The Extrapolation of Near-Surface Wind Speeds under Stable Stratification Using an Equilibrium-Based Single-Column Model Approach

Abstract

Classical approaches to modeling the near-surface (i.e., below 200 m) wind profile are equilibrium based (i.e., no time evolution) and either lack a physical basis or are based on surface-layer physics. In this study, the limits of the equilibrium approach in stable stratification are further tested by applying the method within a more physically comprehensive single-column model (SCM) framework. The SCM considered here is a highly idealized momentum and temperature budget model that uses a range of different parameterizations of turbulent fluxes. A 10-yr observational dataset obtained from the 213-m Cabauw tower in the Netherlands is used to drive the SCM and to assess model performance. Results from this study demonstrate several limitations of this SCM-based equilibrium approach. The existence of two physically meaningful equilibrium solutions for a given value of the surface turbulent temperature flux (used as a lower boundary in the SCM) generally results in either a tendency to underestimate stratification or the breakdown of the model because of runaway cooling and collapsed turbulence. Different representations of the geostrophic wind profile accounting for baroclinic effects caused by the strong land–sea temperature gradient at Cabauw are shown to have only a modest influence on the mean wind profile. The local internal boundary layer (IBL) at Cabauw results in a strong tendency for the SCM to overestimate wind speeds in weakly to moderately stable conditions. In very stable conditions (where the IBL influence was low), the equilibrium approach remained limited because of its inability to account for time-evolving phenomena such as the inertial oscillation and the low-level jet.

New methods to improve the vertical extrapolation of near-surface offshore wind speeds

“…where K m and K h are the eddy diffusivities for momentum and temperature, respectively. These terms are themselves parameterized with a range of possible options in the literature (Optis andMonahan, 2016, 2017). We adopt a relatively simple first-order closure model that includes eddy diffusivities that are related to the wind speed gradient and a stability function that depends on the Richardson number:…”

“…There are a range of proposed formulations for the mixing lengths and stability functions. Here, we use the one developed by Smith (1990), which showed strong results when used in an SCM in previous studies (Optis andMonahan, 2016, 2017). A detailed explanation and the equations of the stability functions and mixing lengths can be found in Smith (1990), Cuxart et al (2006), and Optis and Monahan (2017).…”

“…The key advantage of the SCM is its ability to be forced at the lower boundary by wind and temperature observations. The SCM was used in and Optis and Monahan (2017) to extrapolate 10 m wind speeds up to 200 m at the Cabauw meteorological tower in the Netherlands. Results showed that the SCM performed about the same as the Weather Research and Forecasting (WRF) model (Skamarock et al, 2019) during a 10-year period, highlighting the benefit of local observations driving a highly simplified model.…”

A Comparison of Equilibrium and Time-Evolving Approaches to Modeling the Wind Profile under Stable Stratification

“…Such models are flexible in determining which processes and parameterizations are included (e.g., turbulence, radiation, entrainment, land surface characteristics, etc. ), allow for the specification of lower boundaries above the surface (Optis and Monahan 2016), and generally have low computational requirements. Models range in complexity from those that incorporate detailed physics (similar to a 3D model) to idealized representations that may only consider the budget equations (e.g., momentum and temperature).…”

“…and relationships between parameters (e.g., flux-gradient relationships) can then be evaluated from the quasi-equilibrium state. This approach has been used in a number of studies to explore SBL characteristics (e.g., Weng and Taylor 2006;Sterk et al 2013;Sorbjan 2012Sorbjan , 2014 and to compare different turbulence parameterizations (e.g., Weng and Taylor 2003;Cuxart et al 2006;Edwards et al 2006;Optis and Monahan 2016). In a previous study, we identified several limitations of the equilibrium approach (Optis and Monahan 2016).…”