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https://doi.org/10.5194/egusphere-2025-1124
https://doi.org/10.5194/egusphere-2025-1124
20 Mar 2025
 | 20 Mar 2025

New derivation and interpretation of the complementary relationship for evapotranspiration

Sha Zhou and Bofu Yu

Abstract. The complementary relationship (CR) between actual evapotranspiration (ET) and apparent potential evapotranspiration (PETa) is widely used as a simple yet effective method for ET estimation. However, most existing CR formulations are empirical, lacking rigorous derivation based on physics. In this study, the complementary relationship was derived analytically with a physically meaningful parameter: the wet Bowen ratio, defined as the Bowen ratio when the surface becomes saturated. This parameter can be computed from observations without calibration. Fundamentally, the CR is shown to originate from partitioning of the net radiation, with ET directly linked to the latent heat and PETa proportional to the sensible heat. Additionally, ET is linearly related to and constrained by the energy-based potential evapotranspiration (PETe). The physically-based relationship among ET, PETa, and PETe has important implications for our understanding of the spatial and temporal variations in ET and would promote practical application of the complementary relationship for ET estimation across different environments.

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Sha Zhou and Bofu Yu

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2025-1124', Anonymous Referee #1, 21 Mar 2025
    • AC1: 'Reply on RC1', Sha Zhou, 24 Mar 2025
      • RC2: 'Reply on AC1', Anonymous Referee #1, 25 Mar 2025
        • AC2: 'Reply on RC2', Sha Zhou, 26 Mar 2025
  • RC3: 'Comment on egusphere-2025-1124', Anonymous Referee #2, 01 Jul 2025

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2025-1124', Anonymous Referee #1, 21 Mar 2025
    • AC1: 'Reply on RC1', Sha Zhou, 24 Mar 2025
      • RC2: 'Reply on AC1', Anonymous Referee #1, 25 Mar 2025
        • AC2: 'Reply on RC2', Sha Zhou, 26 Mar 2025
  • RC3: 'Comment on egusphere-2025-1124', Anonymous Referee #2, 01 Jul 2025
Sha Zhou and Bofu Yu

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Short summary
Accurate estimation of evapotranspiration is of considerable importance to hydrology, ecology, and agriculture. The complementary relationship between actual and apparent potential evapotranspiration provides a simple yet powerful framework for evapotranspiration estimation. We derive an alternative complementary relationship with a physically meaningful parameter. It has distinct advantages over existing ones in terms of its sound physical basis and practical applications without calibration.
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