Wind Profiler
For six weeks from January 1 to February 12, 2009 a Triton Sonic Wind Profiler (Second Wind, Inc.) was stationed at the GSO pier. During this time the instrument collected data on horizontal wind speed and direction, vertical wind speed, and surface temperature & pressure. The profiler makes estimates every couple of seconds and averages these over ten minute periods. When internal tests on data quality are satisfied, winds at 20 m intervals from 40 up to 200 m are reported. The profiler operates autonomously, and the data are transmitted via a satellite link and posted on a Web site (https://www.skyserve.net/skyserve/default.aspx). We used Matlab to plot and analyze the wind distributions. The first computation was the distribution of horizontal wind speed at varying heights in the atmosphere.
Horizontal wind speed in general increases with height due to the friction induced by the Earth’s surface. So too does the variability of the wind speed. Because the distribution of speeds is asymmetrical, particularly close to the surface, a simple Gaussian distribution does not depict the probability accurately. We use a Weibull distribution, with W(s) the probability that the wind will be close to speed s, with the distribution varying in height. Shown below are histograms (filled bars) and fitted Weibull distributions (blue curves) for winds at 40 and 160 meters above sea level. Two parameters control the Weibull distribution, λ and k. The probability that the wind speed is close to s in a Weibull distribution is
The fitted values of k and λ are shown on the graphs. When k = 1 the Weibull distribution is an exponentail, whereas when k = 3.4 the function is Gaussian in form. The Gaussian distribution is of the form
Again, s is the wind speed, and μ and σ are the mean and standard deviation of the distribution, respectively. Estimates of the variability of the wind are indicated on the plots. The green dots indicate the speed range from one standard deviation below to one standard deviation above the mean wind. Also shown are the ranges encompassing 10% to 90% of the wind values sampled.
The next figure shows the fitted Weibull distributions for winds at multiple levels, at an interval of 40 m. At the lower levels the distribution is strongly asymmetric, while at higher levels the distribution becomes more nearly Gaussian, with a wider range of speeds observed and a significantly greater mean wind.
With the parameters of the distribution in hand, one can easily calculate the probability (i.e. the fraction of the time) that the winds at a given level will fall in a given range, or exceed some specified wind speed. The speed range might be that range over which a particular turbine operates most efficiently, for example; a limiting value might be the speed above which a turbine should not operate. It is also straightforward to make a direct calculation of the potential power yield from particular turbine types, given the parameters of the distribution.
The typical increase of wind speed with height is a manifestation of wind shear. The observed wind shear is usually greater during the night and less or even negligible during the day. The primary reason for this difference is convective mixing. During the day the sun heats the surface causing the near-surface air to become warm and buoyant. This air rises and is replaced by the denser surrounding air. This exchange mixes the air and removes the stratification of the layers. By contrast, at night, there is no surface heating and thus no mixing. This absence of mixing allows the air to settle into stratified layers, resulting in a stronger vertical gradient of horizontal wind speed. The histograms on the figure that follows show the day versus night shear for the 90 meter level (i.e. the difference in the wind between 80 and 100 meters). The daytime histogram is centered near zero - an absence of shear. The night time histogram is shifted to the right, indicating a positive shear, winds increasing with height. (The legend on the figure indicates the number of wind estimates used at the two levels used in the calculation, and the corresponding fraction of the time when wind estimates were available at these levels.)
So far nothing has been said about the wind direction. In the following three figures the direction and speed distributions at 60, 120 and 180 m are shown as wind roses. That is, the frequency with which the wind blows from each azimuth is shown by the radial thickness of each slice, and the range of wind speeds for each segment is shown by the color of the filled area. It is clear that winds from the northwest are important at all of these levels. As noted above, stronger winds are observed at the higher altitudes. Also apparent is that strong winds blowing directly from the west occur with a significant relative frequency at 120 and 180 m. As indicated, these data are from a mid-winter period. It is to be expected that during the summer months winds from the NW would be less common, with winds from the SW more common. Also, as the height increases, there is a decreases in the fraction of the time over which the profiler yields wind data. Note, in particular, that the radial percentage scale increment is smaller at 180 m than at 60 and 120 m. We have not investigated what biases this data loss might introduce into our estimates of the directional distribution.
This analysis was conducted by Kevin A. Clark, a recent alumnus of URI, and supported by the Rhode Island Ocean SAMP. For additional information, contact John Merrill.
Updated - 07/29/2009