Apparent optical properties (AOPs) are derived from the IOPs defining the medium, combined with the angular distribution of the ambient light field. As such, AOPs will be affected by the time of day, degree of cloud cover, sea surface state and depth within the water column. The most commonly used AOPs are the diffuse attenuation coefficients or "K" functions. K functions, also referred to as quasi-inherent optical properties, because the effects of changes in the incident radiation field are generally small, although that is not always the case (Baker and Smith, 1979, but see Miller and McPherson, 1995). Because the irradiance within a sunlit + skylit water body decreases approximately exponentially with depth, it is conventional to describe that relationship using the Lambert-Beer equation. Thus, the downwelling plane irradiance anywhere within the water column [i.e. Ed(z)] is a function of the in-water irradiance at the surface [Ed(0)], the diffuse attenuation coefficient for downwelling irradiance (Kd), and the depth (z) of the overlying water column:

the submarine light field in terms of a single parameter. For a collimated beam oriented at angle (9 ) relative to the zenith, jjd = cos 9. Thus, the average pathlength of photons traveling downward through the water, and therefore the magnitude of the diffuse attenuation coefficient, is proportional to -j-. The jjd downwelling average cosine can also be calculated from the ratio of the downwelling plane irradiance normalized to the downwelling scalar irradiance:

The upwelling average cosine is defined similarly as

Values of jid typically range from 0.9 to 0.75 in natural waters. A typical value for jlu is about 0.39. If the light field is isotropic (i.e. equal intensity in all directions), jid = jlu = 0.5.

Thus, the diffuse attenuation coefficient is easily approximated from vertical profiles of spectral irra-diance. The diffuse attenuation coefficients for up-welling plane irradiance and scalar irradiance are defined by similar equations. K functions of broadband irradiance (e.g. PAR) provide convenient, albeit much less perfect, descriptors of light attenuation because they do not properly account for the strong wavelength-dependency of absorption. This can be an especially significant problem for estimating light availability for seagrass photosynthesis in green coastal waters (see Chapter 13). The K-functions are dimensionalized with the same units (inverse length) as the IOPs, but it is important to remember that the IOPs refer to the loss of radiant power from a collimated beam. K functions represent the attenuation of naturally diffuse light comprised of photons traveling in all directions.

The average cosine j!, another AOP, provides a useful way to approximate the angular structure of

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