DISPATCHER ADVISES FLT CREW TO DIVERT TO ALT DUE TO WX AT DEST.

Narrative

FLT WAS AIRBORNE WHEN I STARTED MY SHIFT; AND IT WAS SCHEDULED TO ARRIVE AT XC00Z. ZZZ FORECAST CALLED FOR POSSIBLE 500 METER VISIBILITY AT ARR TIME. ZZZ ILS RWY 9L CAT II HAS MINIMUMS OF 400 METERS VISIBILITY. THIS FLT WAS PLANNED WITH ALTERNATES OF XXX AND YYY. AT XA53Z; ZZZ VISIBILITY DROPPED TO 200 METERS. VISIBILITY REMAINED BELOW LIMITS UNTIL XE00Z. FORECAST WAS UPDATED TO SHOW VISIBILITY AT 2000 METERS. I CALCULATED ALTERNATE MINIMUMS TO BE 400 FT CEILING AT 1600 METERS VISIBILITY BASED ON ILS RWY 10 AND ILS RWY 15. I DID CALL ZZZ TWR FOR AN UPDATE ON WX. CTLR INFORMED ME THAT RWYS 15 WERE OPEN AND THAT WX WAS 08005KT 6000 BR BROKEN 008 19/17. FLT NUMBER RPTED THAT THEY WERE ENTERING A HOLDING PATTERN OVER ZZZ AT APPROX XB30Z. I INFORMED FLT NUMBER THAT ZZZ WAS THE PREFERRED ALTERNATE; AND I ASKED THE CREW TO LET ME KNOW WHEN THEY WERE DIVERTING THERE. FLT NUMBER CREW ASKED FOR TIME AND FUEL BURN INFO FROM ZZZ VOR TO ZZZ. I GAVE THEM INFO; CREW THEN ASKED WHAT THEIR CREW LEGALITY TIME WAS. I TOLD THEM THAT I WOULD CHK WITH CREW TRACKING; AND I ASKED IF THEY WERE HEADING TO ZZZ YET. THEIR RESPONSE WAS 'NOT YET.' CREW INFORMED ME THAT THEY WERE DIVERTING TO ZZZ AT APPROX XC50Z. THEIR ETA WAS XD30Z. CURRENT METAR AT ZZZ WAS SHOWING 5000 METERS VISIBILITY AND CEILING OF 1300 FT. AT XD00Z; ZZZ VISIBILITY DROPPED TO 1000 METERS. I SENT THE METAR TO THE CREW. I TOLD THEM THAT VISIBILITY WAS DROPPING THERE; AND I ASKED THE CREW TO GET UPDATE FROM ZZZ TWR. AT XD10Z; VISIBILITY WAS RPTING 500 METERS. AT XD33Z; ZZZ VISIBILITY WAS RPTING 50 METERS WITH RWY 10 RVR AT 900 METERS. FLT WAS NEAR ZZZ; AND I GAVE THE CREW FUEL BURN INFO TO ZZZ1; WHICH WAS THE NEAREST AUTH ARPT TO ZZZ. FLT NUMBER LANDED IN ZZZ1 AT XD45Z. AFTER THE FLT WAS COMPLETED; THE CAPT TOLD ME THAT THEY DECLARED A FUEL EMER AND LANDED BELOW MINIMUMS. I WANT TO NOTE THAT I CHOSE THE PREFERRED ALTERNATE SINCE IT IS STAFFED WITH COMPANY PERSONNEL. ZZZ AND ZZZ HAD A TEMP DEWPOINT SPREAD OF 2 DEGS. TEMP AND DEWPOINT WERE CONVERGED AT 12 DEGS. HAD A CAT II APCH TO RWY 10. THE ILS GLIDE PATH WAS OTS PER NOTAM. ZZZ HAD 1 ILS WITH CAT I MINIMUMS. I WOULD NOT HAVE USED ZZZ AS AN ALTERNATE HAD I KNOWN THE VISIBILITY WOULD DROP TO 50 METERS. THE ZZZ FORECAST NEVER INDICATED SUCH.