Hybrid modeling of evapotranspiration: inferring stomatal and aerodynamic resistances using combined physics-based and machine learning

The process of evapotranspiration transfers liquid water from vegetation and soil surfaces to the atmosphere, the so-called latent heat flux ( ${Q_{{\text{LE}}}}$ ), and modulates the Earth’s energy, water, and carbon cycle. Vegetation controls ${Q_{{\text{LE}}}}$ by regulating leaf stomata opening (surface resistance ${r_{\text{s}}}$ in the Big Leaf approach) and by altering surface roughness (aerodynamic resistance ${r_{\text{a}}}$ ). Estimating ${r_{\text{s}}}$ and ${r_{\text{a}}}$ across different vegetation types is a key challenge in predicting ${Q_{{\text{LE}}}}$ . We propose a hybrid approach that combines mechanistic modeling and machine learning for modeling ${Q_{{\text{LE}}}}$ . The hybrid model combines a feed-forward neural network which estimates the resistances from observations as intermediate variables and a mechanistic model in an end-to-end setting. In the hybrid modeling setup, we make use of the Penman–Monteith equation in conjunction with multi-year flux measurements across different forest and grassland sites from the FLUXNET database. This hybrid model setup is successful in predicting ${Q_{{\text{LE}}}}$ , however, this approach leads to equifinal solutions in terms of estimated physical parameters. We follow two different strategies to constrain the hybrid model and therefore control for the equifinality that arises when the two resistances are estimated simultaneously. One strategy is to impose an a priori constraint on ${r_{\text{a}}}$ based on mechanistic assumptions (theory-driven strategy), while the other strategy makes use of more observational data and adds a constraint in predicting ${r_{\text{a}}}$ through multi-task learning of both latent and sensible heat flux ( ${Q_{\text{H}}}$ ; data-driven strategy) together. Our results show that all hybrid models predict the target variables with a high degree of success, with ${R^2}$ = 0.82–0.89 for grasslands and ${R^2}$ = 0.70–0.80 for forest sites at the mean diurnal scale. The predicted ${r_{\text{s}}}$ and ${r_{\text{a}}}$ show strong physical consistency across the two regularized hybrid models, but are physically implausible in the under-constrained hybrid model. The hybrid models are robust in reproducing consistent results for energy fluxes and resistances across different scales (diurnal, seasonal, and interannual), reflecting their ability to learn the physical dependence of the target variables on the meteorological inputs. As a next step, we propose to test these heavily observation-informed parameterizations derived through hybrid modeling as a substitute for ad hoc formulations in Earth system models.