WX ENCOUNTER DURING LNDG.

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ON A RECENT FLT FROM ORD TO SRQ SCHEDULED TO ARRIVE AT ABOUT XX30. THE WX AT DEST WAS PROJECTED TO BE CLOSE TO MINS REQUIRING A LNDG ALTERNATE WHICH HAPPENED TO BE RSW WITH A FORECAST OF CLR AND 10. CHKING THE WX OF DEST AND ALTERNATE ENRTE SHOWED A DETERIORATION OF THE DEST WX TO MINS WITH EQUAL TEMP/DEW POINT IN FOG HOWEVER THE ALTERNATE WAS STILL CLR AND 10. AFTER 2 APCHS AT SRQ; THE FIRST ABANDONED AT 800 FT DUE TO CAPT'S LOC FAILURE; AND THE SECOND DUE TO DECREASING VISIBILITY; WE HEADED TOWARD OUR PLANNED DIVERSION STATION. AFTER BEING SWITCHED TO MIA CTR; WE CHKED THE RSW WX AND WERE RELIEVED TO FIND IT WAS STILL CLR AND 10 BUT NOW MIA CTR INFORMED US THAT THE TWR WAS CLOSED AT RSW AND THE APCH END OF RWY 6 WAS BLOCKED BY A WDB AND THAT WE SHOULD CONSIDER A VISUAL APCH TO RWY 24. BY NOW WE WERE ABOUT 20 MI FROM RSW WITH 1 HR OF FUEL LEFT. SINCE IT WAS VFR AND WE COULD SEE THE ARPT; WE DECIDED TO TAKE A LOOK AT THE WDB TO SEE WHAT KIND OF AN OBSTRUCTION WE WERE DEALING WITH. WE WERE ADVISED AT THIS TIME BY MIA CTR TO CLOSE OUT OUR FLT PLAN WITH HIM WHEN WE GOT ON THE GND. WE TRIED TO RAISE SOMEONE ON UNICOM WITH NO LUCK; HOWEVER WE WERE ABLE TO CONTACT COMPANY OPS AT RSW AND THEY ADVISED US THAT THE TWR WAS STILL MANNED. SO WE SWITCHED TO TWR FREQ WHILE CONTINUING FOR A VISUAL TO 24 ALTHOUGH IT APPEARED THAT THE WDB WAS NOT ON THE RWY AT ALL. IT WAS LOCATED ON THE TAXIWAY HOLDING SHORT OF 24. THIS INFO WAS CONFIRMED BY THE TWR WHICH THEN CLRED US FOR LNDG ON RWY 6 SO WE CIRCLED TO THE S AND LANDED ON 6. WITH THE TEMP/DEW POINT EQUAL AT RSW; EVEN THOUGH THE ATIS WAS ADVERTISING CLR AND 10; OUR DSCNT TO THE RWY WAS IN THE CLR UNTIL THE LAST 50 FT ABOVE THE GND WHEN PATCHY FOG DEVELOPED RAPIDLY PARTIALLY OBSCURING THE RWY. FORTUNATELY WE WERE ABLE TO COMPLETE A SUCCESSFUL LNDG BEFORE THE FOG OBLITERATED THE RWY COMPLETELY.