B737-800
Flight Crew Air Transport Pilot (ATP)
Flight Crew Total 25000
Fatigue; Situational Awareness
Deviation - Altitude Excursion From Assigned Altitude; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors; Weather
On approach to DCA we requested an RNAV approach with approach control; final controller cleared us for a visual...we were IMC. We told him we wanted the RNAV. He asked who we requested that with. Gave us a vector to final; and cleared us for the approach. I selected LNAV. I believe I then selected minimums then VNAV. The aircraft seemed to react as I expected. We broke out of the bases around 3000 ft aircraft was following the magenta command bars yet after breaking out and descending the visual picture was not right to me. I was checking altitudes when the tower controller advised they had a low alt alert to check our altimeter. I was cross checking everything; determined we were in fact low. Canceled the auto pilot and hand flew to climb back to 1000-1200 ft re-intercepted glide path and landed. I thought about this for quite some time. After sleeping on it I can only figure I was in LVL CHG and not VNAV. But I am still not exactly sure why the jet followed the command bars and ended up low.There were many stress factors that day; from waking up to a blizzard; plowing snow before work; having my sump pump fail at home that morning and arranging to get it fixed on a Saturday of a blizzard. Driving to work in a blizzard. Had aircraft loaded; door closed and ready to depart at XA50; getting deiced twice and not pushing off the gate till after XH00 and all the passenger drama; deice drama; airport open then closed then open. Looking back this had a toll on my decision process by XJ00 that evening (the time of the event). It is many small items - the blizzard; ATC not knowing it's IMC; getting a 'different' vector to final; high but not too high. Many small occurrences can add up to a high work load after a long day.
B737-800 First Officer reported receiving a low altitude alert on approach to DCA after following flight director LVL CHG guidance when he thought he was in VNAV.