Lichuan Wu. Impact of surface gravity waves on air-sea fluxes and upper-ocean mixing

Transcription

1 Lichuan Wu Impact of surface gravity waves on air-sea fluxes and upper-ocean mixing

2 Abstract Surface gravity waves play a vital role in the air-sea interaction. They can alter the turbulence of the bottom atmospheric layer as well as the upper-ocean layer. Accordingly, they can affect the momentum flux, heat fluxes, as well as the upper-ocean mixing. In most numerical models, wave influences are not considered or not fully considered. The wave influences on the atmosphere and the ocean are important for weather forecasts and climate studies. Here, different aspects of wave impact on the atmosphere and the ocean are introduced into numerical models. In the first study, a wave-state-dependent sea spray generation function and Charnock coefficient were applied to a wind stress parameterization under high wind speeds. The newly proposed wind stress parameterization and a sea spray influenced heat flux parameterization were applied to an atmosphere-wave coupled model to study their influence on the simulation of mid-latitude storms. The new wind stress parameterization reduces wind speed simulation error during high wind speed ranges and intensifies the storms. Adding the sea spray impact on heat fluxes improves the model performance concerning the air temperature. Adding the sea spray impact both on the wind stress and heat fluxes results in best model performance in all experiments for wind speed, and air temperature. In the second study, the influence of surface waves on upper-ocean mixing was parameterized into a 1D k ϵ ocean turbulence model though four processes (wave breaking, Stokes drift interaction with the Coriolis force, Langmuir circulation, and stirring by non-breaking waves) based mainly on existing investigations. Considering all the effects of surface gravity waves, rather than just one effect, significantly improves model performance. The non-breaking-waveinduced mixing and Langmuir turbulence are the most important terms when considering the impact of waves on upper-ocean mixing. Sensitivity experiments demonstrate that vertical profiles of the Stokes drift calculated from 2D wave spectrum improve the model performance significantly compared with other methods of calculating the vertical profiles of the Stokes drift. Introducing the wave influences in modelling systems, the results verified against measurements. Concluding from these studies for the further model development, the wave influences should be taken into account to improve the model performance.

3 Sammanfattning Havsvågor är av stor betydelse för interaktionen mellan hav och atmosfär. De påverkar turbulens i nedre atmosfären såväl som i de övre skikten i haven. I de flesta numeriska modeller tar man inte hänsyn till vågornas inverkan (eller tar bara delvis hänsyn) även om vågorna potentiellt kan påverka både väderprognoser och klimatstudier. Här introduceras olika aspekter av vågpåverkan på hav och atmosfär i numeriska modeller. I den första studien introduceras en vågberoende funktion för att beskriva havssprej för höga vindhastigheter. Den nya funktionen som påverkar skrovlighet och värmeflöde introducerades i en kopplad atmosfär-våg modell för att studera utvecklingen av stormar på mellanbredderna. Med den nya parametriseringen för skrovlighet minskar modellfelen och stormen intensifieras. Då på värmeflödet introduceras blir modellerad temperater bättre. Modellsimuleringarna stämmer bäst med mätningar då man tar med både effekter av förbättrad skrovlighet och värmeflöde. I den andra studien studeras vågornas effekt på omblandning i havet. Fyra processer (brytande vågor, Stokes drift/coriolis, Langmuir-turbulens och icke-brytande blandning av vågor) parametriseras i en 1D turbulens-modell. Då man tar hänsyn till alla processerna föbättras modell-simuleringarna väsentligt. Icke-brytande vågor och Langmuir-turbulens är de viktigaste termerna att ta hänsyn till. Även känsligneten i simuleringen för hur vågdata beskrivs studerades. Beräknas Stokes drift från 2D spektra förbättras modellen väsentligt i jämförelse med att använda förenklade metoder. Från dessa studier kan slutsatsen dras att modell-simuleringar av stormutveckling och omblandning förbättras då hänsyn tas till vågor. Våginflytande bör tas med vid utveckling av numeriska modeller för hav och atmosfär.

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5 If we knew what it was we were doing, it would not be called research, would it? Albert Einstein

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7 List of papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I II Wu, L., Rutgersson, A., Sahlée, E., Larsén, X.G. (2015). The impact of waves and sea spray on modelling storm track and development. Tellus. Series A, Dynamic meteorology and oceanography, 67, DOI: /tellusa.v Wu, L., Rutgersson, A., Sahlée, E. (2015). Upper-ocean mixing due to surface gravity waves. Journal of Geophysical Research: Oceans, 120, DOI: /2015JC Reprints were made with permission from the publishers. In Paper I the author had the main responsibility for setting up the RCA-WAM model and analysing the model results. The author had the main responsibility for writing the text. In Paper II the author had the main responsibility for setting up the GOTM model, analysing the simulation results and writing the text.

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9 Contents 1 Introduction Theory Sea spray impact on wind stress and heat fluxes Wind stress Heat fluxes Waves-induced upper-ocean mixing Breaking waves Stokes drift Non-breaking waves Numerical models and measurements Atmosphere-wave coupled model GOTM Measurements Results Sea spray impacts on the simulation of storms Surface waves impact on upper-ocean mixing Concluding remarks Acknowledgements References

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11 1. Introduction Surface gravity waves, nearly always present in the air-sea interface, play a vital role in the air-sea interaction. In the past, surface gravity waves were thought to be neglected in atmospheric and oceanic numerical models because of their small scales in spatial and temporal compared with atmospheric and oceanic dynamic scales. However, with the increasing amount of measurements and the knowledge, the importance of surface gravity waves has been admitted. Even so, the knowledge about the influence of surface waves on the atmosphere and the upper-ocean are still lacking to apply their influences into numerical models. Large eddy simulation (LES) and direct numerical simulation (DNS) have been developed to resolve small scale eddies in the atmosphere and the ocean (i.e. Rutgersson and Sullivan, 2005; Sullivan et al., 2008). However, it is not possible to solve so small scale processes in weather forecast and climate models. Parameterizing surface wave influences into numerical models is a feasible way to introduce the wave influence to models. In most of state-of-the-art climate models, influences of surface waves on the atmosphere and the ocean are still not included (Qiao et al., 2013). The interface between the atmosphere and the ocean regulates the functioning of the earth climate and weather systems. Many processes in the air-sea interface can be affected by surface gravity waves, which are shown in Fig Surface waves can not only affect the momentum flux, heat fluxes, but also affect the mass fluxes on the side of the atmosphere. On the ocean side, they can affect the kinetic energy fluxes through breaking waves, the upperocean mixing, as well as the momentum flux (Cavaleri et al., 2012). Even though the influence of surface waves on these processes have been admitted, the mechanisms behind them are still not clear and needed to be further investigated. Measurements and numerical models indicate that surface waves can influence the momentum and heat fluxes (i.e. Kudryavtsev, 2006; Andreas et al., 2015). For different wave characteristics, the wave influence is significantly different. For instance, under wind wave and moderate wind conditions, the wave-age depended Charnock coefficient relationship agrees well with measurements. However, for swell wave conditions, the drag coefficient C d was found increases/decreases significantly compared with wind wave conditions because of the atmospheric turbulence affected by waves (i.e. Sahlée et al., 2012; Högström et al., 2015). Under very high wind speeds, the drag coefficient is found decreasing with wind speed which is different with that under normal wind conditions (the drag coefficient increases with the wind speed) 11

12 Figure 1.1. A schematic view of the influence of waves on air-sea interaction (figure from Cavaleri et al., 2012). (i.e. Powell et al., 2003; Donelan et al., 2004). As well as, the heat fluxes under high wind speed is much more than the results calculated from traditional ways. The sea spray influence under high wind speed is considered as one possible reason for those phonemes. Wind storms, extreme high wind weather systems, give serious threats to coast areas and offshore activities. During the development of storms, heat fluxes and the momentum flux are very important for the maintain of the intensity of storms. In this sense, developing a better parameterization for the momentum and heat fluxes is very necessary for storm forecast models. So, one of the aims of this thesis is, Parameterize influences of surface waves on the atmosphere into a regional atmosphere-wave model under high wind speeds (Paper I). Surface waves can not only impact on the bottom atmospheric layer but also impact on the upper-ocean mixing. The impact of surface waves on the upperocean mixing is mainly through four processes: wave breaking, Coriolis-Stokes force (CSF), Langmuir circulation (LC), and non-breaking-wave-induced mixing. In ocean general circulation models (OGCMs), the impact of surface waves on upper-ocean mixing is not usually directly considered, though it is sometimes partly considered. Improved simulations on the sea surface temperature (SST) and mixed layer depth (MLD) were reported when including the impact of surface waves on the upper-ocean mixing to OGCMs (i.e. Qiao et al., 2013). However, the mechanisms of wave influence on the upper-ocean mixing are still not fully understood. The parameterizations of surface wave influences on upper-ocean mixing are still on developing. Compared with OG- GMs, 1D ocean model is a useful and easy tool to study turbulence schemes. Therefore, 1D ocean model is chosen as a tool to study the influences of surface gravity waves on upper-ocean mixing. The second aim of this thesis is, 12

13 Apply surface wave influences on upper-ocean mixing into a 1D ocean model to study their influence on simulation results (Paper II). Generally, for the two aims in this thesis, the influences of surface waves are parameterized into numerical models. Through the comparison between the numerical simulations and measurements, the wave influences as well as the model performance are analyzed. 13

14 2. Theory 2.1 Sea spray impact on wind stress and heat fluxes Wind stress In numerical models, bulk formulation is the main method to calculate the wind stress, i.e., τ = ρ a C d U10 2, where ρ a is the air density, U 10 the wind speed at 10-m above the sea surface. Based on the Monin-Obukhov similarity theory (MOST), the drag coefficient under neutral conditions is expressed as ( ) κ 2 C dn = (2.1) ln(10/z 0 ) where z 0 is the sea surface roughness length and κ von Karman constant. The Charnock relationship, i.e., z 0 = αu 2 /g, is a traditional way to calculate the roughness length (Charnock, 1955), where α is the Charnock coefficient, u the air friction velocity, g the acceleration of gravity. Instead of a constant, measurements indicate that α is relate to wave states, such as wave age and wave steepness (i.e. Drennan et al., 2005; Carlsson et al., 2009) If the Charnock relationship is valid under high wind speeds, C d should increase with wind speed. However, field and laboratory measurements indicate that C d may level off during very high wind speeds (i.e. Powell et al., 2003; Donelan et al., 2004). The influence of sea spray is admitted as one of possible reasons for the level off of C d. In Paper I, the wave state influence on the drag coefficient was investigated based on the theory developed by Kudryavtsev et al. (2012) under high wind speeds. The turbulence in the bottom atmospheric layer can be altered through buoyancy force under the sea spray influence. Through introducing the volume source of droplets into the conservation equation for spray, the sea spray effect are considered in the effective roughness length, Z 0. In the theory of Kudryavtsev et al. (2012), the sea spray stress is treated as zero based on the idea that droplets are instantaneously accelerated to the wind speed when they are generated at the height of breaking crests. After applying the closure scheme for the turbulent fluxes of momentum and droplets and with some simplifications (Kudryavtsev and Makin, 2011; Kudryavtsev et al., 2012), the effective roughness length is expressed as follows: 14 Z 0 = z 0 exp( m ) (2.2) m = σf 4κu ln 2 (d/z 0 ) (2.3)

15 where d is the depth of the spray generation layer, and σ = (ρ w ρ a )/ρ a, ρ w is the sea water density. In the parameterization of Kudryavtsev et al. (2012), the sea spray generation function (SSGF) is only related to wind speed (or friction velocity). Based on the wind-speed-dependent SSGF, the volume flux of droplets is expressed as: F = c s u (u 10 /c b ) (2.4) where c s = is an empirical constant and c b = c(k b ) is the phase velocity of the shortest breaking waves producing spume droplets. However, the SSGF is related not only to the wind speed, but also to wave states. Toba et al. (2006) proposed that using the development of wind waves may be more appropriate to describe the air-sea interaction. In Paper I, a wave-state-dependent SSGF and wave-age-dependent α were introduced into the parameterization of Kudryavtsev et al. (2012). Combing the study of Zhao et al. (2006) and Monahan (1986), a wave-statedependent SSGF is expressed as: 0.506Rb df 1.09 r ( r ) exp( B2) 0 r 0 < 20µm = 3 Rb 1.5 r < r 0 < 75µm dr Rb 1.5 r < r 0 < 200µm Rb 1.5 r < r 0 < 500µm (2.5) in which, U10 3 R b = C d gν β w, β w = g (2.6) ω p U 10 where ω p is the wave angular frequency at the wind-sea spectral peak, ν the air kinematic viscosity, β w the wave age of wind waves, r 0 the initial radius of the spray droplet, and B 0 = ( log(r 0 ))/ After the integral of the SSGFs in Eq. 2.5, they are applied to the Eq. 2.3, which represents the basic parameterization of Kudryavtsev et al. (2012), to investigate the impact of the SSGF on the drag coefficient. The wave-age-dependent α under wind-sea conditions from Carlsson et al. (2009) is applied into the parameterization instead of a constant α, α = 0.05(c p /u ) 0.4 (2.7) The influence of the wave-state-dependent SSGF and wave-age-dependent Charnock coefficient on the drag coefficient are shown in Figure 2.1a and b. The results only introduced the wave-state-depended SSGF are shown in Fig. 2.1a. One can see that when the wind-sea is very young, the drag coefficient increases with the wind speed, because the sea spray cannot develop immediately when the wind speed suddenly increases. It will not significantly affect the drag coefficient. However, with the increase of wind-wave age, the influence of sea spray become larger because of the development of wave-wind 15

16 4 β w = β = 0.5, β w = β = 0.3 w β = 0.5 w 3.5 β = 1.1, β = 0.5 w β = 1.3, β = 0.5 w 3 β = 0.7 w β w = β = 1.5, β = 0.5 w β = 1.7, β w = Kudryavtsev et al., Kudryavtsev, Eqs. 2.2 and 2.5, β = 0.5 w Kudryavtsev et al., C d C d (a) 0.5 (b) U 10 (m s 1 ) U 10 (m s 1 ) Figure 2.1. Comparsion of wave state impact on the drag coefficient in the newly proposed parameterisation: (a) parameterisation with Eqs. 2.2 and 2.5; (b) parameterisation with eqs. 2.2, 2.5 and 2.7 (from Paper I). interaction. It can be not described the wave-state influence if only windspeed-dependent SSGF is applied (see the blue line representing Kudryavtsev et al. (2012)). When the impact of wave age on the Charnock coefficient (using Carlsson et al., 2009) is also introduced, the results (Fig. 2.1b) indicate that the drag coefficient decreases with increasing wave age. When the wave state is not very young (i.e. the wind-wave age is approximately β w > 0.3), the drag coefficient starts to decrease at wind speeds of ms 1, which is consistent with the results of Powell et al. (2003). The range of wave states studied here indicates that the wave state has a greater impact on SSGF than on the Charnock coefficient for the calculation of C d Heat fluxes Sea spray affect not only on the wind stress but also on heat fluxes. Under high wind speeds, two different ways are functioning for the air-sea heat fluxes, the interfacial route and the sea spray route. In most numerical models, the sea spray mediated heat fluxes are not included. To include the sea spray impact on the heat fluxes, in the study of Andreas et al. (2015), a parameterization was proposed to calculate heat fluxes from the two different components separately. The total latent and sensible heat fluxes are expressed as, 16 H L,T = H L,int + H L,sp (2.8) H S,T = H S,int + H S,sp (2.9)

17 where, H L,int and H S,int are the interfacial latent and sensible heat fluxes calculated using the COARE algorithm (Fairall et al., 2003), and H L,sp and H S,sp are the sea spray-mediated latent and sensible heat fluxes. The sea spraymediated heat fluxes can be described as follows: H L,sp = ρ w L v {1 [ r(τ f,50) 50µm ]3 }V L (u,b ) (2.10) H S,sp = ρ w c w (T s T eq,100 )V S (u,b ) (2.11) where τ f,50 is the residence time of droplets with a 50 µm initial radius and T eq,100 the equilibrium temperature of droplets with a 100 µm initial radius. The wind functions of V L (u,b ) and V S (u,b ) are based on measurements. 2.2 Waves-induced upper-ocean mixing In Paper II, the influences of surface waves on upper-ocean mixing were introduced into a 1D ocean model through four processes: (1) wave breaking, (2) Coriolis-Stokes force (CSF), (3) Langmuir circulation (LC), and (4) nonbreaking-wave-induced mixing Breaking waves As a normal state over the ocean, breaking waves can make momentum and energy fluxes losses from waves to the ocean. The lost momentum flux is transferred to the underlying currents, while the lost energy flux is transferred mainly to near-surface turbulence (He and Chen, 2011). In the study of Craig and Banner (1994), the influence of breaking waves on energy flux losses from waves was introduced as an additional input into the turbulence kinetic energy (TKE) at the surface boundary, as follows: q wb,0 = m 0 ρ w u 3 w (2.12) where u w is the friction velocity in water, m 0 is a coefficient, treated as 100 in this study, following Craig and Banner (1994). He and Chen (2011) estimated the breaking-wave-induced stress, τ wb (z) = A (z) z, transferred from surface wave breaking to ocean currents, expressed as ˆ z H { } A (z)dz/ γρ a u 2 e bz (2.13) where b is a coefficient depending on the wind speed, A the momentum density, and γ the ratio of the breaking stress to the wind stress. In this study, taking account of the impact of breaking waves means taking account both breaking-wave-induced energy in the surface boundary (Eq. 2.12) and breakingwave-induced stress on mean flows (Eq. 2.13). 17

18 2.2.2 Stokes drift The CSF and the LC are two terms which are caused by the Stokes drift. The Stokes drift can be calculated from the 2D wave spectrum, u s = 16π3 g ˆ ˆ π 0 π f 3 S fθ (f, θ)exp( 8π2 f 2 z )dθdf (2.14) g where f is the wave frequency, θ the wave direction, and S fθ the directional frequency spectrum. The CSF can be understood as originating in the fact that "the Stokes drift attempts to tilt and stretch the planetary vorticity into the horizontal leading to a vortex force on the flow" (Polton et al., 2005). The CSF is usually considered in OGCMs by adding an extra term (i.e., f c u s ) to the momentum equations. In Paper II, the CSF was also introduced by adding the extra term to momentum equations. Some studies introduced the influence of LC as an extra shear production by the Stokes drift into the TKE equation (i.e. Kantha and Clayson, 2004; Ardhuin and Jenkins, 2006). To avoid repeatedly considering other wave influences, in Paper II, we added the LC-generated shear production to the TKE to consider its impact on the ocean vertical mixing, as follows: [ u u s P LC = ν t z z + v z v s z ] (2.15) where ν t is the eddy viscosity and u and v are the velocities in the eastward and northward directions, respectively. The Stokes drift velocities in the eastward and northward directions are denoted u s and v s, respectively Non-breaking waves How to incorporate the effect of non-breaking waves on ocean mixing into OGCMs is an open scientific question. Several studies have proposed the non-breaking-wave-induced mixing parameter (i.e. Qiao et al., 2004; Hu and Wang, 2010; Pleskachevsky et al., 2011). In Paper II, the parameterization of Pleskachevsky et al. (2011) was used to test the influence of non-breaking waves and the parameterizations of Qiao et al. (2004) and Hu and Wang (2010) were used to test the importance of wave spectrum. Pleskachevsky et al. (2011) divided the contribution of wave motion to ocean mixing into two parts: (1) symmetric wave motion subprocesses, which do not contribute to mean currents but do affect the turbulence, and (2) asymmetric wave motion mean-flow processes, which contribute to mean currents. Based on linear wave theory, the wave contribution to these subprocesses is expressed as the wave-induced mixing, expressed as 18 ν wave = l 2 wavem SM wave (2.16)

19 where l wave is the length scale of the wave-induced turbulence, Mwave SM is the contribution of symmetric wave motion to the shear. The contribution of asymmetric-wave-motion shear to the mean flow can be expressed by Mwave AM = kwavem AM wave SM (2.17) where kwave AM is the relationship between wave-energy dissipation and total wave energy. Following Pleskachevsky et al. (2011), we treated kwave AM as constant at The limitation of non-breaking waves generating turbulence is that the Reynolds number is higher than critical Reynolds number 3000 (Babanin, 2006). The wave-induced shear production is then P wave = ν t (M AM wave) 2 (2.18) After considering the terms induced by surface waves, the total shear production, viscosity, and heat diffusion can be expressed as follows: P s = P s + P wave + P LC (2.19) ν t = ν t + ν wave (2.20) where ν h the heat diffusion. ν h = ν h + ν wave (2.21) 19

20 3. Numerical models and measurements 3.1 Atmosphere-wave coupled model In Paper I, an atmosphere-wave coupled model was used to investigate the sea spray impact on the storm simulations. The Rossby Centre regional atmospheric model (RCA) developed at the Swedish Meteorological and Hydrological Institute (SMHI), was used as atmospheric model in the coupled system. The RCA model is a hydrostatic model incorporating terrain-following coordinates and semi-lagrangian semi-implicit calculations. The domain of RCA is shown in Figure 3.1. The resolution of RCA is 0.22 o spherical with a rotated latitude/longitude grid. The time step is 15-min. The boundary and initial field data are provided by ERA-40 data (Uppala et al., 2005) every six hours. The WAM model is a third-generation, full-spectral wave model, which was used in the atmosphere-wave coupled model. The resolution and time step of WAM are same as the RCA model. The RCA model provides wind fields to WAM model. In the coupled system, as a subroutine, the WAM model is called every time step by the RCA. The WAM model provides the wave information to the RCA. 3.2 GOTM The General Ocean Turbulence Model (GOTM) is a 1D water column model of the thermodynamic and hydrodynamic processes related to vertical mixing in water (Umlauf and Burchard, 2005). GOTM has been widely used to study the problems of ocean mixing (i.e. He and Chen, 2011; Drivdal et al., 2014). In GOTM, there are several state-of-the-art parameterizations for vertical turbulent mixing, such as, k ϵ turbulence scheme, Mellor-Yamada 2.5 scheme. In Paper II, the k ϵ turbulence scheme was used to investigate the wave influence on the upper-ocean mixing. The water depth in the model is set to 250-m, which is deep enough to prevent surface mixing from reaching the bottom (Burchard et al., 1999). The initial temperature data were obtained from measurements. The "OWS papa" scenario downloaded from the GOTM website was used as a basic experiment. Surface wave influences were applied into the other experiments. 3.3 Measurements In Paper I, FINO1 data were used to verify the model performances. A 100-m tall mast is installed in FINO1 offshore platform (54 o "N, 6 o "E), 20

21 FINO1 Figure 3.1. The domain of RCA and WAM model used in Paper I (red box area); the red is the FINO1 site. which is located 45 km north of Borkum Island in the North Sea. Meteorological parameters (wind speed, wind direction, pressure, and relative humidity) are measured at multiple levels (from approximately 33 to 100-m). The depth of the FINO1 location is 30-m, which faces rather open ocean conditions in the north and west. Further details about the platform can be found in Neumann and Nolopp (2007). In Paper II, the data from Papa ocean weather station were chosen to do the simulations. The Papa ocean weather station is located in the eastern subarctic Pacific (50 o N, 145 o W ) in 4230 m deep water where the horizontal advection of heat and salt is assumed to be small (e.g. Mellor and Blumberg, 2004). The data from the station are ideal for testing a 1D model. Various authors have used data from this station for validating turbulence closure schemes (e.g. Li et al., 2013). The wave spectrum and wave parameters needed by parameterizations used in Paper II were provied by WAM model simulations forcing by ERA-40 data. 21

22 4. Results In this section, the results are presented based on Paper I and II. The first part, based on Paper I, summarizes the sea spray influence on storm simulations. Adding the sea spray impact on wind stress and heat fluxes is tested in the atmosphere-wave coupled model. The simulation results are compared with measurements to verify model performances. The second part, based on Paper II, summarizes surface wave influences on the upper-ocean mixing in 1D ocean model. All wave-induced processes both separately and combined are applied to 1D ocean model within the same study to evaluate their relative importance. The sensitivity studies about wave spectrum influence are also presented in the second part. Note that Exp-1 to Exp-6 in Paper I (described in section 4.1) and Exp-1 to Exp-6 in Paper II (described in section 4.2) are independent. 4.1 Sea spray impacts on the simulation of storms Six experiments were designed to investigate the wave impact on the simulation results (see Table. 4.1). In this section, the results are based on the simulation of six storms. The hourly mean data from FINO1 are used to compare with the model results. The model errors in different wind bins are shown in Figure 4.1. Compared with the control run (Exp-1, without sea spray impact), the parameterization of Kudryavtsev et al. (2012) does not have significant influence on the statistical results concerning the wind speed. However, adding the wave-state-dependent Table 4.1. Wind stress and heat fluxes parameterizations for the various simulations. The Exp-1 to Exp-6 shown in this table is only for section 4.1. Experiments Notes Exp-1 Basic experiments (default RCA) Exp-2 Basic sea spray parameterization (Kudryavtsev et al., 2012) Exp-3 Wave state dependent SSGF impact on windstress Exp-4 Wave state dependent SSGF and α impact on windstress Exp-5 Sea spray impact on heat fluxes Exp-6 Full coupled case (Exp-4 + Exp-5) 22

23 ME (m s 1 ) Exp 1 Exp 2 Exp 3 Exp U 33_obs (a) MAE (m s 1 ) U 33_obs (b) 1 RMSE (m s ) U 33_obs (c) Figure 4.1. Statistical results for wind speed measured at a height of 33-m from FINO1: (a) mean error, (b) mean absolute error, and (c) root mean square difference (from Paper I). SSGF to Kudryavtsev et al. (2012), Exp-3, improves the model performance concerning the wind speed during high wind speeds. Adding both wave-statedependent SSGF and wave-age-dependent α (Exp-4) has the best performance during high wind speeds. However, it dose not improve the simulation results during low wind speeds. Under low wind conditions, swell is normal, the influence of which is not considered in the parameterization. Adding only the sea spray impact on the heat fluxes (Exp-5) only slightly affects the wind speed in high wind speed ranges compared with the control experiment. The air temperature decreases somewhat when adding only the sea spray impact on wind stress (Exp-4, see Fig. 4.2). Adding only the sea spray impact on heat fluxes (Exp-5), the modelled air temperature increases, especially during high wind speed ranges (Exp-5). If both the sea spray impact on heat fluxes and wind stress are added (Exp-6), it improves the the model performance concerning air temperature, increasing the temperature (see Fig. 4.2). The statistical results show that if both sea spray impact on heat fluxes and wind stress are added (Exp-6), the model results of temperature will be better than if only one influence is added. Adding the sea spray impact on wind stress and heat fluxes (Exp-6) does not have significant influence on the storm track simulations. However, it can influence the simulation results significantly concerning storm intensity. The time series of maximum wind speed at 925 hpa of the six storms are shown in Figure 4.3. It improves the model result only slightly if adding the sea spray influence on the heat fluxes only (Exp-5). Adding the sea spray impact on the drag coefficient, the maximum wind speed error is reduced by an average of approximately 17%. Introducing the sea spray influence on both heat fluxes and wind stress yields the best maximum wind speed performance, reducing the error by an average of 23% from that of control run (Exp-1). The significant influences on the maximum wind speed are exerted mainly during the periods of highest wind speed. 23

24 0 0.2 (a) (b) (c) ME ( o C) MAE ( o C) o RMSE ( C) Exp 1 Exp 4 Exp 5 Exp U 33_obs U 33_obs U 33_obs Figure 4.2. Statistical results for temperature measured at a height of 100-m : (a) mean error, (b) mean absolute error, and (c) root mean square difference (from Paper I). Figure 4.3. The maximum wind speed at 925 hp a of different storms over time: (a) Gero, (b) Erwin/Gudrun, (c) Kyrill, (d) Ulli, (e) Patrick and (f) Klaus (from Paper I). The maximum wind speed at 925 hp a are obtained from Extreme Wind Storms (XWS) catologue, in which the storms are tracked from the ERA-Interim dataset 24

25 Table 4.2. Setup of the six experiments: Exp-1 is the reference case, Exp-2 to Exp-5 are the four experiments in which wave processes are studied separately, and Exp-6 includes all wave contributions (from Paper II). The Exp-1 to Exp-6 in this table is only for section 4.2. Experiments Breaking waves CSF LC Non-breaking waves Exp-1 No No No No Exp-2 Yes No No No Exp-3 No Yes No No Exp-4 No No Yes No Exp-5 No No No Yes Exp-6 Yes Yes Yes Yes 4.2 Surface waves impact on upper-ocean mixing In this section, the results are based on sensitive simulations on the Papa station data in year The simulations partly or fully include the influences of surface waves on upper-ocean mixing, described in section 2.2. The design details of six experiments are shown in Table 4.2. Figure 4.4 shows the simulated and observed SST. In summer, the control experiment (Exp-1, default GOTM with k ϵ turbulence scheme) gives higher SST compared with measurements (red line). Adding the impact of breaking wave or CSF does not have significant influence on the simulation results. So in the following figures, the results of Exp-2 and Exp-3 are not shown. Adding the impact of LC (Exp-4) somewhat improves the results, giving a slightly lower SST. If the impact of non-breaking waves (Exp-5) is added to the model, the SST in summer is several degrees lower and the model performs significantly better than in the other experiments. Adding all the wave impacts to the model (Exp-6) results in the best SST performance of all the experiments. Figure 4.5 shows the statistical results of temperature at various depths. In the surface layer (0-20m), adding the impact of LC not only reduces the mean error (ME) about 0.2 o C but also improves the mean absolute error (MAE) and root mean square deviation (RMSD). Not only the ME but also MAE and RMSD are reduced by more than 0.5 o C in the surface layer (0-20m), when adding the impact of non-breaking waves to the model (Exp-5). When adding all the wave impacts (Exp-6), it shows the best performance concerning the temperature in the surface layer (0-20m). However, adding the non-breaking wave impact worse the model performance on the layer (70-100m), which may be caused by the overestimation of the MLD. In the surface layer (0-20m), the changing of the temperature is mainly dominated by the surface forcing (heat fluxes, momentum flux) which causes that the correlation coefficient (R) does not change significantly when adding the wave influences. From the ME, MAE, RMSD, and R, one can see that Exp-6 performs the best of all the experiments. Comparing the various wave impact aspects indicates that non- 25

26 Figure 4.4. Simulated and observed SST from experiments and observations in 1962 ( o C) (from Paper II). breaking waves exert a dominant effect, the second most important process being LC. The 2D wave spectrum is not always available when calculating the Stokes drift. In some OCGMs, the surface Stokes drift velocity are calculated from wind speed or friction velocity, such as U s0 = τ 1/2 (Madec, 2008). Then, the vertical profiles of the Stokes drift are calculated based on some simplified formulas, such as (Breivik et al., 2015), e 2k ez u s (z) = u s0 1 8k e z (4.1) where k e is the inverse depth scale. To investigate the impact of the 2D wave spectrum, two more experiments were designed: LC-1: the surface Stokes drift is estimated from wind stress, U s0 = τ 1/2, the vertical profile of the Stokes drift being calculated using Eq LC-2: the surface Stokes drift is estimated from wave spectrum, the vertical profiles of the Stokes drift being calculated using Eq The other setting of those two experiments are same as Exp-6. The statistical results for the temperature profiles are shown in Figure 4.6. If we use the surface Stokes drift estimated from wind stress (LC-1), it worse the performance of the simulated temperature not only in ME and MAE but also for RMSD. Compared with LC-1, if we only use the Stokes drift calculated from wave spectrum and use the profiles estimated from Eq. 4.1, it has 26

27 Figure 4.5. Statistical results for temperature at various depths, modelled compared with measured results: (a) mean temperature error, (b) mean absolute temperature error, (c) root mean square difference, and (d) correlation coefficient (from Paper II). 27

28 Figure 4.6. Statistical results for temperature at various depths, modelled compared with measured results: (a) mean temperature error, (b) mean absolute temperature error, (c) root mean square difference, and (d) correlation coefficient for Exp-6, LC-1 and LC-2 (from Paper II). 28

29 Figure 4.7. The difference between simulated results and measurements ( o C) expressed as experimental minus observed results: (a) Exp-6, (b) Bv-1 and (c) Bv-2. (from Paper II) little improvement concerning the sea temperature in deep layer. Although the Stokes drift is mainly in the upper-ocean layer (the upper 40-m in this case), feedback from it influences the simulations in a much deeper layer. Both LC-1 and LC-2 have worse performances compared with Exp-6, which shows that the wave spectrum is necessary for calculating the Stokes drift. As one of the most important terms for wave impact on upper-ocean mixing, non-breaking-wave-induced mixing has been parameterized though several methods. The one used in Exp-6 is based on bulk properties (i.e., significant wave height and wave period). Here we designed two more experiments to do the comparison of different parameterizitions of non-breaking-wave-induced mixing. One is from Qiao et al. (2004), in which the wave spectrum is used to calculate the non-breaking-wave-induced mixing (Bv-1). The other one is from Hu and Wang (2010), in which only the wave age and wave slope are needed (Bv-2). The other settings of the two experiments are same as Exp-6. Qiao et al. (2004) used the full wave spectrum to calculate the non-breakingwave-induced mixing, as follows, ν wave = α w k E( k)e 2kz d k z k ω 2 E( k)e 2kz d k 1/2 (4.2) 29

30 where α w is a coefficient (treated as 1 here), E( k) the wave number spectrum, k the wave number, and ω the wave angular frequency. Hu and Wang (2010) also used the bulk properties to calculate the non-breaking-wave-induced mixing, expressing as ν wave = 2κ2 g δβ3 U10exp( 3 gz β 2 U10 2 ) (4.3) where δ is the wave steepness (δ = 2a/λ, a being the amplitude and λ the wavelength), β the wave age (0 < β < 1 for a growing wave and β = 1 for a mature wave). The temperature difference with measurements are shown in Figure 4.7. The Exp-6 shows the best performance concerning the temperature in the upper layer. In the layer around MLD, the Exp-6 overestimates the temperature. However, Bv-1 still underestimates the MLD. The parameterization from Hu and Wang (2010) overestimates the non-breaking-wave-induced mixing in whole periods, which causes the low temperature in upper layer and higher temperature in deep layer. 30

31 5. Concluding remarks Surface waves alter the turbulence of the atmosphere and the ocean. Accordingly, they effect the momentum and heat fluxes, as well as the upperocean mixing. In most numerical models, wave influences are not considered enough. In this thesis, wave influences are parameterized and introduced into numerical model systems to test their influence. In Paper I, a wave-state-dependent SSGF and wave-age-dependent Charnock coefficient were introduced into a wind stress parameterization during high wind speeds. The newly proposed wind stress parameterization and a sea spray influence heat flux parameterization were applied to an atmosphere-wave coupled model. Based on the simulation of six storms, the influence of sea spray were investigated. Adding the wave-state-dependent SSGF and Charnock coefficient into a drag coefficient parameterization improves the model performance during high wind speeds, however, decreases the air temperature compared with the control experiments. The wave-state-dependent SSGF is more important than the wave-age-dependent Charnock coefficient. Only including the sea spray impact on heat fluxes improves the model performances about air temperature, does not have significant impact on the wind speed. Introducing the sea spray impact on both the wind stress and heat fluxes, the model performs the best not only for temperature, but also for wind speed. As expected, the wind stress parameterization including the sea spray influence intensifies the storms. In Paper II, four processes (wave breaking, Stokes drift interaction with the Coriolis force, Langmuir circulation, and stirring by non-breaking waves) which effect the upper-ocean mixing were parameterized into a 1D ocean model. Simulation results show that adding wave-induced mixing in upper-ocean mixing improves the model performances. The non-breaking-wave-induced mixing and the Langmuir turbulence are the most important terms considering the impact of waves on the upper-ocean mixing. The impact of CSF and breaking waves have relative small influence on the simulation results. Using the 2D wave spectrum to calculate the Stokes drift vertical profiles is more accurate and can improve the model results. In further model development, we suggest using the 2D wave spectrum to calculate the vertical profiles of the Stokes drift if possible. Compared with measurements, including surface wave influences in numerical models improves the agreement between the numerical simulation results and measurements. In the further model development, the influences of surface gravity waves should be included if possible. 31

32 6. Acknowledgements I would like to thank my supervisors Anna Rutgersson and Erik Sahlée for giving me the opportunity to do my PhD study in Uppsala. Thank them for discussing my kinds of ideas and encouraging me to verity my ideas. Without their supports, I could not finished this thesis. A special thank to Anna for answering my kinds of questions (sometimes, they are "stupid" questions) during her busy time. Christian Dieterich in SMHI is thanked for helping me solving many problems that I met during the setting up of the coupled model. Also, I would like to give my thanks to my colleagues at meteorological group for their great suggestions, discussions and comments. Those discussions and comments help me a lot to improve my ideas and manuscripts. All PhD students in meteorology, present and former are thanked for their help and sharing their knowledge. Finally, a big thank to all my friends and my family for their selfless supports and help. Even you never say, I know you are always behind me when I meet problems. You guys always accompany me when I felt alone and sad. Because of you, I know there are no any troubles that I can not solve during my life. 32

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