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  • View in gallery

    The LongEZ flux flight at ~10 m above sea level during the entire CBLAST-Low pilot campaign and the Pelican flight track during the CBLAST-Low main field campaign. The red and the black crosses mark the locations of the ASIT and the MVCO sea node, respectively.

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    The observation heights of sonic anemometers (fast) and temperature and relative humidity (slow) on the ASIT; T1, T2, and T3 mark the time period before the movement of the mobile platform, after the movement and before the damage of the instruments on the platform, and after the repair of the instruments.

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    Bin-averaged relationships (a) between wind and wave directions, (b) between significant wave heights and wind speed V at z = 10 m, (c) between the wave slope and V, and (d) between and the ratio of the roughness length to z = 6 m for peak waves, dominant swell, secondary swell, and wind sea. The wind speed and direction are the 10-m MVCO wind with some gaps filled using the 10-m ASIT data. The observations in (a)–(c) are based on 20-min data segments for the period from 30 Jul to 31 Dec 2013 and those in (d) are based on the data from the ASIT observation period. The vertical bars represent the standard deviations within each wind speed bin.

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    The time series of (a) the SST and the air temperature at z = 7 m during CBLAST-Low, and the surface radiation temperature and the air temperature at z = 6 m during CASES-99 and (b) the differences between SST and for ASIT (black) and between and for CASES-99 (green). (c) The relationships between the composite and wind speed V for CBLAST-Low, and between and V for CASES-99. The virtual potential temperature difference between 7 (subscript 1) and 9 m (subscript 2) as a function of (d) and (h) V. (e) The SST and as functions of V. The differences between different levels as functions of (f) V and (g) wind direction (WD). In (c), (e), (f), and (h), V is at 6 m for CBLAST-Low and at 5 m for CASES-99. Each symbol in (d)–(h) represents a 20-min segment. The vertical red lines in (c) mark the zero lines.

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    Plots of (a) the composite sensible heat flux and (e) the composite moisture flux as functions of wind speed V at 6 m during CLBAST-Low and at 5 m during CASES-99. Relationships between (b) the temperature scale, , at 6 m and the air–sea temperature difference, , where is the air temperature at 7 m; (c) and ; (d) the composite and V for the period of the warmer air over the cold surface; (f) the moisture scale, , at 6 m and the difference between saturated specific humidity based on SST and the specific humidity at 7 m ; (g) and ; and (h) the composite and V. The vertical bars in (a), (d), (e), and (h) represent the standard deviations within each wind speed bin. Each symbol in (b), (c), (f), and (g) represents a 20-min segment.

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    Comparison of the u*(z)–V(z) relationships between CBLAST-Low (solid lines) and CASES-99 (dashed lines), where the relationships for CASES-99 consist of regressed straight lines for and the approximate upper and lower bounds for . The thin vertical lines in the color of each line represent the standard deviation of within each wind speed bin of 2 m s−1. It is evident that 1) the increasing rate of with is smaller for CBLAST-Low than for CASES-99 as a result of the relatively smooth sea surface compared to the land surface and 2) the change of the increasing rate with is smaller for CBLAST-Low than for CASES-99 as the stable stratification is much stronger for CASES-99 than for CBLAST-Low.

  • View in gallery

    The composite as a function of V at (a) 6 and (b) 20 m for the two different air–sea temperature ranges, where vertical bars represent the standard deviations within each V average bin of 2 m s−1. The subscripts 1–4 for represent the temperature/humidity sensor levels at 7, 9, 11, and 13.5 m, respectively. The threshold wind at 5 and 20 m observed from CASES-99 is marked in (a) and (b), respectively. Relationships between the atmospheric turbulent momentum flux at 6 m expressed as and the wave slope for (c) peak waves and (d) wind sea and (e) between wind speed V and at 6 m with different values. The data with wind direction (WD) from the open sea are highlighted in green in (c) and (d), and the data with high wave slopes are marked in red in (e). Each symbol represents a 20-min segment.

  • View in gallery

    The u*V relationship (a) at 6 m during CBLAST-Low (yellow) and at 12 m during SWADE with various sea states and (b) for the SWADE data with different air–sea temperature differences .

  • View in gallery

    The composite drag coefficient as a function of wind speed for (a) CASES-99 and (b) CBLAST-Low, where the data from CASES-99 are the nighttime values, which cover the stable and the nearly neutral regimes. The green line in (a) is for u* = 0.37 m s−1 to represent an example of a self-correlated with V.

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Air–Sea Interactions in Light of New Understanding of Air–Land Interactions

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
  • | 2 University of Wyoming, Laramie, Wyoming
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Abstract

Air–sea interactions are investigated using the data from the Coupled Boundary Layers Air–Sea Transfer experiment under low wind (CBLAST-Low) and the Surface Wave Dynamics Experiment (SWADE) over sea and compared with measurements from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) over land. Based on the concept of the hockey-stick transition (HOST) hypothesis, which emphasizes contributions of large coherent eddies in atmospheric turbulent mixing that are not fully captured by Monin–Obukhov similarity theory, relationships between the atmospheric momentum transfer and the sea surface roughness, and the role of the sea surface temperature (SST) and oceanic waves in the turbulent transfer of atmospheric momentum, heat, and moisture, and variations of drag coefficient Cd(z) over sea and land with wind speed V are studied.

In general, the atmospheric turbulence transfers over sea and land are similar except under weak winds and near the sea surface when wave-induced winds and oceanic currents are relevant to wind shear in generating atmospheric turbulence. The transition of the atmospheric momentum transfer between the stable and the near-neutral regimes is different over land and sea owing to the different strength and formation of atmospheric stable stratification. The relationship between the air–sea temperature difference and the turbulent heat transfer over sea is dominated by large air temperature variations compared to the slowly varying SST. Physically, Cd(z) consists of the surface skin drag and the turbulence drag between z and the surface; the increase of the latter with decreasing V leads to the minimum Cd(z), which is observed, but not limited to, over sea.

Corresponding author address: Jielun Sun, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. E-mail: jsun@ucar.edu

Abstract

Air–sea interactions are investigated using the data from the Coupled Boundary Layers Air–Sea Transfer experiment under low wind (CBLAST-Low) and the Surface Wave Dynamics Experiment (SWADE) over sea and compared with measurements from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) over land. Based on the concept of the hockey-stick transition (HOST) hypothesis, which emphasizes contributions of large coherent eddies in atmospheric turbulent mixing that are not fully captured by Monin–Obukhov similarity theory, relationships between the atmospheric momentum transfer and the sea surface roughness, and the role of the sea surface temperature (SST) and oceanic waves in the turbulent transfer of atmospheric momentum, heat, and moisture, and variations of drag coefficient Cd(z) over sea and land with wind speed V are studied.

In general, the atmospheric turbulence transfers over sea and land are similar except under weak winds and near the sea surface when wave-induced winds and oceanic currents are relevant to wind shear in generating atmospheric turbulence. The transition of the atmospheric momentum transfer between the stable and the near-neutral regimes is different over land and sea owing to the different strength and formation of atmospheric stable stratification. The relationship between the air–sea temperature difference and the turbulent heat transfer over sea is dominated by large air temperature variations compared to the slowly varying SST. Physically, Cd(z) consists of the surface skin drag and the turbulence drag between z and the surface; the increase of the latter with decreasing V leads to the minimum Cd(z), which is observed, but not limited to, over sea.

Corresponding author address: Jielun Sun, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. E-mail: jsun@ucar.edu

1. Introduction

Early advances in understanding the physics of the air–water interface have been reviewed by, for example, Donelan (1990). Validity of Monin–Obukhov similarity theory (MOST) over moving oceanic waves has drawn great interest in the literature. Interactions between wind and oceanic waves have been investigated extensively (e.g., Donelan and Hui 1990; Tolman and Chalikov 1996; Makin and Kudryavtsev 2003; Sajjadi and Bettencourt 2003; Donelan et al. 2012). By examining the turbulence energy balance, Edson and Fairall (1998) and Wilczak et al. (1999) demonstrated that MOST is valid in the marine atmospheric surface layer (MASL) above the wave boundary layer (WBL).

a. Wave effects on atmospheric turbulent mixing

Sjöblom and Smedman (2003) investigated influences of oceanic waves on MOST and found the dependence of turbulent mixing in the MASL on wave state. Makin and Mastenbroek (1996) studied the MASL using a nonlinear model and found that turbulent fluxes increase with height and wave-induced fluxes over water, which are characteristics of the roughness sublayer over land, decrease with height. Riley et al. (1982) found that the sea surface is analogous to a solid wall for momentum transfer. Toba (1998) also noticed that turbulence over sea resembles the atmospheric turbulence over a rough solid wall. Sjöblom and Smedman (2002) examined the TKE budget over oceans and found that TKE production and dissipation vary with wind speed and the sea surface resembles a land surface for moderate wind speeds and saturated waves that do not grow or decay.

The WBL, where the MASL is strongly affected by oceanic waves, is similar to the roughness sublayer over land, where MOST is not valid. Hunt and Carlotti (2001) and Högström et al. (2002) found that an eddy sublayer, where turbulence dissipation is found to be larger than local turbulence generation, exists within the WBL when large eddies transported by the pressure–wind coherent term impinge to the surface. Therefore, invalidity of MOST close to the surface is due to these inactive eddies. The imbalance between the local turbulence production and dissipation has also been confirmed by Yelland and Taylor (1996) and Sjöblom and Smedman (2002). However, Taylor and Yelland (2003) found more scatter in the sea surface roughness for low winds compared to high winds and suggested that any “sheltering” effects are small at least for wind speed less than 25 m s−1. As in a typical roughness sublayer, all the surface roughness parameters for describing wave states are important for the WBL.

Oceanic waves are commonly divided into wind wave or wind sea and swell; the former is generated by local wind and is characterized with high frequencies and the latter is generated by distant air–sea interactions and is characterized with low frequencies. Snodgrass et al. (1966) found that storm-generated swell can travel long distances, and interactions between swell and local wind is unimportant. Influences of oceanic waves on the atmospheric momentum transfer have been investigated in the literature for many years. Liu et al. (1996) found that wind fluctuations were almost in phase with swell wave signals and have large phase shifts from the wind-wave component. Davidson and Frank (1973) also observed wave-related wind fluctuations. Druilhet et al. (1990) investigated the MABL using aircraft measurements of swell and turbulent fluxes at 50 m above sea level and suggested that swell may modify MABL thermodynamics. Using direct numerical simulation above idealized two-dimensional periodic waves, Sullivan et al. (2000) found that below 100zo, where is the roughness length for momentum, the MABL is influenced by swell, and wind profiles depend on wave slopes and wave age defined as , where is the wave phase speed and is the friction velocity. Smedman et al. (1999), Grachev and Fairall (2001), and Hristov et al. (2003) found that momentum can be transferred from waves to the atmosphere but only under conditions of strong swell and weak wind. Grachev et al. (2003) observed the stress direction dependence on wind vector and swell and found that the results are wind speed dependent. However, using measured atmospheric pressure over oceanic waves, Hsiao and Shemdim (1983) found the wave-induced airflow is much smaller than the mean wind speed.

Contribution of oceanic waves to turbulent momentum transfer in the MABL has also been investigated through connections between waves and sea surface roughness, which have been detected through wave spectra, wave slopes, and impacts of wave characteristics on lidar or radar wave (Valenzuela 1978; Jessup et al. 1991; Colton et al. 1995; Walsh et al. 1998; Vandemark et al. 2001, 2004). For example, Smedman et al. (2003) found that the logarithmic wind profile is valid over growing sea characterized with short wind waves but not over long-wave-dominated sea, and the invalidity of the logarithmic wind profile cannot be explained by atmospheric stabilities. Papadimitrakis and Papaioannou (2003) also pointed out that oceanic surface waves can be partitioned into local-wind-generated short waves and remotely generated swell or long waves, and long waves do not always contribute to the surface roughness. By investigating spatial spectra of oceanic waves, Hwang (1995) found the mean-square slope of small-scale waves increasing linearly with wind speed, progressive narrowing of the directional distribution toward shorter wavelengths for a given wind speed, and a gradual broadening of the directional distribution toward high wind velocities for a given wavenumber. Hwang (1997) demonstrated that the contribution of the mean-square slope of oceanic waves is from capillary–gravity waves of wavelength from 4 mm to 6 cm. Marsden and Juszko (1989) also found high correlation between the principal direction of wave slope and the 10-m wind direction under strong winds and between the upwind slope variance and the 10-m wind speed.

Because of the role of the drag coefficient in connecting atmospheric turbulent momentum transfer with wind speed, air–sea interactions have also been investigated through dependence of on the sea state (e.g., Geernaert 1987; Toba et al. 1990; Nordeng 1991). In addition, because the momentum transfer between wind and oceanic waves is important for the momentum and energy balance in the upper ocean, has been investigated through wave models (e.g., Donelan et al. 2012).

b. HOST hypothesis

Recently, limitation of MOST was investigated in the atmospheric boundary layer (ABL) over land by Sun et al. (2012, 2015, 2016) using observations from a 60-m tower. They found that atmospheric turbulence consists of large coherent eddies that scale with the distance between the observation height and the surface under strong wind conditions, and those large coherent eddies dominate turbulent mixing and cannot be properly described by MOST. As a result, MOST is only approximately valid in a relatively thin layer near the surface. Although these large coherent eddies have characteristics of nonlocal eddies mentioned in the literature—for example, Stull (1984) over land and Large et al. (1994) in the ocean—Sun et al. (2012, 2015, 2016) found that these large coherent eddies are well organized in response to the atmospheric stratification and their sizes are constrained by the height of turbulence observations above the surface. Contribution of large coherent eddies was also observed by Gerbi et al. (2008) in analyzing turbulent mixing in the ocean surface boundary layer, in which they also pointed out that this turbulence transfer is related to turbulence generation mechanism not accounted for by MOST.

By further analyzing the diurnal variation of the atmospheric momentum and heat transfer, Sun et al. (2016) proposed the hockey-stick transition (HOST) hypothesis as the role of large coherent eddies in turbulent mixing was first noticed in the hockey-stick transition of turbulence kinetic energy (TKE) with wind speed from stable to nearly neutral conditions. The HOST hypothesis states that turbulent intensity at a given height z is dominated by large coherent eddies of finite scale generated by positive buoyancy or shear through TKE and turbulent potential energy (TPE) balance (Zilitinkevich et al. 2007) in the layer of . Under stable conditions associated with weak winds, shear-generated turbulence eddies at z are relatively small (i.e., ); a significant part of the shear-generated turbulence energy is consumed to increase TPE, leading to relatively small TKE. As wind speed exceeds the threshold wind , the bulk shear leads to generation of large coherent eddies that scale with z, which effectively reduces the vertical temperature gradient between z and the surface, leading to the dramatic decrease of the TPE consumption and the linear increase of any TKE-related turbulent variables with wind speed. Therefore, represents the averaged critical shear needed for the significant reduction of the vertical temperature gradient between z and the surface to nearly neutral. Correspondingly, the temperature variance in the stably stratified atmosphere increases with , reaches its maximum value at , and decreases with for as a result of the reduction of the atmospheric stratification. As z increases, the shear required in generation of strong turbulent mixing to reduce the vertical temperature gradient between z and the surface to a small value would increase. As a result, the linear u*(z)–V(z) relationship would shift toward higher winds; that is, increases with z. Evidently, the reduction of the vertical temperature gradient in the nocturnal ABL depends on the strength of the inversion near the surface, the strength of the wind through turbulence generation, and the length of time for the depletion of the cold air near the surface by turbulent heat transfer. The maximum temperature variance depends on the vertical temperature gradient. In a transition from a weakly stable to a nearly neutral atmosphere, the variation of with would not be dramatic as the TPE does not vary significantly between the weakly stable and the nearly neutral atmosphere. If strong winds are associated with increasing stratification, such as downslope wind, the HOST of any TKE-related variable may not be well correlated with wind speed. Because surface roughness and surface heating/cooling properties associated with soil properties also contribute to the turbulence energy balance, they also impact the HOST of any TKE-related turbulence variables (e.g., van de Wiel et al. 2012; Mahrt et al. 2013). By comparing observations from three field experiments, Mahrt et al. (2013) suggested that may increase with decreasing surface roughness. Furthermore, Sun et al. (2016) found that a heated surface during daytime generates similar large coherent eddies such that approximately increases with under unstable conditions as well, and temperature variances increase linearly with vertical air temperature differences between z and the surface.

Based on the new understanding of turbulent mixing near the land surface, we compare turbulent mixing between over sea and over land in this study (section 4). We first investigate contributions of sea surface waves to air–sea interactions in the MASL (section 4a). We then investigate the role of sea surface temperature (SST) in the atmospheric stratification (section 4b). We then examine atmospheric turbulent fluxes of momentum, heat, and moisture over sea and compare them over land (section 4c). We further study the role of sea surface roughness, especially swell, in the atmospheric momentum transfer (section 4d and 4e) and differences of over land and over sea (section 4f). The field experiment datasets used in this study are described in section 2. The data analysis methods are explained in section 3. Section 5 has the summary of the main conclusions.

2. Field observations

To compare turbulent mixing at the air–land interface with that at the air–sea interface, we use the field data over land from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) (Poulos et al. 2002; Sun et al. 2002, 2013) and over sea from the Coupled Boundary Layers Air–Sea Transfer experiment under low wind (CBLAST-Low) conducted in the Atlantic Ocean south of Martha’s Vineyard, Massachusetts (Edson et al. 2007), and the Surface Wave Dynamics Experiment (SWADE) conducted in the Atlantic Ocean off the coast of Virginia (Donelan et al. 1997).

a. CASES-99

The CASES-99 dataset was collected from a 60-m tower over a dominant senescent short grassland with the averaged grass height of ~0.2 m in Kansas during October 1999 (the data are available at https://www.eol.ucar.edu/field_projects/cases-99). Turbulence data were collected from three-dimensional (3D) sonic anemometers at 0.5, 1.5, 5, 10, 20, 30, 40, 50, and 55 m (Sun et al. 2015). The surface roughness length derived using strong winds and MOST is ~0.05 m.

b. CBLAST-Low

The project was conducted offshore south of Martha’s Vineyard. CBLAST-Low consists of two parts: a pilot experiment in the summer of 2001 and the main field experiment in the summer of 2003 (the data are available at http://www.whoi.edu/science/AOPE/CBLAST/low/data.html). In addition, continuous meteorological and oceanic observations were recorded by Martha’s Vineyard Coastal Observatory (MVCO) (http://www.whoi.edu/mvco) all year around.

1) The pilot experiment

The pilot experiment was conducted by the NOAA LongEZ aircraft, which was equipped to measure atmospheric turbulence and oceanic surface waves (Crescenti et al. 2001; Sun et al. 2001). The LongEZ aircraft flew 20 missions during 15 days in two major patterns: 1) sounding flights with either spiral or slant paths and 2) flux runs at a constant level with repeated flights along either a line, a square, or a daisy pattern (Fig. 1). All the flux runs were at about 10 m above sea level.

Fig. 1.
Fig. 1.

The LongEZ flux flight at ~10 m above sea level during the entire CBLAST-Low pilot campaign and the Pelican flight track during the CBLAST-Low main field campaign. The red and the black crosses mark the locations of the ASIT and the MVCO sea node, respectively.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

2) The main field campaign

The main field campaign took place during the summer of 2003. The field data were collected from the Air–Sea Interaction Tower (ASIT) and the Center for Interdisciplinary Remotely-Piloted Aircraft Studies (CIRPAS) Pelican aircraft (Khelif et al. 2005). The ASIT is at 41.325°N, 70.556°W, which is about 3.2 km south of Edgartown Great Pond, Martha’s Vineyard, and in 15-m-deep water (Austin et al. 2002). The ASIT was equipped with 3D sonic anemometers at five levels: the top two levels were fixed at about 18 and 20 m above water, and the bottom three sonic anemometers as well as three LI-COR-7500 for fast-response water vapor and carbon dioxide were mounted on a mobile platform at 6, 8, and 12 m above water (Fig. 2). All the sonic anemometers pointed to 245° clockwise from north; therefore, the wind direction for infinite fetch is between 140° and 250° (Edson et al. 2007). In addition, aspirated air temperature and humidity were measured at four levels: the top one at ~13.5 m on the fixed platform, and the bottom three at 7, 9, and 11 m on the mobile platform (Fig. 2). On 19 July 2003 (the day of the year is 231), the platform was moved down about 2 m. Afterward, large oceanic waves from a gale storm hit the mobile platform, and instruments on the platform were damaged, and the data at all the levels from this period were removed from the dataset (Fig. 2). We define the time period prior to the platform movement as , the time period after and prior to the storm as , and after the repair of the sensors on the platform as . As a result of the movement of the mobile platform, turbulence measurements are available at 4 and 10 m above sea level for only and , at 8 and 12 m for only , and at 6 m as well as the levels on the fixed platform for , , and (Fig. 2). For the same reason, the air temperature and humidity are available at 5 m for and and at 7 and 9 m for , , and . Because of the sensor issue at 18 m, we use only the data from the turbulence measurements from the mobile platform and the top level on the fixed platform.

Fig. 2.
Fig. 2.

The observation heights of sonic anemometers (fast) and temperature and relative humidity (slow) on the ASIT; T1, T2, and T3 mark the time period before the movement of the mobile platform, after the movement and before the damage of the instruments on the platform, and after the repair of the instruments.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

The CIRPAS Pelican aircraft flew several patterns between 29 July and 28 August 2003. The main flight pattern consisted of four flight tracks: an east–west (E–W) track of about 22.5 km along the south coastline of Martha’s Vineyard and three north–south (N–S) tracks of about 35.5 km perpendicular to the coastline (Fig. 1). We concentrate on only the repeated flights along the E–W track in comparison with measurements from the ASIT. The Pelican aircraft flew along the E–W track at about 30 m above sea level with additional passes at 45 and 90 m on 20 August and at 45 m on 28 August.

3) MVCO meteorological and oceanic data

Wind speed and direction are measured from the onshore MVCO meteorological mast, which is located roughly 60 m from the mean low water mark and about 10 m above mean sea level at South Beach in Edgartown, Massachusetts. Based on Churchill et al. (2006), the wind speed difference between the MVCO meteorological mast and the ASIT is about 1 m s−1 with a standard deviation of 0.6 m s−1 during their 42-day comparison period. The wind data from MVCO are used to fill in the periods when the ASIT 10-m wind is not available to investigate correlations between wind and sea surface roughness in this study.

The oceanic wave measurement is from a bottom-mounted sea node located at 40.34°N, 70.56°W in 12-m-deep water, 1.6 km offshore in the Atlantic Ocean, 2.89 km southwest of the onshore meteorological mast, and about 2 km away from the ASIT. Directional wave data are derived from the acoustic Doppler current profilers (ADCP) at the MVCO site from 30 July to 31 December 2003 by Churchill et al. (2006), which covers the later part of the CBLAST-Low main field campaign until the end of the year. Based on the spectral comparison between the upward-looking ADCP and a Riegl laser altimeter deployed at the ASIT for measuring sea surface variations at a frequency of 20.4 Hz, the wave height spectra from the ADCP with frequencies higher than 0.4 Hz do not compare well with the wave spectra from the laser altimeter and, thus, are not used in the wave analysis. The processed ADCP data are used to derive wave direction, wave period, and significant wave height (the average crest to trough height of the 1/3 highest waves) for peak waves, dominant swell, secondary swell, and wind sea calculated by Churchill et al. (2006). In brief, wind sea is calculated as high-frequency waves with a cutoff wave phase velocity, and the dominant and secondary swells are defined as low-frequency wave bands according to their wave energies.

c. SWADE

Turbulence and wave data from SWADE were measured by the 20-m Small Waterline Area Twin Hull (SWATH) ship Frederick G. Creed from October 1990 to March 1991. The data used in this study are from Table 1 in Donelan et al. (1997), where the observation and the processing method were reported. In this study, we use only the turbulence data measured at 12 m without being converted to 10 m to avoid any issues related to MOST (section 1, more in section 4). In addition, we use only the momentum flux calculated using the eddy correlation method from every 17-min data segment. Turbulent stress for 1) wind sea, 2) wind direction opposite to the swell propagation direction (countering swell), 3) wind across the swell direction (crossing swell), and 4) wind in the same direction as the swell (following swell) were categorized in the SWADE dataset.

3. Data analysis methods

For the CBLAST-Low pilot experiment, turbulent fluxes from the LongEZ aircraft are estimated using the eddy correlation method with turbulent perturbations calculated from 2-km segments using the block average for mean variables (Vickers et al. 2001). During the main experiment, there were 11 Pelican flight missions along the E–W track at 30 m above sea level and 23 passes. We estimate turbulent fluxes for each pass based on ogive cospectra (Friehe et al. 1991)—that is, cumulative momentum fluxes as functions of frequency. We visually inspect every ogive cospectrum and estimate turbulent fluxes by eliminating random submesoscale covariances, which are characterized with large erratic variations at relatively low frequencies. Turbulent fluxes from ASIT are calculated every 20 min (Edson et al. 2013). The CASES-99 data analysis was explained in Sun et al. (2016).

We use to represent the momentum flux at z, where w, V, and U are vertical, along-wind, and crosswind components and the prime represents the perturbation from its block mean. We also examine the buoyancy flux ( is virtual potential temperature), the moisture flux (q is specific humidity), and the corresponding temperature and moisture scales and , respectively. For the ASIT data, the difference between (θ is potential temperature) and at ~6 m is, on average, about 10%. We use mainly the ASIT tower data to investigate turbulent mixing over sea and simply refer to the marine data as CBLAST-Low.

4. Air–sea interactions in comparison with air–land interactions

There are two key differences between air–land and air–sea interactions: 1) the diurnal variation associated with surface heating and cooling is much stronger over land than over water and 2) the surface roughness over sea varies in contrast to a constant value over land for a given location. The former has strong impacts on the atmospheric thermal structure, and the latter strongly affects the mechanical generation of atmospheric turbulence.

a. Sea surface roughness

Over land, surface physical roughness exists as a result of surface elements. Over water, the physical roughness of the sea surface comes from waves generated by various mechanisms: 1) wave generation by wind, such as wind waves and swell; 2) displacement of a large amount of water, such as by an earthquake; and 3) gravitational pull of the moon and the sun, such as tides. Oceanic waves consist of multiple frequencies and move in various directions as a result of nonlinear wave–wave interactions and wave breaking resulting from either wave steepening or shoaling. Often, oceanic waves have large amplitudes within a narrow frequency band, which corresponds to peak oceanic waves.

The surface roughness of either land or sea surfaces is often referred to the derived dynamic surface roughness associated with the atmospheric momentum transfer. Because the atmospheric momentum flux is influenced by the atmospheric stratification, to compare land surface roughness from site to site, the effect of the local atmospheric stratification needs to be removed; that is, needs to be derived under neutral or nearly neutral conditions. Under nearly neutral conditions, is derived from the observed and wind speed near the surface using the MOST bulk formula for momentum as
e1
where κ is von Kármán constant. Based on MOST, between and z should be invariant, but practically the vertical variation of near the surface is assumed to be small. Based on Eq. (1), is the height at which the observed is logarithmically extrapolated down to zero and is not necessarily the physical height where goes to zero (e.g., Sun 1999). Over sea, reflects the dynamic response of the sea surface to the observed . Even though is defined through Eq. (1), over the sea surface is commonly empirically related to through the Charnock relationship (e.g., Charnock 1955) or to wave age, (e.g., Johnson et al. 1998), where is the phase speed of peak waves. Since varies nonlinearly with wave period through the deep-water wave dispersion relationship, for relatively long peak waves does not vary significantly unless the water depth is over 100 m. Therefore, as a function of is dominated by self-correlation (e.g., Hicks 1978; Klipp and Mahrt 2004; Sun et al. 2016) through the dependence of both and on .

We now examine the observed correlation between wind direction at z = 10 m and wave direction (Fig. 3a) and between the significant wave height for peak waves, dominant and secondary swells, and wind sea and at z = 10 m (Fig. 3b) using the data collected at MVCO. We find that the direction of wind sea is well correlated with wind direction, and for wind sea is well correlated with . The above relatively good relationships for wind sea based on the 20-min data segments also imply the relatively fast momentum coupling between the atmosphere and the sea surface.

Fig. 3.
Fig. 3.

Bin-averaged relationships (a) between wind and wave directions, (b) between significant wave heights and wind speed V at z = 10 m, (c) between the wave slope and V, and (d) between and the ratio of the roughness length to z = 6 m for peak waves, dominant swell, secondary swell, and wind sea. The wind speed and direction are the 10-m MVCO wind with some gaps filled using the 10-m ASIT data. The observations in (a)–(c) are based on 20-min data segments for the period from 30 Jul to 31 Dec 2013 and those in (d) are based on the data from the ASIT observation period. The vertical bars represent the standard deviations within each wind speed bin.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

Similar to the physical process of an airflow over hills, low-frequency oceanic waves, such as swell generated remotely by wind or other wave generation mechanisms, induce pressure perturbations and affect wind speed surrounding swell, although the magnitude of pressure perturbations is much smaller over waves than over hills owing to the relatively small size of waves compared to hills and movement of waves. This wave-induced wind modifies the wind shear between the background wind relative to a flat surface or, equivalently, increases the surface drag (i.e., form drag). In other words, one way to interpret form drag is the modification of the atmospheric momentum transfer through the modification of the vertical variation of wind by pressure perturbations induced by hills or waves. Because the pressure perturbation induced by a hill is related to the ratio between the hill height and the hill width (e.g., Smith 1989), we examine the dependence of the wave slope, which is the ratio between and wavelength λ calculated using the observed wave period and the wave phase speed from the deep-water dispersion relationship (Fig. 3c). Because the wave slope is related to the atmospheric momentum transfer (Harris 1966), represents the physical roughness of the sea surface. We find that for peak waves increases approximately linearly with V at z = 10 m, and the relationship is dominated by wind sea, which is only clearly defined for V > 3 m s−1.

We next examine the correlation between the physical and the dynamical sea surface roughnesses—that is, between and (Fig. 3d), where is calculated using Eq. (1) with observed and V at z = 6 m. We find that again, is better correlated with for wind sea (Fig. 3d). Although both for wind sea and peak waves increase with (Fig. 3c) as increases with (section 4c), large for wind sea reaches a plateau with increasing , and for peak waves has a minimum value with increasing (Fig. 3d), suggesting that the sea surface roughness may not vary significantly under strong winds. The correlation between for peak waves and V could be due to the fact that strong winds commonly occur in large areas as swell is generated by strong winds at remote locations.

Because of the close connection between wind speed and atmospheric turbulent mixing (section 4c), the relationships between , V, and for wind sea demonstrate that the momentum coupling between the atmosphere and the physical sea surface roughness is mainly through wind sea unless V is small (Fig. 3c). That is the wavelength of the responsive oceanic wave has the similar size of atmospheric turbulence eddies (Sun et al. 2016), which is much smaller than long oceanic waves of swell O(100 m). The sea surface during CBLAST-Low is much smoother compared to the CASES-99 site even under the wind speed of 10–12 m s−1; the largest zo = 0.0006 m during CBLAST-Low is much smaller than zo = 0.05 m during CASES-99. This result is also consistent with the analogy of low-frequency oceanic waves as a solid surface concluded by Riley et al. (1982).

b. Contribution of SST to the atmospheric stratification

Over land, the large diurnal variation of the surface radiation temperature is through solar heating during daytime and longwave radiative cooling at night, which is, on average, about 25°C (Fig. 4a). During CBLAST-Low, the SST varies from about 20° to about 14°C over a period of about 100 days. Over land, the unstable ABL occurs during daytime and the stable ABL at night. Over sea, the atmospheric stability depends on the relatively fast variation of the air temperature compared to the relatively slow variation of the SST. During CBLAST-Low, the MABL is approximately weakly stable for the first half of the experiment and relatively unstable for the second half when the air temperature decreased significantly compared to the relatively small decrease of the SST (Fig. 4b). During CASES-99, the air temperature at about 6 m is, on average, about 4°C warmer than at night and about 4°C colder than during daytime (Fig. 4c). During CBLAST-Low, the air temperature at 7 m is only about 1°C warmer than the SST for the stable period and about 2°C colder than SST for the unstable period. Overall the variation of the atmospheric stability is much larger over land than over sea.

Fig. 4.
Fig. 4.

The time series of (a) the SST and the air temperature at z = 7 m during CBLAST-Low, and the surface radiation temperature and the air temperature at z = 6 m during CASES-99 and (b) the differences between SST and for ASIT (black) and between and for CASES-99 (green). (c) The relationships between the composite and wind speed V for CBLAST-Low, and between and V for CASES-99. The virtual potential temperature difference between 7 (subscript 1) and 9 m (subscript 2) as a function of (d) and (h) V. (e) The SST and as functions of V. The differences between different levels as functions of (f) V and (g) wind direction (WD). In (c), (e), (f), and (h), V is at 6 m for CBLAST-Low and at 5 m for CASES-99. Each symbol in (d)–(h) represents a 20-min segment. The vertical red lines in (c) mark the zero lines.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

As pointed by Geiger et al. (1995) [its first edition was Geiger (1927)], the coupling between the solid surface and the atmosphere is through movement of molecules. The molecular work for the thermal exchange at the surface is molecular thermal conduction, which transfers heat much slower than turbulent mixing above the molecular layer. Because molecular thermal conduction dominates the heat transfer across the surface even though the molecular layer is only a few millimeters thick, the turbulent heat transfer can quickly and effectively change air temperature, leading to air–sea temperature differences as the SST does not vary fast even though the rate of molecular thermal conduction may vary because of variations of the air–sea temperature difference. Thus, we can use air–sea temperature differences to approximately identify the atmospheric stability regimes but not the atmospheric stratification.

The larger variation of compared to SST (Figs. 4a and 4e) and the larger compared to the small difference between different heights under strong winds during CBLAST-Low (Figs. 4b–d,g,h) suggests that the air and the ocean are indeed not thermally coupled through the fast turbulent mixing but through the slow molecular thermal conduction. The observed relatively large for is mainly associated with weak wind from the northwest with the possible influence of the relatively warm island of Martha’s Vineyard (Fig. 4g) as the atmospheric momentum transfer is relatively large from this wind direction (section 4d).

In contrast to the unstable atmosphere, there are significant differences in formation of the stable stratification in the atmosphere between over land and over sea. Over land, the longwave radiative emission lowers the surface temperature and molecular thermal conduction transfers heat from the atmosphere to the surface, reducing the air temperature adjacent to the surface. The difference between the surface radiation temperature and the air temperature decreases with wind speed as turbulent mixing generated by wind shear transports cold air upward above the cold-air-generation layer near the surface. However, during CBLAST-Low, the stable MABL mainly results from episodic air warming over the cold sea through warm-air advection and the downward turbulent transport of warm air as the SST does not vary quickly owing to the large thermal inertia of water (Fig. 4b). As a result, the air–sea temperature difference increases with wind speed for the entire range of the observed wind speed (Fig. 4c), which was also observed by Mahrt et al. (2016). Because of the relatively smooth sea surface compared to the land (section 4a), turbulence intensity is much less over sea than over land for a given wind speed [Eq. (1); more in section 4c], resulting in the relatively slow increase of the air–sea temperature difference with wind speed during CBLAST-Low compared to the relatively fast decrease of the air–land temperature difference with wind speed during CASES-99 (Fig. 4c).

c. Atmospheric turbulent mixing over sea

Because positive buoyancy generates turbulence spontaneously once the air is warmer below than above, the atmospheric turbulent mixing under unstable conditions is similar over land and sea; that is, the heat source from below controls the atmospheric stratification. Because of the relatively large air–land temperature difference under unstable conditions, the upward heat flux is much larger over land than over sea (Fig. 5a). Similar to CASES-99, the temperature scale for CBLAST-Low is closely related to the atmospheric stratification for the convective to slightly stable marine atmosphere, which covers the entire stability range for CBLAST-Low (Fig. 5b). Because of the lack of air temperature observations near the sea surface, the atmospheric stratification in Fig. 5b is approximately expressed as the air–sea temperature difference, . Because of the small variation of the SST, is approximately related to alone (Fig. 5c). Similar to , the moisture scale is well correlated with the humidity difference between the saturated specific humidity at SST and the air specific humidity at 7 m (Fig. 5f), and the relationship is dominated by the variation (Fig. 5g). Obviously the sea surface provides much more water vapor than the land surface during CASES-99, and the moisture flux is larger over sea than over land under unstable conditions (Fig. 5e).

Fig. 5.
Fig. 5.

Plots of (a) the composite sensible heat flux and (e) the composite moisture flux as functions of wind speed V at 6 m during CLBAST-Low and at 5 m during CASES-99. Relationships between (b) the temperature scale, , at 6 m and the air–sea temperature difference, , where is the air temperature at 7 m; (c) and ; (d) the composite and V for the period of the warmer air over the cold surface; (f) the moisture scale, , at 6 m and the difference between saturated specific humidity based on SST and the specific humidity at 7 m ; (g) and ; and (h) the composite and V. The vertical bars in (a), (d), (e), and (h) represent the standard deviations within each wind speed bin. Each symbol in (b), (c), (f), and (g) represents a 20-min segment.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

We average versus using both aircraft and the ASIT tower data and compare the u*(z)–V(z) relationship between over sea and over land at similar heights (Fig. 6). Similar to the u*(z)–V(z) relationship from CASES-99 described in section 1 and other observations over sea (Oost et al. 2002; Andreas et al. 2012; Edson et al. 2013; Mahrt et al. 2016), the ASIT increases with although the rate of the increase with is much smaller over sea than over land. Also similar to CASES-99, the slope of the u*(z)–V(z) relationship varies with increasing z (Figs. 7a and 7b). Because the air temperature at ~7 m is only about 1°C warmer than the SST in the stable marine atmosphere during CBLAST-Low, which is much smaller than the air–surface temperature in the stable atmosphere during CASES-99, is comparable to or even larger during CBLAST-Low than over land under weak winds even though weaker turbulence is associated with the smaller sea surface roughness. Because of the relatively smooth sea surface, over sea increases more slowly with under strong winds.

Fig. 6.
Fig. 6.

Comparison of the u*(z)–V(z) relationships between CBLAST-Low (solid lines) and CASES-99 (dashed lines), where the relationships for CASES-99 consist of regressed straight lines for and the approximate upper and lower bounds for . The thin vertical lines in the color of each line represent the standard deviation of within each wind speed bin of 2 m s−1. It is evident that 1) the increasing rate of with is smaller for CBLAST-Low than for CASES-99 as a result of the relatively smooth sea surface compared to the land surface and 2) the change of the increasing rate with is smaller for CBLAST-Low than for CASES-99 as the stable stratification is much stronger for CASES-99 than for CBLAST-Low.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

Fig. 7.
Fig. 7.

The composite as a function of V at (a) 6 and (b) 20 m for the two different air–sea temperature ranges, where vertical bars represent the standard deviations within each V average bin of 2 m s−1. The subscripts 1–4 for represent the temperature/humidity sensor levels at 7, 9, 11, and 13.5 m, respectively. The threshold wind at 5 and 20 m observed from CASES-99 is marked in (a) and (b), respectively. Relationships between the atmospheric turbulent momentum flux at 6 m expressed as and the wave slope for (c) peak waves and (d) wind sea and (e) between wind speed V and at 6 m with different values. The data with wind direction (WD) from the open sea are highlighted in green in (c) and (d), and the data with high wave slopes are marked in red in (e). Each symbol represents a 20-min segment.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

The stable stratification during CBLAST-Low is controlled mainly by episodic weak air warming, which is likely associated with the downward turbulent transport of warm air even warm advection is present as the air temperature increases approximately with (Fig. 5c). Consequently, , which is closely related to temperature variances (Sun et al. 2012), increases slightly with for almost the entire observed wind speed range (Fig. 5d). That is, the expected decrease of with under strong winds is noted just at the strongest wind observed during CBLAST-Low. Similar to , the downward heat flux also increases with (Fig. 5a) and is much weaker during CLBAST-Low than during CASES-99. In the slightly stable MABL, which is close to near neutral, the moisture flux fluctuates around zero with its average value smaller than the upward transport of the moisture flux during CASES-99 at night (Fig. 5e). The relatively small is also evident in Fig. 5h as the vertical moisture gradient is relatively small over sea compared to the one in the relatively strong stably stratified atmosphere over land.

Based on the HOST hypothesis, the variations of and with wind speed are due to the turbulence energy conservation between TKE and TPE in the layer between z and the surface. Because turbulence consists of large coherent eddies with scale z generated by bulk shear at nearly neutral conditions, increasing wind speed leads to increasing wind shear, turbulence generation, and any TKE-related variable increase without much turbulence energy consumption for TPE. The HOST hypothesis also explains the variation of and with wind speed over sea. The approximately linear relationship between and over sea is also related to the bulk shear in generation of large coherent eddies in turbulent mixing as the consumption of TPE in the weakly stable or nearly neutral MABL during CBLAST-Low is small.

During CASES-99, the slope change of the u*(z)–V(z) relationship is associated with the change of the atmospheric stable stratification with shear-generated turbulent mixing (Sun et al. 2016). Without strong mixing, the stable stratification would not be significantly reduced as the surface cooling is strong and lasts throughout each night. For CBLAST-Low, we use the vertical temperature difference between 7 and 9 m (i.e., ) to represent the atmospheric stratification below z = 6 m and between 7 and 13.5 m (i.e., ) to represent the atmospheric stratification below z = 10 m as the air temperature measured adjacent to the sea surface is not available. Because of the weak stratification over sea, the absolute air temperature difference may not be accurate; however, we find that the relatively large stable stratification is all associated with low and weak winds at 6 and 20 m (Figs. 7a and 7b), which is consistent with the HOST of over land (e.g., Mahrt et al. 2015; Sun et al. 2016). That is, the slope change of with during CBLAST-Low is due to the turbulence variation between stable and nearly neutral conditions, and the small slope change is related to the weakly stable stratification. Because of the vertical air temperature difference between z and the surface increases with z for even a small vertical temperature gradient, the impact of the stable stratification on is more visibly significant at 20 m than 6 m. As the Pelican flight level is about 30 m above sea level, strong turbulent mixing would require stronger wind shear relative to the sea surface. All the Pelican flights are designed to fly in weak winds; the composite from the Pelican flights is, therefore, relatively low (Fig. 6).

The HOST of over sea suggests that the transition between the stable and nearly neutral regimes is associated with the atmospheric stratification and the two regimes can be achieved differently over land and over sea. Over land, the nearly neutral stratification is achieved through strong shear-generated turbulent mixing as the surface cooling is significant. Over sea, the marine atmosphere is mostly near neutral; the stable stratification is determined by air warming over relatively steady cold water, which is relatively weak during CBLAST-Low. Because of the relatively smooth sea surface, the wind speed for generating turbulence strong enough to further reduce the weakly stable stratification for an enhanced increase of with during CBLAST-Low has to be significantly larger than the one for CASES-99, which is consistent with the observation by Mahrt et al. (2013) for variations of the surface roughness. Oost et al. (2002) noticed that the slope of the u*V relationship over sea was reduced by rain as a result of the smoothing effect of rain on the sea surface.

d. Dependence of the HOST of on wave states

The important factor for mechanical generation of atmospheric turbulence is wind shear, which is the wind speed or direction difference between z and the surface, no matter whether wind shear is generated by a moving surface or by wind blowing over a still surface. As a oceanic wave propagates past a given location, the sea surface moves up and down and back and forth along the wave propagation direction at the wave phase speed. Only oceanic currents lead to consistent wind shear changes relative to the sea surface; thus, the speed of an oceanic current is important to wind shear, not the phase speed of propagating waves. Wind shear can also be significantly modified by wave-induced winds when the magnitude of the wave-induced wind is comparable with the background wind—that is, when the wind is weak or when the height of atmospheric momentum transfer is near the sea surface as wind decreases toward the surface. When this situation occurs, the atmospheric momentum transfer can be from the sea surface to the atmosphere (e.g., Harris 1966; Drennan et al. 1999; Grachev and Fairall 2001).

We further investigate the relationship between at 6 m and the sea surface physical roughness represented by for peak waves (Fig. 7c) and for wind sea (Fig. 7d). We find that increases with the wind sea for the entire wind speed range and large corresponds to high for wind sea, especially from open water (Fig. 7e). The strong correlation between and for wind sea further suggests that the air and sea are fully coupled mechanically at high frequencies of oceanic waves through the atmospheric turbulent momentum transfer across the sea surface as discussed in section 4a. This result is also consistent with observed different wave spectra under the influence of swell and wind sea by Donelan and Dobson (2001).

Because the u*(z)–V(z) relationship systematically shifts toward stronger wind with increasing z as increases with z (section 1), the turbulence measurement at a fixed height would experience periodic variations of bulk shear for a given wind speed as the distance between the observation height and the sea surface varies periodically when swell passes by. Considering the average time period of 20 min for obtaining in this study, the observed swell period O(10) s, and the observed oceanic current O(10−1) m s−1 during CBLAST-Low, the variation of associated with the swell up and down would not be discernible.

Because the measured includes the background modified by the wave-induced wind, form drag has no obvious influence on the u*V relationship as observed in the similar u*(z)–V(z) relationship between z = 4 and 20 m (Fig. 6) even though the effect of the form drag on decreases with z (e.g., Sullivan et al. 2008). In other words, the observed u*(z)–V(z) relationship during CBLAST-Low is independent of swell as the oceanic current and wave-induced winds are negligibly small in their impact on wind shear between the surface and z larger than 6 m. Therefore the important sea surface roughness to the atmospheric turbulent mixing is the skin drag associated with the viscous layer, and the sea surface roughness associated with wind sea during CBLAST-Low while low-frequency oceanic waves are important only under weak winds, for which form drag can be important.

e. Influence of swell propagation relative to wind on the HOST of

Because of the lack of the directional variation of swell and peak waves during CBLAST-Low, we investigate the HOST of using the dataset collected from SWADE where wind countering, crossing, and following swell were observed. We find that overall the u*V relationships between CBLAST-Low and SWADE overlay each other especially under strong winds (Fig. 8a), suggesting that the sea surface roughnesses for the two field campaigns are similar as the dynamic surface roughness is related to under strong winds near the surface. Closely examining the HOST from SWADE, we find that for the following-swell condition tends to be smaller than the countering-swell condition by approximate 0.07 m s−1 as noted by Drennan et al. (1999). For V < 5 m s−1, the SWADE data are dominated by countering-swell cases, and is relatively large in comparison with CBLAST-Low, suggesting that swell may impact when wind is weak, which is consistent with the discussion on the observed physical sea surface roughness in section 4a.

Fig. 8.
Fig. 8.

The u*V relationship (a) at 6 m during CBLAST-Low (yellow) and at 12 m during SWADE with various sea states and (b) for the SWADE data with different air–sea temperature differences .

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

Based on the LES simulation by Sullivan et al. (2008) with the CBLAST-Low sea surface parameters, the change of associated with form drag for countering-swell wind is about 0.2 m s−1 for V = 2.5 m s−1 at z ≈ 10 m. Even though the countering-swell cases dominate the weak wind regime during SWADE, there are only a few cases for which V is about 2.5 m s−1, and the corresponding is about 0.2 m s−1. This result implies that the wave-induced wind may dominate the local shear compared to the background wind.

Further examining the HOST from SWADE, we find that the countering-swell cases are associated with the SST larger than the air temperature and the following-swell cases are associated with the air temperature much larger than the SST (Fig. 8b). The variation of the atmospheric stratification suggests that the difference between the wind-following- and wind-countering-swell cases is likely due to the effect of the atmospheric stratification on the atmospheric turbulent momentum transfer. Oost et al. (2002) also concluded that swell does not have any effect on the u*V relationship.

f. Surface drag coefficient

Another common approach to investigate the wave effect on the MABL is through investigation of the drag coefficient
e2
Based on MOST, in Eq. (1) can be expressed as a function of under neutral condition ; that is,
e3
In the stratified atmosphere, in Eq. (3) would be estimated from through a stability correction. Therefore, the stability-corrected can be used as an alternative parameter to represent the surface influence on the atmospheric turbulent momentum transfer. Because of the definition of , 10% of uncertainty in would lead to 20% uncertainty in . In contrast, 10% of uncertainty in would lead to ~10% uncertainty in .
We first examine how varies with over both land and sea as the similar linear relationship between and under nearly neutral conditions has been observed over both surfaces. The observed approximately linear increase of with under nearly neutral conditions can be approximately expressed as
e4
e5
e6
where represents the threshold wind speed that marks the transition between the stable and the nearly neutral regimes; represents at the surface or at , which is skin drag; and the coefficients and can be solved with the conditions of Eqs. (5) and (6). Substituting the resolved and into Eq. (4), we have
e7
Equation (7) indicates that the slope of the u*(z)–V(z) relationship is related to the surface property . Substituting Eq. (7) into Eq. (2), we have
e8
Equation (8) indicates that consists of its surface skin drag, (the first term), and the additional drag from the turbulent momentum transfer between z and the surface (the second term), which is the turbulence drag. As form drag over sea is related to the atmospheric momentum transfer as a result of vertical variations of wind perturbations associated with pressure perturbations induced by mainly low-frequency waves (section 4a), the turbulence drag here includes form drag. Because the turbulence drag is inversely related to , increases with decreasing and approaches when . As a result of the contribution of both the wind speed–dependent turbulence drag and the skin drag, has a minimum value at when ; that is,
e9
which is the wind speed when the linear u*(z)–V(z) relationship under nearly neutral conditions is extrapolated to zero ; that is, . As increases with z, the minimum would disappear as z approaches zero; that is, approaches the skin drag . Because increases with z (Sun et al. 2012, 2016), Eq. (9) suggests that would increase with z, which is confirmed by comparison of between 5 and 20 m based on the CASES-99 dataset and between 6 and 20 m based on the CBLAST-Low dataset (Figs. 9a and 9b). Because the increase of with is much more significant over the rough land surface compared to over the relatively smooth sea surface (Fig. 6), the turbulence drag decreases with faster over land than over sea. As a result, the variation of with over sea is not dramatic as the one over land. The difference between and in the stratified marine atmosphere has also been noticed by Foreman and Emeis (2010), and a constant under strong winds, which is equivalent to a constant , has been observed in the literature (e.g., Powell et al. 2003; Donelan et al. 2004; French et al. 2007).
Fig. 9.
Fig. 9.

The composite drag coefficient as a function of wind speed for (a) CASES-99 and (b) CBLAST-Low, where the data from CASES-99 are the nighttime values, which cover the stable and the nearly neutral regimes. The green line in (a) is for u* = 0.37 m s−1 to represent an example of a self-correlated with V.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0354.1

Since is a function of by definition, the relationship between and has potential of suffering self-correlation; that is, the Cd(z)–V(z) relationship would be dominated by the dependence of on . As demonstrated in Eq. (8), is indeed related to through the drag associated with the turbulent momentum transfer but only under weak winds. Because Eq. (8) does not describe under weak winds, it only approximately captures the characteristics of for . Because the contribution of large coherent eddies to strong turbulent mixing is improperly described in the MOST bulk formula as explained in Sun et al. (2016), and are essentially zero in the MOST bulk formula, and the minimum cannot be derived based on from the MOST bulk formula.

In the literature, has been investigated as a function of V extensively (e.g., Toba et al. 1990; Donelan et al. 1993; Hedde and Durand 1994; Jones and Toba 1995). The data analyses above may help to understand whether increases with V or approaches a constant under strong winds in the literature (e.g., Donelan et al. 2012). The common practice in derivation of neutral for estimating at 10 m is to correct wind profiles to its neutral value at 10 m using the MOST stability function and assume that the atmospheric momentum flux is constant between the observation height and the sea surface. As observed by Sun et al. (2013), the atmospheric momentum flux near the surface increases slightly with height under near-neutral conditions because of the increasing contribution of large coherent eddies with height even though the high-frequency turbulent momentum flux decreases with height. During CASES-99, the MOST bulk formulas are only approximately valid in the layer below 10 m and above the constantly near-neutral turbulent layer near the surface (Sun et al. 2016). Fundamentally local shear assumed in MOST cannot capture large coherent eddies that dominate turbulent mixing under near-neutral conditions when z is relatively large—that is, about 10 m during CASES-99. Therefore, limitation of MOST may also lead to uncertainty in the debate of the variation of with wind speed in the literature because of the application of the MOST bulk formula.

5. Concluding remarks

Based on the HOST hypothesis proposed by Sun et al. (2012, 2016), which emphasizes the contribution of large coherent eddies to the atmospheric turbulent mixing that MOST fails to properly represent, we investigate the relationships between atmospheric momentum transfer and sea surface roughness during CBLAST-Low and SWADE, the role of the SST in atmospheric turbulent fluxes, and the variation of drag coefficient with wind speed by comparing turbulent mixing over sea with over the land surface from CASES-99.

  1. The air temperature variation is much larger than the SST variation during CBLAST-Low, indicating the air temperature is strongly influenced by atmospheric heat transport. Therefore, the apparent dependence of the atmospheric heat flux on the air–sea temperature difference is mainly related to the variation of the air temperature. Similarly, the relationship between the moisture flux and the humidity difference between the saturated specific humidity at SST and the air specific humidity is dominated by variations of the air specific humidity.
  2. In general, the influence of the surface on the atmospheric turbulent momentum transfer is similar between over land and over sea except the physical sea surface roughness is strongly tied to the atmospheric momentum transfer, for which the size of dominant turbulent eddies is comparable to high-frequency wind sea. The observed wave slope of wind sea is found to increase with wind speed (i.e., with ) and approaches a constant value for the strong wind observed in this study. Because atmospheric turbulence over sea is mainly generated by wind shear, the impact of swell on atmospheric turbulence is only important through wave-induced winds and oceanic currents when the background wind speed is small or atmospheric turbulent mixing is near the sea surface where wind speed is always small. The phase speed of swell describes the speed of vertical and horizontal oscillations of the sea surface under the influence of swell, which is not significant for wind shear under strong winds.
  3. The dependence of and on wind speed over sea can also be explained by the HOST hypothesis developed over land (Sun et al. 2016). Under unstable conditions, the heat source for the surface layer over both land and sea is from below, and buoyancy-generated turbulent mixing is similar. However, stable stratification over land and sea is formed differently, which affects the magnitude of in the stable atmosphere. Over land, the stable stratification results from steady radiative cooling of the surface under weak winds, resulting in relatively small and the increase of with due to the contribution of shear-generated turbulent mixing in transporting cold air up and warm air down. Near-neutral conditions over land are achieved by strong shear-generated turbulent mixing associated with strong winds, and decreases with increasing as a result of the reduction of the vertical temperature gradient. Over sea, episodic stable stratification is developed in the mostly near-neutral atmosphere through air warming over cold water associated with advection and downward heat transfer of warm air and is weak during CBLAST-Low. As a result, is relatively large with weak winds, and increases slightly with for almost the entire range of the observed wind speed during CBLAST-Low. In other words, the transition of any TKE-related variable between the stable and the near-neutral atmosphere is achieved differently between CLBAST-Low and CASES-99 and depends on atmospheric stable stratification and surface roughness. Nonetheless, the approximately linear increase of with over sea is related to large coherent eddies generated by bulk shear as explained by the HOST hypothesis and is not affected by swell during CBLAST-Low and SWADE under strong winds.
  4. The drag coefficient, , consists of the surface skin drag and the turbulence drag, which includes effects of form drag associated with waves on atmospheric momentum transfer. As increases with when the atmosphere is nearly neutral, the turbulence drag is significantly reduced, and approaches the skin drag. The variation of the turbulence drag with wind speed relative to the skin drag leads to a minimum value of . As contribution of large coherent eddies to turbulent mixing is essential in the turbulence drag, which is not properly described by MOST, the minimum cannot be explained by the MOST bulk formula for momentum. The analyses presented in this study may shed light on observed different behaviors of with in the literature.

Acknowledgments

Jielun Sun would like to thank Shuyi Chen for motivating her to pursue the research presented in this paper. We thank James Edson for leading the CBLAST-Low field campaign and providing the ASIT data, Larry Mahrt and Ed Andreas (deceased) at NorthWest Research Associates and Sean Burns at NCAR for their valuable comments, Dean Vickers from Oregon State University for his processing the LongEZ aircraft data, Dr. Haf Jonsson at CIRPAS for his field work in managing the Pelican aircraft, Dr. Djamal Khelif for maintaining instruments on the Pelican aircraft and processing the Pelican data, and Albert Plueddemann for his assistance in obtaining oceanographic and atmospheric data at MVCO. Jielun Sun was supported by ONR Grant N00014-97-109348 for participating in CBLAST-Low and by the National Science Foundation for carrying out this research. The NOAA LongEZ group during CBLAST-Low was supported by ONR Grant N00014-01-F-0008. The University Corporation for Atmospheric Research manages the National Center for Atmospheric Research under sponsorship by the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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