Extending the 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 the weather, climate, and renewable energy sector. Nevertheless, the Monin–Obukhov similarity theory fails above the surface layer over a heterogeneous underlying surface, causing an unreliable wind profile to be obtained from conventional extrapolation methods. To solve this problem, we propose a novel method called the PLM-RF method that combines the power-law method (PLM) with the random forest (RF) algorithm to extend wind profiles beyond the surface layer. The underlying principle is to treat the wind profile as a power-law distribution in the vertical direction, with the power-law exponent (α) determined by the PLM-RF model. First, the PLM-RF model is constructed based on the atmospheric sounding data from 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 PLM-RF, PLM, and RF methods over China is evaluated by comparing them with RS observations. Overall, the wind speed at 100 m from the PLM-RF model exhibits high consistency with RS measurements, with a determination coefficient (R2) of 0.87 and a root mean squared error (RMSE) of 0.92 m s−1. By contrast, the R2 and RMSE of wind speed results from the PLM (RF) method are 0.75 (0.83) and 1.37 (1.04) m s−1, respectively. This indicates that the estimates from the PLM-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 PLM-RF model is relatively large for highlands, while it is small for plains. This result indicates that the performance of the PLM-RF model is affected by the terrain factor. Finally, the PLM-RF model is applied to three atmospheric radiation measurement sites for independent validation, and the wind profiles estimated by the PLM-RF model are found to be consistent with Doppler wind lidar observations. This confirms that the PLM-RF model has good applicability. These findings have great implications for the weather, climate, and renewable energy sector.