# Calibration of Mean Wind Profiles Using Wind Lidar Measurements
## 2 Methodology  
As known, the logarithmic law can be assumed as a possible analytic model to describe the mean wind profile during thermally neutral conditions up to 200 m of elevation [20; 21; 22]. Matching the law of the wall with the velocity defect law in the inertial sublayer (ISL) [4], and considering the vertical displacement due to the surface obstacles, such as buildings or vegetations, the wind speed profile is given by:  
\[u(z)=\frac{u^{*}}{\kappa}\ln\left(\frac{z-z_{d}}{z_{0}}\right) \tag{1}\]  
where \(u^{*}\) is the surface friction velocity; \(\kappa=0.4\) is the von Karman constant [23]; \(z_{0}\) is the surface roughness length; and \(z_{d}\) is the zero plane displacement. The logarithmic law can be also described by the following equation:  
\[u(z)=u_{ref}\ln[(z-z_{d})/z_{0}]/\ln\left[\left(z_{ref}-z_{d}\right)/z_{0}\right] \tag{2}\]where \(u_{ref}\) is the wind speed at the reference elevation \(z_{ref}\), assumed as the elevation of the lowest measurement point; the wind speed takes the value \(u=0\) at the elevation \(z_{d}+z_{0}\) above the ground. In the urban environment, it is important to incorporate the displacement height \(z_{d}\) since this is equivalent to set a base for the logarithmic wind profile that considers the physical bulk of the urban canopy. It corresponds to shifting the ground level upwards where the mean momentum sink for the flow is located. Selection of heights at which to carry out wind measurements in urban areas is a challenge. According to the WMO-_No.8_ Guide [24], in densely built-up areas, it can be assumed that the roughness sublayer, in which the effects of individual roughness elements persist, extends to a height of about 1.5 times the mean height of the roughness elements, \(z_{h}\). Moreover, it is well known from wind tunnel tests and field observations that flow over isolated solid obstacles, e.g., tall buildings, is highly perturbed both immediately over and around it. Consequently, in these cases, it was proposed to place the anemometers at a height larger than the maximum horizontal dimension of the major canopy [25]. This involves, at first, the use of an expensive mast system, which is often not simple to install. As an alternative, the use of Wind Lidars allows acquisition of wind velocities at different heights in a range of a few hundred meters above the ground. These anemometers are based on the principle of an optical Doppler shift between the reference laser beam and the radiation backscattered by aerosols. Due to the high aerosol concentration in urban environments, Lidar measurements can be considered suitable to assess wind profiles in urban areas. In this context, Lidar measurements present some advantages, including the large scan volume, mobility, wind measurements in 3-dimensions, as well as its relatively higher temporal and spatial resolution compared with other measurement devices. Since Lidar only measures radial velocities, some assumptions on the stationarity of the wind velocity field in time and space are required to derive three velocity components from Lidar data. As a consequence, some uncertainties of measurements especially over complex terrain can arise when the homogeneous assumption used in derived methods is violated. These inherent uncertainties are mainly influenced by errors in identifying sensing distance and elevation angle [26]. Moreover, environmental conditions, such as turbulence intensity and precipitation, introduce additional uncertainties in wind measurements [27]. Consequently, it is expected that future development of the Doppler Lidar technique and data processing algorithms will provide ever more accurate measurements with high spatial and temporal resolutions under different environmental conditions. Despite these uncertainties, Lidar measurements can be considered as a reliable alternative in the assessment of the mean wind profile in urban areas especially in neutral conditions.