Learjet 40
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 100; Flight Crew Total 5000; Flight Crew Type 100
Situational Awareness
Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Human Factors
We had planned to fly the LDA DME approach into Sitka.  Upon arriving we realized we had the ceiling and it would be shorter to fly the RNAV RW11.  We had been cleared for the LDA but informed ATC that we would like to fly the RNAV and were cleared for that.  I misread the chart; I read the 3;900 feet within 4 miles in the procedure turn as the altitude needed previous to HESOK; the initial approach fix.  I forget that we were cleared to HESOK at 5;500.  I began to descend to meet 3;900 feet by HESOK.  Just at or just short of HESOK Sitka radio advises us that Center issued an altitude alert.  I checked the altitude that we were at and once again misread the procedure turn altitude as the altitude leading to the fix.  I noted that we were on our intended course and was spooked when we seemed to be on course but getting an altitude alert.  According to what I read we were on course and altitude.  My first officer did not catch my mistake and was on the same page that I was.  We had briefed the missed and also briefed that the coast and the terrain were to the east.  Based on my navigation and ATC's alert I assumed we must not be where we think we are if we are on course and altitude and receiving an altitude alert.  I decided to climb south and turn away from higher terrain towards the VOR and missed approach fix.  We advised ATC of our actions held at BKA; re-briefed the approach as well as speaking to ATC to find our mistake.I failed to follow the missed approach procedure due to me thinking we must be off course or set up on the incorrect approach.  6 miles to the south there is terrain at 3;275.  This terrain is roughly between the initial fix where we deviated altitude and the VOR in which we were headed.  When on the ground we spoke with ATC once again going over what I had done wrong.
A LR40 Captain reported misreading the approach chart on arrival into SIT; descended below charted altitude; and got a terrain warning from ATC.