DSNDING TO 4500 FT AND CLRED FOR A VISUAL APCH TO THE BOI RWY 28 FOLLOWING A PLANNED BACK COURSE APCH; B757 FLT CREW ENCOUNTERS TERRAIN EGPWS WARNING.

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WE WERE DSNDING ON A 310 DEG HDG TO INTERCEPT THE BACK COURSE LOC FOR RWY 28L. THE PROFILE TELLS YOU TO CROSS THE 5.1 FAF AT OR ABOVE 4900 FT MSL. WE WERE SET UP TO DO THE APCH AS A LOC/BACK COURSE; VNAV ON PATH AND DSNDING OUT OF APPROX 6000 FT MSL WHEN WE RPTED THE ARPT IN SIGHT. WE WERE THEN CLRED FOR THE VISUAL APCH AND TOLD TO MAINTAIN 4500 FT MSL UNTIL ON FINAL. WE SET 4500 FT INTO THE ALT WINDOW AS WE WERE JUST SLIGHTLY L OF THE LOC AND APPROX 5 NM FROM THE ARPT. AT THIS POINT WE PICKED UP A FEW SCATTERED CLOUDS BTWN US AND THE RWY WHICH ONLY MOMENTARILY HINDERED OUR VIEW OF THE RWY. AS WE DSNDED THROUGH APPROX 4800 FT MSL; I FELT THAT WE WERE GETTING TOO LOW AND LOOKED AT THE RADAR ALTIMETER AND IT SHOWED US AT 1230 FT AGL. AS THE PF BEGAN TO LEVEL OFF AND ADD PWR; ATC INFORMED US THAT HE WAS GETTING A LOW ALT ALERT ON US AND ASKED IF WE STILL HAD THE RWY IN SIGHT; WHICH WE DID. AT THIS POINT WE RECEIVED A GPWS TERRAIN WARNING AND THE PF APPLIED THE APPROPRIATE ACTION; CLBING TO 5400 FT MSL. WE THEN INTERCEPTED OUR VNAV PATH AND THE REST OF THE APCH AND LNDG WERE NORMAL. I THINK WHAT HELPED TO CAUSE THIS WAS A MISUNDERSTANDING WHEN THE CTLR TOLD US TO MAINTAIN 4500 FT MSL UNTIL ON FINAL. WE INTERPED THIS TO MEAN TO CROSS THE FAF AT 4500 FT MSL. ALSO; ALTHOUGH FLYING A VISUAL APCH IN VMC; IT WAS AS NOTED AT NIGHTTIME; WITH LITTLE TO NO MOONLIGHT ILLUMINATING THE TERRAIN BELOW US. FINALLY; AS THE LAST LEG OF A LONG DUTY NIGHT; BOTH CREW MEMBERS WERE FEELING THE EFFECTS OF FATIGUE; WHICH CONTRIBUTED TO THIS EVENT. SUPPLEMENTAL INFO FROM ACN 682136: WE WERE SET UP TO DO THE APCH AS A LOC/BACK COURSE; VNAV ON PATH AND WERE DSNDING OUT OF APPROX 6000 FT MSL WHEN WE GOT THE ARPT IN SIGHT. WE WERE THEN CLRED FOR THE VISUAL APCH AND TOLD TO MAINTAIN AT OR ABOVE 4500 FT MSL UNTIL ON FINAL. WE SET 4500 FT INTO THE ALT WINDOW AS WE WERE JUST SLIGHTLY L OF THE LOC AND APPROX 5.0 NM FROM THE FAF. I THOUGHT THIS TO BE SOMEWHAT ODD TO BE GIVEN 4500 FT INSTEAD OF THE 4900 FT STATED ON THE PROFILE; BUT WE GET THIS QUITE OFTEN WHEN FLYING AN ILS APCH (ALT SLIGHTLY LOWER THAN THE PUBLISHED INTERCEPT ALT). AT THIS POINT WE PICKED UP A FEW SCATTERED CLOUDS BTWN US AND THE ARPT WHICH HINDERED OUR VIEW OF THE RWY FOR A FEW SECONDS.