Thermal emission from particulate surfaces : a comparison of scattering models with measured spectra

Emissivity spectra of particulate mineral samples are highly dependent on particle size when that size is comparable to the wavelength of light emitted (5–50 μm for the midinfrared). Proper geologic interpretation of data from planetary infrared spectrometers will require that these particle size effects be well understood. To address this issue, samples of quartz powders were produced with narrow, well-characterized particle size distributions. Mean particle diameters in these samples ranged from 15 to 277 μm. Emission spectra of these powders allow the first detailed comparison of the complex spectral variations with particle size observed in laboratory data with the predictions of radiative transfer models. Four such models are considered here. Hapke's reflectance theory (converted to emissivity via Kirchhoff's law) is the first model tested. Hapke's more recently published emission theory is also employed. Both Hapke theories were originally formulated for surfaces composed of closely packed particles, which unlike the situation of interest in this work, are large compared to the wavelength. For this case the particle extinction efficiency approaches unity, and thus diffraction effects become unimportant. The third model, referred to as the “Mie/Conel” model, is a model resurrected from earlier work by others. It uses Mie single scattering with a two-stream approximation for multiple scattering. This model, like the first, is a converted reflectance model. Mie scattering assumes particles are both spherical and well separated, which is not true for the quartz powders, but includes diffraction effects. The fourth model uses the Mie solution for single scattering by spheres and inputs those results into the multiple scattering formalism of Hapke's emission theory. The results of the four models are considered in relation to the values of the optical constants n and k. We have grouped these as class 1 (k large), class 2 (k moderate, n ∼ 2), class 3 (k small, n ∼ 2), and class 4 (k small, n ∼ 1). In general, the Mie/Hapke hybrid model does best at predicting variations with grain size. In particular, it predicts changes of the correct pattern, although incorrect magnitude, for class 1 bands, where large increases in emissivity with decreasing grain size are observed. This model also does an excellent job on moderate (class 2) and very weak and intraband (class 3) regions, and correctly predicts the emission maximum and its invariance with grain size near the Christiansen frequency (class 4). The Mie/Hapke hybrid model also has the fewest free parameters of the four models examined, while maintaining the most physical treatment of the radiative transfer. The two unmodified Hapke models fail to predict any spectral variation in strong bands, predict a significant decrease in emissivity with grain size near the Christiansen frequency, and overpredict the variations in moderate bands. The Mie/Conel model performs as well as the Mie/Hapke hybrid model in strong bands (class 1) but does not accurately model the behavior of moderate (class 2) and very weak (class 3) bands.