Journal cover Journal topic
Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
Journal topic

Journal metrics

Journal metrics

  • IF value: 4.936 IF 4.936
  • IF 5-year value: 5.615 IF 5-year
    5.615
  • CiteScore value: 4.94 CiteScore
    4.94
  • SNIP value: 1.612 SNIP 1.612
  • IPP value: 4.70 IPP 4.70
  • SJR value: 2.134 SJR 2.134
  • Scimago H <br class='hide-on-tablet hide-on-mobile'>index value: 107 Scimago H
    index 107
  • h5-index value: 63 h5-index 63
Volume 20, issue 12
Hydrol. Earth Syst. Sci., 20, 4867–4879, 2016
https://doi.org/10.5194/hess-20-4867-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 20, 4867–4879, 2016
https://doi.org/10.5194/hess-20-4867-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 12 Dec 2016

Research article | 12 Dec 2016

The Budyko functions under non-steady-state conditions

Roger Moussa1 and Jean-Paul Lhomme2 Roger Moussa and Jean-Paul Lhomme
  • 1INRA, UMR LISAH, 2 place Viala, 34060 Montpellier, France
  • 2IRD, UMR LISAH, 2 place Viala, 34060 Montpellier, France

Abstract. The Budyko functions relate the evaporation ratio E ∕ P (E is evaporation and P precipitation) to the aridity index Φ  =  Ep ∕ P (Ep is potential evaporation) and are valid on long timescales under steady-state conditions. A new physically based formulation (noted as Moussa–Lhomme, ML) is proposed to extend the Budyko framework under non-steady-state conditions taking into account the change in terrestrial water storage ΔS. The variation in storage amount ΔS is taken as negative when withdrawn from the area at stake and used for evaporation and positive otherwise, when removed from the precipitation and stored in the area. The ML formulation introduces a dimensionless parameter HE  =  −ΔS ∕ Ep and can be applied with any Budyko function. It represents a generic framework, easy to use at various time steps (year, season or month), with the only data required being Ep, P and ΔS. For the particular case where the Fu–Zhang equation is used, the ML formulation with ΔS  ≤  0 is similar to the analytical solution of Greve et al. (2016) in the standard Budyko space (Ep ∕ P, E ∕ P), a simple relationship existing between their respective parameters. The ML formulation is extended to the space [Ep ∕ (P − ΔS), E ∕ (P − ΔS)] and compared to the formulations of Chen et al. (2013) and Du et al. (2016). The ML (or Greve et al., 2016) feasible domain has a similar upper limit to that of Chen et al. (2013) and Du et al. (2016), but its lower boundary is different. Moreover, the domain of variation of Ep ∕ (P − ΔS) differs: for ΔS  ≤  0, it is bounded by an upper limit 1 ∕ HE in the ML formulation, while it is only bounded by a lower limit in Chen et al.'s (2013) and Du et al.'s (2016) formulations. The ML formulation can also be conducted using the dimensionless parameter HP = −ΔS ∕ P instead of HE, which yields another form of the equations.

Publications Copernicus
Download
Short summary
A new physically based formulation is proposed to extend the Budyko framework under non-steady-state conditions, taking into account the change in water storage. The new formulation, which introduces an additional parameter, represents a generic framework applicable to any Budyko function at various time steps. It is compared to other formulations from the literature and the analytical solution of Greve et al. (2016) appears to be a particular case.
A new physically based formulation is proposed to extend the Budyko framework under...
Citation