Articles | Volume 23, issue 5
https://doi.org/10.5194/hess-23-2339-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-23-2339-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical Note: On the puzzling similarity of two water balance formulas – Turc–Mezentsev vs. Tixeront–Fu
Vazken Andréassian
CORRESPONDING AUTHOR
Irstea, HYCAR Research Unit, Antony, France
Tewfik Sari
ITAP, Univ. Montpellier, Irstea, Montpellier SupAgro, Montpellier, France
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Cited
18 citations as recorded by crossref.
- Linking parametric and water-balance models of the Budyko and Turc spaces E. Daly et al. https://doi.org/10.1016/j.advwatres.2019.103435
- Persistent performance of the power-function complementary relationship in Earth system models under a warming scenario S. Im et al. https://doi.org/10.1016/j.jhydrol.2026.135813
- A structural correction to atmospheric evaporative demand narrows the gap between offline aridity diagnostics and Earth system model projections D. Kim & M. Choi https://doi.org/10.1038/s41612-025-01306-3
- Runoff sensitivity increases with land use/cover change contributing to runoff decline across the middle reaches of the Yellow River basin Y. Wang et al. https://doi.org/10.1016/j.jhydrol.2021.126536
- Decoupling of precipitation and streamflow trends induced by forest expansion: Evidence from time-varying Budyko analysis T. Lee et al. https://doi.org/10.1016/j.ejrh.2026.103317
- Streamflow elasticity as a function of aridity V. Andréassian et al. https://doi.org/10.5194/hess-30-1865-2026
- Budyko framework; towards non-steady state conditions A. Mianabadi et al. https://doi.org/10.1016/j.jhydrol.2020.125089
- Revisiting a Two‐Parameter Budyko Equation With the Complementary Evaporation Principle for Proper Consideration of Surface Energy Balance D. Kim & J. Chun https://doi.org/10.1029/2021WR030838
- Technical note: Do different projections matter for the Budyko framework? R. Nijzink & S. Schymanski https://doi.org/10.5194/hess-26-4575-2022
- Modeling the Distribution of Wild Cotton Gossypium aridum in Mexico Using Flowering Growing Degree Days and Annual Available Soil Water A. Baez-Gonzalez et al. https://doi.org/10.3390/su14116383
- Budyko-Type Models and the Proportionality Hypothesis in Long-Term Water and Energy Balances F. Paz Pellat et al. https://doi.org/10.3390/w14203315
- Theoretical and empirical evidence against the Budyko catchment trajectory conjecture N. Reaver et al. https://doi.org/10.5194/hess-26-1507-2022
- Modeling streamflow variability at the regional scale: (1) perceptual model development through signature analysis F. Fenicia & J. McDonnell https://doi.org/10.1016/j.jhydrol.2021.127287
- Constraining the power-function complementary relationship with a steady-state Budyko equation for predicting terrestrial evapotranspiration globally D. Kim et al. https://doi.org/10.1016/j.agrformet.2023.109808
- Budyko Framework Based Analysis of the Effect of Climate Change on Watershed Evaporation Efficiency and Its Impact on Discharge Over Europe J. Collignan et al. https://doi.org/10.1029/2023WR034509
- Extra constraint on actual evaporation in a semi-distributed conceptual model to improve model physical realism S. Hsu et al. https://doi.org/10.1080/02626667.2025.2468846
- Loss and Gain in Potential Distribution of Threatened Wild Cotton Gossypium thurberi in Mexico under Future Climate A. Baez-Gonzalez et al. https://doi.org/10.3390/su142013144
- Blending the Evaporation Precipitation Ratio With the Complementary Principle Function for the Prediction of Evaporation L. Zhang & W. Brutsaert https://doi.org/10.1029/2021WR029729
18 citations as recorded by crossref.
- Linking parametric and water-balance models of the Budyko and Turc spaces E. Daly et al. https://doi.org/10.1016/j.advwatres.2019.103435
- Persistent performance of the power-function complementary relationship in Earth system models under a warming scenario S. Im et al. https://doi.org/10.1016/j.jhydrol.2026.135813
- A structural correction to atmospheric evaporative demand narrows the gap between offline aridity diagnostics and Earth system model projections D. Kim & M. Choi https://doi.org/10.1038/s41612-025-01306-3
- Runoff sensitivity increases with land use/cover change contributing to runoff decline across the middle reaches of the Yellow River basin Y. Wang et al. https://doi.org/10.1016/j.jhydrol.2021.126536
- Decoupling of precipitation and streamflow trends induced by forest expansion: Evidence from time-varying Budyko analysis T. Lee et al. https://doi.org/10.1016/j.ejrh.2026.103317
- Streamflow elasticity as a function of aridity V. Andréassian et al. https://doi.org/10.5194/hess-30-1865-2026
- Budyko framework; towards non-steady state conditions A. Mianabadi et al. https://doi.org/10.1016/j.jhydrol.2020.125089
- Revisiting a Two‐Parameter Budyko Equation With the Complementary Evaporation Principle for Proper Consideration of Surface Energy Balance D. Kim & J. Chun https://doi.org/10.1029/2021WR030838
- Technical note: Do different projections matter for the Budyko framework? R. Nijzink & S. Schymanski https://doi.org/10.5194/hess-26-4575-2022
- Modeling the Distribution of Wild Cotton Gossypium aridum in Mexico Using Flowering Growing Degree Days and Annual Available Soil Water A. Baez-Gonzalez et al. https://doi.org/10.3390/su14116383
- Budyko-Type Models and the Proportionality Hypothesis in Long-Term Water and Energy Balances F. Paz Pellat et al. https://doi.org/10.3390/w14203315
- Theoretical and empirical evidence against the Budyko catchment trajectory conjecture N. Reaver et al. https://doi.org/10.5194/hess-26-1507-2022
- Modeling streamflow variability at the regional scale: (1) perceptual model development through signature analysis F. Fenicia & J. McDonnell https://doi.org/10.1016/j.jhydrol.2021.127287
- Constraining the power-function complementary relationship with a steady-state Budyko equation for predicting terrestrial evapotranspiration globally D. Kim et al. https://doi.org/10.1016/j.agrformet.2023.109808
- Budyko Framework Based Analysis of the Effect of Climate Change on Watershed Evaporation Efficiency and Its Impact on Discharge Over Europe J. Collignan et al. https://doi.org/10.1029/2023WR034509
- Extra constraint on actual evaporation in a semi-distributed conceptual model to improve model physical realism S. Hsu et al. https://doi.org/10.1080/02626667.2025.2468846
- Loss and Gain in Potential Distribution of Threatened Wild Cotton Gossypium thurberi in Mexico under Future Climate A. Baez-Gonzalez et al. https://doi.org/10.3390/su142013144
- Blending the Evaporation Precipitation Ratio With the Complementary Principle Function for the Prediction of Evaporation L. Zhang & W. Brutsaert https://doi.org/10.1029/2021WR029729
Saved (final revised paper)
Latest update: 09 Jun 2026
Short summary
In this Technical Note, we present two water balance formulas: the Turc–Mezentsev and Tixeront–Fu formulas. These formulas have a puzzling numerical similarity, which we discuss in detail and try to interpret mathematically and hydrologically.
In this Technical Note, we present two water balance formulas: the Turc–Mezentsev and...