A coordinate can be copied perfectly and still put a feature in the wrong place. A height can be measured carefully and still be compared with an incompatible height. A monument can remain firmly attached to bedrock while its position changes within a global reference frame. Geodesy explains why these are ordinary measurement questions rather than paradoxes.
Geodesy studies Earth’s geometry, gravity and rotation, including their changes through time. It supplies the reference systems and measurements that make positions comparable across instruments, countries and years. The gold standard is a location claim whose reference, epoch, measurement method and uncertainty are clear enough for another person to interpret and check.
This guide begins with simple geometry, adds the physical meaning of height, then works through motion, instrument evidence and useful checks. Its numerical cases are original fictional constructions. They demonstrate reasoning without claiming to be survey results, official transformation parameters or operational instructions.
Geodesy connects with surveying, geophysics, cartography and remote sensing. Those fields share tools but ask different questions. Here the central job is to explain the reference beneath the measurements: what makes a coordinate meaningful on a moving planet. The educational aim follows The Gold Standard of Education | Learning That Transfers into Life: understand the relationship, check it and recognise when a changed situation requires another assumption.
Find the explanation you need
Choose a route, or follow the chapters in order. The worked cases are deliberately small enough to check by hand.
Chapter index
Understand the reference · Chapters 1–3
Connect geometry and gravity · Chapters 4–6
Work through movement · Chapters 7–9
Check measurements and practice · Chapters 10–12
Teach, transfer and explore · Chapters 13–16
Imagine receiving a spreadsheet with the numbers 412.6 and 958.2 beside a pump identifier. Before plotting them, ask what they mean. They could be distances in metres from a local origin, coordinates in another unit or values in a temporary construction grid. Two well-formatted columns do not supply their own reference system.
A geographic position needs more than digits. The coordinate reference system establishes how the numbers relate to Earth. Axis order and units establish how to read them. For precise work, the frame realisation and coordinate epoch can also matter. A dataset should preserve these details with the values rather than rely on a person’s memory.
The represented feature matters too. A point could identify the pump’s physical centre, an access gate or a schematic marker displaced to avoid clutter. Geodesy can establish the spatial reference; the data record must still identify what was located. Correct mathematics applied to the wrong feature remains the wrong answer to the practical question.
Suppose two teams report different coordinates for the same asset. Do not begin by averaging them. First establish whether they describe the same physical point, in compatible systems, at relevant times. A mismatch in definitions is not ordinary random measurement noise.
This habit is useful even outside precise geodesy. A public map marker may be adequate for finding a building yet unsuitable for setting out an engineering feature. The required accuracy follows from the decision. Stating the intended use prevents an attractive map from silently acquiring authority it was never measured to support.
The first complete sentence should therefore read something like: this record locates this feature, in this reference, at this epoch, using this method. Numbers become more useful when the sentence carrying their meaning is complete.
CHAPTER 2 OF 16 · Understand the reference
2. Separate a reference system from its realisation
A reference system states conventions: the origin, orientation, scale and treatment of time. A reference frame realises those conventions through observations and estimated positions of physical stations. The distinction resembles the difference between defining a measurement scheme and constructing its actual implementation, although geodetic realisation also includes models of motion.
The International Earth Rotation and Reference Systems Service description of the ITRS makes this relationship explicit. The International Terrestrial Reference System is realised through a reference frame based on estimated station coordinates and velocities. Earth-orientation information connects terrestrial and celestial references.
Why does this distinction matter? Because an ideal definition does not eliminate measurement uncertainty. Stations can move, equipment can change and processing models can improve. A frame has to be maintained and documented so users can relate observations made at different times.
Consider a fictional network with four stations. Reprocessing one station reveals a previously unmodelled equipment offset. The defining system has not necessarily changed; the best available realisation may have improved. Users comparing old and new products need to know what changed rather than interpret every coordinate difference as motion of the ground.
A frame label without a realisation or epoch may be too vague for a demanding task. The necessary detail depends on precision and use. A classroom globe and a regional deformation study do not require the same documentation, but neither benefits from pretending that the distinction is meaningless.
For a learner, the useful question is where the reference enters the calculation. Which convention defines the axes? Which observations anchor them? Which model carries them through time? Answering those questions turns a technical acronym into a working relationship that can be checked rather than a label simply copied into a report.
CHAPTER 3 OF 16 · Understand the reference
3. Begin with an ellipsoid, then remember its limits
Earth’s shape is more complicated than a sphere. A reference ellipsoid provides a smooth mathematical surface useful for defining coordinates. It deliberately omits mountains, buildings and local terrain. Simplicity here is a tool: the reference surface gives measurements a common geometric basis.
Latitude and longitude describe angular relationships, not ordinary distances in a flat grid. Geodetic latitude uses the direction normal to the ellipsoid. Geocentric latitude uses a direction from Earth’s centre. Those definitions are different on a flattened reference surface, even when a small drawing makes the two angles look almost identical.
Longitude also needs its reference convention. A coordinate does not become unambiguous merely because it includes a familiar compass direction. The reference frame, axis conventions and units still belong to the record, especially when values pass between software interfaces.
Projected coordinates are another representation. A map projection converts a curved surface to a plane under specified rules. It cannot preserve every geometric property everywhere. A planar distance computed from projected coordinates and a distance along the ellipsoid therefore answer related but distinct questions.
Take a fictional school map where one centimetre represents 20 metres locally. Doubling a drawn segment doubles the represented planar distance under that map scale. The statement does not establish a universal conversion from a centimetre on every world map to ground distance. The representation and its domain of usefulness matter.
This is the first important limit of the geometric model. An ellipsoid is not a claim that the terrain is smooth; a projection is not a claim that Earth is flat. The model is useful because its purpose is explicit. A good explanation states what it preserves, what it approximates and which next physical question requires additional information rather than more digits from the same formula.
Height is not one universal quantity. A Global Navigation Satellite System solution can provide an ellipsoidal height relative to a geometric reference surface. A physical height related to gravity uses another reference. Confusing them can produce a convincing numerical comparison with the wrong physical meaning.
The geoid is an equipotential surface associated with Earth’s gravity field and used as a reference for physical heights. It is not the mountain surface, nor is it identical to the instantaneous ocean surface at every location. Winds, currents, tides and other processes affect the sea surface actually observed.
The National Geodetic Survey explanation of the geoid helps establish the geometric and physical distinction. Orthometric heights relate to the gravity field, while ellipsoidal heights relate to an ellipsoid. Practical transformations depend on the specified models and datums.
Suppose one dataset reports the elevation of a bridge deck relative to a physical height datum and another reports a receiver’s ellipsoidal height. Subtracting the values without the necessary connection can conceal a reference mismatch. The bridge and receiver may also be different physical points, adding another independent issue.
The beginner’s useful drawing has three surfaces or locations: the reference ellipsoid, the geoid and the observed point. Label the quantities between them before calculating. A sign convention becomes easier to understand when the learner can say which surface lies above or below which reference in the example.
The deeper lesson is that physical meaning comes before arithmetic. Water-flow and flood questions need the appropriate physical and engineering context. A classroom relation between heights is a useful explanation, but it does not supply a project datum, an approved survey or every condition needed to design a drainage system.
CHAPTER 5 OF 16 · Connect geometry and gravity
5. Worked case: convert a height and check the sign
Use the approximate teaching relation H = h − N, where h is ellipsoidal height, N is geoid height relative to that ellipsoid and H is the corresponding orthometric height under compatible conventions. The relation is useful only when its inputs refer to the same point and appropriate reference models.
For fictional point P, let h = 72.4 metres and N = −18.6 metres. Then H = 72.4 − (−18.6) = 91.0 metres. The physical height is larger than the ellipsoidal height in this example because the geoid lies below the ellipsoid according to the chosen sign convention.
Now reverse the calculation. H + N = 91.0 + (−18.6) = 72.4 metres, recovering h. This reverse check catches the common mistake of subtracting the magnitude of N while ignoring its negative sign.
At nearby fictional point Q, take h = 74.1 metres and N = −18.5 metres. Its H is 92.6 metres. The orthometric height difference is 1.6 metres, whereas the ellipsoidal difference is 1.7 metres. The difference between the two differences comes from the change in N.
| Invented point | h, metres | N, metres | H = h − N, metres |
|---|---|---|---|
| P | 72.4 | -18.6 | 91.0 |
| Q | 74.1 | -18.5 | 92.6 |
The NGS geoid-height service documentation illustrates why a model identifier and compatible reference information belong with such conversions. Its specific United States products are not universal height references for every country.
A changed problem replaces N with an unlabelled value from another model. The arithmetic remains possible, but the scientific justification is missing. A strong answer pauses to establish compatibility rather than celebrate the extra decimal place produced by the calculator.
CHAPTER 6 OF 16 · Connect geometry and gravity
6. Understand what gravity measurements add
Gravity reflects Earth’s mass distribution and rotation. Its spatial variations help connect geometry with physical height and reveal aspects of Earth’s internal and surface mass. Changes through time can also carry information about redistribution of water, ice and other material.
The measurement does not arrive with a unique label saying which process caused it. Several contributions can affect an observed signal. Interpretation therefore requires models, spatial coverage, other measurements and appropriate treatment of uncertainty. A change in gravity is evidence to analyse, rather than an automatic identification of one local cause.
Imagine a fictional regional gravity estimate becoming more negative over an interval. Ice loss might be one candidate explanation in an icy region. Changes in water storage, modelling corrections or spatial leakage from neighbouring signals could also matter. The question is which explanations are supported by the combined evidence and the product’s resolution.
A point measurement, a satellite-derived regional estimate and a model grid describe different observational arrangements. Their values should not be compared as if they had identical footprints and processing. The apparent detail of a displayed grid does not necessarily equal independent resolving power at every cell.
The relationship with glaciology is especially useful. Geometry can show changes in surface elevation; gravity can constrain mass redistribution; other observations help interpret density, motion and the surrounding system. Agreement among genuinely different measurements can strengthen a conclusion, while disagreement can expose an assumption needing revision.
For learning, separate the instrument observable from the derived quantity and the proposed Earth process. Write three boxes in that order. The arrows require explanation. This prevents a common shortcut in which a sophisticated sensor is treated as if it directly observed every variable shown in the final scientific graphic. Good geodesy explains the estimation pathway as well as the phenomenon being estimated.
CHAPTER 7 OF 16 · Work through movement
7. Worked case: carry coordinates through time
A coordinate epoch identifies the time associated with a coordinate. When a station moves within the chosen frame, comparing coordinates from different epochs requires an appropriate motion model. A simple constant-velocity model is a useful first example, though real station histories can include non-linear changes and discontinuities.
Suppose fictional station A has local easting 1,000.000 metres at epoch 2020.0 and a constant eastward velocity of 0.012 metres per year. Under this stipulated model, its easting at 2026.0 is 1,000.000 + 6 × 0.012 = 1,000.072 metres. Copying the 2020 value into a 2026 comparison would omit 72 millimetres of modelled motion.
Now station B begins at easting 1,500.000 metres and moves eastward at 0.009 metres per year. Its later coordinate is 1,500.054 metres. The initial separation is 500.000 metres and the later separation is 499.982 metres. Both stations moved east, yet their separation decreased by 18 millimetres.
This distinction between absolute motion in a frame and relative motion between stations matters. Subtract the velocities first: 0.009 − 0.012 = −0.003 metres per year. Over six years, the separation changes by −0.018 metres, matching the coordinate calculation.
The IERS terrestrial reference-system description explains why coordinates and velocities participate in frame realisation. The numbers above are invented; no tectonic velocity for a real place is implied.
For the changed-context check, suppose an earthquake causes an additional offset halfway through the interval. The constant-velocity calculation is no longer a complete model. Add an appropriately supported discontinuity and any necessary subsequent motion. Knowing when to stop using the simple rule is part of understanding the rule.
CHAPTER 8 OF 16 · Work through movement
8. Worked case: separate land motion from sea-surface change
A tide gauge records water level relative to its supporting land and measurement reference. A change in that relative level can reflect ocean change, land motion or both. Geodesy helps connect these observations through compatible reference frames and measurements of the land.
Choose a simple sign convention: upward motion is positive. Let fictional ocean-surface height increase by 2 millimetres per year in a specified external frame, while the land supporting a gauge moves downward by 3 millimetres per year. Land velocity is therefore −3. Relative water-level change is 2 − (−3) = 5 millimetres per year.
After four years under constant rates, the water is 20 millimetres higher relative to the land. That does not mean the ocean-surface term alone increased by 20 millimetres. Its contribution in the stipulated frame was 8 millimetres; land subsidence contributed another 12 millimetres to the relative difference.
Change the land motion to upward at 4 millimetres per year while preserving the fictional ocean term at +2. The relative rate becomes 2 − 4 = −2 millimetres per year. The local relative water level falls in this model even though the ocean-surface coordinate rises.
These are teaching decompositions, not forecasts. Real comparisons require compatible reference information, relevant spatial and temporal coverage, instrument histories and treatment of variability. A short noisy record does not automatically establish a stable long-term rate.
The transfer question is which difference the instrument observed. A gauge’s relative observation and a satellite-derived global-frame estimate are not contradictory merely because their numerical trends differ. First compare their definitions. This same discipline helps with any pair of measurements that use different moving references: the apparent disagreement may reveal an unaccounted reference term rather than a broken instrument or a false observation.
CHAPTER 9 OF 16 · Work through movement
9. Connect Earth-fixed and sky-related observations
Earth rotates, and its orientation is not described by one perfectly uniform turn repeated without variation. Space-geodetic measurements connect stations attached to Earth with satellites and distant astronomical sources. The transformation between terrestrial and celestial references therefore needs orientation information as well as geometry.
The IERS data and products overview identifies Earth orientation and terrestrial and celestial reference systems among its central products. These shared references allow different observing programmes to describe the same physical relationships consistently.
Global Navigation Satellite Systems use signals from orbiting transmitters to estimate receiver position and related quantities. Very Long Baseline Interferometry observes the timing relationships of radio signals arriving at separated antennas. Satellite Laser Ranging measures light-travel information to suitable satellites. The techniques contribute different observations and are combined with models rather than treated as interchangeable direct coordinate readers.
Two instruments at one observatory still occupy different physical reference points. Combining their observations requires knowledge of the relationship between those points. An accurately timed observation cannot repair an incorrectly described physical connection between instruments.
The accessible question is why several techniques help. They offer different sensitivities and systematic errors. Independent information can reveal weaknesses that repeated use of one method might preserve. Combination is valuable when its interfaces are understood; merely placing several datasets in the same folder does not create consistency.
For a changed-context exercise, imagine comparing two clocks without recording the signal path between them. Even perfect readings need an explanation of delays and references. The analogy highlights the role of a connection model. It does not replace the actual relativistic, atmospheric and geometric models needed in precise space geodesy, whose treatment requires specialist knowledge beyond this introductory guide.
CHAPTER 10 OF 16 · Check measurements and practice
10. Read a GNSS position as an estimate
A receiver estimates position from observations whose interpretation depends on satellite information, timing, geometry and propagation. The displayed coordinate is the result of an estimation process. It is useful evidence, but it should not be treated as an unconditional promise of accuracy for every later purpose.
The observation environment matters. Reflections, obstruction, atmospheric effects, antenna characteristics and processing choices can affect results. Repeating observations may reduce some random variation while leaving systematic problems. A stable-looking cluster of points can share a persistent offset.
Imagine an invented series of ten observations tightly grouped around a location 0.8 metres from an independently established point. The small scatter describes repeatability within that series. It does not erase the discrepancy from the reference. Reporting many decimal places would make neither the observation model nor the reference comparison better.
Ask whether the independent reference itself is suitable and uncertain. A comparison against another unverified consumer marker may reveal little about survey accuracy. A check is informative when its own quality and relationship to the intended quantity are understood.
For professional use, retain acquisition and processing context sufficient to assess the result: the method, relevant correction source, observation interval, equipment reference and quality information appropriate to the task. The exact requirements depend on the application and governing framework. This guide does not prescribe a universal survey procedure or tolerance.
The learning target is to distinguish three questions: did the computation run, did the estimate agree with an appropriate check and is its quality sufficient for the decision? Success on the first does not settle the other two. A coordinate becomes trustworthy through the whole chain from observation to interpretation, rather than through the appearance of a number on a screen.
CHAPTER 11 OF 16 · Check measurements and practice
11. Worked case: do not average away an equipment step
Consider fictional monthly vertical positions with random scatter around a stable level. After an antenna change, the series jumps upward by 8 millimetres and stays around the new level. A straight line fitted through the entire record may report an apparent rise, even if the physical monument did not move that way.
The equipment history provides a candidate explanation for the discontinuity. It does not justify deleting data until the trend looks comfortable. Investigate the change, document the evidence and use a model that can distinguish a supported offset from continuing motion.
For a small arithmetic version, suppose an early group has mean 100.000 metres and a late group has mean 100.008 metres. If the groups are two years apart, dividing their difference by time gives 4 millimetres per year. That is a two-group difference rate under the calculation. It is not proof of steady land motion throughout the interval.
Collecting many additional late observations could make the late mean more precise while preserving the same 8-millimetre step. More data do not automatically identify the correct causal interpretation. The missing information concerns the discontinuity and its physical or instrumental origin.
Now change the context: an independently observed earthquake coincides with the step, and neighbouring stations show a physically coherent pattern. That evidence changes the investigation. The analyst should examine an actual displacement rather than assume every step is equipment. Metadata and external evidence help distinguish alternatives.
This case teaches a general scientific habit. A trend is a model fitted to observations, and a model can compress different histories into a similar slope. Preserve the time sequence, inspect plausible changes and ask which history the data support before turning a fitted rate into an explanation of what Earth did.
CHAPTER 12 OF 16 · Check measurements and practice
12. Keep uncertainty attached to the decision
Uncertainty describes the limits of knowledge about a quantity under a measurement and modelling account. It should be interpreted with the quantity and assumptions it belongs to. One small number labelled accuracy cannot necessarily represent every component of a spatial decision.
Suppose fictional h has standard uncertainty 0.03 metres and N has standard uncertainty 0.04 metres. If the two uncertainties are independent and the simple height relation applies, the propagated standard uncertainty of H is approximately the square root of 0.03 squared plus 0.04 squared, which is 0.05 metres. This is an illustrative propagation, not a universal uncertainty claim for GNSS or geoid models.
Independence is an assumption. Correlation can change the propagation, and a reference mismatch is not repaired by this calculation. The NGS GEOID18 technical details explicitly discuss considering uncertainty in both ellipsoidal height and the geoid estimate for that particular product and reference arrangement.
The decision might also depend on the location of a different feature, temporal changes or an interpretation rule. A five-centimetre standard uncertainty in one derived quantity does not by itself establish a construction tolerance, confidence interval or legal acceptability.
A good report connects the uncertainty with the question: is this difference resolved sufficiently for this purpose? If two plausible values imply different actions, further measurement or specialist judgement may be needed. If both lead to the same low-consequence decision, the existing evidence may already be useful.
This makes uncertainty practical. The aim is neither false confidence nor permanent hesitation. It is a proportionate account of what the measurement supports, what could change the answer and which additional information would matter most to the actual task.
CHAPTER 13 OF 16 · Teach, transfer and explore
13. Teach coordinates as relationships
A student who can substitute numbers into a formula may still compare incompatible coordinates. Begin teaching by identifying what the values refer to. A local classroom grid makes the relationship visible: change the origin and the same physical point receives different numbers without moving.
Next change the unit. A displacement of two grid units can represent different physical distances under different scales. Then rotate the axes. These changes let the learner experience why coordinates describe a point relative to a framework rather than becoming the point itself.
Only after that foundation is stable should the lesson add ellipsoids, projections, epochs and gravity-related heights. Introduce one complication at a time. A learner confused by the negative geoid value in chapter five may need a signed-distance diagram, rather than a longer explanation of satellite instruments.
Ask the learner to think aloud. Which quantities can be subtracted? Why are their units compatible? What remains fixed? What changed between epochs? Which reference surface gives this height its meaning? These questions expose the conceptual move that a correct-looking final answer can hide.
Use retrieval and mixed cases. Place a valid height subtraction beside an invalid mixed-datum comparison. Ask the student to justify which can proceed. Later, change a constant velocity into a history with a step. Recognition of the changed assumption is more informative than repeated substitution into an unchanged formula.
The teaching approach in the Secondary 1 Mathematics Tutor Clementi guide similarly starts with the first unstable relationship and checks independent use. In geodesy, good teaching helps the learner see the reference beneath the numbers and explain why a calculation is meaningful before trying to make it fast.
CHAPTER 14 OF 16 · Teach, transfer and explore
14. Test the reference in a changed problem
Try these original exercises without returning to the worked cases. Explain the reference and assumptions as well as the arithmetic.
A fictional point has h = 40 metres and N = +12 metres. Under the compatible approximate relation, H = 28 metres. If your answer is 52, check which direction N measures and reverse the relation to recover h.
Two stations both move east at 7 millimetres per year in the same model. Their east-west separation does not change through that shared motion alone. The individual coordinates change while the difference cancels the common term. Other motion components or unmodelled changes could still matter.
A gauge records a relative water-level rise of 6 millimetres per year and its land subsides at 2 millimetres per year in a compatible frame. Under the simple decomposition, the ocean term is +4 millimetres per year: 4 − (−2) = 6. The rate is not automatically a forecast or an explanation of the physical causes.
A receiver prints an easting to three decimal places. Does that establish millimetre accuracy? No. Display precision is different from evidence about measurement uncertainty and correctness of reference. Ask what independent checks and observation model support the estimate.
Finally, a long coordinate series changes after processing software is updated. Which explanation should be tested first? There is no universal answer from that fact alone. Inspect the processing change, preserved metadata, raw observations and independent evidence. A sound investigation keeps both physical change and analysis artefacts available as hypotheses.
The transferable capability is to notice when apparently comparable numbers use different anchors. This applies to prices with different bases, temperatures under different scales and progress measured under different test conditions. The shared reasoning concerns compatible references; it does not make those subjects identical to geodesy.
Is geodesy just surveying?
They overlap. Geodesy investigates Earth’s reference geometry, gravity, rotation and change. Surveying uses measurement and reference frameworks for tasks at particular scales, with its own professional purposes and requirements.
Is the geoid the same as sea level everywhere?
No. It is a gravity-related reference surface. The observed sea surface also varies through tides, currents and other processes. A specific height comparison needs its defined datum and conventions.
Why record an epoch for a fixed monument?
The monument can move with the crust or through local effects within the selected frame. Its attachment to the ground does not make its global-frame coordinates constant.
Does more averaging guarantee accuracy?
It can reduce some random variation. It does not automatically remove a systematic offset, reference mismatch, equipment discontinuity or incorrect model.
Can these examples be used as survey parameters?
No. All numerical values are invented for reasoning practice. Real work requires the appropriate observations, models, reference products and competent professional procedures.
What is the gold standard here?
A traceable position claim with compatible references, relevant time information, understood uncertainty and an interpretation proportionate to the decision. The phrase is an educational benchmark, not a survey accreditation.
CHAPTER 16 OF 16 · Teach, transfer and explore
16. Choose the next specialist route
Use the subject overview for the wider scientific structure, the mathematics articles for calculations and the surveying and engineering articles for practical evidence chains. Read the neighbouring geophysics and Earth-system roots when the question concerns the cause of motion or mass change, rather than the reference used to measure it.
For a direct bridge between Earth measurement and moving ice, continue to The Gold Standard of Glaciology.
The directory groups these different jobs so a reader can move from a precise uncertainty to the article that addresses it. A map-projection explanation does not replace a frame transformation; a survey guide does not itself establish the cause of a tectonic signal.
Start with geodetic science and its applications
Follow the scientific overview, then distinguish Earth reference systems from the surveying and engineering decisions that depend on them.
- How Science Works | Geodesy — Earth Shape, Gravity, Rotation, Reference Frames and Measuring a Moving Planet
- The Gold Standard of Geospatial Engineering | Correct Coordinates, Reliable Decisions
- The Gold Standard of Surveying
- The Gold Standard of Geophysics
- The Gold Standard of Cartography
Work through coordinate and observation mathematics
These guides develop ellipsoidal distance, satellite-range estimation, survey closure and map representation as different mathematical jobs.
- Why Mathematics? | Vincenty Ellipsoidal Geodesics, Distance and Bearing Iteration
- Why Mathematics? | GPS Navigation, Satellite Ranges, Clock Bias and Position Uncertainty
- Why Mathematics? | Surveying, Triangulation, Levelling and Closure Error
- Why Mathematics? | Earth Maps, Latitude, Longitude and Map Projections
- How Mathematics Improves The World | Giving Every Place on Earth an Address
Connect measured change with Earth systems
Use the relevant physical subject to investigate what changed, while preserving the frame and measurement account that made the change observable.
Sources and scope
Primary institutional references include IERS: the International Terrestrial Reference System, IERS data and products, NGS: what is the geoid?, the NGS geoid-height service and GEOID18 technical details.
The United States model documentation is cited for its explicit reference and uncertainty treatment, not adopted as the height system for every location. Sources and ecosystem destinations were checked on 21 October 2026. Coordinates, velocities, offsets, heights and rates in the worked cases are invented teaching values. No current local survey, site condition, legal boundary or operational transformation is asserted.