Weibull distribution
A two-parameter probability distribution used to describe how often each wind speed occurs at a site, defined by a scale factor c and a shape factor k.
Wind speeds at a site cluster around moderate values with a long tail of strong winds. The Weibull probability density function captures this with two parameters:
The scale factor c (m/s) is close to the mean wind speed (mean = c × Γ(1 + 1/k), about 0.89c for k = 2). The shape factor k describes spread: k around 1.5–2 for variable continental and inland sites, about 2 for many temperate sites, and 2.5–4 for steady trade-wind and some offshore regimes. With k = 2 the distribution is the special Rayleigh case, a common default when only the mean is known.
Because turbine power depends on the cube of speed, the mean cube of wind speed matters, not the cube of the mean. For a Rayleigh distribution the energy pattern factor is about 1.91: the true mean wind power density is nearly twice what the average speed alone suggests. Two sites with the same 7 m/s mean but different k can differ in annual yield by 10% or more.
Combining the Weibull curve with a turbine's power curve gives gross annual energy production. Datasets such as the Global Wind Atlas (DTU/World Bank) publish c and k on a 250 m grid at several heights, and the parameters change with hub height because of wind shear.
Related terms
All terms →- Power curve
The relationship between hub-height wind speed and a turbine's electrical output, used with a wind speed distribution to estimate annual energy production.
- Wind power density
The mean power available in the wind per square metre of area perpendicular to the flow, in W/m², the standard measure of wind resource quality.
- Wind shear
The change in wind speed (and sometimes direction) with height above the surface, driven by surface roughness and atmospheric stability.
- Hub height
The height of a wind turbine's rotor centre above ground or sea level; taller hubs reach stronger, steadier winds and are a main driver of rising capacity factors.
- Capacity factor
The ratio of the energy a power plant actually produces over a period to the energy it would produce running at full nameplate capacity for the whole period.