A FLC UNDERSTOOD THAT THEY WERE ON A VECTOR FOR AN APCH WHICH THEY DID NOT RECEIVE. THEY COMPLIED WITH THE 'NEW' APCH ON RAW DATA; BUT FAILED TO MAINTAIN RADIAL INBOUND; AND CTLR CALLED 'LOW ALT ALERT.'

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PBI ATIS RPTED 6 SCATTERED; 47 SCATTERED; 60 SCATTERED; 10 MI PLUS VISIBILITY; LOC BC RWY 27R IN USE. ABOUT 5 MI S OF KEACH FAF; THE CTLR TURNED AND CLRED US FOR THE VOR RWY 31 APCH; WHICH WE WEREN'T SET UP FOR. WE TUNED OUR VORS; AND APCH COURSE WHICH; INITIALLY; SHOWED US ON COURSE. WE BEGAN OUR DSCNT TO FAF ALT. WINDS; OR WHATEVER; FULLY DISPLACED OUR COURSE SO WE INITIATED A MAP AROUND 1200 FT. AT THE SAME TIME THE CTLR CALLED OUR 'LOW ALT ALERT' AND ISSUED A MISSED APCH CLRNC. WE FOLLOWED THE MAP INSTRUCTIONS; FOLLOWED BY THE LOC BC RWY 27R AND LANDED. CONTRIBUTING FACTORS: 1) ATIS: INDICATED VFR CONDITIONS AT THE FIELD WHEN A MAJOR WX SYS WAS PASSING OVER THE FIELD. 2) COMS: WE WERE NEVER TOLD OF THE VOR RWY 31 APCH UNTIL FINAL TURN. SUPPLEMENTAL INFO FROM ACN 296993: ON VECTOR FOR RWY 27R LOC BACK COURSE TO PBI AND WITHIN 4 MI OF SAME FIX; CTLR CLRED US FOR VOR RWY 31 APCH. I USED RAW DATA SOURCE SINCE TIME DID NOT ALLOW FOR A FMS SET UP. WE EXPERIENCED A SPD VARIATION OF PLUS OR MINUS 15 KTS AT 200-300 FT TO RWY 27R. TIME WAS A PROB AND THE CONFUSION AS TO CORRECT RWY WHILE ON A VECTOR COMPOUNDED THE PROB BECAUSE OF OUR PROX TO INBOUND COURSE. ALSO; OTHER ACFT WERE GIVEN RWY 31 VOR APCH; THIS IS THE REASON I HAD THE CHART OUT; BUT THE LACK OF COMS BY APCH DID NOT ALLOW FOR PROPER PREPARATIONS.