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

Abstract

The process of evapotranspiration transfers liquid water from vegetation and soil surfaces to the atmosphere, the so-called latent heat flux ( Q LE ), and modulates the Earth’s energy, water, and carbon cycle. Vegetation controls Q LE by regulating leaf stomata opening (surface resistance r s in the Big Leaf approach) and by altering surface roughness (aerodynamic resistance r a ). Estimating r s and r a across different vegetation types is a key challenge in predicting Q LE . We propose a hybrid approach that combines mechanistic modeling and machine learning for modeling Q 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 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 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 a through multi-task learning of both latent and sensible heat flux ( Q 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 s and r 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.

Estimating the CO2 Fertilization Effect on Extratropical Forest Productivity From Flux‐Tower Observations

“…However, there is a large spread in β and γ among the various land surface models. Further research should focus on identifying the origins of this inter‐model spread and testing methods where process formulations can be directly informed by the growing number of observations (e.g., ElGhawi et al., 2023). This study paves the way for future investigations into long‐term drivers of change and ecosystem functioning.…”

Integrating machine learning with analytical surface energy balance model improved terrestrial evaporation through biophysical regulation

“…The ML-based approach offers a potential solution to address the challenges associated with estimating M, especially in arid and semi-arid ecosystems or during dry seasons where traditional methods may introduce errors 16,17 . A hybrid modeling approach, integrating biophysical principles with ML, demonstrates better performance and improved generalization ability compared to purely physically-based or datadriven modeling, as suggested by existing studies e.g., Feng, et al 18 , Zhao, et al 19 , and ElGhawi, et al 20 . Machine learning algorithms, including deep learning, excel in solving nonlinear problems without requiring a priori knowledge of intrinsic mechanisms.…”

“…However, the high complexity of the Earth system and the current limitations in obtaining comprehensive observational data for the entire Earth's surface raised concerns about the generalizability of purely data-driven models for Earth system processes 19,20 . Thus, there is a growing consensus that lowering the complexity of the problems addressed by ML can contribute to the development of more robust models.…”

Feasibility of Formulating Ecosystem Biogeochemical Models From Established Physical Rules

“…For conservation rules, for example, those of mass or momentum, tradeoff M k (R l ) should be satisfied exactly, so that considering such rules is equivalent to incorporating an equality constraint, that is, error-free observations encountered in Bayesian inference or data assimilation (Basir & Senocak, 2022;Pan & Wood, 2006). When the above scaling rules are considered in the physics-based or knowledge-guided machine learning approach (ElGhawi et al, 2023;Liu et al, 2022Liu et al, , 2024, M k (R l ) represents the physical knowledge to be incorporated.…”

“…When these regularization terms are ignored, posterior models will be prone to overfitting because parameters are less well‐constrained. The need for regularization is a phenomenon widely observed in machine learning, which is the main driver for the recent surge of interest in physics‐guided machine learning (ElGhawi et al., 2023; Goodfellow et al., 2016; Liu et al., 2022). This regularization also underlies the power of “common sense” in Bloom and Williams (2015).…”