A Global Coupled Atmosphere-Wave Model System Based on C-Coupler2. Part II: Preliminary Results

A global coupled atmosphere-wave model system (MPAS-NWW3) that consists of MPAS-A (Model for Prediction Across Scales-Atmosphere) and NWW3 (the Third Generation Wave Model, WAVEWATHCH III) with C-Coupler2 (the Community Coupler2) is demonstrated with a focus on the atmospheric results in global and the specific marine area in the year 2020. Results from the two-way coupled MPAS-NWW3 model and standalone MPAS-A are compared with reanalysis products. The coupled model performs better in terms of high wind speeds and long valid hours. This indicates that the coupled model has an obvious inhibitory effect on surface wind in areas with strong winds.


Introduction
Over the past few decades, numerous models that coupled with the atmosphere, waves, and ocean models have been produced.Many fully coupled atmosphere-wave-ocean models have been created with the goal of implementing for the simulation of air-sea interactions or operational forecasts [1][2][3][4][5].Coupled models have been shown to enhance air-sea interactions and enable more accurate predictions than uncoupled models, particularly in extreme occurrences, such as the forecasting of tropical cyclones [6].A coupled wind-wave-ocean model was created by Fan et al. (2009), and was examined the effects of wind-wave-current interactions on momentum fluxes into the ocean or wave models in tropical cyclones [3].
The main study focus on investigations of coupled atmosphere-wave models was the impact of wind and swell waves on the coupled model forecasting.The function of breaking wind waves and sea spray, under strongly forced situations in the airflow dynamics in particular in energy, momentum, heat and moisture transfers through the sea surface is theoretically investigated by VK Makin et al. [7].From the viewpoint of climatology, Fan et al. modelled the global ocean surface gravity wave produced by a coupled atmosphere-wave model [8].A regional coupled atmosphere-wave climate model produced superior results for the wind speed when Wu et al. added the effect of swell on atmospheric mixing and wind stress [9].The wind stress is parameterized by the drag coefficient, which is typically assumed to be spatially uniform over water in atmospheric models, as Wahle et al. shown.However, in practice, the wind waves actually take energy and momentum from the atmosphere as they grow due to the wind [6].The influence of the coupled atmosphere-wave model on the typhoons were also research highlights [10].
On the global scale, coupled atmosphere-wave models are not common and they are extremely rarer on the synoptic scale.The Flexible Global Ocean-Atmosphere-Land System Model: Grid-Point Version 3 (FGOALS-g3) is introduced by Li et al. and its fundamental performance is assessed based on some of its involvement in the sixth phase of the Coupled Model Intercomparison Project (CMIP6) experiments [11].Nadao Kohno and Yuhei Takaya (2020) built an atmosphere-wave coupled system based on JMA Global Spectral Model (GSM), JMA wave model MRI-III, and S-CUP developed at Meteorological Research Institute (MRI) in JMA, and demonstrated how different roughness formulae used in wave dependency led to significantly different results.
In this study, the developed MPAS-NWW3 model, which coupled the wave model, WAVEWATCH III (NWW3) with the atmospheric model, Model for Prediction Across Scales-Atmosphere (MPAS-A) via the C-Coupler2, is employed.Daily simulations for the whole year 2020 have been run, and the atmospheric component model results have been used to validated with the reanalysis data.We concentrate on demonstrating its predictability in simulations on global scale in this research.There are five sections in this paper.Section 2 provides a full overview and techniques of the coupled model.The design of numerical simulation is described in Section 3. The preliminary simulation results are presented in section 4. A summary and outlook for future work are concluded in the last section.

The atmospheric component model
Model for Prediction Across Scales-Atmosphere (MPAS-A v5.2) is the atmospheric model in coupled model.For this study, there are 655362 grid cells on the horizontal plane and 64 vertical layers in MPAS-A, corresponding to a horizontal resolution of ~30km with a time step of 180 seconds.The physics parameterization scheme suite including the WRF single-moment 6-class microphysics scheme (WSM6) for microphysics, the rapid radiative transfer model (RRTM) for both long-wave and short-wave radiation, the NOAH land surface scheme, the YSU scheme for gravity wave drag, the Tiedtke scheme for convection were employed by MPAS-A model.

The wave component model
The Third Generation Wave Model, WAVEWATHCH III (NWW3 v4.18), created by the National Oceanic and Atmospheric Administration (NOAA) and National Centers for Environmental Prediction (NCEP) [11], is employed as the wave component model in coupled model.With a horizontal resolution of 1/3°, the global domain in NWW3 is cut off at 78°N and 78°S as the north-south boundary in this study.24 directions with a 15° resolution and 24 frequencies ranging from 0.0418 Hz to 0.4114 Hz with the relationship of are used to discretize the wave spectrum of the wave model.To satisfy the condition of CTL, the time step is set to 450s.

Coupling strategy
The coupled variables in MPAS-A, such as surface wind at 10 meters above sea level, temperature and specific humidity at 2 meters above sea level, directly drive the wave component model.The atmospheric model uses the coupled variables of the NWW3 model, including significant wave height, average wave length, and peak frequency to calculate an improved sea surface roughness.The coupling frequencies are set to the nearest time-step of each component model, which indicates that the coupled variables are exchanged at that time-step.
Instead of using the conventional approach, which is exclusively related to surface wind, to compute surface roughness length in surface layer schemes, the coupled method employed in this research takes the influence of wave steepness based on Taylor and Yelland [12] into account.The formula is shown in (1): where s H is the significant wave height, p L is the mean wave length,  is the kinematic viscosity (

Numerical experiments
Both standalone MPAS-A and NWW3 model were widely utilized in synoptic scale simulation.In this study, batch tests with valid time of 240 hours were conducted daily over the whole year 2020 in consideration of the differences in weather processes in different seasons.
This research primarily contrasts the performance of MPAS-A model in coupled and standalone models in order to evaluate the capacity to predict the surface wind in coupled model.The impact on wave factors receives less focus, which will be highlighted in the further studies.The experiments in this study are divided into two groups.The first group uses the standalone MPAS-A model to show that the sea surface roughness only depends on the surface wind.The second group experiments analyze the impact of wave steepness on the surface roughness length through a two-way coupled simulation in which both component models get the coupled variables.The physics parameterization and other settings for both groups of experiments are identical.Data from the Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) are used to drive the initial state of atmospheric component model.The initial time is set to 12 UTC each day in 2020, and 240 hours forecasting is simulated.
In the coupled MPAS-NWW3 model, the wave component model is driven by surface wind from the atmospheric component model at 10 meters above sea level.Cold-start is utilized daily in the standalone MPAS-A model and the atmospheric component model in the coupled model.Only the simulation of the first day (12UTC January 1st, 2020) in the wave component model uses the coldstart method.Then restart files for the following ten days are generated, which might be used to hotstart the simulation for the next time (12UTC, January 2nd, 2020).The daily simulation updates the restart files in the NWW3 model for hot-start.
The output files from the standalone MPAS-A and atmospheric component model in MPAS-NWW3 are stored in the structure of Voronoi meshes, which is frequently difficult to visualize or immediately cross-reference with other data sets.Therefore, the post-processing after numerical simulations is necessary to convert the unstructured horizontal meshes to the regular equivalent latitude-longitude grids for the further comparison and analysis.

Preliminary results
By affecting the length of sea surface roughness, MPAS-NWW3 takes sea surface momentum into account.As a result, in global or regional domain, comparisons and analyses of surface wind between the standalone MPAS-A and coupled model are conducted.The temporal resolution is set to 3 hours and all fields on land are taken as the default value.

Coupling impact on surface wind and surface roughness
This study examines the monthly averages of global surface wind and roughness length in 2020 for various valid hours.The region with strong wind, which is primarily found at middle and high latitudes, occurs throughout the entire year in the Southern Hemisphere and from October to March in the Northern Hemisphere (Figure 1a 1b).When the surface wind from the standalone MPAS-A model and the coupled MPAS-NWW3 model are compared, the coupled method clearly inhibits the surface wind in regions at middle and high latitudes, such as the Northwest Pacific and the Southern Hemisphere westerlies, but opposite at low latitudes close to the equator.The impact of sea wave makes this occurrence more logical.It is not difficult to understand that the surface wind from the atmospheric component model drives the wave component model in the MPAS-NWW3, and the significant wave height is sent backwards.A rougher sea surface then occurs in the atmospheric component model, which reduces the surface wind.This inhibiting effect is more pronounced where the surface wind speed is higher.To further explore the function of coupled strategy in global simulations, the monthly average of surface roughness length in 2020 with various valid hour are compared in this paper.The surface roughness length is obviously greater in the coupled model than it in the standalone MPAS-A, especially at middle and high latitudes, which is consistent with the inhibition of surface wind.The Southern Hemisphere experiences this phenomenon all year round (Figure 2b), but the Northern Hemisphere experiences it more visibly from September to March (Figure 2a).At low latitudes, the difference between the two models is less noticeable.As a result, in addition to the global area, the following analysis and statistics are also carried out on the Northwest Pacific and the Southern Hemisphere westerlies.

Zonal mean distribution of surface wind
ERA5 is the fifth generation ECMWF atmospheric reanalysis of the global climate, which combines model data with observations from across the world into a globally complete and consistent dataset.To confirm the impact of the coupled strategy, the genuine values of the mean sea level pressure, 2m air temperature, 10m u-component of wind, and 10m v-component of wind every three hours from the ERA5 reanalysis datasets are retrieved.ERA5 is formatted and distributed in the same way as the model results after post-processing, distributed on 0.25°0.25°equidistant longitude-latitude grids.
On the assumption that the sea-land distribution can be distinguished, we compute the zonal mean of surface wind for various valid hours monthly, using data from the MPAS-A run, the MPAS-NWW3 run, and ERA5.It demonstrates that the zonal mean surface wind in both models and ERA5 are comparable.The tendency of surface wind varied with latitude can be simulated in both models.In the middle and high latitudes of the Southern Hemisphere from November to March, the results of the standalone MPAS-A model are more similar to ERA5 than those of the coupled model (Figure 3a), particularly during the most recent valid hours.When the coupled model valid hours increase, it gets progressively closer to ERA5 (Figure 3b, 3c).It is clear that the coupled model performs better from April to October (Figure 3d, 3g) and in the longer valid hours (Figure 3f and 3i).However, the zonal mean results of the coupled model run are more noticeable in the middle and high latitudes of the Northern Hemisphere, especially during the longer valid hours.

RMSEs of surface wind compared with ERA5
The change in momentum flow, rather than heat flux, is the principal consequence of coupled scheme since it alters the surface roughness.The surface wind and pressure in the model results are the key variable fields examined in this paper.We compute several statistics like mean error (ME) and root mean squared error (RMSE) in order to quantitatively assess the effects of the coupled model on surface wind.Considering the sea-land distribution, the fields on land area are set as default values in both model results and ERA5 dataset.ERA5 is still chosen as the control dataset, as all data are distributed on the 0.25°0.25°equidistant longitude-latitude grids.All the statistics are calculated daily in global, the Northwest Pacific or the Southern Hemisphere westerlies area, in order to illustrate the impact of the coupled scheme on specific marine area.The region of global is -78~78°N and 0~360°E, as simulated by the MPAS-A model.The region of the Northwest Pacific is 3~52°N and 99~158°E, and the region of the Southern Hemisphere westerlies is 35~65°S and 0~360°E.The time series of RMSEs of surface wind in the whole year 2020 in specific marine area are analyzed in this study.No noticeable seasonal fluctuations are in global area, but exist in the Northwest Pacific and the Southern Hemisphere westerlies area.In the three areas with the most recent valid hours, the standalone MPAS-A performs obviously better than the coupled MPAS-NWW3 model, and as the valid hours are extended, the growth rate of RMSEs in coupled model is slower than that in standalone MPAS-A.The RMSEs in the Northwest Pacific region are generally smaller in the summer than those in the winter.In simulations in the Southern Hemisphere westerlies region, the difference is more obvious.The coupled model effectively suppresses the surface wind, as evidenced by the mean error of daily averages, by taking the effect of sea waves into account.The Table 1 displays the annual averaged RMSEs with every 24 valid hours over the global, the Northwest Pacific, and the Southern Hemisphere westerlies area.This illustrates the advantages of coupled model in predicting with 120 valid hours.

Summary
This article describes the preliminary applications and results of the global atmosphere-wave coupled model with C-Couple2 (MPAS-NWW3), the impact of wave steepness on sea surface roughness is taken into account.Two groups of experiments with the coupled MPAS-NWW3 model and the standalone MPAS-A model, initialized at 12UTC every day and 240 hours forecasting completed for the entire year 2020, were designed and compared to the ERA5 reanalysis datasets.It is simple to understand that the differences between the two sets of experiments reflects the effects of waveatmosphere interaction on surface wind and ocean waves in global.Compared to the standalone MPAS-A run, the coupled model experiments produced results that were on par with or superior.On a global scale, the spatial distributions of surface wind and sea surface roughness length in the coupled MPAS-NWW3 model are comparable to those in the MPAS-A model.The coupled model has an obvious restraining effect on surface wind in the middle and high latitudes, especially in the region with strong wind.According to this phenomenon, the surface roughness length in coupled model is unmistakably longer than it in MPAS-A.The RMSEs of coupled model surface wind in global, the Northwest Pacific, and the Southern Hemisphere westerlies area are comparable to those of standalone MPAS-A in recent valid hours and are gradually becoming similar with 120-240 valid hours.In this paper, the analysis of the atmospheric variables and roles of the coupled strategy in coupled MPAS-NWW3 are the key foci.High impact weather events like typhoons are still limited in this study, and the verification with buoy or other real observation will be calculate and analysis in the future study.Because the surface momentum flow does not play a significant role compared to heat flux, there is a bias between the coupled and standalone models, but it is less noticeable.In the combined atmosphere-wave-ocean model, it might have a more pronounced improvement effect, and the creation and investigation of the further coupled model will be involved in the future work.

Figure 1 .
Figure 1.The difference of monthly mean surface wind (unit: m s -1 ) between the MPAS-NWW3 coupled model and standalone MPAS-A model.(a) shows the monthly mean value in January with the valid hours 120h; (b) shows the monthly mean value in May with the valid hours 120h.To further explore the function of coupled strategy in global simulations, the monthly average of surface roughness length in 2020 with various valid hour are compared in this paper.The surface roughness length is obviously greater in the coupled model than it in the standalone MPAS-A, especially at middle and high latitudes, which is consistent with the inhibition of surface wind.The Southern Hemisphere experiences this phenomenon all year round (Figure2b), but the Northern Hemisphere experiences it more visibly from September to March (Figure2a).At low latitudes, the difference between the two models is less noticeable.As a result, in addition to the global area, the following analysis and statistics are also carried out on the Northwest Pacific and the Southern Hemisphere westerlies.

Figure 2 .
Figure 2. The difference of monthly mean surface roughness (units: 10 -3 m) between the coupled model and standalone MPAS-A model.The month and valid hours are corresponding to the Figure 1.

Figure 3 .
Figure 3. Zonal mean surface wind.The top, middle and bottom panels show the surface wind in January, May and September, respectively.The left, middle and right panels is with the valid hours 72h, 144h and 196h.The black, red and blue lines in each panel show the field of ERA5 reanalysis, the standalone MPAS-A run and the coupled MPAS-WW3 model run.

Table 1 .
Annual averaged RMSEs (units: m s -1 ) of surface wind over the specific marine area with 240 valid hours in standalone MPAS-A and coupled MPAS-WW3 model run.The bold numbers in the table show the parts where the coupled model is superior to the standalone MPAS-A model.