AN ACR MLG CREW WAS THRUST DOWNWARD AT THE BASE OF TSTMS.

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AN AREA OF TSTMS WERE BUILDING IN THE FT. STOCKTON AREA. AS WE DSNDED INTO EL PASO; WE WEAVED AND DODGED OUR WAY UNEVENTFULLY. AS WE WERE LEVELING AT 11000 FT; WE SAW A MOMENTARY VISUAL BREAK AHEAD AND SAW NO RAIN UNDER A CELL WHICH SHOWED SOME RETURNS (LIGHT) BUT DID NOT LOOK OMINOUS. WE ENTERED THE BASES AND REQUESTED LOWER FROM ZAB; WHICH WAS DENIED FOR MOCA. NO SOONER OUT OF MY MOUTH AND I NOTICED OUR ALT OF 10700 AND DSNDING RAPIDLY. I ADVISED THE CAPT AT WHICH TIME THE AUTOPLT DISENGAGED. THE CAPT TRIED TO ARREST THE DSCNT AND WAS UNABLE TO STOP IT UNTIL 9800 FT AT WHICH TIME WE CLBED BACK TO 11000 FT. AFTER LNDG WE LOOKED BACK TO THE E AND ESTIMATED THE TOPS AT 35000 FT. WE THOUGHT WE WERE CLR OF THE HVY WX; BUT A GROWING TSTM AND DOWNDRAFT CAUGHT US TOTALLY OFF GUARD. SUPPLEMENTAL INFO FROM ACN 271542: ZAB ADVISES OF SIGMET -- LINE OF TSTMS 20 MI WIDE; TOPS 45000 FROM S OF ELP THOUGHT N MOVING NE. CLRED TO DEVIATE L OR R OF COURSE -- DIRECT ELP WHEN ABLE. CLRED FROM 31000-12000 FT. PICKING WAY THROUGH LINE OF TSTMS; EXCELLENT WX RADAR RETURN -- SOLID TO BROKEN. LEVELED AT 12000 FT. DSNDED TO 11000 FT BECAUSE OF TURB TO MAINTAIN ACFT CTL. CTR ADVISED OF WRONG ALT. I ADVISED WE WERE IN TURB. AFTER AIR SMOOTHED OUT. LEVELED AT 12000. ACFT TYPE BOEING 737-220.