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ILS Category 2 approaches use a Radio Altimeter (RA) derived DH (Decision Height). An RA measures the aircraft height directly above the surface immediately below the aircraft. Any sloping terrain, obstacles, etc. that might cause a rapid fluctuation or interference with a stabilized and smooth decrease in RA altitude (near the DH) could result in a less predictable/precise arrival at the DH.

Are there specific runway (displaced threshold or similar) design criteria that require the surface from which the RA takes its measurement at the DH point to be flat?

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Indeed:

To permit the use of the automatic landing system, ICAO also recommends that slope changes must be avoided or, when it is not possible, kept to a maximum of 2% per 30m (i.e. a minimum radius of curvature of 1500m) in the area located just before the threshold (60m wide, 200m long). This limitation is due to the fact that automatic landing systems use radio altimeter and a rapid slope change could disturb the landing.

GETTING TO GRIPS WITH CAT 2 / CAT 3 - Airbus - SKYbrary

The detailed ICAO recommendations referenced above can be found under § "Pre-threshold terrain" in ICAO Doc 9365 (Manual of All-Weather Operations) and Annex 14.

I'm fond of a French workaround; at some locations radar reflectors on masts are used to fool an RA into thinking the pre-threshold area is flat:

enter image description here
lustublog.com

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    $\begingroup$ The details of the reflectors (if a hot link works on the SIA site). The system was added for low cost airlines which are a large part of the traffic here. $\endgroup$
    – mins
    Nov 6 at 18:41

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