NMAC ON GND IN DENSE FOG.

Narrative

UPON ARRIVING IN THE TFC PATTERN AT KANSAS CITY INTL ARPT WE WERE ADVISED BY APCH CTL THAT THE RVR WAS UP TO 1800 FT AND WE WERE CLRED THE ILS 19R. WE LANDED THE ACFT AND WERE TOLD BY THE TWR TO EXPEDITE OFF THE RWY BECAUSE OF LNDG TFC. UPON SLOWING TO TAXI SPD WE EXITED THE RWY AT THE 1ST AVAILABLE TURN OFF. I INFORMED THE TWR THAT WE WERE CLR OF THE RWY BECAUSE THE TWR WAS UNABLE TO SEE THE RWYS OR TXWYS. THE VISIBILITY BECAME MUCH WORSE AND THE TWR WAS RPTING BELOW RVR 1400. I SWITCHED TO GND CTL FREQ. IT TOOK THE CAPT AND I SEVERAL SECONDS OF PEERING THROUGH THE DENSE FOG TO DETERMINE OUR POS ON THE ARPT. THE FOG THINNED FOR A FEW SECONDS AND WE WERE ABLE TO MAKE OUT THE YELLOW A-6 POS ON THE ARPT. THE FOG SUDDENLY BECAME THICK AGAIN AND WE LOST SIGHT OF THE A-6 SIGN. WE CONCLUDED OUR POS WAS ON A-4 (SEE AIRFIELD DIAGRAM ATTACHED). GND CTL TOLD US TO TAXI IN ON ALPHA TXWY. THE CAPT TURNED ON SOME ADDITIONAL LNDG LIGHTS SO OTHER ACFT COULD SEE US. WE COULD SEE ONLY 3 GREEN TAXI LIGHTS AHEAD OF THE ACFT. THE CAPT BEGAN A VERY SLOW TAXI; FOLLOWING THE GREEN LIGHTS THAT LED US OFF OF A-4 TO ALPHA TXWY. THE CAPT CALLED FOR 'FLAPS UP; CLEAN UP' CHKLIST. THE FOLLOWING 20 SECONDS I HAD MY HEAD IN THE COCKPIT PERFORMING MY FO DUTIES. FINISHING MY DUTIES I LOOKED OUT THE FRONT WINDSHIELD AND SAW AN APCHING THICK WHITE LINE. I IMMEDIATELY TOLD THE CAPT THAT WE WERE APCHING THE RWY AND HE STOPPED SHORT OF THE RWY. THE WHITE LINE WAS CLRLY IN FRONT OF OUR ACFT. THE NOSE OF OUR ACFT WAS THE CLOSEST TO THE RWY AND IT WAS APPROX 2 FT FROM THE WHITE LINE. (SEE PICTURE ATTACHED.) ON THE RWY SAT ANOTHER ACFT WITH LNDG LIGHTS ON. IT APPARENTLY HAD STOPPED. THE FOG WAS SO THICK THAT I COULD HARDLY TELL WHAT TYPE OF ACFT IT WAS. I RETURNED TO TWR FREQ AND ADVISED THEM THAT WE NEEDED TO GET OUT OF OUR UNFORTUNATE POSITION. THE TWR CLRED US ONTO AND OFF OF THE RWY. THE REMAINDER OF THE TAXI WAS NORMAL AS THE FOG BECAME THINNER TOWARDS THE PARKING AREA. RECOMMEND THAT KANSAS CITY INTL GET ARPT SURFACE DETECTION EQUIP.