Validation and comparison of two models based on the Mie theory to predict 8–14 µm emissivity spectra of mineral surfaces

Abstract

Remote sensing is a powerful tool for studying the planetary regolith surfaces through emission in the thermal infrared region (TIR, 8–14 µm). Theoretical emissivity models are needed to interpret the measured data and eventually to get surface characteristics (such as the refraction index) through model inversion. A new era of orbiting satellites carrying Hyperspectral TIR sensors is coming, and the necessity of understanding the thermal emission of Earth and other planet surfaces at all wavelengths of the electromagnetic spectrum is of prime interest. In this paper we review most of the existing analytical models for predicting the emissivity spectra of minerals for different viewing angles, which are based on the Mie theory, and validated and compared two of them: the Hapke model with two compactness correction methods not tested yet and a model based on the δ‐Eddington approximation, which has not been validated for mineral surfaces. The validation was performed using measurements over two samples rich in quartz and gypsum, respectively. The Hapke model showed the best results when compared with the Warren‐Wiscombe‐Dozier (WWD) model with respect to measured data, showing a RMSE of ±0.04 in emissivity for particle diameter size of a quartz sample greater than 75 µm. This model also showed improvements with regard to results of past published works, after applying to Mie solutions the compactness correction proposed for the WWD model. These results were confirmed for a gypsum sample, a mineral different to the widely used quartz. Finally, the results showed the deficiencies of both models in simulating mineral emissivity around 8.7 µm, probably due to the underestimation of multiple scattering for large values of the imaginary part of the refractive index.

A Framework for Estimating the 30 m Thermal‐Infrared Broadband Emissivity From Landsat Surface Reflectance Data

“…Fine sand usually covers the surface of the field but can be removed or destroyed during sampling and when transferring the sample from the field to the laboratory. According to previous studies (Cheng et al, ; Garcia‐Santos et al, ), fine sand has a higher emissivity than coarse sand. The measured emissivity in the laboratory may be lower than that in the field without changing its physical state.…”

“…For example, the error that is introduced by ignoring the emissivity directionality when estimating the surface longwave net radiation can reach 17.48 and 14.05 W/m 2 for water and bare ice, respectively, if the sensor scan angle is within ±55° [12]. Unfortunately, the modeling ability of current radiative transfer or analytical models is relatively weak, and these models cannot accurately reproduce the observed directional emissivity of semiinfinite media (Cheng et al, ; Garcia‐Santos et al, ). Therefore, we chose to retrieve directional BBE for bare soils and hemispherical BBE for vegetated surfaces at current stage.…”

Evaluation of Six Directional Canopy Emissivity Models in the Thermal Infrared Using Emissivity Measurements

“…A number of previous works have analyzed the dependence of soil emissivity on viewing angle [8][9][10] and soil moisture [11][12][13] from an empirical perspective. Different theoretical models based on the Mie theory have been proposed to predict the emissivity of these kind of surfaces considering the refraction index, the size particle distribution, etc., [14,15] that have been recently compared with laboratory data [16,17].…”