Date: 202105
Local time of day: 0001-0600
Location: ZZZ.Airport, US
Weather elements / visibility: Wind
Light: Night
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Initial Approach
Airspace: Class E ZZZ
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: First Officer; Pilot Not Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Distraction; Workload; Time Pressure; Human-Machine Interface; Communication Breakdown
Second reporter function: Captain; Pilot Flying
Anomaly: ATC Issue All Types; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Executed Go Around / Missed Approach
Contributing factors: Airspace Structure; Chart Or Publication; Human Factors; Procedure; Software and Automation
Primary problem: Software and Automation

Narrative: On arrival at ZZZ; winds were variable and began to favor Runway XX for landing. We were set up for landing on Runway XY. I; acting as Pilot Monitoring for this leg due to special qualification airport; suggested to Captain that we swap our planned arrival runway due to winds and additional available landing distance (approximately 500 feet) for landing on Runway XX. The FMC was reprogrammed correctly; briefed; and we accepted a heading to intercept final Runway XX. With approximately a 30 degree intercept; approach control cleared us for the ILS XX. Captain selected approach mode early. This caused the aircraft to capture a false glideslope and the aircraft began a descent prior to capturing the localizer. I called this to the Captain's attention; of which he was also aware.Prior to localizer capture I recommended a discontinued approach. Altitude was well above Minimum Safe Altitude and the approach was salvageable but due to my experience level in the jet; I suggested a soft go-around. The Captain elected to continue; to which I agreed and remarked that our subsequent protected altitude would be 2;600 feet; which we were currently above; and that I would monitor. The Captain; slightly flustered about the false glideslope capture began to fiddle with Auto Pilot disconnect; Flight Director reset; and approach mode was re-armed. The new capture mode now is LOC but with a failed Glideslope. The aircraft has defaulted into the current vertical speed. I call slightly below glideslope; Captain again resets Auto pilot; Flight Director; and re-arms the approach mode. Localizer captures; Glideslope has been armed; and we are currently in a 700 to 800 FPM descent; very slightly low on Glideslope; at a safe speed; and safe altitude.I call attention to our protected Final Approach Fix altitude and glideslope intercept at ZZZZZ 2238 feet. If I remember correctly; we were approximately 3 miles from ZZZZZ when I remarked that at our current Flight Path Angle would have us slightly below our target altitude without any correction at ZZZZZ. Let me be clear; the aircraft was; based on our current descent rate; projected to be only slightly below 2;300 feet at the Final Approach Fix. A minor correction would have rectified the approach path angle and captured the glideslope. I called our altitude to the Captains attention once more approximately 1 to 2 miles prior to ZZZZZ; where we had now reached 2;300 feet; the charted approach value. Right as I was going to call for the Go Around at ZZZZZ; the tower controller issued a Low Altitude Alert; the Go Around was called and initiated; and the aircraft was at approximately 2;100 feet; a little less than 200 feet low at the charted glideslope intercept altitude; as well as above 1;000 feet above ground.The Go-Around was accomplished without error and a subsequent ILS was flown to Runway XX without any additional complications. Upon debrief; I became aware that the Captain was unaware that he had not captured the Glideslope. I re-framed the situation for us to consider alternate action and explained my reasoning for a requested discontinued approach prior to localizer capture. I am still low time and in consolidation. I had no reason to expect that we could not become stable with glideslope capture prior to Final Approach Fix. Hindsight is exactly that and this event began and ended all within 4 miles. The Go-round was completed to qual standards with safety and stable approach criteria in mind.False glideslopes capture prior to localizer capture due to not allowing the aircraft to capture in LOC or LNAV prior to arming the approach mode. Again; I believe I was very clear about our impending altitude deviation; however I don't believe I heard any response from the Captain from 3 miles(my initial call) and 1 to 2 miles(my second que). I could be wrong. The whole event spanned a time frame of less than 3 minutes from 'looks good' to 'doesn't look so good' so I could NOT have fit many more altitude callouts in that span. Due to my low experience in the jet; I incorrectly expected a correction that I did not receive. The go around was initiated at or just seconds after the Final Approach Fix. An assumption of understanding is not the greatest way to handle approaching a go around. I do not believe I was hinting and hoping but I will be more aggressive with my descent planning awareness callouts so as not to enter into a [undesirable situation] in the future. However; the correct decision was made concerning the safe operation of the aircraft and the proper response was executed.


Second narrative: Trip was third leg of the day.  Landed from second leg at around XA:40 local and got to sleep room at XB:10L.  Awakened 30 early of show time at approximately XB:40L.  Weather was marginal regionally and at ZZZ. ZZZ1 was filed alternate but also monitored weather at ZZZ2 for second option.  First Officer has less than 75 hours and ZZZ is Special Qual field. Identified the CFIT (Controlled Flight into Terrain) hazard; short runway; marginal weather; etc.  Pre briefed the ILS XY enroute as winds were favoring that runway.  Also talked about EFVS (Enhanced Flight Vision Systems) and auto land contingencies.  Upon contacting ZZZ approach; they asked if we wanted ILS XX due to a wind shift.  Initially decided to stick with XY but reversed the decision seconds later due to shorter usable runway on XY due to displaced threshold and winds favoring XX slightly.I was flying the approach while the First Officer set up and briefed the ILS XX.  We re-accomplished the approach checklist and accepted a clearance direct to the Final Approach Fix to cross at 2;600 feet and maintain until established; cleared for the ILS.  We put the 2;600 foot hard restriction at the Final Approach Fix and were navigating LNAV/VNAV.  Just prior to Final Approach Fix I mistakenly selected the approach mode.  The aircraft immediately intercepted what I believe was a false glide slope and begun to descend before intended.  I turned off both flight directors and attempted to get the aircraft out of approach mode. The aircraft stayed in approach mode because I did not disengage the autopilot.  So; after re-engaging the aircraft tracked the localizer in LOC mode and Vertical Speed with Glideslope Flight Mode Annunciation struck through as a failed mode.  Realizing the error; I disconnected both flight directors and autopilot and immediately re-engaged and re-automated.  At this point I believe the aircraft momentarily intercepted a glide path; and almost immediately and simultaneously with the Tower Controller realized we were about 250 feet low of the glide slope intercept altitude.  We immediately performed a discontinued approach and climbed to 3;000 feet.  We received vectors for another ILS XX and auto landed uneventfully.Fatigue was undeniably a root cause although not the only issue here.  Flying two legs and then getting only 30 minutes opportunity to nap between legs was just a little too much for me despite 'feeling pretty good' ahead of the flight involved. In retrospect I should have used LNAV/VNAV to get solidly on the ILS final before selecting approach mode.  And; also; I should have and will in the future decide to discontinue an approach as soon as any serious mode switching starts happening on the final approach. In the light of day and after a nap I know this solidly; but it is much more difficult with a foggy brain at XF:00.  So; in the future; I'm going to use LNAV/VNAV more and not use APP until later in the approach. Revision of the flight pairing to allow for more rest time...even an hour nap; would help.  Also; making sure to use LNAV/VNAV and protect GSIA (Glide Slope Intercept Altitude) at 1 NM prior to the intermediate fix.


Synopsis: Air carrier flight crew reported the Captain flying descended below the glideslope and Final Approach Fix altitude and received a Low Altitude Alert from the Tower Controller.