Profiles of wind and Weibull distribution parameters in a coastal and marine boundary layer

 

 

Electricity production due to air flow in the lower atmosphere has increased during recent decades, accompanied by technological developments and requirements for wind information up to 300-400 m above the surface. For applied use in wind-energy applications, the Weibull distribution is commonly used due to its simplicity to perform power-density estimates, flexibility and adequate description of the measurements. However, the profile above the lowest 50 m is still not settled and is an issue of current research.

 

Here we present an experimental investigation of long-term profiles of the wind and Weibull distribution parameters up to 600 m. The observations were carried out during a one year period at Høvsøre (2010-2011), a coastal site in western Denmark, as well during a half year period (2013-2014) at the German research platform FINO 3 located in the North Sea 80 km from the closest land.

 

At both sites, a pulsed Doppler lidar was operated during the campaigns in combination with meteorological masts. The horizontal wind velocity for the lidar was obtained with 50 m resolution from 100 m to 2 km height depending on the attainable sensitivity determined by the 10-min averaged carrier-to-noise-ratio.

 

Additionally, simulations with the Weather Research and Forecasting (WRF) model were carried out for both sites.

 

The two parameter Weibull distribution is described by the scale parameter A and the shape parameter k. The profile of the mean wind speed and the scale parameter are rather similar; but the shape parameter has a very pronounced behavior, see Figure.

 

On average during daytime over land, the boundary layer is deep and well mixed throughout the entire layer. At night, the boundary layer is shallow with inhibited diffusion of momentum resulting in a decreasing surface wind. Above the stable boundary layer the wind speed increases in response to the decoupling from the surface. This typical diurnal variability in both atmospheric stability and boundary-layer depth results in a characteristic climatology of the wind profile; the shape parameter in the Weibull distribution of the wind speed increases from near the ground to a maximum located at around 100-200 m height and then reverts to its upper air value. The height at which the maximum in the shape parameter occurs depends on the balance between the diurnal variation of the local meteorological conditions and the variability of the synoptic conditions prevailing in the region.

 

We propose a new parametrization of the k profile, which extends well beyond the height of the maximum:

 

 

The shape parameter increases from its value near the ground, zs  reaching a maximum near zr  and then decreases with height, asymptotically approaching the value of kt  in the upper part of the planetary boundary layer.  Results from the application of the parameterization for both the coastal and the marine site will be presented and discussed, thus elucidating the difference between the meteorology of the coastal zone and the marine atmosphere in terms of the profile of the Weibull distribution.

 

When the WRF forecast of the scale parameter was compared to measurements, the simulated scale parameter was always underestimated. This signifies that the wind speed is underestimated as well. Above 100 m, also the shape parameter was also underestimated by the WRF forecast compared to the measurements. Underestimation of the shape parameter in the simulations indicates that the probability for higher wind speed increases (a wider distribution is related to lower k  values). For the coastal rural site we compared  the modelled and observed profiles of the wind speed variances. It was found that although k was smaller for the model than the observations, the profiles of the variance were nearly identical, indicating that the discrepancy in k is more related to the difference in the mean than the difference in the variances. In a study of Floors et al. (2013)  a 4-week period was simulated at the coastal site; the model simulations were carried out with a fine (63 model levels) and a coarse (41 model levels) vertical resolution. It was found that the wind profile was not sensitive to the vertical resolution, while here it is found that the shape parameter is also not sensitive to the vertical resolution.

 

 

Figure. Measured and simulated profiles of the scale (left) and shape (right) parameter in the Weibull distribution from the coastal site. The full line shows the WRF model simulation, the circles lidar measurements and triangles mast measurements.

 

An analysis performed along these lines will be presented for the measurements from the FINO3 marine site and compared to the results from the coastal site (Høvsøre). Similarities and differences of the meteorology between the marine and coastal site will be discussed.

 

 

Floors R, Vincent C-L, Gryning SE, Peña A, Batchvarova E (2013) Wind profiles in the coastal boundary layer: wind lidar measurements and WRF modelling. Boundary-Layer Meteorol 147:469–491