Spatiotemporal forecasting (STF) extends traditional time series forecasting or spatial interpolation problem to space and time dimensions. Here, we review the statistical, physical and artificial intelligence (AI) methods, data and model uncertainties, predictability and future directions for STF problems. Statistical STF methods have limitations in high-level feature extractions and long-term memory modeling. Physical models are computationally intensive and are imperfect in model structure and parameterization. AI models lack the interpretability and require elaborate training but can model complex nonlinear and non-Gaussian problems. Integrating data-driven and physical model-driven methods could facilitate the improvement of interpretability and forecasting accuracy. The predictive uncertainty comes from data and models, which could be measured by probability distribution and Bayesian inference, respectively. The predictive uncertainty is generally missing in AI models and could be resolved by incorporating Bayesian frameworks. The predictability of dynamic earth systems is spatiotemporally heterogeneous and is generally examined by diagnostic and prognostic approaches. Diagnostic methods analyze the predictability empirically from a theoretical perspective, while prognostic methods investigate the predictability through real experiments. Unraveling the predictability in space and time and the predictability sources will greatly improve earth system understanding and operational forecasting development. Current STF systems are largely not user-friendly to provide probabilistic and understandable forecasting services in near real-time. Intelligent STF systems should automatically prepare various data sources, train the models in a self-adaptative way and provide timely predictive information services for users to make decisions. This review provides state-of-the-art advances in forecasting sciences and highlights new directions for new-generation STF systems.

时空预测 (STF) 将传统的时间序列预测或空间插值问题扩展到空间和时间维度。在这里，我们回顾了 STF 问题的统计、物理和人工智能 (AI) 方法、数据和模型的不确定性、可预测性和未来方向。统计 STF 方法在高级特征提取和长期记忆建模方面存在局限性。物理模型计算量大，模型结构和参数化不完善。AI 模型缺乏可解释性，需要精心训练，但可以对复杂的非线性和非高斯问题进行建模。整合数据驱动和物理模型驱动的方法可以促进可解释性和预测准确性的提高。预测的不确定性来自数据和模型，可以分别通过概率分布和贝叶斯推理来衡量。AI 模型中通常缺少预测不确定性，可以通过结合贝叶斯框架来解决。动态地球系统的可预测性在时空上是异质的，通常通过诊断和预测方法进行检查。诊断方法从理论角度凭经验分析可预测性，而预后方法则通过实际实验研究可预测性。解开空间和时间的可预测性和可预测性来源将大大提高对地球系统的理解和业务预测的发展。当前的 STF 系统在很大程度上不是用户友好的，无法以近乎实时的方式提供概率和可理解的预测服务。智能 STF 系统应自动准备各种数据源，自适应地训练模型，并为用户提供及时的预测信息服务以进行决策。这篇综述提供了预测科学的最新进展，并强调了新一代 STF 系统的新方向。