Abstract
Abstract. This review paper investigates the determinants of modelling choices, for numerous applications of 1-D free-surface flow and erosion equations, across multiple spatiotemporal scales. We aim to characterize each case study by its signature composed of model refinement (Navier-Stokes: NS, Reynolds-Averaged Navier-Stokes: RANS, Saint-Venant: SV or Approximations of Saint-Venant: ASV), spatiotemporal scales (domain length: L from 1 cm to 1000 km; temporal scale: T from 1 second to 1 year; flow depth: H from 1 mm to 10 m), flow typology (Overland: O, High gradient: Hg, Bedforms: B, Fluvial: F) and dimensionless numbers (Dimensionless time period T*, Reynolds number Re, Froude number Fr, Slope S, Inundation ratio Λz, Shields number θ). The determinants of modelling choices are therefore sought in the interplay between flow characteristics, cross-scale and scale-independent views. The influence of spatiotemporal scales on modelling choices is first quantified through the expected correlation between increasing scales and decreasing model refinements, identifying then flow typology a secondary but mattering determinant in the choice of model refinement. This finding is confirmed by the discriminating values of several dimensionless numbers, that prove preferential associations between model refinements and flow typologies. This review is intended to help each modeller positioning his (her) choices with respect to the most frequent practices, within a generic, normative procedure possibly enriched by the community for a larger, comprehensive and updated image of modelling strategies.