Linking parametric and water-balance models of the Budyko and Turc spaces

The Budyko and Turc frameworks have become very popular tools for the estimation of catchment-scale water balance. In their original definition, these frameworks and the resulting equations, which are considered equivalent, apply in the long-term to very large catchments, whose water balance is predominately driven by climatic factors. Several equations similar to Budyko's and Turc's have subsequently been proposed to account also for the effect of catchment characteristics, including parametric formulations as well as equations resulting from a simplified physical representation of the water balance. After highlighting their advantages and disadvantages, we show that models based on the water balance, which account for rainfall variability and feedback between water availability and evapotranspiration, are more versatile to describe catchment-scale rainfall partitioning. They include parameters that have clearer physical meaning and, therefore, can be estimated independently of streamflow and evapotranspiration, thereby making them more amenable to practical use in un-gaged catchments. They show that Budyko's and Turc's point of view are equivalent only for large catchments. Additionally, water balance models have limiting conditions for extremely dry and wet climates that differ from those of the Budyko equations and its parametric formulations, as expected in catchments with a finite water storage capacity; in these models, Budyko's and Turc's points of view become equivalent only for large catchments.