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Dynamic Ocean Topography in a Flat Earth Perspective

Beware the certain science.

I am as bad as many (even in this series of posts) of taking the shorthand of describing a scientific theory in certain terms despite the fact that all theories have some degree of uncertainty (even if relatively small). For our mutual benefit let me state that scientific theory isn’t just any old idea. A scientific theory is a tested and furthermore a testable idea.

Almost 99 years ago a crazy idea from a German scientist was tested by looking for a star that was behind the sun during a solar eclipse. Einstein’s theory of general relativity predicted that even though the star was behind the sun, the sun’s gravitational pull would bend space-time enough to see the star during the eclipse. This flew in the face of Newtonian physics, the accepted theories used to explain the motions of the planets, sun, and other objects seen in the skies. So obviously when the impossible occurred, when the star was seen, Newtonian physics was disgraced and thrown out as being proven wrong… Well, no.

Newtonian physics is still used today to launch rockets into space and to calculate satellite orbits. Why? Because it is accurate enough to describe the motion of the fastest rocket we can make. The New Horizons spacecraft that traveled at a whopping 58,536 km/h or 36,373 mph was still traveling at less than 1/100th of one percent the speed of light. Newtonian physics has very little error until we’re talking about speeds that are a much larger fraction of the speed of light. General relativity, while technically more accurate even at such low speeds, is overly complicated for what is relatively speaking (inadvertent pun) a very small improvement in accuracy.

While I’ve got you convinced for the moment that two different theories can be shown to be accurate (enough) even when one fails to describe some phenomena… Let’s visit for a moment one of those gems of scientific contrarianism, the flat earth theory. Really!

Of course, everybody knows [the earth is round]. But how do they know it? They know it because they’ve been told that it’s so. The average man can’t advance a single reason for believing that the world is round. He accepts that theory on blind faith and rejects the evidence of his own senses. We of the Flat Earth Society have elected to dispute the one premise that our scientific Western civilization regards as indisputable. Nowadays if you say that God is dead, the general reaction is “so what?” but if you say that the earth is flat, then God help you. Even in the days of its greatest power, the Church was more tolerant than our modern scientific establishment. The Church at least allowed for one dissenting viewpoint: the devil’s.


While often derided on social media these days, the flat earth model has plenty of real world applications. As a surveyor myself I often use a flat earth model, although you won’t find me using it to launch a rocket into space. You probably use a flat earth model most of the time without even thinking about it. Assuming things are flat around us is relatively accurate for most of the things you and I will do day to day, and trying to imagine the earth curving away from us won’t usually help. Science has a pretty good understanding of how accurate the flat earth model is, so let’s discuss dynamic ocean topography for a moment… assuming the earth is flat!

When you look out over a lake, it looks flat. Generally, it is easier to think of water as geometrically flat; if you have to deal with curved surfaces the math gets difficult fast and may be unnecessary. Much of the driving forces of DOT can be observed over short periods of time without going any distance, so a flat earth is probably pretty good! If water levels can be measured over several years we can quite accurately predict the tides and then see when the water levels are different. Atmospheric forcing is one of those effects that is quite easy to observe; when a low-pressure storm comes in you will see the water levels rise above what the tides would predict, no spherical earth model needed. Changes in density, while generally a smaller effect on the average tide, are also observable with a stationary tide gauge.

So we can observer non-tidal variations in water levels, but what about if we want to compare those over some distance? A leveling instrument is a common tool for measuring differences in height and is often used with an assumtion of a flat earth because it is relitively small over short distances. For example, over 60 meters the error due to curvature is only 1/4 of a millimeter (in imperial units thats 200 feet and about 1/100th of an inch), we’re talking a couple hairs width. So how fast do sea surface heights change? If you remember from my first post I mentioned that the gulf stream current has at it’s most extreme a height change of 1 meter over 100 kilometers, so over 60 meters that’s a height change of more than 1/2 of a millimeter. If we were really careful and could use a level over the ocean we could probably measure that there was a change in height while assuming the earth was flat!

To quickly summarize, models and theories aren’t right or wrong, they are more or less accurate at describing and predicting observed phenomena. It is important to know the limitations of a model, but if those limitations are less than the precision needed it may be sufficient for your use.

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