Methods to Estimate Surface Roughness Length for Offshore Wind Energy

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, 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. We tested three different methods to calculate z0: 1) analytical, dependent on friction velocity u* and a stability function psi; 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. In general, the median z0 exhibits little seasonal variability and a weak dependency on atmospheric stability, which was predominantly unstable (54-67 delivering unrealistic z0 values at times, gives the best estimates of 60-m winds. The unrealistic z0 values are caused by non-monotonic wind speed profiles, occurring about 41 they produce realistic fits. In summary, if wind speed data from multiple levels are available, the statistical method is recommended. If multi-level wind speeds are not available but advanced sonic anemometry is available at one level, the analytical method is recommended over the Charnock's. If a 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.