# Generic Methodology for Field Calibration of Nacelle-Based Wind Lidars
## 1 Introduction
### The Need for Calibration Procedures  
Lidars are measuring instruments. As such, their measurements are uncertain and, formally, can only be traced back to international standards via a calibration. In essence, the main role of a calibration is to transfer the traceability of reference instruments and their uncertainties. Developing commercial applications of lidars demands uncertainty quantification, particularly power performance testing. Indeed, the power curve is the primary characteristic of a wind turbine guaranteeing its production. The fundamental reasons for developing calibration procedures is to ensure the measurements are valid and quantify their accuracy--i.e., trueness and precision--by assigning uncertainties to the measurand. Doppler wind lidars (DWL) do not measure wind characteristics [6,7] directly. They probe the wind by emitting light through a laser beam and at a known wavelength \(\lambda\). Atmospheric particles following the wind's motion scatter a fraction of the emitted light back to the lidar, at a frequency Doppler-shifted by \(\delta\
u\). Scatterers contained in the lidar probe volume yield a histogram of \(\delta\
u\) values. The power spectrum is estimated via spectral analysis--i.e., Fourier transforms--of the electrical signal generated by the photodetector. An algorithm, for instance peak, centroid or maximum likelihood, is applied to characterise the Doppler power spectrum and retrieve a single \(\delta\
u\) value. \(\delta\
u\) is then converted into a Line-Of-Sight (LOS) velocity \(V_{LOS}\), also called radial wind speed (RWS):  
\[V_{LOS}=\frac{\delta\
u\cdot\lambda}{2} \tag{1}\]  
Wind characteristics are finally estimated by combining multiple \(V_{LOS}\) measurements according to an assumed flow model--e.g., horizontally homogeneous for ground-based lidars using Vertical Azimuth Display, see [8,9]. Depending on the employed flow model, profiling nacelle lidars can reconstruct wind speed (WS) and direction (WD), vertical shear, veer, etc. From first principles (Equation (1)), the LOS velocity is sometimes assumed to be an 'absolute' measurement, in the sense it is derived from well-known physics theory and thus has a negligible uncertainty. Figure 1: Two wind profiling nacelle lidar examples: 5-beam Avent Demonstrator (**left**) and Zephir Dual-Mode (**right**). Most modern Doppler wind lidars operate at a wavelength in the infra-red (IR) region, of \(\approx\)1560 nm. The laser wavelength is certified to be within \(\pm\)1 nm corresponding to a \(V_{LOS}\) uncertainty <0.01 m\(\cdot\)s\({}^{-1}\). Yet, spectral broadening due to probe volume effects (aerosol gradients, presence of inhomogeneous wind structures, etc.) [7] and the chosen Doppler frequency shift estimation method create imperfections in lidar \(V_{LOS}\) measurements: the shape of Doppler spectra in atmospheric conditions is far from ideal Gaussian or Dirac distributions that are obtained under controlled conditions in a laboratory with a hard target (e.g., moving belt, rotating wheel) or in a wind tunnel. These two arguments contradict the assumption of lidar \(V_{LOS}\) being measured 'absolutely'. Unless all the uncertainties of components (optical, mechanical, software) upstream of the \(V_{LOS}\) estimation are thoroughly assessed by certified bodies, the only way to quantify the accuracy of \(V_{LOS}\) is to compare it to a calibrated reference. In practice, due to the length of the lidar probe, this is only possible through field measurements using for instance calibrated cup anemometers. Then, at the reconstructed wind characteristics level, the flow model inadequacy introduces errors due to e.g., terrain effects, thermal stability, etc. Note that eliminating flow model assumptions and measuring a 3D wind vector is however possible using collocated synchronised \(V_{LOS}\) measurements (WindScanner [10] or multi-static systems). For all those reasons, field calibration procedures of lidars are required, at a minimum for power performance applications.