Hybrid Modeling of Evapotranspiration: Inferring Stomatal and
Aerodynamic Resistances Using Combined Physics-Based and Machine
Learning
Abstract
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.