Introducing Surface Gravity Waves Into Earth System Models

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1478

Introducing Surface Gravity Waves into Earth System Models

LICHUAN WU

ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-554-9822-1 UPPSALA urn:nbn:se:uu:diva-314760 2017 Dissertation presented at Uppsala University to be publicly examined in Axel Hambergsalen, Villavägen 16, Uppsala, Wednesday, 12 April 2017 at 10:00 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Dr Peter Janssen (European Centre for Medium-Range Weather Forecasts).

Abstract Wu, L. 2017. Introducing Surface Gravity Waves into Earth System Models. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1478. 50 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9822-1.

Surface gravity waves alter the turbulence of the bottom atmosphere and the upper ocean. Accordingly, they can affect momentum flux, heat fluxes, gas exchange and atmospheric mixing. However, in most state-of-the-art Earth System Models (ESMs), surface wave influences are not fully considered or even included. Here, applying surface wave influences into ESMs is investigated from different aspects. Tuning parameterisations for including instantaneous wave influences has difficulties to capture wave influences. Increasing the horizontal resolution of models intensifies storm simulations for both atmosphere-wave coupled (considering the influence of instantaneous wave-induced stress) and stand-alone atmospheric models. However, coupled models are more sensitive to the horizontal resolution than stand-alone atmospheric models. Under high winds, wave states have a big impact on the sea spray generation. Introducing a wave-state-dependent sea spray generation function and Charnock coefficient into a wind stress parameterisation improves the model performance concerning wind speed (intensifies storms). Adding sea spray impact on heat fluxes improves the simulation results of air temperature. Adding sea spray impact both on the wind stress and heat fluxes results in better model performance on wind speed and air temperature while compared to adding only one wave influence. Swell impact on atmospheric turbulence closure schemes should be taken into account through three terms: the atmospheric mixing length scale, the swell-induced momentum flux at the surface, and the profile of swell-induced momentum flux. Introducing the swell impact on the three terms into turbulence closure schemes shows a better performance than introducing only one of the influences. Considering all surface wave impacts on the upper-ocean turbulence (wave breaking, Stokes drift interaction with the Coriolis force, Langmuir circulation, and stirring by non-breaking waves), rather than just one effect, significantly improves model performance. The non- breaking-wave-induced mixing and Langmuir circulation are the most important terms when considering the impact of waves on upper-ocean mixing. Accurate climate simulations from ESMs are very important references for social and biological systems to adapt the climate change. Comparing simulation results with measurements shows that adding surface wave influences improves model performance. Thus, an accurate description of all important wave impact processes should be correctly represented in ESMs, which are important tools to describe climate and weather. Reducing the uncertainties of simulation results from ESMs through introducing surface gravity wave influences is necessary.

Keywords: Surface gravity waves, Air-sea interaction, Earth-System Model, Atmospheric mixing, Upper-ocean turbulence

Lichuan Wu, Department of Earth Sciences, LUVAL, Villav. 16, Uppsala University, SE-75236 Uppsala, Sweden.

ISSN 1651-6214 ISBN 978-91-554-9822-1 urn:nbn:se:uu:diva-314760 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-314760) Dedicated to my family and friends 仅以此文献给我的家人和朋友们

List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Wu, L., Sproson, D., Sahlée, E., Rutgersson, A. (2017). Surface wave impact when simulating mid-latitude storm development. Journal of Atmospheric and Oceanic Technology, 34(1), 233–248. doi: 10.1175/JT ECH-D-16-0070.1.

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, 27967. doi: 10.3402/tellusa.v67.27967.

III Wu, L., Rutgersson, A., Sahlée, E., Larsén, X.G. (2016). Swell impact on wind stress and atmospheric mixing in a regional coupled atmosphere- wave model. Journal of Geophysical Research: Oceans, 121(7), 4633– 4648. doi: 10.1002/2015JC011576.

IV Wu, L., Rutgersson, A., Nilsson, E. (2017). Atmospheric boundary layer turbulence closure scheme for wind-following swell conditions. Journal of the Atmospheric Sciences (Under review).

V Wu, L., Rutgersson, A., Sahlée, E. (2015). Upper-ocean mixing due to surface gravity waves. Journal of Geophysical Research: Oceans, 120(12), 8210–8228. doi: 10.1002/2015JC011329.

Reprints were made with permission from the publishers.

In the above listed papers, I was responsible for the model developments, experimental designs, numerical modelling, analysis of the results and writing of the papers. In Paper I, D. Sproson contributed to the model development and experimental design. The other co-authors contributed to discussions about the ideas of the studies, giving feedback to the results, writing the manuscripts and sharing measurements.

In addition, I have contributed to the following journal papers during my PhD study, which are not appended to this thesis. Wu, L., Hristov T., Rutgersson, A. (2017). Vertical proﬁle of spectrum- integrated wave-coherent momentum ﬂux and variances (submitted). Jeworrek, J., Wu, L., Christian D., Rutgersson, A. (2017). Character- istics of Convective Snow Bands along the Swedish East Coast. Earth System Dynamics (In press). doi:10.5194/esd-2016-43. Cai, Y., Wen Y., Wu, L., Zhou C., Zhang F. (2017). Impact of wave breaking on upper-ocean turbulence. Journal of Geophysical Research: Oceans (In press). doi: 10.1002/2016JC012654. Wen, Y., Geng, X., Wu, L., Yip, T.L., Huang, L., Wu, D. (2017). Green routing design in short seas. Int. J. Shipping and Transport Logistics (In press). doi: 10.1504/IJSTL.2017.10002963. Wu, L., Wen, Y., Zhou C., Xiao, C., Zhang, J. (2014). Modeling the Vul- nerability of Waterway Networks. Journal of waterway, port, coastal, and ocean engineering 140(4): 04014012. doi: 10.1061/(ASCE)WW.1 943-5460.0000238. Contents

1 Introduction ...... 9

2 Background ...... 12 2.1 Monin-Obukhov similarity theory ...... 12 2.2 Turbulence closure schemes ...... 13 2.2.1 K-theory ...... 13 2.2.2 E − l model ...... 14 2.2.3 MYNN model ...... 14 2.2.4 k − ε Model ...... 15

3 Parameterisations with wave influences ...... 16 3.1 Wave-induced stress ...... 16 3.1.1 Wave spectra model ...... 16 3.1.2 Parameterisation ...... 17 3.2 Sea spray influences ...... 18 3.2.1 Wind stress ...... 18 3.2.2 Heat flux ...... 20 3.3 Swell impact on atmospheric mixing ...... 20 3.3.1 E − l model ...... 20 3.3.2 MYNN model ...... 21 3.4 Wave impact on upper-ocean turbulence ...... 22 3.4.1 Breaking waves ...... 22 3.4.2 Stokes drift ...... 23 3.4.3 Non-breaking waves ...... 23

4 Models and data ...... 25 4.1 Coupled models ...... 25 4.2 1D models ...... 25 4.3 Measurements ...... 26

5 Results ...... 27 5.1 Influence of instantaneous waves ...... 27 5.2 Influence of horizontal resolution ...... 30 5.3 Influence of sea spray ...... 30 5.4 Swell influences ...... 33 5.4.1 Climate simulation ...... 33 5.4.2 WRF-SCM results ...... 34 5.5 Wave impact on upper-ocean turbulence ...... 36 6 Summary and Conclusions ...... 39

7 Sammanfattning på svenska ...... 42

8 Acknowledgements ...... 45

References ...... 47 1. Introduction

The air-sea interface plays a vital role when modelling climate and weather systems since it represents the boundary between the two dominating spheres, i.e., the atmosphere and the ocean. Ocean surface is always covered by surface gravity waves. The existence of surface gravity waves affects air-sea interaction processes, which makes the air-sea interface a complex system. However, influences of surface gravity waves on the air-sea interaction are not included in most of the state-of-the-art Earth System Models (ESMs) (Qiao et al., 2013). ESMs are global climate models with explicit representation of the interaction between different subcomponent systems, i.e., atmosphere, ocean, land surface, sea ice, etc (Flato, 2011). As important tools, ESMs should take wave influences into account in order to improve their performance on climate simulations. Wind blowing over the ocean generates waves, the energy and momentum of the wind are transferred to waves during the process. With growing wave, ocean surface becomes rough, and wave slopes start to increase. When the wave slope reaches a critical value, the waves cannot maintain their slopes and start to break. Through wave breaking, the wave energy is released to underlying currents. Under high winds, sea sprays are generated due to the intensive wave breaking. During the process that sea sprays are thrown into the air, the droplets absorb energy from the wind, and the velocities of the droplets are increased. When the droplets return to the ocean, they release momentum into currents. The heat flux is enhanced during the existence of the sea sprays in the air. When locally generated waves travel to distance oceans with light wind, the phase speed of the waves is higher than the wind speed (i.e., swell wave) which prevails open oceans (Semedo et al., 2011). Considering wave impact on wind stress, many wave-parameter related wind stress formulas have been proposed in order to reduce the scatter between model results and measurements (e.g., Drennan et al., 2005). However, additional work are still needed to reduce the scatter under very light and very high wind conditions. One example is that traditional wind stress parametrizations cannot simulate upward direction momentum flux (from ocean to atmosphere) at the air-sea interface. However, the upward direction momentum flux and the wave-induced wind (low-level wind jet) have been observed in field experiments and shown in numerical simulations under swell wave conditions (Smedman et al., 1994, 2009; Sullivan et al., 2008). Under very high winds, the drag coefficient levels off (e.g., Powell et al., 2003; Potter et al., 2015), which cannot be simulated by traditional wind stress parameterisations

9 either. Surface gravity waves can also affect heat fluxes, atmospheric mixing, gas exchange and mass exchange at the air-sea interface (Veron et al., 2008; Rutgersson et al., 2012). As the interface between the atmosphere and ocean, surface waves can also affect oceanic boundary layer significantly. Most of the oceanic models underestimate the depth of oceanic mixed layer without considering surface wave influences (Qiao et al., 2004). Surface waves affect upper-ocean layer mainly through four processes: (1) wave breaking, (2) the Coriolis- Stokes force (CSF), (3) Langmuir circulation (LC), and (4) nonbreaking-wave- induced mixing. The four processes have different influence mechanisms, which have been proved by laboratory experiments and numerical simulations (Craig and Banner, 1994; Sullivan et al., 2007; Dai et al., 2010; Tsai et al., 2015). Although wave impacts on the boundary layer processes of the atmosphere and ocean have been admitted by the research community, how to parametrise wave influences into ESMs is still an open question which interests modellers, meteorologists, and oceanographers. There are some different voices concerning if it is necessary to explicitly include wave influences in ESMs. In this thesis, the following questions are investigated: • Do we need instantaneous wave information to simulate wave impact on atmospheric/oceanic numerical models? This is a root question before we start to apply wave influences into ESMs. In other words, if tuning classical parameterisations to measurements (without explicitly considering wave information) can simulate wave impacts on atmospheric or oceanic systems well, we may not need to include wave influences explicitly. The question is investigated in Paper I. • How big impact of sea sprays and waves have on storm simulations in numerical models? Sea sprays generated by intensive wave breaking under high winds can affect the momentum and heat fluxes between the atmosphere and the ocean. As a serious threat to coast and offshore activities, wind storms are very hazardous weather systems impacted by the air-sea interaction. The energy transferred between the atmosphere and the ocean is the main energy resource for the intensify or dissipation of wind storms. Take wind storms as an example, in Paper II, the influences of sea sprays and waves on the fluxes of momentum and heat are applied into an atmosphere-wave coupled model to investigate their influences on storm simulations. • How to introduce swell impacts on the atmospheric boundary layer into ESMs?

10 The influence of surface gravity waves on the momentum flux can extend to a much higher layer under swell dominated waves (Smedman et al., 1994). Also, swell can affect the atmospheric mixing in the atmospheric boundary layer. In Papers III and IV, we investigated the swell influence on atmosphere boundary layer turbulence schemes through atmospheric mixing, effective roughness length, and the profile of swell-supported momentum flux based on measurements and Large Eddy Simulations (LESs). • Which process of the wave impact on the upper-ocean layer is the most important one? How do their accumulated influences affect numerical simulations? The four processes (i.e., breaking waves, LC, CSF and nonbreaking- wave induced mixing) that wave impact the upper-ocean turbulence are investigated separately and combined in Paper V. The sensitivity of numerical simulation results with the Stokes drift profile estimated from different methods was also investigated in Paper V. In general, influences of surface waves on the atmosphere and ocean were parametrised into numerical models. Based on the comparison between simulation results and measurements, wave influences and model performances were analysed. The results of this thesis give a contribution on how to introduce wave influences into ESMs.

11 2. Background

Most of the atmospheric boundary layer theories were developed and improved based on measurements over the land. Over the ocean, measurements are much rare, and there are many factors affecting the theories. Thus, the validity of the theories to be applied over the ocean is needed to be veriﬁed. However, in most numerical models, those theories are applied directly into the marine atmospheric boundary layer without or only partly considering the property differences between the land and ocean surface. Even though some numerical models show a good performance over the ocean using the classical theories developed for land surface, the scatter are larger when comparing model simulation results and measurements. Wave characteristic may be a possible reason for the scatter. Before introducing surface wave inﬂuences into classical theories, the basic parameterisations used in this thesis are summarised here.

2.1 Monin-Obukhov similarity theory The vertical flux is assumed to be constant in the atmospheric surface layer. The Monin-Obukhov similarity theory (MOST, Monin and Obukhov, 1954) was developed to describe the vertical behaviour of nondimensionalized mean flow and turbulence properties, κz ∂U = ϕ(z/L) (2.1) u∗ ∂z 2 2 1/4 where u∗ = (uw + vw ) is the friction velocity, U the wind speed, u and v the wind fluctuations in streamwise and crosswind directions, κ the von Kármán constant, ϕ(z/L) a stability function, and L the Obukhov length, u3 L = − ∗ (2.2) κ g q T0 Cpρa in which g is the gravity acceleration, T0 the surface temperature, q the kinematic heat flux, Cp the specific heat, and ρa the air density. In numerical models, the bulk formula is usually used to calculate the wind 2 2 stress, τ = ρau∗ = ρaCdU10, where Cd is the drag coefficient. The drag coefficient under neutral stratification conditions can be expressed as, κ2 CdN = 2 (2.3) ln(10/z0)

12 The Charnock relationship (Charnock, 1955) is usually used to parameterised the roughness length over the ocean in numerical models,

2 z0 = αu∗/g (2.4) where α is the Charnock coefficient. The value of the Charnock coefficient is usually set to be approximately 0.015-0.035 (Powell et al., 2003). In recent field measurements, the Charnock coefficient is found to be related to wave states, such as wave age, wave steepness, and so on (Taylor and Yelland, 2001; Kumar et al., 2009). Under light and very high winds, the roughness length may be related to many parameters due to the effect of swell waves, sea spray, etc (Soloviev et al., 2014; Högström et al., 2015).

2.2 Turbulence closure schemes For turbulent ﬂow equations, the number of unknowns is larger than the number of equations. In other words, the turbulent ﬂow equations are not closed. To be able to solve those equations, turbulence closure schemes are needed. The turbulent terms need to be parameterised through mean variables. Local closure and nonlocal closure are the two main schools of thought of turbulence closure. An unknown quantity is parameterised by values of known quantities at the same points in local closure schemes. For nonlocal closure, an unknown quantity is parameterised by values of known quantities at many points (Stull, 2012). According to the highest order prognostic equations that are retained, closure schemes can be divided into different order closure scheme. The K- theory, E − l, Mellor-Yamada-Nakanishi-Niino (MYNN) and k − ε are local closures, which are summarised as follows.

2.2.1 K-theory Due to the coarse resolution of atmospheric and oceanic models, numerical models can only simulate time-averaged quantities. An instantaneous quantity, ab, can be decomposed into its time-averaged, i.e., A, and fluctuating quantities, i.e., a: ab= A + a (2.5) To close the turbulent flow equations, the unresolved parts (fluctuating parts) in the equations need to be parameterised. Over flat conditions, the turbulence fluctuation (a0) is the total fluctuating part, a = a0. Thus, the total momentum flux uw = u0w0. In the following parts of the thesis, U is the mean wind speed amplitude along with the wind direction, V is the mean crosswind velocity, and W the mean vertical velocity.

13 Under flat conditions, the K-theory (eddy-diffusivity) model is a common way to parameterise the turbulent flux term, which is related to mean gradients, dU u0w0 = K (2.6) m dz where Km is the eddy viscosity coefficient.

2.2.2 E − l model In the E −l turbulent scheme (a 1.5 order scheme), the turbulent kinetic energy (TKE) equation is a prognostic equation and the mixing length equation is a pre-scripted parameterisation (Lenderink and Holtslag, 2004; Lenderink√ and De Rooy, 2000). The eddy viscosity coefﬁcient is expressed as, Km = l E (E is the TKE and l a length scale), in which the length scale is expressed as, 1 1 1 = + (2.7) l lup ldown where lup and ldown are: z l = F(Ri)dz0 (2.8) up ˆ zbottom

ztop 0 lup = F(Ri)dz (2.9) ˆz where F(Ri) is a function of the local Richardson number, zbottom and ztop are the lower and upper boundaries of the mixing domain. The F(Ri) is calculated by 2 αn − π (αc − αn)(αrRi) Ri > 0 F(Ri) = 2 (2.10) αn − π (αc − αn)arctan(αrRi) Ri < 0 where αn, αc, and αr are coefﬁcients.

2.2.3 MYNN model The MYNN scheme (Nakanish, 2001) is a second-order turbulence closure model, which has been used in many atmospheric models. In the MYNN scheme, the eddy viscosity√ is expressed as Km = lMSmq, where lM is the master length scale, q = 2TKE, and Sm the non-dimensional diffusion coefﬁ- cient for momentum ﬂux. The master length scale is calculated based on the relationship between the TKE and dissipation (e.g. Nakanish, 2001),

q3 lM = (2.11) B1ε 14 where B1 is a constant (i.e., B1 = 24) and ε the energy dissipation. Same as most of the turbulence schemes, the master length scale in the MYNN scheme needs to be parameterised, which is determined by three length scales, 1 1 1 1 = + + (2.12) lM lS lT lB where lS is the surface length scale, lT the length scale depending upon the turbulence structure of the planetary boundary layer (PBL), and lB the length scale limited by the buoyancy effect.

2.2.4 k − ε Model The k − ε turbulence model is a two-equation model. To improve the mixing- length model is the original impetus for the k − ε model. The transport equation for the TKE, E, is ∂E ∂ Km ∂E = + Ps + Pb − ε (2.13) ∂t ∂z σk ∂z where σk is the constant Schmidt number, Ps shear production, and Pb buoyancy production. The transport equation for dissipation is ∂ε ∂ Km ∂ε ε = + [cε1Ps + cε3Pb − cε2ε] (2.14) ∂t ∂z σε ∂z q where σε is the Schmidt number for ε, and cε1, cε2, and cε3 are empirical coefﬁcients. Shear production, Ps, is calculated by " # ∂U 2 ∂V 2 Ps = Km + . (2.15) ∂z ∂z

The viscosity is calculated as

1/2 Km = cµ E l (2.16) where cµ is a stability function and l a typical length scale. In Paper V, impacts of surface waves on ocean mixing are introduced into the k − ε two-equation closure model in order to investigate their inﬂuences.

15 3. Parameterisations with wave inﬂuences

Observations and numerical simulations have shown that underlying waves can alter the turbulence of the atmospheric and oceanic boundary layer (Smed- man et al., 2009; Rutgersson et al., 2012). Accordingly, the classical theories developed for ﬂat terrain conditions may need to be revised in order to introduce wave inﬂuences when applying them to the marine atmospheric boundary layer. Here, impacts of surface waves on the classical theories (section 2) are discussed and parameterised. Over surface waves, Eq. 2.5 can be rewritten as,

0 ab= A + a + a˜ (3.1) wherea ˜ is the wave-coherent fluctuation and a0 the turbulence fluctuation part. Thus, over surface waves, the total momentum flux can be written as, uw = (u0 + u˜)(w0 + w˜) = u0w0 + u0w˜ + uw˜ 0 + u˜w˜ (3.2) |{z} |{z} |{z} |{z} (a) (b) (c) (d) where term (a) is the turbulent flux, terms (b) and (c) are the flux interacting between the wave-coherent and turbulent fluctuation, and term (d) is the wave- coherent momentum flux.

3.1 Wave-induced stress In the atmosphere, the total momentum flux can be treated as the sum of the turbulent momentum flux, i.e., τt (term (a) in Eq. 3.2), and the wave-induced momentum flux, i.e., τw (term (d) in Eq. 3.2): τ = τt + τw. Assuming that the wave-coherent filter suppresses the turbulence fluctuation (Hristov and Ruiz- Plancarte, 2014), then terms (b) and (c) are 0. Various scholars use different methods to include the wave-induced stress in wind stress parameterisations (Janssen, 1991; Högström et al., 2015). In section 3.1.1, the wave-induced stress is calculated from the wave spectra. The peak swell contributed momentum flux is parameterised using wave-parameters in section 3.1.2.

3.1.1 Wave spectra model A coupled atmosphere-wave model was developed in European Centre for Medium-Range Weather Forecasts in the middle of the 1990s (Janssen, 2004).

16 In the coupled model, the Integrated Forecasting System (IFS) is coupled with a wave model to consider the wave-induced stress. Later, many atmosphere- wave coupled models were developed to study the impact of wave-induced stress on climate and mesoscale weather systems (e.g., Lee et al., 2004). After introducing the wave-induced stress into coupled models, the roughness length is usually given by, τ z = (3.3) 0 α 1/2 gρa(1 − τw/τ) and the wave-induced stress is expressed as (Janssen, 1991),

τ = ρ ωγS cos(θ − ϕ)d f dθ (3.4) w w ˆ f θ where ρw is the water density, γ the growth rate of waves, ω the angular frequency, S f θ the wave spectrum density, θ the wave direction, f the frequency, and ϕ the wind direction. In wave model WAM (WAMDI, 1988), the Charnock coefﬁcient α is set as 0.010. In Paper I, the wave-induced stress calculated from a spectral wave model is used to investigate if a tuning parameterisation of the roughness length is enough to capture the wave inﬂuence.

3.1.2 Parameterisation Under swell conditions, the atmospheric turbulence structure is more complex than that under wind wave conditions. Comparing the results from the classical drag coefficient parameterisation, i.e., COARE (Fairall et al., 2003), to measurements, the scatter between measurements and model results under swell conditions are significant. Observations show that there is a peak at the swell peak frequency for uw co-spectra, which is due to the swell-induced momentum flux (e.g. Högström et al., 2015). Högström et al. (2009) treated the total stress budget under swell conditions as the sum of four terms: (1) the tangential drag contributed by the swell, (2) the remaining tangential drag, (3) the downward momentum flux contributed by waves moving slower than the wind, and (4) the upward momentum flux contributed by waves moving faster than the wind, however, note that term (4) can be negative (Högström et al., 2015). Based on measurements from several oceanic experiments, the peak-swell contribution stress and the residual wind stress are parameterised through wave and atmospheric parameters, respectively (Högström et al., 2015). Un- der wind-following swell, neutral stratification and moderate wind conditions, the drag coefficient is expressed as (Högström et al., 2015),

2 2 2 (CdN)windsea + (1.25H n )/U C = sd p 10 (3.5) dN 1 + y

17 where (CdN)windsea is the residual drag coefficient, Hsd the peak wave height at swell frequency, np the peak frequency for swell waves, and the coefficient, y, depends on swell parameters. In most atmospheric models, the drag coefficient is calculated based on the surface roughness length. Many other atmospheric parameters (heat flux, moisture flux, etc.) are also calculated based on the surface roughness length. To keep consistency with traditional models, the new swell-related parameterisation (Eq. 3.5) is applied into the surface roughness length following Eq. 2.3, 10 z0 = (3.6) exp( √κ ) CdN for near neutral stratification, wind-following swell and moderate wind conditions in Paper III. Five-year simulation results are used to investigate the swell influence on regional climate simulations.

3.2 Sea spray influences 3.2.1 Wind stress Instead of a continuously increasing drag coefficient based on the Charnock relationship, field and laboratory measurements indicate that Cd may level off under very high winds (Powell et al., 2003; Donelan et al., 2004; Potter et al., 2015). Under high winds, sea sprays are generated by intensive wave breaking. One possible reason for the levelling off of the drag coefficient is because of sea spray influence. Applying the sea spray influence into an effective roughness length, a new wind stress parameterisation was proposed in the studies of Kudryavtsev and Makin (2011) and Kudryavtsev et al. (2012). The effective roughness length is expressed as (Kudryavtsev and Makin, 2011; Kudryavtsev et al., 2012),

Z0 = z0exp(−4m) (3.7)

σF 2 4m = ln (d/z0) (3.8) 4κu∗ where d is the depth of the spray generation layer and σ = (ρw − ρa)/ρa. In the parameterisation of Kudryavtsev et al. (2012), the SSGF is only related to the wind speed (or friction velocity). However, wave states can also affect the sea spray generation. Toba et al. (2006) proposed that using the development of wind waves may be more appropriate to describe the air-sea interaction. In Paper II, a wave-state-dependent SSGF is proposed based on

18 the study of Zhao et al. (2006) and Monahan (1986),

2  1.09 −2.95 1.02 1.19exp(−B0)  0.506Rb r0 (1 + 0.029r0 ) × 10 r0 < 20µm dF  −3 1.5 −1 7.84 × 10 Rb r0 30 < r0 < 75µm = 1 1.5 −3 dr0  4.41 × 10 Rb r0 75 < r0 < 200µm  13 1.5 −8 1.41 × 10 Rb r0 200 < r0 < 500µm (3.9) in which, 3 U10 g Rb = Cd βw, βw = (3.10) gν ωpU10 where ωp is the wave angular frequency at the wind-sea spectral peak, ν the air kinematic viscosity, βw the wave age of wind waves, r0 the initial radius of the spray droplet, and B0 = (0.666−0.976×log(r0))/0.650. After the integral of the SSGF in Eq. 3.9, they are applied to Eq. 3.8, which represents the basic parameterisation of Kudryavtsev et al. (2012), to investigate the impact of the SSGF on the drag coefﬁcient.

4 4 β = 0.1 β= 0.5, β = 0.5 w w β = 0.3 β= 1.1, β = 0.5 3.5 w 3.5 w β = 0.5 β= 1.3, β = 0.5 w w β = 0.7 β= 1.5, β = 0.5 3 w 3 w β = 1.0 β= 1.7, β = 0.5 w w Kudryavtsev et al., 2012 Kudryavtsev, Eqs. 3.7 and 3.9, β = 0.5 2.5 2.5 w Kudryavtsev et al., 2012 d d

2 2 1000·C 1000·C

1.5 1.5

1 1

0.5 0.5 (a) (b)

0 0 0 10 20 30 40 50 0 10 20 30 40 50 − − U (m s 1) U (m s 1) 10 10 Figure 3.1. Comparison of wave state impact on the drag coefﬁcient in the newly proposed parameterisation: (a) parameterisation with Eqs. 3.7 and 3.9; (b) parameterisation with Eqs. 3.7, 3.9 and 3.11 (from Paper II).

The wave-age-dependent α under wind-sea conditions from Carlsson et al. (2009) is applied into the parameterisation instead of a constant α,

−0.4 α = 0.05(cp/u∗) (3.11)

The results only introducing the wave-state-depended SSGF are shown in Figure 3.1a (Paper II). The drag coefficient increases with accelerating wind speed for young wind-sea, which is because that the sea spray cannot develop immediately when the wind speed increases suddenly, and it cannot affect the drag coefficient significantly. However, with increasing wind-wave age, the

19 influence of sea spray increases due to the development of wave-wind interaction. The wave-state influence cannot be described if only the wind-speed- dependent SSGF is applied (see the blue line representing Kudryavtsev et al., 2012). When the impact of wave age (i.e., β = cp/U10) on the Charnock coefficient (using Carlsson et al., 2009) is also introduced, the drag coefficient decreases with increasing wave age (Figure 3.1b). When the wave state is not very young (i.e., the wind-wave age is approximate βw > 0.3), the drag coefficient starts to decrease at wind speeds of 25-30 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 Cd.

3.2.2 Heat flux Sea sprays affect not only the wind stress but also the heat fluxes. Under high winds, the heat fluxes can be considered to be mediated through two different pathways, 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 parameterisation was proposed to calculate the heat fluxes from the two different components separately. The total latent and sensible heat fluxes are expressed as, HL,T = HL,int + HL,sp (3.12)

HS,T = HS,int + HS,sp (3.13) where HL,int and HS,int are the interfacial latent and sensible heat fluxes calculated using the COARE algorithm (Fairall et al., 2003), and HL,sp and HS,sp are the sea spray-mediated latent and sensible heat fluxes. In Paper II, the sea spray impact on the heat fluxes (Andreas et al., 2015) and the wind stress (section 3.2.1) are applied into an atmosphere-wave coupled model to investigate their impacts on wind storm simulations.

3.3 Swell impact on atmospheric mixing 3.3.1 E − l model LES simulations have shown that the atmospheric mixing under swell conditions is increased compared to that under ﬂat terrain conditions (Nilsson et al., 2012; Rutgersson et al., 2012). One possible reason is that turbulent eddies induced by underlying waves extend to a high layer, which alters the turbulent structure of the total atmospheric boundary layer. To apply the swell impact on the atmospheric mixing into the E −l turbulence closure scheme, the length

20 scale in E − l model (section 2.2.2) is modiﬁed to (Rutgersson et al., 2012), z l = F(Ri,c /u )dz0 (3.14) up ˆ p ∗ zbottom

ztop 0 ldown = F(Ri,cp/u∗)dz (3.15) ˆz

The function of F(Ri,cp/u∗) is expressed as

2 αn − π (αc − αn)(αrRi) Ri > 0 F(Ri,cp/u∗) = 2 αn − π (αc − αn)arctan(αr(Ri +Wmix)) Ri < 0 (3.16) The wave inﬂuence on the atmospheric mixing is added into an atmosphere- wave coupled model in Paper III through an additional mixing contribution, i.e., Wmix, for swell conditions. The Wmix reduces to 0 for strong convective stratiﬁcation conditions based on the idea that the wave-induced mixing van- ishes when convection dominates the mixing (Nilsson et al., 2012).

3.3.2 MYNN model Using the simulation results from LESs (Nilsson et al., 2012), the mixing length scale used in MYNN is calculated following Eq. 2.11 in Paper IV (Figure 3.2). The data of TKE and dissipation used in Eq. 2.11 are from LESs. One can see that the length scale under swell conditions is larger than the results from the original MYNN parameterisation. The influence of swell on the atmospheric boundary layer is from the wave surface and then indirectly influence the total boundary layer. With increasing height, the TKE length scale and the buoyancy limitation scale play important roles. Thus, to consider the swell influence on the MYNN length scale parameterisation, the wave contribution is added to the surface length scale, i.e., lS. Accordingly, the surface length scale considering the swell impact is,

lS = lS(1 + lw) (3.17) where lw is the wave contribution to the surface length scale. To agree with the results from LESs, the wave contribution parameter (lw) is parameterised through, 1 1 1 = + (3.18) lw lw1 lw2 where lw1 is an exponential increase term and lw2 an exponential decay term. After considering the swell contribution term lw in the surface length scale, the length scale from the modiﬁed MYNN is shown in Figure 3.2 as red lines. One can see that the agreement between the LES results and the MYNN results

21 Figure 3.2. The length scale for different swell conditions. (a)-(e) for the cases with −1 −1 a geostrophic wind Ug = 5ms , cp = 12.5ms , wave slope ak = 0.1 and varies con- −1 −1 −1 vective conditions: (a) Q∗ = 0Kms , (b) Q∗ = 0.001Kms , (c) Q∗ = 0.005Kms , −1 −1 (e) Q∗ = 0.01Kms and (e) Q∗ = 0.02Kms . The subplot (f) is the case with −1 −1 Ug = 1ms and Q∗ = 0Kms . The black lines are the results calculated using Eq. 2.11 with TKE and dissipation from LES results. The blue lines are calculated using the original MYNN parameterisation (section 2.2.3). The red lines are from the modified MYNN parameterisation. (from Paper IV) is improved significantly when adding the swell contribution term. At the top of the boundary layer, there are some scatter between the LES results and the MYNN length scale. One possible reason is the entrainment influence on the atmospheric mixing.

3.4 Wave impact on upper-ocean turbulence The four processes that surface waves impact the upper-ocean turbulence (i.e., wave breaking, CSF, LC, and non-breaking-wave-induced mixing) are introduced into the k − ε turbulent scheme in a 1-D ocean model in Paper V. The terms (b) and (c) in Eq. 3.2 are represented by non-breaking-wave induced mixing. The term (d) in Eq. 3.2 is represented by the CSF and LC (Wang et al., 2015). Their impacts on the simulation results concerning water temperature are tested separately and combined.

3.4.1 Breaking waves Breaking waves affect the upper-ocean turbulence through two ways: the breaking-wave-induced momentum ﬂux and the breaking-wave-induced TKE

22 flux. In the study of Craig and Banner (1994), the influence of breaking waves on energy flux losses from waves is introduced as an additional input into the TKE at the surface boundary, as follows: 3 qwb,0 = m0ρwu∗w (3.19) where u∗w is the friction velocity in water, m0 is a coefficient, treated as 100 in this study, following Craig and Banner (1994). He and Chen (2011) estimated the breaking-wave-induced stress, τwb(z) = hAi(z)4z, transferred from surface wave breaking to ocean currents, expressed as z 2 bz hAi(z)dz/ γ1ρau∗ ≈ e (3.20) ˆ−H where b is a coefficient depending on the wind speed, hAi the momentum density, and γ1 the ratio of the breaking stress to the wind stress. Here, taking account of the impact of breaking waves means taking account both breaking- wave-induced energy in the surface boundary (Eq. 3.19) and breaking-wave- induced stress on mean flows (Eq. 3.20).

3.4.2 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 , 3 ∞ π 2 2 16π 3 8π f z Us = f S f θ ( f ,θ)exp( )dθd f . (3.21) g ˆ0 ˆ−π g The CSF is usually considered in ocean models by adding an extra term (i.e., fc × Us) to momentum equations. In Paper V, the CSF is also introduced by adding the extra term to momentum equations. Some studies introduce the inﬂuence of LC as an extra shear production by the Stokes drift into the TKE equation (Kantha and Clayson, 2004; Ardhuin and Jenkins, 2006). To avoid repeatedly considering other wave inﬂuences, in Paper V, we added the LC-generated shear production to the TKE to consider its impact on the ocean vertical mixing, as follows: ∂U ∂Us ∂V ∂Vs P = Km + (3.22) LC ∂z ∂z ∂z ∂z where the Stokes drift velocities in the eastward and northward directions are denoted as Us and Vs, respectively.

3.4.3 Non-breaking waves Non-breaking-wave-induced mixing parameterisations have been proposed in several studies (Qiao et al., 2004; Hu and Wang, 2010; Pleskachevsky et al.,

23 2011). In Paper V, the parameterisation of Pleskachevsky et al. (2011) is used to test the inﬂuence of non-breaking waves. 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,

2 SM νwave = lwaveMwave (3.23) SM where lwave is the length scale of the wave-induced turbulence, Mwave 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 AM AM SM Mwave = kwaveMwave (3.24) AM where kwave is the relationship between wave-energy dissipation and total wave AM energy. Following Pleskachevsky et al. (2011), we treated kwave as a constant at 1.5 × 10−4 in Paper V. The limitation of non-breaking waves generating turbulence is that the Reynolds number is higher than the critical Reynolds number 3000 (Babanin, 2006). The wave-induced shear production is then

AM 2 Pwave = Km(Mwave) (3.25) After considering the terms induced by surface waves, the total shear production, viscosity, and heat diffusion can be expressed as follows:

0 Ps = Ps + Pwave + PLC (3.26)

0 Km = Km + νwave (3.27)

0 Kh = Kh + νwave (3.28) where Kh is the heat diffusion.

24 4. Models and data

4.1 Coupled models Atmosphere/ocean-wave coupled models are important tools to study the wave impact on climate simulations and weather forecasts. Surface gravity waves can affect air-sea interaction processes. However, the inﬂuences of surface gravity waves on the air-sea interaction are often poorly represented or ne- glected in coupled models. In this thesis, different atmosphere-wave coupled models are used to study the impact of waves on climate and weather simulations. The RCA4-WAM coupled model is used in Papers II and III. The RCA4 (Rossby Centre Regional Atmospheric model version 4) is a hydrostatic model incorporating terrain-following coordinate and semi-Lagrangian semi-implicit calculation (Jones et al., 2011). The WAM wave model (WAMDI, 1988) is a third-generation, full-spectral wave model. The WAM model provides the wave information needed by the atmospheric model and the atmospheric model provides the wind information to force the WAM model in the RCA4- WAM coupled model. In Paper I, the WRF (Weather Research and Forecast- ing Model, Skamarock et al., 2008) is used as the atmospheric model in the atmosphere-wave (WRF-WAM) coupled model. The domain of the coupled models in Papers I, II and III are mainly in European areas. Different experimental settings of atmosphere-wave coupled models are used to test the surface wave inﬂuence on the simulation results through using the boundary layer parameterisations summarized in section 3.

4.2 1D models One-dimensional (1D) numerical models are ideal models to test turbulent boundary parameterisations, which have been used in many studies. One dimensional simulation results considering wave influences are compared to LES results and measurements in Papers IV and V, respectively. The 1D atmospheric model (WRF-SCM) used in Paper IV, is designed to test the evolution of vertical profiles in the atmospheric boundary layer. The horizontal homogeneity is an assumption in WRF-SCM. The initial, surface forcing and vertical resolution conditions used for WRF-SCM are approximately the same as the LES cases used in Paper IV. Based on the comparison between the LES results and the WRF-SCM simulation results, the ideas of how to consider swell influences are investigated.

25 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). Many state-of-the-art turbulent mixing parameterisations can be chosen in GOTM. 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 are obtained from measurements. Surface wave inﬂuences are applied into the experiments in Paper V.

4.3 Measurements To verify model performances, several observational datasets are used in this thesis. The observational sets are summarised in the following part. The FINO1 platform (54o00053.500N,6o35015.500E) located 45 km north of Borkum Island in the North Sea, is an offshore platform from which the wind speed, wind direction, air temperature, air humidity and air pressure are measured at multiple levels. The measurement mast reaches approximately 100 m above the mean sea level. More details about the platform are presented by Neumann and Nolopp (2007). The FINO1 data are used in Paper II in order to test the sea spray influences on storm simulations. Östergarnsholm is a small flat island with no trees and very sparse vege- tation, situated approximately 4 km east of Gotland. A 30-m-high tower is located in southernmost Östergarnsholm (57o270N,18o590E), its base is approximately 1 m above the sea surface level. The wind, temperature and humidity are measured at different height from the tower. The wind data from the 80o − 220o sector represents open sea conditions in terms of both wave conditions and atmospheric turbulence. In Paper III, only the data from this section (80o − 220o) are used. The Papa ocean weather station is located in the eastern subarctic Pacific (50oN,145oW) 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 the data from this station for validating turbulence closure schemes (e.g. Li et al., 2013). The data in this station are used to force and initialize the 1D model used in Paper V. The wave spectrum and wave parameters needed by parameterisations used in Paper V are provided by WAM model simulations forcing by ERA-40 data (Uppala et al., 2005).

26 5. Results

5.1 Influence of instantaneous waves Tuning parameters (e.g., Charnock coefficient) in wind stress parameterisations to agree with measurements is a common way for considering wave influences without having to introduce a wave model. In contrast, in some studies, atmosphere-wave coupled models are used to take instantaneous wave influences into parameterisations. To investigate if tuning a wind stress parameterisation to measurements to capture the wave influences is enough, four different experiments are designed in Paper I (Group-I in Table 5.1).

Table 5.1. The design of experiments (from Paper I). coupled roughness length resolution Group wrfstd No Charnock relationship 20 km I, II wrfcpl Yes Eq. 3.3 20 km I, II wrfz0 No tuned z0 20 km I wrfz0var No tuned z0 with variation 20 km I wrfstd_15km No Charnock relationship 15 km II wrfstd_10km No Charnock relationship 10 km II wrfcpl_15km Yes Eq. 3.3 15 km II wrfcpl_10km Yes Eq. 3.3 10 km II

The stand-alone atmospheric model (WRF) is used in the control experiment wrfstd. In the WRF model, the roughness length is calculated based on the Charnock relationship. Comparing to the control experiment, the coupled model WRF-WAM is used in the experiment wrfcpl. In the coupled WRF- WAM model, the roughness length over water is provided by WAM model based on wave spectra (Eq. 3.3). Here, the roughness length from WAM model is treated as the “true” wave-related z0 (including the dynamic response of waves). To investigate if tuning parameterisations are enough to capture the wave inﬂuence, the roughness length was tuned to the regressed equation between u∗ and z0 calculated from wrfcpl in wrfz0. The standard deviation of z0 for speciﬁc u∗ bins are parameterised in wrfz0var through adding random variability following the same deviation. Six wind storms are simulated using the four experiments in Paper I. The simulation results of the roughness length and the friction velocity for each storm are shown in Figure 5.1. The roughness length increases with

27 friction velocity in the experiment wrfstd. The roughness length differences between the results from wrfcpl and wrfstd are large under high winds (the roughness length from wrfcpl can be three times larger than that from wrfstd), which may due to the impact of wave states on the wind stress. For the same friction velocity, in general, z0 calculated from the tuned parameterisation (wrfz0) has the same mean value as z0 from the wrfcpl results. However, it cannot simulate the distribution of z0 at same friction velocity from wrfcpl. Adding the parameterised variation of the roughness length, in general, wrfz0var can simulate the distribution of z0 at the same u∗ to some degree. However, it is a “fake” wave-related roughness length.

Figure 5.1. The relationship between the friction velocity and the roughness length of different experiments for each storm: (a) Dagmar, (b) Emma, (c) Kyrill, (d) Christian, (e) Ulli, and (f) Xaver. (from Paper I)

The simulation results of the maximum wind speed at 10 m (U10max) for each storm are shown in Figure 5.2. In general, the U10max from wrfstd has the highest value during the high wind speed periods in Group-I. This agrees with the roughness length results shown in Figure 5.1 that the roughness length from wrfstd under high winds is lower than that from the other experiments. The U10max from wrfz0 is the lowest on average. If the variation of the roughness length is added into wrfz0 (wrfz0var), it gives the second smallest U10max on average. The maximum wind speed in wrfcpl is higher than the results from wrfz0/wrfz0var (close to the results from wrfstd) for the high wind speed time periods. This indicates that tuning parametrisations have difﬁculties to capture the instantaneous wave inﬂuences.

28 35 25 (a) (b) ] -1 30 20 [m s 25 15

10max 20 U

0 10 20 30 40 50 0 20 40 60 80 100 120

25 (c) (d) ] 25 -1 20

[m s wrfstd 20 15 wrfz0 wrfz0var 10max

U 10 wrfcpl 15

0 20 40 60 80 0 20 40 60

(e) (f) ] 25 25 -1 20 20 [m s 15 15

10max 10

U 10

0 50 100 150 200 0 50 100 150 Time [hours] Time [hours] Figure 5.2. The time series of the maximum wind speed at 10 m simulated from different experiments for storms: (a) Dagmar, (b) Emma, (c) Kyrill, (d) Christian, (e) Ulli, and (f) Xaver. (from Paper I)

(a) 25 (b) 35 ] -1 30 20 [m s 25

10max 15

U 20

0 10 20 30 40 50 0 20 40 60 80 100 120

25 (c) (d) ]

-1 25 20 wrfstd [m s wrfstd_15km 20 15 wrfstd_10km wrfcpl 10max wrfcpl_15km U 10 wrfcpl_10km 15

0 20 40 60 80 0 20 40 60

(e) 30 (f)

] 25 -1 25 20

[m s 20 15 15 10max

U 10 10

0 50 100 150 200 0 50 100 150 Time [hours] Time [hours] Figure 5.3. The time series of maximum wind speed (ms−1) at 10 m simulated from different experiments in Group-II for storms: (a) Dagmar, (b) Emma, (c) Kyrill, (d) Christian, (e) Ulli, and (f) Xaver. (from Paper I)

29 5.2 Inﬂuence of horizontal resolution Together with the experiments wrfstd and wrfcpl in Table 5.1, four more experiments with different horizontal resolutions (wrfstd_15km, wrfcpl_15km, wrfstd_10km and wrfcpl_10km) are added in Group-II in order to investigate the horizontal resolution impact on the results of the atmosphere-wave coupled and atmospheric stand-alone models in Paper I (Table 5.1). The simulation results of U10max from the experiments in Group-II are shown in Figure 5.3. In general, the U10max from the high-resolution experiments is higher than that from the low-resolution experiments, which is valid for both coupled (WRF-WAM) and uncoupled (WRF) models. Increasing the horizontal resolution has a bigger impact on U10max for the coupled models compared to the uncoupled models (the value of wrfcpl_10km - wrfcpl/wrfcpl_15km - wrfcpl is larger than that of wrfstd_10km - wrfstd/wrfstd_15km - wrfstd). More detailed storm structures can be resolved in the high-resolution models compared to the low-resolution models. This is one of the possible reasons that the higher wind speed is shown in the high-resolution models. The coupled model is more sensitive to the horizontal resolution, which is may due to the detailed wave inﬂuences on the wind stress in higher resolution experiments.

5.3 Influence of sea spray In Paper II, the sea spray influence on storm simulations are investigated based on six sensitivity experiments (see Table 5.2) and the comparison between the simulation results and the measurements from FINO1. Table 5.2. Wind stress and heat fluxes parameterisations for various simulations. The Exp-1 to Exp-6 shown in this table is only for section 5.3 (from Paper II). 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)

The model errors between the simulation results and FINO1 measurements at different wind bins are shown in Figure 5.4. The parameterisation of Kudryavt- sev et al. (2012) (Exp-2) does not have signiﬁcant inﬂuence on the statistical results concerning the wind speed compared to the control run (Exp-1, without sea spray impact). Adding the wave-state-dependent SSGF (Eq. 3.9) into the experiment, Exp-3, improves the model performance concerning the wind

30 speed under high winds compared to Exp-2. If both the wave-state-dependent SSGF (Eq. 3.9) and wave-age-dependent α (Eq. 3.11) are added into the model (Exp-4), it has the best performance under high winds. However, it dose not improve the simulation results under low winds. Swell waves are normal under low winds. And the inﬂuence of swell on the wind stress is not considered in the experiments.

2 2.5 3.5 (a) (b) (c) 1.5 3 2 1 2.5 ) ) ) −1

0.5 −1 −1 1.5 2 0 1 1.5

ME (m s −0.5 MAE (m s RMSE (m s Exp−1 1 −1 Exp−2 0.5 −1.5 Exp−3 0.5 Exp−4 −2 0 0 2 6 10 14 18 22 2 6 10 14 18 22 2 6 10 14 18 22 U U U 33_obs 33_obs 33_obs Figure 5.4. 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 II).

0 1.4 2 (a) (b) (c) 1.2 −0.2 1.5 1

−0.4 C) C) o

C) 0.8 o o 1 0.6 ME (

−0.6 MAE ( RMSE ( Exp−1 0.4 0.5 −0.8 Exp−4 Exp−5 0.2 Exp−6 −1 0 0 2 6 10 14 18 22 2 6 10 14 18 22 2 6 10 14 18 22 U U U 33_obs 33_obs 33_obs Figure 5.5. Statistical results for temperature measured at a height of 100-m from FINO1: (a) mean error, (b) mean absolute error, and (c) root mean square difference (from Paper II).

The impact of the sea spray on the heat fluxes (Eqs. 3.12 and 3.13) is added into Exp-5, which only slightly affects the wind speed under high winds compared to the control experiment (Figure 5.5). However, adding the sea spray influences (Exp-5) increases the air temperature simulations, especially under high winds. If only the sea spray impact on the wind stress is added (Exp-4), it reduces the air temperature simulation results somewhat. 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 Figure 5.5). The statistical results show that if the sea spray impact

31 on both the heat ﬂuxes and the wind stress are added (Exp-6), the model results of temperature are better than that only one inﬂuence added.

Figure 5.6. The maximum wind speed at 925 hPa of different storms over time: (a) Gero, (b) Erwin/Gudrun, (c) Kyrill, (d) Ulli, (e) Patrick and (f) Klaus (from Paper II).

The simulation results of the storm tracks are not significantly different when adding the sea spray impact on the wind stress and the heat fluxes (Exp- 6). In contrast, it can affect simulation results significantly concerning storm intensity. The simulation results of the maximum wind speed at 925 hPa are shown in Figure 5.6 for each storm. Solely adding the sea spray impact on the heat fluxes improves the model results slightly compared to the measurements. However, adding the sea spray impact on the wind stress reduces the error of the maximum wind speed by approximately 17% on average. It has the best performance if the sea spray impacts on both the heat fluxes and the wind stress are added concerning the maximum wind speed (reducing the error by an average of 23% from that of the control run). The significant influences on the maximum wind speed are mainly exerted during the highest winds.

32 5.4 Swell influences At low latitudes, swell waves dominate the oceans almost all times (Semedo et al., 2011). Under swell conditions, the wind stress parameterisation is more complex than wind wave conditions. The swell-induced momentum flux has been observed and simulated to be directed both upward and downward, depending on the environmental conditions (Sullivan et al., 2008; Högström et al., 2015). In Papers III and IV, swell influences are applied into the RCA- WAM coupled model and a 1-D atmospheric model, separately. The swell impact on the wind stress under moderate winds and the atmospheric mixing are applied into the RCA-WAM coupled model in Paper III. The new parameterisation is still based on the MOST, which is the base of most atmospheric models. The swell impacts on climate simulations are summarized in section 5.4.1 based on the parameterisations discussed in sections 3.1.2 and 3.3.1. In Paper IV, the total momentum flux is calculated though two terms: turbulent momentum flux and wave-induced momentum flux. The parameterisation used in Paper IV is not based on the MOST. The swell impact on the atmospheric mixing is applied into the MYNN model (section 3.3.2).

5.4.1 Climate simulation The swell impact on climate simulations is investigated through four experiments in Paper III. In the control experiment (Exp-Ctl), the default RCA is used, in which the Charnock relationship is used to calculate the roughness length. To test the swell impact on the wind stress and mixing length separately and combined, three more experiments were designed. Exp-Mix introduces the swell wave impact on the atmospheric mixing (section 3.3.1), Exp-Drag introduces the swell wave impact on the wind stress (section 3.1.2), and Exp-Full includes both the swell impact on the atmospheric mixing and the wind stress (sections 3.1.2 and 3.3.1). Five-year simulation results from the four experiments are compared to the measurements from Östergarnsholm site. The statistical results for the wind speed at 10m are shown here. Comparing to the control experiment (Exp- Ctl), the mean absolute error (MAE), standard deviation (STD) and root mean square difference (RMSD) are reduced and the correlation coefficient (R) is increased if the swell impact on the atmospheric mixing length is added (Exp- Mix). Adding the swell influence on the wind stress (Exp-Drag) improves the simulation results concerning ME (mean error) of the wind speed. If both the impact of swell on the atmospheric mixing length and the wind stress are added (Exp-Ful), it has the best performance in the four experiments in terms of ME, MAE, STD, RMSD, and R. Although the improvement of ME for the experiments including swell influence is small, the statistical analysis shows the improvement for Exp-Full has passed the 95% confidence level for Östergarnsholm data. Comparing to Exp-Full, the significant level of the

33 −1 Figure 5.7. The difference in U10 (in ms ) between the control experiment (Exp-Ctl) and the other experiments: (a) Exp-Mix - Exp-Ctl, (b) Exp-Drag - Exp-Ctl and (c) Exp-Full - Exp-Ctl (from Paper IV).

improvement for Exp-Mix and Exp-Drag is relatively lower (70% and 80% respectively). The mean difference for U10 between the three experiments and the control run (Exp-Ctl) is shown in Figure 5.7. Adding the swell impact on the atmospheric mixing (Exp-Mix) only changes the wind speed slightly (-0.1 to 0.1 ms−1 over ocean on average). Comparing to the control experiment, Exp-Mix increases the surface wind speed slightly on average. In contrast with Exp- Mix, adding the swell impact on the wind stress (Exp-Drag) reduces the wind speed by more than 0.15 ms−1 for the Atlantic Ocean, but by less than 0.05 ms−1 for the Baltic Sea. According to the results from Högström et al. (2015) (see their Figure 13), the swell slope has a big impact on the drag coefﬁcient even at the same wind speed. This is a possible reason of the smaller impact over the Baltic sea area. Adding both the swell impact on the atmospheric mixing length and the wind stress (Exp-Ful) reduces (increases) the wind speed compared with Exp-Ctl (Exp-Drag). And this indicates that the swell impact on the wind stress dominates the swell inﬂuences concerning these parameters.

5.4.2 WRF-SCM results The MOST was reported not valid under swell conditions in some studies (Drennan et al., 1999; Smedman et al., 2009; Sullivan and McWilliams, 2009). In Paper IV, a new frame to calculate the total momentum flux was proposed. The total momentum flux is calculated by turbulent momentum flux and wave- induced momentum flux, separately. The wind-following swell LES cases used in Nilsson et al. (2012) (wave-induced upward momentum flux cases) were used to test the new model. The turbulent momentum flux is usually parameterised based on wind gradients and the eddy viscosity. The LES simulations show that the zero tur-

34 bulent momentum flux height is approximately the same height as the zero wind gradient height (the low-level wind jet height) under neutral stratification cases. With increasing atmospheric convection, the difference between the two heights is increased due to the buoyancy influence, which is a common problem for local closure boundary layer schemes (Cohen et al., 2015). In this sense, the turbulent momentum flux still can be parameterised by wind gradients and the eddy viscosity under swell conditions, dU τ (z) = −K (5.1) t m dz the expression of the eddy viscosity Km in MYNN parameterization can be found in sections 2.2.3 and 3.3.2 (considering swell influences on the atmospheric mixing length scale). Under swell conditions, the swell-induced momentum flux can extend to a much higher layer (Smedman et al., 1994; Grachev and Fairall, 2001). To consider the wave-induced momentum flux into the turbulence closure scheme, the wave-induced momentum flux is calculated separately. From the LES cases, the swell-induced momentum flux decays approximately exponentially Aukpz with height (τw(z) = τw0 × e , where τw0 is the wave-induced surface momentum flux, and Au the exponential decay coefficient). The exponential decay coefficient and the surface wave-induced momentum flux vary with convective condition and wave age according to the LES results. Then the total momentum flux is, τ(z) = τt(z) + τw(z) (5.2) In addition, the wind shear production in the prognostic equation for TKE is expressed as 0 0 ∂U 0 0 ∂V ∂U Ps = −(u w ) − (v w ) + τw (5.3) ∂z ∂z ∂z The schematic diagram of swell waves impact on the wind profile is shown in Figure 5.8. Adding only the swell impact on the atmospheric mixing increases slightly the surface wind speed and decreases the wind speed in the high layer (see the red line in Figure 5.8). Introducing only the wave impact on the momentum flux into the effective roughness length based on the MOST reduces/increases the wind speed (see the grey lines in Figure 5.8) for the cases that the effective roughness length is larger/smaller than the results from traditional parametrizations, e.g., COARE (Fairall et al., 2003). However, it cannot simulate the change of the profiles due to the swell influence without considering the profile of wave-induced momentum flux. If all the three terms are added into the model, it improves the model simulation significantly (see the black line in Figure 5.8). Thus, the three terms (the atmospheric mixing length scale, the swell-induced momentum flux on the surface, and the swell-induced momentum flux profile) impacted by swell waves should be all considered directly in numerical models in order to improve the model performance.

35 Figure 5.8. Schematic diagram of introducing different wave impacts. The blue line represents the flat surface. The red line represents the results adding swell impact on the atmospheric mixing. The solid (dashed) grey line represents the results adding the swell impact on the downward (upward) surface momentum flux into the effective roughness length. The black line represents all the wave impacts (atmospheric mixing, surface momentum flux, and wave induced momentum flux profile) are added (from Paper IV).

5.5 Wave impact on upper-ocean turbulence In this section, the results are based on sensitivity simulations on the Papa station data in year 1962. The simulations partially or fully include the inﬂuences of surface waves on upper-ocean mixing in Paper V, described in Section 3.4. The design details of six experiments are shown in Table 5.3.

Table 5.3. 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 V). The Exp-1 to Exp-6 in this table is only for section 5.5. 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

Figure 5.9 shows the statistical results of temperature at various depths. Introducing the LC inﬂuence (Exp-4) reduces the ME about 0.2 oC and also improves the MAE and RMSD in the surface layer (0-20m). Adding the impact of non-breaking waves (Exp-5) not only reduces the ME but also MAE and RMSD in the surface layer (0-20m). If all the wave impacts are added into the model (Exp-6), it shows the best performance concerning the temper-

36 ature in the surface layer (0-20m). However, adding the non-breaking wave impact decreases the model performance in the layer (70-100m), which may be caused by the overestimation of the mixed layer depth. The correlation coefficient does not change significantly for all experiments, which may be due to the temperature change in the surface layer which is mainly dominated by the surface forcing (i.e., heat fluxes, momentum flux). From ME, MAE, RMSD, and R, one can see that Exp-6 performs best of all the experiments. Comparing the various wave impact aspects indicates that non-breaking waves exert a dominant effect, the second most important process being LC.

Figure 5.9. Statistical results for temperature at various depths: (a) ME, (b) MAE, (c) RMSD, and (d) R (from Paper V).

The 2D wave spectrum is not always available when calculating the Stokes drift. In some ocean models, the surface Stokes drift velocity is calculated 1/2 from wind speed or friction velocity, such as Us0 = 0.377|τ| (Madec, 2008). Then, the vertical proﬁles of the Stokes drift are calculated based on some simpliﬁed formulas, such as (Breivik et al., 2015),

e2kez Us(z) = Us0 (5.4) 1 − 8kez where ke is the inverse depth scale. To investigate the impact of the 2D wave spectrum, two more experiments were designed. The setting differences from Exp-6 are:

37 1/2 • LC-1: the surface Stokes drift is estimated using, Us0 = 0.377|τ| , the vertical profile of the Stokes drift being calculated using Eq. 5.4. • LC-2: the surface Stokes drift is estimated from wave spectrum, the vertical profiles of the Stokes drift being calculated using Eq. 5.4. Figure 5.10 shows the statistical results of temperature profiles. Using the surface Stokes drift estimated from wind stress (LC-1) worse the performance of the simulated temperature not only in ME and MAE but also for RMSD. Comparing to LC-1, if only the Stokes drift calculated from wave spectrum and the profiles estimated from Eq. 5.4 are used, it has 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), the feedback from it influences the simulations in a much deeper layer. Both LC-1 and LC- 2 have worse performances compared to Exp-6, which shows that the wave spectrum is necessary for calculating the Stokes drift.

Figure 5.10. Statistical results for temperature at various depths: (a) ME, (b) MAE, (c) RMSD, and (d) R (from Paper V).

38 6. Summary and Conclusions

Measurements, 3D atmosphere-wave coupled models, and 1D models were used to investigate how to introduce wave influences into ESMs and their impact on numerical simulation results. The answers to the four scientific questions proposed in the introduction are summarized here. • Do we need instantaneous wave information to simulate wave impact on atmospheric/oceanic numerical models? The instantaneous wave-induced stress and its corresponding tuning wind stress parameterisations were used to investigate the necessity of the instantaneous wave information in models based on storm simulations (Pa- per I). A group of sensitivity experiments were designed to investigate the wave impacts using both an atmosphere-wave coupled model and an atmospheric stand-alone model. Adding the wave-induced stress weakens the simulation results of storm intensity. Applying a roughness length tuned to an average friction velocity has difficulties to capture the simulation results from the “true” wave-related roughness length. In other words, the instantaneous wave information is necessary to simulate the wave influence on atmospheric and oceanic models. High horizontal resolution models intensify the simulation results of storms, which is validated for both coupled and uncoupled models. The coupled model, considering influences of dynamic roughness length, is more sensitive to the model horizontal resolution than the atmospheric stand-alone model. • How big impact of sea sprays and waves have on storm simulations in numerical models? A wave-state-dependent sea spray generation function (SSGF) and a wave-age-dependent Charnock coefficient were introduced into a wind stress parameterisation in an atmosphere-wave coupled model (Paper II) to investigate the sea spray and waves impact on storm simulations. A heat flux parameterisation considering sea spray influences was also introduced into the atmosphere-wave coupled model. Adding the wave-state-dependent SSGF and Charnock coefficient into a drag coefficient parameterisation improves the model performance under high winds, but, decreases the air temperature compared with the control experiment. The impact of the wave-state-dependent SSGF is larger than the wave-age-dependent Charnock coefficient. Introducing

39 only the sea spray impact on the heat fluxes improves the model performances on air temperature compared to the control experiment, but, does not have significant impact on the wind speed. Introducing both the sea spray impact on the wind stress and the heat fluxes, the model has a better performance of temperature and wind speed than introducing only one impact. As expected, the wind stress parameterisation including the sea spray influences intensifies the simulation results of storms. • How to introduce swell impacts on the atmospheric boundary layer into ESMs? The impact of swell waves on the wind stress and atmospheric mixing were investigated using an atmosphere-wave coupled model (Paper III) and a 1D atmospheric model (Paper IV). The wind stress under wave conditions is calculated by two terms: turbulent momentum flux and wave-induced momentum flux. The wave-induced momentum flux decays approximately exponentially with height. Under swell conditions, the atmospheric mixing length scale in the E −l and the MYNN models is increased compared to that under flat conditions. Based on the MOST, applying the swell impact on the surface wind stress into an effective roughness length in an atmosphere-wave coupled model decreases the surface wind speed. However, adding the swell impact on the atmospheric mixing length increases the surface wind speed. Adding the wave influences improve the model performance compared to the control experiment without considering wave influences (Paper III). Based on 1D simulations, the swell influence should be taken into account through three terms: atmospheric mixing length, swell-induced momentum flux at the surface, and the wave-induced momentum flux profile. Introducing both the swell-induced momentum flux profile and swell impact on the atmospheric mixing improves the model simulation agreement best with LES results (Paper IV). It can simulate the low- level wind jet due to the swell influence, which cannot be simulated if considering only one of the swell influences. • Which process of the wave impact on the upper-ocean layer is the most important one? How do their accumulated influences affect numerical simulations? We introduced the four wave processes affecting upper-ocean turbulence, i.e., wave breaking, Stokes drift interaction with the Coriolis force, Langmuir circulation, and stirring by non-breaking waves, into a 1D ocean model (Paper V). Through the comparison of sea temperature simulation results from sensitivity experiments, their influence were investigated.

40 Adding all the four wave impacts on upper-ocean turbulence processes has the best model performance concerning sea temperature and mixed layer depth compared to that adding only one wave impact process. In the four wave-related processes, 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. Using 2D wave spectrum to calculate the Stokes drift vertical profiles is more accurate compared to estimating the Stokes drift from wind speed, and can improve the model results. In further model development, we suggest using the 2D wave spectrum to calculate vertical profiles of the Stokes drift if possible. ESMs are important tools to describe climate, tropical cyclones, floods, etc. The simulation results of climate and weather from ESMs are important references for social and biological systems to adapt the climate change and avoid hazardous weathers. Reducing the uncertainties of numerical simulation is an important topic for both the atmospheric and oceanic research communi- ties and the social society. All the results from the five papers show that the surface wave influence play an important role to reduce model uncertainties both for the ocean and atmosphere. Thus, wave influences should be correctly represented in ESMs in further model developments to improve model performances.

41 7. Sammanfattning på svenska

Jordsystem-modeller (Earth System Models, ESM-modeller) används för att beskriva atmosfär-jord-havsystemet. Här har mätningar, kopplade 3-dimensionella modeller och endimensionella modeller använts för att undersöka hur man kan beskriva vågeffekter i ESM-modeller och hur modellernas resultat påverkas av havsvågor. De fyra frågeställningar som avhandlingen bygger på är sammanfattade nedan, de är baserade på resultat från de fem artiklarna som ingår i avhandlingen. • Behöver vi fullständig våginformation för att simulera vågeffekter i atmosfäriska/oceanografiska numeriska modeller? För att studera om våginformation (främst genom att ytans friktion varierar i tid och rum) är viktig när man modellerar stormars utveckling gjordes ett antal känslighetssimuleringar av stormar för att undersöka vågef- fekter. Simuleringar gjordes både med en kopplad atmosfär-vågmodell och med enbart en atmosfärsmodell (Artikel I). Resultaten visar att genom att införa friktionen från vågorna minskas stormarnas intensitet. Det är inte tillräckligt att låta ytans skrovlighet bestämmas av den genomsnittliga friktionen från vågfältet, utan ett va- riabelt vågfält behövs för att korrekt simulera vågeffekter i atmosfäriska och oceanografiska modeller. Med högre horisontell upplösning intensifieras stormarna, både med vågeffekter och utan. Den kopplade modellen varierar mer vid en ökning eller minskning av den horisontella upplösningen (när det gäller påverkan från variabel skrovlighet) jämfört med den okopplade modellen. • Hur stor påverkan har havsspray och vågor på simuleringar av stormar? För att undersöka effekten av vattendroppar som avges från ytan (havsspray) och vågor på simuleringar av stormar introducerades en SSGF (Sea Spray Generator Function) som är beroende av det varierande våg- fältet och en Charnock-koefficient som beror på vågornas ålder i en kopplad atmosfär-vågmodell för simulering av höga vindhastigheter (Ar- tikel II). Utöver detta infördes också en parametrisering av värmeflöde som beror på havsspray. Effekten av havsspray på ytfriktionen och vär- meflödet undersöktes med simuleringar av sex stormar. Jämförelse med mätningar visar att genom att införa den uppdaterade SSGF:n och Charnock-koefficienten i parametriseringen av friktionsko- efficienten förbättras modellresultaten vid höga vindar. Effekten från den

42 uppdaterade SSGF:n har större påverkan än den uppdaterade Charnock- koefficienten. Genom jämförelse med mätningar visar det sig att bara införa effekten av havsspray på värmeflödet förbättrar resultatet för temperatur, men har ingen signifikant effekt på vindhastigheten. Att däremot införa effekten av havsspray på både friktionen och värmeflödet ger bäst resultat när det gäller både temperatur och vindhastighet. Som väntat, då man tar hänsyn till havssprayens inverkan på friktionen, intensifieras stormarna. • Hur kan effekterna av dyningsvågor på det atmosfäriska gränsskik- tet introduceras i ESM-modeller? Effekten av dyningsvågor på ytfriktionen och omblandningen i atmosfä- ren undersöktes med en kopplad atmosfär-vågmodell (Artikel III) och en endimensionell atmosfärisk modell (Artikel IV). Vågornas påverkan på ytfriktionen beräknas utifrån två termer: friktionen beroende av skjuv- ning och beroende av vågor. Friktionen inducerad av vågor avtar ungefär exponentiellt med höjden. I turbulensbeskrivningar av typen E − l och MYNN (komponenter i de kopplade modellerna) ökar blandningshöjden vid dyning jämfört med en plan markyta. Genom att införa effekten av dyningsvågor på friktionen vid ytan som en effektiv skrovlighetslängd i en kopplad modell minskar vindhastigheten vid ytan. Att däremot införa dyningseffekten på den atmosfäriska bland- ningshöjden leder till en ökad vindhastighet vid ytan. Jämförelse med mätningar visar att båda metoderna förbättrar modellresultaten (Artikel III). Genom simuleringar med en endimensionell modell visar det sig att effekten av dyningsvågor bör införas i parametriseringen genom tre termer: den atmosfäriska blandningshöjden, den dyningsskapade friktionen vid ytan och den justerade impulsprofilen. Jämförelse med LES (Large Eddy Simulations) visar att resultatet blir bäst om alla tre effekterna in- förs (Artikel IV). Då hänsyn tas till alla tre effekterna kan simuleringarna fånga det ytnära vindmaximum som bildas av dyningsvågor, vilket inte är fallet om endast en av effekterna införs. • Vilken vågproducerad process har störst betydelse för omblandning i de övre delarna av havet? Hur påverkar deras kombinerade effekt simuleringar? De fyra processerna (vågbrytning, Stokes-driftens interaktion med Cori- olis-kraften, Langmuir-cirkulationer och omblandning av icke-brytande vågor) som påverkar turbulensen i havet nära ytan parametriserades i en endimensionell havsmodell (Artikel V). Deras effekt studerades genom att jämföra modellerade och observerade havstemperaturer. Om effekten från alla fyra processerna läggs till ger det bättre resultat vad gäller havstemperaturer och blandningshöjd än om endast en av pro-

43 cesserna införs. Av de fyra processerna visar sig omblandningen av icke- brytande vågor och Langmuir-turbulensen vara de viktigaste. Vid framtida modellutveckling föreslår vi att det två-dimensionella vågspektrumet ska användas för att beräkna vertikalproﬁler av Stokes-driften om det är möjligt, eftersom det ger bättre resultat. ESM-modeller är viktiga verktyg för att beskriva atmosfärs-hav systemet. Dessa används vid simuleringar av klimat, tropiska cykloner, översvämningar och ett stort antal andra tillämpningar. Resultaten från de här fem artiklarna visar att vågor spelar en viktig roll i att minska osäkerheten i både havs-och atmosfärsmodeller. Därför är det viktigt att vågeffekter är korrekt implemen- terade i ESM-modeller vid framtida modellutveckling.

44 8. Acknowledgements

Finally, I come to the last section of my dissertation. It is the only part of the thesis that I can express my brain waves without considering their impacts on the turbulence. From the subject of the navigation technology during my bachelor study to the meteorology, oceanography, waves and turbulence, it is a big decision in my life. However, it is one of the best decisions I have made. The atmosphere-wave-ocean coupled system is so interesting, which always attracts me to test new ideas and make me feel the research is so interesting. I would like to acknowledge many people I met during my PhD study. This thesis could not be finished without the support, help and encouragement from you. First of all, I give my deepest and most sincere thanks to my supervisors Anna Rutgersson and Erik Sahlée. I want to thank you for giving me the opportunity to study in Uppsala and do the interesting project. Your encour- agements and comments always give me motivations and new ideas on how to solve the problems that I met. You are positive for my visiting study in the USA, which gives me a good opportunity to study the critical layer theory. Your passion for scientific research has infected me during my PhD study. A special thank goes to Anna. You always can find some time to discuss with me about my immature ideas even you are very busy. Tihomir Hristov is acknowledged for inviting me to do the visiting study in Johns Hopkins University at the USA. Your rigorous in research gives me a deep understanding of how to be a good researcher. You helped me a lot to understand the mechanism of wind-wave coupling processes. I really enjoy the lunch discussion with you about the research and life. Thank you and Kalina for inviting me to parties which make me feel welcome at Baltimore. Very special thanks to my co-authors. I would like to thank Christian Di- eterich in SMHI for helping me solving many problems when setting up of the coupled model. Xiaoli Guo Larsén in DTU is acknowledged for sharing her measurements, and your quick responses to the questions of our papers speeded up the paper process time. A special thank is given to Erik Nils- son who gives me a lot of help during the beginning of my analysis of the LES data. Dave is thanked for sharing his code and the discussions about the atmosphere-wave coupling. I want to especially thank my master supervisor Prof. Yuanqiao Wen for your patience and supports. You give me an opportunity to step into the area of meteorology and oceanography. Prof. Shiqiu Peng is acknowledged for your help when I start to run oceanic models. The experiences of running

45 oceanic models make me feel easy to set up the atmosphere-wave-ocean coupled model. I wish to thank senior meteorologists Ulf, Ann-Sofi, Conny, Monica, Hans, Marcus, Anna S and Bjorn for the nice presentations and discussions. PhD students and post-docs in meteorology, Johan, Eva, Maria, Petra, Andreas, Kristina, Tito, Jennie, Adam, Nina, Antonin and Olof are acknowledged for the seminars and discussions you gave. Nina, I want to thank you for sharing lots of fun during field works, climbing tanning and lunches. Thank you for help me translating the swedish summary of my thesis. Adam is acknowledged to be my mentor when I arrived in Uppsala. I am really enjoying sharing an office with Lebing, Zhibing, Antonin, Andreas and Byeongju. I will not forget the interesting talks we have. All the PhD students in LUVAL group are acknowledged for sharing a lot of fun during lunches. I wish to thank Shunguo, Fei and Haizhou for enjoying the swimming time, the “special” food and the fun time together. Nahar is thanked for the happy time we spent in Baltimore. Special thanks are given to my Chinese friends I meet during my PhD study: Feiyan Liang, Changqing Ruan, Liang Tian, Fengjiao Zhang, Chunling Shan, Ping Yan, Keqiang Guo, Lanyun Miao, Le Gao, Hongling Deng, Zhina Liu, Na Xiu, Meiyuan Guo, Jiajie Yan, Fengzhen Sun, Weijia Yang, Liguo Wang, Yongmei Gong, Tianyi Song, Jing Guo, Fan Zou, Peng Chen, Peng He, Lei Liu, Xiao Xiao, Zhiliang Zhang, Ruixue Sun, Yaocen Pan, Xiaodong Shang, Huan Wang, Xin Chen, Shihuai Wang, Dou Du, Cuiyan Li, Xiao Huang and others. Thank you all for trips, dinners and happy memories. Without you guys, there would not be so colourful life during my PhD study. The Swedish Research Council (project 2012-3902) is acknowledged for financial supporting of my PhD study. Liljewalch travel scholarship and Wal- lenberg Foundation are acknowledged for financial support of my conference travellings. Finally, the biggest thank goes to my parents and my two sisters. Without your support, I cannot finish this thesis. Whenever I met problems I know you are always behind me. Thank you for your selfless love. The road ahead will be long and my climb will be steep.

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Acta Universitatis Upsaliensis Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1478 Editor: The Dean of the Faculty of Science and Technology

A doctoral dissertation from the Faculty of Science and Technology, Uppsala University, is usually a summary of a number of papers. A few copies of the complete dissertation are kept at major Swedish research libraries, while the summary alone is distributed internationally through the series Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology. (Prior to January, 2005, the series was published under the title “Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology”.)

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