B727 FLT CREW IS DISPATCHED TO A DEST WITH INCLEMENT WX AND NO ALTERNATE DESIGNATED.

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I WAS THE DISPATCHER FOR FLT ON AUG/WED/01 AND SHARED RESPONSIBILITY WITH THE CAPT FOR THE SAFE CONDUCT OF THE FLT IN ACCORDANCE WITH FAR'S 121.627; 121.631; AND 121.557. THE SCHEDULED DEP TIME WAS XD20Z. THE XA30Z NWS FORECAST HAD PROB 40 0004 5SM-TSRA. THE NEWS AMENDED THE FORECAST FOR TVL AT XD48Z TO TEMPO XF02 5 SM-TSRA; OVCST 040 'CB.' THE SCHEDULED ARR TIME WAS XG35Z. I MISSED THE REVISED FORECAST AND ALLOWED THE ACFT TO DEPART WITHOUT AN ALTERNATE AND ONLY 35 MINS OF CONTINGENCY FUEL. IN THE 30-40 MINS PRIOR TO DEP THE WX RADAR BEGAN TO SHOW RAIN COALESCING INTO TSTMS IN THE VICINITY OF TVL. DURING THE NEXT HR THESE TSTMS CONTINUED TO BUILD. I DECIDED TO CONTACT THE FLT WHEN IT WAS IN THE VICINITY OF LITTLE ROCK. BY THAT TIME TSTMS HAD SHUT DOWN THE FIELD AT TVL. I SHOULD HAVE STOPPED THE FLT AND ADVISED THE CAPT TO OFF LAND AT LIT; BUT I ALLOWED THE OP TO CONTINUE. AS THE FLT CONTINUED; I DECIDED IN CONCURRENCE WITH THE CAPT TO DIVERT TO OKC. AT THAT TIME THERE WERE TSTMS IN THE VICINITY OF OKC. HAD OKC CLOSED; I WOULD HAVE HAD INADEQUATE FUEL TO MAKE ICT OR DFW WITHOUT DECLARING AN EMER; AND UTILIZING FAR RESERVE FUEL. I SHOULD HAVE BEEN MORE PROACTIVE AND ASSERTIVE TO ENSURE MORE VIABLE OPTIONS FOR THE CONCLUSION OF THIS FLT.