B757-200 CAPT'S EXERCISE OF COMMAND AUTHORITY TO AVOID THUNDERSTORMS IS DISPUTED BY ARTCC RADAR CTLR.

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30 MI NW OF ZZZ; FL350; CAPT IDENTS LINE OF WX TOPS ABOVE FL350; MOVING VERY RAPIDLY; STEEP GRADIENT IN CALIBRATED MODE; SCALLOPED EDGES; WINDS PARALLEL AT 120 KTS; PRONOUNCED RADAR SHADOW BEYOND. CAPT DECIDES THIS IS AN AREA OF POTENTIALLY SEVERE TURB. CAPT ASKS ATC WHICH WAY FLTS DEVIATING. ATC ADVISES NOT PRACTICAL DUE DISTANCE REQUIRED TO DEVIATE. CAPT ADVISES ABC TO FLTS LEFT LOOKS LIKE BEST SPOT TO TRAVERSE THE LINE. ATC ADVISES CAPT THAT FLT WOULD HAVE TO DEVIATE TO ZZZ TO GET AROUND WX AND THAT FLT COULD GO STRAIGHT AHEAD; HOWEVER IT 'WOULDN'T BE MUCH FUN.' CAPT DECLINES FURTHER PROGRESS AND REQUESTS DIRECT ABC. ATC ADVISES 'STAND BY.' FREQ CONGESTION PREVENTS FURTHER DISCUSSION. CAPT CHKS TCAS AND TURNS L. INTENDS TO EXERCISE CAPT'S EMER AUTH. ATC QUERIES FLT ABOUT TURN. CAPT OFFERS UP CAPT'S EMER AUTH. ATC DECLINES; HOWEVER; WITH A LECTURE ON THE DANGERS OF TURNING WITHOUT ATC CONCURRENCE. CAPT ADVISES THAT FURTHER FLT WOULD HAVE PUT ACFT IN HARM'S WAY. ATC OFFERS OPINION THAT FLT WAS IN THE CLR. ATC NOT CONSIDERING RADIUS OF TURN. CAPT CAN GUARANTEE STRAIGHT AHEAD PENETRATION WOULD HAVE BEEN DISASTROUS. CAPT DELAYED INITIATION OF TURN AS LONG AS POSSIBLE IN A FAILED ATTEMPT TO GET AN AMENDED CLRNC. THIS TURN NOT A MATTER OF CONVENIENCE BUT INSTEAD SAFETY.