A benchmark comparison of numerical methods for infinite Prandtl number thermal convection in two-dimensional Cartesian geometry

Abstract

A comparison is made between seven different numerical methods for calculating two-dimensional thermal convection in an infinite Prandtl number fluid. Among the seven methods are finite difference and finite element techniques that have been used to model thermal convection in the Earth's mantle. We evaluate the performance of each method using a suite of four benchmark problems, ranging from steady-state convection to intrinsically time-dependent convection with recurring thermal boundary layer instabilities. These results can be used to determine the accuracy of other computational methods, and to assist in the development of new ones.     

Predicting copper toxicity in estuarine and marine waters using the Biotic Ligand Model

The Biotic Ligand Model (BLM) has proven efficient in predicting the toxicity of a variety of metals to freshwater organisms. Consequently, the US EPA has proposed its use for calculating freshwater copper criteria. This study evaluates the BLM for use in estuarine and marine waters. Studies were conducted using the bivalve, Mytilus sp. and 48-h embryo-larval development chronic estimator test methods. These are the most sensitive taxa and test in the US EPA saltwater copper criteria database. Samples from five locations around the USA were tested. There is a strong relationship between measured and BLM predicted copper EC50s (log transformed data, r² = 0.76, p < 0.001, n = 44). The BLM predicted within a factor ±2 of measured EC50s in 41 of 44 cases. However, the BLM tends to predict lower EC50s when measured EC50s are approximately 10 μg Cu/L. This may be due to limitations of the metal-dissolved organic matter interaction model.     

Anomalous hydrogen emissions from the San Andreas fault observed at the Cienega Winery,central California

We began continuous monitoring of H₂ concentration in soil along the San Andreas and Calaveras faults in central California in December 1980, using small H₂/O₂ fuel-cell sensors. Ten monitoring stations deployed to date have shown that anomalous H₂ emissions take place occasionally in addition to diurnal changes. Among the ten sites, the Cienega Winery site has produced data that are characterized by very small diurnal changes, a stable baseline, and remarkably distinct spike-like H₂ anomalies since its installation in July 1982. A major peak appeared on 1–10 November 1982, and another on 3 April 1983, and a medium peak on 1 November 1983. The occurrences of these peaks coincided with periods of very low seismicity within a radius of 50 km from the site. In order to methodically assess how these peaks are related to earthquakes, three H₂ degassing models were examined. A plausible correlational pattern was obtained by using a model that (1) adopts a hemicircular spreading pattern of H₂ along an incipient fracture plane from the hypocenter of an earthquake, (2) relies on the FeO–H₂O reaction for H₂ generation, and (3) relates the accumulated amount of H₂ to the mass of serpentinization of underlying ophiolitic rocks; the mass was tentatively assumed to be proportional to the seismic energy of the earthquake.     

Geochemical processes controlling the spatial distribution of selenium in soil and water,west central South Dakota,USA

Selenium (Se) is essential in the human diet, but has a low threshold for toxic concentration. It is recommended that nutrients such as Se should be consumed through foods as part of a normal diet. Se concentrations in crops and meat depend on the amount of labile Se in the soil where crops and forage are grown. Therefore, managing agriculture for optimal Se in grain crops and forage requires an understanding of the distribution and mobility of Se. Elevated concentrations of Se occur in waters, soils, and forage 120 km west of Pierre in west central South Dakota, USA. The research site lies in an elevated, dissected plain where soils developed on gently dipping Pierre Shale. Soils were sampled along catena transects and waters collected from soil, ponds, and shallow borings in areas of known elevated forage and crop Se. Soil extracts from saturated-paste extraction and acid (aqua regia and hydrofluoric acid) extraction were analyzed. Selenate was the dominant Se species in both acid and saturated-paste extracts; selenite and organic Se were below detection (<0.2 ppb) in the same soil extracts. On average, 98% of soil Se was not water-soluble. The distribution of total Se shows much less spatial variation than water-soluble Se in the areas sampled. Se shows correlation with organic carbon in soils and waters, suggesting its association with organic carbon. Ca shows some correlation to Se in acid extracts, but not in saturated-paste extracts or in waters. Total Se shows no significant correlation to Na, Mg, and total S in the soils. Se in saturated-paste extracts and water samples shows good correlations with Na, Mg, and SO₄, suggesting that evaporitic Na–Mg–sulfate minerals may temporarily concentrate water-soluble Se in shallow soils. The dissolution and precipitation of these Na–Mg–sulfate salts together with pH and oxidation–reduction conditions apparently control water-soluble Se distribution and mobilization in shallow subsurface environments.     

An autochthonous Avalonian basement source for the latest Ordovician Brenton Pluton in the Meguma terrane of Nova Scotia: U–Pb–Hf isotopic constraints and paleogeographic implications

International Journal of Earth Sciences - The Ediacaran–Ordovician Meguma Supergroup was thrust over Avalonia basement prior to the intrusion of post-Acadian, ca. 370&nbsp;Ma, S-type...     

Stochastic assessment of GPS carrier phase measurements for precise static relative positioning

 Global positioning system (GPS) carrier phase measurements are used in all precise static relative positioning applications. The GPS carrier phase measurements are generally processed using the least-squares method, for which both functional and stochastic models need to be carefully defined. Whilst the functional model for precise GPS positioning is well documented in the literature, realistic stochastic modelling for the GPS carrier phase measurements is still both a controversial topic and a difficult task to accomplish in practice. The common practice of assuming that the raw GPS measurements are statistically independent in space and time, and have the same accuracy, is certainly not realistic. Any mis-specification in the stochastic model will inevitably lead to unreliable positioning results. A stochastic assessment procedure has been developed to take into account the heteroscedastic, space- and time-correlated error structure of the GPS measurements. Test results indicate that the reliability of the estimated positioning results is improved by applying the developed stochastic assessment procedure. In addition, the quality of ambiguity resolution can be more realistically evaluated. Received: 13 February 2001 / Accepted: 3 September 2001     

Holocene changes in seasonal precipitation highlighted by fire incidence in eastern Canada

Postglacial fire history has been reconstructed for eastern Canada from charcoal-influx anomalies from 30 sites taken from a lacustrine charcoal database. The reconstruction exhibits coherent patterns of fire occurrence in space and time. The early Holocene is characterised by high fire incidence. There is a major change to much lower occurrence slightly after 8 ka BP. A return to more fire appears after 3 ka BP. This sequence does not fit with the hydro-climatic reconstruction deduced from lake level reconstructions for northeastern North America, which indicates a dry early and mid-Holocene, and a wet late-Holocene. Fire occurrence however closely matches summer relative humidity inferred from δ¹⁸O. The differences between fire frequency and lake level history, are due to changes in the seasonality of precipitation and drought frequency. Lake levels are essentially controlled by winter precipitation while summer precipitation controls fire occurrence. The early Holocene before 8–7.5 ka BP experienced dry summers due to higher solar radiation and dry adiabatic winds from the residual Laurentide Ice Sheet. The middle Holocene was dominated by wet summers due to stability of the Atlantic air mass over eastern Canada. After 2.5 ka BP, summers became drier, albeit not as fire-conducive as during the early Holocene. Late-Holocene summers conducive to fire are explained by more frequent incursions of dry Cool Pacific or Cold Arctic air masses over eastern Canada. Received: 25 January 1999 / Accepted: 14 December 1999     

Modeled Sverdrup flow in the North Atlantic from 11 different wind stress climatologies

In studies of large-scale ocean dynamics, often quoted values of Sverdrup transport are computed using the Hellerman–Rosenstein wind stress climatology. The Sverdrup solution varies, however, depending on the wind set used. We examine the differences in the large-scale upper ocean response to different surface momentum forcing fields for the North Atlantic Ocean by comparing the different Sverdrup interior/Munk western boundary layer solutions produced by a 1/16° linear numerical ocean model forced by 11 different wind stress climatologies. Significant differences in the results underscore the importance of careful selection of a wind set for Sverdrup transport calculation and for driving nonlinear models. This high-resolution modeling approach to solving the linear wind-driven ocean circulation problem is a convenient way to discern details of the Sverdrup flow and Munk western boundary layers in areas of complicated geometry such as the Caribbean and Bahamas. In addition, the linear solutions from a large number of wind sets provide a well-understood baseline oceanic response to wind stress forcing and thus, (1) insight into the dynamics of observed circulation features, by themselves and in conjunction with nonlinear models, and (2) insight into nonlinear model sensitivity to the choice of wind-forcing product.The wind stress products are evaluated and insight into the linear dynamics of specific ocean features is obtained by examining wind stress curl patterns in relation to the corresponding high-resolution linear solutions in conjunction with observational knowledge of the ocean circulation. In the Sverdrup/Munk solutions, the Gulf Stream pathway consists of two branches. One separates from the coast at the observed separation point, but penetrates due east in an unrealistic manner. The other, which overshoots the separation point at Cape Hatteras and continues to flow northward along the continental boundary, is required to balance the Sverdrup interior transport. A similar depiction of the Gulf Stream is commonly seen in the mean flow of nonlinear, eddy-resolving basin-scale models of the North Atlantic Ocean. An O(1) change from linear dynamics is required for realistic simulation of the Gulf Stream pathway. Nine of the eleven Sverdrup solutions have a C-shaped subtropical gyre, similar to what is seen in dynamic height contours derived from observations. Three mechanisms are identified that can contribute to this pattern in the Sverdrup transport contours. Along 27°N, several wind sets drive realistic total western boundary current transport (within 10% of observed) when a 14 Sv global thermohaline contribution is added (COADS, ECMWF 10 m re-analysis and operational, Hellerman–Rosenstein and National Centers for Environmental Prediction (NCEP) surface stress re-analysis), a few drive transport that is substantially too high (ECMWF 1000 mb re-analysis and operational and Isemer–Hasse) and Fleet Numerical Meteorology and Oceanography Center (FNMOC) surface stresses give linear transport that is slightly weaker than observed. However, higher order dynamics are required to explain the partitioning of this transport between the Florida Straits and just east of the Bahamas (minimal in the linear solutions vs. 5 Sv observed east of the Bahamas). Part of the Azores Current transport is explained by Sverdrup dynamics. So are the basic path of the North Atlantic Current (NAC) and the circulation features within the Intra-Americas Sea (IAS), when a linear rendition of the northward upper ocean return flow of the global thermohaline circulation is added in the form of a Munk western boundary layer.