Gjerstad et al. (2003) undertook a study aimed at comparing two distinctly different methods of solving the radiative transfer equation for coupled atmosphere-ocean systems. One of these methods was the deterministic discrete-ordinate method (Stamnes et al., 1988; 2000), extended to apply to two adjacent slabs with different indices of refraction, such as a coupled atmosphere-ocean (CAO) system (Jin and Stamnes, 1994). The other method was the Monte Carlo (MC) approach, in which the trajectories of individual photons were simulated (Collins et al., 1972; Lenoble, 1985).
Mobley et al. (1993) compared underwater light fields computed by several different methods, including MC methods and the discrete-ordinate method, and showed that different methods give similar results for a limited set of test cases. However, the models included the atmosphere in different ways, which led to a spread in the downward irradiance of 18% just above the water surface and throughout the underwater column. Also, no comparisons of atmospheric irradiances were made. To remedy this shortcoming Gjerstad et al. (2003) performed a detailed quantitative comparison of irradiances simulated with a Monte Carlo method with those computed with a CAO-DISORT model (Jin and Stamnes, 1994; Thomas and Stamnes, 1999).
The CAO-MC and the CAO-DISORT models used by Gjerstad et al. (2003) had precisely the same physical basis, including coupling between the atmosphere and the ocean, and precisely the same atmospheric and ocean input parameters. Computed results for direct and diffuse upward and downward irradiances are shown in Fig. 9.4. The percentage deviation is less than 0.5% for downward irradiances, and less than 1% for upward irradiances. The CAO-MC code has an
advantage over the CAO-DISORT (Jin and Stamnes, 1994) code in that it can handle surface waves, but the CAO-DISORT code is computationally much faster. Finally, it should be noted that Jin et al. (2006) recently extended the CAO-DISORT code to include the effects of surface waves.
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