In search of catchment-scale hydrological laws: learning from the long-term water balance formulas

In our search for emergent catchment-scale hydrological laws, we discuss here how a class of widely-used water-balance formulas (Turc-Mezentsev and Tixeront-Fu) were conceived by their authors more than 60 years ago. Because these water balance formulas deal with long-term quantities, we discuss various attempts to downscale them temporally, and progressively integrate mathematical formulations able to account for both the short-term (seasonnal) and long-term (multi-year) hydrologial memory observed in catchment systems.

References

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Mezentsev, V.: Back to the computation of total evaporation, Meteorologia i Gidrologia, 5, 24–26, 1955. 

Tixeront, J.: Prediction of streamflow (in French: Prévision des apports des cours d'eau), in: IAHS publication no. 63: General Assembly of Berkeley, IAHS, Gentbrugge, 118–126, available at: http://hydrologie.org/redbooks/a063/063013.pdf (last access: 1 May 2019), 1964. 

Turc, L.: The water balance of soils: relationship between precipitations, evaporation and flow (in French: Le bilan d'eau des sols: relation entre les précipitations, l'évaporation et l'écoulement), Annales Agronomiques, Série A, IV, 491–595, 1954.