A Chebyshev Polynomial‐Based Wind Speed Profile Characterization Framework: Applications in Mesoscale Model Evaluation

ABSTRACT This study presents a polynomial‐based wind speed profile characterization framework that approximates full vertical profiles using five physically meaningful Chebyshev polynomial coefficients. The framework captures key morphological features of wind profiles, including mean wind speed, vertical shear, curvature, inflection‐related behavior, and higher order fluctuations. Its accuracy is demonstrated using well‐documented wind regimes such as well‐mixed, shear‐dominant, logarithmic‐shaped, and low‐level jet (LLJ) profiles, showing consistent performance across diverse atmospheric conditions. To evaluate its practical utility by moving beyond conventional error metrics, the framework was applied to compare simulated wind profiles from a mesoscale model‐generated dataset against lidar observations. Results show that the mesoscale model reliably captured mean and shear structures, especially at coastal sites, while underrepresenting curvature and higher order variations at inland locations. The framework also facilitated a spatial and temporal assessment of model behavior, distinguishing coastal from inland site characteristics and capturing diurnal and seasonal variability, including LLJs driven by sea‐breeze circulation.