The Illusion of a "Wall of Water" at the Horizon

StarGazer

Member
After reviewing my footage in more detail, I had the very strong sensation that between me and the lighthouse there was a wall of water much higher than my elevation.

Most noticeable after zooming out:

The distance from my position to the lighthouse was approx 18,11 km

My tripode + my camera were approx 1.5 m high.

Since there are 14.81 meters hidden, without refraction, is it correct to say that on the straight line of sight midpoint between my camera's elevation and the lighthouse the sea's elevation is 14.81 meters? If not, what is the height?

Mick West

Staff member
After reviewing my footage in more detail, I had the very strong sensation that between me and the lighthouse there was a wall of water much higher than my elevation.

Most noticeable after zooming out:

The distance from my position to the lighthouse was approx 18,11 km

My tripode + my camera were approx 1.5 m high.

Since there are 14.81 meters hidden, without refraction, is it correct to say that on the straight line of sight midpoint between my camera's elevation and the lighthouse the sea's elevation is 14.81 meters? If not, what is the height?

Look at the interactive diagram in the curve calculator. You are probably thinking of the "bulge" value.

Rory

Senior Member.
After reviewing my footage in more detail, I had the very strong sensation that between me and the lighthouse there was a wall of water much higher than my elevation.
It looks that way, but it's not that way. Optical illusion.
Is it correct to say that [...] the sea's elevation is 14.81 meters? If not, what is the height?
The sea will be at sea level, so whichever way you look at it, it doesn't have any elevation: it's below eye level; below surface level; and equidistant from the center of the earth at all points on its surface (give or take).

Trailblazer

Moderator
Staff member
It looks that way, but it's not that way. Optical illusion.
Well, kind of. It depends on how you're defining "higher". We measure altitude relative to sea level, so in that sense the sea isn't higher than where he's standing. But if you draw a line from his eye to the base of the lighthouse, then yes, the sea is higher than that line.

It's not exactly the same as the "bulge" measurement, though. The "visual bulge" when looking towards the hidden base of the lighthouse is actually this, isn't it? It's less than the "bulge" measurement on the curve calculator, which is based on a line drawn from ground level.

If you rotate that so that the direction you are looking (ie towards the base of the lighthouse, the red line) is horizontal, then the additional "height" of the sea is a bit easier to sea:

The sea appears to rise up enough to intersect your eyeline to the base of the lighthouse some distance in front of the horizon. I think that is the effect you are describing (which I agree is a very strong visual effect).

Applying that point to a frame from your GIF, the point where the sea intersects your eyeline is well in front of the horizon, and that is what gives the visual effect of a "wall of water". (This is just an illustration, as the lighthouse is not drawn to scale)

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Rory

Senior Member.
Not sure about that. Why would his eye be looking at an angle corresponding with where the base of the distant and partly hidden object is?

Also, though on the diagram the difference between "bulge" and "visual bulge" is large, in reality it would only be the difference caused by elevating the viewer by around 5.5 feet, which I imagine isn't a great change in sagitta height over 18.1km.

The effect of the optical illusion is still present when there isn't a distant object in view: like when going over the top of a hill near the coast and having the sensation that the sea appears higher than we are, like so:

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Mick West

Staff member
Not sure about that. Why would his eye be looking at an angle coresponding with where the base of the distant and partly hidden object is?

Because if you can see the shape of the object then your brain fills in the rest, and assumes the object is sitting on "ground" level.

Rory

Senior Member.
Because if you can see the shape of the object then your brain fills in the rest, and assumes the object is sitting on "ground" level.
If that were true then all views of partly hidden objects across water would show this 'wall' effect. It's very striking in Stargazer's image, but not so in many others.

This is Chicago from 30 miles away. This time it looks more like a sunken city, rather than a wall of water that rises higher than the camera.

https://yumyummatt.wordpress.com/2014/06/13/chicago-as-seen-from-around-south-lake-michigan/

Staff member

Trailblazer

Moderator
Staff member
I still think it looks like a hump of water. The effect seems to be more pronounced in videos than in still photos, though.

Rory

Senior Member.
Here are two places I've often seen the effect with my own eyes:

Whitstable, Kent

Whitby, North Yorkshire

I think these both demonstrate well that a distant hidden object isn't required to generate the effect. Though as Trailblazer notes, the effect appears even stronger in video/live viewing.

As for whether all views of large bodies of water with objects in the distance make the water appear higher than the eye...

Chicago

Toronto

I don't see a "rising wall of water" in these. Maybe some do and some don't; that would be interesting.

Definitely see it in others, though, like Stargazer's vid, and one that has been posted elsewhere on metabunk showing wind turbines, with strong waves in the foreground:

https://www.metabunk.org/posts/205430/

I still think it looks like a hump of water.
Interesting that you use the word "hump". You know that it is a "hump" (in a sense) - but how can we see that in the picture, given that the 'downward' portion of the "hump" isn't visible?

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Trailblazer

Moderator
Staff member
Interesting that you use the word "hump". You know, in one sense, that it is a "hump" - but how can we see that in the picture, given that the 'downward' portion of the "hump" isn't visible?
Just the visual impression - it looks like you are looking over a hill. I also agree that having visible waves helps, as the decreasing size of the waves into the distance helps to add a sense of depth and "three-dimensionality" to the sea. For this reason the best photos to show the effect are those taken from relatively close to the water, so that the waves appear quite large. The distant skyline photos of Chicago over the lake don't show the effect so clearly because the water looks more uniform.

Rory

Senior Member.
Just the visual impression - it looks like you are looking over a hill.
That first pic of Chicago?

Looks flat to me, with a sense that there's something over the other side of the horizon (could be a downslope, a sheer drop off, a void filled with naughty flying monkeys - who knows? )

Maybe this is one o' them things like 'the dress'?

I think you're right about the waves. Definitely seen several vids with big waves rolling in and that wall of water looks not only weird and real but downright scary.

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StarGazer

Member
When I formulated the question I thought it made sense that the sea would physically form a slight ''hump'' midway between me and the target before it starts to dip down, or maybe since the lighthouse is more elevated than it should be because of refraction, then the horizon might also be more elevated than it should be because of refraction.

Then @Mick West had me look into the graphic of the metabunk calculator and I realised that my eye level (the camera's level) has to be aligned with the astronomical horizon and not the true horizon (the ground horizon):

Image not in scale.

And I also realised that there cannot be a physical ''hump'' midway between me and the lighthouse because from 1.5 meters tripod height, the distance to the horizon is only 4.4 km (distance to the horizon calculator here)

Then @Rory confirmed everything so far by saying: ''The sea will be at sea level, so whichever way you look at it, it doesn't have any elevation: it's below eye level; below surface level; and equidistant from the center of the earth at all points on its surface (give or take)''.

Am I correct so far?

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Trailblazer

Moderator
Staff member
Am I correct so far?

Well, I would say that when you are standing at the sea looking out to the horizon, your eye naturally rests on the horizon, so your "eye level" is actually the "true horizon" direction on your diagram. If you are looking towards an object that is obscured by the horizon, then your brain might even consider that your eyeline is towards the (hidden) base of the object, i.e. below the horizon. I certainly don't think you would ever perceive your eyeline as being the "astronomical horizon", i.e. a small amount above the horizon, perpendicular to your local direction of "down".

As for the "hump of water", that's really just a matter of definition. The elevation of the sea is always the same (sea level), but it is a curved surface, so relative to a straight line, it curves upwards in a convex arc (a hump, if you like) to the point where it meets the horizon.

StarGazer

Member
...I certainly don't think you would ever perceive your eyeline as being the "astronomical horizon", i.e. a small amount above the horizon, perpendicular to your local direction of "down".

As for the "hump of water", that's really just a matter of definition. The elevation of the sea is always the same (sea level), but it is a curved surface, so relative to a straight line, it curves upwards in a convex arc (a hump, if you like) to the point where it meets the horizon.

Then if I rise 10 metres higher from the same spot, the upward convex arc would be almost 3 times higher than from 1.5 meters elevation, since the distance to the horizon from 10 metres is 11.3 km.

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Trailblazer

Moderator
Staff member
Then if I rise 10 metres higher from the same spot, the upward convex arc would be almost 3 times higher than from 1.5 meters elevation, since the distance to the horizon from 10 metres is 11.3 km.
That doesn't follow. The height of the horizon above the straight line to the base of the object doesn't increase linearly with the distance to the horizon, because the sea surface is a curve.

StarGazer

Member
That doesn't follow. The height of the horizon above the straight line to the base of the object doesn't increase linearly with the distance to the horizon, because the sea surface is a curve.

Then, since the height of the horizon doesn't increase with altitude the ground horizon always has to be below the eye level (astronomical horizon) at all times including from (edited) sea level elevation.
We rest our eyes at the horizon, yes, but that is because we cannot rest them in mid-air above the horizon.
If we consider as eye level where the eyes rest, in this case the horizon, then no matter the altitude, the horizon would always remain at eye level. Don't you agree?

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Trailblazer

Moderator
Staff member
Then, since the height of the horizon doesn't increase with altitude the ground horizon always has to be below the eye level (astronomical horizon) at all times including sea level elevation.
We rest our eyes at the horizon, yes, but that is because we cannot rest them in mid-air above the horizon.
If we consider as eye level where the eyes rest, in this case the horizon, then no matter the altitude, the horizon would always remain at eye level. Don't you agree?
The sea-level horizon is always below the astronomical horizon, yes. And of course, if you define eye level as the horizon then the horizon will always be at eye level. But the higher you get, the more you will have to look down (relative to the astronomical horizon) for your eyeline to be at the horizon.

Taken to the extreme, for an astronaut thousands of miles up in space, they will have to look a long way down to see the horizon! (Not that "down" in space has much meaning, but I'm using down to mean towards the centre of the Earth, as on the surface.)

I'm not quite sure where you are going with these questions?

StarGazer

Member
I'm not quite sure where you are going with these questions?

I'm asking those questions to double check with you and everyone the difference between true eye level and apparent eye level, since the apparent eye level gives the impression that the sea level where the horizon is located is equal or higher (like in my case) then the observer's sea level, but in both cases is lower, because away from the observer the surface begins to curve down 8 inches per mile squared.

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Langden

New Member
I would like to make a second comment to address the "wall of water" discussion also happening in this thread.
Rory has two examples, photos that "look like a wall of water" and photos that do not.

The illusion that it occurring here is due to perspective. All of the "wall of water" images are taken at low elevation.

Here are two photos that have been taken from the same position but at different altitudes.
The first image looks drastically different from the second, almost like a wall of cement.

When you are higher, you can see the further parts of the road/water more easily.
When down low, the majority of what you see is that which is closest to you. The road/water in the distance becomes infinitely tiny.

If you were to encounter a wall of water, it would not appear as though there was kilometers of open water in front of you. Instead it would appear that there was a very short distance of water all the way to the horizon (as far as you were able to see, like there was a wall in the way, obscuring the rest of the 'open water') Which is why we perceive the images of open water taken from low elevation to look this way.

Rory

Senior Member.
Sorry, neither of those look like a 'wall of cement' to me.

Majd Saedy

New Member
Maybe the problem is in the phrase "wall of water", wall implies that it looks vertical which it doesn't, a better description could be that it looks like you are standing at the bottom of a ramp.

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