A Probabilistic Method for the Estimation of Surface Roughness and Displacement Height Using Limited Wind Profile Information

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Wednesday, 5 February 2014
Hall C3 (The Georgia World Congress Center )
Richard M. Eckman, NOAA/ARL, Idaho Falls, ID; and D. Finn and K. L. Clawson

Handout (27.6 MB)

The wind speeds encountered by wind turbines are affected by the local surface roughness. Often, estimates of the roughness length zo and displacement height d are rather uncertain because the available near-neutral wind observations are noisy or do not include optimal measurement heights. This paper describes the development of a probabilistic method for the determination of zo and d using datasets from an Idaho National Laboratory (INL) tall tower in Idaho and from the 2011-2012 Wind Forecast Improvement Project (WFIP) in west Texas. The roughness estimates derived from this method are then used to compare the observed wind profiles at the Texas WFIP sites with the expected profiles based on similarity theory.

The method generates probabilistic estimates for zo and d using Bayesian probability theory. It requires a set of near-neutral wind profiles as input and uses a Bayesian Metropolis-Hastings algorithm to generate posterior probability densities for both parameters. For the INL site, the wind profiles were provided by cup anemometers and vanes on a tall tower at heights of 2, 10, 15, 45, and 61 m above ground. For the Texas sites, the profiles consisted of SoDAR data at 10 m intervals from 30 to 60 m above ground combined with sonic anemometer observations closer to the surface. The mismatch in instrumentation at the Texas sites contributed uncertainty to the analysis. Limited measurements close to the surface created additional uncertainty. Point estimates of zo and d were taken to be the median values from the posterior probability densities.

Comparisons between computed logarithmic wind profiles and the observed WFIP wind profiles were based on 10-minute averages and broken out by Obukhov length and wind speed categories. Errors varied by category, but average and absolute errors were commonly up to 2 m/s with fractional errors up to 20%. As expected, the errors are largest for stable conditions with small positive Obukhov lengths. The profile analysis provides useful information on the linkage between surface fluxes and hub-height winds. Best-fit estimates for power law exponents matching the turbine-layer winds are also calculated.