Journal of Geophysical Research: Oceans

Introducing surface waves in a coupled wave-atmosphere regional climate model: Impact on atmospheric mixing length


Corresponding author: A. Rutgersson, Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36 Uppsala, Sweden. (


[1] The marine atmospheric boundary layer is strongly influenced by the moving surface in the presence of surface waves; the impact depends on the wave conditions and the interaction with the atmosphere. Previous studies using measurements as well as numerical simulations with large-eddy simulations have shown that surface waves propagating faster than the wind (swell) alter the surface exchange as well as turbulence properties in the atmosphere. This impact is here introduced in a coupled wave-atmosphere regional climate model with a so-called E − l turbulence scheme (where E is the turbulent kinetic energy and l is a mixing length). A wave age dependent coefficient (here called Wmix) is added to the mixing length in the turbulence parameterization. This acts similarly to inducing additional convection, with larger mixing length and increased eddy diffusivity, when we have near neutral stratification and strong swell. For shallow boundary layers the regional coupled climate model shows a larger response to the introduced wave coupling with increased near surface wind speed and smaller wind gradient between the surface and middle part of the boundary layer. The impact for the studied areas is relatively minor for parameters averaged over 1 year, but for limited periods and specific situations the impact is larger. One could expect a larger impact in areas with stronger swell dominance. We thus conclude that the impact of swell waves on the mixing in the boundary layer is not insignificant and should be taken into account when developing wave-atmosphere coupled regional climate models or global climate models.

1. Introduction

[2] To study the climate system it is common to use global climate models (GCMs) with relatively coarse resolution and to do dynamical downscaling by regional climate models (RCMs) for more detailed studies of regional variations. For a comprehensive study of the climate its variations and changes it is important to include relevant couplings, feedbacks and interaction between processes. This study motivates the necessity to include impact of waves on the atmosphere, specifically wave effects on turbulence mixing length. In atmosphere models it is of crucial importance to describe the conditions at the lower boundary correctly. The ocean surface has a considerable impact on the atmosphere; globally about 70% of the surface is covered by water. The atmosphere-ocean interface is a source of turbulence in the atmosphere as well as in the ocean, and significant exchange of momentum, heat and moisture take place there. A major difference between the atmospheric surface layer over the ocean compared to over land is the presence of surface gravity waves, the surface changes as a direct response to the atmospheric forcing. Surface gravity waves (hereafter designated waves) are mainly generated by the wind; the wavefield is thus dependent on the wind field. Surface waves can be divided into growing sea (young sea) and decaying sea (swell) with very different impact on the atmosphere. The high wind speed situations connected with intense atmospheric synoptic scale weather systems along the mid to high latitudes are the major wave generators. Waves propagate as swell over long distances with very little attenuation. In order to describe the wavefield it is not enough to know the local wind, since also waves that propagated from other areas are of importance. Global wave climatologies show a significant dominance of swell waves for most global oceans [Hanley et al., 2010; Semedo et al., 2011].

[3] To be able to describe the wavefield in a changing climate, an accurate description of the atmospheric conditions and the impact of waves on the atmosphere is needed.

[4] Previous studies using wave–atmosphere coupled models were mostly developed for wave and weather forecasting purposes [e.g., Doyle, 1995; Lionello et al., 1998; Desjardin et al., 2000; Järvenoja and Tuomi, 2002; Jansen et al., 2002].

[5] There are, however, only few previous studies focusing on the impact of waves on regional or global models used for climatic timescales. The impact of a wave dependent momentum transfer on the seasonal climate in the European Centre for Medium Range Weather Forecasts (ECMWF) model showed improvements in the coupled model of global circulation patterns and a reduced mean surface wind [Jansen and Viterbo, 1996]. In these previous studies the focus was on changes in surface friction for growing sea conditions. Carlsson et al. [2009] showed (using data from the Baltic Sea) that the drag coefficient attains different values for growing sea and swell conditions.

[6] An atmosphere–wave coupled modeling system is being developed to describe the atmospheric forcing of the waves as well as to include the feedback effects of the waves on the atmosphere. In Rutgersson et al. [2010] a dynamical downscaling of ERA40 was done using wave-atmosphere coupled RCM for northern Europe, an impact on several atmospheric parameters were shown. When only introducing wave dependent surface roughness for growing waves, near surface wind and fluxes were reduced, but when also including a reduction of surface roughness due to swell waves (as was suggested by Carlsson et al. [2009]) surface winds and fluxes were instead increased. Also significant impact on secondary parameters occurred, for example, increased cloudiness and precipitation over sea.

[7] In a number of studies, using data from several sites [Edson et al., 2007; Donelan and Dobson, 2001; Miller et al., 1997; Rieder et al., 1994; Rutgersson et al., 2001; Smedman et al., 1994, 1999, 2009] it is shown that swell waves form a complex forcing on the atmosphere, since the state of the waves influences not only surface stress but also the turbulence in the atmosphere and atmospheric wind gradients. Field measurements and large-eddy simulations (LES) have indicated that swell waves can influence mean wind profiles as well as the turbulent exchange of momentum [Sullivan et al., 2008; Smedman et al., 2009; Nilsson et al., 2012]. One indirect effect of strong wind-following swell on slightly convective boundary layer winds is that the mean wind speed has been found to vary little with height in the region above the surface layer (outer region). In the surface layer instead a sharp wind gradient near the surface is formed. These observed features are qualitatively similar to how winds typically vary within a boundary layer dominated by convection, when horizontal momentum in the outer region becomes well-mixed by energetic large-scale turbulent motions.

[8] Nilsson et al. [2012] showed that the integral length scale of the vertical wind component (w) was influenced when swell wave forcing was introduced, resulting in increased length scales, this gives (as in the case of convection) a more effective mixing in the boundary layer. There are still gaps in the knowledge on wave–atmosphere interaction, in this study we suggest that the wave impact on turbulence mixing length in the Marine Atmospheric Boundary Layer (MABL) should be introduced in regional and global climate models. In addition we investigate the potential impact on climate model simulations.

[9] The coupled system used is similar to what is described in Rutgersson et al. [2010] and is based on the Rossby Centre regional climate model (RCA), and on the third generation wave model WAM. The coupled model system is forced at the lateral boundaries with the ECMWF ERA-40 re-analysis data, representing the present climate to evaluate the method of coupling and the impact of introducing a two-way coupled system on atmospheric as well as on wave parameters.

[10] Changes in mixing length formulation are introduced to account for increased turbulence length scales in neutral and near neutral conditions due to swell waves inducing turbulent motions that act similar to convectively induced motions [Nilsson et al., 2012]. The results from these changes will serve as a first indication on what impact wavefield modified mixing lengths can have on modeling regional climate with a wave-atmosphere coupled system.

[11] In section 2 the background for introducing wave impact on turbulent mixing are presented. Section 3 describes the models, as well as methodologies to introduce the wave dependent mixing length. In section 4 a first analysis of the impact on atmosphere and wave parameters for a 1 year simulation are shown.

2. Impact of Swell Waves on the Turbulence Mixing Length in the Atmosphere

[12] In Sullivan et al. [2008] and Nilsson et al. [2012] influence from swell waves with neutral stratification (no surface heating) as well as more convective conditions were investigated using large eddy simulation. The LES from Sullivan et al. [2008] have also been used in previous studies to investigate and interpret observed air-side wave-atmosphere interaction [Edson et al., 2006, 2007] in the low-wind/fast-wave regime, where it has been demonstrated to qualitatively reproduce many flow features observed in the marine atmospheric surface layer.

[13] The computional domain (1200, 1200, 800) m was in Sullivan et al. [2008] and Nilsson et al. [2012] discretized using (Nx = 250, Ny = 250, Nz = 96) grid points to have high enough resolution to resolve a two-dimensional waveform (with wavelength λ = 100 m and wave slope ak = 0.1). This boundary condition represents an idealized swell wave moving at a phase speed c = 12.5 m s−1. The moving wave at the lower boundary was shown to influence turbulence statistics (variances and vertical momentum flux) as well as mean wind profiles [Sullivan et al., 2008]. In Nilsson et al. [2012] a wider range of convectively stratified conditions and wind-following swell was investigated and it was shown that the integral length scale of w was influenced when swell wave forcing was introduced, resulting in increased length scales in near neutral conditions in comparison to simulations corresponding to flat terrain.

[14] The numerical simulations from Nilsson et al. [2012] are here further analysed, focusing the scale of the most energetic turbulent w-eddies by calculating the spectral length scale of the vertical velocity component, following Cuxart et al. [2000]. Two-dimensional Fourier energy spectra have been calculated for each grid level from previously archived 3-D volumes stored for the last 3 hours of each simulation [Nilsson et al., 2012]. These spectra are functions of the horizontal wave number vector kh = inline image, inline image. The energy content at different horizontal wave numbers has been evaluated by averaging over circular rings at constant inline image and over time [Sullivan and Patton, 2011]. An approximation to the Fourier transform on a discrete grid ranging from inline image to inline image in steps of inline image and similarly for ky was used.

[15] In Figure 1 we show vertical profiles of the scale at which the pre-multiplied energy spectra attains its maximum value for neutral (Figure 1a), slightly convective (Figure 1b) and moderately convective conditions (Figure 1c). Here z is the nominal height above the surface waves, zi the height of the boundary layer and L the Monin-Obukhov length. From Figure 1 we note that swell waves have a clear impact on the length scales near the surface. The most energetic eddy scale near the surface is for our swell simulations (red) located at the scale of the swell wave which has a wavelength of 100 m. Field measurements from the Rough Evaporation Duct (RED) Experiment on the R/P FLIP that took place from late August to mid-September 2001 at a site 10 km NE of the island of Oahu, Hawaii, also show that much of the near-surface wind variances are explained by wave-induced motions located at the swell peak frequency range (U. Högström, personal communication, 2012).

Figure 1.

Vertical profiles of spectral lengths of the vertical velocity component are shown for (a) neutral, (b) slightly convective, and (c) moderately convective conditions, with dotted lines denoting non-smoothed median values and full lines denoting mean values. Swell cases (FN1, FC1, and FC4 from Nilsson et al. [2012]) with atmospheric stability values zi/L equal to (0, −1.0, and −17.3) are shown in red. Flat terrain cases (ZN1, ZC1, and ZC3) with zi/L equal to (0, −2.1, and −15.1) are shown in black.

[16] For neutral (Figure 1a) and slightly convective conditions (Figure 1b) we note from LES that length scales are increased in mid-boundary layer for swell cases (red) in comparison to flat terrain (black). This was in Nilsson et al. [2012] explained by directly wave induced and detached turbulent motions which are present flow features in these strongly swell dominated simulations. Due to the limited domain size it was not possible to make a quantitative prediction of the actual scale of the most energetic eddies, but qualitatively they vary similar to length scales for more convective conditions and flat terrain [i.e., Khanna and Brasseur, 1998]. Cuxart et al. [2000] also discussed that a height variation with a maximum near mid-boundary layer is similar to how mixing lengths are prescribed for the mixed layer in boundary layer parameterizations. Following Cuxart et al. [2000] we interpret the LES results to suggest that wave induced motions can lead to a considerable mixing and organization of the turbulence into large-scale energetic eddies in near-neutral conditions.

[17] For more moderate levels of convection (Figure 1c) with higher turbulence intensity the scale of the swell wave (100 m) is only recognized as the most energetic eddy scale up to about half the height in comparison to neutral conditions. The height is decreasing with increasing surface heating. In Sullivan et al. [2010] it is discussed that in swell conditions with increased turbulence levels due to increased wind speed the coherence of wave-induced near surface pressure signals and turbulent fluctuations of the vertical wind component becomes destroyed by strong turbulence. The LES results presented here and in Nilsson et al. [2012] indicates that also increased turbulent mixing and turbulence intensity due to increased surface heat flux forcing can act to destroy the wave induced signals. Large, mutually weakly correlated fluctuations in the u- and w- components during low wind speed conditions in the RED experiment are also interpreted to be due to strong streamline displacement of the air flow caused by the proximity of swell waves. For higher wind speed the streamline displacement is shown to be reduced. Increased turbulent mixing is likely responsible for destroying this wavefield signature in the air flow. Wind variances located at or near the peak of the swell in the field data from the RED experiment were found to fall off almost exponentially with height.

[18] The length scales in moderately convective swell conditions is shown in Figure 1c to be somewhat reduced in the outer region in comparison to the flat terrain case. This could possibly be an artifact of our limited domain size influencing the evolution of the mixed-layer rolls that occur in such conditions [see Nilsson et al., 2012, Figure 5]. It could, however, also be that turbulence structure is altered by swell during convective stratification causing less organization of wind eddies into elongated regions oriented in the mean wind direction during wind-following swell in comparison to flat terrain and growing sea [Högström et al., 2008; Nilsson et al., 2012]. Close to the surface the dominant air motions are however related to the characteristics of the wavefield in all simulations with an increase in TKE in comparison to the cases with no waves. Hence we recognize that also adopting a length scale formulation similar to that of Teixeira and Cheinet [2004] which directly relates the mixing length to the square root of the turbulent kinetic energy would lead to an increase of the near surface mixing length in cases of swell.

[19] At higher z-levels, where the directly wave-induced motions tend to interact and get mixed up with background turbulence, LES for wind-following swell shows reduced turbulent kinetic energy in comparison to flat terrain consistent with having reduced turbulence production from reduced wind shear [Nilsson et al., 2012]. For wind-opposing swell instead LES has indicated greatly increased TKE-levels in comparison to simulations of no waves throughout the entire boundary layer [Sullivan et al., 2008, Figure 13]. The question if swell introduces reduced or increased turbulent mixing in the outer region can be considered as a struggle between how much variance and TKE the near-surface wave-induced motions contain and what the indirect effects of the changed turbulence structure during swell are. In the case of wind-opposing swell LES indicates that also the indirect effects of swell can increase TKE in the outer region, but for wind-following swell instead the reduced wind shear in the outer region can decrease TKE production. The direct effect of the swell waves which occurs in the surface layer appears to always act to increase wind variance (especially for the longitudinal and vertical wind component) thereby increasing the near surface TKE. This motivates us to introduce wave-modified increased mixing lengths during swell.

[20] A more complete length scale formulation for the atmospheric boundary layer will need to entail both surface characteristics as well as parameterizations of upper and internal boundary layer dynamics since stably stratified layers are well-known to reduce variances and mixing lengths. [Teixeira and Cheinet, 2004, p. 437] also recognizes that “…there is no such thing as a mixing length formulation that is robust, flexible and simple enough to allow for a realistic simulation of the variety of convective boundary layers that occur in the Earth's atmosphere.” The current study provides a way to introduce some of the influence that swell waves have on mixing lengths.

3. Models and Coupling Method

3.1. RCA

[21] The atmosphere model RCA is developed at SMHI (Swedish Meteorological and Hydrological Institute), the domain used in this study covers Europe (see Figure 2). The RCA version 3 is used, it is a hydrostatic model, with terrain-following coordinates and the calculations are semi-Lagrangian, semi-implicit and with 15 or 30 min time step depending on the resolution. Two horizontal resolutions are used (c. 22 and 44 km) and 24 vertical levels is used between about 90 m above the surface and 10 hPa. For the present study no climate model is used for the atmospheric boundary forcing to the RCA (for present or future climate), but re-analysis data from ERA-40 [Uppala et al., 2005]. The ERA-40 data is also used for information about sea surface temperature and ice cover. The ERA-40 data is the ECMWF re-analysis and uses all available observations integrated into a 3-D model to give the best possible global gridded data base on atmospheric parameters. The purpose of using re-analysis data is to evaluate the coupled model, and investigate the impact on the atmosphere as well as on the wavefield when introducing wave effects on the mixing in the atmosphere. For more details on the RCA model, see Jones et al. [2004]. Four regions are investigated in more detail, dotted areas in Figure 2, representing areas in the Baltic Sea, Mediterranean, the North Sea and the Atlantic.

Figure 2.

Dotted line shows the model domain for regional climate model (RCA) and third generation wave model (WAM) used in the present study. Dotted areas represent the four selected areas investigated in detail (the Baltic Sea (BS), the North Sea (NS), Atlantic (AT), and Mediterranean (MT)).

3.1.1. Mixing Length Formulation

[22] We modify the mixing length parameterization presently used in RCA [Lenderink and de Rooy, 2000; Lenderink and Holtslag, 2004] to introduce the impact of waves.

[23] The turbulence scheme is a so-called E-l scheme (where E is turbulent kinetic energy and l a diagnostic length scale) to compute eddy diffusivity coefficients. As in general E-l schemes, the equation for E is prognostic and the prescription of the diagnostic length scale, l, is rather empirical. The scheme is based on the CBR scheme [Cuxart et al., 2000] using the parcel method by Bougeault and Lacarrere [1989]. The method uses mixing length as a function of the local stability, but also non-local effects are included. This is very important for convective situations (as well as when introducing wave effects as in the present study). The CBR scheme has previously been adjusted to reduce mixing in near neutral conditions as described in Lenderink and de Rooy [2000].

[24] The basis of a E − l scheme is the E-equation [see, e.g., Stull, 1989]:

display math

where P is the shear production, B the buoyancy production/consumption, T transport by turbulence and pressure forces and the dissipation is ϵ. Primed symbols denote turbulent quantities, θv is the virtual potential temperature and ρ the density. The shear production is expressed as:

display math

and dissipation by:

display math

where cd is a constant and Km is the eddy diffusivity for momentum, defined by:

display math

[25] In near-neutral to unstable conditions the final length scale is computed using a combination of two separate length scales, lup starting at the surface and ldown starting at the top of the mixing domain. The final length scale is given by

display math

These two length scales are defined as integrals over stability as:

display math

where F(Ri) is a function of the local Richardson number inline image, where zbottom and ztop are the lower and upper boundaries of the mixing domain. The following form for F(Ri) is used

display math

where αn, αc and αr are coefficients adjusting the equation in the neutral and convective limits. For very unstable conditions lup and ldown are given by the distance from the top and the bottom of the mixing domain, for more neutral conditions, both length scales are reduced.

[26] Figure 3a shows examples of l for very unstable and moderately unstable condtions, where dotted lines show ldown and lup for the two situations respectively. See Lenderink and de Rooy [2000] and Lenderink and Holtslag [2004] for a more detailed description of the turbulence formulation.

Figure 3.

Illustration showing the variation of length scale with height in the boundary layer. Thick solid lines represent near neutral conditions, thin solid lines represent very unstable stratification. In Figure 3a, only Ri-dependence is used; dotted line indicates lup and ldown. In Figure 3b, dashed lines show resulting length scales when introducing both stability and wave effects for near neutral (thick) and very unstable (thin).

3.1.2. New Mixing Length Formulation

[27] The impact of swell on mixing length is introduced mimicing the impact of convection on the lup and ldown mixing lengths for swell conditions and unstable atmospheric stratification. Swell conditions are assumed to be present when cp/u > 30, where cp is the phase velocity of the dominant wave (for deep water inline image, λ is the wavelength of the dominating waves) and u is the friction velocity of the atmosphere. For near neutral conditions swell introduces additional mixing in the boundary layer. When there is strong convection, buoyancy is expected to dominate and for stable conditions no impact of waves on mixing length is assumed. The wave impact is introduced by adding a wave-dependent term to the bottom up and top down length scales as:

display math

[28] Full wave impact is assumed for cp/u > 50 and in the range 30 < cp/u < 50 swell impact is expected to increase continously. Equation (7) is changed to introduce wave effect according to

display math

where Wmix is the additional mixing factor due to waves. For cp/u > 50 and near neutral conditions (−1 < Ri < 0) maximum Wmix is expected to occur, we choose maximum value Wmix = 0.5 for the present study. For (−1.5 < Ri < −1.0) Wmix decrease continously. Figure 3b shows examples of the mixing length with and without wave impact (dashed and solid lines respectively) for near neutral and very unstable conditions (thick and thin lines respectively).

[29] Figure 4a shows the mixing length at one position in the Atlantic basin (59.11°N, 18.96°E) and Figure 4b shows the difference between the original formulation and when wave impact is added. During unstable atmospheric stratification (upward surface sensible heat flux, seen in Figure 4d) and swell conditions (wave age is shown in Figure 4c) there is an addition to the mixing length, the resulting mixing length is in the figure increased by up to 20 m (Figure 4b).

Figure 4.

For 1 month of the simulation (July 1996), data from one grid point in the Baltic Sea basin are shown: (a) the mixing length (in m), (b) difference in mixing length (in m) when introducing wave impact (lwave minus lnowave), (c) wave age (solid thick line; thin lines show swell limits (cp/u = 30, 50)), and (d) surface sensible heat flux (in W m−2). Upward heat flux is positive.

3.2. WAM

[30] The wave model used in the coupled system is the third-generation full-spectral wave model WAM [Hasselmann et al., 1988; Komen et al., 1994], in which the wave spectrum is computed by integrating the so-called wave energy balance equation, without any prior restrictions of the spectral shape. The wave energy balance equation describes the evolution of the 2D wave spectrum (Fw(fα)) as the sum of the local wind input (Sin), wave dissipation due to wave breaking (Sds), nonlinear wave-wave interaction (Snl), and an additional term that accounts for energy loss due to bottom friction in shallow waters (Sbot):

display math

[31] Wind speed at 10 meters from RCA is used as input to the model. From the full 2-D spectrum, several integrated parameters, like the significant wave height, or mean wave periods, are computed. In WAM the wave induced stress, τw, is parameterized from the quasi-linear theory [Jansen, 1991]. At the surface the wave induced stress is related to the rate of change of wave momentum due to wind [Komen et al., 1994]. For simplicity, in the present study wave boundary condition at the domain boundaries are not included, since that would have almost no impact on the semi-enclosed basins (Baltic Sea and Mediterranean), it is assumed that the direct impact on the North Sea is limited, and can be assumed as negligible. The domain resolution of the wave model is coincident with the atmospheric model for both resolutions used in the study. The bottom topography was interpolated to each of the grid points.

3.3. Coupled System

[32] In Rutgersson et al. [2010] the same coupled system was used for investigating wave impact on surface roughness. Here we use the C1 coupling from Rutgersson et al. [2010] (one-way coupling concerning the roughness), but the wave age is used to modify the mixing length. The wave model is forced using wind speed at 10 m.

[33] Compared to the simulations in Rutgersson et al. [2010] we use finer horizontal resolution in the present study (22 km). Figure 5 shows mean significant wave height for four years of simulation using 22 and 44 km resolution. In general there are small differences in annual or monthly averages of parameters between simulations with 22 and 44 km resolution (only significant wave height is shown here). This is in contrast to earlier results by Jansen et al. [2002] where the forecast scores was shown to depend in a sensitive manner on the resolution of the atmospheric model in a coupled atmosphere-wave system. In Jansen et al. [2002] specific situations were investigated, here we look at the annual mean impact. There is however more spatially detailed structure of the wavefield using the finer resolution, this is particularly true for smaller basins and near coastlines.

Figure 5.

Mean significant wave height (SWH, in m) for four years using (a) 44 km and (b) 22 km horizontal resolution.

4. Results From the Coupled Model

[34] Figure 6 shows mean differences for the 1996 period of boundary layer height (MLH) and wind speed at 10 m (U10) when including impact on mixing length on waves or not (including waves, W1, minus control run, CR). There are differences between the two simulations over the sea. As annual averages the difference between the two simulations range between ±20 m and ±0.2 m/s respectively, for different regions.

Figure 6.

Mean difference between reference run and introducing wave impact (WI minus CR) for (a) boundary layer height (in m) and (b) wind speed at 10 m (in m s−1).

[35] Higher near surface winds generally corresponds to higher boundary layer heights and lower near surface winds to lower boundary layer heights, even though there are variation between the areas. The frequency of occurence fulfilling the wave impact criteria (cp/u > 50 and −1 < Ri < 0) varies significantly between the basins, with highest frequencies in the Atlantic and Mediterranean basins (Figure 7). This qualitatively agrees with Carlsson et al. [2009] showing higher frequency of swell cases in Mediterranean in comparison with the Baltic and North seas.

Figure 7.

Frequency of time steps fulfilling the criteria for introducing wave impact for the four basins in Figure 2.

[36] A shift in near surface wind of a few decimals of a m s−1 can seem to be of minor importance for climate purposes. When investigating in more detail the differences are, however, larger. Figures 8, 9, and 10 show MLH, U10, Uz4−z1 and Hs (significant wave height) averaged over MLH intervals for the CR simulation MLHCR. Uz4−z1 is the wind speed differences between the fourth and lowest model layer (corresponding to 750 and 90 m approximately). The gradient between the model layer closest to the surface (Uz1) and the fourth model layer (Uz4, representing the wind in the central part of the boundary layer), indicates the wind gradient. In Figures 810 only data fulfilling the full wave-impact criteria is included (cp/u > 50 and −1 < Ri < 0). It is clear that the impact of introducing wave effects on the mixed layer height is larger for situations with low MLH, there is an increase in MLH for all these three areas when MLHCR < 300 m. For situations fulfilling the wave impact criteria the mean wind speed is generally low (mean wind is significantly below 5 m/s), for low MLH all areas show an increase in U10 when including wave effects on mixing length. For some MLH intervals the increase exceeds 0.5 m s−1, this effect is larger for the smaller basins (BS and NS). In particularly for NS (being the basin with the lowest frequency of swell conditions with near neutral stratification) the increase in near surface winds for low MLH and direct wave impact is compensated by indirect wave effects giving decreasing winds in situations when the wave criteria is not fulfilled. For all the investigated basins the mean difference in wind speed between the lowest model layer and the fourth model layer decreases when including wave effects (Figures 8c, 9c, and 10c). This is most clear for the lower MLH and smaller basins. This agrees with the wave impact being introduced similarly to convective conditions, which increases the mixing giving decreased winds in the middle parts of the boundary layer and increased winds in the lower part of the boundary layer. The wave effects are smaller in the Atlantic Basin compared to the other basins in spite of a high frequency of occurence of the wave criteria. This can be explained by the dominance of high MLH compared to the other basins (in AT zi > 1000 m for 29% of the time, corresponding for BS and NS are 12% and 22% respectively). This agrees also for the MT basin with zi < 1000 m during 32% of the time, and relatively small direct impact by introducing wave effect (not shown). The impact of swell on the mixing in the NS and AT basin might be underestimated, since the impact of incoming swell at the boundaries is not included.

Figure 8.

Averages over intervals of zi from the CR simulation for (a) zi, (b) U10, (c) Uz4−z1, and (d) Hs for the BS basin in Figure 2. Stars show reference simulation, and circles show simulations when wave impact is introduced (W1, with Wmix = 0.5); in addition, data from case W2 (Wmix = 0.1) and W3 (Wmix = 1.0) are shown. Only data when wave impact criteria is fulfilled are included.

Figure 9.

Same as Figure 8 but for the NS basin.

Figure 10.

Same as Figure 8 but for the AT basin.

[37] The wave forcing parameter Wmix is a relatively crude tuning parameter. Here it is chosen to Wmix = 0.5, motivated by assuming a maximum mixing due to waves similar as the mixing we get due to convection (and no waves) when Ri = 0.5. The sensitivity of the choice is investigated for two simulations with Wmix = 0.1 and Wmix = 1.0 (cases W2 and W3 respectively). In Figures 810 it can be seen that for all three cases with wave impact on the mixing we see similar results (increase of MLH, increased winds at 10 m and decreased wind gradients). The impact is, however, not linearly dependent on the magnitude of Wmix.

5. Discussion

[38] When investigating the impact of waves on the mixing in the atmospheric boundary layer in a regional model, there are several uncertainties. Main limitations are due to the lack of knowledge, mainly in presence of stable stratification (here we assumed that waves do not influence mixing during stable stratification). The wind drag and thereby the bulk value of the mean wind speed in the boundary layer is, however, significantly altered for wind-following swell and unstable stratification in comparison to flat terrain because the near-surface momentum flux balance has changed due to changed pressure stresses. In addition what happens when the waves are counter or cross the mean wind direction is relatively uncertain. Sullivan et al. [2008] discuss that many flow features are dependent on wind-wave direction. For wind-opposing swell waves Sullivan et al. [2008] shows that swell waves can generate vigorous turbulence that fills the PBL. Strongly wave induced motions is hence indicated to be present and provide mixing of the boundary layer air also in situations with wind-opposing swell.

[39] The expected effect of an increased mixing length is higher MLH and an altered wind gradient with higher winds near the surface and lower at higher levels. This is seen in the simulations, in particularly for situations with relatively low MLH. There are also additional feedback mechanisms and indirect effects making the behaviour of the coupled system less predictable. Increased winds in the lower part of the boundary layer increases the surface stress. This would also increase the phase speed of the surface waves, but the net effect is a reduction of the wave age and a reduction of the wave effect. There is also a tendency for the increased mixing to decrease the near surface temperature, this increases the near surface heat flux giving more unstable stratification. A very slightly unstable situation dominated by wave-induced mixing can thus be shifted to a more traditionally convective situation with no wave impact.

[40] One could also expect an indirect effect when the swell is decaying (and wave age decreases below 30) and the reduced winds at higher levels will remain and give lower winds also near the surface. This is a possible explanation for the average reduction of the mean winds in the North Sea region. Here the periods dominated by swell conditions are characterised by being short-lived. In those regions the mean wind at 10 m increases for swell situations, but is reduced (on the average) for lower wave age conditions, and giving a long term reduction of the near surface wind speed. Indirect effects may be responsible for the non-linearity in the magnitude of the impact with respect the value of Wmix shown in section 4.

[41] This study focuses on a region which is less swell dominated than other regions of the world. In regions where we have a combination of strong swell and relatively limited convective forcing it is probable that the impact is significantly greater than indicated from the present investigation.

6. Summary and Conclusions

[42] New results from measurements as well as LES have indicated that the presence of waves going faster than the wind (swell) alters not only the surface roughness, but also has an impact on the turbulence properties in the atmosphere. In general the results indicates that in the presence of swell waves the length scale of the turbulence increases and the boundary layer behaves more like a convectively driven boundary layer. In order to investigate the potential impact in global or regional climate models we used the coupled atmosphere-wave regional climate model RCA-WAM. The increased mixing in the presence of waves was introduced adding an additional wave-mixing parameter in the present E − l mixing length formulation of the RCA. When increasing the mixing, the overall results behave as expected with increased BL-height over sea, reduced wind gradients over the bulk of the boundary layer and increased near surface wind speed for part of the simulated data, in particular for situations dominated by a shallow boundary layer. Due to indirect effects and feedback mechanisms there are also situations with decreasing near surface winds, which partly balances the introduced swell induced effect. The net impact thus varies for varying regions depending on the wave characteristics.

[43] The magnitude of the change depend also on the wave-forcing parameter Wmix, which is a relatively crude tuning parameter. To adjust the formulation and introduce all impact further knowledge is needed concerning the behavior during slightly stable stratification as well as more information on what happens when the waves are counter the wind.

[44] We can, however, conclude that impact of swell waves on the mixing in the boundary layer is not insignificant and should be taken into account when developing wave-atmosphere coupled RCMs or GCMs.


[45] SMHI is acknowledged for the use of the RCA model, and we would in particular like to thank Anders Ullerstig for technical assistance and Ralf Döscher for discussions concerning the coupled system. Øyvind Sætra, Øyvind Breivik, and Alvaro Semedo are acknowledged for help with the WAM model setup.