Comparing mixing-length models of the diabatic wind profile over homogeneous terrain

Abstract

Models of the diabatic wind profile over homogeneous terrain for the entire atmospheric boundary layer are developed using mixing-length theory and are compared to wind speed observations up to 300 m at the National Test Station for Wind Turbines at Høvsøre, Denmark. The measurements are performed within a wide range of atmospheric stability conditions, which allows a comparison of the models with the average wind profile computed in seven stability classes, showing a better agreement than compared to the traditional surface-layer wind profile. The wind profile is measured by combining cup anemometer and lidar observations, showing good agreement at the overlapping heights. The height of the boundary layer, a parameter required for the wind profile models, is estimated under neutral and stable conditions using surface-layer turbulence measurements, and under unstable conditions based on the aerosol backscatter profile from ceilometer observations.

Appendix A: Boundary-layer height from aerosol backscatter

The ceilometer measures the volume backscatter coefficient, β, which is fitted to an idealized backscatter profile using the technique in Steyn et al. (1999). The idealized profile has the form:

$$ \beta=\frac{B_u+B_a}{2}-\frac{B_u-B_a}{2}\textrm{erf}\left(\frac{z-z_i}{s}\right), $$

(15)

where B _a is the mean backscatter coefficient above the entrainment layer, B _u is the mean backscatter coefficient in the stable, neutral, or unstable layer, and s is related to the depth of the entrainment layer. For each stability class in Table 1, the 10-min backscatter profiles are averaged and a least-squares fit is performed on the average profile using Eq. 15. Profiles that showed an enhanced aerosol backscatter for heights below 1,000 m were removed from the analysis, due to the presence of low clouds. The results of the fitting procedure are illustrated in Fig. 6.

Fig. 6

Ceilometer observations of the volume backscatter coefficient, β, for different stability conditions. The 10-min observations are shown in gray color and the mean of the observation in black circles. The fit with Eq. 15 is shown in black solid lines, the estimated z _i with Eq. 15 in dashed lines, and the entrainment zone depth between the dotted lines. For the neutral case, the estimation of z _i from Eq. 14 is shown in a dash-dotted line