Structures and Characteristics of the Windy Atmospheric Boundary Layer in the South China Sea Region during Cold Surges

Boundary layers were first investigated at the beginning of the 20th century by (Prandtl, 1904), and the first geophysical application of boundary layer theory belongs to (Ekman, 1905). Until now, there has been a theory system (which can be referred to as classical theory) on the structures and dynamical characteristics of the atmospheric boundary layer (ABL) (Kolmogorov, 1941, 1962; Sutton, 1953; Monin and Obukhov, 1954; Lumley and Panofsky, 1964; Stull, 1988; Sorbjan, 1989; Kaimal and Finnigan, 1994; Wyngaard, 2010); and these classical results have been widely used in weather and climate forecasting models, such as the general circulation models of the National Center for Atmospheric Research (NCAR), Geophysical Fluid Dynamics Laboratory (GFDL), European Centre for Medium-Range Weather Forecasts (ECMWF), and the Weather Research and Forecasting Model (WRF), as well as various other practical atmospheric models.

However, these studies are based on the condition of weak average wind speed. Under that condition, following the theory, the average speed \(\overlineu(z)\) changes with height as a logarithmic function, and the turbulent spectrum obeys a -2/3 power law. In fact, in the real ABL, there are many cases of cold air outbreaks (cold surges; Ding et al., 2009). Usually, in these cases, the wind speed averaged for 10 min, \(\overlineu\), at the 10 m height above ground, is larger than 10 m s^-1. Moreover, values of \(\overlineu>30\) m s^-1 and even \(\overlineu>40\) m s^-1 are very often found for storms and typhoons. It is important to study the structures and dynamical characteristics of windy ABLs and to recognize their differences from classical theoretical results.

In the land ABL, many observations have long been made during strong wind episodes, and by analyzing these valuable data it has been possible to show many differences compared with weak wind situations (Cheng et al., 2007; Zeng et al., 2007a; 2007b; Zeng et al., 2010; Cheng et al., 2011; Cheng et al., 2012a, 2012b, 2012c). For example: (1) the power function is better than the logarithmic function in fitting the vertical distribution of average wind speed, \(\overlineu(z)\); (2) wind fluctuations are better divided into two types, i.e. (I) high frequency turbulent fluctuations (turbulent fluctuations, or simply "turbulence" for short) with a frequency greater than 1/60 Hz (period<1 min), which is random and possesses weak coherency, and (II) gusty wind disturbances ("gusts" for short) with a frequency between 1/60 and 1/600 Hz (period of 1-10 min), which possesses rather regular structure and strong coherency; (3) turbulence lies in the inertial sub-range, and its spectrum obeys a -2/3 scaling law, as does the classical theory, but gusts are far from the inertial sub-range and the spectrum has a different form, even with a discrete maximum at some main frequencies (usually in the range 1/120-1/240 Hz); (4) the constant flux layer does not exist, and the downward flux of momentum reaches its maximum at some lower level within the boundary layer; (5) the downward flux of horizontal momentum contributed by gusts is as large as that by turbulence; (6) both the turbulent kinetic energy and momentum flux are large in the lower layer, then decrease very quickly with height, showing that turbulence is generated by land-air interactions near the ground surface; and (7) the maxima of kinetic energy and momentum flux of gusts are at a level higher than those of turbulence, showing its generation is due to disturbances within the ABL, but the influence of the ground surface is small.

For the marine boundary layer, current models (such as the models of the NCAR, GFDL, and WRF) and the associated literature (Andreas, 1992, 1998, 2010; Fairall et al., 1994) are all based on the classical turbulent and boundary layer theories. In particular, \(\overlineu(z)\) is taken as a logarithmic distribution in all these models and studies. However, in fact, the occurrence of strong winds over the sea surface is much more frequent than over land. Therefore, the structures and characteristics of the marine boundary layer during strong wind episodes might also be different to those during weak wind episodes, and a logarithmic profile of \(\overlineu(z)\) might be doubtful. There have been some observational experiments conducted that were specifically focused on the marine boundary layer, such as Humidity Exchange over the Sea Program (HEXOS) and Fronts and Atlantic Storm-Track Experiment (FASTEX), the Meetpost Noordwijk platform in the North Sea (DeCosmo, 1991; Smith et al., 1993; Andreas and DeCosmo, 1999; Andreas, 2010), and Coupled Ocean-Atmosphere Response Experiment (COARE) (Zeng et al., 2002). However, apart from (Zeng et al., 2002), the analyses of these data have largely been based on the classical theory of the boundary layer. Although there were 322 hours of data in the FASTEX datasets, and sometimes the wind speed \(\overlineu\) reached 22 m s^-1, (Andreas, 1998) derived the 10 m wind speed as 32 m s^-1 by the logarithmic profile, and the bulk turbulent flux algorithm was also used.

Only (Zeng et al., 2002) noticed the existence of gusts and used the drag coefficient D when calculating the momentum and thermal fluxes in the marine boundary layer; and in the calculation of D, \(\overlineu\) was replaced by \(\overlineu+\) a correction term considering the statistical characteristics of gustiness. We have no intention of making a reanalysis of those observation data. Fortunately, we have some new data regarding the marine boundary layer during cold surges from January-May 2012 and 2013. These data were obtained during the Marine Meteorological Experiment Complex (MMEC) at Bohe, Guangdong Province, in a cooperative effort by the Institute of Tropical and Marine Meteorology/China Meteorological Administration, the Maoming Meteorological Bureau/Guangdong Province, the Institute of Atmospheric Physics/Chinese Academy of Sciences, and China Ocean University. In this paper, we analyze these data to present the structures and characteristics of the marine ABL during the cold air outbreak, and compare them with those at land surface stations.

The MMEC at Bohe, Guangdong Province, comprises three sites: (2) Beishan Station, which is located on Lotus Head (a small and very narrow peninsula, like an arrow intruding into the sea) at a height of about 10 m; (3) Near Beishan Station, there is an observation platform (21^°26'21"N, 111^°23'44"E) above the sea surface and 6.5 km from the shore, where the depth of the water is 16 m; (4) A 100 m meteorological tower (21^°27'3"N, 111^°22'28"E) installed on a very small rocky island named Zhizi, which is located at a height of 10 m and 4.4 km from the shore, where the depth of the surrounding sea is 6-10 m. A map showing the locations of the sites and also a picture of the platform are provided in Fig. 1.

Figure 1.  The marine meteorological science experiment complex at Bohe and the observation platform.

A set of Doppler boundary layer wind profilers (Sumitomo Electric Industries, Osaka, Japan) is utilized at Beishan Station to measure the wind profile within the whole ABL. The effective observation height of this set of instruments is from 100 m to 3500 m, the vertical resolution is 100 m, and the average sampling time is 10 min. These observations provide the large-scale background for the analysis of the finer-scale observations made at the observation platform and on Zhizi Island.

There is a 25 m high tower on the observation platform with three sets of Gill R3-50 ultrasonic anemometers (Gill Instruments Limited, Hampshire, UK, measuring resolution: 0.01 m s^-1; measurement accuracy: <1% RMS (root mean square)), which are installed at 24 m, 16 m and 9 m above the tower base, and the tower base is 11 m above the sea surface. Besides, there is also a small annex tower with one set of Gill R3-50 ultrasonic anemometers at 8 m above sea level. Accompanying these four sets of ultrasonic anemometers, there are four sets of XW-TS1130 inclinometers (Beijing Starneto Technology CO. Ltd, Beijing, China, angle measuring range: 15^°; measurement accuracy: 0.1^°) for monitoring the attitudes of these anemometers. The frequency of the ultrasonic anemometers and inclinometers is 20 Hz. The instruments used for measuring other meteorological variables are supplementary (for checking the quality of the ultrasonic anemometer observations) and hence are not described here.

On Zhizi Island there is a meteorological tower with six levels of NRG-Symphonic anemometers (NRG systems, Hinsburg, USA) at 10, 20, 40, 60, 80 and 100 m above the island and three levels of anemoscopes (NRG systems, Hinsburg, USA) at 10, 60 and 100 m above the island. These data are used for multiple checks of the observations of \(\overlineu(z)\) by the observation platform and its extension to higher altitude.

In order to ensure the quality of observations, abnormal data recorded by the Gill R3-50 ultrasonic anemometers were eliminated. For example, data were removed if the anemometers were contaminated by precipitation. Also, any extraordinarily large values beyond the reasonable range of the data, or exceeded the threshold of six times larger than the variance of the data obtained from the computation of the probability density function, were also removed. The supplementary data for replacing the eliminated data were obtained by interpolation from adjacent data.

The inclination of an ultrasonic anemometer can cause horizontal wind velocity fluctuation to produce a relatively large component in the vertical direction, so the vertical fluctuations as well as the vertical velocity become contaminated. Usually, the inclination of an ultrasonic anemometer can be corrected by all of the three coordinate system transforming methods of the double rotation (DR) or planar-fit (PF) methods (Wilczak et al., 2001). In the present study we used the inclinometer settled on the reference plane of the anemometer to obtain the synchronous signals of inclination angles, and put these angles into the coordinate transformation to obtain the new velocity data:

\begin{equation} \label{eq1} \begin{array}{l} u=u_0\cos(\beta)\\[1mm] v=v_0\cos(\alpha)\\[1mm] w=w_0+u_0\sin(\beta)+v_0\sin(\alpha) \end{array} , \end{equation}

where u₀,v₀,w₀ are the original signal of velocities, u,v,w are the revised velocities, and α,β are the inclination angles around the x axis (pitch angle) and y axis (yaw angle) respectively. Note, that α and β are slowly variable or even constant. After a single rotation, u is defined as the horizontal wind speed along the downwind direction (the direction in which the horizontal velocity vector is heading), and hence the average velocity of v, i.e. \(\overlinev\), is exactly zero according to such decomposition.

The data obtained from MMEC during cold air outbreaks (cold surges) from January-May 2012 and 2013 are analyzed in detail. During the period January-May 2012 there were 289 hours when wind velocities reached 10 m s^-1 at 9 m height above the tower base of the observation platform (20 m above sea level), and 103 hours when they reached 12 m s^-1. The period 23-24 March 2012 was a typical case during which a stream of cold air quickly descended over Guangdong Province and the South China Sea region, and above sea surface the cold surge enhanced the northeast wind obviously. There was moderate to heavy rainfall over the north of the province, and light to moderate rainfall over central and southern regions. Some cities and counties suffered strong convective weather, such as short-term thunderstorms and highly intense rainfall. At the sea surface there were northeasterly winds at force 7 accompanied by force 8 gusts. Figure 2 shows the 850 hPa weather map at 0800 LST 24 March 2012. We can see that the strong wind with a northern component does not appear at the top of the boundary layer (approximately 850 hPa). Figure 3 is the one-hour-averaged time-height wind profile at Beishan Station. Together, Figs. 2 and 3 show that the cold air outbreak was very shallow and strong wind was a phenomenon that occurred in the boundary layer. They also show that very strong wind was present between 2100 LST 23 March and 1000 LST 24 March 2012, but below 1000 m. In such a large-scale background, the observations at the observation platform and on Zhizi Island show that the strong horizontal wind speed in the low layer of the ABL appeared with a peak at 0001 LST 24 March and lasted for almost 1 day (seen in Figs. 4a and b). Note that there is very good structural consistency between the curves \(\overlineu(z,t)\) in Figs. 4a and b.

Figure 2.  850 hPa weather map at 0800 LST 24 March 2012 (provided by Guangdong Meteorological Bureau).

Figure 3.  Time-height wind profiles of one-hour-averaged \(\overlineu(z,t)\) during 23-24 March 2012 at Beishan Station.

Figure 4.  10-min-averaged horizontal and vertical velocities during 23-24 March 2012: (a) \(\overlineu\) at four levels and \(\overlinew\) at two levels of the observation platform; (b) \(\overlineu\) at six levels on Zhizi Island; (c) the distribution of \(\overlineu\) at every level of the observation platform; (d) the distribution of \(\overlineu\) at every level of the tower on Zhizi Island; (e) as in (c) except for \(\overlinew\) at two levels; (f) the pair (\(\overlineu,\overlinew\)) for cold surge cases.

Here, we apply the method suggested by (Zeng et al., 2010) to analyze the characteristics of the windy marine ABL; that is, to divide the variable f into three parts: 10-min-averaged (\(\overlinef\)); gusty value (f _g); and turbulent value (f _t). Taking wind velocity V for example, we have \(\bmV(t)=\overline\bmV(t)+\bmV_\rm g(t)+\bmV_\rm t(t)\), where the subscripts "g" and "t" represent gusty wind disturbance and turbulent fluctuation, respectively. Conventionally, V is decomposed as \(\bmV(t)=\overline\bmV(t)+\bmV'(t)\), and V' is called fluctuation (even turbulence), but here we divide V' into two further parts, i.e. V'=V _g+V _t. Besides, the three directional components of the vector V are denoted as (u,v,w), where u is the horizontal speed in the downwind direction, then \(\overlinev=0\), and \begin{equation} \label{eq2} \left\{ \begin{array}{rcl} u&=&\overline{u}+u_{\rm g}+u_{\rm t}\\[1mm] v&=&v_{\rm g}+v_{\rm t}\\[1mm] w&=&\overline{w}+w_{\rm g}+w_{\rm t} \end{array} \right. . \end{equation}

The average time is 10 min. Here, we use the simplest method to separate turbulent fluctuation and gusty wind disturbance. That is, the frequency of the former is larger than 1/60 Hz, and the latter is between 1/60 Hz and 1/600 Hz. Although the frequency dividing these into two parts might be slightly different, and may change from case to case for strong and weak wind situations, it is sufficient to take the value in applications as 1/60 Hz. We focus on analyzing the characteristics of turbulence and gusts, and the relationship between them with average wind (primarily the horizontal average velocity \(\overlineu\)). Denoting the kinetic energy, friction velocity and the coherent index as E_i,u_i* and C_i respectively, where i= g,t, we have

\begin{eqnarray} \label{eq3} E_{\rm g}&=&A_{\rm gu}^2+A_{\rm gv}^2+A_{\rm gw}^2\equiv\dfrac{(\overline{u_{\rm g}^2}+\overline{v_{\rm g}^2}+\overline{w_{\rm g}^2})}{2} ,\\[0.5mm] \label{eq4} E_{\rm t}&=&A_{\rm tu}^2+A_{\rm tv}^2+A_{\rm tw}^2\equiv\dfrac{(\overline{u_{\rm t}^2}+\overline{v_{\rm t}^2}+\overline{w_{\rm t}^2})}{2} ,\\[0.5mm] \label{eq5} u_{\rm g\ast}&\equiv&[\overline{u_{\rm g}w_{\rm g}}^2+\overline{v_{\rm g}w_{\rm g}}^2]^{\frac{1}{4}} ,\\[0.5mm] \label{eq6} u_{\rm t\ast}&\equiv&[\overline{u_{\rm t}w_{\rm t}}^2+\overline{v_{\rm t}w_{\rm t}}^2]^{\frac{1}{4}} ,\\[0.5mm] \label{eq7} C_{\rm g}&\equiv&\dfrac{u_{\rm g\ast}}{(A_{\rm gh}A_{\rm gw})^{\frac{1}{2}}} ,\\ \label{eq8} C_{\rm t}&\equiv&\dfrac{u_{\rm t\ast}}{(A_{\rm th}A_{\rm tw})^{\frac{1}{2}}} , \end{eqnarray}

where A_ij are the amplitudes of the i fluctuation of the j component, and i= g (gust) and t (turbulence), and j=u, v, w. Besides, \(A_ih\equiv(A_iu^2+A_iv^2)^\frac12\), 0≤ C_i≤ 1(i= g, t). The larger C_i is, the higher the coherency and greater the regularity of the structure.

Figure 4a shows the 10-min-averaged time series of the wind speed \(\overlineu\) obtained by the observation platform ultrasonic anemometers at four levels during 23-24 March 2012. Note that during this cold surge the wind direction (not given here) was very stable. For comparison, Fig. 4b shows the same information but obtained by the anemometers on Zhizi Island at six levels. In Fig. 4a the vertical velocities \(\overlinew\) at the levels 27 m and 35 m (above the sea surface) are also shown, and they are all positive. Note that \(\overlinew\) at the low levels of 8m and 20 m are influenced by the platform; hence, the results are not meaningful and not presented here. Furthermore, except for in summer, unfortunately there was no ultrasonic anemometer at the tower on Zhizi Island; hence, there is no \(\overlinew\) presented in Fig. 4b. Figure 4c shows the distribution of \(\overlineu\) values at every level of the observation platform during 23-24 March 2012. The points are the ensemble means of the speeds. Figure 4d is the same as Fig. 4c but for Zhizi Island. These two figures show that the wind speeds \(\overlineu\) were almost the same at every level, and the difference between levels was small. Therefore, the velocity \(\overlineu\) generally did not change with height below 110 m above sea level, or at least below 35 m above sea level, during the cold surge episode. However, there are still some differences between Figs. 4a and b, e.g. the 1 m s^-1 difference of \(\overlineu\) and the slight phase difference. These may be due to the different locations of the two sets of observations. Note that the vertical profile of \(\overlineu\) is valid for all cold surge cases in the 2012 and 2013 winter-spring seasons (figure not shown), which is one important characteristic of the windy marine ABL, and it shows that the logarithmic profile of \(\overlineu\) is not valid in such cases.

Figure 4e shows the vertical velocity \(\overlinew\) at the two levels mentioned above for the cold surge case during 23-24 March 2012, and Fig. 4f shows the relationship between \(\overlineu\) and \(\overlinew\). These figures show another important feature of the windy marine ABL, i.e. that there is ascending atmospheric motion above the sea surface, and it can be parameterized well by one parameter, \(\overline u\).

Figure 5 gives an example of original velocity (u,w) measured by ultrasonic anemometers and the decompositions, (u _g,w _g) and (u _t,w _t), at the 8 m level.

Figures 6 and 7 show the amplitudes of turbulent fluctuations, (\(A_\rm t\equiv E_\rm t^1/2\)), and gusty disturbances, (\(A_\rm g \equiv E_\rm g^1/2\)), and their components (A _tu,A _tv,A _tw,A _gu,A _gv,A _gw) against the average wind speed \(\overline u\) (\(\overline u\) is simplified as U in the figures). The regressions (parameterization formulas) are also given in these figures. Note that all data obtained by MMEC for every case of whole air outbreak processes (0.5 m s\(^-1<\overlineu<16\) m s^-1) in January-May 2012 and 2013 were analyzed and are presented in Figs. 6-10, except for Fig. 8; and the regressions in Figs. 6 and 7 are for all levels because their differences between every level are small due to the fact that all four levels are in the lowest layer below 35 m height (above sea level) and the independence of \(\overline u\) to height. Figures 6 and 7 show that: (2) the gusty wind disturbances are anisotropic, and the amplitude A _gu is larger than A _gv, and both are larger than the vertical amplitude, i.e. A _gu>A _gv>A _gw. However, the turbulence is almost isotropic on the horizontal plane, A _tu and A _tv are almost the same, and only the vertical amplitude A _tw is somewhat smaller. (3) Because \(\overlineu\) is almost independent of height, the parameterization formulas for A_ij can be developed by using the vertically averaged wind speed as the unique parameter, and this parameter can also be considered as the 10 m wind speed, as commonly accepted in the literature. (4) The accuracies of these regressions are high——except that of A _gv, which is moderate——especially for turbulent parameters.

Figure 4 shows that the velocity increased obviously from 1800 LST 23 March and that the strong wind lasted until 1200 LST 24 March 2012. During this period the vertical fluxes of horizontal momentum caused by both turbulence and gusts at various levels were also obviously large (Figs. 8a-d). Figure 8e presents the vertical profiles of these fluxes during this period.

Figure 8 shows that the turbulent downward flux was larger than the gusty one, and that they were equally large only at the 35 m level. Besides, the turbulent (gusty) fluxes decreased (increased) slightly with height. The friction velocities u _t* and u _g* against \(\overlineu\) are shown in Figs. 9a and b, and their vertical profiles and distributions at every level are given in Figs. 9c and d. Figures 9a and b show that the u _g* and u _t* at all levels for all cases of cold surges can be very well expressed by parameterization formulas with a single parameter \(\overlineu\). Furthermore, Figs. 9c and d show u _g*<u _t* at all levels, except for the 35 m level where u _g*≈ u _t*, and that both u _g* and u _t* are independent of height (error <10%), albeit u _g* definitely increases with height slightly.

Once we have the kinetic energy and friction velocity of turbulence and gusts, their coherent indices, C _g and C _t, can be easily calculated according to Eqs. (8) and (9). The C _g and C _t values for the case in March 2012 are given in Table 1. The results indicate that most C _g values are much larger than C _t during the strong wind period, and the gusty disturbances possess a well-organized structure.

The equivalent period T _g of gusts was introduced by (Zeng et al., 2010) to approximately present the real gusty trains whose period is variable from time to time but within some range. Such a defined equivalent period of gusts is very useful for solving the problem of aerosol transport (Cheng et al., 2012c).

Figure 9.  Friction velocity change with average velocity (a, b) and their profiles and distributions at every level (c, d).

During the cold surge periods in January-May 2012 and 2013, the T _g computed from the observed u _g at four levels is presented in Fig. 10. It can be seen that T _g is located in the domain (2 min, 6 min), and the period is stable at strong wind and almost reaches the saturation value of 2.6 minutes. Compared to the equivalent period of gusts over land, where the T _g is located in the domain (3 min, 8 min) and the saturation period seems to be about 4 min (Cheng et al., 2012a), the gusts in the marine boundary layer with strong wind are smaller in scale than those over land. This phenomenon, and the independence of \(\overlineu\) to height, indicate that in oceanic regions the movable interface, the air-sea interaction and the sea-waves greatly influence the characteristics of the ABL.

Figure 10.  The change in equivalent period T _g with horizontal velocity \(\overlineu\).

In the present reported study we analyzed the structures and characteristics of the marine ABL during strong cold surges in the South China Sea region. The results showed that most characteristics are consistent with the situation of strong wind over land. For example:

(1) There are both gusty wind disturbances and high frequency turbulent fluctuations superposed on the basic strong wind; the turbulence is random, nearly isotropic and weakly coherent, but the gusts possess rather more regular and stronger coherency, as well as anisotropy. With an increase in the average velocity \(\overlineu\), the equivalent period of gusts decreases and reaches saturation.

(2) The characteristics of turbulence and gusts, such as the kinetic energy and momentum flux, can be expressed by parameterization formulas.

Meanwhile, there are some differences, such as:

(1) In the lower atmospheric layer above the oceanic surface, the average horizontal speed \(\overlineu\) is almost independent of height (unlike the increase with height over land), and the vertical velocity \(\overlinew>0\) (unlike \(\overlinew<0\) over land).

(2) There is a constant flux layer (the vertical fluxes of horizontal momentum are almost independent of height) in both the turbulence and gusts above the oceanic surface.

(3) In oceanic regions, the parameterization formulas for the characteristics of the ABL can be presented well by \(\overlineu\), rather than \(\partial\overlineu/\partial z\) over land.

The strong winds analyzed in our earlier studies over land and in the present study over the ocean all took place during cold air outbreaks. The common laws indicate a similar influence of the underlying surface on the atmospheric motion, and the differences are due to the different characteristics of the underlying surface. In the oceanic region the underlying surface is movable and possesses multiple temporal- and spatial-scale motions; and around this interface the air-sea interactions are strong and highly complex. Therefore, more observations and analyses are needed.

We have also carried out similar work but during the passage of typhoons. The preliminary results show that the major characteristics are similar to those reported in this paper, although the average wind speed, gusts and turbulence are all very much stronger. We hope to report the results in a future paper.

Acknowledgements. This work was supported by the National Nature Science Foundation of China (NSFC, Grant Nos. 40830103 and 41375018), a National Program on Key Basic Research project (973 Program) (Grant No. 2010CB951804), the plan of the State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics, Chinese Academy of Sciences (Grant No. LAPC-KF-2013-11), China Special Fund for Meteorological Research in the Public Interest (Grant No. GYHY200906008), and the program of the Chinese Academy of Sciences (Grant No. XDA10010403). We are also very grateful for the help provided by LIN L. X. (Chief Scientist of weather forecasts) and ZENG C. (Officer) at the Weather Forecast Division of Guangdong Meteorological Bureau, and ZHAO Y. J. (Senior Engineer) and LUO W. D. from the Institute of Atmospheric Physics, Chinese Academy of Sciences.