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.