Current research based on various approaches including the use of numerical weather prediction models, statistical models, and machine learning models have provided some encouraging results in the area of longterm weather forecasting. But at the level of mesoscale and even microscale severe weather phenomena (involving very short-term chaotic perturbations) such as turbulence and wind shear phenomena, these approaches have not been so successful. This research focuses on the use of chaotic oscillatory-based neural networks for the study of a mesoscale weather phenomenon, namely, wind shear, a challenging and complex meteorological problem that has a vital impact on aviation safety. Using lidar data collected at the Hong Kong International Airport via the Hong Kong Observatory, it is possible to forecast the Doppler velocities with satisfactory accuracy and validate the prediction model with the potential to generate the wind shear alert. Experimental results are found to be comparable to the actual measurement. Moreover, the selected testing cases and results show that the value of correlation coefficient between the predicted and lidar-measured wind velocities exceeds 0.9 with various window sizes ranging from 1 to 3 h. These provide areas for further research of the proposed model and lidar technology for turbulence and wind shear forecasts.