## Partial vertical attenuation coefficients

In any medium containing a number of absorbing and scattering components, the contributions of the different components to any one of the absorption and scattering coefficients (normal, diffuse, forward, back) are additive, e.g. if there are n components, then atotal = a1 + a2 + ... + an and similar relations hold for b, ad(z), bbd(z) etc. Consequently, for an aquatic medium containing n absorbing/scattering components we can expand eqn 1.63 to

Rearranging, we obtain

which can be written in the form

Thus the vertical attenuation coefficient for downward irradiance in a natural water can be partitioned into a set of partial vertical attenuation coefficients, each corresponding to a different component of the medium. The partial vertical attenuation coefficient for the ith component is given by

It is important to remember that although the contributions of the different components of the medium to total attenuation of irradiance can be simply added together in accordance with eqn 6.31, the nature of their contributions to attenuation can vary markedly from one component to another. Consider, for example, a water in which component j is dissolved yellow colour, and component j+1 consists of suspended mineral particles, scattering intensely but with little intrinsic colour. For the jth component, Kd (z)j will consist mainly of the absorption term, ad (z)j, in eqn 6.31, whereas for the (j+1)th component, Kd (z)j+1 will consist mainly of the backscattering term, bbd(z)j+1.

It is also important to remember that the value of Kd (z)i, and consequently the contribution of the ith component to Kd (z), is not a linear function of the concentration of that component. Any substantial change in the absorption and/or scattering characteristics of the medium resulting from a change in concentration of one of the components will inevitably affect the radiance distribution at depth z. The absorption and scattering coefficients on the right-hand side of eqn 6.31, being quasi-inherent rather than inherent optical properties (see ยง1.5) are functions of the radiance distribution as well as of the concentration of the component in question. Consequently, although their values will increase with the concentration of the component, the increase will not be linear with concentration. Furthermore, R, being a function of the radiance distribution, will also change as the concentration of any component changes. In short, Kd (z)i and Kd (z) will certainly increase as the amount of any of the components of the medium increases, but except for small increments in concentration, the increases will not be linearly related to the increase in concentration.