The aircraft was cruising at 500 feet above some Sydney area beaches. Following an ATC instruction, the pilot applied full power in order to climb to 2000 feet. The engine ran roughly for a short period then lost all power and the pilot was committed to a forced landing in shallow water. Touchdown occurred about 5 metres from the shore-line and the aircraft came to rest inverted in the water. No pre-existing fault could be found with the aircraft engine or ancillaries. Atmospheric conditions were conducive to the formation of moderate carburettor icing. Carburettor heat had not been applied when the engine began to run roughly and lose power.