The color of water: visibility under water

ABSTRACT
Visibility during dives vary. Variance not only occurs between different dive sites. Even at one site visibility may vary over a fairly short period of days. This section describes the factors which influence visibility under water when diving. Physical principles of absorbtion and scattering are explaned. Influence on visibility of the water itself, of dissolved/particle organic/inorganic matter is described.

Usually, divers are happy when they are having great visibility underwater. Divers travel all around the world to dive in crystal clear oceans. This section describes the factors influencing visibility under water.

Physical principles

Light

Light propagates rectilinear. This means light propagates in strait lines. In vacuum light travels at a speed c of 300.000 km/s. In matter, light travels less fast. The refractive index n of such matter is defined as the speed in vacuum divided by the speed in the matter v:

n  =   c v

(1)

Light is actually electro-magnetic radiation like Röntgen radiation, radio waves, gamma rays, ultraviolet and infrared radiation. Like all other electro-magnetic radiation light consists of waves, with an associated wavelength λ. Colored light is light of a particular wavelength. In fact white light is a combination of light with different wavelengths. Besides a wave nature, light also exhibits a particle nature: light consists of photons which can be regarded as particles making up the light. A photon represents an amount of light energy E_ph, depending on the wavelength of the light.

E ph  =   h c λ

(2)

E_photon

Photon energy (J)

c

Velocity of light (m/s)

h

Plack's constant 6.62620 10³⁴ Js

λ

Wavelength of the light (m)

Coherent light is light in which each photon progates in the same direction.

Light traveling a certain distance through gas, liquid or solid matter is attenuated by absorption and scattering. This attenuation is exponential and is described for coherent light (all light traveling in the same direction) by

I(d)

Intensity of the light after traveling a distance d (W/m²)

I₀

Initial intensity (W/m²)

d

Distance traveled by the light (m)

α

attenuation coefficient, might depend on wavelength (1/m)

Absorption

Absorption is the process of transferring of light into thermal energy (heat motion of the molecules). In the absorption process light disappears. The amount of absorption varies with wavelength of the incident light. In solids and liquids we see absorbtion bands: over a range of wavelength we have continous absorbtion, fading off gradually at the ends. Even materials that are transparent for visible light (like glass) show absorption (are opaque) in other wavelength regions like ultraviolet and infrared. Figure ? shows the absorption bands for water: whereas blue light is hardly absorbed, infrared is absorbed heavily. On the other hand, a material like rubber is opaque for visible light but transparent for infrared. In low pressure gasses absorbtion lines are present: light of particular wavelengths (photon energy) is absorbed. Photons with this energy kick molecules of the absorbing matter in a higher vibrational state. Beside absorbtion lines gasses may exhibit absorbtion bands as well.

Scattering

Scattering is the process of changing direction of the light. Photons may change direction on collision with molecules of the matter or with particles present in the matter. We distinguish three types of scattering:

• Rayleigh scattering
• Mie scattering
• Raman scattering

Rayleigh scattering is scattering at molecules and particles that are small with respect to the wavelength of the light (say, up to a tenth of the wavelength). This scattering is more effective for shorter wavelengths (blue). In fact, the scattered intensity is proportional to 1/λ⁴

I scatter α  1 λ 4

(4)

Rayleigh scattering is the main reason for the sky being blue. Light from the sun is scattered by molecules in the atmosphere to all directions, including towards the observer at the earth's surface. Since scattering is more effective for light at shorter wavelengths (the blue side of the spectrum), the scattered light is predominantly blue. This makes the sun itself appear red/orange, since the blue light is scattered in other directions than towards the observer. This is best visible when the sun is at the horizon. The reason for this is that when the sun is at the horizon, light travels a large distance through the atmosphere when compared to the situation where the sun is right above the observer. We can estimate the ratio between the distance traveled by the light in both situations. The diameter of the earth r_earth=6378 km. An order of magnitude of atmosphere thickness is Δr_atm=10 km. One could show the distance traveled by the light when looking at the horizon is given by ( 2 r_earth Δr - Δr² )^1/2. In this case this distance is 357 km. Compared to looking strait up, sun light travels through 36 times more air towards the observer.

The amount of Rayleigh scattering is not constant but varies with direction with respect to the incident light. The relation for Rayleigh scattering is:

I  =  I 0  8 π 4 N α 2 λ 4 R 2   [ 1 + cos 2  ( θ )  ]

(5)

The (1 + cos²θ) dependency is shown in Figure 1: scattering strength is symetrical in the direction of the incidence light.

Raman scattering is the scattering in which the wavelength (or photon energy) of the scattered light is different from the wavelength of the incident light. In the process energy from the incident photons is transferred to the molecule, leaving the molecule in a higher vibrational state and the photon at lower energy. Scattering of a photon off a molecule in a higher vibrational state will result in scattered photons with higher energy and a molecule in a lower vibrational state. Scattered intensities are low resulting in difficult detection of the the Raman effect. Raman scattering does not play a significant role in under water visibility so it will not be discussed here further.

Figure 1: Direction dependency of scattering

Mie scattering is scattering due to particles that are larger than the wavelength of the incident light. Mie scattering is not (or hardly) wavelength dependent. Scattered light will look white or light bluish, depending on the size of the scattering particles. In Mie scattering, the direction of the scattered light peeks forward, as is shown in Figure 1. An example of this directional scattering is shown in the photograph of the Duane wreck (Figure 2): there is a white halo around the sun. Sunlight is scattered by particles in the water. Since this scattering is mainly forward directed, it shows to the observer as a halo around the sun. Since there is hardly wavelength dependency, this halo is white.

Figure 2: Diver at wreck of Duane at 30m/110ft Key Largo, Florida (photo: David Rhea, GUE)

Water

Now we will look at the water we dive in. Visibility varies: tropical oceans are clear, whereas lakes often have lower visibility. Equation (3) can be extended to cover all situations:

with

α

Attenuation coefficient (1/m)

α_water

Attenuation coefficient of pure water (1/m)

α_dissolved

Attenuation coefficient determining attenuation due to dissolved matter. This may be Dissolved Organic Matter (DOM) or Dissolved Inorganic Matter (DIM). (1/m).

α_particle

Attenuation coefficient determining attenuation due to particles in the water. These may be Particle Organic Matter (POM) or Particle Inorganic Matter (PIM). (1/m)

In next section we'll have a closer look to each of the attenuations.

Pure water

First of all water itself is responsible for the attenuation of light. This attenuation is mainly due to absorption. The absorbtion is characterized by a wavelength dependent coefficient α_water(λ) as given in equation (3). In Figure 3 this absorbtion coefficient of pure water is plotted against wavelength. The absorption coefficient is plotted on logarithmic scale.

Figure 3: Absorption coefficient for pure water

Independent measurements of the absorption coefficient are quite consistent. They only differ little in the blue/violet area, as can be seen from the two series of measurements that are plotted in Figure 3. As can be seen in Figure 3 absorption is largest for the red color. This is the reason why clear sea water is blue. For pure water the color is plotted versus depth in Figure 4. I assumed α_water(blue)=0.01 m^-1, α_water(green)=0.02 m^-1 and α_water(red)=0.5 m^-1. These values have been taken from Figure 3.

Figure 3: Color versus depth for pure water

POM

Figure 5: Phytoplanton Figure 6: plankton bloom

One of the most important factors controlling underwater visibility is phytoplankton, which make up Particle Organic Matter (POM). Phytoplankton are microscopic organisms that freely float in the water. The organisms are smaller than 2 μm. Phytoplankton form the base of the oceanic food chain and is the main supply of food and energy for oceanic ecosystem: phytoplankton this grazed by zooplankton, zooplankton is eaten by small fish, small fish are eaten by larger fish, etc. Phytoplankton grow by converting nutrients, sunlight and Carbon Dioxide into plant material. This is performed by a process called photosynthesis. For this phytoplankton uses chlorophyll. Chlorophyll, which is also found within plants, absorbs sunlight, whereas phytoplankton itself scatters light. This changes the color of the water. An example is shown in the photograph of the plankton bloom for the coast off Angola, taken by a Space Shuttle astronaut (Figure 6). Chlorophyll comes in two flavors: chlorophyll a and chlorophyll b. Chlorophyll a absorbs blue, violet and red light. It reflects green light. Chlorophyll b mainly absorbs blue and orange, whereas it reflects yellow-green light. Satellites like SeaWiFS measure the ocean colors in several wavelength bands. From this phytoplankton concentrations can be calculated. This results in images like Figure 7.

Figure 7: chlorophyll concentration in the oceans

PIM

DIM

References

• [1] 'Fundamentals of Optics' Fourth edition, Jenkins & White. ISBN 0-07-085346-0. Chapter 22.