Cross-Spectra Over the Sea from Observations and Mesoscale Modelling

Cospectra and quadrature spectra are calculated for six pairs of tall offshore measurement masts near the Horns Rev I wind farm in the Danish North Sea and the Nysted wind farm in the Baltic sea. The mast-pairs are separated from one another by horizontal distances of 2.13–12.4 km. Cospectra and quadrature spectra for the two sites are classified in terms of the angle between the mean wind direction and the line connecting each pair of masts. The frequency axes of the spectra are normalized to remove the effect of mean wind speed and separation distance. Results indicate a larger contribution to the quadrature spectrum for flow from the sea than for flow from the land, and the patterns in the spectra are clearer and better defined for Horns Rev I (which has a long uninterrupted sea-fetch from the west) than for Nysted (which is surrounded by a more complicated coastline). The analysis is replicated based on 3-month simulations using the weather research and forecasting (WRF) numerical model with a horizontal grid spacing of 2 km. For the sea-fetch directions, good agreement in spectral properties between the model and observations is found. Analytical expressions based on the properties of the cross-correlation function and an exponentially decaying coherence function are fitted to the normalized cospectra and quadrature spectra. The expressions are shown to be a good fit to the spectra calculated from the WRF simulations and to the observed spectra for directions with a long sea-fetch, which suggests that to a good approximation, the average cospectra and quadrature spectra over the sea can be written as functions of frequency, mean wind speed, separation distance and the angle between the wind direction and the orientation of the masts.