Transfer and deep learning models for daily reference evapotranspiration estimation and forecasting in Spain from local to national scale

Abstract

Accurate estimation and forecasting of Reference Evapotranspiration ($E{T}_0$) is critical for almost all agricultural activities and water resource management. However, the most commonly used Penman-Monteith model (FAO56-PM) requires a large amount of input data and it is difficult to compute for general users. Machine Learning (ML) techniques can be used to address this shortcoming. Nevertheless, most studies are site-specific and lack generalizability. This study compares standard ML and Deep Learning (DL) algorithms for estimating and forecasting daily $E{T}_0$ at different spatial scales in Spain. While Transfer Learning (TL) is a well-established ML technique, its application in $E{T}_0$ computation remains largely unexplored. We applied TL in a novel approach to retrain DL models, enabling adaptation to diverse local climatic conditions, which is particularly important in this domain. All possible combinations of FAO56-PM inputs were evaluated. The results showed that with three or more climatic variables, the TL process can consistently reduce errors by using an appropriate amount of new data to retrain the models. In estimation, with 20% (120 days) of new data, TL models can provide the same performance as if they were trained with local data, both regionally and nationally (improvement of MAE from 26.4% to 99.5%). During forecasting, we used predicted weather data as input, and despite inherent biases in some variables, the TL models successfully adapted using 9-36 days of new data, significantly improving predictive performance (reducing MAE from -1.1% to 134.3%). Thus, the TL process is highly recommended as a promising methodology for increasing the generalization capability of DL models in both daily $E{T}_0$ estimation and forecasting under diverse climatic conditions with limited local data.