Spatiotemporal Forecasting in Climate Data Using EOFs and Machine Learning Models: A Case Study in Chile

Effective resource management and environmental planning in regions with high climatic variability, such as Chile, demand advanced predictive tools. This study addresses this challenge by employing an innovative and computationally efficient hybrid methodology that integrates machine learning (ML) methods for time series forecasting with established statistical techniques. The spatiotemporal data undergo decomposition using time-dependent Empirical Orthogonal Functions (EOFs), denoted as \(\phi_{k}(t)\), and their corresponding spatial coefficients, \(\alpha_{k}(s)\), to reduce dimensionality. Wavelet analysis provides high-resolution time and frequency information from the \(\phi_{k}(t)\) functions, while neural networks forecast these functions within a medium-range horizon \(h\). By utilizing various ML models, particularly a Wavelet - ANN hybrid model, we forecast \(\phi_{k}(t+h)\) up to a time horizon \(h\), and subsequently reconstruct the spatiotemporal data using these extended EOFs. This methodology is applied to a grid of climate data covering the territory of Chile. It transitions from a high-dimensional multivariate spatiotemporal data forecasting problem to a low-dimensional univariate forecasting problem. Additionally, cluster analysis with Dynamic Time Warping for defining similarities between rainfall time series, along with spatial coherence and predictability assessments, has been instrumental in identifying geographic areas where model performance is enhanced. This approach also elucidates the reasons behind poor forecast performance in regions or clusters with low spatial coherence and predictability. By utilizing cluster medoids, the forecasting process becomes more practical and efficient. This compound approach significantly reduces computational complexity while generating forecasts of reasonable accuracy and utility.