Color Memory Game
By John K.··13 min read

Why is the ocean blue: the measured answer, and the sky's share of it

Pure water is blue on its own, by absorption, with its clearest window at 417.5 nm. Rendered from the Pope and Fry absorption spectrum, the open ocean comes out #030951 and returns 0.81 percent of the light that falls on it. But 82.9 percent of what reaches your eye at the surface is reflected sky, even looking straight down.

The ocean is blue because water is blue. Not because it reflects the sky, and not because of the scattering that makes the sky blue in the first place. Water is one of the very few common substances that is colored by what it removes from light rather than by what it bounces back, and it is so weakly colored that you need metres of it before anyone notices.

Rendered from the measured absorption spectrum of pure water, the open sea comes out at #030951, a dominant wavelength of 465.5 nm, and a luminous reflectance of 0.81 percent, which makes deep clear water darker than fresh asphalt. Then I checked the folk explanation, and it turns out the people saying the sea reflects the sky are right about roughly 83 percent of the photons and wrong about the color anyway. That contradiction is the most interesting thing in this piece, so it gets its own section.

How I measured it

This is a direct sequel to why the sky is blue, which was built from the reference solar spectrum. The ocean needs a different dataset, and for a long time the good one was hard to get hold of. Pope and Fry measured the absorption spectrum of pure water from 380 to 700 nm in 1997 using an integrating cavity, a technique that finally got round the problem that had wrecked every previous attempt: in the blue, water absorbs so little that stray light and container walls swamp the signal. Their table is the reference everyone in ocean optics uses, and it is posted in full by the Oregon Medical Laser Center.

The model has three pieces and no fitted parameters:

  • Absorption from Pope and Fry, 380 to 700 nm at 2.5 nm steps, converted from inverse centimetres to inverse metres.
  • Scattering from Morel’s pure water law, 0.0029 per metre at 500 nm falling off as the wavelength to the power of negative 4.32. Molecular scattering is symmetric fore and aft, so half of it goes backwards.
  • The color from the CIE 1931 two degree observer under D65, then into sRGB, with dominant wavelength and excitation purity taken against the D65 white point. Distances are CIEDE2000.

One check before trusting any of it. Run the pipeline and ask where pure water is at its most transparent, and it answers 0.00442 per metre at 417.5 nm. The published figure from the paper is 0.0044 plus or minus 0.0006 per metre at 418 nm. That is the model reproducing the headline result of the source it was built from, so everything downstream can be taken at face value.

Water is an absorber, not a scatterer

Here is the split that separates the ocean from the sky. For every band, the top bar is how much light a metre of pure water absorbs and the bottom bar is how much it scatters. The number on the right is the ratio.

418 nm0.7x
450 nm2.0x
500 nm7.0x
550 nm29x
600 nm169x
650 nm364x
700 nm921x

Pink is absorption, blue is scattering, both per metre of pure water. Bars are clipped at 0.65 per metre.

The two curves cross at 435.0 nm, where both sit at 0.0053 per metre. Below that line water genuinely is a scattering medium like the atmosphere. Above it, absorption takes over and never gives the lead back, finishing 921 times ahead at the red end of the visible range. Over the band where most daylight energy actually lives, water is an absorber by one to two orders of magnitude.

That single fact is why the sea and the sky are different problems wearing the same color. The sky is blue because short wavelengths are preferentially sent to you. The sea is blue because long wavelengths are preferentially taken away. Two opposite mechanisms, and as it turns out they do not land in the same place.

The color of the open ocean

For deep clear water with nothing living in it, the fraction of light that comes back up is set by the ratio of backscatter to absorption. Feed that through the observer and you get a hex code.

Open ocean, as it actually is
#030951 · dominant 465.5 nm · 86.8% pure, L* 7.3
The same color raised to a readable lightness
#2A46FF · identical hue and purity · L* 49.5

The first swatch is the honest one and it looks wrong, which is the point worth sitting with. Clear deep water returns 0.81 percent of the light that lands on it. Asphalt returns four to twelve percent. Grass returns about twenty five. The open ocean is one of the darkest large surfaces on the planet, and the only reason it does not read as black is that the small amount coming back is extraordinarily saturated: 86.8 percent excitation purity, against 29.1 percent for the clear sky. Nothing you own is that pure a blue. The second swatch is the same chromaticity scaled up so you can actually see the hue.

And there is that violet problem again. Water’s clearest window is at 417.5 nm, deep in the violet, and yet the light that comes back out has a dominant wavelength of 465.5 nm. The gap is 48 nanometres. The reason is the same one that keeps the sky from looking violet: the eye barely responds down there, and D65 does not have much to send. Two completely different physical systems, both with their peak transmission in the violet, both reporting blue, for the same reason in your retina rather than in the water or the air.

The blue is a path length, so it is really a depth

Absorption per metre is tiny, so the color of water is entirely a question of how far the light travelled. Put a white tile at the bottom and vary the depth. Light goes down and comes back, so the path is twice the depth.

10 cm#F8FEFF · 488.5 nm · 1.6%
50 cm#DFFAFF · 488.2 nm · 7.5%
1 m#C1F5FF · 487.8 nm · 14.1%
2 m#8DEAFE · 487.0 nm · 25.3%
5 m#00CCFB · 484.5 nm · 46.5%
10 m#00A3F4 · 480.7 nm · 64.2%
20 m#0067E4 · 474.6 nm · 81.1%
50 m#0000B7 · 463.6 nm · 95.0%

The tile stops being white sooner than most people would guess. Water crosses the just noticeable difference threshold of 2.3 CIEDE2000 at a depth of 8.8 centimetres, and reaches a full unit of difference at 3.7 centimetres. A filled bathtub is already past both. If your bath does not look blue, it is because you have nothing white and unlit to compare it against, not because the color is absent.

Now look at the dominant wavelength column, because that is the finding this piece exists for. It runs from 488.6 nm in a shallow puddle to 454.4 nm at a hundred metres, a sweep of 34.2 nm. Water does not have one blue. It has a continuous run of them, ordered by depth, from a cyan you would call turquoise through to an indigo.

Compare that to the sky, where I found the exact opposite. Push the haze from a mountaintop to city smog and the sky’s purity collapses from 35.1 percent to 14.6 percent while its dominant wavelength stays welded to 476 nm at every single turbidity. The sky can only change how blue it is. The sea changes which blue it is as well. That is the cleanest way I have found to state the difference between a scattering color and an absorbing one, and it drops out of the measurements without anyone having to argue for it.

Testing the claim that water absorbs red

This one is repeated everywhere and it is true, but the size of the effect is almost never quoted, and it is much larger than the phrasing suggests.

  • After 1 metre, 71 percent of red at 650 nm survives against 99 percent of blue at 450 nm. Barely a difference.
  • After 10 metres, red is down to 3.3 percent and blue is still at 91 percent. Blue is now winning 27 to one.
  • After 20 metres, red is at 0.11 percent and blue at 83 percent. The ratio is 747 to one.

Put in terms of how far each color gets before only one percent of it is left: red at 650 nm makes it 13.5 metres. Blue at 450 nm makes it 499 metres. Light at the 417.5 nm minimum makes it 1,042 metres, which is 77 times further than the red. This is why divers describe blood turning green at depth and why underwater photographs need a red filter, and it is the same phenomenon as the depth ladder above, just told per wavelength instead of per swatch.

The scale of it is also worth holding onto for its own sake. A 77 to one spread in penetration is enormous, and it happens in a substance that looks perfectly clear in a glass. Water is a strong colorant that happens to be spread very thin.

Does the ocean just reflect the sky?

This is the explanation everyone has heard and most sources dismiss with a sentence. It deserves better, because when you put numbers on it the answer is genuinely split.

Two things reach your eye from a patch of open sea. Light that went into the water, got scattered around and came back out, and light that never entered at all because it bounced off the surface. The first is set by the reflectance computed above, reduced by the transmission factor for light crossing the water to air boundary. The second is the Fresnel reflectance of a flat water surface, which is 2.11 percent looking straight down. Assume a sky of even brightness and the two are directly comparable.

Water-leaving light supplies 0.436 percent. Reflected sky supplies 2.11 percent. Even looking vertically downwards from a boat into water hundreds of metres deep, 82.9 percent of what reaches you is sky. There is no crossover angle to find, because the sky is ahead at every angle including zero. On the photon count, the folk explanation wins.

On the color it loses anyway, and the reason is purity. The water contributes a sixth of the light but that sixth is 86.8 percent pure, while the sky it competes against is 29.1 percent pure. Chroma is not shared out in proportion to brightness. Mix them properly and the result lands at a chroma of 51.9, when the sky alone would give 22.2. A minority of the light more than doubles the saturation of the whole.

#5B70C9 · 82.9% sky · dominant 470.0 nm
30°#5B70C7 · 83.6% sky · dominant 470.1 nm
45°#5C72BF · 86.8% sky · dominant 470.8 nm
60°#5F74AF · 93.3% sky · dominant 472.7 nm
70°#6075A5 · 96.9% sky · dominant 474.2 nm
80°#61769F · 98.8% sky · dominant 475.3 nm

Angles measured from straight down. All six swatches normalised to a common lightness so the hue shift is the only thing moving.

Three numbers come out of that series and together they describe what looking at the sea is actually like.

  • The sea does not visibly change color until 50.7 degrees from vertical. Everything from your feet out to halfway to the horizon is one color, within a just noticeable difference of itself.
  • At 59.5 degrees the color is exactly as far from the sea as it is from the sky. That is the handover point.
  • By 69.9 degrees it is within a just noticeable difference of pure sky, and no measurement of the color could tell you there was water there at all.

So both camps are describing something real and they are looking in different directions. The sea near the horizon is the sky. The sea at your feet is water, and it sits 6.85 CIEDE2000 from the sky color, which is about three just noticeable differences, small but not arguable. The whole transition happens across roughly twenty degrees of view angle.

This also explains the single most familiar photographic trick involving water. A polarising filter cuts surface reflection hard, and surface reflection is 83 percent of what you are photographing, so the sea goes from pale grey blue to a deep saturated blue the moment you rotate the filter. You are not enhancing the water. You are deleting the sky and finally seeing the water underneath.

Why a swimming pool is a different color from the sea

Same substance, same absorption spectrum, and the two look nothing alike.

Swimming pool, 1.5 m over white plaster
#9BDFED · dominant 487.4 nm · 20.1% pure
Open ocean
#030951 · dominant 465.5 nm · 86.8% pure

The gap is 22 nanometres of dominant wavelength and 85.6 degrees of hue angle, which is most of the way from a cyan to a blue violet. The pool is a transmission spectrum: light goes down three metres of round trip, comes off a white floor, and what survives is whatever water failed to absorb, which peaks near 488 nm. The ocean is a backscatter spectrum, and backscatter itself falls off as the wavelength to the negative 4.32, which pulls the peak much further into the blue before absorption gets a say. One color is what is left. The other is what was returned. If you want a name for the pool color, it sits in the family covered by shades of teal, while the open sea belongs with the darkest entries in shades of blue.

The same reasoning covers the tropical shallows everyone photographs. Turquoise water is white sand at two to five metres, so it is the pool case with a bigger pool. Move past the reef edge where the bottom drops away and the color switches mechanism, not just depth, which is why the change looks like a hard line drawn on the water rather than a gradient.

What this leaves out

Everything here is pure water. Real seawater carries phytoplankton, dissolved organic matter and suspended sediment, all of which absorb hard in the blue and push the color towards green. That is the entire basis of satellite ocean color work: the departure from the pure water case measures what is living in it. The clearest natural waters, in the middle of subtropical gyres, come close to the model here, which is exactly why they look almost black from a boat and startlingly blue in a photograph taken with a polariser.

The single scattering treatment is also a simplification, the same one I flagged in the sky piece. It is accurate while backscatter stays far below absorption, which holds across the visible range for pure water, and it would fail in turbid coastal water where multiple scattering dominates. Salt makes almost no difference to visible absorption, which is why the model gets the open ocean right without knowing anything about salinity.

The part that matters if you care about color

Two things I keep coming back to after building this.

The first is that a mechanism leaves a signature you can read off a chart. The sky pins its hue and varies its purity. Water varies both. Once you know that, you can look at a body of water and make a decent guess about whether you are seeing transmitted light or returned light without measuring anything, purely from whether the blue is a cyan or an indigo. That is the same skill that makes color constancy work, applied deliberately instead of automatically.

The second is how much of an everyday color is not in the object. Eighty three percent of the sea is the sky. A mirror is measurably green because of its glass, not its silver. The famous dress problem is an illuminant problem. Color is almost never a property of the thing you are pointing at, and the practical consequence is that you get much better at color by learning what to subtract.

That is a trainable skill, and it is what the color memory game is built to exercise. If you want the version that drills the fine distinctions this article is full of, the gradient mode puts shades of one hue next to each other and asks you to hold the difference in your head, and training your eye for color covers the rest. If you would rather read on, the sky and the sun were built from the same toolkit and answer the other two questions in the set.