Fei LIAO, Hua DENG, and Pak-wai CHAN

1 Guangzhou Meteorological Observatory, Guangzhou 511430

2 Guangzhou Institute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou 510080

3 Guangdong Ecological Meteorology Center, Guangzhou 510080

4 Hong Kong Observatory, Hong Kong 999077

ABSTRACT We analyzed the frequency distribution characteristics of wind speeds occurring at different offshore sites within a range of 0–200 km based on the sea surface wind data captured via buoys and oil platforms located along the east coast of Guangdong Province. The results of the analysis showed that average wind speed measured for each station reached a maximum in winter while minima occurred in summer, corresponding to obvious seasonal variation, and average wind speed increased with offshore distance. The prevailing wind direction at the nearshore site is the easterly wind, and the frequency of winds within 6–10 m s–1 is considerable with that of winds at ＞ 10 m s–1. With the increase of the offshore distance, the winds were less affected by the land, and the prevailing wind direction gradually became northerly winds, predominately those at ＞ 10 m s–1. For areas of shorter offshore distance (＜ 100 km), surface wind speeds fundamentally conformed to a two-parameter Weibull distribution, but there was a significant difference between wind speed probability distributions and the Weibull distribution in areas more than 100 km offshore. The mean wind speeds and wind speed standard deviations increased with the offshore distance, indicating that with the increase of the wind speed, the pulsation of the winds increased obviously, resulting in an increase in the ratio of the mean wind speed to the standard deviation of wind speed. When the ratio was large, the skewness became negative. When a relatively great degree of dispersion was noted between the observed skewness and the skewness corresponding to the theoretical Weibull curve, the wind speed probability distribution could not be adequately described by a Weibull distribution. This study provides a basis for the verification of the adaptability of Weibull distribution in different sea areas.

Key words: sea surface wind, probability distribution, observation, buoy, oil platform

1. Introduction

The distribution of sea surface wind speed has very profound effects on air–sea momentum transfer (Donelan et al., 2002), which will lead to changes in sea surface temperature and in turn affect the distribution of sea surface winds (Shi et al., 2015) and marine atmospheric boundary layer (Wang et al., 2010). Such feedback phenomenon means that the bulk parameterizations of air–sea fluxes are nonlinear in the sea surface wind speed, so average air–sea fluxes is not equal to the fluxes diagnosed from the mean wind speed but its estimation can be improved by in situ measurement (Wang et al., 2013). On average, air–sea fluxes depend on higher-order moments of the sea surface wind speed (Isemer and Hasse, 1991),which means that it is need for parameterizations of the probability distribution of sea surface wind speed.

A number of studies have shown that surface wind speed distributions over land or sea can be well approximated via a two-parameter Weibull distribution function (Bauer, 1996), which provides a good represented to the probability density function of wind speed. Even in North Atlantic, the tropical cyclone wind speed distributions can also be well represented by the Weibull distribution with different scale and shape parameters (Tye et al., 2014). But the studies also showed that observed wind speeds may be large different with Weather Research and Forecasting (WRF) model simulation results when using different reanalysis data (Floors et al., 2013).Thus, it is necessary to assimilate boundary layer observation, such as wind lidar and tower data, to reduce the scatter between the simulated and measured wind speeds(Gryning et al., 2013). In order to study the distribution of sea surface winds more accurately, it is necessary to carry out direct observation of sea surface winds at high spatial and temporal resolution to the greatest extent possible, but coverage provided by direct observation stations, whether buoys, oil platforms, or island observation stations, remains limited. For example, Pavia and O’Brien(1986) performed rough observations of surface wind speeds occuring in the Northern Hemisphere.

He et al. (2010) noted that away from open water, the Weibull distribution generally underestimates wind speed extremes at night. The mean and the standard deviation of wind speed are most in fl uenced by large-scale “weather”variability, and the intermittent mixing process determined by the asymptotic fl ux Richardson number affects the shape of the Weibull distribution (He et al., 2012).Sea surface wind speed data obtained via ERA-40 and NCEP-NCAR data reanalysis were also sometimes found to display non-Weibull behavior (Monahan, 2006b). This has made understanding the distribution of sea surface wind speeds (especially in coastal waters with land–sea contrasts and complex topography; Ha et al., 2009) and corresponding parameterization problems difficult(Thompson et al., 1983; Wanninkhof and McGillis,1999), which also demonstrate that the Weibull distribution cannot be used to fully represent the actual distribution of sea surface winds (Erickson et al., 1989).

Seasonal variation in wind direction and velocity field along the coastal zone of Guangdong Province in China is related to changes of summer monsoon and winter monsoon in the South China Sea. The variation is complex because the coastal surface is the zone with land–sea contrasts, complex topography, and urban areas. Since 2012, the Guangdong Meteorological Service has gradually established various maritime observation systems in the northern waters of the South China Sea, which provide rich direct observation data, to study the characteristics of sea surface wind speeds in coastal areas.Thus, in this paper, we focus on the statistical distribution of sea surface winds measured at different offshore distances falling within the bounds of northern South China Sea, analyze the seasonal variation in wind speed distribution, and discuss the applicability of the Weibull distribution in northern South China Sea. We hope that will help future efforts to understand the distribution of sea surface winds in the South China Sea.

2. Data and methods

2.1 Description of the data

Continuous 10-m altitude sea surface direct observation data were obtained primarily from automated island weather stations, buoy stations, and offshore oil platforms, with observations taken at a frequency of every 10 minutes from 2012 to 2016. Because sea surface wind speeds (especially those occurring near the coastline) are significantly affected by the presence of the coastline,distance from the coastline was determined according to latitude and longitude information provided for different sites, and each site was assigned to one of four categories: Class 1: offshore distance ＜ 10 km; Class 2: offshore distance within 10–100 km; Class 3: offshore distance within 100–200 km; and Class 4: offshore distance ＞ 200 km.

In addition, due to the potential for instrument failure or other abnormalities to produce abnormal data, a threefold variance approach was used to pre-process raw observation data and during processing, sliding of data within a 24-h window was performed in order to eliminate potential outliers. Furthermore, whilst implementing that above classification and processing scheme in the event that a given station showed daily mean wind speeds, which significantly deviated (wind speed ＞ 3 m s–1and wind direction ＞ 10°) from daily mean winds speeds measured at two or more neighboring stations (i.e., stations within 50 km) for 10 or more continuous days, the above-mentioned stations were treated as an outliers.

Fig. 1. Specific locations corresponding to each station (the station number, e.g., 1_59506, means that station 59506 belongs to Class 1;the same as follows).

2.2 Calculation of probability distribution parameters

The ordinary (two-parameter) Weibull distribution is a special case of the generalized three-parameter Gamma distribution. The Weibull probability density function may be expressed as follows:

The parameters k and λ denote, respectively, the corresponding shape and scale parameters of the distribution. The mean, skewness, and kurtosis are given by(Monahan, 2006a)

where Γ is the Gamma function and it can be approximated by

Skewness is a measure of the asymmetry of a PDF: a positive skewness of a variable v indicates that the PDF is characterized by an elongated tail in the direction of positive fluctuations away from the mean. A positive kurtosis of its PDF is more sharply peaked and has longer tails.

When evaluating Eqs. (3) and (4), the two parameters k and λ are required, according to the approximate direct estimation method (Justus et al., 1978), estimate of Weibull paramters k and λ can be approximately inverted to

Based on the actual observation data pertaining to sea surface wind speeds, the skewness and kurtosis can be approximately given by

where v corresponds to the wind speed,ˉ corresponds to the mean wind speed, and std corresponds to the standard deviation of the wind speed.

Monte Carlo experiments using simulated Weibull data indicate that each of these estimator is unbiased(Pang et al., 2001), and estimate method by Eqs. (6) and(7) is easy to compute, which is used in this study.

3. The probability distribution of sea surface wind speeds

3.1 Parameter characteristics

Station HKHMZ (a Class-1 station), G5942 (a Class-2 station), G3597 (a Class-3 station), and G3598 (a Class-4 station) are selected as a representative station for a comparative analysis. Figures 2 and 3 show the distributions of wind speed mean values, standard deviations, skewness, and kurtosis that were calculated based on wind speed data at each station. The distribution of the various physical fields shows obvious seasonal variation in mean wind speeds, which reach a maximum in winter (November–January) and a minimum in summer (around July).Corresponding variation was observed for mean wind speeds at different offshore distances, with more distant locations generally showing a greater maximum mean wind speed in winter (Fig. 2a), and the greater the sustained duration, the greater the corresponding summer mean wind speed observed. The magnitude of fluctuations in the standard deviation of wind speed was relatively small for stations closer to shore (Fig. 2b) while the standard deviation of wind speed was relatively large for stations farther from shore, and the fluctuation range was correspondingly large. Furthermore, a relatively large standard deviation in wind speed tended to correspond to relatively smaller mean wind speeds, indicating that stations farther from shore were subject to more significant weather system-related effects in the summer, with a significant degree of fluctuation in wind speeds.

Fig. 2. Changes in (a) average wind speed and (b) wind speed standard deviation over time for each station.

Fig. 3. Changes in wind speed probability distribution skewness value of station G3598 over time.

Wind speed probability distribution parameters were calculated by using Eq. (6). The skewness distribution included both positive and negative values for each season at an equal probability (figure omitted), but for stations far from the shore (Fig. 3), the summer period included primarily positive values while the winter period did primarily negative values. Corresponding kurtosis values were mainly negative (figure omitted), but an analysis conducted by Monahan (2006b) shows that kurtosis values observed in the tropics are essentially entirely positive. We therefore see that parameters corresponding to the distribution of wind speed probability in the northern coastal area of the South China Sea feature their own distinct distribution properties.

3.2 Wind speed probability distribution characteristics

When we attempt to fit a Weibull distribution to an actual wind speed probability distribution, we find that there is a difference between the actual wind speed probability distribution and the Weibull distribution due to seasonal variation in the corresponding distribution parameters. A fitted Weibull distribution tends to show a higher kurtosis value compared to the corresponding actual distribution, and the skewness will also be greater.Looking at the distribution obtained from different stations, it is clear that as offshore distance increases, the observed wind speed probability distribution increasingly deviates from the Weibull distribution, and the wind velocity probability distribution becomes significantly more complex when offshore distance increases beyond 100 km.

Compared to Class-1 and Class-2 stations, distributions obtained for Class-3 and Class-4 stations show more sharply peaked (the corresponding maximum probability wind speed from 6 to 10 m s–1), and have longer tails (maximum wind speed expanded to more than 20 m s–1) with a reduction in the corresponding kurtosis value(Fig. 4). If we nevertheless attempt to use a Weibull distribution to obtain an approximate fit, a larger deviation is observed to the right of the maximum kurtosis value,implying that using the Weibull distribution to fit a probability distribution will result in a relatively large deviation for high wind speeds.

The seasonal distribution of scale parameters describing the Weibull distribution is very similar to the distribution of mean wind speeds, indicating that scale parameters reach their maximum in the winter and their minimum in the summer. Shape parameters appear to be stable with respect to seasonal variation, but larger fluctuations are observed in November and December, indicating that changes to wind speed in the winter are more significant.

Fig. 4. Observed and fitted wind velocity probability distributions of a station for each class.

Table 1 shows the parameters of the Weibull distribution calculated by using wind speeds observed at each site and corresponding calculated physical quantities.Weibull distributions fitted for stations of different offshore distances showed only small differences in terms of the shape parameter, which has the same variation characteristics with mean/std, while the scale parameter showed significant changes from station to station. The magnitude of variation in the shape parameter across different stations ranged of 1.77–2.253, with an average value of 2.06, and the magnitude of variation largely remained within 10%. The mean scale parameter value for all stations examined was 8.83, with the magnitude of fluctuation calculated at 22%, so fitted Weibull distributions were affected primarily by the scale parameter,which manifested a significant difference, and this characteristic was also manifested in terms of both skewness and kurtosis. Differences in Weibull distributions were even more obvious in terms of skewness (with a fluctuation of approximately 34%), while kurtosis did not show much of a difference (fluctuation of approximately 4%).In general, stations farther from the shore showed larger average wind speeds as well as a larger standard deviation. When the standard deviation exceeded 4 m s–1, the corresponding Weibull distribution showed a larger difference relative to the actual wind speed probability distribution.

These four-class stations are in separate sea surface,and their statistical wind roses are completely different(Fig. 5). The wind directions recorded by HKHMZ station were mainly easterly, and the prevalence of ENE(eastern northeast) and E (east) winds was comparable with a probability of about 25% respectively, and mainly winds at 6 m s–1or above. The winds within 6–10 m s–1occurred comparably with those at ＞ 10 m s–1, which also reflected that wind directions were more evenly distributed due to the influence of coastline at the stations in coastal areas. With the increase of the offshore distance,the wind direction was gradually more obvious in a certain direction. For Class-2 and Class-3 stations, the winds mainly came from the ENE direction with a probability of nearly 30%, and among the main wind directions recorded at G3597, a Class-3 station, the winds at ＞ 10 m s–1predominated, accounting for about 20%, more than the corresponding proportion (about 12%) for G5942. In addition, when the offshore distance reached more than 100 km, the prevailing wind direction began to change with increased probability of N (north) winds, and decreased probability of E winds. The second largest part of winds recorded at G3597 was N wind with a proportion significantly more than G5942. At the Class-4 station, the frequency of N winds was the largest, reaching 33%, and the probability of wind speed exceeding 10 m s–1accounted for a large proportion in the primary wind direction and the secondary wind direction. Therefore,there were obvious variations in the frequencies of winds recorded by different-class stations. With the increase of offshore distance, the N winds became more obvious with obviously greater probability of occurrence of winds exceeding 10 m s–1. This phenomenon showed that, compared with stations away from the shore, the underlying surface was smoother due to free from the impact of land. Therefore, there was greater probability of oceanic winds turning strong winds. The greater probability of strong winds corresponded to significant fluctuations in speed probability distributions recorded at Class-3 and Class-4 stations as shown in Fig. 4, indicating that the non-Weibull distribution of wind speeds was gradually obvious when the wind speeds were high.

Figure 6 shows corresponding wind speed probability distributions as well as scatter distributions for mean/std and skewness using the data at 59506 (a Class-1 station),G5942 (a Class-2 station), G3597 (a Class-3 station), and G3598 (a Class-4 station) as a basis for a comparitive analysis and the months of March, June, September, and December to represent each season of the year. Despitethe fact that the offshore distances of the four observations were different from the corresponding Weibull variable distribution curves showed similar characteristics.That is, when the ratio is relatively small (＜ 3), the skewness value is positive and the distribution is steeper than the Weibull curve. Conversely, when the ratio is large,the curve becomes relatively straight, while the corresponding skewness value gradually becomes negative.

Table 1. Weibull distribution parameters and corresponding calculated physical quantities. The shaded column is highlighted that the standard deviation exceeds 4 m s–1

Fig. 5. Statistical wind roses for four class stations.

According to Eq. (1), the distributions of the skewness and the ratio (corresponding to the black scatterplot data in Fig. 6) can be calculated by using daily wind speed observation data. When the ratio is relatively small, the correlation between the skewness and the ratio becomes even steeper (i.e., when the ratio is kept constant, the observed skewness is often less than the skewness given by the Weibull distribution); however, when the ratio gradually increased, the correlation between the skewness and the ratio straightens (i.e., when the ratio is kept constant, the observed skewness is greater than the skewness given by the Weibull distribution). Both the“steepness” manifest in the observed distribution when the ratio is relatively small and the “flatness” manifest in the observed distribution when the ratio is relatively large imply the existence of fluctuations in the skewness of the wind speed probability distribution curve.

3.3 The seasonal characteristics of wind speed probability distributions

The wind speed probability distribution shows different characteristics for different stations due to differences in offshore distance (Fig. 4), and this phenomenon is embodied in the fact that the farther the offshore distance, the less the corresponding actual distribution conforms to a Weibull distribution. Compared to stations located closer to shore, stations farther away from shore show significantly increased average wind speeds in the winter while the standard deviation of wind speeds is also large in the summer, indicating that the seasonal distribution of wind speed, which is mostly influenced by the strong seasonal variations of large-scale wind pattern,i.e., the northeast wind in winter and southwest monsoon wind. The non-Weibull distribution of wind speed with larger offshore distance is in stark contrast with close shore wind speed, and the difference is probabily due to the higher occurrence of high wind speed in the open ocean that statistically changes the shape of wind speed histogram to the higher end.

Fig. 6. Station wind speed probability distributions for different months (a solid line indicates the observed distribution and a dotted line indicates the fitted Weibull distribution) as well as mean/std and skew scatter distributions (dots indicate the observed data and crosses indicate values computed from the corresponding fitted Weibull function). Different color indicate different month as showed in (a) and (c).

Among the four types of stations, monthly wind speed distributions measured for Class-1 stations could be closely fitted with a Weibull distribution (Fig. 6a) while a more significant difference was noted between March wind speed distributions measured for Class-2 stations and corresponding fitted Weibull distributions (Fig. 6b);autumn and winter wind speed frequencies measured for Class-3 stations were relatively consistent with a fitted Weibull distribution (Fig. 6c), while only autumn wind speed distributions were consistent with a fitted Weibull distribution in the case of Class-4 stations (Fig. 6d). It is not difficult to see that, with the exception of Class-1 stations, in the spring (March) all stations showed wind velocity distributions that did not conform to the Weibull distribution. As distance from shore increases, the summer wind speed frequency distributions of all stations increasingly deviated from the Weibull distribution in terms of their characteristics and deviation was particularly significant for Class-3 and Class-4 stations relatively far from shore. In the winter, only the wind speed frequency distributions of Class-4 stations were inconsistent with the Weibull distribution. The above observations show that Class-1 stations conform to a Weibull distribution throughout the year, Class-2 stations generally conform to a Weibull distribution throughout the year except spring, Class-3 stations conform to a Weibull distribution only in the autumn and winter, and Class-4 stations are consistent with a Weibull distribution only in the autumn.

The characteristics of Weibull distributions fitted for each of the four station types examined were different for different seasons. In the winter, central wind speeds measured for all stations tended to shift to the higher end of the observed range and although the wind speed range of the distributions was narrow, central wind speeds were significantly biased toward the high end relative to the other seasons and they manifested at a higher frequency,indicating that the winter is characterized by sustained large winds. For the other seasons, central wind speeds indicated by the corresponding Weibull distribution were relatively low, within 5–10-m s–1winds in the greatest frequency. Furthermore, the farther a given stations was from the shore, the greater the wind speed range observed, and an increase in speeds also corresponded to a gradual increase in corresponding central wind speed.

Figure 6 also shows the correlation between the ratio of mean wind speed value to wind speed standard deviation (mean/std; abbreviated as “the ratio”) and the skewness of the Weibull distribution (skewness; Eqs. (6) and(3) are used to calculate observation results and the skewness of the corresponding fitted Weibull distribution, respectively). In general, when the ratio is relatively small ( ＜ 3), skewnesss calculated by both methods will be positive and as the ratio increases the skewness gradually turns negative. The standard deviation of wind speeds observed across all stations in September was relatively large (Fig. 2b); thus, compared to other months,the ratio was relatively small and this manifested as a relative concentration of the ratio and skewness distributions around the positive skewness region, and distributions also show similar characteristics for Class-1 stations during the other seasons, but no similarity was observed for the other three types of stations. The farther the offshore distance, the greater the tendency of both the ratio and skewness distributions to show primarily negative values for skewness, and this property can be most easily observed in the winter (December).

When the ratio is smaller ( ＜ 3), the observed skewness is smaller than the skewness of the corresponding Weibull distribution, and the greater the offshore distance, the more likely the observed skewness will have a negative value, with a more highly discrete observed skewness, and in this scenario, a greater discrepancy between the observed wind speed frequency distribution and fitted Weibull distribution is observed. As offshore distance increases, the observed skewness in virtually all cases will become larger than the skewness of the corresponding Weibull distribution. However, the observed skewness including a relatively high number of instances where it is smaller than the skewness of the corresponding Weibull distribution implies that the observed wind speed frequency distribution is characterized by a greater degree of fluctuation and will differ significantly from a fitted Weibull distribution.

4. Conclusions

In order to understand the characteristics of the frequency distributions of sea surface wind speeds in the northern South China Sea, we employed four sites of different distances from the shore and analyzed information such as the frequency distribution characteristics of wind speeds and corresponding Weibull distribution characteristic physical quantities to reach the following conclusions:

(1) Affected by the South China Sea summer and winter monsoons, obvious seasonal variations in mean wind speeds were observed at the four-class stations,with average wind speeds reaching to a maximum in winter (November–January) and a minimum in summer(around July). Locations farther offshore produced greater mean wind speeds, longer durations, the greater standard deviation in wind speed observed, and the more significant magnitude of the fluctuations observed.

(2) The prevailing wind directions at the nearshore stations were mainly from the east. With the increase of the offshore distance, the winds were less affected by the land, and the prevailing wind directions gradually turned into N winds, predominately those at ＞ 10 m s–1. At this time, the mean wind speeds became higher with increased duration and greater standard deviation of wind speed, indicating that pulsation of the wind speeds increased obviously under situation of strong N winds.

(3) For stations located more than 100 km offshore, as the frequency of strong winds increased significantly, the fluctuation of the wind speeds increased, resulting in the increase in the standard deviation of wind speed, and great fluctuation in variations of scale parameters. At this time, the skewness became negative. When a more discrete distribution characterizes the observed skewness data and the Weibull distribution curve, the wind speed probability distribution cannot be accurately represented by the Weibull distribution.