ACR FLT CREW RECEIVED A GPWS TERRAIN WARNING WHILE CONDUCTING A CIRCLING APCH TO RWY 4 AT MHLM.

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ON ZZZ-MHLM LEG; WE BRIEFED THE VOR DME ILS 22. THE CAPTAIN HAD NEVER FLOWN INTO MHLM; SO I DID AS THOROUGH AND COMPLETE A BRIEFING AS POSSIBLE; INCLUDING THE POSSIBILITY OF CIRCLING TO RUNWAY 4 IF THE WINDS PICK UP. ALSO BRIEFED WAS THE HILL ABOUT 4 MILES SOUTHWEST OF THE AIRPORT; AND THE FACT IT IS NOT CHARTED ON THE AREA CHART; BUT IS AS AN ANTENNA ON THE APPROACH CHART. ALSO DURING THE APPROACH BRIEF; I MENTIONED THAT THE VISIBILITY WOULD NOT BE AS GOOD AS PERCEIVED FROM THE METAR; AS IT WAS EXTREMELY HAZY. WHEN IN CONTACT WITH LA MESA APPROACH; THEY INFORMED US OF THE WINDS WHICH WERE AT OUR MAX TAILWIND COMPONENT; SO THE CAPTAIN AND I ELECTED TO CIRCLE TO RUNWAY 4 IN CASE THEY CONTINUE TO INCREASE. ATC CLEARED US FOR THE 'VISUAL CIRCLING APPROACH RUNWAY 4.' I ELECTED TO FLY THE FULL VOR DME ILS RWY 22; FOLLOWED BY A VISUAL CIRCLING MANEUVER AT 1300 FT. THE INITIAL APPROACH WAS FLOWN WELL; AND DELIBERATELY SLOW SO AS NOT TO GET BEHIND. I DECIDED TO USE RIGHT TRAFFIC BECAUSE WITH THE RESTRICTED VISIBILITY; I WANTED TO HAVE A GOOD VIEW OF THE RUNWAY. I HAD THE CAPTAIN INSERT THE VISUAL APPROACH RWY 4 IN THE FMS. ON DOWNWIND; I WAS PLANNING TO TURN BASE AND DESCEND INSIDE OF THE HILL WHICH IS ABOUT 4 NM SOUTHWEST OF THE AIRPORT. I HAD DONE THIS SAME EXACT APPROACH AND MANEUVER TWO DAYS PRIOR (ATC DIRECTED US TO USE RIGHT TRAFFIC THEN); AND FELT IT WORKED OUT VERY WELL. HOWEVER; THE CAPTAIN PREFERRED TO EXTEND THE DOWNWIND BEYOND THE HILL; THEN TURN BASE. I FEEL THERE IS NO RIGHT OR WRONG WAY TO DO THIS; AS IT IS PERSONAL PREFERENCE -- SO WE THEN CONTINUED DOWNWIND AS PER THE CAPTAIN'S SUGGESTION. THROUGHOUT THE ENTIRE MANEUVER; WE HAD THE HILL IN SIGHT. BT THE WAY; THIS HILL DOES NOT APPEAR ON THE EGPWS TERRAIN DISPLAY. THIS HAS ALSO BEEN BRIEFED; AS I NOTICED THIS PECULIARITY TWO DAYS PRIOR. WHILE ON THE BASE LEG AND DESCENDING (HAND FLYING); WE RECEIVED A SINGLE 'TERRAIN AHEAD' ALERT; IMMEDIATELY FOLLOWED BY A 'PULL UP' WARNING; IMMEDIATELY FOLLOWED BY NO WARNING. THE ENTIRE SEQUENCE LASTED ABOUT 2 SECONDS. DURING THE 'TERRAIN AHEAD;' I BEGAN TO LEVEL OUR DESCENT; AND AFTER THE 'PULL UP;' I BEGAN TO ADD POWER AND PITCHED UP. THE ENTIRE WARNING WAS OVER BY THE TIME THE ENGINES BEGAN TO SPOOL UP. WE WERE STILL IN A POSITION TO MAINTAIN OUR PROJECTED PATH TO THE RUNWAY; SO THE CAPTAIN AND I DECIDED TO CONTINUE THE APPROACH; AND I BELIEVE WE MET ALL STABLE APPROACH CRITERIA AT 1000 FT. THIS HILL WAS NOT IN THE TERRAIN DATABASE; SO I BELIEVE THE GPWS WAS TRIGGERED BY THE RA; AND THE UPSLOPE OF THE HILL'S BASE AS I BEGAN MY TURN AND DESCENT. IN THE FUTURE; I WILL CONSIDER LEFT TRAFFIC; BUT LEFT TRAFFIC HAS ITS OWN SET OF HILLS NORTH OF THE AIRPORT. THEREFORE; I DON'T KNOW WHICH PATTERN OFFERS GREATER SAFETY MARGINS; BUT FEEL IT IS IMPORTANT TO MAINTAIN PROFICIENCY ON BOTH PATTERNS AS SOMETIMES ATC WILL DICTATE THE PATTERN.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE REPORTER STATED THAT IT IS LIKELY THAT THE TERRAIN IN THE ACFT DATABASE DOES INCLUDE THE HILL WHICH TRIGGERED THE WARNING. THE ACFT TERRAIN REPRESENTATION DISPLAYS TERRAIN IN A PIE-SHAPED AREA AHEAD OF THE ACFT; SHOWING TERRAIN 45 DEGREES AZIMUTH RIGHT AND LEFT OF THE NOSE. THEREFORE; SINCE THE BASE TURN WAS OVER THE VALLEY; THE HILL MAY HAVE BEEN OUTSIDE THE LIMITS OF THE DISPLAY; BUT THE GPWS TRIGGERED THE WARNING FOR CLOSURE TO THE RISING TERRAIN. HIS COMPANY DOES PROVIDE A TOPOGRAPHIC DISPLAY OF THE ARPT AREA; BUT THE REPORTER WOULD PREFER A MULTICOLORED GRAPHIC OF THE AREA. HAZY CONDITIONS OFTEN EXIST IN THE AREA; AND IN MOST CASES; THE DIRECTION OF THE CIRCLING APCH IS AT THE DISCRETION OF THE FLT CREW.