The data-driven solution of energy imbalance-induced structural error in evapotranspiration models

Due to the energy imbalance problem that the sum of latent and sensible heat fluxes is not equivalent to available energy, there exists a structural error in energy balance-based evapotranspiration models. In this study, the data-driven solution was proposed to address this problem. We combined three machine learning algorithms, deep neural network, long-short term memory, and random forest, with observations from 69 FLXUNET sites to quantify instantaneous energy balance ratio (EBR), then corrected the energy imbalance-induced structural error in evapotranspiration models. The contributions of the environmental factors to the energy imbalance problem was evaluated using the Sobol sensitivity analysis. Our results showed that the data-driven methods obtained a good estimation of EBR, and further decreased the error of evapotranspiration estimation. The data-driven solution performed well from the scale of individual site to global, which demonstrated a good generalization performance. The three machine learning algorithms had similar performances on overcoming the energy imbalance-induced structural error. Friction velocity and atmospheric stability were detected as the most sensitive factors to the energy imbalance problem, which can be explained by the vital influence of advection on the energy imbalance problem. Our work provided new insight into the improvement of evapotranspiration models.

Automated summary

This study proposed a data-driven solution to correct the structural error in energy balance-based evapotranspiration models, by utilizing machine learning algorithms to estimate instantaneous energy balance ratio (EBR) and decrease estimation errors. Environmental factors contributing to the energy imbalance problem, as well as the sensitivity of friction velocity and atmospheric stability, were evaluated and explained. The data-driven approach showed good generalization performance and the three machine learning algorithms performed similarly in overcoming the energy imbalance-induced structural error.