Wind Statistics from a Forested Landscape

Abstract

An analysis and interpretation of measurements from a 138-m tall tower located in a forested landscape is presented. Measurement errors and statistical uncertainties are carefully evaluated to ensure high data quality. A 40$^\circ$ wide wind-direction sector is selected as the most representative for large-scale forest conditions, and from that sector first-, second- and third-order statistics, as well as analyses regarding the characteristic length scale, the flux-profile relationship and surface roughness are presented for a wide range of stability conditions. The results are discussed with focus on the validity of different scaling regimes. Significant wind veer, decay of momentum fluxes and reduction in shear length scales with height are observed for all stability classes, indicating the influence of the limited depth of the boundary layer on the measured profiles. Roughness sublayer characteristics are however not detected in the presented analysis. Dimensionless gradients are shown to follow theoretical curves up to 100 m in stable conditions despite surface-layer approximations being invalid. This is attributed to a balance of momentum decay and reduced shear length scale growth with height. The wind profile shows a strong stability dependence of the aerodynamic roughness length, with a 50 % decrease from neutral to stable conditions.

Appendix 1

The widely used despiking algorithm by Højstrup (1993) is based on the idea that the instantaneous velocity fluctuation around the mean, normalized by the velocity standard deviation, should be less than a given threshold. However, this method is inadequate when spikes have small amplitude or when the turbulence intensity is particularly high, a situation likely to occur near the canopy top. Therefore a new despiking algorithm was developed. In the algorithm, spikes were identified as events where the absolute value of the difference between consecutive samples of the time series, $X\left( n\right)$

$$\begin{aligned} \delta _X\left( n\right) =\left[ X\left( n+1\right) -X\left( n\right) \right] \, , \end{aligned}$$

(9)

exceeded a threshold of $5\sigma _X$, where $\sigma _X$ is the standard deviation of $X\left( n\right)$. This approach is similar to the traditional ones, but it allows to discern between turbulent ramps, that can be associated to sudden gradients, and spikes. Furthermore, it was required that the spike event should be simultaneously present in at least two of the velocity signals $u, v$ or $w$, since it was observed to be the case for all data available. This observation indicates that the spike really occurs on one of the sonic paths, which in turn points to the possibility that one of the sonic transducers may be affected by ice/snow/dew. Once a spike was identified, its associated value was replaced by the average of the neighboring points, in order to avoid distortions of the power spectral density. This procedure was adopted in the analysis of all available time series from the sonic anemometers, including the temperature signals. To demonstrate the effect of the despiking algorithm and the data selection, the Theiss cup anemometer (sampled at 1 Hz) mean wind speed, $S$, and the mean wind speed in the mean wind direction, $U$, from the sonic anemometer, are compared in Fig. 10. The proportionality constant was 0.98 and the offset 0.17 m s$^{-1}$. The comparison is limited to the western sector where both set-ups were unaffected by tower and turbine wakes.

Fig. 10

Comparison between sonic and cup anemometry performed at all vertical levels and stability conditions without the stationarity requirement within the western sector. The gray dots show all data, while the black dots are the quality approved data in the western sector and the dashed line is the one-to-one line