A B757-200 APCHING ZZZ IN TSTM CONDITIONS DISCONTINUED THE ILS APCH BECAUSE OF TURBULENCE AND WINDSHEAR. A LATER APCH WAS SUCCESSFUL.

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ON ARR AND APCH TO ZZZ ON FLT FROM PHOENIX; NOTICED AN AREA OF PRECIP WITH MODERATE AND GREATER RETURNS FROM ONBOARD RADAR. THE PRIMARY COVERAGE OF THIS AREA WAS SW OF NE OF ZZZ TERMINAL AREA; WITH MOVEMENT TO N; NE. WE WERE RECEIVING MODERATE TURB AND PRECIP ON ARR WHILE BEING VECTORED FOR AN APCH TO RWY 14R. THE APCH CTLR WAS BUSY WITH ARR TFC; SO IT WAS DIFFICULT TO GET A WORD IN UNLESS A SPECIFIC INSTRUCTION REQUIRED A RESPONSE TO CTLR; WHICH BURDENED THE SIT LATER TRYING TO COORDINATE WX AVOIDANCE. AT THIS TIME ATIS WAS RPTING BROKEN TO OVCST SKIES WITH RAIN SHOWERS; BUT IT APPEARED THAT THE PRECIP AREA WAS BUILDING IN INTENSITY AS SOME ACFT WERE ALREADY DECIDING TO DIVERT; WHILE OTHERS WERE CONTINUING THE APCH WITH SUCCESSFUL LNDGS. AT 4000 FT ESTABLISHED ON THE LOC; WE WERE GIVEN DSCNT TO 2500 FT AND CLRNC FOR THE ILS RWY 14R. WHILE DSNDING TO CAPTURE THE GS (FO PF) WE BEGAN TO ENCOUNTER MODERATE TURB AND RAIN SHOWERS; THERE RADAR WAS DIFFICULT TO INTERPRET AT THIS POINT; AS TO WHAT WAS GND CLUTTER AND RETURNING ECHOES. ABOUT 3-5 MI FROM THE OM; THE FO COMMENTED THAT IT WAS DIFFICULT TO MAINTAIN A STABILIZED APCH EVEN WITH THE AUTOPLT ON; ABOUT THIS TIME I NOTICED A 20-30 KT INCREASE IN AIRSPD; THEN IT BEGAN TO FLUCTUATE WILDLY. WE ELECTED TO BREAK OFF THE APCH AT THIS TIME HAVING DIFFICULTY MAINTAINING ALT; HDG AND AIRSPD; BELIEVING WE WERE IN THE INITIAL STAGES OF A WINDSHEAR OR MICROBURST EVENT. WITH STRONG ECHOES NOW MORE EVIDENT AHEAD OF US; WE ELECTED TO TURN L; TOWARD THE E; TO AVOID; INITIATED A CALL TO APCH CTL WITH MISSED APCH AND DECLARED AN EMER FOR WX AVOIDANCE. WE CONTINUED E OVER THE LAKE; AND AFTER CONSULTATION WITH DISPATCH AND FURTHER WX INFO WE WERE ABLE TO GATHER; WERE VECTORED BACK S AND EVENTUALLY W FOR ANOTHER APCH TO RWY 14R ONCE THE WX HAD MOVED THROUGH THE ZZZ TERMINAL AREA. FROM OVER A HUNDRED MI S THIS WX MOVING INTO THE ZZZ AREA DID NOT SEEM THAT SIGNIFICANT; BUT DID APPEAR TO BE QUICKLY CHANGING AS WE APCHED. I PROBABLY SHOULD HAVE ELECTED TO ENTER A HOLD W OF THE ARPT UNTIL I WAS SURE ANY HAZARDOUS WX HAD MOVED THROUGH; YET I HAVE HAD SUCCESSFUL APCHS AND LNDGS WITH CONDITIONS ON THE ONBOARD RADAR LOOKING FAR WORSE IN THE TERMINAL AREA. THE LATEST ATIS AT THE TIME OF OUR APCH WAS SIMPLY RPTING BROKEN TO OVCST CONDITIONS AT ZZZ WITH CEILINGS AROUND 3500 FT TO 6000 FT AND RAIN. SHORTLY AFTER OUR MISSED APCH AT APPROX XA00Z A SPECIAL ATIS CAME OUT WITH: 19025G32KT 3SM R14R/5000VP6000FT +TSRA BR SCT029 BKN044CB OVC070 16/14 A2973.