B727 FLC ACCEPT NEW DEP CLRNC AND ENCOUNTER GPWS ALERT.

Narrative

WE PICKED UP THE ATIS AND WERE PLANNING TO USE RWY 7R FOR DEP. HOWEVER; ON OUR TAXI OUT; WE NOTICED THE WINDSOCK SHOWING A NW WIND (310 DEGS AT 10 KTS GUSTING TO 20 KTS). I TOLD GND CTL WE WERE UNABLE TO USE RWY 7R AND NEEDED RWY 1R FOR DEP. (WE USED MAX PWR WHICH GAVE US A 6000 LB BUFFER.) OUR NEW CLRNC WAS 'AFTER TKOF; TURN R TO A HDG OF 050 DEGS; CLB AND MAINTAIN 7000 FT FOR RADAR VECTORS FOR THE OVETO 3 DEP; BRYCE CANYON TRANSITION.' AFTER LIFTING OFF AND REACHING 400 FT AGL (COMPANY POLICY) WE TURNED R HDG 050 DEGS. DEP CTL ASKED WHAT OUR CLB RATE WOULD BE AND I REPLIED 1000-1500 FPM. HE SAID WE HAD TFC AT 12 O'CLOCK BELOW US. HE ALSO ASKED IF WE HAD THE TERRAIN IN SIGHT. I RESPONDED WITH A 'YES; WE HAVE BOTH THE TFC AND THE TERRAIN IN SIGHT.' HE TOLD US TO MAINTAIN A VISUAL ON THE TFC AND THE TERRAIN AND WE WERE CLRED DIRECT TO OVETO WHEN ABLE. I REQUESTED TO CONTINUE ON OUR HDG FOR A FEW MORE MI SO WE COULD CLR ALL OBSTACLES. HE APPROVED OUR REQUEST. ABOUT THAT TIME; OUR GPWS SOUNDED 'TERRAIN!' WE INCREASED OUR CLB. I WAS POSITIVE OF OUR CLRNC DUE TO A VISUAL ON THE TERRAIN. I FEEL THIS VECTOR NEEDS TO BE REVISED IN ORDER TO STAY WELL CLR OF ALL TERRAIN. IF THE WX HAD BEEN LOW; OR OUR CLB RATE WAS LESS; IT COULD CAUSE A PROB. I FEEL THE WINDS OUT OF THE WNW MIGHT HAVE CONTRIBUTED TO THIS PROB.