Date: 202001
Local time of day: 1201-1800
Location: ZZZ.Tower, US
Flight conditions: VMC
Aircraft: EMB ERJ 140 ER/LR
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Reporter organization: Air Carrier
Reporter function: Pilot Flying; First Officer
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Communication Breakdown
Second reporter function: Captain; Pilot Not Flying
Anomaly: Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Descending into ZZZ for a visual approach into Runway XX I realized we were at 4;000 ft. 5 miles from the FAF. ATC wanted us to call the airport in sight to clear us for a visual and we had the airport in sight for the past 10 miles or so. I thought when we called it in sight to each other; the PM (Pilot Monitoring) told ATC and that we were clear for a visual approach. I set 2;700 ft. in the ALT selector and the autopilot began a descent. Passing through 3;000 ft. with the airport and surroundings in sight ATC said climb to 3;000 ft. and as we just had passed it I leveled the plane out and was about to climb back up from 2;900 ft. GPWS called out terrain terrain but this was not a factor because we saw the terrain and were clear of all obstacles. I disconnected the autopilot and climbed to 3;000 ft. as instructed. Then we came in and landed with no issue.This was a miscommunication between ATC; the PM; and PF (Pilot Flying). I thought the PM told ATC we had the visual and we were cleared for the visual approach. There was a small mountain below us but this was no factor and we were clear of it according to my visual sight and chart markings. The error I believe was when I set 2;700 ft. in the ALT window without communicating it clearly with my PM. If I would've brought it to his attention and he would have understood it; I believe he would have brought up that he had not heard ATC clear us for a visual approach yet like I thought he did. I was caught up in being too high for the approach and took an action that I had not completely communicated with my crew about.


Second narrative: My FO was flying into ZZZ and was assigned 4;000 feet. When we were 10 miles away; ATC told us to report airport in sight. We saw the airport and wanted to wait till we got a little closer to call airport in sight. I than looked at my IPAD to look over the taxi and airport diagram and published miss approach. I than heard ATC say to climb to 3;000 feet and 3;000 feet was his MSA. I looked at the altitude and saw that it was set to 2;700 and we had descended to 2;900 feet. My FO began to climb and I set 3;000 feet for our altitude. Just as my FO began to climb; we got a GPWS of Terrain; Terrain. We did not go below 2;900 feet and we did not get a pull up. Also; the MSA for the Terminal Chart was 2;000 feet. We than told ATC we had the airport in sight. When the FO set a new altitude he should of announced it; so that I could of told him we were not cleared to a lower altitude. The FO should of announced his actions before descending to a lower altitude.


Synopsis: Air carrier flight crew began a descent for a visual approach before being cleared; which resulted in an automated terrain warning and ATC directing a climb.