Deep learning-based direct and indirect potential evapotranspiration prediction, a case of the Nakdong River basin, South Korea

초록

Accurate estimation of the potential evapotranspiration (PET) is crucial for hydrological modeling and water resource management. This study develops and compares two deep learning (DL) models, namely an indirect graph convolutional recurrent network (GCRN) and a direct GraphWaveNet model, to predict daily PET in the Nakdong River basin, South Korea. Reference PET was calculated from 52 years (1973–2024) of meteorological data using the FAO-56 Penman-Monteith (PM) method. The indirect framework predicts variables (net radiation, vapor pressure, and vapor-pressure deficit) prior to PET recomposition, whereas the direct framework predicts PET with reduced inputs on a data-scarce basis. Quantitative evaluation across 13 stations demonstrates that GraphWaveNet outperforms GCRN, with RMSE ranging from 0.52 to 0.68 mm/day and MAE values ranging from 0.40 to 0.50 mm/day, which are 50–65% lower than GCRN's (RMSE values ranging from 1.3 to 1.6 mm/day). The direct model also yielded a higher R2 (0.85–0.92) than GCRN (0.14–0.48) and had a slight bias (<0.08). GraphWaveNet captured seasonal and short-term variations while maintaining variance; however, the indirect GCRN was underestimated under high-PET conditions due to errors propagated through the reconstructed PM components. Findings confirm that adaptive spatiotemporal graph-based DL has a robust, precise, and physically coherent approach to PET estimation. © 2026 European Regional Centre for Ecohydrology of the Polish Academy of Sciences

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