AN ACR DISPATCHER ADMITS THAT HE DIVERTED AN ACFT TO A CLOSED ARPT. TO HASTEN THE OPENING OF THE ATCT; THE RPTR DIRECTED THE CAPT TO DECLARE A LOW FUEL EMER.

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FLT X WAS INBOUND TO MIA FROM EZE. THE FLT CALLED DISPATCH AND WAS CONCERNED ABOUT MIA WX WHICH WAS BELOW LNDG MINIMUMS. I HAD JUST COMPLETED A PHONE CALL TO FLL TWR TO OBTAIN CURRENT WX CONDITION. THE WX RPT I HAD SHOWED FLL WAS 3 SM BROKEN SCATTERED. I WANTED TO MAKE SURE IT WAS STILL GOOD FOR ALTERNATE MINIMUMS. THE TWR CTLR ADVISED ME THE WX WAS DETERIORATING FAST AND SURFACE VISIBILITY WAS 1/2 SM. I INFORMED FLT X OF THE WX CONDITION AT MIA AS WELL AS SURROUNDING AREA AND TOLD FLT X TO DIVERT TO NQX WHICH WX WAS 25 SCATTERED 250 SCATTERED 6 SM WHICH I JUST ATTAINED ALSO. FLT X AGREED AND STARTED TO DIVERT TO NQX. I THEN CALLED NQX TO TELL THEM THAT FLT X WAS DIVERTING. IT WAS THEN THEY INFORMED ME THE CTL TWR WAS NOT OPEN AND WOULD NEED APPROX 15 MINS TO OPEN. NOTE: THIS WAS THE FIRST TIME I REALIZED THE TWR WAS CLOSED. ALL INFO SUPPLIED TO THIS DISPATCHER BY THE ACR SHOWED THE CTL TWR OPEN 24 HRS. I ADVISED FLT X OF THE SIT AND NQX SAID IT WOULD NOT BE A PROB TO MAN THE TWR FOR HIS ETA AT NQX. JUST A FEW MINS LATER; FLT X CALLED DISPATCH AGAIN AND TOLD ME THAT ATC HAD INFORMED NQX TWR WOULD NOT OPEN FOR ANOTHER 45 MINS. I WAS ON THE PHONE AGAIN TO NQX; THEY SAID IT WAS HAVING A SMALL PROB OF GETTING PERSONNEL TO THE TWR; BUT SOMEONE SHOULD BE AT THE TWR IN APPROX 7 MINS. I PASSED THIS INFO TO THE FLT AND TOLD THEM TO CONTINUE TO NQX. CAPT Y THEN ADVISED ME THAT ATC TOLD HIM MIA HAD 1 SM VISIBILITY; AND HE WAS HEADED BACK TO MIA SINCE HE WAS ABOUT TO GO INTO HIS RESERVE FUEL. I THEN AGAIN EXPLAINED TO CAPT Y THAT THE SURROUNDING AREA WX WAS STILL DETERIORATING AND THAT THE FLT DIDN'T HAVE ADEQUATE FUEL TO MAKE AN APCH INTO MIA AND MAINTAIN AN ALTERNATE WHICH WAS NEEDED. I ASKED CAPT Y TO DECLARE A LOW FUEL EMER INTO NQX TO EXPEDITE THE MANNING OF NQX TWR. HE AGREED. I THEN CALLED ZMA TO ADVISE THEM AS WELL AS THE NQX PERSONNEL AND TOLD THEM THAT FLT X HAD DECLARED A LOW FUEL EMER IN NQX. THEY TOLD ME THAT THE TWR WOULD BE OPEN IN LESS THAN 2 MINS. BY THE TIME I FINISHED THE PHONE CALL WITH NQX; FLT X WAS CALLING DISPATCH TO ADVISE ME THAT NQX TWR WAS OPEN AND THE RWY LIGHTS ON. IF I HAD KNOWN THAT NQX TWR WAS NOT AVAILABLE/OPEN ON THE 24 HR BASIS AS INDICATED IN OUR ARPT REFS; I WOULD HAVE INSTRUCTED FLT X TO MAKE AN ENRTE LNDG AT EITHER MBJ OR KIN AS I HAVE DONE BEFORE FOR ADDITIONAL FUEL WHEN WX CONDITIONS AT MIA WARRANTED IT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ACFT INVOLVED WAS AN MD11. THE RWY LIGHTS ARE NOT ON AT NQX WHEN THE ATCT IS CLOSED. THE CAT III APCH TO MIA WAS UNAVAILABLE. NQX WAS THE ONLY VMC ARPT IN REACH OF THE ACFT AND THE ONLY ARPT THAT DID NOT NEED AN ALTERNATE FOR DISPATCH OR REDISPATCH. THE RPTR'S ACR PUBLISHED A MEMO THE DAY OF THIS INCIDENT INFORMING THE DISPATCHERS THAT NQX WAS NO LONGER A 24 HR ARPT.