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

Abstract

Abstract The process of evapotranspiration transfers liquid water from vegetation and soil surfaces to the atmosphere, the so-called latent heat flux ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>LE</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ), and modulates the Earth’s energy, water, and carbon cycle. Vegetation controls <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>LE</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> by regulating leaf stomata opening (surface resistance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mtext>s</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> in the Big Leaf approach) and by altering surface roughness (aerodynamic resistance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mtext>a</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). Estimating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mtext>s</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mtext>a</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> across different vegetation types is a key challenge in predicting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>LE</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . We propose a hybrid approach that combines mechanistic modeling and machine learning for modeling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>LE</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>LE</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>r</mml:mi> <mml:mrow> <mml:mtext>a</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> based on mechanistic assumptions (theory-driven strategy),

Topics & Concepts