A B747 FLT CREW DEPARTING HKG ON OCEAN 2B SID TURNED TOO SOON; IN PART BECAUSE OF GPWS DISTRS.

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DEPARTED VHHH ON SID OCEAN 2B RWY 25L (COMMERCIAL CHART PLATE 10-3V6). AS WE APCHED FLYOVER POINT DRAWN; I MISTOOK LINEAR DISTANCE (5 NM FROM END OF RWY 25L TO PRAWN) AS DME DISTANCE FOR FOP AND MOVED HDG BUG TO COMMAND FO TO TURN. WHEN IN THE TURN I REALIZED THE ERROR AND STATED SO TO THE FO. AFTER REACHING CRUISE; WE REFLECTED ON THE EVENT. AT APPROX 500 FT THE GPWS ALERTED US WITH A TERRAIN WARNING. WX AT THE TIME WAS VFR WITH HAZE AND TKOF WAS INTO THE SUN. THE ALERT PROMPTED US TO RECHK ALTIMETERS AND OUTSIDE AS WELL. I FEEL THAT THE GPWS ALERTS MIGHT HAVE PLAYED A PART IN DISTRACTING US DURING THAT PHASE OF FLT. OTHER FACTORS INCLUDE: GPS LEG CHANGE IN AUTO SWITCHES TO NEXT TRACK 2-4 MI EARLY GIVING A FALSE PROMPT. A MIX OF TRIPLE GPS AND 1 UNIVERSAL FMS WITH TAWS FORCES A LOT OF XCHKING BTWN EACH AND RAW DATA. IT MAKES FOR A BUSY TIME IN A BUSY ENVIRONMENT. CONCLUSION: BETTER COORD XCOCKPIT WILL RESULT IN HIGHER AWARENESS AT CRITICAL TIMES. SUPPLEMENTAL INFO FROM ACN 704756: DEPARTING HONG KONG; TAWS SYS REPEATEDLY GAVE 'TERRAIN; PULL UP' WARNINGS. IT WAS VERY DISTRACTING. CAPT CALLED A TURN TOO EARLY AND TURNED THE HDG BUG. I FOLLOWED THE HDG BUG. I SHOULD HAVE DISREGARDED THE TURN AND CONTINUED TO THE FLY-OVER WAYPOINT; ANOTHER 1.9 MI BEFORE TURNING. MINIMUM CREW REST CONTRIBUTED TO THIS INCIDENT.