A hybrid WOA-KDE and mixed copula framework for directional wind assessment in complex terrain

Accurate wind energy assessment in complex terrain remains a significant challenge due to the difficulty of reliably modeling the bivariate probabilistic relationship between wind speed and direction. To address such concern, this study proposes a novel hybrid framework that integrates advanced marginal and joint distribution modeling techniques. Wind speed is modeled using Kernel Density Estimation (KDE), optimized through the Whale Optimization Algorithm (WOA), resulting in superior performance over conventional parametric approaches. For wind direction, the Von Mises distribution is employed, demonstrating a 2–13 % improvement (measured by R²) in goodness-of- fit compared to traditional harmonic models. These optimized marginal distributions are then coupled via a mixed copula constructed as a linear combination of Gumbel, Clayton, and Frank copulas. The resulting joint probability density function (JPDF) exhibits significantly enhanced performance, achieving a comprehensive evaluation metric of 4.92 and outperforming five widely used single copulas, as well as the Angular-Linear (AL) and multiplication models. The mixed copula approach yields a 5–20% improvement (measured by composite metric) in JPDF accuracy compared to these classic models, producing more realistic and reliable estimates of wind characteristics. The validated model is applied to conduct a comprehensive directional wind energy assessment, offering a high-resolution analytical tool for wind energy applications.