Ensemble Deep Learning for Improving Numerical Weather Prediction of Daily Maximum Air Temperature

    Reliable forecasts of maximum air temperatures are essential to prevent heat-related disasters, efficiently mitigate the damages caused by high-temperature disasters and appropriately respond to them. Deviations usually exist in the prediction of near-surface elements from numerical models due to complex factors such as atmospheric dynamic processes, physical processes, local topography and geomorphology. In particular, the deviation between the prediction and observation of daily maximum temperature is relatively larger when the weather changes drastically. Therefore, it is still a challenge to realize refined and accurate forecasts for daily maximum temperature. 
    Given the complexity of the interactions between the atmosphere and the Earth’s surface, no single machine learning method can consistently and effectively eliminate biases in numerical weather prediction (NWP) models. This is primarily because different regression variables in machine learning can significantly affect forecast performance. Furthermore, due to the randomness of initial weight parameters, neural network models generally have high variances. Consequently, individual machine learning models, particularly deep learning networks, often suffer from the “bias-variance” trade-off, and the ensemble machine learning can be an effective way to address this issue. A successful way to reduce the high variance of neural network models is to train multiple models instead of a single model and integrate the predictions of these models, i.e., integration learning. Integration learning not only reduces the variance of predictions, but also yields better predictions than any single model. Using ensemble models can effectively reduce the variance and enhance the model generalization ability. 
    Here, we proposed a stacking ensemble model named FLT, which consists of a fully connected neural network with embedded layers (ED-FCNN), a long short-term memory (LSTM) network and a temporal convolutional network (TCN) to overcome the high variance of a single neural network and to improve prediction of maximum air temper-ature. The case study of daily maximum temperature forecast evaluated with observation of al-most 2400 weather stations shows substantial improvement over that of single neural network model, ECMWF-IFS and statistical post-processing model. The FLT model can more effectively improve the forecast bias of the ECMWF-IFS model than that of any of the above single neural network model, with the RMSE reduced by 52.36% and the accuracy of temperature forecast in-creased by 43.12% compared with the ECMWF-IFS model. The average RMSEs of the FLT model decreases by 8.39%, 1.50%, 2.96% and 16.03%, respectively, compared with ED-FCNN, LSTM, TCN and the decaying average method.
    This study demonstrates that ensemble learning models constructed using stacked generalization methods can effectively reduce the forecasting bias associated with single neural network models, enhance the models’ generalization ability, and improve the accuracy of maximum temperature forecasts.