Does a link exist between rainfall-runoff models at the interannual time step?
Over time steps of several years, the water balance approach provides rainfall-runoff models as simple mathematical formulations linking runoff (Q) to rain (P) and the potential evapotranspiration (E), expressed in millimetres per year (mm•year-1). Generally, the runoff is estimated by the difference between rainfall and actua; evapotranspiration. The other terms of the balance are assumed to be negligible. For a better use and understanding of this type of model, this paper addresses the following questions: Which relations exist among models? What are their performances and their limits? How could their performances be improved? Answering these questions first required the choice of the most widespread models from the hydrological literature: we looked for expressions using usual mathematical shapes such as the hyperbolic tangent or exponential. Then, using an nondimensional analysis, the general shape of these models as well as their domain of definition was defined. By adapting a methodology of modeling to the several-year time step requirement, and using data from 407 catchments with diverse hydro-climatic features, we determined how the performance of the models could be improved: either by introducing a parameter linked to the evapotranspiration, or by introducing a new variable, the Rain Distribution Indication (IRP), depending on data availability.