By the end of this century the Earth Observing System (EOS) will provide worldwide, thermal infrared, multispectral images of the Earth, presenting geologists with a new kind of remote sensing data for interpretation. Thus it has become essential to understand the spectral emittance behavior of terrestrial surface materials. Perhaps the most fundamental question to be answereed is the extent to which such materials follow Kirchhoff's law (epsilon = 1 -R) under laboratory and field conditions, especially when a sample displays a thermal gradient. We present the first rigorous quantitative comparison of directional and hemispherical reflectance and directional emittance of rock and soil samples in the laboratory, with thermal gradients induced by heating them from below and allowing them to radiate to a colder background. The results show that only an extemeley low density sample composed of fine particles sifted into a 'fairy castle' structure displays a thermal gradient steep enough within the infrared skin depth to cause significant (6%) departure from Kirchhoff's law. There is no detectable effect on the more normal terrestrial samples, such as soils and rocks measured in the laboratory, even when semitransparent coatings are involved. Thus both emittance and reflectance measurements can be used to calculate sample emissivity for most terrestrial surface materieals. However, the effect on Kirchhoffian behavior of different field environments, which may induce a steeper thermal gradient in particulate samples, has yet to be determined, and some low-density surface materials like newly fallen snow, frost, and efflorescent salts on playas have yet to be measured in emittance.

Thermal‐infrared remote sensing and Kirchhoff's law: 1. Laboratory measurements

Surface emissivity is a critical parameter for studying city-, meso-, and micro-scale climate and energy balance. The emissivity of complex surfaces e.g. a forest or an urban canopy is an effective surface property since it depends on both surface materials and geometry. This study presents a novel methodology for estimating effective emissivity using sky view factor retrieved from airborne Lidar data, building GIS data, and land use and land cover classification data. First, a high correlation between the effective emissivity retrieved from ASTER TIR bands 10–14 and the sky view factor was observed (r2 = 0.93, 0.99, 0.99, 0.97, 0.97). When the sky view factor decreases, the effective emissivity tends to increase, which is mainly due to multiple scattering (cavity effect), thus increases the effective emissivity. A simplified model which assumes that reflection and scattering only occurs within a single pixel was developed. Results showed that the correlations between the modeled and the spectral (band) emissivity retrieved from the ASTER multispectral TIR data (five spectral bands) are high (r2 = 0.93, 0.99, 0.98, 0.93, 0.97), and with low RMSE (0.019, 0.016, 0.012, 0.003 and 0.004 from band 10–14 respectively). The emissivity derived from this simplified model, however, tends to be overestimated in band 10–12. Thus, a refined urban emissivity model based on sky view factor (UEM-SVF) which considers the scattering and reflection from adjacent pixels was developed in this study. Results show a good agreement with ASTER spectral (band) emissivity: r2 = 0.90, 0.98, 0.96, 0.94 and 0.96, and very low RMSE (0.006, 0.003, 0.004, 0.002 and 0.004). This study illustrates that the UEM-SVF can be useful for estimation of land surface emissivity of complex surfaces, and can further be used for accurate land surface temperature retrieval.

Modeling the effective emissivity of the urban canopy using sky view factor

Contrary to common belief, neither reciprocity of the bidirectional
reflectance distribution function (BRDF) nor the directional form
of Kirchhoff’s electromagnetic radiation law can be demonstrated on
the basis of energy conservation. The BRDF is generally considered
reciprocal as an extension of Helmholtz reciprocity, but Helmholtz
reciprocity does not always hold. We describe the flaw in a
thermodynamic demonstration of reciprocity that uses an enclosure
calculation. Some conclusions can be drawn from the enclosure
calculation, but reciprocity requires more restrictive
conditions. We conclude that, although they can be violated,
reciprocity and the directional form of Kirchhoff’s law generally hold
because of the quantum-mechanical principle of time-reversal
invariance, which applies to most materials.

Thermodynamic constraints on reflectance reciprocity and Kirchhoff’s law

Extension of emission-transmission technique to particulate samples using FT-IR

Since the days of Kirchhoff, blackbody radiation has been considered to be a universal process, independent of the nature and shape of the emitter. Nonetheless, in promoting this concept, Kirchhoff did require, at the minimum, thermal equilibrium with an enclosure. Recently, the author stated (P.-M. Robitaille, IEEE Trans. Plasma Sci., 2003, v. 31(6), 1263–1267; P.-M. Robitaille, Progr. in Phys., 2006, v. 2, 22–23), that blackbody radiation is not universal and has called for a return to Stewart’s law (P.-M. Robitaille, Progr. in Phys., 2008, v. 3, 30–35). In this work, a historical analysis of thermal radiation is presented. It is demonstrated that soot, or lampblack, was the standard for blackbody experiments throughout the 1800s. Furthermore, graphite and carbon black continue to play a central role in the construction of blackbody cavities. The advent of universality is reviewed through the writings of Pierre Prevost, Pierre Louis Dulong, Alexis Therese Petit, Jean Baptiste Joseph Fourier, Simeon Denis Poisson, Frederick Herve de la Provostaye, Paul Quentin Desain, Balfour Stewart, Gustav Robert Kirchhoff, and Max Karl Ernst Ludwig Planck. These writings illustrate that blackbody radiation, as experimentally produced in cavities and as discussed theoretically, has remained dependent on thermal equilibrium with at least the smallest carbon particle. Finally, Planck’s treatment of Kirchhoff’s law is examined in detail and the shortcomings of his derivation are outlined. It is shown once again, that universality does not exist. Only Stewart’s law of thermal emission, not Kirchhoff’s, is fully valid.

Blackbody Radiation and the Carbon Particle

Publisher Summary Kirchhoff's law of heat radiation states that the emissivity of radiating bodies is equal to their absorptivity. Kirchhoff's law seems to remain valid in the case of nonequilibrium if induced emission is considered as negative absorption as was first shown for freely radiating weakly absorbing bodies. Absorptivity is redefined as induced absorption minus induced emission, whereas emissivity is understood as being due to spontaneous emission only. In addition, from studying the original concepts of Kirchhoff, it can be inferred that the quantities compared in Kirchhoff's law are the spontaneous emission and the net absorption. The emissivity is exclusively due to spontaneous emission and is consequently independent of the environmental radiation field. Therefore, one expects Kirchhoff's law to hold as well for freely radiating bodies, provided that the distribution of the material states of the sample is the equilibrium distribution.

H.P. Baltes

Papers

I On the Validity of Kirchhoff'S Law of Heat Radiation for a Body in a Nonequilibrium Environment*