Optimal interpretation of remote sensing imagery requires characterizing the atmospheric composition between a sensor and the area it is observing. Timely estimates of atmospheric temperature, water vapor, and other constituents from the ground to the edge of the space environment are not always readily available. In those cases, we must supplement our knowledge of the atmosphere's composition to fill in any gaps in knowledge and empirical models of the atmosphere are useful tools for this purpose. The Standardized Atmosphere Generator (SAG) was constructed is one such empirical. It has been designed to allow all the major known, systematic variability in the atmosphere and may be used to generate atmospheric profile from the ground to 300 km consistent with user-specified temporal, geophysical, and geographical information Output provides reasonable estimates for temperature, pressure, and densities of atmospheric constituents and can be directly incorporated into radiative transfer forward models or retrieval algorithms. SAG draws upon a number of existing empirical atmospheric models and ensures consistency of output between them. It can be used either as a stand-alone interactive program or scripted for batch execution and assist in determining atmospheric attenuation, refraction, scattering, chemical kinetic temperature profiles, and a host of other naturally occurring processes. Here, we will discuss the capabilities and performance of the SAG model for a variety of applications including its interactive and batch processing use. We will also demonstrate the physical realism of SAG through a small number of relevant use cases.

In this paper, we present examples of aerosol and Cirrus cloud altitude profiles over Hanoi, Vietnam, measured with the ground LIDAR setup of the Institute of Physics. Comparisons are made to LIDAR data collected by the Calipso satellite of the NASA A-Train during its orbits over the Hanoi area. The height distributions for both surface aerosols and Cirrus clouds derived from ground and satellite observations are generally consistent, with distributions between 2km-3km, and 8km-15km respectively for aerosols and Cirrus clouds. Cirrus cloud locations inferred from an analysis of limb spectral radiances obtained by the SCIAMACHY satellite are also consistent with the LIDAR data.

This paper presents a new factorization technique for hyperspectral signal processing based on a constrained singular value decomposition (SVD) approach. Hyperpectral images typically have a large number of contiguous bands that are highly correlated. Likewise the field of view typically contains a limited number of materials and the spectra are also correlated. Only a selected number of bands, the extreme bands that include the dominant materials spectral signatures, are needed to express the data. Factorization can provide a means for interpretation and compression of the spectral data. Hyperspectral images are represented as non-negative matrices by graphic concatenation, with the pixels arranged into columns and each row corresponding to a spectral band. SVD and principal component analysis enjoy a broad range of applications, including, rank estimation, noise reduction, classification and compression, with the resulting singular vectors forming orthogonal basis sets for subspace projection techniques. A key property of non-negative matrices is that their columns/rows form non-negative cones, with any non-negative linear combination of the columns/rows belonging to the cone. Data sets of spectral images and time series reside in non-negative orthants and while subspaces spanned by SVD include all orthants, SVD projections can be constrained to the non-negative orthants. In this paper we utilize constraint sets that confine projections of SVD singular vectors to lie within the cones formed by the spectral data. The extreme vectors of the cone are found and these vectors form a basis for the factorization of the data. The approach is illustrated in an application to hyperspectral data of a mining area collected by an airborne sensor.

This paper presents a new factorization approach for hyperspectral data based on non-negativity constraints. The method does not assume a one to one correspondence between the pseudo-rank of the data matrix and the number of unique components present. Rather it assumes that the number of unique components is related to the number of extreme points of the cone formed by the data matrix. The cone is represented by singular vectors and a set of linear homogeneous inequality constraints. The extraction of extremes is based on the identification of non-redundant inequalities. The approach is illustrated in an application to an AVIRIS spectral image of the Cuprite mining site.

The Strategic High-Altitude Radiance Code (SHARC ) is a new computer code that calculates atmospheric radiation for paths from 60 to 300 km altitude in the 2-40 micro spectral region. It models radiation due to NLTE (Non-Local Thermodynamic Equilibrium) molecular emissions which are the dominant sources at these altitudes. The initial version of SHARC, which is described in this paper, includes the five strongest IR radiators, CO/sub 2/, NO, O/sub 3/, H/sub 2/O and CO. Calculation of excited state populations is accomplished by interfacing a Monte Carlo model for radiative excitation and energy transfer with a highly flexible chemical kinetics module derived from the Sandia CHEMKIN Code. An equivalent-width, line-by-line approach for the radiation transport gives a spectral resolution of about 0.50/cm. The radiative-transport calculation includes the effects of combined Doppler-Lorentz (Voigt) line shapes. Particular emphasis was placed on modular construction and supporting data files so that models and model parameters can be modified or upgraded as additional data become available. The initial version of SHARC is now ready for distribution.

Singular value decomposition (SVD) and principal component analysis enjoy a broad range of applications, including, rank estimation, noise reduction, classification and compression. The resulting singular vectors form orthogonal basis sets for subspace projection techniques. The procedures are applicable to general data matrices. Spectral matrices belong to a special class known as non-negative matrices. A key property of non-negative matrices is that their columns/rows form non-negative cones, with any non-negative linear combination of the columns/rows belonging to the cone. This special property has been implicitly used in popular rank estimation techniques know as virtual dimension (VD) and hyperspectral signal identification by minimum error (HySime). Data sets of spectra reside in non-negative orthants. The subspace spanned by a SVD of a set of spectra includes all orthants. However SVD projections can be constrained to the non-negative orthants. In this paper two types of singular vector projection constraints are identified, one that confines the projection to lie within the cone formed by the spectral data set, and a second that only restricts projections to the non-negative orthant. The former is referred to here as the inner constraint set, the latter the outer constraint set. The outer constraint set forms a broader cone since it includes projections outside the cone formed by the data array. The two cones form boundaries for the cones formed by non-negative matrix factorizations (NNF). Ambiguities in the NNF lead to a variety of possible sets of left and right non-negative vectors and their cones. The paper presents the constraint set approach and illustrates it with applications to spectral classification.

Series solutions to the radial auxiliary integrals that are needed for the evaluation of many electron integrals are given. These auxiliary integrals will facilitate the calculation of all the many electron integrals which occur in Hylleraas type wave functions, which involve rr terms with linked indicies.

This paper reviews the capabilities of SAMM2, a high‐fidelity background radiance code. SAMM2 incorporates atmospheric climate and chemistry, line‐of‐sight geometry, spectroscopy and radiation transport into a unified and extensible code. It is capable of accurately predicting atmospheric radiances under both low‐altitude local thermodynamic equilibrium as well as upper‐altitude non‐equilibrium conditions. SAMM2 provides comprehensive coverage in the .4 to 40 micron (250 to 25,000 wavenumber) wavelength region for arbitrary line‐of‐sight inputs. The capabilities of SAMM2 are demonstrated by computing radiance values for typical atmospheric conditions.

This paper presents results that demonstrate the auroral modeling capabilities of the Air Force Research Laboratory (AFRL) SAMM2 (SHARC And MODTRAN (R) Merged 2) radiance code. A scene generation capability is obtained by coupling SAMM2 with a recently developed Clutter Region Atmosphere and Scene Module (CRASMO), which provides an approach for rapid generation of time sequences and images of radiance clutter. Modeled results will be compared to data collected by the Midcourse Space Experiment (MSX)(1) in the IR and UV-visible spectral regions during an auroral event on November 10, 1996.The paper is organized as follows. We first present a brief history of the AFRL SHARC/SAMM codes, leading up to the current version, SAMM2 v.2. The SAMM2 UV-visible auroral kinetic model will then be described, followed by a comparison of modeled results to the MSX data.

Subspace methods for hyperspectral imagery enable detection and identification of targets under unknown environmental conditions (i.e., atmospheric, illumination, surface temperature, etc.) by specifying a subspace of possible target spectral signatures (and, optionally, a background subspace) and identifying closely fitting spectra in the image. The subspaces, defined from a set of exemplar spectra, are compactly expanded in singular value decomposition basis vectors or, less commonly, endmember basis spectra, linear combinations of which are used to fit the image data. In the present study we compared detection performance in the thermal infrared using several different constrained and unconstrained basis set expansions of low-dimensional subspaces, including a method based on the Sequential Maximum Angle Convex Cone (SMACC) endmember algorithm. Constrained expansions were found to provide a modest improvement in algorithm robustness in our test cases.

Subspace methods for hyperspectral imagery enable detection and identification of targets under unknown environmental conditions by specifying a subspace of possible target spectral signatures (and, optionally, a background subspace) and identifying closely fitting spectra in the image. In this study, detection performance in the thermal infrared (IR) was compared using various constrained and unconstrained basis set expansions of low-dimensional target subspaces. An initial investigation of detection using retrieved atmospheric parameters to reduce subspace size and/or dimensionality has also been performed.

We investigated the contributions of the hydroxyl (OH) airglow to the illumination of resident space objects. During nighttime, in a moonless sky, the airglow is the largest contributor to the sky brightness in the visible (vis), the near-infrared (NIR) and short-wave infrared (SWIR) spectral region. The dominant contributors to the airglow are vibrationally excited hydroxyl radicals, OH(ν). The radicals are formed in vibrational states up to υ=9 by the reaction of hydrogen atoms with ozone. The strong emissions, known as Meinel emissions, are sequences with σν= 1-6. Emissions with υ = 3, 4, 5 and 6 occur in the visible and NIR between .4 and 1.0 µm. From 1.0 to 2.5 µm there are very strong emissions from the δν= 2 sequences. The σν= 1 emissions extend into the thermal infrared to 4.5 μm. In this work, we considered four band passes, a vis-NIR band pass, two SABER band passes centered at 1.6 and 2.0 μm, respectively, and a broad band pass around 2.7 µm. SAMM2 was utilized to compute spectra and line of sight radiances. We used line of sight (LOS) radiances to compute the irradiance on a space object that was taken as a flat plate with a Lambertian surface reflectance. Profiles of irradiance versus orientation were calculated. The OH airglow will illuminate a facet even if it is pointing somewhat upward. However, the irradiance in the 2.7 μm band pass comes almost entirely from the atmosphere in the low altitude and the earth emission.

A new correlated-k algorithm has recently been incorporated into SAMM-2, the Air Force Research Laboratory background radiance and transmission code. SAMM-2 incorporates all of the major components necessary for background scene generation at all altitudes: atmospheric characterization, solar irradiance, molecular chemical kinetics and molecular spectroscopic data. The underlying physical models are applicable for both low-altitude local thermodynamic equilibrium (LTE) conditions as well as high-altitude non-LTE (NLTE) conditions. Comprehensive coverage in the .4 to 40 micron (250 to 25,000 wavenumber) wavelength region for arbitrary lines-of-sight (LOS) in the 0 to 300 kilometer altitude regime is provided. A novel 1 cm-1 resolution correlated-k algorithm has been developed in order to provide the orders-of-magnitude increase in computational efficiency when compared to the existing SAMM-2 line-by-line (LBL) algorithm and applicable to both LTE and NLTE atmospheric conditions. The SAMM-2 correlated-k algorithm processes molecular lines at runtime by reading line center information from the HITRAN 2000 database and computing statistical cumulative probability distributions within a spectral interval under the presumption of a Voigt line shape profile. This algorithm is useful for treating atmospheric phenomena at all altitudes requiring a spectrally monochromatic treatment of the atmospheric transmission and/or radiance, including multiple scattering or atmospheric structure.

A new non-negative factorization method has been developed. The method is based on the concept of non-negative rank (NNR). Bounds for the NNR of certain non-negative matrices are determined relative to the rank of the matrix, with the lower bound being equal to the rank. The method requires that the data matrix be non-negative and have a large first singular value. Unlike other non-negative factorization methods, the approach does not assume or require that the factors be linearly independent and no assumption of statistical independence is required. The rank of the matrix provides the number of linearly independent components present in the data while the non-negative rank provides the number of non-negative independent components present in the data. The method is described and illustrated in application to hyperspectral data sets.

A new endmember extraction method has been developed that is based on a convex cone model for representing vector data. The endmembers are selected directly from the data set. The algorithm for finding the endmembers is sequential: the convex cone model starts with a single endmember and increases incrementally in dimension. Abundance maps are simultaneously generated and updated at each step. A new endmember is identified based on the angle it makes with the existing cone. The data vector making the maximum angle with the existing cone is chosen as the next endmember to add to enlarge the endmember set. The algorithm updates the abundances of previous endmembers and ensures that the abundances of previous and current endmembers remain positive or zero. The algorithm terminates when all of the data vectors are within the convex cone, to some tolerance. The method offers advantages for hyperspectral data sets where high correlation among channels and pixels can impair un-mixing by standard techniques. The method can also be applied as a band-selection tool, finding end-images that are unique and forming a convex cone for modeling the remaining hyperspectral channels. The method is described and applied to hyperspectral data sets.

A multiple simplex endmember extraction method has been developed. Unlike convex methods that rely on a single simplex, the number of endmembers is not restricted by the number of linearly independent spectral channels. The endmembers are identified as the extreme points in the data set. The algorithm for finding the endmembers can simultaneously find endmember abundance maps. Multispectral and hyperspectral scenes can be complex and contain many materials under a variety of illumination and environmental conditions, but individual pixels typically contain only a few materials in a small subset of the illumination and environmental conditions which exist in the scene. This forms the physical basis for the approach that restricts the number of endmembers that combine to model a single pixel. No restriction is placed on the total number of endmembers, however. The algorithm for finding the endmembers and their abundances maps is sequential. Extreme points are identified based on the angle they make with the existing set. The point making the maximum angle with the existing set is chosen as the next endmember to add to enlarge the endmember set. The maximum number of endmembers that are allowed to be in a subset model for individual pixels is controlled by an input parameter. The subset selection algorithm is sequential and takes place simultaneously with the overall endmember extraction. The algorithm updates the abundances of previous endmembers and ensures that the abundances of previous and current endmembers remain positive or zero. The method offers advantages in multispectral data sets where the limited number of channels impairs material un-mixing by standard techniques. A description of the method is presented herein and applied to real and synthetic hyperspectral and multispectral data sets.