Shear Aggregation Methods

A shear aggregation method is an algorithm to calculate the wind shear parameter that characterizes a period comprising multiple time steps. Windographer offers two approaches. The first, which we could call the aggregate profile approach, is to calculate the mean (or mean of monthly means) wind speed at each height, and then calculate the shear parameter from a single curve fit through that aggregate shear profile. The second, which we call the time series approach, is to calculate the shear parameter in every time step and then calculate the mean or median value of that time series.

Windographer offers four shear aggregation methods:

The time series and aggregate profile approaches typically give different results due to the nonlinear nature of the power law and the log law. We will demonstrate this with an example. Consider a 10-minute dataset reporting wind speeds at 50m and 32m above ground, from which we want to calculate the mean shear over a twelve-hour period.

Time Series Approach

The table below shows the wind speeds in each of the 72 time steps, as well as the power law exponent and surface roughness calculated in each time step from those wind speeds:

The second-last row in that table contains the results of the 'Time series - mean' method, while the last row contains the results of the 'Time series - median' method.

Aggregate Profile Approach

The aggregate profile approach is to calculate the mean speed at each height, which for our example is 7.197 m/s at 58m and 6.233 m/s at 32m, and find the shear parameter that best fits that aggregate profile. The curve fit process is the same as in the time series approach, but the speeds used in the curve fit are averages over the 12-hour period, rather than 10-minute averages. The 'Aggregate profile - mean' method gives a power law exponent of 0.24168 and a surface roughness of 0.6827m.

With a longer time series, we could also apply the 'Aggregate profile - MoMM' method by calculating the mean of monthly means speed at each height for use in the curve fit.

Comparison

The table below summarizes the results we obtain from the two approaches in this example.

The logarithmic law is more nonlinear than the power law, making it more sensitive to the order in which one performs the averaging and the curve fitting. In other words, the surface roughness values span a very large range, over multiple orders of magnitude, and the larger values tend to dominate the average. So the 'Time series - mean' method is virtually guaranteed to produce a larger value of surface roughness than the aggregate profile methods. The same is true, though to a lesser extent, of the power law exponent. The 'Time series - median' method is less strongly affected by outliers.

Because of the nonlinearity of the shear curve fit process, we believe the aggregate profile approach is the more mathematically defensible. The time series approach, however, has the advantage of being well suited to a changing displacement height. The aggregate profile approach has trouble with a non-constant displacement height because it makes for non-constant effective heights, so it becomes unclear what heights to enter into the curve fit. Windographer resolves this issue in an approximate way: it calculates the mean displacement height over the relevant time period and subtracts that from the nominal heights to calculate the effective height of each sensor.

Tip: In the Configure Dataset window you can select the shear aggregation method that applies to the dataset, and in the Options window you can specify the default shear aggregation method.

See also

Wind shear

Power law exponent

Surface roughness

Displacement height

Effective height

Mean of monthly means

Wind Shear window

Configure Dataset window

Options window

Written by: Tom Lambert
Contact: windographer.support@ul.com
Last modified: September 25, 2018