## Angular structure

The shape of the volume scattering function, as defined by ¡(6), the normalized volume scattering function (§1.4), can have a major influence on the character of the light field. In the majority of natural waters, however, scattering is particle dominated to such an extent that ¡3(6) curves are rather similar in shape from one water to another. To begin with, therefore, we shall not consider the effects of variation in ¡¡(6), and shall assume that the waters under consideration have a typical particle-dominated volume scattering function, similar to that measured by Petzold in San Diego harbour (Fig. 4.9).

To give the conclusions as much generality as possible, our analysis will be in terms of optical depth (Z = Kdz) rather than actual depth. This makes it permissible to confine our attention to the ratio of scattering to absorption coefficients, b/a, rather than to their absolute values. A convenient optical depth at which to study the effects of changes in b/a is zm, the mid-point of the euphotic zone (Z = 2.3). Figure 6.16 shows the total and downward average cosines, and reflectance at zm as a function of b/a, determined by Monte Carlo calculation.702 As scattering increases relative to absorption, so the underwater light field at this depth becomes less vertical, more diffuse, as shown by the decrease in ft and ftd. Reflectance increases almost linearly with b/a over much of the range, but the curve as a whole has a slightly sigmoid character. If the zenith angle of the incident light is changed from 0 to 45°, it makes very little difference to the reflectance, and not much to the average cosine except at low values of b/a.

In addition to delineating the quantitative dependence of the angular structure of the light field on b/a, Fig. 6.16 illustrates a useful general conclusion. Namely, that for water with a given ¡(6), the relations between ft,ftd, ftu, R at a specified optical depth, and b/a, are fixed at any given angle of incident light, and indeed are largely independent of

Fig. 6.16 Average cosines and irradiance reflectance at mid-point (zm) of euphotic zone as a function of b/a. Data obtained by Monte Carlo calculation.702 (Vertically incident light_Light incident at 45° )

Fig. 6.16 Average cosines and irradiance reflectance at mid-point (zm) of euphotic zone as a function of b/a. Data obtained by Monte Carlo calculation.702 (Vertically incident light_Light incident at 45° )

the angle of incident light. The fixed nature of the relation between ft, R and b/a provides the basis for a method of estimating the absolute values of both b and a for any real water body, using only measurements of underwater irradiance (see §4.2).

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