# 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. 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. 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). 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

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).

• "Now imagine yourself on top of a monument, this monument has x and y ellipsoid coordinates. You then [...] climb straight up (with reference to gravity). Your handheld GNSS receiver will not show different x and y values for two reasons": I'm not sure you're right. The gravity vector is normal to the geoid (per definition of the geoid), but not normal to the ellipsoid (else the geoid would be just an ellipsoid). If you climb along a vector not normal to the ellipsoid, then the ellipsoidal coordinates change.
– mins
Jun 19 '20 at 11:59
• "Cockpits show neither to the pilots". I would only says this with the caveat that some cockpits do display height above geoid or "GSL" altitude on certain pages a cross-check. Additionally, this data is used in terrain awareness, including synthetic vision, which is then shown to the pilots. Sep 16 '20 at 19:12

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. Sep 23 '17 at 15:11

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.

Those who are saying 'everything in aviation is referenced only to the altimeter' are oversimplifying the situation today with GNSS based instrument approaches providing vertical guidance. A barometric altitude will be used to determine the point at which the pilot must go-around if runway environment isn't visible, but the glideslope that the aircraft follows will be generated by a GNSS navigation system onboard using a Geiod undulation corrected 'zero height' datum at the touchdown point on the runway.

It's well known that there will often be differences between the specified check altitude at a certain point on the descent path and the actual barometric altitude, which is why such approaches may specify a minimum temperature below which the approach can not be used.

• Geoid undulation publication is a recommendation from ICAO. Not all countries are ready for it, and therefore the information is often missing. GNSS are sensors able to deliver the height above ellipsoid, to get the MSL value, one need to subtract the geoid undulation (some GNSS do this operation themselves, some not).

• Undulation is not used by crews, and regulation prohibits the use of GNSS altitudes. For ATC officers and aircraft crews, enroute and terminal vertical navigation is done exclusively with barometric values, even when GNSS is used by the avionics in the background (like in LPV/GBS approaches).

• Therefore at the moment, altitudes in charts are all expressed as above sea level (MSL) values, the common altitude reference.

• Designing an approach with a GNSS vertical guidance requires knowing the geoid undulation as the procedure starts from MSL altitudes, but the final point (threshold crossing) of the procedure is encoded in the navigation database using ellipsoidal heights. Example, for a GBAAS approach the points LTP, GPIP and FPAP are not referenced to MSL, but to the ellipsoid (which differ from MSL by the geoid undulation):

GBAAS (GLS) approach design with LTP, GPIP and FPAP referenced to ellipsoidal height h. Source

• It may take a long time before some countries are able to publish the undulation value for runways, as determining the undulation at the point of interest with a precision of 25 cm requires an extended leveling system, based on detailed gravimetric data from surveys connected to WGS-84 altitude reference points.

Undulation value is recommended by ICAO

1.4.8: GNSS-derived heights are referenced to the WGS-84 ellipsoid which will usually differ from the “normal” (orthometric) height at the same point. The difference will be of significance in the aerodrome environment when navigating with GNSS sensors. The difference between orthometric height (geoid height, elevation) and WGS-84 ellipsoidal height must therefore be made available to the aviation community. The height that separates geoid and WGS-84 ellipsoid is the geoid undulation.

1.4.9: Geoid undulation is required for airport elevations, runway thresholds and touchdown and lift-off areas (TLOFs) or thresholds of final approach and take-off areas (FATOs) at heliports. (See also Appendix B.)

This recommendation is therefore also found in Annex 4 (Aeronautical Charts) of the Chicago Convention:

2.18.2.1 Mean sea level (MSL) datum, which gives the relationship of gravity-related height (elevation) to a surface known as the geoid, shall be used as the vertical reference system.

2.18.2.2 In addition to the elevations referenced to MSL, for the specific surveyed ground positions, geoid undulation (referenced to the WGS-84 ellipsoid) for those positions shall also be published as specified for a particular chart.

and in Annex 15 (Aeronautical Information Services) which also recommends to determine the geoid undulation from the EGM96 gravimetric model, and when not used, to include proper transforms from the model used to EGM96.

ICAO related recommendations are not yet implemented everywhere

This doesn't mean all ICAO members currently implement these recommendations, e.g. in UK, from AIP GEN 1.7 section (differences with ICAO):

• In the UK, OSGM02 is the geoid model used for determining heights above MSL.
• Parameters for height transformation between OSGM02 and EGM-96 are not published.
• Geoid undulation of the geometric centre of TLOF or of each threshold of FATO not published.

or for India, GEN 1.7:

The WSG-84 geoid undulation is not published

From a pilot point of view, GNSS altitudes are not used in flight, navigation is based on barometric levels (QNE) or barometric altitudes (QNH). For France, the example in the question, the AIP includes this warning:

GEN 2.1.4.2: User’s attention is drawn towards that publication of the geoid undulation does not modify the GPS restrictions for use. Particularly, the altitude information given by GPS has not to be used.

MSL vs geoid height vs GPS/ellipsoid height

MSL is by definition the height (or altitude) above mean tidal height. The reference has been determined using tidal gauges until recently. Since WGS-84 has been established as the global reference for aeronautical charts (1998), the MSL is approximated by the geoid surface. The height above the geoid is named orthometric height, and referred to as H.

Ellipsoid and geoid, source: Trimble

MSL and H are nearly equivalent, still the definition of the geoid refers to the equipotential of gravity coinciding with the shape the ocean surface would take under the influence of the gravity and rotation of Earth alone, if other influences such as winds and tides were absent. The actual mean sea level can be influenced by local events (like currents) taken into account by a tidal gauge, while the geoid is a surface of equal gravity.

On the other hand, WGS-84 ellipsoid is the approximation of Earth volume as perfect oblate sphere of radius 6378x6357 km. It also tries to coincide with sea level over the globe. The height above the ellipsoid is known as ellipsoidal height, height above ellipsoid (HAE) or h.

While the ellipsoid is a geometric model, the geoid is a physical (gravity) model. With no surprise the ellipsoid and the geoid don't coincide. The geoid can be locally above (up to +86m) or below (down to -107m) the ellipsoid, depending on the local gravity anomalies (mountains, oceanic trenches, crust density, etc). The difference is referred to as the geoid undulation (or geoid height) N.

Of course H = h - N, a vector form, as the geoid and the ellipsoid are generally not locally parallel.

GNSS receivers are able to determine h, any value of H is computed from h and a value of N interpolated from points in a built-in grid established from a gravitational model, ICAO recommends EGM-96 as the global gravity model, but older GNSS use NATO STANAG 4294 Appendix 6.

The way the altitude is computed is:

• GNSS determines a 3D position from satellites, expressed as x,y,z in a Cartesian Earth centered frame.
• The position is converted into latitude, longitude and h using the ellipsoid model and a polar frame.
• Optionally H is computed from h using the geoid model.

Wording used in aviation for GNSS altitudes

The wording related to heights is abused enough in the geodetic field. In the aviation/GNSS field, there is often a specific wording to prevent further confusion:

• HAE (height above ellipsoid) should be used for h.
• HAG (height above geoid) should be used for H.

and GNSS MSL altitude is sometimes also referred to as Height-Above-Geoid (HAG) (EASA)! Both heights are also qualified geometric, in the sense they are actual distances, not a pressure differences.

GNSS altimetry is not directly shown to the crew (as noted Cody P some avionics may have an option to display them), but appears in automatic processing, like in LPV approaches and ADS-B messages, or in TAWS (as noted by Cody P).

Designing a SBAS approach requires knowing the geoid undulation information

Approaches were the vertical guidance is based on GNSS work with a satellite based augmentation system (SBAS) (well known are WAAS in the US and EGNOS in Europe, but there are other, including MSAS, GAGAN, SDCM, SNAS, see this map), or a GBAS/LAAS. The final approach segment of the procedure is described in ARINC-424 by a FAS data block embedding altitude as HAE, e.g. to describe the landing reference point (LTP/FTP).

However these values are used only by the flight management system (FMS, FMGS) which computes the GNSS approach path. The crew still works with the barometric/radioaltimeter indications to assess minimums and take decisions and the approach is monitored using the standard ILS course deviation indicator.

As the procedure and the aircraft sensors use only HAE values, there is not need to convert them into HAG, the geoid undulation is not required for the process to work. However the procedure designers will likely start with MSL altitudes, and convert them into HAE heights as required, using the undulation information.

The use of GNSS in aviation is still in its infancy, maturity will likely come with future ATS/ATM models and the integration at forced march of the growing unmanned traffic. Whether the geoid or ellipsoidal height, or both will be used is still to define, but...

ADS-B is going to use the GNSS ellipsoidal height

Mode S ADS-B messages contain the barometric altitude (1013.2 hPa) as in mode C and optionally a GNSS altitude which can be based on geoid or ellipsoid height, e.g. for Airbus, it's dependent on the ADS-B transponder standard (DO-260):

• A320 and A330
• DO-260: MSL
• DO-260A HAE or if not available MSL
• DO-260B: HAE
• A350 and A380: Always HAE

Regulation needs to better define how altitudes will be measured, FAA tries to move forward in AC 20-165B:

Geometric altitude for ADS-B purposes is the height above the WGS-84 ellipsoid (HAE). Geometric altitude is required to be transmitted by 14 CFR 91.227

The choice for h (HAE) is motivated by the fact h is the raw value computed by a GNSS receiver, while H requires an additional built-in lookup-table.

As ADS-B is going to use only HAE, the published undulation information is also useless in this application.

• Fantastic answer, although I have two things to add to the "wording" section. First, there is actually an FAA Advisory Circular, AC 20-163, dedicating to naming orthometric height, which recommends it be kept from confusion with barometric MSL and kept short, with a suggestion of "GSL". Second, some pages on some devices do display HAG/GSL. See the Garmin 750 for example. Sep 16 '20 at 19:20
• @CodyP: Thanks for the comment, interesting points, useful additions. I didn't know TAWS was using the GPS altitude, as ACAS uses QNE, but that makes sense.
– mins
Sep 16 '20 at 20:37