Practical Determination of the Zero-plane Displacement Height using Empirical Equations for Wind Profile

A Study on the zero-plane displacement height from measured wind profiles (II)

Abstract

The various and practical methods of determining the zero-plane displacement height, d, were examined by using wind profiles, which were measured in the constant flux layer under the conditions of neutral stability, and by using the friction velocities, u_*, measured by the eddy correlation method.In these methods, the two empirical equations of the power function of elevation, z, and the second-order polynominals in ln (z) were used to fit to measured wind profiles.The value of d was determined from the logarithmic wind profile law by using approximated wind velocities with the empirical equations.The results obtained are summarized as follows:
1) If wind velocities were measured with cup anemometers over a field, then the appropriate value of d could be determined at k=0.39 by using approximated wind velocities with the power function, where k is von Karman's constant. On the other hand, the appropriate value of d could be determined at k=0.35 by using approximated wind velocities with both empirical equations. These two values of d determined here did not agree to each other.
2) If wind velocities were measured with high accuracy, then the appropriate value of d could be determined by the methods applied in 1).The appropriate value of d could be also determined from the logarithmic law by using approximated wind velocities with the second-order polynominals in ln (z), or by using measured wind velocities.These four values of d determined here fairly closely agreed to one another.
3) When the previously proposed flux-profile relationships for wind and others with k=0.4 or 0.35 are extended to a flow over a tall canopy, the value of d can be determined by the respective methods with k=0.39 or 0.35 as shown above.