Hybrid deep learning model with joint water-carbon constraints for simultaneous estimation of evapotranspiration and gross primary production

Abstract

Accurately quantifying evapotranspiration (ET) and gross primary production (GPP) is essential for sustainable agroecosystem management. Hybrid deep learning (DL) models, which integrate physical knowledge with data-driven techniques, have demonstrated strong potential in improving flux predictions. However, most existing frameworks estimated ET and GPP separately, thereby overlooking their intrinsic coupling via shared physiological mechanisms such as stomatal regulation. In this perspective, we proposed a novel hybrid modeling framework that incorporated DL-based canopy stomatal conductance (G_s) as an intermediary biophysical variable within process-based host models to simultaneously estimate ET and GPP. The framework was evaluated using multi-year eddy covariance observations from sunflower and maize agroecosystems under three constraint strategies: water-only (HDW), carbon-only (HDC), and joint water-carbon (HDWC). Results showed that although HDW and HDC achieved high target-specific accuracies, they exhibited limited generalization in cross-target predictions. In contrast, the HDWC model, optimized with weighting coefficients of 0.5 for sunflower and 0.6 for maize, effectively balanced the trade-off between ET and GPP, achieving average Kling-Gupta Efficiency (KGE) values of 0.881 for sunflower and 0.931 for maize. Multi-year evaluations further revealed that HDWC reduced root mean square errors (RMSE) to 0.45 and 0.50 mm d⁻¹ for ET, and 0.97 and 1.35 g C m⁻² d⁻¹ for GPP in sunflower and maize, respectively, while minimizing interannual variability and extreme biases. Notably, the inter-model differences in G_s estimates highlighted the enhanced interpretability of HDWC, which more realistically captured the physiological coupling between water and carbon fluxes. Overall, our findings demonstrated that the joint constraint strategy provided a robust and interpretable framework for the simultaneous prediction of ET and GPP, offering a valuable tool for advancing intelligent simulations of agroecosystem processes.