A theoretical framework for critical canopy temperature and its application to improve remote-sensing-based estimation of evapotranspiration

Abstract Surface energy balance (SEB) models are widely employed for remote-sensing-based evapotranspiration estimation. A critical parameter in most SEB models is the surface temperature of wet or dry boundaries where sensible heat ( H ) or latent heat (LE) equals 0, which is difficult to measure or estimate. The wide application of SEB models is seriously limited due to this challenge. Therefore, this study introduces ‘critical canopy temperature ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cc</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> )’, defined as the canopy temperature at which LE equals 0, corresponding to the dry boundary in SEB models. We develop a physics-constrained machine learning (ML) model (hybrid model) that conserves the SEB equation to predict <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cc</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> using meteorological measurements from 103 eddy-covariance (EC) stations combined with remote-sensing data. The predicted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cc</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> is integrated into the Surface Energy Balance Algorithm for Land (SEBAL) model to replace the dry boundary, thereby to improve the estimation of LE estimation. Results demonstrate that the hybrid model effectively captures canopy temperature anomalies during stomatal closure and achieve better generalization than pure ML approaches in LE estimation, particularly under extreme conditions. Compared with conventional dry-boundary selection scheme without SEB constraints, incorporating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cc</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> significantly improve SEBAL performance, reducing the root mean square error for LE from 119.33 to 81.71 W m −2 against EC observations (at 31.52% reduction). At regional scales, the hybrid model enables pixel-level estimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cc</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , addressing the long-standing challenge of dry-boundary underrepresentation. Overall, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cc</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> hybrid model provides a robust and accurate framework for predicting theoretical dry-boundary temperatures while conserving the SEB, supporting improved monitoring of vegetation physiological status and enhancing the accuracy of SEB models.