First Officer of C-9b (military DC-9-30) reacts inappropriately to false GPWS Terrain Warning while in cruise at FL340. Reporter cites fatigue and diurnal desynchronosis for the loss of situational awareness.

Narrative

At FL340; in the vicinity of ZZZ VORTAC. Aircraft Commander left cockpit momentarily for lavatory use. Copilot was monitoring instruments when 2 minutes later GPWS system was activated; stating 'Terrain; Terrain; Terrain; Pull Up; Pull Up; Pull Up.' Copilot instinctively performed immediate action steps for GPWS activation then realized that it was a faulty system failure. Copilot immediately initiated recovery back to assigned altitude and heading. Aircraft deviated 800 FT above assigned altitude. Aircraft Commander relayed to ATC deviation of altitude and return back to assigned altitude and heading. No other instructions were provided by ATC. C-9B NATOPS states that GPWS alarm needs to be acted upon with immediate action steps which pilots are trained to respond to immediately. However; Copilot's situational awareness was focused more on immediate execution of action items instead of realizing that aircraft was at FL340 and; therefore; only a system failure. Copilot affected by human factors to include shift in circadian rhythm; multiple time zone changes in 5 days; and emphasis on action versus careful evaluation of alarm with corresponding emergency steps. Had Copilot paused for a minute and recognized that no such terrain is possible at FL340; no action would have been taken. However; due to intensive simulated training in emergency procedures; immediate action steps of GPWS alarm warning were performed automatically and in accordance with NATOPS Flight Manual. Had steps been performed during a final approach in IMC near actual terrain; CFIT would have been avoided.