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Jakob Mann, Donald H. Lenschow, and Leif Kristensen

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David Schlipf, Po Wen Cheng, and Jakob Mann

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Investigations of lidar-assisted control to optimize the energy yield and to reduce loads of wind turbines have increased significantly in recent years. For this kind of control, it is crucial to know the correlation between the rotor effective wind speed and the wind preview provided by a nacelle- or spinner-based lidar system. If on the one hand, the assumed correlation is overestimated, then the uncorrelated frequencies of the preview will cause unnecessary control action, inducing undesired loads. On the other hand, the benefits of the lidar-assisted controller will not be fully exhausted, if correlated frequencies are filtered out. To avoid these miscalculations, this work presents a method to model the correlation between lidar systems and wind turbines using Kaimal wind spectra. The derived model accounts for different measurement configurations and spatial averaging of the lidar system, different rotor sizes, and wind evolution. The method is compared to real measurement data with promising results. In addition, examples depict how this model can be used to design an optimal controller and how the configuration of a lidar system is optimized for a given turbine to improve the correlation.

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Jacob Berg, Jakob Mann, and Edward G. Patton

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This study demonstrates that a pulsed wind lidar is a reliable instrument for measuring angles between horizontal vectors of significance in the atmospheric boundary layer. Three different angles are considered: the wind turning, the angle between the stress vector and the mean wind direction, and the angle between the stress vector and the vertical gradient of the mean velocity vector. The latter is assumed to be zero by the often applied turbulent-viscosity hypothesis, so that the stress vector can be described through the vertical gradient of velocity. In the atmospheric surface layer, where the Coriolis force is negligible, this is supposedly a good approximation. High-resolution large-eddy simulation data show that this is indeed the case even beyond the surface layer. In contrast, through analysis of WindCube lidar measurements supported by sonic measurements, the study shows that it is only valid very close to the surface. The deviation may be significant even at 100 m. This behavior is attributed to mesoscale effects.

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Abhijit Chougule, Jakob Mann, Mark Kelly, and Gunner C. Larsen

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A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate ε, length scale of energy-containing eddies L, a turbulence anisotropy parameter , gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance . Model output includes velocity and temperature spectra and associated cospectra, including those of longitudinal and vertical temperature fluxes. The model also produces two-point statistics, such as coherences and phases of velocity components and temperature. The statistics of uniformly sheared and stratified turbulence from the model are compared with atmospheric observations taken from the Horizontal Array Turbulence Study (HATS) field program, and model results fit observed one-dimensional spectra quite well. For highly unstable stratification, however, the model has deficiencies at low wavenumbers that limit its prediction of longitudinal velocity component spectra at scales on the order of 0.6 km. The model predicts coherences well for horizontal separations but overestimates vertical coherence with increasing separation. Finally, it is shown that the RDT output can deviate from Monin–Obukhov similarity theory.

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Alfredo Peña, Sven-Erik Gryning, Jakob Mann, and Charlotte B. Hasager

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The wind speed profile for the neutral boundary layer is derived for a number of mixing-length parameterizations, which account for the height of the boundary layer. The wind speed profiles show good agreement with the reanalysis of the Leipzig wind profile (950 m high) and with combined cup–sonic anemometer and lidar measurements (300 m high) performed over flat and homogeneous terrain at Høvsøre, Denmark. In the surface layer, the mixing-length parameterizations agree well with the traditional surface-layer theory, but the wind speed profile is underestimated when the surface-layer scaling is extended to the entire boundary layer, demonstrating the importance of the boundary layer height as a scaling parameter. The turbulence measurements, performed up to 160-m height only at the Høvsøre site, provide the opportunity to derive the spectral-length scales from two spectral models. Good agreement is found between the behaviors of the mixing- and spectral-length scales.

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Xiaoli Guo Larsén, Søren Ott, Jake Badger, Andrea N. Hahmann, and Jakob Mann

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Extreme winds derived from simulations using mesoscale models are underestimated because of the effective spatial and temporal resolutions. This is reflected in the spectral domain as an energy deficit in the mesoscale range. The energy deficit implies smaller spectral moments and thus underestimation in the extreme winds. The authors have developed two approaches for correcting the smoothing effect resulting from the mesoscale model resolution that impacts the extreme wind estimation by taking into account the difference between the modeled and measured spectra in the high-frequency range. Both approaches give estimates of the smoothing effect that are in good agreement with measurements from several sites in Denmark and Germany.

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Shane D. Mayor, Donald H. Lenschow, Ronald L. Schwiesow, Jakob Mann, Charles L. Frush, and Melinda K. Simon

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The capability of the NCAR 10.6-μm-wavelength CO2 Doppler lidar to measure radial air motion is validated by examining hard-target test data, comparing measurements with those from a two-axis propeller anemometer and a 915-MHz profiling radar, and analyzing power spectra and autocovariance functions of the lidar radial velocities in a daytime convective boundary layer. Results demonstrate that the lidar is capable of measuring radial velocity to less than 0.5 m s−1 precision from 20 laser pulse averages under high signal-to-noise ratio conditions. Hard-target test data and comparisons with other sensors show that the lidar data can be biased by as much as ±2 m s−1 when operating in the coherent oscillator mode and that correlated errors are negligible. Correlation coefficients are as large as 0.96 for 90-min comparisons of horizontal velocities averaged for 1 min from the lidar and anemometer, and 0.87 for 2.5-h comparisons between vertical velocities averaged for 30 s from the lidar and profiler. Comparisons of the lidar and profiler vertical velocities are particularly encouraging for the profiler since these results show that 915-MHz profilers are capable of making good vertical velocity measurements in strong convective boundary layers. The authors conclude that despite the commonplace systematic bias in lidar radial velocity, ground-based operation of the NCAR CO2 Doppler lidar can provide valuable velocity data for meso- and microscale meteorological studies. The lidar can also provide filtered velocity statistics that may be useful for boundary layer turbulence research.

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