Remote sensing hyperspectral and more generally spectral instruments are common tools to decipher surface features in Earth and Planetary science. While linear mixture is the most common approximation for compounds detection (mineral, water, ice, etc...), the transfer of light in surface and atmospheric medium are highly non-linear. The exact simulation of non-linearities can be estimated at very high numerical cost. Here I propose a very simple non-linear form (that includes the regular linear area mixture) of radiative transfer to approximate surface spectral feature. I demonstrate that this analytical form is able to approximate the grain size and intimate mixture dependence of surface features. In addition, the same analytical form can approximate the effect of Martian mineral aerosols. Unfortunately, Earth aerosols are more complex (water droplet, water ice, soot,...) and are not expected to follow the same trend.

翻译：遥感高光谱及更广泛的光谱仪器是解读地球与行星科学中地表特征的常用工具。尽管线性混合是化合物检测（矿物、水、冰等）中最常见的近似方法，但光在地表与大气介质中的传输过程具有高度非线性特性。精确模拟非线性效应需要极高的数值计算成本。本文提出一种包含常规线性区域混合的极简非线性辐射传输形式，用以近似地表光谱特征。论证表明，该解析形式能够近似表征颗粒尺寸与紧密混合依赖性对地表特征的影响。同时，同一解析形式可近似模拟火星矿物气溶胶的效应。遗憾的是，地球气溶胶（如液滴、水冰、黑碳等）更为复杂，预计不遵循相同规律。