Date: 202103
Local time of day: 1201-1800
Location: ZZZZ.ARTCC, FO
Aircraft: B737-800
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Final Approach; Initial Approach
ATC / advisory: Center ZZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Human-Machine Interface; Workload; Time Pressure; Distraction; Situational Awareness; Confusion
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Altitude Overshoot; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence; Inflight Event / Encounter Unstabilized Approach; Inflight Event / Encounter CFTT / CFIT
Detector: Automation Aircraft Terrain Warning; Person Flight Crew
When detected: In-flight
Result: Flight Crew Overrode Automation; Flight Crew Became Reoriented
Contributing factors: Company Policy; Chart Or Publication; Human Factors; Procedure
Primary problem: Human Factors

Narrative: Turning final ZZZZ fully configured at 150 knots I armed the Localizer first than the Approach mode. First Officer inquired and received the landing clearance. I noticed that the glide slope didn't capture and that we were going above the path. I tried to descend in Vertical Speed; but it didn't come active; so it wouldn't work. Approach mode light still on. I disconnected the Autopilot; lowered the nose and started a descend using the VGSI (Visual Glideslope) path indicator and the outside PAPI (Precision Approach Path Indicator). During the descent we tried to reset the Approach/Glideslope unsuccessfully. The approach was pretty bumpy with some good downdrafts. The aircraft went below the glide slope and I started to correct back when the pull up warning came on then stopped right away. Then the glide slope warning followed. I was just under the path recovering and had 3 red lights and 1 white on the PAPI. Speed around 10 knots above Vref and decreasing toward Vref. I was very focused on the approach and continued to an uneventful normal landing.We were configured early; ready for approach; but the Glideslope not capturing and the uncertainty concerning the landing clearance created a distraction that put me behind the aircraft and I developed some tunnel vision trying to remedy the approach. I became fixated and continued when I should have discontinued the approach and gone around. After landing the First Officer said to me that she had mentioned going around; but it hadn't registered with me during the approach. I tell First Officers that there is no mission; but today I didn't follow my own advice. It's easy to become over focused without realizing it. When in doubt; go-around.


Second narrative: The event began while beginning the ILS Approach. The company notes on the approach dictate not to arm the ILS until reaching a certain position because of the possibility of false localizer signals. The Captain was the Pilot Flying and I was the Pilot Monitoring.  I remember thinking that the Pilot Flying armed the approach later than I would have since we were well beyond the designated point. My best guess on what happened is that because of the delay the localizer armed but the glideslope never captured because we were already too high. Whatever the reason for the automation not doing what we had expected; the result was that we realized that the Glideslope never captured and were trying to get the aircraft to come down.Not only were we distracted with being above the intended glide path; but we were handed over to tower late and I was busy with getting clearance to land while the Pilot Flying was flying the plane trying to get back to a stabilized approach. As the aircraft was getting back to a normal glide path (3 red; 1 white on PAPI) around the 500 foot mark I gave my stabilized approach callout and realizing we were slightly above speed and correcting; but the vertical speed exceeded what is acceptable. At this point I said 'I think we should go around'. I can't remember if it was just before or after I said this that we got a 'PULL UP' alert. The Captain elected to continue the landing. Later after discussion; I learned he may have had tunnel vision to the point where my go around call didn't register with him.My unfamiliarity with ZZZZ did not help our situational awareness as well as being distracted with getting switched over to tower (late) and attempting to get landing clearance around the same time we realized the automation did not perform as expected. As a FO/PM not being assertive enough when a go-around was needed.Abiding by company SOP to the letter. No matter what; at 500 feet if stabilized approach criteria aren't met; it's an automatic and firm 'GO AROUND'.


Synopsis: B737 flight crew reported they descended below the glidepath on their approach resulting in an unstable approach and a  terrain warning but the flying pilot continued the approach and landed.