In eqn 7.23, for each pixel, pw(1,d0,dv, f) is what is measured, and nt(&0,1)<(0') can be calculated. As we saw in Chapter 6, however, the f/Q ratio, although it is commonly in the region of 0.08 to 0.09, is a function of solar altitude, solar azimuth and satellite viewing angle, and also varies with the optical character of the water, e.g. colour dominated versus turbidity dominated.824 We saw earlier (§6.4, eqn 6.4) that f (indicated by C[m0]) can be expressed in terms of the cosine of the refracted solar beam (m0), and a coefficient (M) determined by the shape of the scattering phase function. For clear ocean water, Q can be calculated from solar elevation using eqn 6.13 or 6.14. Thus at least an approximate estimate of f/Q can be arrived at.
Morel and Gentili (1996) have developed a much more detailed procedure, which uses precomputed lookup tables to provide values of the f/Q ratio in all the necessary conditions. To get the process underway, an approximate initial estimate of the chlorophyll content of the rs water is required. It is assumed to begin with that for each of two wavebands (443 and 555 nm), f/Q is the same for all pixels in the scene, and appropriate average values from the literature are assigned. From eqn 7.23 (in fact from the equivalent expression for Lw) the (bb/a) values at the two wavelengths are obtained from the remotely sensed Lw(4) values, and in turn these are used to provide the so-called blue-to-green ratio
In Case 1 ocean waters, the blue-to-green ratio is mainly determined by the level of phytoplankton. Approximate relationships between the ratio of (bb/a)4 values at selected pairs of wavelengths and the chlorophyll concentration can be derived empirically (see below). Morel and Gentili use such a relationship - a polynomial expressing ln p443 555 as a function of ln [Chl] - to arrive at the first estimate of chlorophyll concentration, Chl;, on the basis of the blue-to-green ratio determined as above. With this value of [Chl], appropriate f/Q values, using 00, 0', f, and [Chl] as inputs, are obtained from the precomputed lookup table. With the second set of f/Q data, a second set of (bb/a) values is obtained from remotely sensed Lw at 443 and 555 nm, and for each pixel a new chlorophyll concentration, Chl2. This is in turn entered into the lookup table, and the iteration is continued in this way until acceptable accuracy is achieved.
Once realistic values for the various terms in eqn 7.23 have been arrived at, then bb/a, the ratio of the backscattering coefficient to the absorption coefficient, can be estimated from the remotely sensed pw(4). If, on the basis of other information, a plausible value could be selected for bb, then an approximate value for a could be obtained. In the far-red/ near-infrared region, absorption is normally almost entirely attributable to water itself, and a is known, and so for waters turbid enough to exhibit significant water-leaving radiance in this highly absorbing spectral region, bb can be estimated. If measurements are made at three wavelengths, and reasonable assumptions are made about the manner in which bb and the values of a for the different absorbing components (water, phytoplank-ton, non-living colour) vary with wavelength, then the actual concentrations of phytoplankton and non-living pigmented material can be estimated: the theoretical basis for such calculations is given by Morel (1980).
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