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

An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.

Bidirectional reflectance spectroscopy: 1. Theory

Bidirectional reflectance spectroscopy 3. Correction for macroscopic roughness

The variety of evidence bearing on the nature of space weathering is reviewed. The effects of space weathering include spectral darkening, reddening and subdued absorption bands, and the distinctive magnetic electron spin resonance caused by single-domain metallic iron particles. Ever since the Apollo missions, two paradigms have dominated the thinking of the planetary science community concerning space weathering: (1) the optical effects are caused by impact-vitrified glass in agglutinates, and (2) the submicroscopic metallic iron results from the reduction of ferrous iron by the impact melting of minerals whose surfaces have been saturated with hydrogen from the solar wind. However, studies carried out since the Apollo program showed that both of these paradigms are invalid. A hypothesis first suggested by the author and his colleagues 26 years ago, but not generally accepted at that time, now appears to be essentially correct: Both the optical and magnetic effects are caused by metallic iron particles smaller than the wavelength in ubiquitous vapor-deposited coatings on soil particle surfaces and inside agglutinates. The vapor is generated by both solar wind sputtering and micrometeorite impact vaporization and injected preferentially downward into the porous regolith. The iron is reduced by a physical process, the selective loss of oxygen that occurs during deposition of the vapor, and does not require heating, melting, or a reducing environment. A mathematical theory that describes the optical effects of the submicroscopic iron quantitatively is derived and applied to the regoliths of the Moon, Mercury and an S asteroid.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JE001338

Bruce Hapke

Papers

Theory of Reflectance and Emittance Spectroscopy

Bidirectional reflectance spectroscopy: 1. Theory

Bidirectional reflectance spectroscopy 3. Correction for macroscopic roughness

Space weathering from Mercury to the asteroid belt

Bidirectional reflectance spectroscopy. IV - The extinction coefficient and the opposition effect