In the UK, CAP746 will get you started. Chapter 4 page 6 and appendix C seem to cover HORVR and IRVR.
Shallow fog is going to be a major hinderance or a 'thing of nothing' depending on where to look at it from. If the vis in the fog is 200m but it's only 10m deep, you'll easily see through it from above, but on or near the ground you won't see much.
CAP 746: Meteorological Observations at Aerodromes | Publications | CAA