Enhancing temperature forecasting models through atmospheric physical equations

Atmospheric temperature prediction is fundamentally a physical problem governed by deterministic equations. This paper introduces a hybrid architecture, Pi-ConvLSTM, to investigate how physical principles can guide neural network design and refinement for forecasting regional temperature variations by embedding existing physical knowledge into optimization. In the experimental framework, Pi-ConvLSTM achieves higher Structural Similarity Index Measure (SSIM) than the baseline ConvLSTM across the four forecast time steps, indicating improved performance and temporal stability. Significant reductions are also observed in the mean squared error (MSE) and mean absolute error (MAE). Moreover, analysis of the final loss across different layer counts identified the optimal number of setting layers as a hyperparameter, consistent with theoretical results indicating that the appropriate number of setting layers in this study is no more than two. Notably, Pi-ConvLSTM performs better over ocean than over land, a tendency predicted by analysis of the governing physical equations. Comparisons of SSIM and MSE indicate that state-of-the-art models such as GraphCast, FourCastNet and PanguLM still exhibit this limitation.