Approximation of radiative transfer for surface spectral features

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