Limitations and breakdown of Monin-Obukhov similarity theory for wind profile extrapolation under stable stratification

The intent of this study is to investigate the limitations of the Monin–Obukhov similarity theory (MOST) for wind profile extrapolation—particularly its breakdown in stable stratification—and to explore several modifications intended to circumvent aspects of this breakdown. Using 10years of 10min averaged data from the 213m Cabauw meteorological tower in the Netherlands, we first demonstrate the sensitivity of the logarithmic wind speed model to highly uncertain estimates of the roughness length, z0, and the associated limitations of applying the model in horizontally inhomogeneous conditions. We then demonstrate that these limitations can be mitigated by avoiding the use of z0 in the logarithmic wind speed model. Rather, by using a lower boundary above z0 (e.g. 10m) and a ‘bulk’ Obukhov length measured between two near-surface altitudes, substantial improvements in wind speed extrapolation accuracy are found. Next, we demonstrate the limitations in applying the logarithmic wind speed model above the surface layer (SL), specifically the divergence of different forms of the MOST stability function, the role of the Coriolis force and the decoupling of surface winds from those aloft. Finally, we explore similarity-based modifications to the logarithmic wind speed model that are intended to improve its accuracy above the SL, but we find that such modifications cannot circumvent the limitations described earlier. Given that modern hub heights and altitudes swept out by a wind turbine blade extend well beyond the range of applicability of MOST under conditions of stable stratification, new extrapolation models are required that are more applicable at these altitudes.