Statistical and deep learning models for reference evapotranspiration time series forecasting: A comparison of accuracy, complexity, and data efficiency

Reference evapotranspiration (ETo) is an essential variable in agricultural water resources management and irrigation scheduling. An accurate and reliable forecast of ETo facilitates effective decision-making in agriculture. Although numerous studies assessed various methodologies for ETo forecasting, an in-depth multi-dimensional analysis evaluating different aspects of these methodologies is missing. This study systematically evaluates the complexity, computational cost, data efficiency, and accuracy of ten models that have been used or could potentially be used for ETo forecasting. These models range from well-known statistical forecasting models like seasonal autoregressive integrated moving average (SARIMA) to state-of-the-art deep learning (DL) algorithms like temporal fusion transformer (TFT). This study categorizes monthly ETo time series from 107 weather stations across California according to their length to better understand the forecasting models' data efficiency. Moreover, two forecasting strategies (i.e., recursive and multi-input multi-output) are employed for machine learning and DL models, and forecasts are assessed for different multi-step horizons. Our findings show that statistical forecasting models like Holt-Winters' exponential smoothing perform almost as well as complex DL models. Unlike statistical models, DL models generally suffer from low data efficiency and perform well only when enough data is available. Importantly, although the computational costs of most DL models are higher than statistical methods, this is not the case for all. Considering computational cost, data efficiency, and forecasting accuracy, our findings point to the superiority of the neural basis expansion analysis for interpretable time series forecasting (N-BEATS) architecture for univariate ETo time series forecasting. Moreover, our results suggest HoltWinters and Theta methods outperform SARIMA - the most employed statistical model for ETo forecasting in the literature - in accuracy and efficiency.