The process of evapotranspiration transfers water vapour from vegetation and soil surfaces to the atmosphere, the so-called latent heat flux (π LE), and thus crucially modulates Earthβs energy, water, and carbon cycles. Vegetation controls π LE through regulating the leaf stomata (i.e., surface resistance π s) and through altering surface roughness (aerodynamic resistance π a). Estimating π s and π a across different vegetation types proves to be a key challenge in predicting π LE. Here, we propose a hybrid modeling approach (i.e., combining mechanistic modeling and machine learning) for π LE where neural networks independently learn the resistances from observations as intermediate variables. In our hybrid modeling setup, we make use of the Penman-Monteith equation based on the Big Leaf theory in conjunction with multi-year flux measurements across different forest and grassland sites from the FLUXNET database. We follow two conceptually different strategies to constrain the hybrid model to control for equifinality arising when estimating the two resistances simultaneously. One strategy is to impose an a priori constraint on π a based on our mechanistic understanding (theory-driven strategy), while the other strategy makes use of more observational data and adds a constraint in predicting π a through multi-task learning of the latent as well as the sensible heat flux (π H ; data-driven strategy). Our results show that all hybrid models exhibit a fairly high predictive skill for the target variables with π
2 = 0.82-0.89 for grasslands and π
2 = 0.70-0.80 for forests sites at the mean diurnal scale. The predictions of π s and π a show 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, 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 overly simple ad hoc formulations in Earth system models.
