@article{fdi:010068805,
  title = {{T}he {B}udyko functions under non-steady-state conditions},
  author = {{M}oussa, {R}. and {L}homme, {J}ean-{P}aul},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he {B}udyko functions relate the evaporation ratio {E} / {P} ({E} is evaporation and {P} precipitation) to the aridity index {P}hi = {E}-p = {P} ({E}-p is potential evaporation) and are valid on long timescales under steady-state conditions. {A} new physically based formulation (noted as {M}oussa-{L}homme, {ML}) is proposed to extend the {B}udyko framework under non-steady-state conditions taking into account the change in terrestrial water storage {D}elta {S}. {T}he variation in storage amount {D}elta {S} is taken as negative when withdrawn from the area at stake and used for evaporation and positive otherwise, when removed from the precipitation and stored in the area. {T}he {ML} formulation introduces a dimensionless parameter {H}-{E} = -{D}elta {S} / {E}-p and can be applied with any {B}udyko function. {I}t represents a generic framework, easy to use at various time steps (year, season or month), with the only data required being {E}-p, {P} and {D}elta {S}. {F}or the particular case where the {F}u-{Z}hang equation is used, the {ML} formulation with {D}elta {S} <= 0 is similar to the analytical solution of {G}reve et al. (2016) in the standard {B}udyko space ({E}p / {P}, {E} / {P}), a simple relationship existing between their respective parameters. {T}he {ML} formulation is extended to the space [{E}-p / {P} - {D}elta {S}), {E} / ({P} - {D}elta {S})] and compared to the formulations of {C}hen et al. (2013) and {D}u et al. (2016). {T}he {ML} (or {G}reve et al., 2016) feasible domain has a similar upper limit to that of {C}hen et al. (2013) and {D}u et al. (2016), but its lower boundary is different. {M}oreover, the domain of variation of {E}-p - ({P} - {D}elta {S}) differs: for {D}elta {S} <= 0, it is bounded by an upper limit 1 / {H}-{E} in the {ML} formulation, while it is only bounded by a lower limit in {C}hen et al.'s (2013) and {D}u et al.'s (2016) formulations. {T}he {ML} formulation can also be conducted using the dimensionless parameter {H}-{P} = -{D}elta {S} / {P} instead of {H}-{E}, which yields another form of the equations.},
  keywords = {},
  booktitle = {},
  journal = {{H}ydrology and {E}arth {S}ystem {S}ciences},
  volume = {20},
  numero = {12},
  pages = {4867--4879},
  ISSN = {1027-5606},
  year = {2016},
  DOI = {10.5194/hess-20-4867-2016},
  URL = {https://www.documentation.ird.fr/hor/fdi:010068805},
}