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Forces external to the oblate spheroid shape, observed from planetary to galactic scales, are demonstrably non-central, which has important ramifications for planetary science. We simplify historic formulae and derive new analytical solutions for the gravitational potential and force outside a constant density oblate. Numerical calculations that sum point mass contributions in a >10 9 element mesh confirm our equations. We show that contours of constant force and potential about oblate bodies are closely approximated by two confocal families whose foci ( f ) respectively are (9/10) ½ ae and (3/5) ½ ae for a body with f  =  ae . This leads to useful approximations that address internal density variations. We demonstrate that the force on a general point is not directed towards the oblate's center, nor are forces simply proportional to the inverse square of that distance, despite forces in the equatorial and axial directions pointing towards the center. Our results explain complex dynamics of galactic systems. Because most planets and stars have an aspect ratio >0.9, the spherical approximation is reasonable except for orbits within ∼2 body radii. We show that applying the “generalized” potential, which assumes central forces, yields J 2 values half those expected for oblate bodies, and probably underestimates masses of Uranus and Neptune by ∼0.2%. We show that the inner Saturnian moons are subject to non-central forces, which may affect calculations of their orbital precession. Our new series should improve interpretation of flyby data. [ABSTRACT FROM AUTHOR]

High frequency monitoring of water quality and stable isotopes quantify large hydrological and geochemical differences across a rural to urban land use gradient that includes three watersheds and two of their subbasins. Following precipitation events, floods on a rural stream feature hydrographs with low peak discharges and long lag times, high baseflow contributions, and small geochemical variations. In contrast, the flows of an urban stream and its tributary respond in a flashy manner, with average lag times decreasing by at least 55% compared to the rural stream. We also observed that baseflow contributions during floods decreased by an average of 40% in the urban streams. Importantly, we find that reduced baseflow as a function of increasing impervious surface area is not a linear trend among the streams, and suburban streams are less impacted than would be predicted by impervious surface area alone. The urban streams also exhibit large variations in water quality parameters during flooding events, often with five times the variability of the rural end-member. These differences are observed among all physical and geochemical characteristics that were monitored, including flow magnitude, stable isotope ratios, temperature, dissolved oxygen (DO), pH, turbidity, specific conductivity, concentrations of Cl − and nutrients, and bacterial loads. The great variability of urban streams following storms is paralleled by their larger diurnal and seasonal oscillations. Collectively, the extreme variations in the physical and geochemical character of urban streams have negative consequences to environmental quality and aquatic life. [ABSTRACT FROM AUTHOR]

Abstract: Previous studies attribute abnormal boron (B) levels in streams and groundwaters to wastewater and fertilizer inputs. This study shows that municipal drinking water used for lawn irrigation contributes substantial non-point loads of B and other chemicals (S-species, Li, and Cu) to surface waters and shallow groundwaters in the St. Louis, Missouri, area. Background levels and potential B sources were characterized by analysis of lawn and street runoff, streams, rivers, springs, local rainfall, wastewater influent and effluent, and fertilizers. Urban surface waters and groundwaters are highly enriched in B (to 250μg/L) compared to background levels found in rain and pristine, carbonate-hosted streams and springs (<25μg/L), but have similar concentrations (150 to 259μg/L) compared to municipal drinking waters derived from the Missouri River. Other data including B/SO4 2-−S and B/Li ratios confirm major contributions from this source. Moreover, sequential samples of runoff collected during storms show that B concentrations decrease with increased discharge, proving that elevated B levels are not primarily derived from combined sewer overflows (CSOs) during flooding. Instead, non-point source B exhibits complex behavior depending on land use. In urban settings B is rapidly mobilized from lawns during “first flush” events, likely representing surficial salt residues from drinking water used to irrigate lawns, and is also associated with the baseflow fraction, likely derived from the shallow groundwater reservoir that over time accumulates B from drinking water that percolates into the subsurface. The opposite occurs in small rural watersheds, where B is leached from soils by recent rainfall and covaries with the event water fraction. [Copyright &y& Elsevier]

Abstract: Dissolved O2 (DO) and pH data provide a novel, inexpensive field method to detect open cave passages in karst spring systems that can be complemented by laboratory measurements of major elements and nutrients, total suspended solids (TSS), Escherichia coli (E. coli) levels, and stable isotopes. Karst springs in east-central Missouri that have no known air-filled passages (“phreatic” springs) typically have low DO and pH values (<80% saturation and <7.7, respectively), which are characteristic of groundwaters that do not communicate with the atmosphere. In contrast, springs draining vadose cave passages have higher DO and pH values (>60% saturation and >7.7, respectively) that resemble surface waters due to the equilibration of DO with the overlying cave atmosphere and the simultaneous degassing of dissolved CO2. Traverses down phreatic spring branches show exchange with the atmosphere causes an increase in DO only a short distance downstream of the spring orifice, while the pH concurrently increases due to the degassing of CO2. Further downstream both parameters tend to level off reflecting a general approach to equilibrium under surface conditions, though this process is more rapid for DO than for pH. In contrast, the DO and pH along cave spring branches change little from values at the cave entrance. Additionally, (1) degassing processes affect the saturation state of calcite, with cave springs being the most saturated with respect to calcite, (2) phreatic springs typically have lower TSS and E. coli levels than open cave springs due to slower and less variable flow delivery, longer residence times, and less turbulent flow, and (3) phreatic springs tend to plot on the global meteoric water line (MWL), while waters from open cave systems tend to be enriched in 18O and D and can plot below the line due to evaporation and exchange of the water with the overlying cave atmosphere. [Copyright &y& Elsevier]

Abstract: The fundamental and shared rotational characteristics of the Solar System (nearly circular, co-planar orbits and mostly upright axial spins of the planets) record conditions of origin, yet are not explained by prevailing 2-dimensional disk models. Current planetary spin and orbital rotational energies (R.E.) each nearly equal and linearly depend on gravitational self-potential of formation (U g ), revealing mechanical energy conservation. We derive −ΔU g ≅Δ.R.E. and stability criteria from thermodynamic principles, and parlay these relationships into a detailed model of simultaneous accretion of the protoSun and planets from the dust-bearing 3-d pre-solar nebula (PSN). Gravitational heating is insignificant because U g is negative, the 2nd law of thermodynamics must be fulfilled, and ideal gas conditions pertain to the rarified PSN until the objects were nearly fully formed. Combined conservation of angular momentum and mechanical energy during 3-dimensional collapse of spheroidal dust shells in a contracting nebula provides ΔR.E.≅R.E. for the central body, whereas for formation of orbiting bodies, ΔR.E.≅R.E. f (1−I f /I i ), where I is the moment of inertia. Orbital data for the inner planets follow 0.04×R.E. f ≅−U g which confirms conservation of angular momentum. Significant loss of spin, attributed to viscous dissipation during differential rotation, masks the initial spin of the un-ignited protoSun predicted by R.E.=−U g . Heat production occurs after nearly final sizes are reached via mechanisms such as shear during differential rotation and radioactivity. We focus on the dilute stage, showing that the PSN was compositionally graded due to light molecules diffusing preferentially, providing the observed planetary chemistry, and set limits on PSN mass, density, and temperature. From measured planetary masses and orbital characteristics, accounting for dissipation of spin, we deduce mechanisms and the sequence of converting a 3-d dusty cloud to the present 2-d Solar System, and infer the evolution of dust and gas densities. Duration of events is obtained from the time-dependent virial theorem. As the PSN slowly contracted, collapse of pre-solar dust in spheroidal shells simultaneously formed rocky protoplanets embedded in a dusty debris disk, creating their nearly circular co-planar orbits and upright axial spins with the same sense as orbital rotation, which were then enhanced via subsequent local contraction of nearby nebulae. Because rocky kernels at great distance out-competed the pull of the co-accreting star, gas giants formed in the outer reaches within ∼3Ma as PSN contraction hastened. This pattern repeated to form satellite systems. The PSN imploded, once constricted to within Jupiter''s orbit. Afterwards, disk debris slowly spiraled toward the protoSun, cratering and heating intercepted surfaces. Our conservative 3-d model, which allows for different behaviors of gas and dust, explains key Solar System characteristics (spin, orbits, gas giants and their compositions) and second-order features (dwarf planets, comet mineralogy, satellite system sizes). [Copyright &y& Elsevier]

Abstract: To obtain the desired answer in support of a popular, previous cooling model for the sea floor, Wei and Sandwell provide a construct that is contrary to the simple physics governing subsidence of cooling oceanic crust and is also fraught with mathematical errors. Seven of their eight equations are either misused or incorrect or both. Errors made by Wei and Sandwell include not conserving rock-mass, incorrect differentiation, dividing by zero, moving variable parameters freely in and out of integrals, and neglecting variations in density that embody the essence of the phenomenon being modeled. We demonstrate all the above, show that their construct is closely related to the half-space cooling model, and that the linear, not volumetric thermal expansivity should have been used. [Copyright &y& Elsevier]

• A modified Bayesian sequential updating approach is proposed to estimate GSI. • Multi-source information can be integrated in the approach. • GSI can be estimated using limited data based on various rock mass classifications. • Evaluated probabilistic characteristics of the GSI agree with the observed GSI data. • Rational result is achieved by taking model uncertainties as random normal variables. Explicit determination of geotechnical parameters is an important but difficult task in rock engineering. Paradoxically, data are often limited even though data from multiple sources (e.g., different testing procedures, testing positions, and estimation models) are commonly available, and the integration of multi-source information for the determination of geotechnical parameters in a probabilistic context remains a great challenge. We have modified an existing Bayesian sequential updating approach and used it for the first time to estimate the geological strength index (GSI) of rock masses by integrating multi-source information in a way that considers prior information, multiple estimation models and probabilistic properties of model uncertainties. The argillaceous siltstone in Zigui County in the Three Gorges Reservoir region of China was used to quantitatively illustrate this method. Three data sets using rock mass rating (RMR)-, tunneling quality index (Q)-, and rock mass index (RMi)-based estimation models were sequentially incorporated into the Bayesian sequential updating framework, through which the information on the mean value and standard deviation of the GSI can be updated. Then a large number of equivalent GSI samples were generated through Markov chain Monte Carlo (MCMC) simulation for further statistical analysis. The results showed that the proposed Bayesian sequential updating approach can provide reasonable probabilistic estimates of the GSI, which compared well with observed data using the standard GSI chart. The Bayesian sequential updating approach is a promising tool for geotechnical parameter estimation and can combine large amounts of information, thereby effectively depicting the probabilistic characteristics of GSI. [ABSTRACT FROM AUTHOR]