This section describes the methodology used to estimate wind speed at heights other than those directly provided by the source dataset (e.g., 10 m and 100 m in ERA5), using the power law formulation. This method is particularly relevant for datasets such as climate projections and seasonal forecasts, which typically only provide wind speed at 10 m. In such cases, wind speed at hub height (commonly 100 m) must be reconstructed to support wind energy modelling and other applications.
To address this gap, vertical wind speed profiles are estimated using a power law based on the 10 m wind speed and a scaling coefficient known as alpha (α).
Power Law Formulation
The power law expresses the relationship between wind speed and height above ground as:
\[ v_2 = v_1 \left( \frac{h_2}{h_1} \right)^{\alpha} \]Where:
v1: wind speed at height h1 (e.g., 10 m)
v2: wind speed at height h2 (e.g., 100 m)
α: wind shear exponent (dimensionless)
This relationship assumes a logarithmic boundary layer profile under neutral atmospheric conditions and provides a reasonable approximation for many locations and time periods.
Calculation of the Alpha Coefficient
The alpha coefficient is computed using bias-adjusted ERA5 wind speed data at 10 m and 100 m over the period 2011–2021. The expression used is:
\[ \alpha = \frac{\ln(v_2) - \ln(v_1)}{\ln(h_2) - \ln(h_1)} \]To account for diurnal and seasonal variability, alpha is computed for each hour and each month. This results in 288 values (24 hours × 12 months) per grid cell, capturing both local and temporal variations in wind profile characteristics.
An 11-year period was selected to ensure statistical stability while maintaining representativeness of recent climate conditions. The use of bias-adjusted data ensures consistency with the wind speed fields used for energy indicator computation.
Application in Projections and Seasonal Forecasts
Once computed, the alpha coefficients are applied to 10 m wind speed from datasets that do not provide 100 m wind data, enabling consistent estimation of WS100. This approach ensures compatibility across data streams while preserving key orographic and temporal features.
Statistical Distribution of Alpha
Figure 4.1 shows a global summary of the alpha coefficient distributions across the 24 hours of the day. On average, alpha is slightly higher during stable nighttime hours and lower during the daytime, when convective turbulence enhances vertical mixing and reduces wind shear.
Figure 4.1: Boxplot showing the global distribution of hourly alpha coefficients across the 24 hours of the day.
