Air carrier Captain reported an Enhanced Ground Proximity Warning System (EGPWS) warning as the aircraft trended below the glide slope as the pilot flying transitioned to visual cues at low altitude in moderate rain. The Captain called for a go-around and returned for a safe landing.

Narrative

We diverted around thunderstorms and had multiple arrival and runway changes. Ultimately we were setup for the ILS 35R at SDF. I was the PM and the FO was the PF. The approach was normal and stable through 500 AGL. We broke about 400 AGL prior to me making the approaching minimums call and on glideslope. The FO called the runway in sight and turned the autopilot off. It was a very variable deck that caused a non standard visual illusion and there was moderate rain. Above minimums I noticed the PAPIs had turned to 3 red and we were trending below glideslope. I announced to the PF that we were starting to duck under. Shortly thereafter I saw the fourth PAPI beginning to turn red. We received an EGPWS (Enhanced Ground Proximity Warning System) alert. I called a go-around and the FO executed it. The aircraft behind us went around as well. We landed uneventfully on a subsequent approach. We debriefed the importance of continuing to maintain a good instrument scan inside when transitioning outside to land in the weather.