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.

The Budyko functions are matched with the complementary evaporation relationship. We show that there is a functional dependence between the Budyko functions and the drying power of the air. Examining the case where potential evaporation is calculated by means of a Priestley–Taylor type equation with a varying coefficient, we show that this coefficient should have a specified value as a function of the Budyko shape parameter and the aridity index.

This review paper investigates the determinants of modelling choices for numerous applications of 1-D free-surface flow and morphodynamics in hydrology and hydraulics. Each case study has a signature composed of given contexts (spatiotemporal scales, flow typology, and phenomenology) and chosen concepts (refinement and subscales of the flow model). This review proposes a normative procedure possibly enriched by the community for a larger, comprehensive and updated image of modelling strategies.