How should I insulate my concrete ceiling in a safe room under a concrete porch?
Given it's 10 feet tall a dropped ceiling and insulation batts would be the &quot;most obvious&quot; approach (to me) if you deal with the leaks from above by sealing them above. Come down to 8 feet with a grid and place batts on top of the panels.
If you let it leak, then you need to come up with a way to redirect the leaking before you hit the insulation, or use insulation that doesn't care (and costs more.) Something like a set of sloped 2x4 &quot;rafters&quot; to support a piece of plastic attached at the high side and directed into a gutter on the low side, then hang ceiling below them and insulate between.
If the concrete walls to the porch floor are partially above-grade and uninsulated inside or out, then they are also contributing to the cold, since concrete is a terrible insulator, at roughly R1 for 15 inch thickness. Concrete below grade transitions to seeing less extreme temperatures on the outside, but still generally below &quot;comfortable&quot; for people for much time.