Sathyendranath S, Platt T
Appl Opt. 1997 Apr 20;36(12):2620-9. doi: 10.1364/ao.36.002620.
Ocean color is determined by spectral variations in reflectance at the sea surface. In the analytic model presented here, reflectance at the sea surface is estimated with the quasi-single-scattering approximation that ignores transspectral processes. The analytic solutions we obtained are valid for a vertically homogeneous water column. The solution provides a theoretical expression for the dimensionless, quasi-stable parameter (r), with a value of ~0.33, that appears in many models in which reflectance at the sea surface is expressed as a function of absorption coefficient (a) and backscattering coefficient (b(b)). In the solution this parameter is represented as a function of the mean cosines for downwelling and upwelling irradiances and as the ratio of the upward-scattering coefficient to the backscattering coefficient. Implementation of the model is discussed for two cases: (1) that in which molecular scattering is the main source of upwelling light, and (2) that in which particle scattering is responsible for all the upwelled light. Computations for the two cases are compared with Monte Carlo simulations, which accounts for processes not considered in the analytic model (multiple scattering, and consequent depth-dependent changes in apparent optical properties). The Monte Carlo models show variations in reflectance with the zenith angle of the incident light. The analytic model can be used to reproduce these variations fairly well for the case of molecular scattering. For the particle-scattering case also, the analytic and Monte Carlo models show similar variations in r with zenith angle. However, the analytic model (as implemented here) appears to underestimate r when the value of the backscattering coefficient b(b) increases relative to the absorption coefficient a. The errors also vary with the zenith angle of the incident light field, with the maximum underestimate being approximately 0.06 (equivalent to relative errors from 12 to 17%) for the range of b(b)/a studied here. One implication of this result is that the model could also be used to obtain approximate solutions for the Q factor, defined for a given look angle as the ratio of the upwelling irradiance at the surface to the upwelling radiance at the surface at that angle. This is a quantity that is important in remote-sensing applications of ocean-color models. An advantage of the model discussed here is that its implementation requires inputs that are in principle accessible only in a remote-sensing context.
海洋颜色由海面反射率的光谱变化决定。在此处提出的分析模型中，海面反射率采用忽略跨光谱过程的准单次散射近似进行估算。我们获得的解析解对于垂直均匀的水柱是有效的。该解为无量纲的准稳定参数（r）提供了一个理论表达式，其值约为0.33，该参数出现在许多将海面反射率表示为吸收系数（a）和后向散射系数（b(b)）函数的模型中。在该解中，此参数表示为下行辐照度和上行辐照度的平均余弦的函数，以及上行散射系数与后向散射系数的比值。针对两种情况讨论了该模型的实现：（1）分子散射是上行光的主要来源的情况，以及（2）粒子散射是所有上行光的原因的情况。将这两种情况的计算结果与蒙特卡罗模拟进行了比较，蒙特卡罗模拟考虑了分析模型中未考虑的过程（多次散射以及由此导致的表观光学性质随深度的变化）。蒙特卡罗模型显示反射率随入射光天顶角的变化。对于分子散射情况，分析模型可用于较好地再现这些变化。对于粒子散射情况，分析模型和蒙特卡罗模型也显示r随天顶角有类似变化。然而，当后向散射系数b(b)相对于吸收系数a的值增加时，分析模型（如此处实现的）似乎低估了r。误差也随入射光场的天顶角变化，在此处研究的b(b)/a范围内，最大低估约为0.06（相当于12%至17%的相对误差）。该结果的一个含义是，该模型还可用于获得Q因子的近似解，Q因子针对给定视角定义为该角度下海面的上行辐照度与上行辐射率之比。这是海洋颜色模型遥感应用中的一个重要量。此处讨论的模型的一个优点是其实现所需的输入原则上仅在遥感背景下才可获取。
