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DA and DH aren't interchangeable phrases, they're two completely different things. Let's look at the difference..
In the lowest of weather conditions, you'll likely find yourself flying a CAT I ILS or RNAV LPV approach. And if your airplane is certified for extremely low weather conditions, you might even fly a CAT II/III approach.
The type of approach flown determines whether you'll use a DA or DH for your minimums. For simplicity, we'll explain the concept using ILS approaches.
Decision Altitude (DA) is an MSL altitude. When you fly a Category I ILS, which is what almost all general aviation pilots will fly, you fly to a DA.
Looking at the ILS approach in the image below, the published minimums for the straight-in ILS 35R are "6085 - 1/2".
That means DA is at 6,085' MSL. As you're descending on the glideslope, when you reach 6,085', you're at DA.
You'll see in smaller numbers "200" published next to the minimums for the approach. That's the decision height (DH). That means you'll be 200' above the touchdown zone elevation (TDZE) when you reach DA.
Most Cat I ILS approaches get you down to 200 feet above TDZE, but that's not always the case.
Looking at the Olympia Regional Airport (KOLM) ILS 17 below, the ILS DA is published at 425' MSL. That's 218' above TDZE.
So why is this the case? As pilots, we don't know for sure, but it's likely due to an obstacle on final approach.
Decision Height (DH) is your height above the touchdown zone elevation (TDZE). If you fly a CAT II/III precision approach, you'll fly it to a radio-altimeter (RA) based DH. This requires your aircraft to be equipped with a radar altimeter, which measures your height above the terrain presently beneath your aircraft.
CAT II/III approaches are flown to DH minimums less than 200' above the runway's TDZE. That's why they're published as a CAT II/III approach, and not a standard CAT I approach.
As you fly a CAT II/III approach, you'll reference your aircraft's RA reading to determine when you've reached DH.
If you're flying a Cat I approach, which most of us are, you're flying to DA minimums. And if you're flying a CAT II/III approach, you're flying to DH minimums using a radar altimeter.
Whether you're starting your instrument training or brushing up for your next flight, this course gives you the knowledge, confidence, and flexibility to be a great instrument pilot.