Quantifying the Directional Coupling of Wind Speed and Wind Direction Using Circular-Linear Model
Abstract
Wind speed and direction are fundamentally coupled, but standard linear models fail to capture the circular nature of direction. This study applies first, second, and third -order circular-linear models to daily wind data. The parameter estimates were used to calculate the Phase and Amplitude of the relationship. The analysis revealed significant daily variability. Days with high amplitude like Day 8, A=45.48, indicated highly organized flow from a specific direction (NNE). Days with low amplitude indicated weak variable wind regimes. In the second order model, Dominant Direction is based on the first harmonic component of the model. Days 3, 5, 6, 7, 8, and 9 show very high amplitudes, larger than the others, indicating that the first harmonic completely dominates the wind pattern. The third order model showed a very clear pattern for most days (1, 3, 4, 5,7 ) showing a dominant wind speed maximum from the east-southeast (ESE) quadrant (between 102° and 112°), likely driven by a robust sea breeze or another recurring mesoscale pattern. Days 2 and 6 show a shift to southwesterly and southeasterly flow, respectively The method successfully quantifies the wind speed-direction relationship, providing valuable metrics for applications in renewable energy, pollution dispersion, and weather pattern diagnosis .
