A BAE146-700 AFTER LNDG IN HIGH GUSTING XWINDS AND POSSIBLY A TAILWIND ON TOUCHDOWN; OVERRAN THE RWY END IN PATCHY ICE.

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150 NM OUT OF TEB; ASKED SIC TO CHK ATIS. ATIS RPTING WINDS 320 DEGS AT 26 KTS GUSTING TO 37 KTS. NO ADVERSE BRAKING CONDITIONS RPTED. CLOSER TO THE ARPT; AT 3000 FT MSL AND BELOW; EXPERIENCED MODERATE TO SEVERE TURB AND RADIO COMS BECAME DIFFICULT. ON FINAL APCH TO RWY 1 (7000 FT); REQUESTED A WIND CHK. TWR ADVISED WIND 320 DEGS AT 27 KTS GUSTING TO 38 KTS. FLEW THE FINAL AT VREF +25 KTS; SLOWING TO VREF +15 KTS OVER THE THRESHOLD; WITH FLAPS AT 25 DEGS; TO ACCOUNT FOR THE 50 DEG GUSTING XWIND. ACFT TOUCHED DOWN NO FURTHER THAN 25 FT NE OF THE TOUCHDOWN ZONE AT VREF +10 KTS. IMMEDIATELY CALLED FOR FULL FLAPS AND ACTIVATED LIFT DUMP. BRAKING AT THAT POINT FELT NORMAL. ABOUT 1/2 WAY DOWN THE RWY; THE ACFT BEGAN TO FEEL LIKE IT WAS ACCELERATING; RATHER THAN SLOWING. THE ANTISKID BEGAN TO WORK; WITH THE ACFT YAWING VERY SLIGHTLY FROM L TO R. IT APPEARED THAT THE ACFT WOULD STOP BY THE END OF THE RWY; BUT THE ACFT DID NOT DECELERATE NORMALLY; AND WENT OFF THE END OF THE RWY AT A SPD OF APPROX 30-40 KTS. THERE WAS NO SIGNIFICANT DAMAGE AND NO INJURIES. THIS WAS AN INCIDENT; NOT AN ACCIDENT. AFTER BEING CLRED FROM THE AREA; THE CREW WERE ADVISED THAT A G-III HAD MADE 2 MISSED APCHS AT ABOUT THE SAME TIME DUE TO TURB AND GUSTING WINDS. WE WERE ALSO ADVISED AT THAT TIME THAT BRAKING ON THE FIRST 1/2 OF THE RWY WAS BEING RPTED AS GOOD; BUT THAT THERE WERE PATCHES OF ICE ON THE SECOND 1/2 OF THE RWY. I BELIEVE THAT I WAS THE VICTIM OF UNFORECAST AND UNRPTED SIGNIFICANT WINDSHEAR WHICH ADDED A SIGNIFICANT DOWNWIND COMPONENT TO MY GND SPD SHORTLY AFTER TOUCHDOWN. SINCE I WAS ALREADY CARRYING SOME ADDITIONAL SPD AS THE RESULT OF MY PROPER GUSTING XWIND TECHNIQUE; THE SWITCH FROM A QUARTERING HEADWIND TO A TAILWIND ALTERED THE STOPPING DISTANCE TO SUCH AN EXTENT THAT A CTLED STOP ON THE RWY WAS NOT POSSIBLE AT THAT MOMENT. IT IS ALSO POSSIBLE THAT I MAY HAVE HIT A PATCH OF ICE ON THE SECOND 1/2 OF THE RWY WHICH REDUCED THE EFFECTIVENESS OF BRAKING.