# Calibration of Mean Wind Profiles Using Wind Lidar Measurements
## 5 Conclusions  
In this paper, pseudo-experimental neutral mean wind profiles were used to investigate the capability of available Wind Lidars at identifying the model parameters of the logarithmic law. It was found that the technical limitation of the lowest possible measurement point at 30 m is a bottleneck for the accuracy of the results; this is particularly the case in open country or suburban exposures where both the roughness length and the zero-plane displacement are low. In fact, not only the scatter of the identified parameters is quite large, but even if a large number of profiles is available, the mean values of the identified parameters do not converge to the exact one; in other words, identification introduces a bias. To overcome this limitation, two strategies were investigated. The first is that of optimising the choice of the elevations of measure by concentrating a large number of them only slightly above 30 m; this choice is expected to bring a better definition of the derivatives of the mean profile at \(z=30\) m, therefore improving the accuracy of its extrapolation below 30 m. Unfortunately, this expedient proved unsuccessful. The second strategy is related to the possibility of adding a further measurement point below 30 m, using either a sonic or a cup anemometer; this of course brings extra costs. An additional point of measure definitely improves the reliability of the results but does not necessarily eliminate the bias; as a matter of fact, some bias on \(z_{0}\) remains even if the extra measurement point is located at a very low elevation. The results presented are part of a wider research on the quantification and modelling of the uncertainty on wind loads, some of which is associated with the uncertainty on the characteristics of the wind flow in the atmospheric boundary layer. It is concluded that, if properly designed, full scale measurements can be very helpful in reducing such accuracy but do not allow to eliminate it. As an alternative, a combination with other methods, e.g., morphometric methods, could be of help. Figure 10: Bias and Coefficient of Variation of \(\mu_{z0}\) and \(\mu_{zd}\) as a function of the sample size \(N\) of available measured profile: Case (d) (\(z_{0}=1.5\) m, \(z_{d}=20\) m). **Author Contributions:** Conceptualization, A.M.A., V.S., F.R. ([PERSON]) and F.R. ([PERSON]); methodology, A.M.A., V.S., F.R. ([PERSON]) and F.R. ([PERSON]); software, A.M.A., V.S., F.R. ([PERSON]) and F.R. ([PERSON]); validation, A.M.A., V.S., F.R. ([PERSON]) and F.R. ([PERSON]); writing--original draft preparation, A.M.A., V.S., F.R. ([PERSON]) and F.R. ([PERSON]); writing--review and editing, A.M.A., V.S., F.R. ([PERSON]). and F.R. ([PERSON]); supervision, A.M.A., V.S., F.R. ([PERSON]) and F.R. ([PERSON]). All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. List of abbreviations and symbols. \begin{tabular}{l l} ABL & Atmospheric boundary layer \\ ISL & Inertial sublayer \\ \(N\) & number of profile samples in a set \\ \(M\) & number of sets of pseudo-experimental profiles \\ \(\kappa\) & von [PERSON] constant \\ \(n\) & number of available elevations \\ \(u^{\star}\) & surface friction velocity \\ \(u(z)\) & wind speed profile \\ \(z\) & elevation \\ \(z_{d}\) & zero-plane displacement \\ \(z_{h}\) & mean height of roughness elements \\ \(z_{m\!f}\) & reference elevation \\ \(z_{0}\) & roughness length \\ \(z_{1,L\!i\!d\!ar}\) & elevation of the lowest measurement point of Lidar \\ CoV\({}_{zd}\)(N) & ensemble coefficient of variation of \(z_{d}\) \\ CoV\({}_{z0}\)(N) & ensemble coefficient of variation of \(z_{0}\) \\ \(\mu_{zd}\) (N) & ensemble average of \(z_{d}\) \\ \(\mu_{z0}\) (N) & ensemble average of \(z_{0}\) \\ \(\sigma_{zd}\) (N) & ensemble standard deviation of \(z_{d}\) \\ \(\sigma_{zd}\) (N) & ensemble standard deviation of \(z_{0}\) \\ \end{tabular}