Plio-/Pleistocene climate modeling based on oxygen isotope time series from deep-sea sediment cores: The Grassberger-Procaccia algorithm and chaotic climate systems

The question whether paleoclimatic systems are governed by a small number of significant variables (low-dimensional systems) is of importance for modeling such systems. As indicators for global Plio-/Pleistocene climate variability, four marine, sedimentary oxygen isotope time series are analyzed with regard to their dimensionality using a modified Grassberger-Procaccia algorithm. An artificial, low-dimensional chaotic time series (Hénon map) is included for the validation of the method. In order to extract equidistant data the raw data are interpolated with the Akima-subspline method since this method minimizes the change in variance due to the interpolation. The nonlinear least-squares Gauss-Marquardt regression method is used instead of the linear least-squares fit to the logarithmically transformed points, in order to acquire an unbiased estimate of the correlation dimension. The dependences of the estimated correlation dimension on the embedding dimension do not indicate a small number (i.e., less than 5) of influencing variables on the investigated paleoclimatic system, whereas the low dimension for the Hénon map is verified (dimension 1.22–1.28). Because of the limited amount of data in the oxygen isotope records, dimensions greater than about 5 cannot be examined.     

Stresses due to vertical subsurface loading for an inhomogeneous cross‐anisotropic half‐space

In this article, we present the solutions for the stresses induced by four different loads associated with an axially loaded pile in a continuously inhomogeneous cross‐anisotropic half‐space. The planes of cross‐anisotropy are parallel to the horizontal surface of the half‐space, and the Young's and shear moduli are assumed to vary exponentially with depth. The four loading types are: an embedded point load for an end‐bearing pile, uniform skin friction, linear variation of skin friction, and non‐linear parabolic variation of skin friction for a friction pile. The solutions for the stresses due to the pile load are expressed in terms of the Hankel integral and are obtained from the point load solutions of the same inhomogeneous cross‐anisotropic half‐space which were derived recently by the authors (Int. J. Rock Mech. Min. Sci. 2003; 40 (5):667–685). A numerical procedure is proposed to carry out the integral. For the special case of homogeneous isotropic and cross‐anisotropic half‐space, the stresses predicted by the numerical procedure agree well with the solutions of Geddes and Wang (Geotechnique 1966; 16 (3):231–255; Soils Found. 2003; 43 (5):41–52). An illustrative example is also given to investigate the effect of soil inhomogeneity, the type and degree of soil anisotropy, and the four different loading types on the vertical normal stress. The presented solutions are more realistic in simulating the actual stratum of loading problem in many areas of engineering practice. Copyright © 2004 John Wiley & Sons, Ltd.     

A hybrid Bayesian back‐propagation neural network approach to multivariate modelling

There is growing interest in the use of back‐propagation neural networks to model non‐linear multivariate problems in geotehnical engineering. To overcome the shortcomings of the conventional back‐propagation neural network, such as overfitting, where the neural network learns the spurious details and noise in the training examples, a hybrid back‐propagation algorithm has been developed. The method utilizes the genetic algorithms search technique and the Bayesian neural network methodology. The genetic algorithms enhance the stochastic search to locate the global minima for the neural network model. The Bayesian inference procedures essentially provide better generalization and a statistical approach to deal with data uncertainty in comparison with the conventional back‐propagation. The uncertainty of data can be indicated using error bars. Two examples are presented to demonstrate the convergence and generalization capabilities of this hybrid algorithm. Copyright © 2003 John Wiley & Sons, Ltd.     

Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.     

Suspended sediment dynamics in a steep,glacier‐fed mountain stream,Place Creek,Canada

This study examined suspended sediment concentration (SSC) during the ablation seasons of 2000 and 2001 in Place Creek, Canada, a steep, glacier‐fed mountain stream. Comparison of stream flow in Place Creek with that in an adjacent, almost unglacierized catchment provided a rational basis for separating the ablation seasons into nival, nival–glacial, glacial and autumn recession subseasons. Distinct groupings of points in plots of electrical conductivity against discharge supported the validity of the subseasonal divisions in terms of varying hydrological conditions. Relationships between SSC and discharge (Q) varied between the two study seasons, and between subseasons. Hysteresis in the SSC–Q relationship was evident at both event and weekly time‐scales. Some suspended sediment released from pro‐glacial Place Lake (the source of Place Creek) appeared to be lost to channel storage at low flows, especially early in the ablation season, with re‐entrainment at higher flows. Multiple regression models were derived for the subseasons using predictor variables including Q, Q², the change in Q over the previous 3 h, cumulative discharge over the ablation season, total precipitation over the previous 24 h and SSC measured at 1500 hours as an index value for each day. The models produced adjusted R² values ranging from 0·71 to 0·91, and provided tentative insights into the differences in SSC dynamics amongst subseasons. Introduction of the index value of SSC significantly improved the model fit during the nival–glacial and glacial subseasons for both years, as it adjusts the model to the current condition of sediment supply. Copyright © 2003 John Wiley & Sons, Ltd.     

MULTICOMPONENT DETERMINATIONS BY A MEMBRANE-DISCRIMINATED GAS PHASE ANALYZER AND SUCCESSIVE REGRESSION IN THE FIDUCIARY REGION

A membrane-discriminated gas phase analyzer is proposed for multicomponent determinations. Nitrogengas flows countercurrent through outer and inner channels in a tube-in-tube arrangement. The onlycommunication between the two channels occurs through a 500μm aperture covered by a porous PTFEmembrane. A mixture of organic compounds (up to four components) is injected into the inner channelby a heated backflushed injector and the sample components diffusing into the outer channel aremonitored by a flame ionization detector (FID). A calibration set, consisting of pure components, binary,ternary and quaternary mixtures (a total of 64 samples), provides the known data base: temporal profilesof the FID output as a function of sample composition, Although the overall response behavior is nota linearly additive function of individual analyte concentrations, the use of successive inverse multiplelinear regression (while continually altering the choice of the calibration samples considered for theforward regression, on the basis of the most recent values of the predicted unknown sample composition)is shown to yield analytical results for unknown samples that are in good agreement with their true values.     

Long-term growth of the oil industry in the United States

A number of growth models have been developed and used in an attempt to project the historical pattern of oil activities to some estimate of their upper limit. Techniques are outlined for the estimation of parameters of the logistic and Gompertz curves. Factor analysis indicated a close relationship between production and demand, whereas annual discoveries and discoveries classified by year of discovery tended to comprise unique factors which were indifferent to changes in time. The growth models projected relatively high values for ultimate demand and production in comparison to the figures for ultimate reserves. Inasmuch as these trends seemed to be occurring independently, some reconciliation of the results was necessary. Using the highest projections of estimates for reserves suggests that over 420 billion barrels of oil in place will eventually be discovered in the United States, with perhaps 200 billion barrels of this eventually to be proved in the form of reserves. Projections for production were higher, corresponding to a trend indicating high levels in demand for crude oil. The only credible long-term estimate of demand was given by a bounded exponential growth model, in which ultimate cumulative demand for crude oil would reach about 416 billion barrels. These figures imply that over 150 billion barrels of oil would be imported into the United States from 1970 to 2070. Provided the time pattern for one of the variables has been determined, then estimates of the other variables probably would be facilitated because of the high interrelationship between variables. Models are suggested in which accurate pivotal forecasting in the short term might be possible—assuming the particular future trend in some of the independent variables has been predetermined.Research Council of Alberta Contribution No. 596.     

Meixner functions for derivation of the unit hydrograph

The Meixner functions are utilized to relate the effective rainfall, the direct runoff and the unit hydrograph through linkage equations. The linkage equations are then employed to derive the unit hydrograph for given rainfall-runoff data on a small agricultural watershed. These functions are tested with regard to their ability to reproduce and predict the direct runoff hydrograph. The Meixner functions are found to be an effective analytical tool for hydrograph synthesis. Further, they compare well with the least squares and linear programming methods of the unit hydrograph derivation.     

Variation of chemical composition of alkaline granitic rocks in the central part of the Kola Peninsula

Chemical composition and origin of alkaline granitic rocks in the Keivy area on the Kola Peninsula were investigated. Linear correlation analysis and principal-component analysis were used to determine the interrelation of major petrogenetic elements in alkaline granite and surrounding alkaline metasomatites. Estimates of linear correlation coefficients turned out to be different, and principal-component analysis of the chemical data revealed that there were three main components influencing variation of chemical composition. These factors can be interpreted in terms of petrological processes, which are different for alkaline granite and for the surrounding metasomatites, indicating a different origin of the rocks.     

Nonlinear regression for dependent variables

Nonlinear regression methods can be used to fit functions for two related variables where both variables are subject to error. A computer program for nonlinear estimation described previously has been modified to fit such functions for a given set of data. A numerical example is provided for a second-degree equation in xand y.A closer fit to an observed set of data is possible if the error structure for the variables is specified.