The total absorption coefficient is often separated into operationally defined components such as the dissolved and particulate fractions and water:
a_t = a_g + a_p + a_w

The subscripts t, g, p, and w represent total, dissolved (historically called gelbstoff or gilvin), particulate, and water, respectively. 

Operationally, the dissolved fraction typically comprises all substances that pass through a 0.2 µm filter. Another commonly used parameter is a_pg, defined as the quantity (a_p + a_g).

For algorithms focusing on the absorption by phytoplankton, an additional partitioning of the particulate component is often made:   a_p = a_f + a_d , where the f and d subscripts represent the algal and non-algal components, respectively. The non-algal component is comprised of non-living particulate organic material, living particles such as bacteria, inorganic minerals, and bubbles. 

Most of the following material is from: Mueller, J.L., G.S. Fargion, and C.R. McClain [Eds]. 2003. Ocean Optics Protocols For Satellite Ocean Color Sensor Validation, Revision 4, Volumes I, IV. NASA, Goddard Space Flight Center, Greenbelt, MD.

Absorption by Pure Water
Table 1.1 (pg 5) from the Ocean Optics Protocols gives the absorption coefficient for pure water. Note that this table is also given in the ac-9 Protocol document (Table 2).

Absorption by Suspended Particulates and Colored Dissolved Organic Material (CDOM)
Variations in the spectral absorption of natural waters result directly from variations in the concentrations and chemical compositions of material substances distributed within the water volume. These absorbing materials may be present in seawater either in suspended particulates, such as pigment-bearing phytoplankton, or as solutes (i.e. CDOM). Fig. 1.1a illustrates qualitative comparisons between the absorption spectrum of pure water, a _w (l) (Table 1.1), a non-dimensional Chl-specific absorption spectrum of phytoplankton pigment concentration, a*_chl (l) (Prieur and Sathyendranath 1981), and a typically exponential absorption spectrum of CDOM, a_g (l)  (Bricaud et al. 1981). The amplitude of each absorption spectrum in Fig. 1.1a is arbitrarily scaled to illustrate the characteristic difference in shapes between the constant water background absorption and two varying absorption components associated with Chl and CDOM concentrations. The unique shape and magnitude of the specific absorption spectrum for each individual constituent allows measured values of, e.g., Chl and CDOM concentrations to be determined from measurements of a (l) at several appropriate wavelengths. The strong inverse dependence of remote sensing reflectance on a (l) (Vol. III, Ch. 4), together with the distinctive shape and magnitude characteristics of the constituents, similarly provides the physical basis for ocean color algorithms for determining their concentrations from satellite measurements of water leaving radiance at several wavelengths.

In Case 1 waters, it is often useful to assume (Gordon and Morel 1983; Morel and Maritorena 2001; Mobley and Sundman 2000) that particle absorption a_p (l) is dominated by phytoplankton pigments and may be expressed as a function of Chl concentration [mg m^-3] and a Chl-specific absorption spectrum a*_chl (l) (Prieur and Sathyendranath 1981), and that CDOM concentration is correlated with Chl so that a_g (l)  may also be calculated as an exponential function of wavelength (Bricaud et al. 1981) scaled as a function of Chl. Fig. 1.1b shows the sum a _m(l;Chl) = a_p(l;Chl) + a _g(l;Chl) calculated, for Chl = 1, 3, and 10 mg m ^-3 , using this simple model, as implemented in one of the standard IOP specification options within the HYDROLIGHT radiative transfer model (Mobley and Sundman 2000). The subscript “m” indicates that the spectra shown in Fig. 1.1b are those that would be measured by an instrument that was calibrated using pure water as a standard reference medium (Chapter 3).  The absorption of pure water a _w(l) is compared with a _m(l;Chl)  in Fig. 1.1b, and the corresponding total absorption coefficient spectra a (l;Chl) = a _w(l) +  a _m(l;Chl) are illustrated in Fig. 1.1c. The illustrated examples are admittedly an oversimplification, but they are adequate as a basis for considering the nature of IOP components of the signal measured by an absorption meter, or transmissometer, at individual wavelengths.