The exponential store: a correct formulation for rainfall-runoff modelling

Stores are widely used tools in conceptual soil-moisture accounting rainfall-runoff models. Various mathematical laws are used to describe the outflow of such stores. The exponential store has received less attention than the linear store, but it has proved to be a highly efficient tool in streamflow modelling. The aim of this study is to show that the common way of dealing with this store-without integration in time-is mathematically and physically flawed. This misuse can result in poorer reliability and efficiency of rainfall-runoff models that include such a store. Surprisingly, this inconsistency had a significant impact on only a limited number of catchments among the 138 used to carry out the tests. However, it can have dramatic consequences for the simulation of large flood events. Therefore, an exact discrete formulation should be preferred in rainfall-runoff models.