Kriging with imprecise (fuzzy) variograms. I: Theory

Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.     

Greenhouse Gas Emissions and Costs over the Life Cycle of Wood and Alternative Flooring Materials

Increased use of wood can substitute more energy demanding products and thus contribute to a long-term solution to the global warming problem. The aim of this article is to provide an empirical study on this substitution impact, its cost-effectiveness, and which methodological assumptions that are of highest importance for the results obtained. We have made a case study where we compare use of various flooring materials. The results show that floor covering in solid oak causes lower greenhouse gas (GHG) emissions than the other materials. The difference can be ranked in the following order, after their potential for reduction in GHG emissions: Carpet in wool, carpet in polyamide, vinyl, and linoleum. At 2% pro anno discount rate, the avoided GHG emission in tons per m³ of oak flooring used is 0.1–1.9 for linoleum, and 11.8–15.5 for wool carpets. Unless the solution in solid oak is on total less expensive over the lifetime of the building, only the price of avoided emissions from a substitution between solid oak and carpet in wool is reasonable, compared to present carbon fees. The assumptions that influence the result most are choice of discount rate, carbon fixation on forest area, and waste handling. Empirical case studies like this indicate GHG emission reduction potentials caused by substitution, but should be complemented by dynamic input/output analyses and econometric studies. To analyse the flow of CO₂ over time, they should also be linked to forest management models.     

Training Images from Process-Imitating Methods

The lack of a suitable training image is one of the main limitations of the application of multiple-point statistics (MPS) for the characterization of heterogeneity in real case studies. Process-imitating facies modeling techniques can potentially provide training images. However, the parameterization of these process-imitating techniques is not straightforward. Moreover, reproducing the resulting heterogeneous patterns with standard MPS can be challenging. Here the statistical properties of the paleoclimatic data set are used to select the best parameter sets for the process-imitating methods. The data set is composed of 278 lithological logs drilled in the lower Namoi catchment, New South Wales, Australia. A good understanding of the hydrogeological connectivity of this aquifer is needed to tackle groundwater management issues. The spatial variability of the facies within the lithological logs and calculated models is measured using fractal dimension, transition probability, and vertical facies proportion. To accommodate the vertical proportions trend of the data set, four different training images are simulated. The grain size is simulated alongside the lithological codes and used as an auxiliary variable in the direct sampling implementation of MPS. In this way, one can obtain conditional MPS simulations that preserve the quality and the realism of the training images simulated with the process-imitating method. The main outcome of this study is the possibility of obtaining MPS simulations that respect the statistical properties observed in the real data set and honor the observed conditioning data, while preserving the complex heterogeneity generated by the process-imitating method. In addition, it is demonstrated that an equilibrium of good fit among all the statistical properties of the data set should be considered when selecting a suitable set of parameters for the process-imitating simulations.     

Two-body motion in the post-Newtonian approximation

The motion of two massive particles is considered within the framework of the first post-Newtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closed-form solutions for the Delaunay elements in the phase space are obtained. The bridge between the phase space and the state space of the Lagrangian of the motion is provided by a velocity-dependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions.     

Exploring the X-ray spectral variability of MCG–6-30-15 with XMM–Newton

We present a study of the spectral variability of the Seyfert I galaxy MCG–6-30-15 based on the two long XMM–Newton observations from 2000 and 2001. The X–ray spectrum and variability properties of the 2001 data have previously been well described with a two-component model consisting of a variable power-law and a much less variable reflection component, containing a broad relativistic iron line from the accretion disc around a rapidly rotating Kerr black hole. The lack of variability of the reflection component has been interpreted as an effect of strong gravitational light bending very close to the central black hole. Using an improved reflection model, we fit the two-component model to time-resolved spectra of both observations. Assuming that the photon index of the power law is constant, we reconfirm the old result and show that this does not depend on the time-scale of the analysis.     

A Comparison of Public Lands and Farmlands for Grassland Bird Conservation

Midwestern states have invested extensively in grasslands for wildlife conservation, yet these public lands make up a minority of grassland habitat. How effective are public grasslands, relative to private lands, for conserving native songbird populations? I compare private and public lands in southern Minnesota using bird survey data from Conservation Reserve Program (CRP) fields and public lands and assessing fragmentation in a GIS. Bird abundance and diversity were greater on CRP lands. Vegetation composition, field isolation, and field size appear to explain differences in bird counts. Land cover data show that grassland habitat on public lands is scarce and widely scattered. The CRP provides more, and here better, habitat for grassland birds. Funding partly explains this disparity. Trends in farm set‐aside program rules and distribution, which can be vary greatly over time, will strongly influence the success or failure of biodiversity conservation in this region.     

The barometric tides at Zürich and on the summit of Säntis

Summary Lunar barometric tidal determinations (L ₂) have been made by the Chapman-Miller method for Zürich (493 m) and Säntis (2000 m) based on 49 years' data. The seasonal variations ofL ₂ are much larger at Zürich than on the Säntis summit. However, a comparison with the five other pairs of stations for which tidal determinations at different altitudes, but short horizontal distances, are available do not indicate that this result is as an altitude effect, nor do they show any other systematic differences betweenL ₂ at the lower and the higher station. The solar tidal determinations agree well with those made byEggenberger (1944) and fit in with those obtained for other stations. From the difference between the pressure oscillations at Zürich and on Säntis the corresponding meantemperature oscillations of the air column between the two stations has been computed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Stratospheric ozone: Impact of human activity

Current knowledge of the chemistry of the stratosphere is reviewed using measurements from the Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment to test the accuracy of our treatment of processes at mid-latitudes, and results from the Airborne Antarctic Ozone Experiment (AAOE) to examine our understanding of processes for the polar environment. It is shown that, except for some difficulties with N₂O₅ and possibly ClNO₃, gas phase models for nitrogen and chlorine species at 30°N in spring are in excellent agreement with the data from ATMOS. Heterogeneous processes may have an influence on the concentrations of NO₂, N₂O₅, HNO₃, and ClNO₃ for the lower stratosphere at 48°S in fall. Comparison of model and observed concentrations of O₃ indicate good agreement at 30°N, with less satisfactory results at 48°S. The discrepancy between the loss rate of O₃ observed over the course of the AAOE mission in 1987 and loss rates calculated using measured concentrations of ClO and BrO is found to be even larger than that reported by Anderson et al. (1989, J. geophys. Res. 94, 11480). There appear to be loss processes for removal of O₃ additional to the HOC1 mechanism proposed by Solomon et al. (1986, Nature 321, 755), the ClO-BrO scheme favored by McElroy et al. (1986, Nature 321, 759), and the ClO dimer mechanism introduced by Molina and Molina (1987, J. phys. Chem. 91, 433). There is little doubt that industrial halocarbons have a significant impact on stratospheric O₃. Controls on emissions more stringent than those defined by the Montreal Protocol will be required if the Antarctic Ozone Hole is not to persist as a permanent feature of the stratosphere.