MD11 CREW HAD TO EXERCISE EMER AUTH TO AVOID CONVECTIVE WX ON THEIR ASSIGNED TRACK.

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DECLARATION OF EMER; DEV AROUND WX. I WAS RELIEF PLT ON TRIP AND WAS IN BACK OF THE ACFT. WHEN I RETURNED TO THE COCKPIT; THE CAPT INFORMED ME OF THE FOLLOWING. AT XX49Z WHILE ESTABLISHED ON TRACK D; THE CAPT AND FO OBSERVED SUBSTANTIAL WX IN OUR PATH. THE TSTMS WERE ESTIMATED TO TOP OUT AT FL330; WE WERE FLYING AT FL310. THE CAPT REQUESTED A HIGHER ALT FROM GANDER RADIO AND WAS DENIED DUE TO CONFLICTING TFC. THE CAPT THEN REQUESTED A DEV OFF OF TRACK D TO THE N. AGAIN; THE REQUEST WAS DENIED AND HE WAS DIRECTED TO DEV S OF COURSE. A SOUTHERLY DEV WOULD HAVE PUT THE ACFT INTO THE HEART OF THE TSTM; AND THE CAPT ELECTED TO DECLARE AN EMER AND DEVIATE N OF COURSE. THE APPROX DEV OFF COURSE WAS 6-8 NM. AS I RE-ENTERED THE COCKPIT AFTER MY BREAK; THE CAPT AND FO WERE IN THE PROCESS OF REJOINING THE PUBLISHED TRACK D. GANDER HAD ALSO CLRED US TO FL320 BY THIS TIME; AND THE ACFT WAS LEVELING AT THE NEWLY ASSIGNED FLT LEVEL. THE DISPATCH DESK WAS NOTIFIED AT YY55 OF THE SIT VIA SATCOM. DISPATCH LATER INDICATED THAT THEY HAD CONTACTED GANDER AND THAT GANDER CONSIDERED THE MATTER CLOSED WITH NO FURTHER ACTION ON ANYONE'S PART.