A BME solution of the inverse problem for saturated groundwater flow

In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined. This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069.     

Effects of benzene and dimethylnaphthalene on homeostatic processes in two species of crabs

Long-term exposure of animals to sub-lethal doses of toxicants such as benzene (B) and dimethylnaphthalene (DMN) may result in subtle changes in their physiology and biochemistry. In crustaceans such changes include decreased rate of limb regeneration, extended time to molt and decreased growth increment at molt.^1,2 These processes depend upon an adequate supply of stored nutrients in the tissues and appropriate release of neuroendocrine substances from the central nervous system.^3,4 We are examining the effects of sub-lethal doses of B and DMN on osmotic and ionic regulation and on nutrient storage in the blue crab, Callinectes sapidus, and the green crab, Carcinus maenas. Disturbances in these physiological processes may reflect alterations in neuroendocrine functions brought about by the presence of toxicants. We find that exposure of C. maenas to B or DMN, followed by transfer to a dilute medium, results in impaired osmoregulatory capacity, while addition of these compounds to a dilute medium to which the animal is already acclimated does not affect their regulatory ability. Storage of carbohydrate in the midgut gland (hepatopancreas) is decreased by B or DMN, while the accessory storage tissues (gill, muscle) are not significantly affected.     

Sedimentary facies of barataria bay,Louisiana determined by multivariate statistical techniques

A multivariate statistical strategy employing cluster analysis, discriminant analysis, and ordination was used to classify and interpret depositional environments of Barataria Bay, Louisiana, from grain-size data tabulated by Krumbein and Aberdeen (1937). Weight-percent whole-phi variables for 69 samples were tested for redundancy using R-mode cluster analysis. These samples were partitioned into five environmentally significant facies using Q-mode cluster analysis: (1) beach-ridge sand; (2) shallow wave-zone sand; (3) channel sand and silty sand; (4) channel-margin silty sand; and (5) low-energy sandy silt and clayey silt. Then the classification was extended with discriminant analysis to the remaining 29 samples which exhibited incipient flocculation and whose constituents did not total unity. Environments of deposition were associated with each facies following the method of Visher (1969) and using gradient analysis on a two-dimensional Q-mode ordination. Wilk's lambda and discriminant analysis tested the statistical significance of these facies; they were further tested by comparing their distribution with field relations and known environmental processes.     

Hyperfine interactions and spin transfer between Cr3+ and Al3+ in a synthetic single crystal of Mg2SiO4. A theoretical approach to the interpretation of EPR data

The occurrence of Cr-Al pairs in Mg₂SiO₄ has been detected by EPR spectroscopy. In the case where Cr³⁺ replaces Mg at the M2 position three different neighboring Si sites may be substituted by Al³⁺, which should yield different superhyperfine interactions. A new spectrum is presented which shows the presence of two of these possible pair configurations. An assignment of the spectral features to a specific Cr-Al pair with Cr at M2 from the experimental data alone was not possible, therefore, MSX _α cluster calculations have been performed from which the differences in the superhyperfine interaction for the various pair configurations could be obtained. Best agreement with the data of the Cr³⁺(M2)-Al pair exhibiting the most intense group of lines in the EPR spectrum was obtained for the situation where Al³⁺ is at the Si position with the shortest distance to M2. The second observed Cr³⁺(M2)-Al pair, which is significantly weaker in intensity, could not yet be assigned.     

Spherical harmonic analysis of steady photospheric flows

Steady photospheric flows can be represented by a spectrum of spherical harmonic modes. A technique is described in which full disc doppler velocity measurements are analysed using the spherical harmonic functions to determine the characteristics of this spectrum and the nature of these flows. Synthetic data is constructed for testing this technique. This data contains limb shift, rotation, differential rotation, meridional circulation, supergranules, giant cells and various levels of noise.The data is analysed in several steps. First, the limb shift is calculated by finding the average velocity in concentric rings about disc center. A polynomial representation of the limb shift is then removed from the data. Secondly, the rotation profile is calculated by finding an average slope in the velocity across the disc at each latitude position. This rotation profile is fit with Legendre polynomials and removed from the data. The third step is to find the meridional circulation by calculating the spherical harmonic transform for the axisymmetric poloidal modes and correcting for the effects of the limb shift analysis. The final step is to calculate the full spectrum of spherical harmonic components for the convective flows. Supergranules are separated from giant cells by spectral filtering for high (l >32) and low (l <32) wavenumbers, respectively.Some information about the spectrum is lost because only one hemisphere is seen, only the line-of-sight velocity is measured and the measurements contain noise. The lack of information about the motions on the backside of the Sun produces a broad smearing of the spectrum into nearby modes. The lack of information about the transverse velocity component produces a mixing between modes whose longitudinal wavenumbers differ by two and between the poloidal and toroidal components with the same wavenumber. In spite of this mode mixing much can be learned from this analysis. Solar rotation and differential rotation can be accurately measured and monitored for secular changes. Meridional circulations with small amplitudes can be measured and monitored and giant cells can be separated from supergranules.     

Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = \(-25.97\pm 0.05 ''/\)cent\(^{2}\), da/dt = 38.30 ± 0.08 mm/year, and di/dt = ?0.5 ± 0.1 \(\upmu \)as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives \(\sim \) \(3\times 10^{-12}\)/year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = \((1.50 \pm 0.10)\times 10^{-11}\)/year. For total dn/dt, there is \(\le \)1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is \(-1316 ''\)/cent\(^{2}\) or 87.5 s/cent\(^{2}\) for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 \(\upmu \)as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.