LOW ALT WARNING WAS GIVEN TO THE FLC OF AN MLG ACR ACFT DURING THE SECOND INST APCH IN HVY TURB BY THE ACFT GND PROX SYS AND THE TWR CTLR.

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LDA TO RWY 6. CONDITIONS AT THE FIELD WERE LOW SCUD CLOUDS IN 2 MI VISIBILITY. ADDED TO THIS WAS CONTINUOUS MODERATE TURB. WE DISCOVERED LATER THAT THE TURB WAS SO UNCOMFORTABLE IN THE BACK OF THE ACFT EVEN THE FLT ATTENDANTS WERE PHYSICALLY SICK. WE SAW THE FIELD AT THE MISSED APCH POINT OF 1.3 MI BUT WERE TOO HIGH FOR A SAFE APCH AFTER HAVING DIFFICULTY GETTING DOWN. I TOLD THE FO WE WERE GOING AROUND. I ALSO INDICATED WE HAD ENOUGH FUEL REMAINING FOR SEVERAL MORE APCHS BUT WOULD ATTEMPT ONLY ONE MORE BEFORE GOING TO THE ALTERNATE. I COULD IMAGINE WHAT THE PAX WERE FEELING AND DID NOT WANT TO SUBJECT THEM TO ANY MORE DISCOMFORT. WE WERE ASSIGNED TO EXECUTE THE STANDARD MISSED APCH PROC FOR RWY 6. OUR ASSIGNED ALT WAS 5000 FT. THIS WAS 500 FT ABOVE THE IAF ALT. BECAUSE THE PMS WAS NOT ENGAGING AND KNOWING WE SAW THE FIELD AT THE MISSED APCH POINT ON THE PREVIOUS APCH; I ELECTED TO BRIEF AND FLY THE HAND FLOWN NON PRECISION PORTION OF THE LDA 6 APCH. THIS WAS IN HOPES OF GETTING TO MDA ASAP; KNOWING WE HAD A SIGNIFICANT TAILWIND AND TURB TO HINDER US PICKING UP THE FIELD THE FIRST TIME. PASSING THE IAF (AGAIN STILL AT THE MISSED APCH ASSIGNED ALT OF 5000 FT; 500 FT ABOVE THE PUBLISHED IAF ALT) I INITIATED A 2000 FPM RATE OF DSCNT TO THE STEP-DOWN FIX APPROX 4.9 DME AND AT 2800 FT. ONCE INSIDE THE STEP-DOWN I AGAIN INITIATED A 2000 FPM RATE OF DSCNT TO GET DOWN EARLY TO THE MDA; NOW 1800 FT. AT THIS TIME THE 'TERRAIN; TERRAIN' ALERT; A 'WIND SHEAR' WARNING ALERT; AND A CALL FROM TWR FOR US TO CHK OUR ALT ALL HAPPENED SIMULTANEOUSLY. THIS WAS ACCOMPANIED BY A 15 KT LOSS OF AIRSPD AND THE NEED FOR SIGNIFICANT PWR APPLICATION. AT NO TIME DID I FEEL THE ACFT WAS IN DANGER; HOWEVER; AS THE AIRSPD CAME BACK WITHIN A FEW SECONDS AND THE APCH WAS STILL STABILIZED AND NO FURTHER WARNINGS OCCURRED. I ELECTED TO CONTINUE THE APCH. MY THOUGHT WAS THAT THE ALT ALERT SYS IN THE TWR HAD PREDICTED A PREMATURE TOUCHDOWN POINT BASED UPON OUR DSCNT RATE AND AIRSPD SETTING OFF THE ALARM. AT THE TIME THE TWR NOTIFIED US OF THE NEED TO CHK OUR ALT THE FO NOTED WE WERE WITHIN THE STEP-DOWN FIX AND STILL ABOVE THE MDA; NOW 1800 FT. WE FELT WE KNEW OUR POS AT THAT POINT AND THE WARNING WAS SPURIOUS. THE TURB WAS A SIGNIFICANT FACTOR; HOWEVER. IT WAS DIFFICULT TO KEEP PRECISE ALT CTL. FOR THIS REASON IT IS POSSIBLE WE WERE PLUS OR MINUS 100 FT OF THE MDA. WE PICKED UP THE FIELD AT APPROX 1.5 MI. AN UNEVENTFUL LNDG FOLLOWED. IN RETROSPECT; I WOULD HAVE DISCONNECTED THE AUTOPLT BEFORE THE FIRST APCH AND HAND FLOWN THE GS FOR A MORE PRECISE APCH AFTER THE PMS DISCONNECTED. I INSTEAD ATTEMPTED TO USE PARTS OF USABLE EQUIP COMPENSATING WITH NOT EVERY DAY USE OF MANUAL PITCH; OVERRIDE TO CREATE A MENTAL AND PHYSICAL OVERLOAD.