Forward modeling of linear mixing in thermal IR ground leaving radiance spectra

Hyperspectral thermal IR remote sensing is an effective tool for the detection and identification of gas plumes and solid materials. Virtually all remotely sensed thermal IR pixels are mixtures of different materials or temperatures. As sensors improve and hyperspectral thermal IR remote sensing becomes more quantitative, the concept of homogeneous pixels becomes inadequate. The contributions of the constituents to the pixel spectral ground leaving radiance are weighted by their spectral emissivity as well as their temperature, or more correctly, temperature distributions, because real pixels are rarely thermally homogeneous. Planck's Law defines a relationship between temperature and radiance that is strongly wavelength dependent, even for blackbodies. Spectral ground leaving radiance (GLR) from mixed pixels is temperature and wavelength dependent and the relationship between observed radiance spectra from mixed pixels and library emissivity spectra of mixtures of 'pure' materials is indirect. This paper presents results from a simple model of linear mixing of pixel spectral GLR. A pixel consists of one or more materials each with a temperature distribution and an emissivity spectrum. Temperature distributions consistent with high resolution thermal images are used as inputs to the model. The impact of spatial-temporal fluctuation of skin temperature on skin temperature variability will be discussed. The results show the strong sensitivity of spectral GLR at shorter wavelengths to temperature and significant variation of radiance mixture proportions with wavelength in the mid-infrared (3-5 μm). Spectral GLR of mixtures in the 8-12 μm domain are more modestly impacted but the impact of subpixel mixing and variability is still significant. A demonstration of the effects of linear mixing on linear un-mixing is also presented.