The Sensitivity of Potential Wind Power Output to Vertical Turbulent Flux Parameterization Schemes for Stable Boundary Layers

The vertical wind speed profile as simulated in a numerical weather prediction model provides the basis for a wind power forecast, and often contributes most of the error. This error is typically largest for the stable boundary layer (SBL), where weak and intermittent vertical turbulent fluxes lead to unique boundary layer characteristics – such as the formation of low-level jets, the decoupling of winds aloft from the surface, and the increased influence of gravity waves – making the vertical wind speed profile in the SBL a challenge to model. The SBL is common at night and is characterized by higher wind speeds at hub-height compared to neutral or unstable boundary layers. Thus, the modeling of the vertical wind speed profile in the SBL is an important and developing field in wind power meteorology.

The vertical wind speed profile is controlled predominately by vertical turbulent fluxes of momentum and heat, and substantial research over the last several decades has improved the parameterization of these fluxes for the SBL. First-order approaches (commonly used in synoptic-scale operational models) relate the flux magnitude to the local bulk Richardson number, whereas higher-order approaches (commonly used in mesoscale and regional models with higher vertical resolution) relate the flux magnitude to the turbulence kinetic energy (TKE). The use of either of these approaches requires the specification of several additional parameters – including mixing length, stability function, TKE transport, TKE dissipation and several constants – the forms of which can vary considerably between different atmospheric models.

The purpose of this study is to determine the sensitivity of the vertical wind speed profile to the various turbulent flux parameterization schemes currently used in different atmospheric models. The focus here is on heights typically swept out by a large wind turbine rotor blade (i.e. heights from 70 to 200 metres). Given the wind shear across this height, the potential wind power output can be calculated and compared across different flux parameterization schemes.

An idealized single-column model of the SBL momentum budget is developed for this study. Monin-Obukhov similarity theory is applied in the surface layer. The height dependence of eddy diffusivity above the surface layer results in a non-linear system which is difficult to solve analytically. Instead, the system is solved numerically using appropriate boundary conditions. Different stability regimes are considered by prescribing variable geostrophic forcing and vertical temperature profiles. Steady-state solutions are examined to compare potential wind power output under these different external forcings and turbulent flux parameterization schemes. Time-evolving solutions are also examined to compare the temporal evolution of the SBL under different flux parameterization schemes and the associated differences in potential wind power output over given time intervals. Particular attention is given to the very stable regimes, where the formation, duration, strength, and height of the low-level jet are examined in detail.

Results from these simulations show substantial differences in potential wind power output between first and higher-order turbulent flux parameterization schemes. These differences are most pronounced in the very stable regime. Potential wind power output is also quite sensitive to different forms of mixing length and stability function parameters. Consequently, the selection of a particular NWP model and its inherent turbulent flux parameterization scheme can significantly affect the accuracy of a wind power forecast. Some schemes are not based on boundary layer observations and should not be used for wind power forecasting purposes. Schemes that are based on observations are typically measured in specific climates and geographies, and consequently take different functional forms. The error in a wind power forecast might then be reduced by choosing a flux parameterization scheme most suitable to the climate and geography where the wind turbine or farm is located.