Date: 202201
Local time of day: 1201-1800
Location: COS.Airport, CO
Flight conditions: VMC
Light: Daylight
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
Airspace: Class C COS
ATC / advisory: Tower COS
Reporter organization: Air Carrier
Reporter function: Pilot Flying; First Officer
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Second reporter function: Pilot Not Flying; Captain
Anomaly: Deviation - Altitude Overshoot; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Detector: Automation Aircraft Other Automation; Person Flight Crew
When detected: In-flight
Result: Flight Crew Returned To Clearance
Contributing factors: Environment - Non Weather Related; Human Factors; Airspace Structure
Primary problem: Environment - Non Weather Related

Narrative: On downwind for Runway 13; I set altitude pre-select to I believe 7;200 feet (1;000 ft above TDZE); when I should have chosen 7;700 (1;500 feet above TDZE) or even 8;000. Due to up sloping terrain to the north of the airport; I realized my I was getting too low visually out the cockpit window; and about the same time the gear horn went off. Shortly after ATC called with a low altitude alert. At that time I was already adding power to climb a few hundred feet in preparation for the base turn. I finished configuring the plane prior to being unstable on final; and landed without further incident.Sloppy math and poor planning. I had quickly calculated my base turn to final 1;000 feet above the field instead of 1;500. The rising terrain on the left downwind for Runway 13 made this mistake more problematic. A company reference briefing warning of the rising terrain on runway 13's left downwind could have helped as well.Flying DMA [Direct Memory Access] mostly these days; it had been a while since I've done a real visual approach in the pattern. My lack of currency and my inattention to the math led to this stupid mistake. A second corrective action would be a company briefing page for Runway 13 pattern; warning of the rising terrain to the north of the field.


Second narrative: We were executing a visual approach into COS Runway 13; left traffic when we ATC called out an altitude alert as we got too low over the rising terrain to the northwest of the airport.  we were cleared on a visual approach from the approach controller from the left downwind; once cleared for the visual approach; the First Officer/Pilot Flying called for me to bug an altitude of 7;200 and he started a descent.  I had the feeling that was too low; I quickly cross referenced the chart to see what an appropriate pattern altitude would be.  I realized that we wanted me to bug an altitude that would give us a 1;000 feet pattern altitude; so I bugged and told him we were going to fly 7;700 feet as that would result in the normal 1;500 foot pattern altitude in which we fly.  At that time; we were about 8;000 feet and still descending and I realized that we were in close proximity to the ground.  The radio altimeter was just showing descending through 1;000 AGL; and at that very time ATC called with an altitude alert.  I instructed to First Officer to climb above 1;000 AGL.  We continued the pattern and landed without further incident and meeting the stable criteria prior to reaching final.  We did not get low enough to receive an EGPWS alert.Poor planning of the approach; and failure to take into account that standard traffic pattern altitudes would result in rising terrain coming up to within 1;000 feet of our standard TPA's; while on left downwind; while north and northwest of the airport.  Also; as a CA and PM I failed to promptly realize; or plan that we would need a higher altitude that what was bugged.  I corrected the First Officer by bugging a correct TPA; but even that was too close to terrain; and we were 300 feet above that altitude when we crossed the 1;000 AGL barrier.Although I take full responsibility for this event; I think a note of this threat listed within our Jepp 10-7 charts for this airport is warranted and would be adequate for preventing future similar events.


Synopsis: Air carrier flight crew reported receiving a low altitude alert warning from ATC during approach to COS airport.