Correlation and coherence of mesoscale wind speeds over the sea

Abstract

A large offshore observational dataset from stations across the North and Baltic Seas is used to investigate the planetary boundary-layer wind characteristics and their coherence, correlation and power spectra. The data from thirteen sites, with pairs of sites at horizontal distances of 4 to 848 km, are analyzed for typical wind turbine nacelle heights. Mean wind characteristics, correlation and coherence are also calculated for analogous wind data from simulations with the Weather Research and Forecasting (WRF) model.Results indicate a general good agreement for the coherence calculated based on measurements and the WRF-derived time series. By normalizing the frequency axes with the distance and mean wind speed, it can be demonstrated that, even for data with a wide range of distances, the coherence is a function of the frequency, mean wind and distance, which is consistent with earlier studies. However the correlation coefficient as a function of distance calculated from WRF is higher than observed in the measurements. For the power spectra, wind speed and wind speed step change distribution, the results for all sites are quite similar. The land masses strongly influence the individual wind direction distribution at each site. The ability of the WRF model to reproduce the coherence of the measurements demonstrates that its output can be used to estimate the coherence of fluctuations for the integration of offshore energy. The power spectra of WRF time series underestimates the high-frequency fluctuations. Due to the large number of measurement sites, the results can be used for further plausibility validation for mesoscale model runs over the sea.

Characterizing wind gusts in complex terrain

“…sensor (the lowest height included in this analysis) have the lowest coherence values (and highest decay rate). The vertical coherence functions from Perdigão towers decay to their minimum value at a reduced frequency of ∼ 0.3, which is similar to the value of 0.36 calculated for wind over water (Mehrens et al, 2016). Coherence functions derived using wind speeds from ZephIR lidar z423 show slightly larger C values that are derived from sonic anemometer data from the nearby Tower 25 and exhibit high C values between measurements at 60 m a.g.l.…”

“…The decay of coherence functions for vertical displacements is in the range found in flat terrain (Solari, 1987;Vigueras-Rodríguez et al, 2012). However, coherences for the large horizontal displacements (> 700 m) among towers do not fully conform to an exponential fit (as with those presented in Mehrens et al, 2016) and are characterized by smaller decay coefficients than have been found in research conducted in less complex terrain.…”

“…U mean is used herein to facilitate comparison of the coherence functions between sonic anemometers deployed on different towers and with previous research (Solari, 1987;Mehrens et al, 2016). Empirical estimates of a coherence function are influenced (and their accuracy limited) by the number of sub-series used in the cross-spectral density calculation.…”

“…Previous research has indicated large C values are most frequently observed in unstable conditions and that coherence decays quickly with reduced frequency (Kristensen and Jensen, 1979). For 10 min mean wind speeds over water an average value of C = 4.3 has been proposed for horizontal separations of < 5 km (Vigueras-Rodríguez et al, 2012), and the correlation between two measured time series displaced horizontally asymptotes to a constant value (i.e., the coherence floor) at a normalized frequency ≈ 0.36 (Mehrens et al, 2016). Due to the relatively low sampling rate of the ZephIR lidars (∼ 17 s), coherences of horizontal wind speeds from the ZephIR lidars are calculated over a 72 h period with a fast Fourier transform (FFT) window length of 256 (2 8 ), while the coherence functions calculated from the sonic anemometer observations are based on 2 h periods of 18 Hz longitudinal wind speed data, transformed into the frequency domain using an FFT window length of 16 384 (2 14 ).…”

Vertical Coherence of Turbulence in the Atmospheric Surface Layer: Connecting the Hypotheses of Townsend and Davenport

“…2013). We refer to these papers for details beyond the short overview provided coherence of various velocity components in tower micrometeorological data (Davenport, 1961a;Panofsky and Singer, 1965;Pielke and Panofsky, 1971;Naito and Kondo, 1974;Panofsky et al, 1974;Brook, 1975;Seginer and Mulhearn, 1978;Kanda and Royles, 1978;Soucy et al, 1982;Bowen et al, 1983;Saranyasoontorn et al, 2004), investigations including the lateral/spanwise coherence (Kristensen and Jensen, 1979;Ropelewski et al, 1973;Panofsky and Mizuno, 1975;Perry et al, 1978;Kristensen, 1979;Kristensen et al, 1981;Schlez and Infield, 1998), the coherence of temperature fluctuations (Davison, 1976) and even meso-scale applications (typically in the horizontal directions) (Hanna and Chang, 1992;Woods et al, 2011;Vincent et al, 2013;Larsén et al, 2013;Mehrens et al, 2016). Together, these measurements cover a great variety of terrain and topography.…”