This study discusses the role of the aridity index in controlling the long-term fluxes of direct (Qd) and baseflow (Qd). Here we present an analytical derivation starting from similar assumptions as the one presented in the original work of Budyko that leads to two simple expressions for the control of the aridity index on Qb and Qd. These two analytical equations can be combined into a single expression with the same properties as the original Budyko equation. Our study provides a method for predicting long term baseflow and direct runoff for poorly gaged basins as well as permit the derivation of sensitivity equations for the assessment of the impact of these fluxes with respect to changes in aridity index.