A correspondence is established between flows of air above stationary water, and flows of water below air at atmospheric pressure. Flows in the latter category are well studied, and all such hydrodynamic flows can be "turned upside-down" to generate flows of air in which the free surface deforms under gravity, due to a balance between aerodynamic and hydrostatic pressures. Examples are given of some exact inverse solutions, and a general semiinverse approach is outlined for numerical solutions via an integral formulation.