Date: 202110
Local time of day: 0601-1200
Location: CHA.TRACON, TN
Flight conditions: IMC
Weather elements / visibility: Turbulence; 6
Light: Daylight
Aircraft: Light Transport
Operator: Air Taxi
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class C CHA
ATC / advisory: TRACON CHA
Reporter organization: Corporate
Reporter function: First Officer; Pilot Not Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Situational Awareness; Training / Qualification
Second reporter function: Check Pilot; Pilot Flying; Captain
Anomaly: Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Provided Assistance; Flight Crew Returned To Clearance; Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: During descent to CHA from 11;000; expecting the visual approach Runway 20. ATIS ceilings were SCT 3;100 and Broken 4;500. ATC said descend maintain 3;600; left heading 110; altimeter 29.90 advise airport in sight. I read back altimeter 29.90; left 110; altitudes 3;600. When selecting our given instructions; I was going to adjust our altimeter first. Captain told me to select altitude to 3;100 first. I selected and announced '3;100 Altitude Set'. Captain acknowledged and we proceeded our descent. Upon 3;300 feet; ATC announce terrain alert climb 3;600. Captain disengaged autopilot and climb. I read back instructions and selected 3;600 altitude. We proceeded to climb back to 3;600 feet.After the event. The Captain called ATC to confirm we were given instructions of 3;100. ATC replied saying he gave us 3;600 feet. During the event; the Captain and I minds were set ATC gave us instructions to descend 3;100.


Second narrative: On our descent into Chattanooga; the flight crew was issued heading of 110 to enter a right base for a visual to Runway 20 and an altitude of 3;600 feet. During that descent the First Officer had some difficulty reading back the instructions and ultimately setting the appropriate altitude. I had set the assigned heading and after waiting for him to set the altitude I instructed the First Officer to set 3;100 feet in the altitude selector which he did. Just prior to that time I had been thinking of what altitude I was anticipating obtaining visual contact with the airport and must have transposed what was the lowest cloud layer at CHA of 3;100 into our assigned altitude. Once we descended below 3;600 feet ATC issued a low altitude alert and instructed us to climb back to 3;600 feet which we did immediately. We were then vectored for the ILS approach to 20. I requested the approach control phone number which I called once we were on the ground to follow up.  ATC verified we accurately read back 3;600.  I thanked them and advised I would file a report.As an instructor pilot; it can be difficult at times to decide to whether to let your trainee attempt to complete a task on their own for the purposes of gaining experience or to intervene and assure the appropriate outcome.  In this instance I tried to let my trainee First Officer attempt the read back the clearance and set the altitude as assigned. The reason I did not intervene was that he had been having some difficulty with these tasks and I wanted him to get as much as experience as possible. I believe that while I waited for him to accomplish these tasks I had become distracted by the delay and unfortunately instructed him incorrectly to set the wrong altitude. A significant contributing factor in this sequence of events is the lack of experience that the First Officer has flying in the IFR environment. I had to spend an extra amount of time monitoring and correcting him during this flight and our previous flights in his communications and IFR procedures as most of his previous experience was as a pilot for [another] business for the last three years in mostly VFR conditions.  That being said; in the future regardless of my desire to give my trainees the added benefit of more experience; I will have to be more diligent in intervening when they are not complying with their tasks in a timely manner and I will also have to better assess the ability or lack of ability that my trainees have and limit when and where I allow them to gain additional experience.


Synopsis: Light Transport aircraft flight crew reported a CFTT event during approach to CHA airport.  The crew selected 3;100 rather than the cleared altitude of 3;600 feet.  ATC announced the terrain alert and the crew took evasive action by climbing.