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On the Dependence of Wind Variability on Surface Wind Speed, Richardson Number and Height Above Terrain

Maurice B. DanardMeteorological Service of Canada, Toronto, Ontario

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Abstract

Some results obtained from double-theodolite measurements of the wind variability near Shilo, Manitoba, are presented. Wind variability [σ(s,t)] is defined here as the standard vector deviation of the difference between two winds at the same height measured at different points in space (s) and/or time (t). The investigation is restricted to winds below 10,000 ft above terrain and to intervals of distance and time of 0 to 30 mi and 0 to 3 hr, respectively. Observational error is assessed by direct measurement. Increase of error with height and wind speed is noted.

Theoretical justification is advanced for expecting the spatial variability to obey the formula &sigma2 (s,0) = a+bs2+cs4. By defining s = t |V̄| where V̄ the mean wind, temporal as well as spatial variabilities an used to determine the regression coefficients of the best-fitting 4th order polynomial given above. The regression coefficients are then classified according to surface wind speed, Richardson number and height. Results suggest that the polynomial may be appropriate in cases of small wind speeds and large Richardson numbers, but In other, conditions the time-scale of the motion is so small that the quadratic and quartic terms appear to be of minor importance.

Increase of wind variability with increasing surface wind speed and height above terrain is clearly demonstrated. This may, however, be due in larger part to observational error.

Abstract

Some results obtained from double-theodolite measurements of the wind variability near Shilo, Manitoba, are presented. Wind variability [σ(s,t)] is defined here as the standard vector deviation of the difference between two winds at the same height measured at different points in space (s) and/or time (t). The investigation is restricted to winds below 10,000 ft above terrain and to intervals of distance and time of 0 to 30 mi and 0 to 3 hr, respectively. Observational error is assessed by direct measurement. Increase of error with height and wind speed is noted.

Theoretical justification is advanced for expecting the spatial variability to obey the formula &sigma2 (s,0) = a+bs2+cs4. By defining s = t |V̄| where V̄ the mean wind, temporal as well as spatial variabilities an used to determine the regression coefficients of the best-fitting 4th order polynomial given above. The regression coefficients are then classified according to surface wind speed, Richardson number and height. Results suggest that the polynomial may be appropriate in cases of small wind speeds and large Richardson numbers, but In other, conditions the time-scale of the motion is so small that the quadratic and quartic terms appear to be of minor importance.

Increase of wind variability with increasing surface wind speed and height above terrain is clearly demonstrated. This may, however, be due in larger part to observational error.

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