Methods to Estimate Surface Roughness Length for Offshore Wind Energy

Abstract

The northeastern coast of the U.S. is projected to expand its offshore wind capacity from the existing 30 MW to over 22 GW in the next decade, yet, only a few wind measurements are available in the region and none at hub height (around 100 m today); thus, extrapolations are needed to estimate wind speed as a function of height. A common method is the log-law, which is based on surface roughness length (z0). No reliable estimates of z0 for the region have been presented in the literature. Here, we fill this knowledge gap using two field campaigns that were conducted in the Nantucket Sound at the Cape Wind (CW) platform: the 2003–2009 “CW Historical”, which collected wind measurements on a meteorological tower at three levels (20, 41, and 60 m AMSL) with sonic and cup/vane anemometers, and the 2013–2014 IMPOWR (Improving the Mapping and Prediction of Offshore Wind Resources), which collected high-frequency wind and flux measurements at 12 m AMSL. We tested three different methods to calculate z0: (1) analytical method, dependent on friction velocity u∗ and a stability function ψ; (2) the Charnock relationship between z0 and u∗; and (3) a statistical method based on wind speed observed at the three levels. The first two methods are physical, whereas the statistical method is purely mathematical. Comparing mean and median of z0, we find that the median is a more robust statistics because the mean varies by over four orders of magnitude across the three methods and the two campaigns. In general, the median z0 exhibits little seasonal variability and a weak dependency on atmospheric stability, which was predominantly unstable (54–67%). With the goal of providing the most accurate estimates of wind speed near the hub height of modern turbines, the statistical method, despite delivering unrealistic z0 values at times, gives the best estimates of 60 m winds, even when the 5 m wind speed from a nearby buoy is used as the reference. The unrealistic z0 values are caused by nonmonotonic wind speed profiles, occurring about 41% of the time, and should not be rejected because they produce realistic fits. Furthermore, the statistical method outperforms the other two even though it does not need any stability information. In summary, if wind speed data from multiple levels are available, as is the case with vertically pointing floating lidar and meteorological towers, the statistical method is recommended, regardless of the seemingly unrealistic z0 values at times. If multilevel wind speeds are not available but advanced sonic anemometry is available at one level, the analytical method is recommended over Charnock’s. Lastly, if a single, constant value of z0 is sought after to characterize the region, we recommend the median from the statistical method, i.e., 6.09×10−3 m, which is typical of rough seas.