. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography Fig. 1. R,IR„ for layers of optical thickness t. The parameter neit to each curve is w0. T90 is the value of t for which R r/R . = Zw{li')K(0,-) - (1 + m). (2) Direct substitution into Eq. (2) shows that 2 9o(m')^(0,—) is almost independent of n', and in fact zt0(n'MO,-) be 1. (3) The near independence of 290(m') and n' suggests an alternate definition of the penetration depth that is independent of m'- This is KJR. , where R2 is the d
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography Fig. 1. R,IR„ for layers of optical thickness t. The parameter neit to each curve is w0. T90 is the value of t for which R r/R . = Zw{li')K(0,-) - (1 + m). (2) Direct substitution into Eq. (2) shows that 2 9o(m')^(0,—) is almost independent of n', and in fact zt0(n'MO,-) be 1. (3) The near independence of 290(m') and n' suggests an alternate definition of the penetration depth that is independent of m'- This is KJR. , where R2 is the diffuse reflectance of the ocean due to a surface layer of thickness z and is given by for an axisymmetric incident radiance distribution. It is clear that in the quasi-single-scattering approxi- mation, z90tf(0-) (3') Comparison of Eq. (3') with Exact Calculations In studying the influence of a reflecting bottom on the diffuse reflectance of the ocean, Gordon and Brown5 have computed RT (where r = cz is the opti- cal depth) using Monte Carlo techniques as a func- tion of t for the three scattering phase functions given in Ref. 3. They have also computed6 K(t,—)/c for the same phase functions, so it is possible to com- pare Eq. (3') with the results of their exact calcula- tions. To effect such a comparison, t90 is first determined by plotting Rr/R«, against r for each phase function and various values of u.'0. An example of this for phase function fi:! is shown in Fig. 1. twi can be read directly from the curves for each value of (, from Fig. 1 T90 s 1 for u.'o = ). Then since r;H) = cz 90, M .9 .9 o o> rsi r o" * .9 " PHASE B (diffuse) .2 .4 .5 .6 .8 Fig. 2. Comparison of K{0,—)zgo w'th unity as a function of wo for the three phase functions for the case of collimated incident ir- radiance from the zenith and for perfectly diffuse incident irra- diance [phase B (diffuse)j. TjjflO -)/c] = 290/rt0,-) is formed and compare
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