Common vertical datum
A Socratic walk-through of the common vertical datum — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why do two countries struggle to agree how high above the sea a mountain stands?
For decades Nepal and China published different heights for the same mountain. Nepal used 8,848 metres, inherited from a Survey of India measurement in the 1950s; China published 8,844.43 metres in 2005. Only in December 2020 did the two governments jointly announce a single agreed figure, 8,848.86 metres.
It is tempting to file this under national pride, or under measurement error. Neither explains it. Both surveys were competent, and part of the gap was a straightforward disagreement about whether to include the snow cap. But the deeper part was this: the two countries were not measuring from the same place. And it turns out that "the same place" is far harder to establish than it sounds.
Reasoning it through
REASONING #Ask the innocent question. Height above sea level — above which sea, measured when?
The sea is not a level surface. It has permanent slopes of a metre or more, produced by currents, prevailing winds, temperature and salinity differences. Mean sea level at one coast is genuinely not the same height as mean sea level at another. So a nation that defines zero from a tide gauge on its own coast has picked a perfectly reasonable local surface that does not coincide with its neighbour's.
Nepal's older height traced back through Indian levelling to the Bay of Bengal. China's traced to a gauge at Qingdao on the Yellow Sea. Two seas, two zeros, thousands of kilometres of levelling in between. The disagreement was baked in before anyone climbed anything.
So what should zero be instead? The natural candidate is the geoid: the equipotential surface of Earth's gravity field that best matches global mean sea level — roughly, the shape the oceans would take if they were still and free to flow under gravity alone. It is a physically meaningful surface, because water flows downhill with respect to it, which is exactly what a height for engineering purposes must respect.
But notice what we have done. We have swapped a problem of choosing a tide gauge for a problem of modelling a gravity field — one that is lumpy, that must be inferred from satellite gravimetry and surface measurements, and that is revised as those improve. Two countries can now agree to use the geoid in principle and still differ, because they use different geoid models.
There is a third layer. Satellites do not measure height above the geoid at all. GNSS gives an ellipsoidal height — distance above a smooth mathematical ellipsoid, which is easy to define but has no physical meaning for water flow. Converting one to the other requires subtracting a geoid model, and that model's error passes directly into the answer. The 2020 Everest campaign did exactly this, combining GNSS on the summit with gravity measurements to tie the result to a single agreed geoid.
And a fourth, which surprises people: there are competing conventions for how to handle the permanent deformation of the Earth by the Sun and Moon. Mean-tide, zero-tide and tide-free systems differ by centimetres to a decimetre depending on latitude. Two agencies using the same geoid model with different tide conventions still disagree.
Every one of these layers is a choice, not a discovery. Which is the point.
The analogy
THE ANALOGY #Think of two nations that each ran their railways on local time before timetables forced the issue. Neither clock was wrong. Noon really was when the sun stood highest, in each town. But two correct clocks cannot produce one timetable, and the fix was not a better clock — it was an agreement to abandon the local definition for a shared one nobody's own observations directly supported.
A time standard, once agreed, can simply be broadcast and adopted, whereas a vertical datum has to be physically realised at every benchmark on the ground — so adopting a new one means re-surveying a country, which is why old datums persist for decades after better ones exist.
Clarifying the model
THE MODEL #Three refinements.
First, this is a coordination problem rather than an accuracy problem. There is no experiment that determines the correct zero, because zero is a convention. What makes a datum good is that it is physically sensible, precisely realised, and shared. The third property is the hard one, and it depends on other people, not on instruments.
Second, the cost of switching is what sustains the mess. The United States has spent decades on this: NGVD29 was tied to twenty-six tide gauges, NAVD88 to a single one at Father Point in Quebec, and NAVD88 is now known to be tilted by roughly a metre across the continent relative to a modern global geoid. A gravity-based replacement has been in preparation for years and repeatedly rescheduled, because the moment it lands, every recorded elevation, every flood map and every airport approach chart has to be re-referenced.
Third, the disagreements are small but the consequences are not proportional. A metre of datum offset is irrelevant to a mountaineer and decisive for a drainage scheme, a levee crest, a sea level rise projection or a tunnel meeting in the middle. Vertical datum problems surface mostly at boundaries — between countries, between agencies, between an old survey and a new one.
A picture of it
THE PICTURE #How to readRead the top box as the goal and the three below it as conditions that must all hold together, not as steps in sequence. Each carries its own risk level and its own way of being checked. The summit at the bottom satisfies the goal only when all three conditions are met at once, which is why two careful surveys with different conventions still produce two different numbers.
What became clearer
WHAT CLEARED #Height above sea level sounds like an observation and is actually an agreement. The sea has no single level, gravity is lumpy, satellites measure something else entirely, and even the treatment of tidal deformation is a matter of convention. Everest got one number in 2020 not because someone finally measured it properly, but because two states negotiated a shared frame and then measured within it.
Where to go next
ONWARD #- How GNSS plus a geoid model is displacing spirit levelling as the practical way to realise a datum.
- What a national datum change actually costs, and who has to redo work when it happens.
- Why sea level rise records depend on separating land motion from ocean change.
Key terms
TERMS #| Term | What it means |
|---|---|
| Vertical datum | the agreed reference surface from which heights are measured. |
| Geoid | the equipotential surface of Earth's gravity field approximating global mean sea level; the physically meaningful zero for heights. |
| Ellipsoidal height | height above a smooth mathematical ellipsoid, as returned by GNSS; convertible to an orthometric height only by subtracting a geoid model. |
| Orthometric height | height above the geoid, the quantity that governs which way water flows. |
| Permanent tide convention | the choice of whether to retain, remove or partly remove the steady tidal deformation of the Earth, differing by centimetres. |
| Dynamic ocean topography | the departure of actual mean sea level from the geoid, caused by currents, winds, temperature and salinity. |
Every term the collection defines is gathered in the glossary.