In order to understand the relationship between the subsurface irradiance reflectance over a water body and related substratum visibility it is necessary to first understand the subsurface irradiance reflectance of a water body where only the water column is visible, i.e. in optically deep waters. Very clear natural waters may be 30, 40 or more than 50 m deep before the water can be considered optically deep. In waters with very high concentrations of absorbing and scattering substances such an 'optically deep' water body may occur when the benthic vegetation or substratum is only submerged under half a meter of water. Thus, benthic vegetation may be detectable to depths of tens of meters in the clearest waters but only to tens of centimeters in high light absorbing and scattering waters.

We refer to Aas (1987) for a complete derivation of the analytical model for the irradiance reflectance over an optically deep water body. The reason for choosing this model is that it acts as a reference for understanding all other models of this kind found in the literature (Dekker et al., 2001). In terms of the backscattering and absorption coefficients, the Aas (1987) analytical model for irradiance reflectance can be written as

rd/xu bb

To specify the model in Eq. (1), four parameters are required, namely fxu, rd, and ru, where ru and rd are the shape factors for up and downward scattering, respectively (the average cosines for down-welling and upwelling light fxA, fxu are explained in Chapter 12). The shape factors describe the difference between the backward and upward scattered fraction of light and the forward and downward fractions of light. For vertically incident irradiance these are unity. Despite the approximations applied in this model (Aas, 1987), it may be expected to yield quite accurate results for turbid waters.

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