Fractional jet crew reported a conflict with another aircraft during climb from a non-towered airport in marginal VMC weather conditions. The crew received a terrain warning while maneuvering away from the conflict then continued the flight to destination.
Synopsis
Fractional jet crew reported a conflict with another aircraft during climb from a non-towered airport in marginal VMC weather conditions. The crew received a terrain warning while maneuvering away from the conflict then continued the flight to destination.
Narrative
We arrived in MYEF in rapidly changing weather conditions; and called owner services to advise them that thunderstorm activity was coming into the area; and we might not be able to get out if the owner was late. The sooner he could get there; the better. I called to describe the situation with the Chief Pilot that we needed 4000/3 miles vis to get out. I described the situation to him; and he agreed that we should do the best we can and depart when we thought we could do so safely. (There is no official weather reporting system on the field.) The weather was changing rapidly; but myself and the other two crews took a best look at what we had and decided that departing Runway 12 and climbing out in visual conditions we could see to the south of the runway (right side of the active runway.) Aircraft Y departed first; and was able to get out in visual conditions. We were next to depart; but an airline had to land before we could depart. We started to back taxi to depart normally from Runway 12 when we heard what sounded like an Aircraft Z operator coming in to land Runway 12; and that he was '20 miles out'. That should have given us plenty of time to depart; so I elected to continue to taxi back and departed the runway normally. When we got airborne; I acquired the inbound flight on the TCAS display; and found that the target was in front of us and was already fairly close to the pattern; and was descending rapidly. I started a right turn to depart as we had announced on CTAF we would; and the incoming target seemed to turn WITH us and continued to descend. I expected him to enter a left traffic pattern; (standard) but he turned into a right downwind right on top of us; and continued to descend. I could not acquire the target visually when I had the chance to scan for it; there were clouds between us and the target. I continued my right turn and started a shallow descent to deconflict with the traffic that seemed to be on a collision course with us; and was descending rapidly into our altitude. We were basically turned to a right downwind; and started a shallow descent when I looked forward and could see that we were descending about 1000 feet above the water when I heard the GPWS call 'TOO LOW; GEAR'. At that point; I had a choice; I had an aircraft right on top of us on the TCAS that was descending into us. I could climb and possibly hit the airplane; or I could continue forward into what I could see in front of me; and say clear of the aircraft. I elected to continue my shallow descent to deconflict with the aircraft. I do not believe I got below more than about 700 feet at the lowest before I felt comfortable enough to continue my climb in visual conditions so that we could pick up our IFR clearance and continue. We continued and landed at destination without further incident.Suggestions: I had to stay in visual conditions to depart this airport; this is difficult to do when there is not an official weather source on the field. (What reliable way do we have to determine if it is 4000/3) This is an airport that we should NOT be operating in/out of when the weather is inclement; in any way. It is very difficult to tell what visibility and ceilings are. I also learned that position reports made by traffic may not be accurate. I could not see the aircraft that was coming in; and I have no idea why they elected to turn into a right traffic pattern. (Directly into our flight path; as we were departing) In the future; it might be best to wait until there is NO traffic at all to depart from an airport like this.
Second reporter narrative
We were departing out of MYEF off Runway 12; VFR; with weather coming in that we were trying to depart before conditions turned IFR. Traffic was know to be inbound but was not giving regular traffic calls at this un-towered field. While we were making a right crosswind then a right turn to downwind to the north we had had to de-conflict with traffic. While de-conflicting to avoid a TCAS alert from the traffic that was 600 feet above us and descending into us we received a GPWS alert for to low gear and the altimeter showed approximately 700 feet. I inhibited the GPWS alert to concentrate on giving traffic; altitude callouts; while helping the pilot flying navigate the weather. We de-conflicted with traffic and preceded VFR till we were able to pick up our IFR flight plan to ZZZ.Suggestions: I would suggest being more aware of traffic in the area while flying outside of the US National airspace system. Not knowing the local knowledge of how aircraft operate; if they are following normal traffic patterns; and standard calls I would give more space between the traffic and our aircraft and ask them where they are in the pattern before initiating a take off.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.