As we saw in our discussion of radiation transfer theory (§1.7), certain quasi-inherent optical properties of the medium - the diffuse scattering coefficients - play an essential role in our understanding of the underwater light field. These scattering coefficients have been defined previously (§1.5) in terms of the light scattered backwards or forwards by a thin layer of medium from an incident light field that is not a parallel beam at right angles (as in the case of the normal scattering coefficients) but has a radiance distribution identical to the downwelling or upwelling parts of a given underwater light field existing at a certain depth in a certain water body. There is no way at present of directly measuring the diffuse scattering coefficients. If, however, the radiance distribution at a given depth in the water body and the volume scattering function for the water are known, then it is possible to calculate the diffuse scattering coefficients.700
To calculate, for example, the backscattering coefficient for downwel-ling flux, the downwelling radiance distribution is distributed into a manageable number, e.g. 15, of angular intervals. Using the volume scattering function, the proportion of the incident flux in each angular interval that is scattered in an upwards or a downwards direction by a thin layer of medium is calculated. The summed flux (for all incident angles) travelling upwards after scattering, expressed as a proportion of the total downwelling flux, divided by the thickness of the layer of medium, is bbd (z), the diffuse backscattering coefficient for downwelling flux at depth z m in that particular water body: bbd (z) is commonly two- to five-fold greater than bb in natural water bodies.700 The radiance distribution data necessary for such calculations may be obtained by direct measurement (§5.1), or derived from the inherent optical properties by computer modelling (§5.2).
An approximate estimate of the diffuse backscattering coefficient can be obtained much more simply from underwater irradiance measurements. Rearranging eqn 1.51 we obtain where zm is the depth at which downward irradiance is 10% of the subsurface value. R(zm) and K(zm) are obtained from the irradiance data, and bbd(zm) is calculated accordingly.
From the value of the diffuse backscattering coefficient derived in this way we canthengoontoobtainanestimateofthe normal backscatteringandtotal scattering coefficients, bb and b. Kirk (1989a) presents a Monte Carlo-derived curve, for optical water types covering the range b/a = 0.5-30, showing the ratio of diffuse to normal backscattering coefficient plotted against reflectance at depth zm. From the observed value of reflectance, the ratio bbd(zm)/bb is read off, and is then used, in conjunction with eqn 4.8 to give bb. Assuming b ~ 53bb (a reasonable estimate for most inland and coastal waters), the total scattering coefficient may then be obtained. Values of b calculated in this way are in good agreement with those obtained from irradiance data by the other indirect procedure, described in the previous section.
bbd (z)=R(z)[Kd (z) + K(z)] which with help of eqn 1.52 can be rewritten bbd(z) « 3.5R(zm)Kd(zm)
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