DC9 ACR DISPATCHER RECOMMENDED; AS A WX DIVERSION ALT; A FIELD THAT DID NOT HAVE ALT MINIMUMS. MINIMUM FUEL ALERT WAS DECLARED.

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DC9 SCHEDULED ACR OPERATING BTWN MEM-ICT; ICT WX RPTING AT XA56Z DEP TIME. 1/8 SM VISIBILITY RWY 1L; 2200V2400 -DZ FOG OVCST 001. (NOTE: CAT II LNDG MINIMUMS FOR RWY 1L RVR 1800 FT/200 HAT.) CAPT ASKED DISPATCH WHERE WE WOULD LIKE THE FLT TO DIVERT SHOULD THEY BE UNABLE TO MAKE IT INTO ICT. AFTER LOOKING AROUND THE MEM AREA AND AFTER DISCUSSIONS WITH 2 OF OUR SURFACE METEOROLOGISTS; I AGREED WITH METEOROLOGY THAT THE VISIBILITY AND CEILINGS AT MEM WOULD REMAIN ABOVE LNDG MINIMUMS. THE CAPT SUGGESTED GOING TO FSD AFTER 1 MISSED APCH AT ICT. AFTER DISCUSSING THE OPTIONS WITH THE CREW; THE CAPT AND I AGREED THAT THE CURRENT FUEL ON BOARD WOULD ONLY ALLOW FOR 1 APCH. I (DISPATCH) DISCUSSED WITH THE CAPT THE AREA WX BASED ON SATELLITE; AREA METAR'S AND TAF'S AND FELT CONFIDENT THE MEM WX (CIG'S AND VISIBILITY) WOULD REMAIN ABOVE LNDG MINIMUMS FOR THE RETURN FLT. THE CAPT AGREED THAT IF AFTER 1 MISSED APCH HE WOULD PROCEED TO HIS ALTERNATE OF ME. (FUEL ON BOARD AT START OF APCH 13.1; FLT PLAN RESERVE FUEL 4.0; ALTERNATE BURN TO MEM (INCLUDING MISSED APCH) 6.5. ICT WX AT START OF APCH RWY 1L 1800 FT; OVCST 001. TWR RPTED RWY 1L RVR 1900 FT. FLT MISSED AT ICT AND PROCEEDED TO MEM ALTERNATE. AT XD00Z (MEM WX AT XC53Z 1700 FT 7 KTS; 6 NM VISIBILITY -RA BR OVCST 003 13/12 A3010. WHILE ENRTE; MEM SPECIAL AT XD39Z 1800 FT AT 5 KTS; 1 1/2 SM VISIBILITY BR OVCST 003 13/12 A3010). I CONTACTED THE MEM TWR FOR A TFC UPDATE; THE TWR INFORMED ME THERE HAD BEEN NO MISSED APCHS DUE TO WX AND OUR ICT DIVERSION CAN EXPECT 35 MI FINAL. I ASKED OUR CHIEF DISPATCHER TO REQUEST PRIORITY HANDLING DUE TO MINIMUM FUEL AND DECREASING WX AT ME. I INFORMED THE CREW TO EXPECT A 35 MI FINAL BUT THAT WE (DISPATCH) ARE TALKING TO ATC TO GET PRIORITY HANDLING. DISPATCH AND ATC COORDINATED TO SWAP OUT ONE OF OUR ARRS AHEAD OF THE ICT FLT AND RECEIVED PRIORITY HANDLING. THE CAPT INFORMED ME THAT HE WAS GOING TO DECLARE 'FUEL CRITICAL' TO ATC. MEM WX AT XE58Z 1800 FT AT 8 KTS; 1/2 SM VISIBILITY RWY 36L; 4000V6000 OVCST 001 13/13/ A3010. FLT WAS GIVEN SHORTENED FINAL AND ARRIVED MEM WITHOUT FURTHER INCIDENT.