Remote sensing from satellite or airborne platforms of land or sea surfaces in the visible and near infrared is strongly affected by the presence of the atmosphere along the path from Sun to target (surface) to sensor. This paper presents 6S (Second Simulation of the Satellite Signal in the Solar Spectrum), a computer code which can accurately simulate the above problems. The 6S code is an improved version of 5S (Simulation of the Satellite Signal in the Solar Spectrum), developed by the Laboratoire d'Optique Atmospherique ten years ago. The new version now permits calculations of near-nadir (down-looking) aircraft observations, accounting for target elevation, non lambertian surface conditions, and new absorbing species (CH/sub 4/, N/sub 2/O, CO). The computational accuracy for Rayleigh and aerosol scattering effects has been improved by the use of state-of-the-art approximations and implementation of the successive order of scattering (SOS) algorithm. The step size (resolution) used for spectral integration has been improved to 2.5 nm. The goal of this paper is not to provide a complete description of the methods used as that information is detailed in the 6S manual, but rather to illustrate the impact of the improvements between 5S and 6S by examining some typical remote sensing situations. Nevertheless, the 6S code has still limitations. It cannot handle spherical atmosphere and as a result, it cannot be used for limb observations. In addition, the decoupling the authors are using for absorption and scattering effects does not allow to use the code in presence of strong absorption bands.

Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

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Vertex component analysis: a fast algorithm to unmix hyperspectral data

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.

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Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Rates and reactions of biogeochemical processes vary in space and time to produce both hot spots and hot moments of elemental cycling. We define biogeochemical hot spots as patches that show disproportionately high reaction rates relative to the surrounding matrix, whereas hot moments are defined as short periods of time that exhibit disproportionately high reaction rates relative to longer intervening time periods. As has been appreciated by ecologists for decades, hot spot and hot moment activity is often enhanced at terrestrial-aquatic interfaces. Using examples from the carbon (C) and nitrogen (N) cycles, we show that hot spots occur where hydrological flowpaths converge with substrates or other flowpaths containing complementary or missing reactants. Hot moments occur when episodic hydrological flowpaths reactivate and/or mobilize accumulated reactants. By focusing on the delivery of specific missing reactants via hydrologic flowpaths, we can forge a better mechanistic understanding of the factors that create hot spots and hot moments. Such a mechanistic understanding is necessary so that biogeochemical hot spots can be identified at broader spatiotemporal scales and factored into quantitative models. We specifically recommend that resource managers incorporate both natural and artificially created biogeochemical hot spots into their plans for water quality management. Finally, we emphasize the needs for further research to assess the potential importance of hot spot and hot moment phenomena in the cycling of different bioactive elements, improve our ability to predict their occurrence, assess their importance in landscape biogeochemistry, and evaluate their utility as tools for resource management.

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Biogeochemical Hot Spots and Hot Moments at the Interface of Terrestrial and Aquatic Ecosystems

Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Theory of Reflectance and Emittance Spectroscopy

The Opposition Effect (OE) is the non-linear increase in the intensity of light scattered from a surface as phase angle approaches 0 deg. It is seen in laboratory experiments and in remote sensing observations of planetary surfaces. Understanding the OE is a requirement to fitting photometric models which will produce meaningful results about regolith texture. Our previous laboratory studies are consistent with the hypothesis that the OE in particulate materials is due to two processes, Shadow Hiding (SHOE) and Coherent Backscattering (CBOE). SHOE arises because, as phase angle approaches zero, shadows cast by regolith grains on other grains become invisible to the observer. CBOE results from constructive interference between rays traveling the same path but in opposite directions. In this study we measured the angular scattering properties of 9 mixtures of Aluminum Oxide and Boron Carbide powders of the same particle diameter (25 microns). The reflectance of the materials ranged from 7% (pure B4C) to 91% (pure Al2O3). Along with the reflectance phase curve we measured the circular polarization ratio (CPR) - the ratio of the intensity of the light returned with the same helicity as the incident light to that with the opposite helicity. An increase in CPR with decreasing phase angle indicates increased multiple scattering and is consistent with CBOE (Hapke, 1993). Popular conceptions of CBOE (Belskaya et al, 2003) hold that materials of higher albedo would exhibit increased multiple scattering and that the contribution of CBOE to the OE would increase as albedo increases. Remarkably, we find the highest albedo samples did not have the strongest CBOE opposition peaks. Instead, the maximum CBOE contribution is observed in samples with reflectance between 15 and 40%.

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Planetary Regolith Microstructure: An Unexpected Opposition Effect Result

The reflectance spectra of individual meteorites of all classes are being measured in the vacuum ultraviolet (VUV) spectral wavelength region from 89 to 248 nm to evaluate the potential of VUV spectroscopy as a remote sensing method for planetary studies. In the present investigation, specimens of 15 group L chondrites, 13 group LL chondrites, 7 group E chondrites, and 18 achondrites were studied. Spectra were measured of both polished thin sections and powders of the meteorites, where both were available. Attention is given to measurements of mineral standards, shock effects, and meteorite data. It is concluded that the VUV spectra of meteorites should provide a useful basis for comparisons with spectra of asteroids and comet nuclei taken from spacecraft. VUV spectroscopy should make it possible to identify the major minerals present in a meteorite or asteroid.

Vacuum ultraviolet reflectance spectra of groups L, LL, and E chondrites and of achondrites

The nature of the scattering of light is thought to be well understood when the medium is made up of independent scatterers that are much larger than the wavelength of that light. This is not the case when the size of the scattering objects is similar to or smaller than the wavelength or the scatterers are not independent. In an attempt to examine the applicability of independent particle scattering models, to planetary regoliths, a dataset of experimental results were compared with theoretical predictions.

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Size-dependent Measurements of the Scattering Properties of Planetary Regolith Analogs: A Challenge to Theory

A Particle Size Dependence of the Opposition Effect

Introduction The opposition effect is a sharp surge observed in the reflected brightness of a particulate medium around zero phase angle. Its name derives from the fact that the phase angle is zero for solar-system objects at astronomical opposition when the Sun, the Earth, and the object are aligned. Depending on the material the angular width of the peak can range from about 1° to more than 20°. It has many names including the heiligenschein (literally “ holy glow ”), hot spot, bright shadow and backscatter peak . We have already encountered the opposition effect peak in Figures 8.12 and 8.18. and it is further illustrated in Figures 9.1–9.3. It should not be confused with the glory in the phase function of a sphere (Chapter 5), which is also often called the heiligenschein. The opposition effect is a nearly ubiquitous property of particulate media, including vegetation (Hapke et al ., 1996), laboratory powders (Hapke andVan Horn, 1963; Oetking, 1966; Egan and Hilgeman, 1976; Montgomery and Kohl, 1980; Nelson et al ., 1998, 2000), and regoliths of the Moon (Gehrels et al ., 1964; Whitaker, 1969; Wildey, 1978; Buratti et al ., 1996), Mars (Thorpe, 1978), asteroids (Gehrels et al ., 1964; Bowell and Lumme, 1979; Belskaya and Shevchenko, 2000), satellites of the outer planets (Brown and Cruikshank, 1983; Domingue et al ., 1991), and the rings of Saturn (French et al ., 2007). On a clear day you can see it as a glow around the shadow of your head when your shadow falls on grass or soil.

Bruce Hapke

Papers

Planetary Regolith Microstructure: An Unexpected Opposition Effect Result

Vacuum ultraviolet reflectance spectra of groups L, LL, and E chondrites and of achondrites

Size-dependent Measurements of the Scattering Properties of Planetary Regolith Analogs: A Challenge to Theory

A Particle Size Dependence of the Opposition Effect

The Opposition Effect