Beakery!

A site where I can beak off about whatever comes to mind…

The Colour of Glacial Lakes

I do a lot of hiking in the mountains and especially so near glaciers and glacial lakes.  Some people who have been near a glacial lake in the early summer may have found that the colour of the lake seems to be a much richer blue than that of lakes at lower elevations or those that are not fed by glacial meltwater.  What almost everyone will have noticed, however, is that in the late summer the colour of glacier-fed lakes almost inevitably becomes a teal-green colour.  Why the lakes are the colours that they are, and at different times of the year, is a question that has interested me for a long time.  I have had a rough idea of what the mechanism is, but it is only recently that I’ve found some actual research that has dealt with the problem.

Two different colours for the upper Dunbar lakes – teal green on the left and deep blue on the right – show the different colours found in glacial lakes.

The simplest explanation for the colour is to use the same explanation as to why the sky is blue.  The standard explanation for that is a process known as dipole scattering.  In electrodynamics, which is the field of physics that governs the interaction of light with matter, the simplest object that can radiate an electromagnetic (EM) field is an oscillating dipole – basically a charge oscillates back and forth along a line with frequency ω.  Interestingly, this is not the simplest radiator for other systems: in acoustics, a monopole, a balloon that expands and contracts, is the simplest radiator.  But I digress.  If one has an oscillating dipole of zero size (what is known as a Hertz dipole), it radiates electromagnetic energy at a frequency ω with a total power output that scales as ω4, or for EM radiation, as λ-4 where λ is the wavelength of the optical radiation.

So what does this have to do with the colour of the sky?  Well, the realistic condition for a Hertz dipole is that the wavelength of the emitted radiation has to be much larger than the size of the radiating dipole.  The sky is full of atoms, molecules, and small dust particles which have sizes that are much smaller than the wavelength of optical radiation.  Okay, the dust particles might not, but they have sizes on the order of the wavelength of optical fields.  These dipoles are being constantly bombarded by broadband radiation from the sun, and thus they oscillate at many different frequencies at the same time.  But how much power they radiate after being excited by the sun’s light scales as λ-4.  Thus, shorter wavelength light – blues, violets and UV rays – will be much more preferentially scattered than the longer wavelength light – oranges, reds, and the near-infrared.  This suggests that we should see a sky that is colourless or violet, not blue.  The extra ingredient is that our eyes are much more sensitive in the blue than they are in the violet, so our brains interpret the colour of the sky as blue.

Incidentally, this strong scattering of the shorter wavelength light is also why at sunrise or sunset the sky near the sun changes from blue to orange and red.  At sunrise and sunset the sun is at a lower angle, and the light from the sun has to travel through a lot more atmosphere than it does when it is directly overhead at midday.  As a result, much of the shorter wavelength light is removed from the spectrum of the sunlight by scattering, and what remains near the location of the sun is a lot of reds and oranges.

Pure water is similar to the sky in that it contains a lot of very good Hertz dipoles – water molecules.  Therefore, one would expect that water would behave in a very similar fashion.  In fact it does – it scatters light mostly into the shorter wavelengths and very little into the longer wavelengths.  This is why we see water as having a slight blue tinge to it.  However, as was pointed out to me by a friend, what we don’t see is that if one looks at a light through a very long column of water that the light has a reddish tinge to it.  The reason for that is the absorption of light by the water molecules; this is a process that does not occur over broad ranges of the optical spectrum in air (although it does occur at select wavelengths).  As it turns out, water strongly absorbs in the red region of the spectrum: the absorption coefficient for light at 650 nm is nearly fifty times greater than at its minimum in the blue at 475 nm (see Fig. 1). All the red light gets absorbed, and all the blue light gets scattered in a long column of water, so what one sees is nothing at all.

Figure 1: Scattering and absorption of light by water, taken from Ref 1. aw and bw are the absorption and scattering coefficients, respectively, for pure water. The a’s and b’s with the subscript p are for particles, and the particle size is given by D.

Now that we have an idea of why pure water has a slight blue colour, we can move to the question of why glacial lakes have a much deeper blue and even green colour.  The meltwater from glaciers tends to have a very large amount of suspended sediment, and much of this sediment is comprised of particles with small diameters – what is known as rock flour.  The sizes of the particles vary from below 2 µm to about 100 µm.   Of course, none of these particles are smaller than an optical wavelength (<700 nm) which means that none of them act as Hertz dipoles.  This is a good thing for explaining the change of the water colour, because if they acted as Hertz dipoles then they would have absolutely no influence on the colour of glacial water.  As the size of the particles increases, their absorption and scattering coefficients have less variation with wavelength for the short wavelengths than for the longer wavelengths.  This means that short wavelengths are absorbed and scattered more-or-less equally by the particles.  For large enough particle size, the absorption and scattering coefficients do not change appreciably over the optical spectrum, as can be seen from Fig. 1.  Therefore, particles with sizes above about 20 µm will not significantly affect the colour of the water as long as their concentration is not too high.  Particles with sizes that are about 2 µm or less are the particles that will have an effect on the colour of the water.

What matters in determining the colour of the water is how much light is scattered back from the water to our eyes.  The ratio of the amount of light scattered backwards compared to what continues downwards into the water is termed the irradiance ratio, and one can shown that it is given as the ratio of the backscattering coefficient to the absorption (Ref. 2).  This makes intuitive sense, as the larger the backscattering coefficient the more light should reach our eyes, and the larger the absorption the less light should reach our eyes.  Looking at Fig. 1, we can see that although particles with sizes less than 2 µm scatter and absorb strongly in the blue the ratio between them (a difference in Fig. 1) is much larger for longer wavelengths than for shorter wavelengths.  Combining this with the absorption and scattering coefficients of water, we see that the short wavelength light that is preferentially scattered back to our eyes by water will be absorbed by the small suspended particles.  For low concentrations, this will shift the maximum of the irradiance ratio from the violets and blues more towards the blue.  For even higher concentrations, the maximum of the irradiance ratio will shift from the blue to the green.  A representative plot of the irradiance ratio as a function of wavelength is shown in Fig. 2, where for a suspension dominated by small particles the maximum irradiance ratio is in the green.

Figure 2: Irradiance ratio for pure water and various different particle sizes (from Ref. 1).

For larger particles, one sees that the absorption spectrum flattens out at the short wavelengths, and for even larger particle sizes the spectrum is almost completely flat – indicating that the water is a milky white or grey.

This argument is not only restricted to glacial lakes – it applies to any kind of water where there is suspended sediment or other particles and one cannot see the bottom of the lake/ocean/container.  I have neglected two other considerations here, however.  The first is the presence of algae or other biological matter that will shift the colour of the water to either green or brown depending on the colour of the plant matter.  A related consideration is if the sediment itself has strong absorption at particular wavelengths.  This will also shift the spectrum of the scattered light to different wavelengths.  Regardless, for water with colourless suspended particles and no biological matter, the simple model that I have summarized here provides a rather robust and neat explanation.

References

[1] E. Aas and J. Bogen, Colors of glacier water, Water Resources Research, 24 561 (1988).

[2] E. Aas, Two-stream irradiance model for deep waters, Applied Optics26 2095 (1987).

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