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61 Absorption

The absorption spectrum of pure water. The x-axis shows wavelength in the visible spectrum. The y-axis shows the absorption coefficient in units of inverse meters on a logarithmic scale. There is minimum absorption between 420-460 nm and generally increasing absorption with wavelength for longer wavelengths.
Light absorption coefficient of pure water as a function of wavelength.

Here, we will not consider the detailed physics behind wavelength-dependent absorption, but an excellent summary can be found in the Ocean Optics Web Book article by Collin Roessler and Curtis Mobley. We will start with the fact that molecules, such as water, and photosynthetic pigments, absorb light in specific wavelength ranges.

Let’s quantify the absorption of light as it enters the ocean, directed downward. The fraction of light absorbed for a given distance (also called the path-length), \Delta z, is called the absorbance (A). As light continues deeper into the ocean, more and more is absorbed. The absorbance per meter of material (or, in our case, seawater) is called the absorption or attenuation or extinction coefficient, a (sometimes written instead as k_d).

    \[a=\frac{\Delta I / I}{\Delta z}=\frac{1}{I}\frac{\partial I}{\partial z}. \]

This leads to a differential equation,

    \[ \frac{\partial I}{\partial z}=aI, \]

that is solved, for constant a, by the exponential function (try it!),

    \[ I(z)=I_0 e^{az}. \]

Thus, there is an exponential decay in energy flux (aka the intensity, or irradiance as it is often called in this context) moving deeper below the surface of the ocean (z<0), with a decay-scale given by 1/a. The absorbance is A = -az. The transmittance, T, is the fraction of initial energy flux remaining at a given depth, so

    \[ T =\frac{I}{I_0}= e^{az}=e^{-A} \quad or \quad A=-ln(T) \]

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Absorption spectra for chlorophyll-a and chlorophyll-b pigments. The x-axis shows wavelength over the visible band. The y-axis shows relative absorbance. Chlorophyll-a is seen to have peaks at around 430 and 662 nm. Chlorophyll-b is seen to have peaks at around 453 and 642 nm.
Absorption spectra for chlorophyll-a and b.

In a complex situation like the upper ocean, we define a bulk absorption coefficient based on the relative concentration (c) of its various constituents, including phytoplankton.

    \[ a_{total}=a_{water}+a_{phyto} c_{phyto}+\ldots \]

This is a form of what is more generally called the Beer-Lambert Law.  Measurements of the transmittance will yield estimates for the bulk absorption coefficient.

Bulk transmittance as a function of wavelength has been measured empirically in many different parts of the ocean. Water types are often classified according to their optical properties. Perhaps the most common of these classifications historically have been the Jerlov water types, as shown below in a figure from that section of the Ocean Optics Web Book.

Different curves for different Jerlov water types plotted as transmittance (0 to 100%) on the vertical axis vs wavelength on the horizontal axis (300 to 700 nm).
Jerlov’s water mass clasification based on transmitance along 1m of sea water. Based on data from Jerlov (1968), Optical Oceanography, Elsevier Oceanography Series 5.

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Physics Across Oceanography: Fluid Mechanics and Waves Copyright © 2020 by Susan Hautala is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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