A new roughness parameterization accounting for wind-wave (mis)alignment

Two-way feedback occurs between offshore wind and waves. However, the influence of the waves on the wind profile remains understudied, in particular the momentum transfer between the sea surface and the atmosphere. Previous studies showed that for swell waves it is possible to have increasing wind speeds in case of aligned wind-wave directions. However, the opposite is valid for opposed wind-wave directions, where a decrease in wind velocity is observed. Up to now, this behavior has not been included in most numerical models due to the lack of an appropriate parameterization of the resulting effective 5 roughness length. Using an extensive data set of offshore measurements in the North Sea and the Atlantic Ocean, we show that the wave roughness affecting the wind is indeed dependent on the alignment between the wind and wave direction. Moreover, we propose a new roughness parameterization taking into account the dependence on alignment, consisting of an enhanced roughness for increasing misalignment. Using this new roughness parameterization in numerical models will facilitate a better representation of offshore wind, which is relevant to many applications including offshore wind energy and climate modeling. 10 Copyright statement. TEXT


Introduction
During the past years there has been an increased interest in wind turbines.Wind energy has been proposed as an ideal alternative for non-clean energy sources, and a good candidate to meet the rising energy demands.Moreover, there is more and more interest in offshore wind turbines because of their societal benefits and their higher wind extraction possibilities compared to onshore wind turbines.The last ten years the European offshore capacity increased by 11 GW (WindEurope Business Intelligence, 2017).Additionally, by 2020, 20% of the total energy should be renewable, this in order to meet the renewable energy directive (Directive 2009/28/EC).As such the estimated installed wind energy capacity by then will be 40 GW (EWEA, 2011).However, due to the high cost of offshore wind turbines, it is important to have accurate information about the vertical structure of the wind profile at offshore wind farm locations.Such accurate profiles will help estimate the energy production, the dynamic loads and fatigue, which influence the design of the wind turbine, the operation of the wind farm, the wind turbine wakes and finally the lay-out and allocation of new wind farms.In order to model offshore wind profiles accurately, the wind-wave interaction should be better understood.This physical understanding will result in more physical relationships that can be included in coupled atmosphere-wave models.Hence, it is important to have offshore measurement data available to improve our understanding of the wind-wave interaction.
The wind-wave interaction is located within the Marine Atmospheric Boundary Layer (MABL), which is the lowest part of the atmosphere directly influenced by the sea surface.Contrary to the atmospheric boundary layer (ABL) over land, the effect of the diurnal cycle of the atmospheric stability is negligible due to the high heat capacity of the ocean.Moreover, the characteristics of the MABL are mainly influenced by the variations in the momentum flux from the sea surface to the atmosphere, such as varying wave length, wave speed and wave height.In addition, higher wind speeds with lower turbulence intensities are present for MABLs related to reduced wind drag (Ardhuin et al., 2009;Stull, 1988).Throughout the years, the wind-wave interaction has been thoroughly investigated, both by numerical and experimental characterization (Sullivan et al., 2008;Kalvig et al., 2013;Drennan et al., 2005;Edson et al., 2007).However, the effect of alignment between wind and wave directions has not received sufficient attention, while there are preliminary indications that it can have an impact on momentum transfer (Grachev et al., 2003;Patton et al., 2015;Drennan et al., 2005).

State of the art in parameterizing wind-wave interactions
In order to investigate wind-wave interactions, a good understanding of the momentum transfer between the sea surface and the atmosphere is necessary.Critical in modeling these complex interactions (Fig. 1) is the roughness parameterization.
An important way through which the momentum transfer is correctly represented in numerical models is by imposing the right shear stress, which depends on the roughness parameterization.The total shear stress, τ tot , and thus the offshore momentum transfer, is dependent on the turbulent shear stress, τ turb , the wave induced shear stress, τ wave , and the viscous shear stress, τ visc (Phillips, 1977).
The viscous shear stress is assumed to be negligible because of the large scales involved.The wave shear stress, however, is considerable in the MABL and its effect decreases with height.As can be seen in Fig. 1, momentum transfer can go two ways; from the wind to the waves and vice versa.The sign of the wave shear stress is strongly dependent on the wave age, which is most often defined as In this equation U 10 is the wind speed at 10 m and c p is the wave phase speed at the peak of the wave energy spectrum.
When χ < 1.2, the wind is dominant and the waves present are called wind waves or young waves.As χ approaches 1.2, wind and waves reach equilibruim and the sea is fully developed.However, when χ > 1.2, the wave speed is dominant over the wind speed and we speak about swell waves or old waves (Donelan, 2011).This can also be written as a function of the air friction velocity, u * , shown in Eq. ( 3) where χ < 20 corresponds to young waves and χ > 20 to old waves (Drennan et al., 2003).
For swell waves the wave shear stress, and thus the momentum flux caused by it, is small compared to the total shear stress.
However, this is not the case for young waves, where most of the momentum flux is determined by the wave stress.As such, it is important to include the wave age parameter in a roughness parameterization (Janssen, 1991), as will be shown later.For wind waves, the wave shear stress is positive.As such, there is a downward momentum flux from the atmosphere to the sea surface, and the aerodynamic roughness (z 0 ) increases with increasing shear stress.On the other hand, for swell waves, the aerodynamic roughness can decrease down to a point where the wave shear stress can become negative.This can cause the total shear stress to become negative which results in a upward momentum flux.Because of this, momentum is transported from the sea surface to the atmosphere (Cathelain, 2017;Sullivan et al., 2000).
In order to model the momentum transfer from the atmosphere to the sea correctly, most atmospheric models use the Charnock aerodynamical roughness parameterization (Eq.( 4)), where α is the Charnock parameter that depends on the sea state and is assumed to be constant and g is the gravitational constant (Charnock, 1955).
An important application where this parameterization is used is in atmospheric models uncoupled to an ocean model, an example of which is the Weather Research and Forecasting (WRF) model (Skamarock et al., 2008), where the Charnock pa-rameter used for offshore conditions is constant and equal to 0.018.In this model the Charnock constant is only derived for fully developed, wind waves over deep water.Jiménez and Dudhia (2018) recommends to have a modified sea surface roughness formulation for shallow waters as this formulation for deep water is resulting in a positive wind speed bias.Additionally, Larsén et al. (2012) showed that the wind at hub height is underestimated for storm conditions, caused by this simple roughness length parameterization proposed by Charnock (1955).Hsu (1973) suggested that the Charnock parameter should include information of the sea surface characteristics.As such, it included the wave steepness H s /L implicitly, where H s is the significant wave height and L the wave length of the dominant waves.For deep water waves, where the depth of the sea (h) is bigger than half the wave length, the wave speed is related to the wave length by Eq. ( 5), while for shallow regions it is equal to Eq. ( 6).
Hsu (1973) modified the roughness parameterization based on the available field and laboratory measurements for nearneutral stability and deep water, which resulted in Eq. ( 7), where A is a constant.
A more general roughness parameterization was found by Donelan (1990) and is shown in Eq. ( 8).
However, no consensus for the constants A and B was found because every data set resulted in different values.As such, Drennan et al. (2003) tried to avoid this problem by estimating the roughness relation using multiple data, taking into account a wide range of variable offshore conditions.Drennan et al. (2003) found Eq. ( 9) to be an improved roughness parameterization, especially for pure wind-sea, rough-flow, deep-water data.The parameterization was used by Bruneau and Toumi (2016) for the study of a fully coupled atmosphere-ocean-wave model for the Caspian Sea.
Almost simultaneously with Donelan (1990), Maat et al. (1991)  The parameters µ and n are equal to 0.8 and -1 respectively and are obtained from measurements of the HEXOS campaign 9 km out of the Dutch coast (Katsaros at al., 1987).Based on the same measurements, Smith et al. (1992) found µ equal to 0.43 and n equal to -0.96.Even though both authors have different parameters, they agree that young waves are rougher than older ones.Other values for µ and n have been proposed by Monbaliu (1994), which used the HEXOS campaign and Vickers and Mahrt (1997) and Johnson et al. (1998), both using the RASEX campaign.Clearly, different sites result in different constants for the roughness parameterization.The approach of Drennan et al. (2003) combines different data sets from different measurement sites and obtains only one set of constants.
An alternative roughness parameterization was proposed by Taylor and Yelland (2001), which is based on the wave steepness, Eq. ( 11), where L p is the wave length at the peak wave spectrum.
To obtain this roughness parameterization three measurement data sets describing different sea states were used.This parameterization is used in coupled atmosphere wave models by Warner et al. (2010) and Bolaños et al. (2014).Warner et al.
(2010) used the new roughnesss parameterization by Taylor and Yelland (2001)  (11) but did not actively couple it to a wave model.Instead, the wave length and height of the roughness parameterization are estimated based on the 10 m wind speed assuming fully developed sea conditions.Drennan et al. (2005) compared the performance of the roughness parameterization of Taylor and Yelland (2001) and Drennan et al. (2003) on eight distinct data sets corresponding to different sea states.This comparison resulted in a good performance of the roughness parameterizations for young waves, especially for the measurement data that were used to develop the parameterizations.However, these roughness parameterization performed poorly in regions of swell and Drennan et al.
(2005) proposed a more elaborated roughness parameterization including not only the swell magnitude but also the direction of the swell waves.The effect of the stress vector not aligned with the main wind, but somewhere between the wind direction and the wave direction was first described by Rieder et al. (1994).Additional roughness parameterizations were proposed by Janssen (1991), Fan et al. (2012) and Liu et al. (2011), all with a different focus (e.g., the later including sea-spray induced roughness).
The focus of this paper, however, will be on the influence of the difference between the direction of the waves and the wind on the roughness parameterization.While a wind-wave direction-based roughness parameterization has not yet been investigated, the importance of this effect has been proposed by Drennan et al. (2005) based on experimental observations.The importance of the swell direction has also been investigated by numerical simulations.Sullivan et al. (2008) performed Large Eddy Simulations (LES) and found that the drag of aligned swell waves is much smaller than that of opposed swell waves.
Likewise, Kalvig et al. (2013) 12), where θ is the angle between the wave direction and the wind speed.
Unfortunately, this new roughness parameterization is not finalized yet.For young wave ages, unrealistic dimensionless roughness values are obtained and the constant A is undefined.Additionally, this parameterization has only been tested on the results of LES simulations.A final shortcoming is that these simulations included only imposed waves and a one-way wind-wave interaction.As such, only the effects of the waves on the wind, were studied.Important here is that Drennan et al. (2003) and Patton et al. (2015) suggested that a new roughness parameterization should include the angle between the wind and the wave direction, consistent with the wind profiles obtained by the LES and RANS simulations of Sullivan et al. (2000) and Kalvig et al. (2013).In this study we investigate the presence, and impact, of a possible effect of the wind-wave alignment using offshore measurements.With these results we propose a new roughness parameterization, which will enable future research to improve the modeling of the transfer of momentum between the sea surface and the atmosphere, in particular for swell waves.
On a broader scope, this will result in a more correct representation of the wind-wave interaction in atmospheric and climate models.

Offshore field measurement data sets
The Forschungsplattformen in Nord-und Ostsee Nr.1 (FINO1) is one of the few offshore measurement platforms where measurements are simultaneously obtained for both atmospheric and oceanographic parameters.The measurement mast is located   the north nor by shallow water to the east and west.Moreover, directions between 0 • and 150 • are affected by flow distortions by the tower itself (Edson et al., 2007), resulting in wind shadow distortions.The ASIT tower is designed as a low-profile, fixed structure in order to minimize these flow distortions.Even though in theory no correction is required, it was decided to exclude measurements from the wind shadow region to ensure no wind shadow effect and for consistency in methodology.
The instrumentation of the ASIT tower is shown on Fig. 3 (C).In this study on wind-wave interaction, measurements from a Gill R3-sonic anemometer are used.These measurements are taken 18 m above sea level with a measuring frequency of 20 Hz. Fluxes of momentum and virtual heat are calculated for 20 minute averaging periods.Slow response measurements of air temperature, pressure and relative humidity are available from a vaisala RH/T sensor.The oceanic variables are obtained from the subsurface node (Fig. 3 (B), point B) located 1.5 km south of Martha's Vineyard at 12 m depth.Wave characteristics, such as significant wave height and peak wave direction are measured here.Even though the oceanographic data and the atmospheric data are not co-located, we assume that the marginal distance of 1.7 km and a water depth difference of 3 m are small enough to assume the same oceanographic features.Furthermore, the wind measurements are averaged over 20 minutes, a time period during which the wave conditions are not expected to change significantly.When comparing the slow response atmospheric measurements (wind speed, wind direction, temperature ...) between the meteorologic mast (Fig. 3 (B), point A) and the ASIT tower (Fig. 3 (B), point C), no significant differences have been noticed.For these reasons we assume that the ASIT measurements can be combined with the subsurface node to investigate the wave induced velocity changes.The same assumption was also made by Sullivan et al. (2008).No such exclusions were necessary for the FINO1 data.Additionally, the wind shadow zones resulting in flow distortion were excluded for both data sets.Moreover, wind speeds below 1 m/s were removed from the data sets, because in these conditions the uncertainty on the mean wind direction increases (Anfossi et al., 2005).These corrections resulted in a total of 74 108 measurements from both measurement masts.Combining observations from different locations, similar to the approach by Drennan et al. (2003), reduces the effect of site specific parameters and a more general form can be found.
An investigation of the dominant wind and wave direction for the two measurement locations is presented in Appendix A.
In this study the effect of the (mis)alignment between the wind and wave direction is of major interest.The histogram of the angle between the wind and wave direction is shown in Fig. 4. Wind-wave direction alignment (θ < 30 • ) occurs most of the time (32.77%), which means that a wind-wave equilibrium is present.However, as can be seen from Fig. 4, there is significant probability of occurrence of misalignment events of different degrees, while opposed wind and wave directions (θ > 150 • ) is a less frequent scenario (7.58%).This behavior is seen for both FINO1 and ASIT measurements.
In order to validate the ASIT and FINO1 measurements against the existing roughness parameterization of Drennan et al. (2003), we processed the data following Drennan et al. (2005).The choice of the parameterization of Drennan et al. (2003) as a starting point comes from the fact that Patton et al. (2015) already set the first step in improving this roughness parameterization based on their simulations.Moreover, the law of Drennan et al. (2003) is already implemented in recent models (Bruneau and Toumi, 2016) and can be easily incorporated in other coupled wave-atmosphere models (Warner et al., 2010).A first step required is the calculation of the friction velocity (Eq.( 13)), which is based on the measured alongwind, < w ′ u ′ >, and crosswind, < w ′ v ′ > kinematic momentum fluxes (Phillips, 1977).For the ASIT measurement tower these velocity flux measurements where calculated using the eddy correlation technique with an averaging period of 20 minutes and were already available.For the FINO1 measurement campaign of 2010 the flux measurements where processed by Muñoz-Esparza et al. ( 2012), also using the eddy correlation technique and averaging over 30 minute periods, and with the averaging time determined from an Ogive analysis.For the additional FINO1 measurement campaign of 2015-2016 only the raw data were available.The fluxes for this data set were calculated using the eddy correlation technique implemented in EddyPro© (v 6.2.1; standard settings) and averaged every 30 minutes, consistently with the FINO1 2010 data set.This software is extensively used in atmospheric sciences (Mammarella et al., 2016;Fratini and Mauder, 2014).
The aerodynamic roughness, z 0 , is calculated from the logarithmic wind profile assumption shown in Eq. ( 14), where κ is the von Karman constant, U z is the corrected wind speed and U 0 is the surface drift speed.The latter is small and assumed to be zero.
The corrected wind speed, U z , is calculated based on Eq.( 15), where U z0 is the wind speed at a height of z m above sea level and ψ u is the integrated stability function according to Barthelmie (1999).
In order to find the integrated stability function, ψ u , the stability of the atmosphere should be classified in stable and unstable atmospheric conditions.This distinction is made based on the Obukhov length (Eq.( 16)), where θ v is the virtual potential temperature and < w ′ θ ′ v > is the virtual potential temperature flux (Donelan, 1990).For the ASIT measurements, the latter is directly available from the measurements and averaged over 20 min intervals while the former is calculated based on the Clasius-Clapeyron relation, employing the relative humidity and the pressure.For the FINO1 measurements both the virtual potential temperature as well as the virtual potential temperature flux were computed by Muñoz-Esparza et al. (2012) or directly available as output from the EddyPro© software.
The classification of the atmosphere in different stability classes according to Wijk et al. (1990)  measurement mast unstable conditions are often present due to cold air advecting above the much warmer ocean, this is consistent with other locations in the North-Sea (Patton et al., 2015;Barthelmie, 1999).However, for the ASIT measurement mast stable conditions do occur often in late spring to early summer when the ocean is slowly warming by warm ocean water flowing over the colder ocean, typically identified with cool summer weather and fog (Edson et al., 2007;Crofoot, 2004).The integrated stability function can be calculated by Eq. ( 17) for stable conditions (L > 0) and by a combination of Eq. ( 18) and Eq. ( 19) for unstable conditions (L < 0) (Barthelmie, 1999).

Results and discussion
To validate the roughness law of Drennan et al. (2003), the dimensionless roughness, z 0 /H s , is plotted against the inverse wave age parameter u * /c p (Fig. 5).The curve proposed by Drennan et al. (2003) performs well in regions of young waves, however, for swell dominated seas (low u * /c p ) the proposed roughness parameterization performs poorly.This indicates that the roughness of swell waves is not only dependent on the wave age, but also on other parameters, like the orientation between the propagation of the waves relative to the wind direction, as it will be demonstrated in the next section.
While Drennan et al. (2003) improved the roughness parameterization by including wave age and taking into account multiple measurement sites, one major drawback remained.As the (mis)alignment between wind and waves was not considered, even though research has shown that this might be important (Grachev et al., 2003;Drennan et al., 2003;Sullivan et al., 2008; 11  .Kalvig et al., 2013;Patton et al., 2015).In order to see if there is an effect of the (mis)alignment of the wind-wave direction, the dimensionless roughness is divided into six groups based on the degree of alignment.The alignment is calculated by taking the absolute value of the difference in direction between the wave and wind propagation.The frequency of measurement points in each of these groups is shown in Table 2; 0 • corresponds to waves traveling in the same direction as the wind, while 180 • corresponds to waves traveling opposed to the wind direction.Comparing the probability density function of the dimensionless roughness of these six groups (Fig. 6), it is found that the dimensionless roughness increases for increasing misalignment.
This finding is confirmed by an analysis of variance statistical test where we tested if there were differences between the group means.All alignment groups showed that they significantly (p-value < 0.05) differ from each other, except the group of 120 • -150 • which did not show a significantly different (p-value > 0.05) behavior to the group of 150 • -180 • .
Previous studies not only predicted that roughness depends on the degree of (mis)alignment, they also implicated that the effect of reduced roughness is more pronounced for swell waves aligned with the wind compared to young waves aligned with the wind, due to a reduced shear stress.This reduction in shear stress should thus be more pronounced at higher wave ages.To investigate this effect, the inverse wave age parameter is subdivided in three bins, bin 1 corresponds to 2 • 10 −2.75 < u * /c p ≤ 2 • 10 −2.15 , bin 2 to 2 • 10 −2.15 < u * /c p ≤ 2 • 10 −1.9 and bin 3 to 2 • 10 −1.9 < u * /c p ≤ 2 • 10 −1 .These bins are obtained in such a way that the same amount of measurement points is present in each bin.The results indicate that the reduced roughness for aligned wind and wave direction is more pronounced at low inverse wave age numbers (swell waves, bin 1), while for Table 2. Frequency measurement points in each alignment section and the dimensionless roughness corresponding to the maximum probability for each section, for the combined ASIT and FINO1 data set. .high inverse wave age numbers (wind waves, bin 3) the difference between the roughness parameters is less distinct (Fig. 7).
This can be explained by a stronger difference in momentum flux for swell waves that are aligned or opposed, compared to conditions of young waves.
It can therefore be concluded that the roughness is dependent on the alignment between the wind and the waves and more specifically that the roughness increases with increasing misalignment.This effect is more pronounced for old waves.Therefore 5 we propose a new roughness parameterization formulated by correlating the dimensionless roughness against the inverse wave age parameter.This is done for six groups of different degrees of (mis)alignment (0  Bins containing less than 100 data points were excluded.This happened mostly for bin 5.The new roughness parameterization is then developed in such a way that the mean difference of the fit of the (logarithmic) bin means and the new parameterization is as small as possible.The formula for the new roughness parameterization taking into account the alignment between the wind and the wave direction is shown in Eq. ( 20) and its performance is shown in Fig. 8.In this equation the angle is expressed in radians.For the exponential term a cosine function is used in agreement with Patton et al. (2015).Similarly, a cosine function is also used for the constant term for consistency between both terms.
The law of Drennan et al. (2003) under-performs for different degrees of alignment, in particular for increasing degrees of misalignment between the wind and wave direction.A negative bias is even more prominent for swell waves.These results show 10 that the dimensionless roughness is influenced by the degree of (mis)alignment.As such, they confirm that a new roughness parameterization is justified.This is also clear in Fig. 9, where the two parameterizations are compared.The roughness based on Drennan et al. (2003) is independent on the angle between the wind and wave direction (Fig. 9 (A)), while this is not the case for the new proposed roughness parameterization.Here (Fig. 9 (B)) we can see, that the roughness, for a constant wave age, increases with increasing misalignment between the wind and wave direction.This effect is less pronounced for younger sea states (log(u * /c p ) > −1), with almost no effect of the misalignment on the roughness.Looking at the difference in roughness prediction between the parameterization of Drennan et al. (2003) and the new roughness including the misalignment of the direction between the wind and the waves, Fig. 9 (C), the effect of increasing roughness is clear for increasing inverse wave age and increasing misalignment between the wind and wave direction.The measurements of FINO1 and the ASIT measurement tower, Fig. 9 (D), show that the increase of roughness with increasing misalignment is weak in the case of swell waves.
These results confirm that the new parameterization appears to be a good fit for different degree of (mis)alignment.More specifically, the slope of the curve is decreasing with increasing misalignment, indicating that more misaligned waves result in 10 an increased roughness.Moreover, as the difference between the new parameterization and the one from Drennan et al. (2003) is most obvious for lower inverse wave ages, the effect of misalignment on roughness has more impact on swell waves.This is expected, as young waves are wind generated and thus are more likely to be aligned a priori.processes occurring in the MABL are adequately described.This leaves room for future improvements, e.g. by including additional parameters.Liu et al. (2011) found that sea spray, again an interplay between wind and wave, also influences the roughness.Furthermore, not only sea spray but also wave steepness of swell waves alter the momentum transfer between the sea and the atmosphere, which in turn influences the roughness.The wind stress decreases if the swell steepness increases (Ocampo-Torres et al., 2011).In fact, García-Nava et al. ( 2012) proposed a new roughness parameterization which includes both the effect of the wave age and the swell steepness on the roughness parameter.Unfortunately, the swell height and sea spray information were not available for our measurement sites.As such, future work could investigate the combined effect of wind-wave misalignment and the effect of sea spray and swell steepness in order to further improve the roughness parameterization.Additionally, more measurement locations should be included in the analysis, in order to reduce the site specific parameters even further.

Conclusions
In this study we combined two large data sets to investigate the influence of the (mis)alignment between wind and wave direction on the momentum transfer between the sea surface and the atmosphere.We identified a clear difference in roughness between aligned and opposed wind and wave directions.So far, no roughness parameterization had been proposed that includes this discrepancy.We used multi-year data from FINO1 and ASIT sites to define a new roughness parameterization that performs better than state-of-the-art parameterizations.
This new roughness parameterization will aid in micro-and meso-scale meteorological models.Indeed, the new roughness paremeterization can easily be implemented in atmospheric models such as COAWST and WRF (Warner et al., 2010;Skamarock et al., 2008).These implementations in mesoscale and microscale atmospheric models can then be used for wind energy assessment studies, estimating the dynamic loads and fatigue as well as the wind turbine wakes, the design of the wind turbine and ultimately the operation of the wind farm (Zeng et al., 1998;Powers and Stoelinga, 2000;Temel et al., 2018).On a larger scale this parameterization is expected to contribute to a better understanding of global wind and wave climates, and global climate change studies in general (Drobynin et al., 2012).While the direct benefits of the new parameterization might seem limited to wind engineering and climate applications, it is also important for a wide range of other applications ranging from the parameterization of optical turbulence over sea, where the vertical fluxes within the surface layer might vary with  respect to the wave formations (Frederickcson et al., 2000) to planetary science applications to determine the meteorological conditions for extra-terrestrial atmospheres interacting with lakes, as is the case for Titan (Mitri et al., 2007;Hayes et al., 2013).Moreover, wind-wave equilibrium often occurs at higher wind speeds than opposed wind-wave directions (Fig. A3).The waves traveling opposed to the wind direction with a lower wind speed are mostly remotely generated swell moving towards the measurement tower.

Figure 1 .
Figure 1.Schematic of the wind-wave interactions, upward momentum transfer to the atmosphere or negative shear is possible in case of swell waves.Swell waves are generated by non local wind and can travel long distances.Local winds further influence swell waves, but can also produce wind waves through downward momentum transfer.In atmospheric models, a parameterization of the aerodynamic roughness is used to represent all these processes.
in the Coupled Atmosphere Ocean Wave Sediment Transport (COAWST) model.This model couples the WRF atmospheric model with the SWAN wave model by using Eq.(11) as a boundary condition for the atmospheric model.To enable this, the wave length and wave height obtained by the wave model are passed on to the atmospheric model.Bolaños et al. (2014) used the roughness parameterization shown in Eq.
looked into the wave wind alignment applying the Reynolds-Averaging Navier-Stokes (RANS) Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-726Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 29 August 2018 c Author(s) 2018.CC BY 4.0 License.equations and found that swell waves opposed to the wind can ensure reduced and even reversed wind speeds in the lowest meters.LES investigations by Patton et al. (2015) found that the wind speed at hub-height of wind turbines can decrease by 15% for opposed wind-wave alignment compared to aligned cases, with turbulence intensities increased by a factor two for opposed cases.All these numerical modeling efforts indicate that the correct representation of the momentum fluxes between the sea surface and the atmosphere, and thus a good roughness parameterization, are of crucial importance.An attempt for a new roughness parameterization was made by Patton et al. (2015) based on their LES results, including the effect of the alignment between the wind and waves.This parameterization is based on Drennan et al. (2003) and shown in Eq. ( in the North Sea, 45 km north of the coast of Borkum Island, Germany.The exact coordinates of the mast are N 54 • 0'53.5"E 6 • 35'15.5"as shown on Fig.2 (A).The measurement tower is exposed to an unlimited fetch area for northwesterly to north wind directions, while in the other directions it is fetch limited due to coastal presence of the Netherlands, Germany and Denmark.The measurement mast itself extends 100 m above mean sea level and the mean water depth at this specific location is 30 m. Measurements are continuously collected since 2003.The measurement mast is equipped with different sensors to measure wind speed and direction, air and sea temperature and air pressure and humidity.Cup anemometers measure the velocity at33, 40, 50, 60, 70, 80, 90  and 100 m while sonic

Figure 2 .
Figure 2. (a) Location of the FINO1 measurement mast in the North Sea.(b) View of the FINO1 measurement mast and the location of the two sonic anemometers used to obtain the new roughness parameterization (Modified from Muñoz-Esparza et al. (2012)).

Figure 3 .
Figure 3. (a) Location of the ASIT measurement mast in the Atlantic Ocean.(b) Location of the ASIT measurement mast compared to Martha's Vineyard, point A is the meteorological mast, point B is a subsurface node and point C is the ASIT measurement tower (c) ASIT measurement tower.

Figure 4 .
Figure 4. Probability density function (PDF) of the angle between the wind and wave direction for both ASIT and FINO measurements.

3. 2
Data selection and processing From the 2003-2012 period, the measurements of 2005, 2009 and 2012 of the ASIT mast were excluded, because they did not contain high resolution velocity and temperature measurements coupled with the simultaneously occurring wave parameters.

Figure 5 .
Figure 5. (a) The dimensionless roughness, z0/Hs, plotted against the inverse wave age parameter u * /cp for the combined data set of 74 108 points (ASIT and FINO1).The solid line represents the roughness parameterization proposed by Drennan et al. (2003), Eq. (9).The color scale to the right indicates the probability of occurrence (%) of the measurement points.(b) The root mean square error of the measurement points compared to the parameterization proposed by Drennan et al. (2003).

Figure 6 .
Figure 6.Probability density function of the dimensionless roughness parameter for six different alignment groups, from aligned to opposed cases for the combined ASIT and FINO1 data set.

Figure 8 .
Figure 8.The dimensionless roughness is plotted against the inverse wave age parameter for six different groups of alignment for the combined ASIT and FINO1 date set.In each figure the data are bin-averaged, with the bin means (logarithmic) indicated by black dots.The solid black line represents the roughness parameterization proposed by Drennan et al. (2003), the dotted red line is the fit through the bin averages and the dashed red line is the new proposed roughness parameterization.The color scale to the right indicates the probability of occurrence (%) of the measurement points.
Atmos.Chem.Phys.Discuss., https://doi.org/10.5194/acp-2018-726Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 29 August 2018 c Author(s) 2018.CC BY 4.0 License.Note that no precipitation filter was applied on the sonic anemometer measurements, even thoughZang et al. (2016) suggested to correct the sonic temperature in case of precipitation.An analysis on the FINO1 measurements of the year 2010 was done in order to investigate if the new proposed roughness parameterization would have a systematic bias due the presence of measurements influenced by precipitation, as applying a precipitation filter to the ASIT data was not possible (Appendix B).This precipitation analyses showed no significant influence of precipitation on the new z 0 /H su * /c p relation.This new roughness parameterization, including the alignment of the wind and wave direction, reduces the scatter around theDrennan et al. (2003) parameterization considerably.The remaining scatter indicates, however, that not all relevant physical

Figure 9 .
Figure 9. (a) Dimensionless roughness parameter in function of the inverse wave age and the alignment between the wind and wave direction according to Drennan et al. (2003).(b) The new proposed dimensionless roughness parameter in function of the inverse wave age and the alignment between the wind and wave direction.(c) The differences in roughness between the law of Drennan et al. (2003) and the new proposed roughness parameterization in function of the inverse wave age and the alignment between the wind and wave direction.(d) Dimensionless roughness for the measurements of FINO1 and ASIT as a function of the inverse wave age and alignment between the wind and wave direction.

Figure A1 .
Figure A1.On the left side the wind rose excluding the wind shadow zones at z=18 m, while on the right the peak wave direction is shown.Data corresponding to the ASIT measurement mast (65 128 measurement points) during the 2003-2012 period.

Figure A2 .
Figure A2.On the left side the wind rose excluding the wind shadow zones at z=40 m or z=15 m depending on the measurement campaign, while on the right the peak wave direction is shown.Data corresponding to the FINO1 measurement mast during the year 2010 for z=40m (5 470 measurement points) and 2015-2016 for z=15 m (3 510 measurement points).

Figure A3 .
Figure A3.Wind speed probability density function (PDF) for aligned wind-wave direction and opposed wind-wave direction, for the ASIT measurement mast.

Figure B1 .
Figure B1.The dimensionless roughness is plotted against the inverse wave age parameter for six different groups of alignment.In each figure the data are bin-averaged, with the bin means (logarithmic) indicated by black stars.While the bin means of the measurement data excluding the precipitation measurements are indicated by red stars.The color scale to the right indicates the probability of occurrence (%) of the measurement points.
suggested that the Charnock parameter should be function of the wave age and proposed Eq. (10) for the Charnock parameter.

Table 1 .
Stability classification based on Obukhov Length, L, for the combined ASIT and FINO1 data set