logarithmic wind profile fitting

Wind speed data measured at several height levels can be fitted to logarithmic wind speed profiles in accordance with the atmospheric boundary layer theory.

The fitting of the wind data can be calculated for the 2-parameter model (friction
velocity u_{*}, roughness length z_{0}) and for the
3-parameter model (friction velocity u_{*}, roughness length z_{0},
displacement height D).

Besides the classical method using least squares fit, the logarithmic wind speed profile can also be calculated by using an 1-dimensional flow model. The least squares fit is a pure mathematical fitting, whereas the 1-dimensional flow model will use all available relevant measured data in order to determine the actual physical processes within the air column.

WindDataSuite can determine the atmospheric stratification within the height range of the wind speed measurements. The resulting stratification indices give information not only about the type of stratification (positive: stable, 0: neutral, negative: unstabe), but also about its intensity. The analysis technique is based on an analysis of the shape of the vertical profile of the horizontal wind speeds and thus does not need any air temperature data.

Download short article on the determination of the atmospheric stratification (PDF)

In the following example, the height profiles of the measured
wind speeds (black curves) have been fitted to the logarithmic
wind speed profile (3-parameter model, red curves).
The results from the least squares fit are depicted in **Fig.1** and **Fig.2**,
the results from the 1-dimensional flow model in **Fig.3** and **Fig.4**,
at two consecutive time steps, respectively.

In **Fig.5** the resulting mean roughness lengths z0 and displacement heights D
in the distinct wind direction sectors are depicted (results from the 1-dimensional flow model)
and show the effects of the wind fetch and of the canopy in the surroundings.

The mean diurnal variation of the stratification index SI is depicted in **Fig.6**.
For comparison and for validation, the mean diurnal variation of the height-averaged
vertical wind velocity component, HAv-w, has been calculated.
As can be seen in **Fig.6**, HAv-w correlates quite well with SI.
A correlation calculation yields a maximal correlation coefficient of
r=0.89 at a phase shift of SI of +6 hours = +π/2 of the diurnal cycle.

Fig.1:

Logarithmic wind profile fit, 3-parameter model, least squares fit,
t = t_{1}

Fig.2:

Logarithmic wind profile fit, 3-parameter model, least squares fit,
t = t_{1} + Δt

Fig.3:

Logarithmic wind profile fit, 3-parameter model, 1D flow model,
t = t_{1}

Fig.4:

Logarithmic wind profile fit, 3-parameter model, 1D flow model,
t = t_{1} + Δt

Fig.5:

Mean roughness length z0 and displacement height D
in the distinct wind direction sectors.

Fig.6:

Mean diurnal variation of the stratification index SI and the height-averaged vertical wind velocity component HAv-w.

SI: + = stable, 0 = neutral, − = unstable.

SI: + = stable, 0 = neutral, − = unstable.