An atmosphere-wave regional coupled model: improving predictions of wave heights and surface winds in the Southern North Sea

Reduction of wave forecasting errors is a challenge especially in dynamically complicated coastal ocean areas as the southern part of the North Sea area – the German Bight. Coupling of different models is a favoured approach to address this issue as it accounts for the complex interactions of waves, currents and 15 the atmosphere. Here we study the effects of coupling between an atmospheric model and a wind wave model, which in the present study is enabled through an introduction of wave induced drag in the atmosphere model. This, on one side, leads to a reduction of the surface wind speeds, and on the other side, to a reduction of simulated wave heights. The sensitivity of atmospheric parameters such as wind speed, and atmospheric pressure to wave-induced drag, in particular under storm conditions, is studied. 20 Additionally, the impact of the two-way coupling on wave model performance is investigated. The performance of the coupled model system has been demonstrated for extreme events and calm conditions. The results revealed that the effect of coupling results in significant changes in both wind and waves. The simulations are compared to data from in-situ and satellite observations. The results indicate that the twoway coupling improves the agreement between observations and simulation for both wind and wave 25 parameters in comparison to the one-way coupled model. In addition, the errors of the high-resolution German Bight wave model compared to the observations have been significantly reduced in the coupled model. The improved skills resulting from the proposed method justifies its implementations for both operational and climate simulations. 30 Ocean Sci. Discuss., doi:10.5194/os-2016-51, 2016 Manuscript under review for journal Ocean Sci. Published: 28 June 2016 c © Author(s) 2016. CC-BY 3.0 License.

In our setup we use a spatial resolution of about 10km and 40 vertical coordinate levels to discretize the area around the North Sea and Baltic Sea (Fig.1a). Forcing and boundary condition data are taken from the coastDat-2 hindcast data base for the North Sea (Geyer 2014) covering the period 1948-2013with Ocean Sci. Discuss., doi:10.5194/os-2016-51, 2016 Manuscript under review for journal Ocean Sci. To couple WAM and COSMO using the coupling library of this coupler, modifications in source code of 160 WAM and COSMO have to be done. The source code of CCLM was modified for the coupled system WAM/COSMO-CLM in a similar way used for the atmosphere-ocean-sea ice coupled system model Ocean Sci. Discuss., doi:10.5194/os-2016-51, 2016 Manuscript under review for journal Ocean Sci. Published: 28 June 2016 c Author(s) 2016. CC-BY 3.0 License. study are only wind and sea surface roughness length.
For our perturbation experiment we perform one-way and two-way coupled simulation. In the one-way 165 coupled mode only the atmospheric model sends wind data to the North Sea wave model. This is thus equivalent to the familiar forcing of a wave model by 10m wind fields. We will refer to the results of this simulation as COSMO-1wc and WAM-NS-1wc, respectively, where '1wc' and 'NS' stay for 'one-way coupled' and 'North Sea'. In the two-way coupled mode the North Sea wave model sends back sea surface roughness lengths obtained from the atmospheric model wind forcing which in return might 170 reduce wind speeds, i.e. the two-way coupling results in a non-linear interaction between the two models.
We will refer to the results of this simulation as COSMO-2wc and WAM-NS-2wc, respectively. The coupling time step in either simulation is 3 minutes. This small coupling time step is a big advantage for modelling fast moving storms compared to an uncoupled run, where wind fields are usually available at the most hourly. 175 The German Bight wave model is forced in the two simulations by the respective wind and boundary data. Although the German Bight model does not send roughness information to the atmosphere we will refer to the two differently forced setups as WAM-GB-1wc and WAM-GB-2wc, because in the second experiment roughness information is sent to the atmospheric model by WAM-NS-2wc. 180

Integration Period and Data Availability
The described models were used to simulate the three months period from October to December 2013.
This period was chosen since it includes on December 6 th the storm 'Xaver' one of the most severe storms of the last decade. 'Xaver' originated south of Greenland and rapidly deepened as it moved 185 eastwards from Iceland over the Norwegian Sea to South-Sweden and further to the Baltic Sea and Russia. Exceptional was also the long duration of the storm event of nearly two days. The German Bight coast was affected by three surges due to the storm coming almost constant from Northwest.
In our study we perform a statistical analysis for the whole period of integration and investigate the stormy period in more detail. Figure 2 shows the distribution over the selected period of wind speeds and 190 directions at the in-situ platform FINO-1 data station (see Figure 1c for its location). North-westerly winds are generally dominant, but during 'Xaver' strong winds are also coming from west and south-west as the storm moved eastwards. For the validation of our experiment we used wind speed and significant wave height measured by altimeter satellites SARAL/AltiKa, Jason-2 and CryoSat-2 over the North Sea.
The first two carry on-board a classical pulse-limited altimeter which operates in low resolution mode 195 (LRM), while the CryoSat-2 instrument operates in LRM or in Delay Doppler (DD) mode. The CryoSat-2 Ocean Sci. Discuss., doi:10.5194/os-2016Discuss., doi:10.5194/os- -51, 2016 Manuscript under review for journal Ocean Sci. Published: 28 June 2016 c Author(s) 2016. CC-BY 3.0 License. data used here have been extracted from the RADS database (Scharroo et al. 2013), where CryoSat-2 data acquired in DD mode in our region has been processed to generate pseudo-LRM data (PLRM). Accuracy and precision of PLRM data are slightly lower than LRM and SAR data (Smith and Scharroo, 2015). The altimeter satellites measure along their ground-track offshore up to few kilometres from the coast (see 200 Figure 1b). Their ground track pattern and the repeat period are different for each mission, for the three missions above the same location is revisited every 27, 10, 350 days respectively (Chelton et al., 2001).
The data from SARAL/AltiKa data is here of special interest since this satellite passed over the German Bight during the storm 'Xaver' when the surge was at his maximum (Fenoglio-Marc et al. 2015).
Additionally, we used wave data from four directional Datawell wave riders in the German Bight 205 operated by the Federal Maritime and Hydrographic Agency (BSH) (see Figure 1b for satellite tracks). At station FINO-1 there were also wind speed measurements at 50 and 100 m available for the selected period.

Validation of models
To quantify the performance of one-way versus two-way coupling we compared the atmospheric and wave model output against in situ and remotely sensed data. Table 1 gives for both wave height and wind speed the statistics of the difference between model and the altimeter-derived values over the selected 215 three-month period, which is bias and standard deviations of differences. For all the three satellites the standard deviation in the two-way coupled setup is smaller than in the one-way setup. Similarly, for Jason-2 and SARAL/Altika the bias in the two-way coupled setup is smaller than in the one-way setup and measured values are below modelled ones. In the one-way coupled setup biases are about 30 cm and 0.7 m/s for wave height and wind speed, respectively while in the two-way coupled setup these values are 220 nearly halved due to the reasons explained above, thus giving a first indication of improved model skills in this case. For Cryosat-2 instead the opposite is true and measured values are above modelled ones in mean for both wave height and wind speed. CryoSat-2 biases in the one-way setup (18 cm and 0.4 m/s for wave height and wind speeds respectively) have similar magnitude than biases in the two-way coupled setup of the other two satellite (e.g. -0.12 and -0.33 for SARAL/Altika). Fenoglio-Marc et al. (2015) also 225 found that CryoSat-2 derived wave height data overestimate the LSM wave model data from the DWD.
For the wind speed they however found the opposite, which is that CryoSat-2 derived wind speed underestimates the COSMO wind model data from the DWD. This using both RADS PRM data and from SAR. On the other hand the coastDat2 data used to force our COSMO model with used NCEP/NCAR data as driving fields which might explain this disagreement. Moreover, it is well know that the 230 Below we will analyse the temporal variability of the significant wave heights in the German Bight under stormy conditions. This allows us to investigate not only the impact of two-way coupling but also of model resolution on the model performance. Figure 4 shows a comparison between data from two wave rider buoy (the location of the buoys is shown in Fig. 1) during the storm 'Xaver' and model output from Additionally, wind speeds were validated against measured data from FINO-1 in 50 and 100m height over the whole modelling period (Table 2). Even though differences between COSMO-1w/2wc decrease with 295 increasing height of the atmosphere, we still found a better agreement in the two-way coupled run. The bias in wind speed is negative for the one-way coupled setup, thus modelled wind speeds overestimate the The rmse is about 3m/s in either case but slightly improved for the full coupled setup.
For a more quantitative validation of the WAM-GB-1wc/2wc results we used four buoys (see Figure 1c  300 for their locations) in water depths from 13 to 30 m. Table 3 gives statistics for significant wave height (Hs) over the three months period. In either water depth and regardless of the way of coupling the bias for Hs is slightly negative, i.e. the modelled data over-predict the measured values. For WAM-GB1wc the bias is about 15 cm except for buoy Elbe where it is 7 cm. Modelled wave heights are smaller in WAM-GB-2wc, and thus bias is reduced from 15 cm by about 10 cm and from 7 to 1 cm at buoy Elbe. The rmse 305 of about 50 cm is unaffected by the two-way coupling except for the buoy FINO-1 where it is reduced by about 5%. In any case the error distribution (not shown here) becomes more symmetrical in the two-way coupled cases.

310
In the following the impact of coupling will be analysed for the North Sea focusing on the spatial patterns under different physical conditions. Three months averaged significant wave height and wind speed is reduced significantly (Figure 5) due to the two-way coupling which results in an extraction of energy and momentum by waves from the atmosphere. The bias in wave height gives values of about 20 cm which is 315 a reduction of about 8% of the three month mean value (~2.3 m). The root mean squared difference (rms) between two simulations is about 40cm in the central North Sea. For the wind speeds the bias is about 30 cm/s when averaged over the model area, corresponding to a reduction in wind speed of about 3% of the three month mean value (~10m/s) with an rmse of about 80cm/s. The spatial patterns in the bias in Figure 5 can be explained by the dominating westerly winds. As the 320 wind coming from land (Great Britain) hits the North Sea, the differences in the wind speed between the two models are larger closer to the coast because of differences in the of sea surface roughness. Moving further to the east, the atmospheric boundary layer adapts in either case to the winds over sea and the differences between one-and two-way coupled setups become smaller. This theory is supported when looking on the effect of coupling for the wind stress ( Figure 6). One can clearly see how rapidly the stress 325 decreases in the two-way coupled setup east off the British coast and then, after adaptation to the new wind, the differences in wind stress between one-and two-way coupled setup stay nearly constant at a low value. For the wave height, differences in bias close to the western coasts and in the English Channel are smallest since it needs some fetch for the waves to evolve and this fetch is too short here.
The differences in the mean sea-level pressure between COSMO-1wc/2wc for the storm 'Xaver' period is 330 analysed in the following addressing the hypotheses that the higher friction should in case of a low Ocean Sci. Discuss., doi:10.5194/os-2016Discuss., doi:10.5194/os- -51, 2016 Manuscript under review for journal Ocean Sci. Published: 28 June 2016 c Author(s) 2016. CC-BY 3.0 License.
pressure system result in an air flow which tends to fill the low, i.e. increased pressure in the pressure low minimum is expected (Janssen and Viterbo, 1996). The mean sea level pressure at the peak of the storm ( Figure 7a) shows values of about 900 hPa over Norway and of about 1000 hPa over the North Sea. with several storms coming from the North Sea (including 'Xaver') and thus with higher wave ages ( Figure 8b). The differences in significant wave height and wind speed between the one-and two-way coupled models are mostly positive, i.e. both parameters are reduced in the two-way coupled model run.
Largest differences can be observed when wave age (the ratio of phase velocity at the peak of the wave spectrum with friction velocity) is well below 20 and occurs for the waves before the maximum wave 350 height is reached (this can be well seen for 'Xaver', Figure 8b) thus the waves grow slower in the twoway coupled model. Negative differences occur seldom and only when wave age rapidly increases (we do not consider situations where wave age exceeds 50 since there the wind speeds go to zero and thus wave age to infinity).

Summary and Outlook
We have setup a two-way coupled wave-atmosphere model for the North Sea which includes the possibility of nesting a local wave model simultaneously. This was done by using the coupling software OASIS3-MCT which allowed the parallel run of several models on different model grids. Model 360 intercomparisons gave encouraging results: the two-way coupled model were in a better agreement with the in-situ and remotely sensed data of significant wave height and wind speed compared to the one-way coupled model (COSMO forces WAM). We observe a general good agreement between model results and satellite-derived parameters except for a known degradation of wind speed in storm conditions, which Ocean Sci. Discuss., doi:10.5194/os-2016Discuss., doi:10.5194/os- -51, 2016 Manuscript under review for journal Ocean Sci.