Forecasting global climate drivers using Gaussian processes and convolutional autoencoders

Machine learning (ML) methods have become an important tool for modelling and forecasting complex high -dimensional spatiotemporal datasets such as those found in environmental and climate modelling applications. ML approaches can offer a fast, low-cost alternative to short-term forecasting than expensive numerical simu-lation while addressing a significant outstanding limitation of numerical modelling by being able to robustly and dynamically quantify predictive uncertainty. Low-cost and near-instantaneous forecasting of high-level climate variables has clear applications in early warning systems, nowcasting, and parameterising small-scale locally relevant simulations. This paper presents a novel approach for multi-task spatiotemporal regression by combining data-driven autoencoders with Gaussian Processes (GP) to produce a probabilistic tensor-based regression model. The proposed method is demonstrated for forecasting one-step-ahead temperature and pressure on a global scale simultaneously. By conducting probabilistic regression in the learned latent space, samples can be propagated back to the original feature space to produce uncertainty estimates at a vastly reduced computational cost. The composite GP-autoencoder model was able to simultaneously forecast global temperature and pressure values with average errors of 3.82 degrees C and 638 hPa, respectively. Further, on average the true values were within the proposed posterior distribution 95.6% of the time illustrating that the model produces a well-calibrated predictive posterior distribution.