PSLE Science Reality Lab 370 | GPS Altitude, Ellipsoid Height and Mean Sea Level

PSLE-SCI-REALITY-0370

Wait, What? A Height Number Needs a Reference Surface

A hiking app shows Altitude: 100 m. A learner says, “That means I am exactly 100 m above mean sea level.”

Maybe—but the number alone does not tell us that.

Global Navigation Satellite System positioning, including GPS, naturally determines position relative to a mathematical reference ellipsoid. Many apps, maps and devices can convert that geometric height into another kind of elevation using a geoid model or another vertical reference. Other systems may label transformed values simply as “altitude”.

The learner’s job is therefore not to distrust satellite positioning. It is to ask one precise evidence question: 100 metres above which reference surface?

Quick Answer

A height value is incomplete without knowing its reference surface or vertical datum.
GNSS can produce an ellipsoidal height relative to a mathematical ellipsoid.
Elevation used on many maps is often an orthometric height referenced to a geoid or defined vertical datum that approximates mean sea level.
Ellipsoidal height and orthometric height are not generally the same number.
A device or app may convert between them using a geoid model, so do not assume the screen is showing the raw GNSS ellipsoidal height.
Two altitude readings can differ because they use different reference systems, models, sensors or measurement conditions even when the observer has not moved.
Before comparing heights, match the reference system as well as the unit.

The Exact Learner Job This Reality Lab Owns

This volume owns one narrow real-world job: how to evaluate a GPS/GNSS altitude readout by checking whether the displayed height is referenced to an ellipsoid, a geoid/vertical datum, terrain, pressure calibration or another defined surface before calling it “metres above mean sea level”.

It does not own GPS physics, map contours, measurement uncertainty, coordinate systems or elevation as a science concept. Those remain with existing owners. This page applies their logic to one communication object: the altitude number on a device, app or dataset.

Rebuild the Evidence Object: Three Screens, Three “100 m” Claims

Imagine three original display cards for the same fictional observation point.

Display	Shown value	Metadata
Receiver A	100 m	Ellipsoidal height
Mapping App B	72 m	Elevation using a geoid/vertical datum conversion
Terrain App C	74 m	Elevation read from a terrain model grid

A learner who sees only the numbers may think two systems must be wrong. But the evidence objects are not yet matched. The three values may refer to different surfaces or methods.

Observed, Claimed and Inferred

Layer	Example	Strong response
Observed	The screen displays “100 m”	Record the number and unit
Claimed	The software labels the field “altitude”	Check metadata or documentation for the reference
Inferred	It must be exactly 100 m above mean sea level	Do not infer until the reference is known
Inferred	A second device showing 72 m is definitely inaccurate	First check whether both devices report the same kind of height

Why a Reference Surface Is Necessary

“Height” sounds simple until we ask where measurement begins. A classroom ruler starts at its zero mark. A thermometer scale has a defined reference. A map elevation also needs a zero surface.

For satellite positioning, the convenient reference is a mathematically defined ellipsoid: a smooth model approximating Earth’s shape. For many practical elevations, people instead want a height related to gravity and mean sea level. A geoid is a model of an equipotential surface of Earth’s gravity field that closely represents global mean sea level and extends conceptually beneath the continents.

The National Geodetic Survey explains that GPS/GNSS heights are typically ellipsoidal heights and that conversion to orthometric elevation requires a geoid model or appropriate vertical-datum transformation.

Two Height Ideas Without the Heavy Mathematics

Height idea	Reference	Useful learner description
Ellipsoidal height	Smooth mathematical Earth ellipsoid	Geometric height used naturally in GNSS coordinate calculations
Orthometric height / mapped elevation	Geoid or defined vertical datum related to gravity	Height used to describe elevation in a mean-sea-level-like reference system

The two surfaces are not identical. Therefore a single physical point can have one ellipsoidal height and a different orthometric elevation without contradiction.

A Reference-Surface Diagram You Can Draw on Paper

Draw three curves across a page. The highest curve is the ground at a hill. Beneath it draw a gently wavy line labelled geoid / vertical reference. Then draw a smoother oval-like line labelled ellipsoid. Place one point on the hill and draw two vertical arrows down from it, one to each reference surface.

The arrows can have different lengths even though they begin at the same point. That is the core idea. The physical location did not move; the reference changed.

Representation Check: “Altitude” Is a Friendly Label, Not a Complete Definition

Consumer interfaces often use simple labels because most users do not want a paragraph of geodesy on the screen. “Altitude” may be useful shorthand, but scientists still need the metadata behind the shorthand.

When accuracy matters, ask whether the displayed value is:

a GNSS ellipsoidal height;
a GNSS height corrected with a geoid model;
a map or terrain-model elevation;
a barometric estimate adjusted using pressure and calibration;
or a fused estimate combining several sources.

Different devices and applications can make different choices.

Comparison Check: Match the Datum Before Comparing the Numbers

Suppose Dataset P lists a station at 84 m and Dataset Q lists it at 111 m. A careless reader subtracts and announces a 27 m error.

A stronger reader checks the vertical reference first. If P is an orthometric elevation and Q an ellipsoidal height, the difference may largely reflect the reference surfaces rather than a measurement mistake.

This is a general PSLE Science habit: before comparing two measurements, make sure they represent the same quantity under compatible definitions.

Method Check: Satellite Height and Terrain Height Are Different Evidence Routes

A terrain app may obtain elevation from a stored digital elevation model rather than from the phone’s immediate GNSS solution. The displayed number can therefore represent the mapped ground surface near the coordinates instead of the exact height of the phone.

That matters on bridges, balconies, tall buildings and steep slopes. The coordinates may lie above a terrain cell whose modelled ground elevation is lower than the device itself.

Alternative Explanations for Two Different Altitude Readings

The devices use different vertical reference surfaces.
One applies a geoid model and the other displays ellipsoidal height.
One uses a terrain database rather than a live vertical position.
A barometric sensor has a different pressure calibration.
The GNSS signal geometry and measurement uncertainty differ.
The readings were taken at different times or exact positions.
One software package rounds the value more coarsely.

The existence of alternatives is not an excuse to shrug. It tells us which metadata to inspect next.

What Evidence Strengthens an Altitude Claim?

The vertical reference or datum is named.
The system explains whether the height is ellipsoidal or orthometric.
If a conversion is used, the geoid or elevation model is identified where precision requires it.
The coordinate reference and units are stated.
Measurement uncertainty or expected accuracy is available.
The value is compared with an independent benchmark using the same reference system.
The observation time and location are appropriate for the claim.

What Weakens an Overconfident Claim?

A screen number is called “above mean sea level” without checking the reference.
Two heights using different datums are subtracted as if they were directly comparable.
A terrain-model elevation is treated as the exact vertical position of a phone on a bridge or building.
Many decimal places are interpreted as guaranteed accuracy.
One momentary GNSS reading is treated as a perfect benchmark.
A reference-surface difference is mislabelled as device failure.

Worked Case 1: Same Place, 100 m and 72 m

Receiver A reports ellipsoidal height = 100 m. Mapping software reports orthometric elevation = 72 m after applying an appropriate model for the location.

Can both be internally correct? Yes. They can describe the same point relative to different reference surfaces. Do not call the 28 m difference an error until the definitions are matched.

Worked Case 2: The Bridge Problem

A learner stands on a high bridge. A terrain app reports 18 m while a positioning receiver reports a larger vertical position value.

One possible explanation is that the terrain app is returning modelled ground elevation for the coordinate, while the receiver is estimating the device’s position. The two systems may be answering different questions.

Worked Case 3: The Mountain Sign

A trail sign says “Elevation 850 m”. A GNSS receiver displays 875 m. A student says the sign must be wrong.

Before deciding, check the receiver’s height type, the sign’s vertical datum, the exact location, rounding and measurement uncertainty. A disagreement is a clue to investigate, not instant proof of which source failed.

Worked Case 4: Many Decimal Places

An app shows altitude 103.742 m. Does the display prove the user’s height is known to the nearest millimetre?

No. Display precision and measurement accuracy are different. The extra digits may come from calculation or formatting. Use the stated uncertainty or validated performance, not the number of decimals, to judge confidence.

Worked Case 5: “Sea Level Is Zero Everywhere”

A learner imagines mean sea level as a perfectly smooth sphere passing through every coastline. In precise geodesy, Earth’s gravity field and the shape of the geoid are irregular. Tides, currents and local sea conditions also mean the instantaneous ocean surface is not a universal fixed zero.

The useful Primary-level conclusion is simple: scientific height systems define a reference carefully; “sea level” is not a casual visual line drawn around Earth.

Tempting Reasoning That Fails

“GPS altitude always means metres above mean sea level.” GNSS naturally provides ellipsoidal height; software may or may not transform it.
“Different numbers mean one device is broken.” First compare the reference systems and methods.
“Altitude and elevation are always identical words in every dataset.” Definitions and interface labels vary; read metadata.
“More decimal places mean more accuracy.” Display resolution is not the same as validated uncertainty.
“Mean sea level is a perfectly smooth universal zero surface.” Precise vertical datums use defined geodetic and gravity-based references.

Model and Measurement Limits

GNSS vertical positioning is generally more difficult than horizontal positioning and is affected by satellite geometry, signal conditions, atmospheric effects and receiver processing. Geoid models are approximations of a complex gravity field. Terrain models have finite spatial resolution. Barometric height depends on atmospheric pressure and calibration. Every route to a height number therefore has limits.

A strong scientific explanation names the route instead of pretending all “altitude” numbers are produced in the same way.

How Far Can the Conclusion Travel?

If a dataset states that a height is orthometric elevation in a defined vertical datum, you can compare it with other values using the same compatible reference. If a receiver reports ellipsoidal height, you can use it as that geometric quantity. You should not silently convert one into the other, label either one “exact mean-sea-level height” without metadata, or use a terrain-model value as the exact vertical position of an elevated object.

PSLE-Style Transfer Case

An original field note shows:

Source	Height	Reference information
Receiver P	126 m	Ellipsoidal height
Map Q	97 m	Elevation in a defined vertical datum

Question: A student says, “One source has an error of 29 m because both measured the same place.” Evaluate the claim.

Reasoned answer: The two values use different vertical references, so they are not directly comparable as written. Receiver P gives height relative to an ellipsoid while Map Q gives elevation in a vertical datum. The reference systems must first be converted or matched before a measurement error can be calculated.

Explained Practice

Practice A: A phone says “Altitude 50 m”. What is the first evidence question? Ask what reference or method the app uses.

Practice B: Why can one point have two different valid height numbers? The numbers may be measured from different reference surfaces.

Practice C: A terrain database says 20 m while a person is on the tenth floor. Why might this happen? The database may represent ground elevation rather than the person’s vertical position.

Practice D: What must be matched before subtracting two heights? Units, location and especially the vertical reference/datum.

Delayed Independent Return: Leave GPS Behind

Later, give the learner two temperatures: “20°C above room baseline” and “20°C on a thermometer scale”. Ask whether equal numbers must describe the same quantity. The point is not temperature; it is the habit of checking the reference before comparing values.

Parent and Tutor Teaching Guide

Use the paper three-surface drawing rather than trying to test phone altitude outdoors. Put one sticker representing a mountain point above two different reference curves and ask the learner to measure both arrow lengths with a ruler. The point stays fixed while the reference changes, so the two “heights” differ.

Then give three fictional app screenshots with the same unit but different metadata: ellipsoid, geoid-corrected elevation and terrain model. Ask which values may be compared directly and what extra information is needed.

This makes a difficult geodesy idea accessible through a Primary Science habit: define what your number is measured from.

Authoritative Sources

The Quiet Return

A height is never just a distance. It is a distance from somewhere.

Before trusting the altitude number, find its zero.

Small Group Tutorials

PSLE Science Reality Lab Vol No.370 | “GPS Altitude = 100 m” — Is That Automatically 100 m Above Mean Sea Level?