Linking stream flow to rainfall at the annual time step: The Manabe bucket model revisited

Trying to determine annual stream flow only from annual rainfall and possibly annual potential evapotranspiration is a challenge that forces hydrologists to focus on very basic questions such as: Is stream flow of the current year only dependent on this year’s rainfall? Does previous years’ rainfall play a role? Is the role, if any, of antecedent rainfall confined to the transfer function, to the production function or both? How much complexity (i.e. how many free parameters) is required to describe the rainfall–runoff transformation at the annual time step? Our analysis starts with the bucket model of Manabe [Manabe, S., 1969. Climate and the ocean circulation. 1. The atmospheric circulation and the hydrology of the Earth’s surface. Mon. Weather Rev. 97(11), 739–774]. We assess this model using data from a large set of basins located in five different countries. We follow a new approach to compare the Manabe model performance to that of other models. The poor relevance of this model at the annual time step is demonstrated, and we put forward a new model that is both simple and clearly better than Manabe bucket model. This model provides new insight on crucial questions raised in the area of annual rainfall–runoff modelling.