For a remote sensing pixel with 3D surface

the directionality of thermal emission depends on the component parameters of the pixel

such as component temperatures

component emissivities and structural parameters. The contribution of the multiple scattering between components to the directional thermal emission is mainly affected by the 3D structure of pixel. In this paper

we present an analytical model to describe the multiple scattering between components and its contribution to the pixel’s emission. The modeling work is based on the conceptual geometric-optical thermal emission model. For the non-isothermal pixel with random distributed components

at the pixel’s scale

the openness coefficient and viewing factor is defined

the effect of multiple scattering between components is modeled with the principle of multiple bouncing. Then the directional thermal emission of pixel is derived based on the areal weighted emission of components by taking the ambient radiation into account. The model is validated using measurement data indoor. The two experimental data sets are on different observing object （samples of pingpong spheres and simulated trees made of cotton）. Each set of measurement data includes directional thermal emission of pixel

the emission of components

the ambient thermal radiance

and the structural parameters of the pixel. These measured data of components are as input of the model

the brightness temperature of the pixel is calculated. The model predicted brightness temperatures and their comparison with the measured brightness temperature in pixel scale are presented in the paper. The directionality of the effect of multiple scattering is also discussed. The result demonstrates that in pixel scale the analytical model prediction fits the measurement well. Note that in the multiple scattering effect model

when the samples on the background are very close to each other and the viewing facrot VF 2-2can not be ignored

our modeling methodology can still apply. But the results formula will then be very complicated. In such case

a two layer multiple bouncing model would be more appropriate.