FALSE WARNING ON GPWS INDUCES PIC OF ACR MLG TO EXERCISE AN ALTDEV ALT EXCURSION.

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DEPARTING ONT RWY 8R ON THE POMONA 6 DEP; WE TURNED TO 255 DEGS TO INTERCEPT THE POM 114 DEG RADIAL. OUR CLRNC WAS TO 14000 FT; HOWEVER; THERE WAS A PUBLISHED RESTRICTION TO CROSS POM VOR AT OR BELOW 8000 FT. WE STARTED TO INTERCEPT THE 114 DEG RADIAL; AND WE WERE LEVEL AT 8000 FT. THERE WAS HVY RAIN AND LIGHT TO MODERATE CHOP. THE GPWS LIGHT CAME ON (RED) FOLLOWED BY 'WHOOP; WHOOP; PULL UP' AUDIO WARNING; THEN SHORTLY THEREAFTER; 'TERRAIN; TERRAIN' WARNING. WE STARTED A CLB AND INFORMED THE CTLR WE WERE CLBING BECAUSE OF A GPWS WARNING. THE CTLR STATED THERE WAS NOT TFC IN THE AREA AND ASKED IF WE WOULD BE STOPPING THE CLB. THE GPWS WARNING STOPPED AT APPROX 9600 FT. WE ASKED IF WE COULD CONTINUE CLBING AND THE CTLR ISSUED A CLB TO FL230 WITH A RESTRICTION TO CROSS BUCCK INTXN AT OR ABOVE 14000 FT. THE CAPT WROTE UP THE GPWS ON ARR AT SJC AND MAINT SAID THE SYS GND CHKED 'NORMAL.' WHEN WE TOLD ONT DEP THAT WE WERE CLBING BECAUSE OF A GPWS WARNING; I BELIEVE HE THOUGHT WE WERE CLBING BECAUSE OF A TCASII WARNING. WE SUSPECT THIS IS TRUE BECAUSE HE STATED THAT THERE WAS 'NO TFC IN THE AREA.' WHEN YOU'VE READ THE HORROR STORIES OF OTHERS FOR NOT FOLLOWING GPWS WARNINGS; AND YOU BELIEVE YOUR POS TO BE SAFE IN RELATION TO THE GND; IT CREATES A TOUGH CONFLICT WHEN THE GPWS ISSUES SUCH A WARNING (MOST LIKELY A FALSE ONE). WE FOLLOWED WHAT WE BELIEVED TO BE THE SAFEST ACTION AND CLBED. PLEASE CONTINUE TO SHARE THE EXPERIENCES OF OTHERS. IT DEFINITELY HELPS IN MAKING DIFFICULT AND TIMELY DECISIONS.