A water-desalination and carbon dioxide extraction method employs a greenhouse having a transparent, double-pane roof structure and containing an open-top receptacle for a receiving quantity of saline water or an aqueous mixture, derived from flue gas, of dissolved and suspended alkaline metal salts, which roof structure and receptacle are substantially coextensive and rectangular. A series of remotely controllable nozzles, capable of producing sheet-like discharges, withdraw the saline water or the aqueous mixture from the receptacle and discharges it into the overlying space for exposure to solar radiation passing through the roof structure, for controlled absorption of solar energy by the saline water or for effecting release carbon dioxide at elevated temperatures. Ambient air, heated during passage through channels in the transparent roof structure, may be used in a second greenhouse for promoting evaporation of free water or in other method steps.