Verification of the local similaritytheory above forests

Abstract: In this study, the local similarity theory functions were calculated with two different approaches and on the other hand the mean hub height wind speed was compared with the rotor equivalent wind speed. Both calculations are based on two independent data-sets from measurement campaigns Hornamossen and Ryningsnäs which were conducted in the south of Sweden between May 2015 and June 2017, and November 2010 and February 2012. The first campaign includes measurements between 100 and 173 m and the second 98 and 138 m. In general, the aims were to validate if the results with reference functions and to compare the results from both approaches. The local similarity theory was used, because well above the ground, the assumption of a constant flux layer typically does not hold especially in the stable boundary layer. The used approaches are the flux-gradient and Richardson number formulation. Based on those, the non-dimensional universal functions for momentum and heat could be calculated and those could be presented as functions of the stability parameter. As shown in this study, the scatter the Richardson number formulation results are significant smaller compared to the flux-gradient formulation. One reason can be that the stability parameter and the universal functions for momentum and heat depend solely on the Richardson number. Despite the higher scatter, the medians of the universal function for momentum based on the flux-gradient formulations for both data-sets agree also with the references. Furthermore, for the results of the universal function for heat based on the flux-gradient formulation agree with the references if the minimum limit for the kinetic heat flux is significantly higher than for the universal function for momentum. Furthermore, in the publication from England & McNider 1995, who derived the Richardson number formulation, includes two erroneous equations for stable stratification. One of them has a tipping error and the other was incorrectly derived. Thus, the corrected equations are presented in this work. This work also presents new equations which are not based on the assumption that the constants of the empirical formulation for the universal function for momentum and heat with the same value. A comparison of the old and new equations show for a generated Richardson number vales a agreement of the results over the defined Richardson number range. Finally, in the wind industry it is a common practice to use the mean wind speed at the hub height as the representative mean wind speed over the entire rotor swept area. However, this assumption differs increasingly from the reality, because turbine sizes increase constantly. Thus, in this study, this common method is compared with another averaging concept. Hence, the work focuses on a area-weighted mean wind speed which is called the rotor equivalent wind speed. This average gives a better estimation of the existing wind field because it is based on multiple measurements at various heights. Since the wind gradient changes with height, those two velocities are plotted as functions of the same stability parameter as above. The main results in unstable stratification are that the hub height wind speed underestimates the rotor equivalent wind speed by about 1 to 1.5 %. In stable stratification the results vary: Two calculations show a overestimates by about 1 % and another shows no difference between those averages. Hence, the conclusion based on those findings are that the hub height wind speed is a source for a higher modelling uncertainty. On the contrary, the rotor equivalent wind speed gives more accurate modelling results.