While there is NO DH for Cat.III operations you see "Alert Height" sometimes mentioned.
It is not published in CAT.III minimums, It is a "company procedure".
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Right or wrong, I generally say Cat.IIIa has a AH of (about) 50 ft above TDZ.
And for Cat.IIIb, a AH is (about) 35 ft above TDZ.
That is for a 747-200... Some were Cat.IIIa. None were certificated Cat.IIIb.
We discontinued Cat.IIIa... Company only does Cat.II minimums.
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Happy contrails