Extending wind profile beyond the surface layer by combining physical and machine learning approaches

Abstract. Accurate estimation of the wind profile, especially in the lowest few hundred meters of the atmosphere, is of great significance for weather, climate and renewable energy. Nevertheless, the Monin–Obukhov similarity theory fails above the surface layer over the heterogeneous underlying surface, resulting in an unreliable wind profile obtained from the conventional extrapolation methods. To solve this problem, we propose a novel method that combines the power law method (PLM) with the random forest (RF) algorithm to extend wind profiles beyond the surface layer, called the Phy-RF method. The underlying principle is to treat the wind profile as a power law distribution in the vertical direction, in which the power law exponent (α) is determined by the Phy-RF model. First, the Phy-RF model is constructed based on the atmosphere sounding data at 119 radiosonde (RS) stations across China and in conjunction with other data such as surface wind speed, land cover type, surface roughness, friction velocity, geographical location, and meteorological parameters from June 2020 to May 2021. Afterwards, the performance of the Phy-RF, PLM and RF methods over China are evaluated by comparing them with RS observations. Overall, the wind speed at 100 m of the Phy-RF model exhibits high consistency with RS measurements, with a correlation coefficient (R) of 0.93 and a root mean squared error (RMSE) of 0.92 m s⁻¹. By contrast, the R and RMSE of wind speed results from PLM (RF) method are 0.87 (0.91) and 1.37 (1.04) m s⁻¹, respectively. This indicates that the estimates from the Phy-RF method are much closer to observations than those from the PLM and RF methods. Moreover, the RMSE of the wind profiles estimated by the Phy-RF model is relatively larger at highlands, while is small in plains. The result indicates that the performance of the Phy-RF model is affected by the terrain factor. Finally, the Phy-RF model is applied to three atmospheric radiation measurement sites for independent validation, and the wind profiles estimated by the Phy-RF model are found consistent with the Doppler Lidar observations. This confirms that the Phy-RF model has good applicability. These findings have great implications for the weather, climate and renewable energy.