We study a 3-D generalization of Budyko's framework that captures the interdependence among actual and potential evapotranspiration and precipitation. We demonstrate that Budyko-type equations present an inconsistency in humid environments, which we overcome by proposing a physically consistent power law that incorporates the complementary relationship of evapotranspiration into the Budyko curve. Evidence of space-time symmetry and signs of co-evolution of catchments are also found in Amazonia.