Introducing Surface Gravity Waves into Earth System Models

Transcription

1 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 UPPSALA 2017 ISSN ISBN urn:nbn:se:uu:diva

2 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 Introducing Surface Gravity Waves into Earth System Models. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 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 nonbreaking-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 Uppsala, Sweden. Lichuan Wu 2017 ISSN ISBN urn:nbn:se:uu:diva (

3 Dedicated to my family and friends 仅以此文献给我的家人和朋友们

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5 List of papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I II III IV V 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), doi: /JT ECH-D 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., Larsén, X.G. (2016). Swell impact on wind stress and atmospheric mixing in a regional coupled atmospherewave model. Journal of Geophysical Research: Oceans, 121(7), doi: /2015JC 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). Wu, L., Rutgersson, A., Sahlée, E. (2015). Upper-ocean mixing due to surface gravity waves. Journal of Geophysical Research: Oceans, 120(12), doi: /2015JC 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.

6 Wu, L., Hristov T., Rutgersson, A. (2017). Vertical profile of spectrumintegrated wave-coherent momentum flux and variances (submitted). Jeworrek, J., Wu, L., Christian D., Rutgersson, A. (2017). Characteristics of Convective Snow Bands along the Swedish East Coast. Earth System Dynamics (In press). doi: /esd 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: /2016JC 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: /IJSTL Wu, L., Wen, Y., Zhou C., Xiao, C., Zhang, J. (2014). Modeling the Vulnerability of Waterway Networks. Journal of waterway, port, coastal, and ocean engineering 140(4): doi: /(ASCE)WW

7 Contents 1 Introduction Background Monin-Obukhov similarity theory Turbulence closure schemes K-theory E l model MYNN model k ε Model Parameterisations with wave influences Wave-induced stress Wave spectra model Parameterisation Sea spray influences Wind stress Heat flux Swell impact on atmospheric mixing E l model MYNN model Wave impact on upper-ocean turbulence Breaking waves Stokes drift Non-breaking waves Models and data Coupled models D models Measurements Results Influence of instantaneous waves Influence of horizontal resolution Influence of sea spray Swell influences Climate simulation WRF-SCM results Wave impact on upper-ocean turbulence

8 6 Summary and Conclusions Sammanfattning på svenska Acknowledgements References

9 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

10 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-waveinduced 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

11 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 nonbreakingwave 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

12 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 u z = ϕ(z/l) (2.1) where u = (uw 2 + vw 2 ) 1/4 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, L = u3 κ g q T 0 C p ρ a (2.2) in which g is the gravity acceleration, T 0 the surface temperature, q the kinematic heat flux, C p the specific heat, and ρ a the air density. In numerical models, the bulk formula is usually used to calculate the wind stress, τ = ρ a u 2 = ρ a C d U 2 10, where C d is the drag coefficient. The drag coefficient under neutral stratification conditions can be expressed as, 12 C dn = κ 2 ln(10/z 0 ) 2 (2.3)

13 The Charnock relationship (Charnock, 1955) is usually used to parameterised the roughness length over the ocean in numerical models, z 0 = αu 2 /g (2.4) where α is the Charnock coefficient. The value of the Charnock coefficient is usually set to be approximately (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 K-theory Due to the coarse resolution of atmospheric and oceanic models, numerical models can only simulate time-averaged quantities. An instantaneous quantity, â, can be decomposed into its time-averaged, i.e., A, and fluctuating quantities, i.e., a: â = 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 (a ) is the total fluctuating part, a = a. Thus, the total momentum flux uw = u w. 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

14 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, u w = K m du dz where K m is the eddy viscosity coefficient. (2.6) 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, K m = l E (E is the TKE and l a length scale), in which the length scale is expressed as, where l up and l down are: 1 l = 1 l up + 1 l down (2.7) ˆ z l up = F(Ri)dz z bottom (2.8) l up = ˆ ztop z F(Ri)dz (2.9) where F(Ri) is a function of the local Richardson number, z bottom and z top are the lower and upper boundaries of the mixing domain. The F(Ri) is calculated by { αn 2 F(Ri) = π (α c α n )(α r Ri) Ri > 0 α n π 2 (α (2.10) c α n )arctan(α r Ri) Ri < 0 where α n, α c, and α r are coefficients 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 K m = l M S m q, where l M is the master length scale, q = 2T KE, and S m the non-dimensional diffusion coefficient for momentum flux. The master length scale is calculated based on the relationship between the TKE and dissipation (e.g. Nakanish, 2001), l M = q3 B 1 ε (2.11) 14

15 where B 1 is a constant (i.e., B 1 = 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 = (2.12) l M l S l T l B where l S is the surface length scale, l T the length scale depending upon the turbulence structure of the planetary boundary layer (PBL), and l B the length scale limited by the buoyancy effect k ε Model The k ε turbulence model is a two-equation model. To improve the mixinglength model is the original impetus for the k ε model. The transport equation for the TKE, E, is E t = z ( ) Km E + P s + P b ε (2.13) σ k z where σ k is the constant Schmidt number, P s shear production, and P b buoyancy production. The transport equation for dissipation is ε t = ( ) Km ε + ε z σ ε z q [c ε1p s + c ε3 P b c ε2 ε] (2.14) where σ ε is the Schmidt number for ε, and c ε1, c ε2, and c ε3 are empirical coefficients. Shear production, P s, is calculated by [ ( U ) 2 ( ) ] V 2 P s = K m +. (2.15) z z The viscosity is calculated as K m = c µ E 1/2 l (2.16) where c µ 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

16 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 (Smedman 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, â = A + a + ã (3.1) where ã is the wave-coherent fluctuation and a the turbulence fluctuation part. Thus, over surface waves, the total momentum flux can be written as, uw = (u + ũ)(w + w) = }{{} u w + }{{} u w + }{{} ũw + }{{} ũ w (a) (b) (c) (d) (3.2) 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 wavecoherent 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., τ t (term (a) in Eq. 3.2), and the wave-induced momentum flux, i.e., τ w (term (d) in Eq. 3.2): τ = τ t + τ w. 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 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

17 In the coupled model, the Integrated Forecasting System (IFS) is coupled with a wave model to consider the wave-induced stress. Later, many atmospherewave 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 0 = α gρ a (1 τ w /τ) 1/2 (3.3) and the wave-induced stress is expressed as (Janssen, 1991), τ w = ρ w ˆ ωγs f θ cos(θ ϕ)d f dθ (3.4) where ρ w 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 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 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). Under wind-following swell, neutral stratification and moderate wind conditions, the drag coefficient is expressed as (Högström et al., 2015), C dn = (C dn) windsea + (1.25H 2 sd n2 p)/u y (3.5) 17

18 where (C dn ) windsea is the residual drag coefficient, H sd the peak wave height at swell frequency, n p 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 z 0 = κ (3.6) exp( 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 Wind stress Instead of a continuously increasing drag coefficient based on the Charnock relationship, field and laboratory measurements indicate that C d 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), Z 0 = z 0 exp( m ) (3.7) m = σf 4κu ln 2 (d/z 0 ) (3.8) where d is the depth of the spray generation layer and σ = (ρ w ρ a )/ρ a. 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

19 the study of Zhao et al. (2006) and Monahan (1986), 0.506R df 1.09 b r ( r ) exp( B2 0 ) r 0 < 20µm = 3 R 1.5 b r < r 0 < 75µm dr R 1.5 b r < r 0 < 200µm R 1.5 b r < r 0 < 500µm (3.9) in which, U10 3 R b = C d gν β w, β w = g (3.10) 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 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 β w = β= 0.5, β w = β w = 0.3 β = 0.5 w 3.5 β= 1.1, β w = 0.5 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. 3.7 and 3.9, β = 0.5 w Kudryavtsev et al., C d C d U 10 (m s 1 ) (a) U 10 (m s 1 ) (b) 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, α = 0.05(c p /u ) 0.4 (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

20 influence of sea spray increases due to the development of wave-wind interaction. The wave-state influence cannot be described if only the wind-speeddependent SSGF is applied (see the blue line representing Kudryavtsev et al., 2012). When the impact of wave age (i.e., β = c p /U 10 ) 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 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 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, H L,T = H L,int + H L,sp (3.12) H S,T = H S,int + H S,sp (3.13) 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. 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 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

21 scale in E l model (section 2.2.2) is modified to (Rutgersson et al., 2012), l up = l down = ˆ z z bottom F(Ri,c p /u )dz (3.14) ˆ ztop The function of F(Ri,c p /u ) is expressed as z F(Ri,c p /u )dz (3.15) { αn 2 F(Ri,c p /u ) = π (α c α n )(α r Ri) Ri > 0 α n π 2 (α c α n )arctan(α r (Ri +W mix )) Ri < 0 (3.16) The wave influence on the atmospheric mixing is added into an atmospherewave coupled model in Paper III through an additional mixing contribution, i.e., W mix, for swell conditions. The W mix reduces to 0 for strong convective stratification conditions based on the idea that the wave-induced mixing vanishes when convection dominates the mixing (Nilsson et al., 2012) MYNN model Using the simulation results from LESs (Nilsson et al., 2012), the mixing length scale used in MYNN is calculated following Eq in Paper IV (Figure 3.2). The data of TKE and dissipation used in Eq 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., l S. Accordingly, the surface length scale considering the swell impact is, l S = l S (1 + l w ) (3.17) where l w is the wave contribution to the surface length scale. To agree with the results from LESs, the wave contribution parameter (l w ) is parameterised through, 1 = (3.18) l w l w1 l w2 where l w1 is an exponential increase term and l w2 an exponential decay term. After considering the swell contribution term l w 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

22 Figure 3.2. The length scale for different swell conditions. (a)-(e) for the cases with a geostrophic wind U g = 5ms 1, c p = 12.5ms 1, wave slope ak = 0.1 and varies convective conditions: (a) Q = 0Kms 1, (b) Q = 0.001Kms 1, (c) Q = 0.005Kms 1, (e) Q = 0.01Kms 1 and (e) Q = 0.02Kms 1. The subplot (f) is the case with U g = 1ms 1 and Q = 0Kms 1. The black lines are the results calculated using Eq 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 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

23 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: q wb,0 = m 0 ρ w u 3 w (3.19) 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/ { γ 1 ρ a u 2 } e bz (3.20) where b is a coefficient depending on the wind speed, A the momentum density, and γ 1 the ratio of the breaking stress to the wind stress. Here, taking account of the impact of breaking waves means taking account both breakingwave-induced energy in the surface boundary (Eq. 3.19) and breaking-waveinduced stress on mean flows (Eq. 3.20) 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 f θ ( f,θ)exp( 8π2 f 2 z )dθd f. (3.21) g The CSF is usually considered in ocean models by adding an extra term (i.e., f c U s ) 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 U s P LC = K m z z + V z ] V s z (3.22) where the Stokes drift velocities in the eastward and northward directions are denoted as U s and V s, respectively 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

24 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, ν wave = l 2 wavem SM wave (3.23) 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 (3.24) where kwave AM is the relationship between wave-energy dissipation and total wave energy. Following Pleskachevsky et al. (2011), we treated kwave AM as a constant at 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 P wave = K m (M AM wave) 2 (3.25) 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 (3.26) K m = K m + ν wave (3.27) where K h is the heat diffusion. K h = K h + ν wave (3.28) 24

25 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 neglected 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 Forecasting 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 D 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

26 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 (54 o N,6 o E) 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 vegetation, situated approximately 4 km east of Gotland. A 30-m-high tower is located in southernmost Östergarnsholm (57 o 27 N,18 o 59 E), 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 80 o 220 o sector represents open sea conditions in terms of both wave conditions and atmospheric turbulence. In Paper III, only the data from this section (80 o 220 o ) are used. 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 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

27 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 km I, II wrfz0 No tuned z 0 20 km I wrfz0var No tuned z 0 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 km II wrfcpl_10km Yes Eq 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 z 0 (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 z 0 calculated from wrfcpl in wrfz0. The standard deviation of z 0 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

28 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, z 0 calculated from the tuned parameterisation (wrfz0) has the same mean value as z 0 from the wrfcpl results. However, it cannot simulate the distribution of z 0 at same friction velocity from wrfcpl. Adding the parameterised variation of the roughness length, in general, wrfz0var can simulate the distribution of z 0 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 (U 10max ) for each storm are shown in Figure 5.2. In general, the U 10max 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 U 10max from wrfz0 is the lowest on average. If the variation of the roughness length is added into wrfz0 (wrfz0var), it gives the second smallest U 10max 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