ICONGETM v1.0 – Flexible two-way coupling via exchange grids between the unstructured-grid atmospheric model ICON and the structured-grid coastal ocean model GETM

Coupled atmosphere-ocean models are developed for process understanding at the air-sea interface. Over the last 20 years, there have been studies involving simulations in the range of sub-annual simulations to climate scenarios. The development of coupled models highly depends on the kind and quality of the required data exchange between the model interfaces. This work achieved the development of a two-way coupled atmosphere-ocean model ICONGETM with flexible data exchange via exchange grids provided by the widely used ESMF regridding package. The regridding of flux data between 5 the unstructured atmosphere model ICON and the structured regional ocean model GETM is conducted via these exchange grids. The newly developed model ICONGETM has been demonstrated for a coastal upwelling scenario in the Central Baltic Sea.


Coupling with ESMF/NUOPC
ICONGETM is built on ESMF/NUOPC. It is hierarchically structured into main program, driver, model and coupler compo-  shortwave net flux at surface sob_s relative humidity in 2 m rh_2m 1 × 10 −2 =⇒ hum 1 × 10 −2 total cloud cover clct Table 1. List of quantities which can be exchanged in ICONGETM. The direction is indicated by the arrow. The units of the source and target variables are given in square brackets. Data conversion and aggregation is done in the coupler. precip and evap are obtained by division with the reference density of fresh water. If graupel, ice and hail are activated in ICON, then the corresponding contributions to precipitation must also be considered. Wind data need to be rotated (R) to the local coordinate system in GETM. The humidity quantity is correctly identified by the name of the exchanged ESMF field. The exchange of flux data (3rd block) or state variables (last block) offers the comparison of different coupling strategies within the same model environment. The last column indicates which data are exchanged during the performed one-and two-way coupled simulations.

Initialization
ICONGETM is initialized and configured in different stages. At first, ESMF itself is initialized. Next, the coupled model is configured from a user-provided configuration file with the number of processes for each model component, the names of the data to be received by each model component as well as the coupling time step.

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A NUOPC-Driver is applied, which creates NUOPC-Model components for ICON and GETM as well as a NUOPC-Mediator, which serves as a data exchange component between the model components. The current implementation only supports a concurrent distribution of the components among all available computing units. For the time management, a run sequence defines in which order the mediator and model components will interact during the simulation.
Next, the initialization routines of each NUOPC-Model component are called. They have access to the initializing rou-105 tines of the individual models themselves. Additionally, the horizontal grid structures are translated into an ESMF_Grid and ESMF_Mesh for structured and unstructured discretizations, respectively, see Sec. 3.1 and 3.2. Moreover, ESMF_Fields are created to advertise all data which are available for exchange. However, based on the user-specified lists of data that should be received by each model component, the model system automatically detects the required subset of fields which are finally connected and realized. The current implementation supports the exchange of flux and state data, see Tab. 1 for a list of 110 exchangeable quantities and their optional conversion by the mediator.
The data transfer between the NUOPC-Models via the NUOPC-Mediator is then prepared generically, i.e. by the NUOPC layer. NUOPC-Connectors are set up to redistribute the data between the different computing units used by the coupler and model components. For the actual regridding (interpolation) between the horizontal triangular grid from ICON and the horizontal latitude-longitude grid from GETM, one ESMF_XGrid is created for each direction. For details see Sec. 3. The in-115 terpolation weights are calculated only once during initialization and will be used in the Run phase. The generation of the ESMF_XGrid and the interpolation weights is the most expensive part of the overall overhead due to coupling. The later performed interpolation in the Run phase is relatively cheap.
In the present implementation, no model receives data during Initialization phase. However, the first data exchange takes place at the beginning of the Run phase, as specified in the run sequence. All model components update their export fields at 120 the end of the Initialization phase.

Run
During runtime the coupled model system is integrated in time by repeating the prescribed run sequence with the given coupling intervals until the simulation end time is reached. At the beginning of the run sequence new input data are provided to each model component by data exchange and regridding via the mediator component. In ICON, the received data must be copied to 125 model internal memory locations. For GETM, the ESMF_Fields already contain pointers to the internal memory. With the new data from the import fields each model advances with its own time step until the next coupling time point is reached. At the end of the run sequence all model components prepare the following data exchange by updating their export fields from the internal model memory.

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This phase finalizes all ESMF and NUOPC components. The finalization of the model compoents is included by calling the finalizing interface in ICON and GETM. The overall last step is the finalization of ESMF.
The data exchange between ICON and GETM is based on the regridding from the source model grid to an exchange grid and the regridding from the exchange grid to the target model grid. The ESMF exchange grid (ESMF_XGrid) infrastructure is used 135 for the conservative interpolation at the air-sea interface, i.e. in the NUOPC-Mediator, compare with Fig. 1. The aim is to apply an interpolation approach which is independent of any horizontal resolution in ICON and GETM. Before the ESMF_XGrid and how it is utilized in ICONGETM is explained in detail, the horizontal discretization of ICON and GETM is presented.
Furthermore, the interpolation is schematically described.

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The horizontal grid structure of ICON is described in detail by Linardakis et al. (2011). The very first assumption for the horizontal grid is that the Earth is approximated as a sphere. It is based on the projection of an icosahedron onto the sphere.
The edges of each triangle of the icosahedron can now be interpreted as an arc of great circles on the sphere. A refinement of the grid, i.e. to increase the resolution by using smaller triangles, is achieved by a combination of two steps. The first step is an initial division of the original icosahedron triangle edges by n ∈ N. The second step are k ∈ N bisections of the remaining 145 smaller triangles. The final grid is then described by RnBk. The number of triangles on the sphere for a grid RnBk is given by 20n 2 4 k , see Zängl et al. (2015). The effective grid resolution is given by with Earth radius r E . Table 1 in Zängl et al. (2015) shows different R2Bk grids with effective grid resolutions. The DWD applies a global R3B07 grid, a R3B08 Europe-grid and a R3B09 Germany-grid for the weather forecast simulations, which 150 have effective resolutions of 13.15 km, 6.58 km and 3.29 km, respectively.
The construction of refined grids supports a straight-forward nesting. An example for the Baltic Sea region based on R2B08, R2B09 and R2B10 grids with effective resolutions of 9.89 km, 4.93 km and 2.47 km is shown in Fig. 2.

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The grid in GETM is structured and supports curvilinear horizontal coordinates in Cartesian and latitude-longitude space.
For coupling with ICON only grids in spherical coordinates can be used. A land mask defines land and water cells, see represents cells that consist of more than 50% of ocean (blue), forest (green), urban areas (red) or non-specific land classifications (yellow).
GETM only distinguishes between ocean (blue) and land (yellow). The white rectangles frame the area shown in Fig. 4.  1.

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Figure 5. Exemplary 2D exchange grid formed by a triangular atmosphere (red) and a rectangular ocean (blue) grid. The exchange grid consists of edges from the original triangular and rectangular grids (thick red and blue) and additional edges from the triangulation (black).
Assuming that only water cells are shown, the four possible combinations of land/ocean masks are labeled. Here the exchange grid is shown for the interpolation from the ocean to the atmosphere grid, therefore, excluding the elements of case 3.    ICON does not need any specific settings when run two-way coupled in ICONGETM, because the coupler will simply overwrite the ICON-internal sea surface temperature with the data provided from GETM. parameters have to be changed for the uncoupled and coupled simulations. The first one specifies whether atmospheric data should be read from file or whether an external coupler will take care of the data provision. A second one specifies whether GETM needs to compute the air-sea fluxes during runtime or whether air-sea fluxes are already provided. In the uncoupled simulation GETM calculates the air-sea fluxes according to the bulk parameterization of Kondo (1975) in terms of hourly meteorological CFSv2 data (Saha et al., 2014) read from file. During the one-and two-way coupled simulations the coupler 235 will provide the air-sea fluxes from ICON.

ICONGETM configuration
The exchanged data for the one-and two-way coupled simulations are listed in Tab

Effects of interactive coupling on meteorology
In the uncoupled and one-way coupled simulations ICON uses its prescribed internal sea surface temperature (SST), which does not show any pronounced temperature gradients due to oceanic eddies or coastal upwelling. Short-term and small-scale variations are only considered in the two-way coupled ICONGETM run (see Fig. 7), with the SST simulated and provided in 245 high-resolution by GETM.
In July 2012, the simulated SST ranged around 289 K, with values below 282 K in the upwelling areas south of the coast of mainland Sweden and the islands of Öland and Gotland. The ICON-internal SST is between 0.5 K and 2 K colder. The overall warmer surface of the Baltic Sea in the two-way coupled ICONGETM run causes a predominantly warmer lower troposphere.
As a result, the daily-mean 2-m temperature is about 0.5 K to 2 K higher (Fig. 8).

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Over the upwelling regions, however, where cold deep water has risen to the surface, only the two-way coupled ICONGETM run is able to reproduce the cooling in the 2 m temperatures of between minus 1 K to 2 K against the surroundings. The twoway coupled atmosphere-ocean simulation thus provide a more realistic representation of actual weather conditions. This is also reflected in a better agreement when comparing the model results with air temperature measured onboard the RV Meteor off the island of Gotland during the above-mentioned field campaign. While the temperature is occasionally significantly 255 underestimated by up to 2.5 K by the uncoupled/one-way coupled ICON simulation, the values from the two-way coupled ICONGETM run are in the same range as the measurements and the temporal development also agrees much better with the observations (Fig. 9), especially after 10 days of simulations.  The interactive coupling between ICON and GETM also affects the synoptic-scale dynamic meteorology and leads to local effects in the atmospheric boundary layer. The warmer Baltic Sea and higher lower-troposphere temperatures in the two-way 260 coupled ICONGETM simulation result in a mean sea-level pressure that is up to 1 hPa lower over sea and adjacent land than in the uncoupled/one-way coupled ICON run (Fig. 10).
Thus, the low-pressure area over the northern Baltic Sea, which causes the observed upwelling event, is even stronger in the two-way coupled simulation. The resulting higher pressure gradient between the Baltic low and the high over Western Europe (Fig. 10) leads to an increase of the near-surface wind field over a large part of the water surface, while locally wind 265 14 https://doi.org/10.5194/gmd-2020-269 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.  velocity is reduced in the upwelling regions (Fig. 11). The weather conditions leading to the upwelling event are therefore more pronounced in the two-way coupled model run.
The effects of the interactive atmosphere-ocean coupling on the boundary layer dynamics is most evident for the upwelling regions. Fig. 12 shows vertical profiles of potential temperature and specific humidity over the upwelling area east of Öland.
Compared are the profiles for 16 July 2012 at noon and midnight, when the upwelling event was most pronounced in this area.

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As a result of the upwelling of cold deep water, the potential temperature is reduced by up to 1.5 K to 2 K and atmospheric strat- ification is increased in the lowermost 50 m to 150 m at noon and mid-night, respectively. The two-way coupled ICONGETM run also shows slightly enhanced gradients in the potential temperature profile at the upper boundary layer. The more stable stratification has an effect on the boundary-layer mixing, whereby humid air is more concentrated in the central to upper part of the boundary layer while it is less in the lowermost part due to reduced evaporation. In addition, there is less momentum 275 mixed downwards (Fig. 12). This is also a likely explanation for the locally reduced wind velocity in the upwelling regions, in addition to the strengthening of the local land-sea circulation (cf. Fig. 11).

Coupling effects in the ocean
In Fig. 13, the sea surface temperature (SST) from all model simulations are compared to satellite data.
Due to the forcing with meteorological reanalysis data, the SST from the uncoupled simulation shows best agreement with 280 the satellite data and most pronounced upwelling activity. The SST from the two-way coupled simulation is only slightly colder, but is clearly overestimated in the one-way coupled simulation. This overestimation results from a continuous increase of near surface temperature, see Fig. 14 for the evolution in the Eastern Gotland Basin.
The evolution indicates that the surface heat flux used in the one-way coupled GETM simulation is overestimated after 12 July 2012. For the one-way coupled simulation, the heat flux provided by ICON is calculated in terms of the too cold ICON- In the upper 20 m the temperatures from the uncoupled and two-way coupled simulations are very similar and do excellently 290 agree with the measurements, cf. Fig. 15 B. The temperature from the one-way coupled simulation is approximately 1.5 K too inertial internal waves, are subsequently causing the differences between the analysed profiles.
The salinity differences between the simulations show, in analogy to the temperature, deviations in the thermocline, but are also within the variability observed over an 8 day time period. In contrast to the surface, the deep water below the thermocline is virtually not affected by the different atmospheric forcing. This is caused by the strong density gradients in the thermo-and  Due to the nature of the conservative interpolation, small differences such as in the sea surface temperature from ICON and GETM in Fig. 7 and 13, respectively, can occur. Fig. 6 shows the very same effect already for a very academic example. However, conservation over the whole coupling interface is ensured. Additionally, conservation has to be guaranteed for energetic consistency.
The two-way coupled simulation presented in the previous section was conducted with a coupling time step of 3 min and 320 showed an overhead of approximately 15 % compared to the uncoupled simulation. The majority is spent for the initialization.
This demonstrates the excellent performance of the developed model system based on ESMF/NUOPC and its potential for future high-resolution coupled atmosphere-ocean simulations with fast feedback integration.

Conclusions and outlook
The newly developed model ICONGETM combines a conservative flux interpolation between the atmosphere model ICON 325 and the regional ocean model GETM. Furthermore, it uses an exchange grid for the data exchange based on the NUOPC routines provided through the ESMF library. The demonstration example shows that there is now a coupled model available which allows the investigation of processes at the air-sea interface with high-resolved model simulations.