Modeling the vertical structure of turbulence characteristics in the atmospheric boundary layer: A physics-informed neural operator and symbolic regression method

Abstract

Accurately modeling turbulence intensity (TI) and gust factor (GU) is crucial for ensuring the structural integrity and operational efficiency of wind turbines. This study develops a physics-informed model for turbulence characteristics in the complex atmospheric boundary layer, leveraging 1 year of Doppler wind lidar observations and Weather Research and Forecasting numerical simulations for both stationary and non-stationary models. A combined analysis of observations and simulations reveals a distinct vertical structure of turbulence. Based on this, we further develop an explicit symbolic regression physical model and a physics-informed neural operator deep learning model. The results show that both TI and GU exhibit a C-shaped vertical profile below 200 m under various atmospheric stability conditions, decreasing with height up to an inflection point at approximately 120 m, then increasing. A genetic algorithm-driven symbolic regression method yields a physically interpretable analytical model (coefficient of determination R2 ≥ 0.953) that accurately captures this structure, significantly outperforming traditional empirical formulas. Furthermore, a hybrid model integrating bidirectional long short-term temporal modeling, neural operator architecture, and embedded physical constraints is developed. It achieves maximum R2 values of 0.960 for TI and 0.962 for GU, while maintaining superior consistency in representing vertical profiles. This work demonstrates that embedding explicit physical knowledge into neural operator learning frameworks effectively improves the fidelity and physical consistency of turbulence vertical-structure representation in the present dataset. It offers a potentially useful, physically consistent pathway for wind resource assessment and load-related turbulence-risk evaluation in complex terrain.