Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Situational Awareness; Communication Breakdown
ATC Issue All Types; Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Flight Crew Returned To Clearance; Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Procedure; Airspace Structure
We were assigned the RNAV Rwy 35; and given direct MEYRS.  We briefed the approach and confirmed altitudes in the FMS.  ATC gave us the clearance 'Cross MEYRS at or above 14;000 [feet]; cleared for the RNAV 35.'  I was the Pilot Monitoring; and I dialed 14;000 into to the autopilot pre-select.  The Pilot Flying entered 14000 in the FMS at MEYRS and executed a direct VNAV descent to MEYRS.  This caused the altitude to turn yellow in the FMS because the next altitude on the approach; at YARUB; was 14;800 [feet].  We discussed this for a moment and I deleted the 14;800 from the FMS.  The Pilot Flying then stated; and I agreed; that we should follow the charted altitudes and we entered 15;000 for MEYRS so that we would be above the published MEA of 14800 between MEYRS and YARUB.  With my intention being to put the YARUB altitude back into the FMS; I referenced the chart and then entered 12000 for YURUB (which was an error).  After crossing MEYRS at 15;000 [feet] we began a slow VNAV descent for 12;000 [feet]; but we should have been level at 14;800 [feet] all the way to YARUB.  While cross checking our position between the map display and the Jepp chart; I began to suspect that we had made an error.  Passing about 13;000 [feet]; I asked the Pilot Flying to level off; which he did; and then I stated that we were not at the correct altitude and that we should climb.  At that moment we received a GPWS caution that gave us a one time audible alert; and the Pilot Flying began a climb.  Shortly afterwards we passed the YARUB fix; and the MEA was now 12;000 so we continued the descent.While monitoring our progress on the approach; I noticed that our altitude was below the charted MEA.  I was confused for a minute while I tried to determine if we had made an error and then realized that I had deleted an altitude; and then re-enter it; but had in fact programmed the incorrect altitude.  Looking back I can't quite explain my thought process; and after the fact my mistake seems very obvious and amateur.  I did reference the chart for the YARUB altitude; and looking at it again '12;000' is written very close to YARUB; and that's my only explanation for how I matched that altitude to that fix; but of course 12;000 is the altitude after YARUB.  While I was monitoring our progress I remember thinking that something didn't seem quite right; and it took me a minute to piece together the ATC clearance; our ensuing actions; and to come to the conclusion that I had made a mistake.  The ATC clearance to an altitude that was already below a charted MEA caused a moment of confusion and second guessing.  I removed an altitude from the FMS that was auto loaded with the approach.  A few minutes later; when I realized I had made an error; I attempted to correct it but I put the wrong altitude back in the FMS after incorrectly reading the chart.  I asked the Pilot Flying to level off while I cross checked the chart and; FMS; and our position.  I then stated that we should climb; which we did.I should not have been so quick to delete an altitude from the FMS which was loaded by selecting the approach.  Also; when entering an altitude into the FMS I need to be more careful while referencing the chart and also confirm with the Pilot Flying that I am entering the correct altitude.
While descending into MJT we were cleared by ATC to pass over MEYRS at or above 14;000 feet and cleared the RNAV 35 approach. We had already briefed the approach and checked the altitudes in the FMS. The first segment between MEYRS and the next point on the approach YARUB is 14;800 feet. Just before reaching MEYRS we decided to stop our descent to pass over MEYRS at 14;000 [feet]and hold at 15;000 [feet]. After YARUB the next step down is 12;000 feet. We had been descending in VNAV to make the cross at Myers. My First Officer put 12;000 feet at YARUB and I confirmed it. In VNAV we then started a slow descent to pass over YARUB at 12;000 feet. This was a mistake on my part. We realized at about 12;700 we where wrong and below a published minimum. I stopped the descent and started a climb. We did get a momentary GPWS terrain and responded according. We climbed about 20 feet and it was gone. We had already stopped descending when we got the GPWS. Realizing we where doing the wrong thing by descending in VNAV to cross YARUB at 12;000 [feet].Allowing the Pilot Monitoring to put 12000 feet n the FMS at YARUB. Immediate once we realized our mistake.. Autopilot off. Start a climb. We never did get to 14;800 [feet] because of how we where close to YARUB. I realized that we where low but also safe and never in any danger. I feel like I should have queried ATC about the descent clearance. I should have been more vigilant with the cross at YARUB.
Air taxi flight crew reported confusing ATC clearance; automation mismanagement; and MEA confusion resulted in a GPWS warning.