Determination of the roughness length and Von Karman constant using Meteorological Towers at the NWTC
The evaluation of roughness length by experimental data set is one of most important topics to determine given that this parameter is fundamental for vertical reconstruction of wind profiles. At National Wind Technology Center (NWTC) are collected different towers and we analyzed data of the M5 tower for all 2012 year. The National Renewable Energy Laboratory is located on the eastern side of the NWTC grounds. The NWTC is approximately 8 km south of Boulder, Colorado and 36 km north west of Denver at an elevation of approximately 1850 m above sea level. A long-term wind time series of turbulence variables (as the L, TKE, U*, etc) is available from the M5 tower at different heights (from 3 up to 134m). From data, we selected wind profiles having constant wind direction and u*. The work was concentrated on neutral conditions. These neutral profiles are extracted by one year data assuming:
2- To minimize the variations along Z of wind direction is lesser than 1% of the observed average
3- To minimize the variation along Z of U* is lesser than 15% of the observed average U*
The last criteria is very important because it assures the vertical homogeneity of U*,i.e. of mechanical turbulence constancy (during the selected neutral conditions). As known, the roughness length is linked to the scale parameter coming from Monin Obhukov Similarity Theory (MOST). Usually, Z0 is calculated by geometrical information and different formulations is usually used: the morphometric estimation methods [1,2] and the regression methods. In our work, we assume that the displacement height is zero and we applied only the regression methods. We evaluated also the Von Karman constant k applying the regression analysis for each neutral profile. As known, k is considered as a constant, but it depends by the Rosby number and can be associated in general with the local roughness . In the study, the selected profiles regard only strictly neutral profiles and an excellent approximations has been observed with the classical logarithmic law. The focal point of this work is that regression model involves, other than Z0, also the Von Karman constant as experimental parameter to be determined and the estimation of Von Karman derive directly as result of regression models to the wind neutral profiles.
Results and conclusions
We analyzed data using criteria 1)-2)-3) to select the values of Z0 and k. The total number of neutral profiles for each month are shown in table 1.
Table 1: number of neutral profiles selected for the analysis
We can note that maximum neutral conditions happen during winter seasons. Conversely, the minimum neutrals profiles are during the summer. The parameters Z0 and k derived classical neutral wind profiles by regression is really representative of the NTWC site; the wind profiles are reproduced with high correlation (R(0.94÷0.98)). The average Z0 and k, on all data, are 0.034±0.060m and 0.57±0.15 respectively. The Z0 shows skew distribution, with a marked modal value at 0.025m for all seasons. The main sector is along the W-NW direction (figure 1), with average values of 0.031±0.050m, while in NNW-W direction few other values are observed of 0.028±0.019m. The observed Z0 are in according with the assumption of displacement height equal to zero and the hypothesis of flat terrain is confirmed by the results of theoretical regression model.
Figure 1: Z0 wind sector distribution.
The k values are much higher respect to classic values of 0.4. In Figure 2 are shown the k as function of the observed Z0. As evident, it seems to exist a non linear relationship between k and Z0.
In figure 2, are shown also the classic value of 0.4 (red line). By the figure, the average k values can be connected with Z0 by following power law:
With a= -0.06 and b=0.2962. The correlation is high (R=0.81) for (1). The classic k value (k=0.4) can be valid only in that cases of high observed values Z0 (Z0»0.1m). In cases of low Z0 (Z0 » 1cm) the k assume an average values 0.58.
Figure 1: K vs Z0 as calculated at NREL site by regression. BIN analysis and observed parameters.
As wait, the NREL M5 field campaigns suggest that Z0 is not constant, being link to the seasons effect and wind direction. The other important results concerns the values of k, that increase with the decrease of Z0. These effect could be linked to the different rate between the mechanical turbulence and the vertical wind gradient, but, at the moment, further analysis could be necessary for explanation.
 Kastner-Klein, P., and M. W. Rotach, 2004: Mean flow and turbulence characteristics in an urban roughness sublayer. Boundary-Layer Meteor., 111, 55-84.
 MacDonald, R. W., R. S. Griffiths, and D. J. Hall, 1998: An Improved Method for the Estimation of Surface Roughness of Obstacle Arrays. Atmos. Environ., 32, 1857–1894.
 Högström U, 1996: Review of some basic characteristics of the atmospheric surface layer.
Boundary-Layer Meteor., 78, 3-4,215-246