# Calibration of Mean Wind Profiles Using Wind Lidar Measurements
## 1 Introduction  
An accurate representation of winds in the Atmospheric Boundary Layer (ABL) is of great interest to engineers, both to evaluate wind loading on structures and to assess expected wind energy production. In a neutral surface layer, the wind speed profile can be usefully defined according to different analytical models including Power Law, Logarithmic Law and the Deaves and Harris model [1; 2; 3; 4]. Both the Logarithmic Law and the Deaves and Harris model are based on the definition of a roughness length \(z_{0}\). Moreover, it is widely accepted that, in the urban environment, any analytical law for the mean wind speed profile has to include, as a starting point for the elevation coordinate, a zero-plane displacement \(z_{d}\), i.e., the level below which the flow is nearly blocked by the obstructing buildings. Although the values of these parameters are mainly related to surface morphology, their estimation remains difficult. This particularly occurs in urban areas where the marked variability in heights and density of roughness elements produces a complex surface morphology. In this context, few tall buildings often rise above mid-rise buildings or low-rise buildings, whilst in suburbs more homogeneous values of height and density of roughness elements are common. Generally, the methods used to assess the values of \(z_{0}\) and \(z_{d}\) can be classified in three types: (i) _reference-based_, (ii) _morphometric_ (or _geometric_) and (iii) _anemometric_ (or _micrometecological_). Methods of the first type are based on the comparison of a neighbourhood plan and site photography with figures or reference tables available in the literature, e.g., [5; 6; 7; 8]. Methods of the second type consist of relating aerodynamic parameters to measures of surface morphometry in terms of the plan area index, e.g., [9]. The last methods use field observations of wind or turbulence to solve for aerodynamic parameters included in theoretical relationships, e.g., those derived from the logarithmic wind profile [10; 11]. Within the _anemometric_ methods, measurement of the wind velocity field at a given site is essential for defining and validating analytical and numerical models for wind actions on structures. In the last decades, observations of wind speed profiles through Doppler Lidar anemometry have become popular [12; 13; 14; 15; 16; 17; 18] despite the inaccuracies associated with non-synchronous measurement and space averaging. Lidars allow a relatively easy acquisition of wind velocities at different heights in a range of several hundred meters above the ground. On the other hand, it is difficult or impossible to measure through Lidars the wind speed close to the ground. Depending on the characteristics of this device, in fact, the wind velocity can be measured only at points whose distance from Lidar is larger than a given threshold, usually around 30 m. As a matter of fact, the variation of the mean wind speed is more pronounced near the ground; therefore, calibration of the parameters that characterize analytical models is deeply influenced by wind speed values at low elevations, and this may be particularly important in urban areas where the wind flow near the ground interacts with the built environment. Within this topic, this paper explores to which extent Wind Lidars can be used to calibrate mean wind profiles depending on the available measurements; it is a part of a wider research on the effectiveness of the Lidar methodology for the experimental characterization of wind fields [19]. Numerical analyses are developed to investigate how the identification of the roughness length \(z_{0}\) and zero-plane displacement \(z_{d}\) is affected by the extension in time and space of the available measurements.