A case study of spatiotemporal forecasting techniques for weather forecasting

The majority of real-world processes are spatiotemporal, and the data generated by them exhibits both spatial and temporal evolution. Weather is one of the most essential processes in this domain, and weather forecasting has become a crucial part of our daily routine. Weather data analysis is considered the most complex and challenging task. Although numerical weather prediction models are currently state-of-the-art, they are resource-intensive and time-consuming. Numerous studies have proposed time series-based models as a viable alternative to numerical forecasts. Recent research in the area of time series analysis indicates significant advancements, particularly regarding the use of state-space-based models (white box) and, more recently, the integration of machine learning and deep neural network-based models (black box). The most famous examples of such models are RNNs and transformers. These models have demonstrated remarkable results in the field of time-series analysis and have demonstrated effectiveness in modelling temporal correlations. It is crucial to capture both temporal and spatial correlations for a spatiotemporal process, as the values at nearby locations and time affect the values of a spatiotemporal process at a specific point. This self-contained paper explores various regional data-driven weather forecasting methods, i.e., forecasting over multiple latitude-longitude points (matrix-shaped spatial grid) to capture spatiotemporal correlations. The results showed that spatiotemporal prediction models reduced computational costs while improving accuracy. In particular, the proposed tensor train dynamic mode decomposition-based forecasting model has comparable accuracy to the state-of-the-art models without the need for training. We provide convincing numerical experiments to show that the proposed approach is practical.