Falcon 2000
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Flight Instructor; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 50; Flight Crew Total 7000; Flight Crew Type 250
Situational Awareness; Time Pressure; Workload; Confusion; Fatigue
ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
General None Reported / Taken
Human Factors; Procedure
First Officer (FO) [Pilot Not Flying] received IFR clearance from Seattle Center while on the ramp at RDM. He read back the entire clearance and there were no errors noted.  FO briefed the Captain on clearance and setup the cockpit accordingly. The altitude clearance limit was for 4;000 feet MSL. The altitude of the airport is 3;080 feet with mountainous terrain in the vicinity. A normal altitude limit for this airport is 14;000 feet.  It is highly unusual for the clearance limit to be that low and the pilots did not catch it due to fatigue. All checklists were complied with prior to takeoff. Taxi and takeoff were normal except being rushed for a wheels up time limit for flow to [destination]. The Captain performed the takeoff from Runway 04 with a left turn to heading 310.  Once in the climb; the 4;000 feet level-off came very quickly and while in the turn to 310 heading. Both pilots immediately were alert to our low altitude status. The low AGL altitude and mountainous terrain were verbalized by both pilots. Later; the mountains that exceeded 4;000 feet MSL were calculated to be within 4 miles in front of the flight path of the plane; this is less than minute to impact at 200 kts.PNF immediately contacted Seattle Center while we were leveling off to check in. A clearance to 14;000 feet was then received. Normal climb ensued. Neither terrain alerter was triggered nor were we ever below 1;000 feet AGL. If PNF had not been expeditious in calling Center for further clearance or if we had been distracted by some other concern; a CFIT event would have been close at hand. Fatigue had been discussed at length; so we were aware of our fatigue state. We were also a little rushed due to a wheels up time for flow into [destination]. At time of event; pilots had been on duty for 13hrs with only 3.7hrs of flight for the day. Pilots were unable to nap at the previous station due to unsuitable sleeping facilities. Duration of sleep in the two prior nights had been poor due to early morning show times and inability to shift sleep schedule adequately.
A possible CFTT event departing RDM was avoided by the crew through good situational awareness and an expeditious climb.