DURING ILS APCH; ACFT ENCOUNTERED HVY RAIN AND WINDSHEAR. FLYING PLT; FO; DIDN'T RECOGNIZE THE WINDSHEAR AT FIRST AND CAPT TOOK CTL AND DID GAR.

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WE WERE ON VECTORS TO ILS RWY 19 AT SFO. WX WAS VMC WITH BROKEN LAYERS OF CLOUDS. ATIS RPTING 23 BROKEN; 5 MI WITH LIGHT RAIN; WINDS DOWN THE RWY AT 14 KTS. FIELD NOT IN SIGHT. APCHED FAF AT 180 KTS; FLAPS 3 DEGS; ON GS AND AUTOTHROTTLES ENGAGED. AT FAF; LOWERED GEAR; FULL FLAPS; STARTED SLOWING TO APCH SPD AND SIMULTANEOUSLY ENTERED A RAIN SHAFT AS THE CAPT CONTACTED TWR AND RAN CHKLISTS. STARTED GOING BELOW GS BUT AS I ATTEMPTED TO REINTERCEPT; SPD DROPPED BELOW APCH. RECEIVED GS WARNING; PUSHED THROTTLES UP BUT STILL WAS DSNDING. CAPT DIRECTED A GAR. I CALLED FOR FLAPS 3 DEGS TO BEGIN GS. RECEIVED 'TOO LOW- TERRAIN' WARNING AND PULLED FURTHER AFT. WE WERE IFR AND IN HVY RAIN ALL THIS TIME. THE CAPT TOOK CTL OF THE ACFT WHICH FINALLY BEGAN TO CLB AND LEVELED AT 4000 FT. SHORTLY AFTER LNDG WINDSHEAR ALERTS WERE BEING GENERATED ON THE FIELD. WITH THE QUIET ENGS AND NO THROTTLE MOVEMENT; I WAS SLOW TO RECOGNIZE THE WINDSHEAR ENCOUNTER AND BEGIN RECOVERY. THE VOLUME LEVEL OF THE WARNINGS IN THE COCKPIT; ALONG WITH THE HVY RAIN POUNDING THE ACFT ALSO MADE COMS WITH THE CAPT DIFFICULT. THIS INCIDENT REENFORCES THE NEED TO COMPLETE ROUTINE TASKS EARLY SO ATTN CAN FOCUS ON ACFT PERFORMANCE. SUPPLEMENTAL INFO FROM ACN 329960: WITHIN AN HR; THE AUTOMATIC MONITORING EQUIP ON THE FIELD WAS GENERATING WINDSHEAR ALERTS. AT THE TIME OF OUR APCH; HOWEVER; THERE WAS NO REASON TO SUSPECT THAT WE MIGHT ENCOUNTER SUCH AN EVENT. THERE WAS NO CONVECTIVE WX IN THE AREA. THERE WERE NO RPTS. THE WIND WAS STEADY OUT OF THE S; NO GUSTS. I WAS LULLED INTO THE COMPLACENCY OF A ROUTINE APCH. THIS WAS COMPLICATED BY THE DISTRACTIONS OF CHKLISTS AND TWR CONTACTS; WHICH OCCURRED SIMULTANEOUSLY AND A LITTLE LATE AS WE ENTERED THIS RAIN SHAFT WITH PERHAPS STRONG DOWN-DRAFT AND MAYBE SOME HORIZ SHEAR. I WAS VERY AWARE THAT WE WERE DRIFTING LOW; BUT WITH THE AUTOTHROTTLE ON; DID NOT NOTICE THAT WE WERE ALSO SLOW. THE ROUTINE OP OF THE A320 AUTOTHROTTLE MAKES IT EASY FOR ENG PERFORMANCE TO DROP OUT OF THE SCAN. THE ENGS ARE QUIET; THE THROTTLES DO NOT MOVE. THE TRIM IS AUTOMATIC AND SILENT. CONSEQUENTLY; WE WERE BOTH SLOW TO REALIZE THAT THE PLANE WAS OUT OF PERFORMANCE IN THE APCH CONFIGN AND THAT WE NEEDED TO GAR. THIS EXPERIENCE PUNCTUATES THE NECESSITY OF EARLY COMPLETION OF THE ROUTINE TASKS OF AN APCH; EVEN WHEN EVERYTHING SEEMS TO BE WELL UNDER CTL; COMING INTO VFR WX.