Air carrier flight crew reported on departure worsening weather and an airborne conflict at MYAM resulted in a GPWS terrain caution.
Synopsis
Air carrier flight crew reported on departure worsening weather and an airborne conflict at MYAM resulted in a GPWS terrain caution.
Narrative
Upon taxiing out in MHH we heard 3 aircraft make calls in the area; one overflying the field; one entering a 45 to the downwind and one 15 miles to the south. We saw the first two on ADSB and visually. Off of the departure end of RWY 27 about 5 miles was a rain shower with low clouds. We knew that off to the south it was clear so our plan was to take off and fly the pattern exiting on the downwind. We made the call of our intentions and took off. At 600 ft we initiated a left turn to the crosswind but quickly saw traffic that had said they were 15 to the south however they were about 2-3 miles to the west. I took controls from my student and leveled at 2000' and turned back west onto the departure leg. The clouds were dropping to the west and light to moderate rain was associated. A right turn to the north would have been worse as well; the only open area with no clouds was to the south/east. I descended with the clouds visually and reached an altitude of 1200' while maintaining visual separation with the traffic. At that altitude a GPWS caution 'do not sink' sounded. Finally when able to turn onto the downwind I began the turn and while trying not to enter the precipitation a 'bank angle' aural message sounded momentarily; I was visual but my FO said they did not think I was more than about 35-40 degree. We then climbed to 7000' and got our clearance with Miami Center and the flight continued without further incident. Cause: Inbound aircraft made one call with incorrect location. I took off with only one way out; could've waited for traffic to clear. Despite company pages; approach did not let us pickup IFR off the field.
Second reporter narrative
The event occurred in MHH just after takeoff. Before taxiing out we knew it was going to be difficult getting out of the airport since we had to transfer to approach when coming into the airport to get lower than 7;000 feet to see the field. Because of this; we knew it would be difficult to remain VFR when coming back out of MHH so we attempted to pick up IFR on the ground via phone number. We were then told to pick up in the air after departing. So; we took off with a planned level off at 5000 feet; however; shortly after takeoff; we realized the clouds were much lower than expected so we had to level off around 1;500 feet to remain clear of the clouds. At this same time; there was a flight entering the pattern that caused extra confusion at an already busy point. Around this time is when we got the ground prox and momentary bank angle. We avoided the aircraft and clouds to the best of our abilities until we could turn toward the hole to climb above the clouds. Cause:The event occurred due to a combination of factors. These include worsening weather; traffic-dense dense untowered airport (about 3-4 aircraft in and around the pattern at time of departure); and being inexperienced myself in the area and aircraft.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.