B757 FLIGHT CREW REPORTS EXERCISING CAPTAINS EMERGENCY AUTHORITY WHEN CENTER CANNOT AUTHORIZE A TURN TO AVOID BUILD UPS. TURBULENCE IS ENCOUNTERED AS AIRCRAFT PASSES THROUGH CLOUD IN TURN.

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TKOF AND CLB FROM ZZZ IN LIGHT OCCASIONAL MODERATE TURB. ACFT ENTERED IMC APPROX 2000 FT AGL. RADAR SHOWED LINE OF WX 10 NM N OF AND PARALLEL TO ACFT TRACK. NUMEROUS CELLS WITH LEVEL 3 INTENSITY; EACH A FEW MI WIDE WITH GOOD GAPS IN BTWN. NO RADAR RETURNS DISPLAYED IN FRONT OF ACFT PATH. CLRED TO CLB AND MAINTAIN 10000 FT ON A HDG OF 270M DEG. AUTOPLT ENGAGED. STILL IMC WITH MODERATE TURB. HANDED OFF FROM ZZZ DEP CTL TO CTR. WE ATTEMPTED TO MAKE CONTACT; BUT WERE UNABLE DUE TO FREQ CONGESTION. WE THEN BROKE OUT OF WX INTO THE CLR AND SAW NUMEROUS; TIGHTLY DEFINED CUMULUS CLOUDS IN OUR PATH. TOPS WERE ESTIMATED AT 16000 FT WITH NUMEROUS 'VALLEYS' IN BTWN SLIGHTLY ABOVE OUR ALT. NONE DISPLAYED ON OUR WX RADAR REGARDLESS OF TILT ANGLE. AFTER A FEW MORE ATTEMPTS; WE ESTABLISHED CONTACT WITH CTR AND REQUESTED HIGHER OR A NEW HDG FOR WX AVOIDANCE. WE WERE TOLD TO MAINTAIN HDG AND ALT. ALL ACFT WERE TOLD TO JUST STAND BY BECAUSE HE WAS QUITE BUSY. I INITIATED A TURN TO THE N TO AVOID WX AND ASKED MY FO TO TELL CTR WE WERE TURNING FOR WEATHER. AFTER A FEW ATTEMPTS HE GOT THE MESSAGE OUT. CTR THEN REPLIED TO MAINTAIN HDG 270 DEGS. I TOOK THE RADIO AND BROADCAST THAT WE WERE TURNING TO HDG 350 DEGS ON CAPT'S EMER AUTH FOR WX AVOIDANCE. THERE WAS NO IMMEDIATE REPLY FROM CTR. DURING THE TURN I REDUCED SPD FROM 280 KIAS TO 250 KTS; AND SET MAX BANK OF 30 DEG ON AUTOPLT TO REDUCE RADIUS OF TURN. DESPITE EFFORTS WE ENTERED THE EDGE OF THE WX. HVY TURB ENCOUNTERED WITH DEVS OF +/-30-40 KIAS AND +/-600 FPM. ACTUAL ALTDEVS WERE +/-300 FT. AUTOPLT REMAINED ENGAGED AND WE EXITED THE WX AFTER APPROX 30 SECONDS. RIDE IMPROVED; WITH CONCURRENCE OF CTR WE TURNED BACK TO THE W AND RESUMED FLT WITH NO FURTHER DIFFICULTIES. NO KNOWN TFC CONFLICTS. NO INJURIES RPTED FROM CREW OR PAX. NO APPARENT ACFT DAMAGE NOTED. IN AN ABUNDANCE OF CAUTION WE ENTERED AN ITEM IN THE ACFT LOGBOOK TO REFLECT TURB ENCOUNTERED. MAINT REMOVED ACFT FROM SVC TO PERFORM REQUIRED CHKS. I DO NOT KNOW THE RESULTS OF THAT INSPECTION.