A GLF4 LNDG NUQ WERE PUT ON A VECTOR TO RWY 14 FOR A VISUAL APCH; BUT LOST SIGHT OF ARPT ON BASE BECAUSE OF DETERIORATING WX.

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OUR FLT WAS APCHING MOFFETT FEDERAL AIRFIELD FROM THE EAST. CTR RTED US THROUGH SALINAS FOR A S ARR TO THE FIELD. FROM SALINAS; WE WERE TURNED NW WITH A DSCNT TO 8000 FT BEFORE BEING TURNED OVER TO SIERRA APCH. WE CHKED IN WITH APCH CTL AT 8000 FT WITH MOFFETT FIELD (AND SAN JOSE) IN SIGHT OVER 20 MI AHEAD. WE RECEIVED VECTORS FROM APCH; WHICH TOOK US W AND INTO IMC CONDITIONS OVER THE COASTAL HILLS. ADDITIONAL VECTORS HEADED US NW WITH A DSCNT TO 4000 FT. AT 4000 FT APCH ASKED IF WE STILL HAD THE FIELD IN SIGHT. IN IMC CONDITIONS; WE COULDN'T SEE MOFFETT; BUT SAN JOSE WAS VISIBLE. WE RECEIVED MULTIPLE POINTOUTS FOR MOFFETT AND ADDITIONAL DSCNTS TO 3000 AND 2000 FT. WE PICKED UP THE S BOUNDER AND AT 2200 FT MID-FIELD; WE RPTED THE MOFFETT IN SIGHT. APCH TURNED US OVER FOR THE VISUAL TO RWY 14 AT MOFFETT. FOR THE TIME OF OUR ARR; ATIS WAS RPTING 20 MI VISIBILITY; FEW TO SCATTERED CLOUDS AT 11000 FT; WITH A BROKEN CLOUD CEILING AT 13000 FT (ROUGHLY) -- WINDS OF 140 AT 18 KTS GUSTING TO 31 KTS. PREVIOUS ATIS INFO WAS RPTING SIMILAR WINDS WITH CLOUDS AROUND 3000 FT AND A CEILING IN THE MID 4000 FT RANGE. UNUSUAL FOR THE DSCNT INTO THE PATTERN; ONCE WE BROKE OUT AT AROUND 2200 FT MSL; WE WERE VMC WITH 20 MI OR GREATER VISIBILITY OUT THE R SIDE OF THE ACFT TO THE N AND IMC IMMEDIATELY TO THE W. ABEAM THE APCH END NUMBERS OF RWY 14; WE CHKED IN WITH MOFFETT TWR ON A R DOWNWIND AND RECEIVED LNDG CLRNC TO RWY 14R. ABEAM; WE WERE BOTH TIGHT AND HIGH FOR AN IMMEDIATE TURN FOR THE RWY; SO WE EXTENDED A BIT TO GET DOWN AND BACK ON PROFILE FOR A STABILIZED FINAL; AND REQUESTED LNDG FOR RWY 14L. AS THE PNF; I WAS KEEPING THE FIELD IN SIGHT TO THE R; WHILE COMPLETING THE LNDG CHKS WITH THE CREW CHIEF (SEATED IN THE JUMPSEAT). PASSING THROUGH A DEEP 90 DEG BASE LEG; THE STICK SHAKER WENT OFF TWICE. I SCANNED THE AIRSPD AND SAW WE WERE FLYING AT VREF PLUS 20-30 KTS. WE MENTIONED THE GUSTY WIND (AGAIN) AND CONTINUED THE DSNDING TURN FOR THE RWY. WHEN I LOOKED OUT FOR THE RWY; I HAD LOST SIGHT OF THE FIELD. WE APPARENTLY WERE RIDING THE EDGE OF APCHING RAIN AND LOW CLOUDS; WHICH WERE NOW BLANKETING THE AIRFIELD. I ASKED THE PF AND THE CREW CHIEF IF THEY STILL HAVE THE FIELD IN SIGHT -- THEY DIDN'T; I MADE A QUICK CALL TO TWR TO SEE IF THEY HAD US IN SIGHT; THEY DIDN'T. TWR RECOMMENDED A TURN TO THE E; WHICH DIDN'T MATCH UP WITH OUR NAV MAP DISPLAY OR MATCH OUR BELIEVED POS IN RELATION TO THE RWY. AT AN ALT OF AROUND 1000 FT; WE LEVELED OFF IN A R TURN TOWARD THE FIELD. THE PF CALLED FOR THE GAR AND MISSED APCH; AND LEVELED THE WINGS. AS THE PNF; I BEGAN CLEANING UP THE ACFT AND NOTIFIED THE TWR. TWR ISSUED A 140 HDG AND CLB TO 2000 FT WITH A SWITCH TO APCH. I SET THE HDG AND ALT IN THE FLT GUIDANCE PANEL (FGC) AND NOTICED WE WERE ON A SOUTHERLY HDG. THE PF CALLED FOR FLAPS UP. FLAPS MOVING; I CHKED IN WITH APCH WHILE ATTEMPTING TO FINALIZE THE FLT GUIDANCE PANEL SETTINGS IN INCREASING TURB. APCH REISSUED THE HDG 140 DEGS AND FURTHER CLB TO 4000 FT AS THE ACFT ENTERED MODERATE TURB. THE PF CALLED WINDSHEAR; AND WE OBSERVED THE AMBER WINDSHEAR ALERT LIGHT ON THE INST PANEL. AS THE PNF; I BEGAN CALLING VSI AND AIRSPD WHILE THE ACFT CONTINUED IN MODERATE TURB. AIRSPD AND VSI DISPLAY TAPES CYCLED FROM 250 FPM DOWN TO 200 FPM CLB; AND AIRSPD RANGING FROM 160-200 KTS -- AVERAGING AROUND 180 KTS WITH GAR PWR SET. WE CONTINUED WITH OUR WINDSHEAR RECOVER UNTIL CLBING AND ACCELERATING WHEN TCASII CALLED TFC. THE TCASII POPPED UP ON THE CTR DISPLAY AND CALLED 'ADJUST VERT SPD;' THEN 'DSND; DSND NOW; INCREASE RATE OF DSCNT.' NOT IMMEDIATELY APPARENT WAS THAT THE #1 AIR DATA COMPUTER (ADC) DISCONNECTING THE TRIM AND YAW DAMPER; LEAVING THE PF VISIBLY WORKING GREATER THAN NORMAL PITCH FORCES. WE NEVER GOT THE AUTOTHROTTLES ON FOLLOWING THE INITIAL GAR AND WINDSHEAR; AND NOW WE WERE NOSED OVER WITH MANUAL CTL OF THE ENGS AT GAR PWR. I BEGAN LOOKING FOR THE TCASII TFC AND SPOTTED OUR TFC AT OUR 10 O'CLOCK. FROM A BREAK IN THE WX A DC9 APPEARED TO BE BELLY UP TO US IN A CLBING R TURN AT A RANGE OF 1000-2000 FT AND A COUPLE HUNDRED FT ABOVE US. I STATED THE TFC WAS NO LONGER A FACTOR; AND WE BEGAN CORRECTING BACK TO HDG AND ALT. SHORTLY THEREAFTER; THE PF CALLED 'GPWS TERRAIN' (EGPWS -- GND PROX WARNING). THE PF BROUGHT THE NOSE OF THE ACFT QUICKLY TO 20 DEGS NOSE UP. EGPWS ON OUR NAV DISPLAYS WERE NEARLY ALL RED WITH DEEP YELLOW IN THE UPPER R QUADRANT. CLBING AGAIN; WE WERE RAPIDLY APCHING OUR ASSIGNED ALT OF 4000 FT. THE PF WAS STILL WORKING HARD WITH PITCH FORCES UNTIL WE RE-ENGAGE THE YAW DAMPER AND PITCH TRIM. WE GOT OUR RATE OF CLB UNDER CTL; BUT BLEW THROUGH 4000 FT. WE CHKED IN WITH APCH AGAIN; STATING WINDSHEAR; AND THAT WE WERE THROUGH OUR ALT. WE FINALLY LEVELED OFF AT 5600 FT HDG APPROX 140 DEGS. THIS WHOLE EVOLUTION LASTED LESS THAN WHAT I BELIEVE TO BE 2 MINS. THE CREW BRIEFED THE WX AND POSSIBLE S ARR OPTIONS INTO THE BAY AREA BEFORE FLT. THE CREW SET UP AND BRIEFED THE LOCALIZED RWY 14L APCH LONG BEFORE ARR; AND DIDN'T GIVE UP THE IDEA OF FLYING THE LOC APCH UNTIL ABEAM THE RWY WHERE THE VISUAL APCH SEEMED REASONABLE. EVERYTHING APPEARED NORMAL OR AT LEAST WITHIN REASON; UP TO THE AIRSPD DEVS ON THE APCH TURN -- UNTIL THE ACFT EXPERIENCED 2 STICK SHAKER HITS. NEITHER OUR WX BRIEF NOR THE ATIS (WHICH ACTUALLY SHOWED IMPROVED CEILINGS) LED US TO BELIEVE IT WOULD BE ANYTHING OTHER THAN A BUMPY RIDE WITH MAYBE 10-15 KTS AIRSPD DEVS ON FINAL -- WHICH WERE ANTICIPATED WITH A VREF SPD ADJUSTMENT. ALL SAID; CONTRIBUTING FACTORS WERE: DECISION TO CONTINUE VISUAL APCH IN DETERIORATING WX CONDITIONS. NOT STAYING WITH THE ORIGINALLY PLANNED APCH. NOT MAINTAINING RWY HDG ONCE LOSING SIGHT OF THE RWY. NOT MAINTAINING ASSIGNED HDG. RECOMMENDATIONS: STAY WITH A PUBLISHED APCH WHEN CONDITIONS WARRANT. BE READY FOR THE UNEXPECTED.