U. S. Department of Housing and Urban Development

Power Law Wind Profile

The measured power law exponent, 1/, is shown in Figures 6 through 11 for all of the wind events combined. Separate plots are provided for estimates of the power law exponent based on the peak gust and the 1-minute, 10-minute, and hourly mean wind speeds. The plots are based on measurements between the 187-ft (57 m) tower anemometer and the mean of the 5 near ground stations, as well as the 33-ft (10-m) tower anemometer.

As seen Figures 6 through 11 the estimated power law exponent (1/d) varied according to wind speed. However, this trend is most evident for the 1-minute and 10-minute mean wind speeds where the  decreased in value (power law exponent increased) as wind speed increased. At the lower wind speeds (e.g. less than 20 mph), this effect is mostly attributed to thermal effects; however, at higher wind speeds the decrease may be a result of some dependence of surface friction on wind velocity (as noted in the literature survey). As wind speeds increase further, the rate of change of the exponent decreases to a more constant rate where it is governed primarily by increased surface friction as a result of the kinematic viscosity of the faster moving, well mixed (i.e. neutral stability) air. More data at higher wind speeds will provide greater insights into the rate of change of  at higher (i.e. design level) wind conditions for 3-second gust wind speeds. The  scatter is more severe when determined from the 187’ to 33’ data. When  is plotted from 187’ to 10’ data the values are more clustered. As additional data is recorded and higher daily wind events encountered the relationship of  to wind speed for exposure B conditions will be more clearly defined. The COV of  was plotted as a function of wind speed (Figures 12 through 14). These figures reveal that the COV of  increases slightly with wind speed for the 3 second gust basis and decreases with increasing wind speed for the 1-minute and 10-minute mean wind speeds. These trends will be better defined when more data is collected over the course of a year.

Based on a commonly assumed gradient height of 1,200 ft (366 m) for suburban or wooded terrain [1] and calibrating to the 187-ft (57-m) tower anemometer readings, the power law wind velocity profile plots are shown for each of the 10-foot near ground anemometers in Figures 15 through 17. Also shown on the plots is the actual 33-ft (10-m) tower anemometer reading (peak gust, 1-minute, or 10-minute average as indicated). The theoretical profiles are shown for peak gusts and maximum 1-minute and 10-minute means for the reporting period. The calculated  coefficients used to derive the wind profiles for each station are found in the legend for each figure. The relatively high  value for near-ground station 4 is attributed to a topographic effect for the wind direction at the time of the peak gust record. It should be noted that these profiles are not intended to represent the actual wind profile but are provided for comparison sake in roughly evaluating the use of the power law representation of the wind profile for engineering purposes.