Air carrier flight crew reported receiving an aural alert tower advisory for an obstacle during approach in IMC. Flight crew entered visual conditions and continued to a landing.

Reporter 1

On the approach into DCA we received a " Caution obstacle" aural. The visibility was improving from 1/4NM to 7, but the ceiling was still BKN 00 according to the ATIS, which required the use of the LDA Z. FO (First Officer) was flying and briefed the approach, during the briefing we set 720 as the MDA, unfortunately I did not verify this as I was task saturated due to the early morning, fatigue, a significant tail wind and some late approach briefing. Once cleared for the approach we were given direct to FERGI, 3K until established cleared for the LDA. During the approach we had a significant x-wind of roughly 47 knots from the right, roughly 180, which put us left of the 147 degree approach course. I noticed that we were quite far to the left of course and was focused on correcting this. FO switched to white needles to try and get the auto pilot to recapture the Localizer course which helped a bit, but I felt that we were still too far left of course and in danger of encroaching on PLVIA. FO started descending just after FERGI and was using the direct intercept page as his vertical guidance. Unfortunately a combination of task saturation, my target fixation and lack of situational awareness lead to us being right around 800 ft right over WEVPU. We broke out at roughly 1000 ft which is when I saw the buildings we were descending near. Once I heard the aural as well as the tower's advisory, I asked the FO to turn off the auto pilot and start following the river so as to avoid any further conflict, we had the runway and PAPIs in sight at this time. We continued following the river and landed without further incident. Cause: This was a combination of situational awareness, task saturation, fatigue and target fixation. The low Ceilings were a concern and I was fixated on the thought that we were going to have to go around or divert to ZZZ. Once we got to the approach I was further fixated on the fact that the plane was not following the localizer course very accurately and in fact putting us in line with a restricted area. I have been crediting an average of 100 hrs a month and can certainly feel the fatigue, the early morning combined with my commute further exacerbates this issue. Suggestion: More details for this approach in the company pages would be very helpful. Due to a lack of glide-slope as well as the runway not on the approach a procedure to set the field altitude, much like a localizer approach, would be helpful. I debriefed with the FO how we needed to utilize the special procedures manual for an approach such as this, which we do very infrequently.

Reporter 2

We followed the LDA Z 19 in DCA and received an obstacle alert. We set 800 ft and the autopilot followed the vertical speed set by the PF to comply with the altitude restrictions set forth in the procedure. Just before leveling off at 800 ft the aircraft issued an obstacle alert. The autopilot leveled at 800 ft and the PF disengaged the autopilot, turned away from the building, and followed the river to land uneventfully from a stabilized descent. Cause: The procedure has us descend directly toward a building on the approach course. The altitude selection is to be set at 800 ft and the building has a height of 470 ft.