For depth-specific measurements the equation is
where Ed is downwelling cosine irradiance measured at two depths, Z1 and Z2 (Kirk, 1994a; Kirk, 1994b). When Ed is measured continuously with depth by a UV profiling instrument the equation becomes
The value of Kd in equation (2) is typically estimated for a specific wavelength (?) by regression analysis, solving for the slope of the straight line formed by plotting Loge(Ed,Z) versus depth, Z, after correcting Ed,Z for dark signal & other noise (Hargreaves, 2003). With either method an average value for Kd,? is attributed to a specific depth range. The value of Kd,? will be approximately constant throughout depths that are uniformly mixed but can increase or decrease somewhat with depth until an equilibrium extent of diffuseness develops (Gordon, 1989). Variations in Kd near the surface of well-mixed water are related to surface waves (Zaneveld et al., 2001) and to changes in diffuseness determined by sky conditions and sun angle (up to 20–25% for UV wavelengths, Hargreaves, 2003). It is because of the response of Kd to diffuseness and light angle that Kd has been called an apparent optical property (AOP) of the water body, in contrast to inherent optical properties discussed below.
Kd and other optical measurements respond to the concentration of particulate and dissolved matter and can be used to investigate factors controlling transparency of natural waters. In addition to Kd, (an AOP) these include inherent optical properties of the water, or IOPs (Tyler & Presiendorfer 1962), properties controlled by the composition of the water and not influenced by the light field. IOPs include the beam absorption coefficient, a, the beam scattering coefficient, b, and their sum, the beam attenuation coefficient, c. Direct measurement of c in the water column has been common for years using the beam transmissometer, typically with a red (e.g. 660 nm) light source. When measured at a long wavelength where CDOM absorption is negligible, variations in c are correlated with the concentration of particles because of their impact on scattering. Particulate organic carbon (POC), microbial biomass, or phytoplankton cells are the dominant particles in many aquatic systems (Boss et al., this issue). At the typical wavelength of 660 nm used in transmissometers to measure beam c, the relatively constant absorption of water (cw660 = 0.411 m-1, varying slightly with temperature, Pope & Fry 1997; Morel 1974; Pegau etal., 1997) can be subtracted to yield the particulate beam attenuation coefficient, cp660.
