How do I calculate sea level on a planet with no seas?

Question

On one (of many) of the planets that I am planning out, there are no seas. The planet is mainly composed of enormous mountains, with some deserts in between.

There are no seas or large bodies of water anywhere on the planet. Not many people like to live on this desolate planet, but those that brave its harsh condition face a boring and necessary consideration.

They need a method to determine the elevation of certain mountains, but without oceans, it is difficult to determine a standard sea-level.

In a planet without seas or any large bodies of water, how do the habitants determine a standard sea-level?

These people have the technology level of the 1700's of Earth, so no futuristic tech.

Answer 1

We use sea level as a base line. For the most part, there won't be much land below 0 long term. So sea level makes a nice point of reference.

But inland (not near the coast) no one cares about sea level in daily life. While it's interesting to know we're 300 feet above sea level, real life calculations are more like "that house is 1000 feet above me."

Eventually scientists will want an absolute measurement of height for comparing geographically displaced areas. I'm not sure how they would measure this accurately in the 1700s, but assuming they found a method, here are a few options they might consider.

1. Arbitrary "Sea Level". If they are aware of other worlds (perhaps trying to impress a superior power from one of those worlds), they might try to keep the concept of sea level. This would involve guessing at a volume of water and computing where it would rise to, similar to HDE 226868's geoids.

2. Baseline. If the planet is well-explored or relatively flat, they could decide that the lowest point is 0 and measure everything from there.

3. Midline. Similar to baseline, but computing a median height and measuring things from that point as either +/-.

4. Totally arbitrary. I think this is the most likely - for proof, see our measurements of longitude. The scientist who comes up with the concept and popularizes it will choose either the elevation of his own house or the elevation of some important landmark (temple, palace, roadway) as 0 and everything will be based on that for no obvious reason.

Answer 2

You could use air pressure. Pressure varies with altitude in a regular fashion, so you can make pressure-based altimeters. Pressure also varies with weather conditions, so it's not perfect, but by taking the average pressure over long time periods, it should equalize pretty well.

Then, you just pick some baseline. Maybe a capital city, maybe the altitude most people live, maybe you follow a herd of deer until one gets eaten by a wolf. Then everything else is relative to that point. If you're trying to make a "standard" sea level, you can just pick the point where the air pressure is ~1 bar/14.7 psi/100 kPa/whatever other unit you like.

The barometer was invented in 1643, so this fits with your 18th century tech level.

Answer 3

Use a geoid.

A geoid is, to quote Wikipedia

the shape that the surface of the oceans would take under the influence of Earth's gravitation and rotation alone, in the absence of other influences such as winds and tides.

It can be expressed in part using spherical harmonics. This might sound overly complicated, but Laplace had developed the basics of spherical harmonics in the late 18th century.

Collecting data to calculate the precise shape may be difficult, but so would any other method of gathering enough data to use as a reference point.

An even simpler metric is the reference ellipsoid, but a geoid is closer to actual sea level.

A colorful picture to represent a geoid (because why not?):

^{Image in the public domain.}

Answer 4

Sea level has no meaning if there are no seas. But I think what we're trying to achieve is some global reference point. So I think the question should be: what can or should we pick as a global reference point?

In the absence of seas, we might pick the average elevation of the ground, assuming we can measure it with sufficient accuracy.

Alternatively, we might simply pick the center of the planet, and measure everything with respect to that. For practicality, we might introduce an offset, say 6000 km, which is the radius of the earth.

In the past sea level was simply chosen since it provided an easy reference point that could globally be referred to - easy to define, easy to reproduce. Nowadays we actually know that sea level is not as good a reference point as we would like, since it varies many meters around the globe. So we started using a "virtual" sea level that compensates for this.

In practice heights are measured with respect to some local reference point that is completely arbitrary. And on a larger scale, those reference points are measured with respect to each other.

When we want to pick a global reference point, a typical choice might be the average elevation of the ground. As a first approximation this could be the average of all defined reference points.

Answer 5

Datum Height

The "standard height" (Datum) will be the average land altitude.

Although sea level really only applies to Earth geography, scientists often look at other bodies and need/want a similar reference altitude. What is often used is called the datum. This is

Datum:

The arbitrary level from which vertical displacement is measured. The datum for height measurement is the terrain directly below the aircraft or some specified datum; for pressure altitude, the level at which the atmospheric pressure is 29.92 inches of mercury (1013.2 m.bs); and for true altitude, mean sea level.

Often what scientists use as the reference altitude for bodies with no water is the average height.

Here's what the Moon and Mars would look like if you supplied enough water to cover them up to the datum point:

Images of Moon and Mars if supplied with enough water to make the average datum filled with water:

I included the image as a visual reference.

Answer 6

The natural way to measure would be to compare with yourself. As you are able to subsume yourself to larger groupings, you would extend your notion of self to larger organizations. So medievally, you could relate to the local lord. By the 1700s, you might relate to the King's castle or to a site with religious significance (Vatican City, Jerusalem, Mecca, etc.).

Eventually the world might standardize on one location, the way that time zones all relate to Greenwich.

I wouldn't be surprised if this standard location was a relatively high one. Many such comparisons are easier to make on a line of sight basis, and high locations are within the line of sight of more of their surroundings than low ones. So instead of measuring up from sea level, you might measure down from Mt. Everest level.

Answer 7

The height of different places on earth is measured with the help of the 'altimeter'. The instrument used for measuring the height at a place is basically a barometer. At sea level, the height of the barometric liquid (mercury) is 76 cm. When we go to higher altitudes, the barometric height goes on decreasing, and right on top, where the atmospheric pressure is zero, the mercury column also dips to zero. This decrease is not uniform. At different ranges, the rate of decrease too is different. In modern barometers, mercury is not used. Such dial-type barometers are called 'Aneroid barometers'. When such barometers are manufactured, instead of the pressure graduating, the corresponding height graduates. This instrument is called the 'Altimeter' and is used in aircraft by skydivers, mountaineers etc.