What is the geoid undulation used for in aviation?

In addition of the altitude found on aerodrome information, the French AIP also mentions the value of the geoid undulation::

AIP for Lyon - Saint Exupéry (LFLL)

Geoid undulation is also found in Belgium, Switzerland, Poland, Morocco, Qatar, Sweden... AIP to name the ones that appear on the first pages of Google results.

US FAA on its side mentions the ellipsoidal height directly.

On the figure below:

• Ellipsoidal height is $h$,
• Geoid undulation is $N$
• Orthometric height is $H$

A GNSS receiver determines the ellipsoidal height $h$, and can display the orthometric height $H$ by adding/subtracting $N$ from grid values embedded in the device.

• Is there any use of $N$ in aviation? In the cockpit?

• Are the values of altitudes found on aviation charts equal to $h$ or to $H$ or something else? Does 821 ft expresses $H$ or $h$ for this aerodrome?

Note: As visible on the figure, the vertical direction determined by using $H$ is different than the one determined by using $h$, and if an aircraft is 35,000 ft above the ARP of Saint Exupéry, this gives two possible horizontal positions, which for aircraft can be very distant.

• The question title asks about "use in aviation," but as edited the question seems to be asking more about "use in surveying". Aviation, once you get to the point that an aircraft is involved, uses baro altitude and not much else -- meaning, no, what you're asking about isn't used "in aviation". Used in the mapping & surveying that goes into the products aviators use, absolutely yes, but in the cockpit, we want to know "what's the field elevation" and there is one answer to that, a published number, which is also read on the altimeter. We care not about geoid or spheroid or etc. – Ralph J Sep 22 '17 at 19:23
• @RalphJ: I asked why the geoid undulation is found in the AIP, but if you want to migrate it to another stack, I'm not against it, provided they can answer this question. – mins Sep 22 '17 at 19:27
• I'm not overly concerned about any need to migrate the question; all I'd say is that the geoid undulation number in the French AIP is a parameter that I've never encountered in US documents, neither in airline nor military operations. Somebody out there may use it, but I suspect it's much more used in the surveying/mapping realm than in any aviation operational capacity. Maybe it's just easier to publish that value in the AIP than in its own separate document. – Ralph J Sep 22 '17 at 19:35
• I think gis.SE is the better place to ask. Anyway: usually the WGS84 (the original revision) is used as standard GPS reference. GPS altitude will (usually) give just this. Then other global models (updated more often) give the geoid (and possible referencing newer WGS84 revisions). I'm not sure if FR use one of such model, or a own measures (std global model are also not so precise). It give you just the difference about GPS altitude and "real" altitude (which is also not very well defined). – Giacomo Catenazzi Sep 23 '17 at 5:18
• The geoid has more to do with mapping coordinates to the globe horizontally and measuring distance traveled between coordinates than with actual altitude. Maps will almost always specify which geoid reference they use. This VFR sectional claims to use World Geodetic System 1984, which is WGS 84: (aeronav.faa.gov/content/aeronav/sectional_files/PDFs/…) – user9394 Sep 24 '17 at 10:35

As already explained, in aircraft equipped for IFR, GPS height is not displayed. It is used in EGPWS, but whether that has the map coded with geoid heights and a separate geoid model, or whether it has the map coded directly in ellipsoid elevations is implementation detail of the EGPWS.

However, ultralights may not be equipped with standard instruments and many pilots complement what little they have with GPS units. These are often simple hand-held outdoor units that may not have geoid model in them and thus may show ellipsoid height instead of geoid height (= altitude above sea level).

So my educated guess is that the geoid undulation is published for the benefit of ultralight (including paraglider; also balloon etc.) pilots flying with GPS.

Earth gravity is not uniform due to the non-uniform distribution of mass/matter. Above is the standard model used to describe the undulation (up/down differences) of the geoid: Earth's sea surface's shape based on gravity and rotation (winds and waves are unaccounted for).

GNSS satellites orbit around Earth's center of gravity (a single point). So there will be differences between what a GNSS measures based on its model of the Earth (based on this single point: ellipsoid), and the actual.

Not all countries adhere to the standard above, hence the difficulty is agreeing to a model. GNSS devices use look-up tables to correct for the difference (the two spheres in your post are the difference between what the satellite sees and what it should see).

Cockpits show neither to the pilots. They use indicated or pressure altitudes/levels that work on the barometric pressure.

For cockpit indications: GNSS systems can't substitute for pitot-static measurements because everyone needs to have the same system and have a reliable refresh rate that is independent of external sources. As the image below shows, a pressure based altitude/level is also undulating due to the non-uniform surface pressure and lapse-rates. Planes fly up and down in level flight but it's hard to notice.

(Source)

For charting the terrain: Whichever system a country uses to mark the terrain on its charts, they will state the source in the AIP, as you've demonstrated. For the geoid, countries may even use different models as I wrote earlier.

The good news is each local station will correct the QNH based on the sea level pressure based on the country they are in.

RE edit:

821 ft is the 'H', which is the above MSL elevation after taking into account the geoid. 'h' is what an uncorrected GNSS receiver measures (982' in that picture), and needs to correct by 'N' (161'). Positive undulation is removed since it's above the 'ellipsoid datum'.

What is it used for?

Not used in the cockpit. It is used for local charting (standards differ from place to place; AIP's mention the source).

RE note:

If an aircraft is 35,000 ft above Saint Exupéry airport, then this gives two possible horizontal positions, which for aircraft can be very distant.

No. But I have to explain why. There is no diagram online to explain it since it's a no, so I made my own erroneous diagram.

• blue is geoid
• dashed in ellipsoid
• red is uncorrected receiver height (minus the bit travelling through the Earth)
• green circle shows the different surface locations based on the normals from the different ellipsoid heights down to the geoid (what is proposed; it is not correct)
• (ξ, η) is the deflection of the vertical, the angle stems from the ground, since the topography (different from geoid) is not illustrated above, it stems from where the geoid and ellipsoid meet (a correct sea level for both models)

Deflection of the vertical:

Imagine a table with non-uniform legs, such that two opposite corners are at on the same level, and the other two are not. If I place a ball on that table, it will move toward the lower corner.

If I want to measure this table's level against the ceiling/ground, I will need two vertical angles, one north-south and one east-west. If we had one angle, we wouldn't know the level's direction. That's why two angles are used.

Measuring this deflection is a key element in knowing the undulation (it changes from location to location). That's the angle that is causing this confusion.

x and y:

Now imagine yourself on top of a monument, this monument has x and y ellipsoid coordinates. You then attach yourself to a weather balloon and climb straight up (with reference to gravity). Your handheld GNSS receiver will not show different x and y values for two reasons:

1. x and y are not derived from z (whether corrected or not)
2. your ellipsoid (x, y) location has nothing to do with the undulation

The undulation is a correction for the z, it does not shift your [physical and measured] present location regardless of altitude. If the height (red line) is straight up from the monument, then left and right of the red line are different undulations for different locations.

Note that I couldn't draw the erroneous normals on the other side of the red line if I wanted to.

Check this article: How do GNSS-derived heights differ from other height systems? It explains where high accuracy is needed, and the issues that may arise when two countries with different geoid systems decide to build a bridge between them.

As @JanHudec mentioned, EGPWS needs the correction because its model is ellipsoid. So country x needs to have a system by which they measure the geoid, its undulation, and report to the aviation industry the correction. That's why when an airport is not in the database, the pilot gets, "caution, terrain," when they are on a good approach.

Another application is minimizing the drift of the inertial navigation systems, since they inherently indicate the astronomic vertical. It's cheaper to just correct the drift via the GNSS such as on the Boeing 787 (align-in-motion).

As a pilot, everything is referenced to the altimeter, or the radio altimeter below 200 feet AGL. It is understood that “GPS Altitude” is somewhat close but won’t exactly match up, but that’s as far as we care.

For military pilots doing targeteering (on the ground, pre-mission), they may well get fairly deep into this sort of thing, but in the airline world, it’s all & only about your altimeter in the panel in front of you.

• Is 821 ft ARP altitude determined with a barometer? – mins Sep 22 '17 at 17:50
• @mins most likely surveyed and referenced from a specific vertical datum. – casey Sep 23 '17 at 15:11