Retrieving wind statistics from average  spectrum of continuous-wave lidar

Branlard, Emmanuel; Pedersen, Anders Tegtmeier; Mann, Jakob; Angelou, Nikolas; Fischer, Andreas; Mikkelsen, Torben; Harris, Michael; Slinger, Chris; Montes, Belen Fernández

doi:10.5194/amt-6-1673-2013

Cited by 43 publications

(49 citation statements)

References 21 publications

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“…Accordingly, uncertainties in lidar-derived mean wind velocity estimates have been well characterized Lindelöw-Marsden, 2009) and methods and procedures have been developed for error reduction and uncertainty control (Clifton et al, 2013;Gottschall et al, 2012). However, use of lidar for turbulence measurements, while possible (Newman et al, 2016;Branlard et al, 2013;Mann et al, 2010), is less established (Sathe et al, 2015;Sathe and Mann, 2013). Two methods are commonly used to derive the second-order moments (i.e., velocity variances and momentum fluxes) of turbulent flow from lidar data (Sathe and Mann, 2013).…”

Section: Motivation and Approachmentioning

confidence: 99%

Errors in radial velocity variance from Doppler wind lidar

et al. 2016

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Abstract. A high-fidelity lidar turbulence measurement technique relies on accurate estimates of radial velocity variance that are subject to both systematic and random errors determined by the autocorrelation function of radial velocity, the sampling rate, and the sampling duration. Using both statistically simulated and observed data, this paper quantifies the effect of the volumetric averaging in lidar radial velocity measurements on the autocorrelation function and the dependence of the systematic and random errors on the sampling duration. For current-generation scanning lidars and sampling durations of about 30 min and longer, during which the stationarity assumption is valid for atmospheric flows, the systematic error is negligible but the random error exceeds about 10 %.

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Section: Motivation and Approachmentioning

confidence: 99%

Errors in radial velocity variance from Doppler wind lidar

et al. 2016

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“…5.1), we extract the normalized Doppler radial velocity spectrum for each of the samples within that 10-min and bin position. We then sum all the normalized Doppler spectra within the 10-min period and the resulting Doppler 5 spectrum is normalized to unit area before we estimate the variance in two ways: by computing the second moment from the spectrum and by fitting a normal distribution to the spectrum to extract its variance Branlard et al, 2013). computing the second moment from the spectrum and by fitting a normal distribution to the spectrum to extract its variance Branlard et al, 2013).…”

Section: Ensemble-average Doppler Radial Velocity Spectrummentioning

confidence: 99%

“…Following the steps in Mann et al (2010) or Branlard et al (2013), the ensembleaverage Doppler spectrum of the radial velocity S (v r ) can be assumed to be equal to the probability density function of v r , i.e., S (v r ) = p(v r ). This is because the average of v r along the beam does not change highly with radial distance, as FL nacelle lidars use a small cone angle and so the velocity gradient along the probe volume is negligible.…”

Section: Unfiltered Lidar Radial Velocity Variancementioning

confidence: 99%

“…We then sum all the normalized Doppler spectra within the 10-min period and the resulting Doppler 5 spectrum is normalized to unit area before we estimate the variance in two ways: by computing the second moment from the spectrum and by fitting a normal distribution to the spectrum to extract its variance Branlard et al, 2013). computing the second moment from the spectrum and by fitting a normal distribution to the spectrum to extract its variance Branlard et al, 2013). Figure 12 illustrates examples of ensemble-average Doppler spectra for different 10 min periods for the positions of bins 0 and 31, where we intentionally show 10 min radial velocity distributions with high and low mean values, and high and low variances, including double-peak distributions (there are only a few of them).…”

Section: Ensemble-average Doppler Radial Velocity Spectrummentioning

confidence: 99%

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Turbulence characterization from a forward-looking nacelle lidar

2017

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Abstract. We present two methods to characterize turbulence in the turbine inflow using radial velocity measurements from nacelle-mounted lidars. The first uses a model of the three-dimensional spectral velocity tensor combined with a model of the spatial radial velocity averaging of the lidars, and the second uses the ensembleaveraged Doppler radial velocity spectrum. With the former, filtered turbulence estimates can be predicted, whereas the latter model-free method allows us to estimate unfiltered turbulence measures. Two types of forwardlooking nacelle lidars are investigated: a pulsed system that uses a five-beam configuration and a continuouswave system that scans conically. For both types of lidars, we show how the radial velocity spectra of the lidar beams are influenced by turbulence characteristics, and how to extract the velocity-tensor parameters that are useful to predict the loads on a turbine. We also show how the velocity-component variances and co-variances can be estimated from the radial-velocity unfiltered variances of the lidar beams. We demonstrate the methods using measurements from an experiment conducted at the Nørrekaer Enge wind farm in northern Denmark, where both types of lidars were installed on the nacelle of a wind turbine. Comparison of the lidar-based along-wind unfiltered variances with those from a cup anemometer installed on a meteorological mast close to the turbine shows a bias of just 2 %. The ratios of the unfiltered and filtered radial velocity variances of the lidar beams to the cup-anemometer variances are well predicted by the spectral model. However, other lidar-derived estimates of velocity-component variances and co-variances do not agree with those from a sonic anemometer on the mast, which we mostly attribute to the small cone angle of the lidar. The velocity-tensor parameters derived from sonic-anemometer velocity spectra and those derived from lidar radial velocity spectra agree well under both near-neutral atmospheric stability and high wind-speed conditions, with differences increasing with decreasing wind speed and increasing stability. We also partly attribute these differences to the lidar beam configuration.

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“…The method of using average Doppler spectra (typically 10 or 30 minute averages) has also been studied to derive turbulence statistics (Branlard et al, 2013). However, using this approach only statistics can be derived, namely the wind speed PDF and its statistical moments.…”

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confidence: 99%

Comparison of Methods to Derive Radial Wind Speed from a Continuous-Wave Coherent Lidar Doppler Spectrum

Held¹,

Mann²

2018

Preprint

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Abstract. Continuous-wave lidar systems offer the possibility to remotely sense wind speed but are also affected by inherent differences in their measurement process compared to more traditional anemometry like cup or sonic anemometers. Their large measurement volume leads to an attenuation of turbulence. In this paper we study how different methods to derive the radial wind speed from a lidar Doppler spectrum can mitigate turbulence attenuation. The centroid, median and maximum methods are compared by estimating transfer functions and calculating root mean squared errors (RMSE) between a lidar and a sonic 5 anemometer. Numerical simulations and experimental results both indicate that the maximum method, even though using the least amount of information from the Doppler spectrum, performs best at mitigating the volume averaging effect. However, this benefit is paid by increased signal noise due to the discretisation of the maximum method. The median method shows slight improvements over the centroid method in terms of volume averaging reduction and also resulted in the overall lowest RMSE.Thus, when the aim is to obtain point-like wind speed time series with high temporal resolution, the median method is superior 10 to the centroid and maximum method. When comparing 10 minute averages there is no difference between the methods.

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Retrieving wind statistics from average spectrum of continuous-wave lidar

Cited by 43 publications

References 21 publications

Errors in radial velocity variance from Doppler wind lidar

Errors in radial velocity variance from Doppler wind lidar

Turbulence characterization from a forward-looking nacelle lidar

Comparison of Methods to Derive Radial Wind Speed from a Continuous-Wave Coherent Lidar Doppler Spectrum

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