Singularity and Nonnormality in the Classification of Compositional Data

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore–Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.     

Computational parameter estimation for a maize crop

During a whole growing season, the evolution of the displacement height, d, and roughness length, z ₀, of a maize crop has been estimated by a measurement programme. The results have been used to check different types of existing models to calculate these parameters from canopy characteristics only; a simple geometric model and two matching models have been investigated. A geometric model is based on geometric features of the surface only. After a simple modification, the geometric model gives good results for the displacement height as well as for the roughness length.A matching model, based on gradient-diffusion theory, yields good results for the displacement height. The roughness parameter, however, is overestimated by 17%. By a simple modification, the model results could be improved considerably.A matching model, based on a second-order closure procedure, yields excellent results for the displacement height and good results for the roughness length. But it appears that, when applying this model, the plant density index and plant area density distribution as a function of height must be well known.     

Modeling the temperature of the polar mesopause region: Part II—Intra-seasonal monthly oscillations

Measurements show that the polar mesospheric clouds (PMC) can vary, in the zonal mean, with periods around 1 month [Bailey et al., 2005. Observations of polar mesospheric clouds by the Student Nitric Oxide Explorer. J. Geophys. Res. 110, D13203, doi:10.1029/2004JD005422]. This observation has been the impetus for the present paper, where we describe corresponding temperature oscillations generated by the Numerical Spectral Model (NSM). Our numerical results are taken from the 3D and 2D versions of the NSM, which produce inter-annual and long-term variations in the polar mesopause region, as discussed in the accompanying paper (Part I). In the NSM, the intra-seasonal temperature variations with periods around 2 months are generated by the meridional winds that in turn are accelerated by the momentum deposition from small-scale gravity waves (GW) propagating north/south. The wave-driven dynamical process underlying the oscillations is intrinsically non-linear like that generating the quasi-biennial oscillation (QBO). Our analysis demonstrates that the seasonal annual and semi-annual variations excite the oscillation frequencies through non-linear cascading.     

Practical kinetic modeling of petroleum generation and expulsion

Models for petroleum generation used by the industry are often limited by (a) sub-optimal laboratory pyrolysis methods for studying hydrocarbon generation, (b) over-simple models of petroleum generation, (c) inappropriate mathematical methods to derive kinetic parameters by fitting laboratory data, (d) primitive models of primary migration/expulsion and its coupling with petroleum generation, and (e) insufficient use of subsurface data to constrain the models. Problems (a), (b) and (c) lead to forced compensation effects between the activation energies and frequency factors of reaction kinetics that are wholly artificial, and which yield poor extrapolations to geological conditions. Simple switch or adsorption models of expulsion are insufficient to describe the residence time of species in source rocks. Yet, the residence time controls the thermal stresses to which the species are subjected for cracking to lighter species.     

Application of Compositional Techniques in the Field of Crystal Chemistry: A Case Study of Luzonite, a Sn-Bearing Mineral

Out-of-equilibrium crystallization often produces complex compositional variability in minerals, generating zoning and other mixing phenomena. The appropriate microchemical characterization of the resulting out-of-equilibrium patterns is of critical importance in understanding the overall physical and chemical properties of the host crystalline phases. In this framework, the modeling of compositional changes assumes a fundamental role. However, when compositional data are used, their management with standard exploratory, statistical, graphical, and numerical tools may give misleading results attributable to the phenomenon of induced correlations. To avoid these problems, methods able to extract compositional data from their constrained space (the simplex) in order to apply standard statistics, have to be adopted. As an alternative, the use of tools having properties able to work in the simplex geometry has to be considered. A luzonite single crystal (ideal composition, Cu₃AsS₄) exhibiting concentric and sector zoning was studied using electron probe microanalysis in order to understand the mechanisms which give rise to chemical variability and conditions in the developing environment. Compositional variations were determined by collecting data along three different transects. The major and minor elements (Cu, As, S, Fe, Sb, Sn) were analyzed with the aim of characterizing their patterns of association in the crystal and, hence, crystal evolution. The whole covariance structure as well as the chemical relationships between the successive zones was investigated by means of compositional methods, considering both data transformation and the stay in the simplex approach. Results indicate that the crystal grew under quiescent conditions, where chemical control was primarily exercised by the mineral’s surface and only minor effects were due to changes in the composition of the surrounding fluid. Consequently, an oscillatory uptake of chemical components occurred in which a competition between famatinite-like (Cu₃SbS₄) and kuramite-like (Cu₃SnS₄) domains characterized the As-poor zones.     

Solar System Observations with MIRI, The Mid InfraRed Instrument on the James Webb Space Telescope

MIRI is the Mid InfraRed Instrument for the James Webb Space Telescope (JWST) and will provide imaging, coronography and integral field spectroscopy in the range between 4.9 and 28.6  $\upmu \hbox{m}.$ We summarise solar system observations which may be possible with this instrument, drawing on examples of observations made with previous space missions such as IRAS, ISO and Spitzer.