辐射传输中的一个伪极限问题及其数学物理原理

A false limit in atmospheric radiative transfer and the physics behind it

当太阳入射角度和观测角都趋向于水平时,由平面平行大气辐射传输方程计算得到的大气顶的反射辐射值不唯一,其值依赖于太阳和观测角的趋近于水平方向的路径曲线,即从数学角度称为出现极限的不唯一或极限不连续.事实上这违背了辐射场物理原理,这种不连续是由于常规算法中忽略了大气辐射传输中一个隐含的物理原理而导出的.在极限条件下必须引入满足Snell光学定律的界面边界条件,否则会导致错误的结论.

When both the solar and view zenith direction approach horizontal, the reflected radiance at the top of the atmosphere, derived from the plain-parallel atmospheric radiative transfer equation, is different and it depends on the path how the incidence and reflected directions tend to be horizontal. This phenomenon under extreme condition is called limit discontinuity in mathematics. However, the discontinuity of the limits is contradictory to the physical nature of atmospheric radiative transfer and it is obtained by neglecting an implicit physics principles, the Snell＇s law. The Snell＇s law must be used in the radiative transfer algorithm for radiance under this extreme condition to avoid obtaining wrong results.