Gordon H R, Ding K, Gong W
Appl Opt. 1993 Mar 20;32(9):1606-19. doi: 10.1364/AO.32.001606.
The asymptotic daylight field in a homogeneous ocean is, like the absorption (a), scattering (b), and attenuation (c) coefficients and the volume scattering function (VSF), an inherent optical property (IOP) of the medium. A simple relationship in the spirit of the van de Hulst similarity relationships is developed from which the diffuse attenuation coefficient K(infinity) of the asymptotic light field can be obtained from a, b, and the VSF with an error of < 2%. In this relationship, the shape of the VSF is characterized by its asymmetry parameter g, whereas omega(0) = b/c characterizes the other IOP's. The relationship applies approximately to other quantities as well, particularly tau(x), which is the optical depth at which the downwelling irradiance attenuation coefficient K(d) can be replaced by K(infinity) with an error no greater than x%. Computations of tau(5) and tau(10) are presented as a function of g, omega(0) and the incident light field, and it is shown that for overcast conditions K(d) can be within 5% of K(infinity) at depths at which the downwelling irradiance is greater than 50% of its value at the surface. Simulations of radiative transfer in verticall inhomogeneous waters reveal that for sufficiently large depth (z), the value of K(infinity)(z) determined from the asymptotic theory that uses the values of the IOP's at z is a good approximation to K(d)(z). Thus our results suggest that in addition to being a pedagogically interesting concept, the asymptotic theory may actually be useful in ocean optics research. The influence of inelastic processes (fluorescence and Raman scattering) on K(infinity) are briefly examined, and it is shown that for an ocean of pure sea water, i.e., no particles or fluorescent compounds, K(infinity)(lambda) approximately 0.02 m(-1) for lambda >/= 430 nm with little spectral variation.
在均匀海洋中，渐近日光场与吸收系数（a）、散射系数（b）、衰减系数（c）以及体积散射函数（VSF）一样，都是该介质的固有光学特性（IOP）。基于范德胡尔斯相似关系的精神，推导出了一个简单的关系式，利用该式可从a、b和VSF得出渐近光场的漫衰减系数K(∞)，误差小于2%。在这个关系式中，VSF的形状由其不对称参数g表征，而ω(0) = b/c表征其他固有光学特性。该关系式对其他量也大致适用，特别是τ(x)，它是下行辐照度衰减系数K(d)可以被K(∞)替代且误差不大于x%时的光学深度。给出了τ(5)和τ(10)作为g、ω(0)和入射光场函数的计算结果，结果表明，在阴天条件下，当下行辐照度大于其表面值的50%时，K(d)在深度处的值可以在K(∞)的5%以内。垂直非均匀水体中辐射传输的模拟结果表明，对于足够大的深度（z），根据使用z处固有光学特性值的渐近理论确定的K(∞)(z)值是K(d)(z)的良好近似。因此，我们的结果表明，渐近理论除了是一个在教学上有趣的概念外，实际上在海洋光学研究中可能也是有用的。简要研究了非弹性过程（荧光和拉曼散射）对K(∞)的影响，结果表明，对于纯海水海洋，即没有颗粒或荧光化合物的海洋，当λ≥430 nm时，K(∞)(λ)约为0.02 m⁻¹，光谱变化很小。
