Light Transport; Low Wing; 2 Turbojet Eng
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 118; Flight Crew Total 5000; Flight Crew Type 118
Situational Awareness
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued Advisory / Alert; Flight Crew Diverted; Flight Crew Took Evasive Action
Human Factors; Weather
We were flying to ASE and I was the Pilot Monitoring. As we approached Aspen; we were given vectors to intercept LOC E into ASE. We accepted clearance to maintain 13;000 ft until established and clearance to execute LOC E approach. As we were intercepting LOC we picked up visual with the airport and commenced descent towards it while having visual reference with the airport and all the terrain around. In the midst of all things happening quickly and the excitement of having visual with the airport; I failed to communicate to ATC my intention of executing visual approach. At some point we lost the visual with the airport due to a cloud layer just ahead of us; but not the terrain. At the same time ATC issued an altitude alert to us due to us being lower than what LOC approach altitudes called for. I advised that we had terrain in sight but lost the visual with the airport and said that we would be going missed and starting a climb. We got another altitude alert from ATC. We advised we are in a climb and asked vectors; until we decide what to do. We proceeded to ZZZ airport afterwards.  At no time we were in IMC conditions and maintained visual clearance from all the terrain. My mistake in this case was deviating from ATC clearance and going visual without communicating that to ATC. And also; not staying on a LOC due to a cloud layer over the airport. At no time was the aircraft in IMC conditions and we were maintaining clearance with terrain at all times. By all means the aircraft was never put in any unsafe condition.  I did learn from this experience to clearly and concisely communicate any and all of my intentions with ATC; so there is no misunderstanding at any point of the flight.
Corporate jet non-flying Captain reported diverting to an alternate airport after receiving a low altitude alert from ATC on approach to ASE airport.