TMRE: Novel Algorithm for Computing Daily Reference Evapotranspiration Using Transformer-Based Models

Reference Evapotranspiration (ETo) is widely used to assess total water loss between land and atmosphere due to its importance in maintaining the atmospheric water balance, especially in agricultural and environmental management. Accurate estimation of ETo is challenging due to its dependency on multiple climatic variables, including temperature, humidity, and solar radiation, making it a complex multivariate time-series problem. Traditional machine learning and deep learning models have been applied to forecast ETo, achieving moderate success. However, the introduction of transformer-based architectures in time-series forecasting has opened new possibilities for more precise ETo predictions. In this study, a novel algorithm for ETo forecasting is proposed, focusing on four transformer-based models: Vanilla Transformer, Informer, Autoformer, and FEDformer (Frequency Enhanced Decomposed Transformer), applied to an ETo dataset from the Andalusian region. The novelty of the proposed algorithm lies in determining optimized window sizes based on seasonal trends and variations, which were then used with each model to enhance prediction accuracy. This custom window-sizing method allows the models to capture ETo’s unique seasonal patterns more effectively. Finally, results demonstrate that the Informer model outperformed other transformer-based models, achieving mean square error (MSE) values of 0.1404 and 0.1445 for forecast windows (15,7) and (30,15), respectively. The Vanilla Transformer also showed strong performance, closely following the Informer model. These findings suggest that the proposed optimized window-sizing approach, combined with transformer-based architectures, is highly effective for ETo modelling. This novel strategy has the potential to be adapted in other multivariate time-series forecasting tasks that require seasonality-sensitive approaches.