002). This version became the core of the second generation POSEIDON weather forecasting system (Papadopoulos and Katsafados, 2009) and is fully parallelized to run efficiently on any parallel computer platform. It uses a two-dimensional scheme for partitioning grid-point space to message-passing interface (MPI) tasks. MPI is a protocol for the data exchange and synchronization between the executing tasks of a parallel job.
The Eta model is designed to use either the hydrostatic approximation or the
non-hydrostatic correction in order to be able to resolve high-resolution
atmospheric processes. Eta is formulated as a grid-point model and the
partial differential equations are represented by finite-difference schemes.
The ETA model
The E-grid stagger. The mass points represent by
The Eta model is well-documented and detailed descriptions of its dynamics and physics components can be found in several studies (e.g., Mesinger et al., 1988; Janjic, 1994; Janjić et al., 2001, and references therein). The air–sea momentum fluxes are mainly parameterized in the surface layer scheme based on the well-established Monin–Obukhov similarity theory. It provides the lower boundary conditions for the 2.5 level turbulence model and introduces the viscous sublayer for a more realistic representation of the near-surface fluxes. Different viscous sublayer approaches are applied over ground and over water surfaces in the model. For this specific application, special care was taken in the calculation of the 10 m wind. The calculations of the surface parameters within this viscous sublayer have an obvious advantage that decreases the level of uncertainty in the wind, air temperature, and humidity fields near the surface.
The wave forecasting system is based on WAM Cycle-4 code parallelized using only OMP directives. In order to reduce unrealistic energy loss at boundary points in cases where the waves propagate parallel and near the coast, the technique of Monbaliu et al. (2000) was applied wherein an alternative octant propagation coordinate system was introduced in the original WAM model code. For the octant advection scheme, eight propagation directions are defined instead of four in the classical quadrant scheme. Although in terms of computational workload, the octant scheme almost doubles the CPU time required by the upwind advection quadrant scheme, it has clear advantages over other conventional schemes, especially near the coastlines (Cavaleri and Sclavo, 1998).
The grid of the wave model for the Mediterranean and Black seas expands over
the geographical area 8
The Mediterranean and Black seas wave model is a stand alone model since it
has no open boundary towards the Atlantic basin. This is justified in the
sense that no significant swell from the Atlantic Ocean is expected to
propagate into the Mediterranean basin through the Strait of Gibraltar. The
Dardanelles and Bosporus straits are also considered to be closed boundaries;
thus, no wave energy is advected between Black Sea and Marmara Sea and
between the Marmara Sea and the Aegean. The model uses 24 directional bins
(15
In the offline coupled mode, the atmospheric model parameterizes the
momentum exchange at the air–sea interface by applying a viscous sublayer
scheme (Janjić, 1994), where the roughness
In parallel, the WAM model considers a wind input source function to the
wave spectrum equation based on the quasi-linear
theory of Janssen (1989, 1991), where the transfer of momentum from the wind to the wave field
depends simultaneously on the wind stress and the sea state itself. Hence,
the WAM model includes a set of diagnostic equations for modeling the sea
surface roughness feedback on the near-surface atmospheric boundary layer
(Janssen, 1989). The spatial and temporal variability of the Charnock
coefficient is estimated at each WAM time step by
In the current WEW version
The wave-induced stress is mainly determined by the high-frequency part of
the wave spectrum consisting of the waves that have the largest growth rate
due to the wind. In Eq. (3)
The estimated sea surface roughness length is
Finally, the computed friction velocity
Therefore, in the fully coupled mode, WAM can provide the atmospheric model
with consistent values of the Charnock coefficient, roughness, and the
friction velocity at each time step. In the current version of WEW, the
atmospheric model applies the variable Charnock parameter
The Mellor–Yamada surface layer with the viscous sublayer over the
ocean. The symbol
The friction velocity of the atmospheric model is then estimated by
In the two-way coupled mode, the Eta and WAM models utilize different domain projections, integration time step, grid geometry, and cell size. Therefore, a major effort has been undertaken in order to homogenize and handle the data exchange between the atmospheric and the ocean wave components of the coupled system. These exchanges are built upon the MPI directives since it became a standard for developing parallel applications (Snir et al., 1998). Under the parallel environment of Multiple Program Multiple Data (MPMD), the two components are carried out as parallel tasks on different processors and they exchange information indirectly (Fig. 3). Thus, the parallel execution of the system is handled entirely by the mpirun/mpiexec commands and the two components maintain their own executables. The communication between the two models is performed using MPI_Send and MPI_Recv calls at every source time step of the ocean wave model integration and the system runs flawlessly combining both MPICH and OMP environments. After the initial development, the modification of each component source code is relatively simple, just adding some data exchange routines and inserting the appropriate commands in the original model code, which call the coupling routines, while each component keeps its original structure.
The WEW exchanges near-surface
At the initialization stage, the atmospheric model initializes and loads the
inter- and intra-communicators. The atmospheric model sends the near-surface
wind components to the wave model and receives the variable Charnock
coefficient array, which is then used for the estimation of
Sketch of the WEW multi-grid structure. The transformations from the Arakawa E grid to the regular lat–long grid and vice versa are also depicted.
The WEW intra- and inter-communicators.
The initial version (v.0) of WEW was configured on a
A multi-level flowchart of the system and the data exchanges are depicted in Fig. 6. In the offline coupling mode (CTRL hereafter), the atmospheric component sends hourly near-surface wind velocity to the ocean wave model without any other interaction between the two models (red line). In the two-way fully coupled mode (WEW hereafter), the atmospheric model sends the near-surface wind components at every WAM model time step and receives various near sea surface variables. In more details, for each time step WAM can provide the atmospheric model with consistent values of the Charnock coefficient, friction velocity, total surface stress, etc. In the current version, the atmospheric model ingests Charnock coefficient and friction velocity values into the Mellor–Yamada surface layer parameterization scheme for the estimation of the near-surface wind components for the next time step as well as the accurate determination of the viscous sublayer and the parameterization of the air–sea momentum fluxes.
Informational flowchart for the offline coupled (red lines) and the two-way coupled simulations (blue lines).
WEW has been configured on a domain encompassing the Mediterranean Sea and
the Black Sea with a horizontal resolution of
Current domain configurations of the atmospheric (blue line) and the ocean wave models (black line).
Each component of WEW maintained its own time step. The propagation time step
of the WAM model was 120 s while its source time step was 360 s. The
coupling procedure exchanges data on the source time step of WAM model,
DT
The configuration of the WEW.
WEW has been tested for its consistency and performance in a high-impact atmospheric and sea-state case study of an explosive cyclogenesis over the Ligurian Sea. The coupling efficiency was quantitatively estimated over sea areas using traditional statistical scores. Thus, the performance of the fully two-way coupled system (WEW) was compared against its performance in the CTRL based on a point-to-point comparison with in situ observations from a network of 39 buoys in the Mediterranean Sea (Fig. 8). The consistency of WEW was also assessed against remotely sensed data retrieved from CRYOSAT, ENVISAT and JASON1/2.
Spatial distribution of the Mediterranean buoys applied for the sensitivity test of the system. Data were made available from ISPRA in the framework of MyWave project.
The incident of 4–11 January 2012 has been selected due to the severity of
the prevailing atmospheric conditions characterized by an explosive
cyclogenesis over the Ligurian Sea (Varlas et al., 2014). In more detail, on
5 January 2012 a low-pressure system formed over the cyclogenetic area of
the Ligurian Sea. It was mainly triggered by a widespread upper-level trough
extending from central Europe to the Mediterranean Sea (Fig. 9a). The
upper-level trough rapidly intensified the system and supported its
southeastern movement (Fig. 9b). On 6 January, the system moved toward the
eastern Mediterranean, where the pressure dropped more than 1 Bergeron,
satisfying the criteria for an explosive cyclogenesis event (Fig. 10a and
b). Sanders and Gyakum (1980), defined an extratropical cyclone as a
meteorological bomb when the mean sea-level pressure of its center falls by
at least 1 hPa per hour for 24 h at 60
Mean sea level pressure (contours in hPa) and geopotential height
at 500 hPa (colored shaded in gpm) for
Surface pressure analysis map (mb) for
The horizontal distributions of the wind speed and the SWH as well as their
differences between WEW and the CTRL experiments are depicted in Fig. 11. On
6 January 2012 at 18:00 UTC, winds exceeding the 22 ms
Panel of the horizontal distribution for the
The outputs from both simulations, CTRL and WEW, have been statistically assessed based on a point-to-point hourly comparison between model-generated variables and the available Mediterranean buoy measurements. Hourly pairs of observed and estimated values were obtained using the nearest-neighbor interpolation technique, taking care of whether this nearest source point is a sea masked grid point. Despite the known problems of the issues associated with comparing point measurements with area-averaged predictions, the in situ measurements from the buoy network are valuable in providing wind data for comparing the error statistics between the uncoupled and coupled simulations. Figure 12 summarizes the main statistical scores for both simulations. As indicated in Fig. 12a both simulations slightly underestimate the near-surface wind speed (negative bias scores). Although the CTRL gives less biased wind speed estimation than WEW, the latter exhibits a slight improvement of the RMSE (root mean square error) by approximately 2 %. Additionally, WEW reduces the standard deviation of the model towards that of the buoy's measurements. In accordance with the wind speed, the bias scores of the SWH indicate an underestimation, which is more prominent in the WEW simulation (Fig. 12b). However, WEW exhibits an overall improvement of more than 7 % regarding the SWH RMSE, with 0.53 instead of 0.57 m, and better correlation coefficients.
Scatter plots of the near-surface wind speed exceeding 1 ms
The respective error properties are quite similar in the open sea. Comparison with the remotely sensed data referenced in this section showed that WEW has slightly better statistics (e.g., lower RMSE) than CTRL, despite the fact that it seems to enhance the underestimation of the wind speed and the SWH. In particular, Fig. 12c indicates that WEW tends to increase the underestimation of the wind speed already present in the CTRL, reducing the respective RMSE by 1.5 % at the same time. Also, Fig. 12d shows that the RMSE is smaller for WEW SWH values compared to CTRL values by almost 11 %, in contrast to the slight overestimation of the CTRL SWH and the slight underestimation of the SWH occurring in WEW. The error statistics are significant at the 95 % confidence level. Although WEW increases the wind and the SWH underestimation, it overall improves the SWH RMSE by approximately 7 % against buoys data and by 11 % against remotely sensed data. In contrast to the bias scores, RMSE penalizes the variance between in situ or remotely sensed data and the simulations implying a deterioration of the RMSE in CTRL run (Chai and Draxler, 2014). Similar RMSE improvements by the coupled systems have been also confirmed in the relevant literature (e.g., Lionello et al., 2003; Renault et al., 2012). Moreover, in a parallel to WEW research effort within the MyWave project the Italian team consisting of the Institute of Marine Sciences (ISMAR) and the Italian Meteorological Service (CNMCA) coupled WAM with the COSMO (Consortium for Small-scale Modeling) atmospheric model over the Mediterranean Sea (at a lower horizontal resolution though) showing similar results especially in terms of winds and significant wave height RMSE reduction (Torrisi et al., 2014). Overall, WEW offers a more realistic representation of the air–sea interaction processes although it is not reflected in an exceptional improvement of the statistical scores. This is attributed to the fact that the application of the two-way fully coupled system can generate and support a more realistic near sea surface atmospheric circulation pattern by fully resolving air–sea interaction mechanisms at the relevant interface, including the wind speed regime and wave patterns.
The particular interactions considered in WEW are mainly driven by the
momentum exchanges in the ocean wind–wave system. The fully coupled
wind–wave parameterization scheme includes the effects of the resolved wave
spectrum on the drag coefficient and its feedback on the momentum flux. In
general, the feedbacks create non-linear interactions in the dynamic
structure of a storm or a cyclone due to the time–space sea surface friction
variability. In WEW simulations, the maximum friction velocity and sea
surface roughness are much larger than their counterparts in CTRL, with the
maxima located in areas with small wave ages and wind speeds above 20 ms
Spatial distribution of the averaged PBL height (in m) difference (WEW – CTRL) for the period 6–7 January 2012.
The reduction of the near-surface wind speed, as was evident in the WEW
simulation and depicted in Fig. 11c, is mainly attributed to the variable
Charnock coefficient directly ingested in Eq. (1) for the roughness length
estimation in the MYJ surface layer parameterization scheme. In the CTRL and
WEW experiments, the Charnock coefficient logarithmically increases with
wind speed at approximately 22 ms
Charnock coefficient dependence to the wind speed in
Roughness length (m) dependence to the friction velocity
(ms
The roughness length as a function of the friction velocity is characterized
by an initial decrease as the surface condition goes from an aerodynamically
smooth to an aerodynamically rougher regime (Fig. 15). This is the result of an
aerodynamically smooth surface where the molecular motions are dominant in
the developed viscous sublayer (Csanady, 2001). In moderate and fully rough
sea-state regimes, the roughness length is exponentially increasing with the
friction velocity. The roughness length in WEW is substantially larger than
in CTRL for friction velocities exceeding 0.60 ms
WEW is the recently developed two-way fully coupled atmosphere–ocean wave system designed to support air–sea interaction research and operational activities at HCMR. This new coupled system has made it possible for the atmospheric model to ingest a physically based momentum roughness length based on sea state. The system is built in the MPMD environment where the atmospheric and the ocean wave components are handled as parallel tasks on different processors. In the offline coupled mode, the atmospheric component parameterizes the air–sea momentum by estimating the roughness length over the sea surface as a function of a constant Charnock coefficient throughout the simulation. The ocean wave component passively receives the near-surface wind components and there is no interaction between the two models. In WEW, the atmospheric model sends the near-surface wind components to the wave model on its time step frequency and receives the space–time variable Charnock field, which is directly applied in the surface layer parameterization scheme for the estimation of the roughness length.
Interactions considered in WEW are mainly driven by the momentum exchanges
in the ocean wind–wave system and include the effects of the resolved wave
spectrum on the drag coefficient and its feedback on the momentum flux. As a
general outcome, the maximum friction velocity and sea surface roughness are
much larger than their counterparts in the offline coupled mode, which
resulted in a more turbulent and deeper marine PBL. The reduction of the
near-surface wind speed in the fully coupled simulation is mainly attributed
to the enhanced Charnock coefficient, which increases the roughness length
and finally decreases the SWH. The Charnock coefficient logarithmically
increases with wind speed at approximately 22 ms
This aspect was tested in a high-impact atmospheric and sea-state case study of an explosive cyclogenesis in the Mediterranean Sea. Despite the increased underestimation, affecting both wind speed and significant wave height, WEW offers an overall improvement in their RMSE up to 11 %. The underestimation is attributed to the direct implementation of the variable Charnock coefficient in the current surface layer parameterization scheme and is more prominent at gale force wind speeds. Therefore, an extended modification of the current MYJ scheme is recommended, and it is in the authors' future plan, in order to adjust it to the updated sea surface forcing dynamically obtained from the ocean wave component. To this end, an alternative parameterization scheme is under development for the more realistic representation of the sea surface momentum exchange and its feedbacks in WEW.
For ETA model and WAM model users, the relevant code modifications for coupling the two numerical systems can be made available by Petros Katsafados (pkatsaf@hua.gr), Anastasios Papadopoulos (tpapa@hcmr.gr), and Gerasimos Korres (gkorres@hcmr.gr).
This research is supported by the EU-funded project MyWave (FP7-SPACE-2011-1/CP-FP, SPA.2011.1.5-03). ISPRA and IFREMER (Globwave project) are gratefully acknowledged for the provision of buoy and satellite data, respectively. ECMWF is acknowledged for the kind provision of the gridded analyses data. The authors are also grateful to the editor A. Yool for his feedback concerning the improvement of the manuscript.Edited by: A. Yool