Narrative:

Clearance was depart runway xx SID; but intercept airway; not to track to ZZZ VOR; maintain 8;000 ft. I briefed my captain (his leg) on the clearance and he said it was normal during clear weather to depart on the SID; only to be given a direct to clearance in the turn. Off the crosswind leg; we selected direct zzzzz; as it offered the most logical track with optimal terrain clearance. It was hot; but we were climbing well at 73K lbs. At around 4;100 ft. We began accelerating to 250 kts. And the rate of climb slowed to 500 FPM. There was no green; yellow; or red terrain in the map. It was all black; meaning not a threat. We recieved a radio call from ATC; giving as an altitude alert and querying us of possibly leveling at 4;000 ft. (We were cleared to 15;000 ft.; which was in the alerter). At that point we were in a slower climb as we were accelerating to 250. He directed us to expedite our climb for terrain and further turned us 30 degrees right; although we were well clear of everything. Captain selected man speed 210 kts. And increased our rate of climb. 10-15 seconds later; center reported clear of all terrain and we resumed on coarse. A few minutes later; center advised us of a possible deviation and passed a number to call. We were VMC and clear for the entire evolution; which lasted about 30 seconds.in hindsight; I will either fly the full SID if there's any question (at a minimum; clarify with clearance delivery); or possibly request a heading departure if that's what it sounds like I'm doing anyway. I think I might have focused too much on the 'intercept the V386' verbiage when they were possibly expecting us to fly a climbing course reversal procedure over a VOR; as depicted. Sometimes what's most logical; economical; or 'how it's historically flown' is actually a recipe for a violation. I don't think this event would have been an issue; except that the ATC software triggered an alarm; based on the decrease in climb rate (as the aircraft decreased pitched momentarily - ap engaged - in an effort to attain 250 kts.) with the associated terrain in the distance. Slowing increasing the airspeed in manual fashion; while keeping the rate of climb consistently between 2;800-4;000 fpm would have kept us trending in a conflict-free direction. It was only my second time into ZZZ and it bit me. It's a special airport for a reason and this a great example of why every crew has to bring their a game; every time.

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Original NASA ASRS Text

Title: E175 flight crew reported 'low altitude alert' from ATC during a mountainous terrain departure.

Narrative: Clearance was depart Runway XX SID; but intercept airway; not to track to ZZZ VOR; maintain 8;000 ft. I briefed my Captain (his leg) on the clearance and he said it was normal during clear weather to depart on the SID; only to be given a direct to clearance in the turn. Off the crosswind leg; we selected direct ZZZZZ; as it offered the most logical track with optimal terrain clearance. It was hot; but we were climbing well at 73K Lbs. At around 4;100 ft. we began accelerating to 250 kts. and the rate of climb slowed to 500 FPM. There was no green; yellow; or red terrain in the map. It was all black; meaning not a threat. We recieved a radio call from ATC; giving as an altitude alert and querying us of possibly leveling at 4;000 ft. (we were cleared to 15;000 ft.; which was in the alerter). At that point we were in a slower climb as we were accelerating to 250. He directed us to expedite our climb for terrain and further turned us 30 degrees right; although we were well clear of everything. Captain selected man speed 210 kts. and increased our rate of climb. 10-15 seconds later; center reported clear of all terrain and we resumed on coarse. A few minutes later; center advised us of a possible deviation and passed a number to call. We were VMC and clear for the entire evolution; which lasted about 30 seconds.In hindsight; I will either fly the full SID if there's any question (at a minimum; clarify with clearance delivery); or possibly request a heading departure if that's what it sounds like I'm doing anyway. I think I might have focused too much on the 'intercept the V386' verbiage when they were possibly expecting us to fly a climbing course reversal procedure over a VOR; as depicted. Sometimes what's most logical; economical; or 'how it's historically flown' is actually a recipe for a violation. I don't think this event would have been an issue; except that the ATC software triggered an alarm; based on the decrease in climb rate (as the aircraft decreased pitched momentarily - AP Engaged - in an effort to attain 250 kts.) with the associated terrain in the distance. Slowing increasing the airspeed in manual fashion; while keeping the rate of climb consistently between 2;800-4;000 fpm would have kept us trending in a conflict-free direction. It was only my second time into ZZZ and it bit me. It's a special airport for a reason and this a great example of why every crew has to bring their A game; every time.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.