I was a "scope dope" in USN 1981 - 1994. My duties on the radar navigation team for leaving/entering port was shipping and later piloting officer. We would practice/simulate low visibility navigation from time to time and were even required to maintain qualifications on a yearly basis. However, being a warm water sailor in Mayport, Florida, I only experienced TRUE low vis (heavy fog) conditions twice, sailing in and out of Newport, RI, and New York, NY. It was considered too risky to attempt during peacetime simply because we didn't want to run over some poor sailboat or fisherman. But this was because VISUAL conditions were hindered, not radar. We had an AN/SPS-55 surface search/navigation radar that was basically the MILSPEC version of the common "pathfinder" radars found on damned near every merchant/commercial vessel in the world. It performed admirably during fog; if the fog was truly dense you could tell by the noise on the PPI but it didn't have much effect on radar returns. What DID have effect besides very heavy seas where contacts would disappear/reappear in "valleys" was high winds. As noted earlier, this would cause a large garbage ring around own ship that could be controlled by carefully adjusting gain but it was very annoying. Hope I didn't put 'yall to sleep; and radar propogation and theory is one of my faves so ask away if you want...Zeke.
Edit: Oh yeah, I know SURFACE sonar/wave path propogation/target motion analysis (TMA) pretty well too. That TMA stuff was classified forever, but I've seen it in games from folks like Sonalyst and it's pretty darned accurate...