The weather is 200 and ½. You just flew the ILS and see the runway. You abandon the approach and go visual. Your landing attempt goes awry and you have to do a go-around. Remaining visual is best, but you cannot, and re-enter the clouds. What is your next move?
To me, the logical move is to fly the missed approach procedure you briefed a few minutes ago and tell ATC you are on the missed approach from a bounced landing (meaning you were on the runway). While it is true the missed approach guarantees terrain separation, it is also true that safety net begins at the missed approach point (MAP) and altitude at the MAP. You are obviously well below and well past that point. However, until or unless ATC tells you otherwise, that is all you have.
Are there any other options or opinions? Feel free to chime in and add your own thoughts.
From a legal perspective, unless/until you cancel IFR, you're still cleared to perform the published or otherwise assigned missed approach. Even at a tower-controlled airport where they cancel your IFR on landing, they're not going to do that if they see you bounce and go around.
Wherever you are, you have to consider what Hoss said about obstruction clearance from lower and farther downstream than the MDA/DA and MAP. The AIM discusses this in detail in Section 5-4-21h. You should also be considering any non-standard ODP for that runway – and you're not going to have time to look that up while you're climbing out from that balked landing. That's something you may wish to make part of your preflight planning.
All that said, I don't think you need to tell the controller you're off a balked landing. At a tower-controlled airport, they know that already – either they saw it, or it's so foggy they couldn't see it and they won't care. At a non-towered airport, they don't much care initially why you went missed, just that you did. You can give them the details later after you're in radar contact and are stabilized on the missed. Initially all they want is your altitude, an IDENT, and your intentions.
You should be thinking about the safest alternative given the lack of visibility and the possibility of terrain around you. The published missed approach plus any ODPs will keep you clear of terrain. You can tell ATC what's going on after you stabilize on the missed approach.