Modelling the spectral shape of continuous-wave lidar measurements in a turbulent wind tunnel

Abstract

Abstract. This paper describes the development of a theoretical model for the turbulence spectrum measured by a short-range, continuous-wave lidar (light detection and ranging). The lidar performance was assessed by measurements conducted with two WindScanners in an open-jet wind tunnel equipped with an active grid, for a range of different turbulent wind conditions. A hot-wire anemometer is used as reference to assess the lidar's measured statistics, time series and spectra. In addition to evaluating the statistics, the correlation between the time series and the root-mean-square error (RMSE) on the wind speed, the turbulence spectrum measured by the lidar is compared with a modelled spectrum. The theoretical spectral model is applied in the frequency domain, using a Lorentzian filter in combination with Taylor's frozen turbulence hypothesis for the probe length averaging effect and an added white noise term, evaluated by qualitatively matching the lidar measurement spectrum. High goodness-of-fit coefficients and low RMSE values between the hot wire and WindScanner were observed for the measured time series. The correlation showed an inverse relationship with the prevalent turbulence intensity in the flow for cases with a comparable power spectrum shape. Larger flow structures can be captured more accurately by the lidar, whereas small-scale turbulent flow structures are partly filtered out as a result of the lidar's probe volume averaging effect. It is demonstrated that an accurate way to define the cut-off frequency at which the lidar's power spectrum starts to deviate from the hot-wire reference spectrum is the frequency at which the coherence drops below 0.5. This coherence-based cut-off frequency increases linearly with the mean wind speed and is generally an order of magnitude lower than the probe length equivalent cut-off frequency, estimated according to a simple model based on the full width at half maximum (FWHM) of the laser beam intensity along the line of sight and assuming Taylor's frozen turbulence hypothesis. A convincing match between the modelled and the measured WindScanner power spectrum was found for various different cases, which confirmed that the deviation of the lidar's measured power spectrum in the higher frequency range can be analytically explained and modelled as a combination of a Lorentzian-shaped intensity function and white noise in the lidar measurement. Although the models were developed on the basis of wind tunnel measurements, they should be applicable to atmospheric boundary layer field measurements as well.

High-Fidelity Processing of Instantaneous Line-of-Sight Returns from Nacelle-Mounted Lidar including Supervised Machine Learning

“…Courtney et al (2008) reported instantaneous errors between co-located lidar probe volumes and cup anemometers to have standard deviation of 0.2 m/s and mean bias between -0.2 to 0.2 m/s, though they noted that the actual values depend on the distribution of wind speeds. A wind tunnel experiment by Van Dooren et al (2021) showed instantaneous velocity from a co-located lidar probe volume and hotwire anemometer with coefficients of determination much smaller than the 10-minute-averaged results above (i.e., 0.65 < 𝑅 2 < 0.95). As Pedersen and Courtney (2021), for instance, have shown that the standard error in line-of-sight velocity measured versus a hard target for a CW lidar is on the order of 0.1%, the main source of errors observed by Courtney et al 2021) is understood to be flow inhomogeneity and amplitude noise (neither of these cases included solid interference effects).…”

The lidar probe volume averaging effect: A wind tunnel investigation in streamwise turbulence with continuous-wave lidar

“…1b), was used in staring mode with a sampling rate of 451.7 Hz. It has been previously used in the wind tunnel to model spectral shape of the lidar [11], to measure 2D velocity fields [3] and turbine wake deflection [10]. The measurement range of the WindScanner is between 20 m and 300 m [11].…”

“…It has been previously used in the wind tunnel to model spectral shape of the lidar [11], to measure 2D velocity fields [3] and turbine wake deflection [10]. The measurement range of the WindScanner is between 20 m and 300 m [11]. The probe volume of the WindScanner (l p ) is defined as the full width at half maximum of the Lorentzian intensity profile centered about its focus point and estimated using Equation 1.…”

Superstatistical wind fields from point-wise atmospheric turbulence measurements

“…Latter issue, however, can be addressed by tensor decompositions such as matrix product states. Further potential future applications include the small-scale enhancement of LIDAR measurements, where small-scale turbulent fluctuations are averaged over probe volumes [9,28], as well as the study of particle transport in the here-proposed synthetic fields. As far as basic turbulence research is concerned, the proposed joint multipoint statistics could also be applied to the hierarchical problem in a statistical description of the Navier-Stokes equation [55].…”

“…Second, we propose a method that constrains such random fields on sparse, point-wise atmospheric turbulence measurements; in our case propeller anemometers in a meteorological mast array. Our approach thus addresses the problem of incomplete measurements which arises for instance in laserbased Doppler anemometer measurements [27,28] or due to large surface areas covered by aerial measurements of the wakes of large wind park clusters [29]. It has to be stressed that although the present work discusses the reconstruction of a wind field in front of a wind turbine, our methodology is applicable to a broad range of problems in atmospherics physics and beyond.…”