Using an approximation of the three-point Gauss–Hermite quadrature formula for model prediction and quantification of uncertainty

 Computer models are commonly used by regulators and managers to make predictions regarding groundwater flow and contaminant concentrations at various locations and times. However, the uncertainty associated with those predictions is often overlooked, despite the fact that an assessment of such uncertainty is critical in the formulation of policy decisions. One method of quantifying the uncertainty of model predictions, based on the collective uncertainties of the model parameter input values, is to use an approximation of the three-point Gauss–Hermite quadrature formula. The Gauss–Hermite approximation is a convenient substitute for simple Monte Carlo sampling, because it requires fewer model runs and provides an immediate sensitivity analysis of parameter main effects and two-way interactions. For example, a model with four parameters, each with its own associated uncertainty, needs to be run only 33 times to complete the Gauss–Hermite analysis. For an application to a contaminant-transport model, the Gauss–Hermite approximation compares well to the full method, with considerable savings in computing effort. By comparison, Latin hypercube sampling can be more flexible, but it is more complex to use in some circumstances and cannot as easily generate the detailed sensitivity analysis that the Gauss–Hermite approach offers. Received, October 1997 Revised, August 1998 Accepted, August 1998     

Orbital Forcing and Endogenous Nonlinearity in the Pleistocene: The Greenland Ice Core

The succession of ice ages and interglacials during the Pleistocene is understood to have been caused primarily by shifts in the earth's orbit. At the same time, there is evidence of high variability in climate at suborbital frequencies. This paper conducts a statistical analysis of Pleistocene climate using the Greenland Ice Core Research Project (GRIP) data. Factoring temperature into the component explained by orbital forcing and a residual demonstrates that variations at suborbital frequencies are nonlinear and aperiodic. There is evidence of a regular cycle at 7.9 kyr, evidently a subharmonic of the orbital frequencies. Apart from this, however, the proximate memory of both the actual data and the residual decays slowly over a period of 15 kyr. Residual variations in temperature show two prominent features, alternating periods of high and low volatility, and states of distance from and proximity to the path implied by orbital forcing. A parametric model incorporating both of these properties is fit to the data, and is found to significantly improve the forecastability of climate. Transitions between states of proximity and distance from the orbital path can be partially predicted using the statistical model.     

The hydrous phase equilibria (to 3 kbar) of an andesite and basaltic andesite from western Mexico: constraints on water content and conditions of phenocryst growth

We have conducted high pressure (to 3 kbar), water saturated melting experiments on an andesite (62 wt% SiO₂) and a basaltic andesite (55 wt% SiO₂) from western Mexico. A close comparison between the experimental phase assemblages and their compositions, and the phenocryst assemblages of the lavas, is found in water saturated liquids, suggesting that the CO₂ content was minimal in the fluid phase. Thus the historic lavas from Volcan Colima (with phenocrysts of orthopyroxene, augite, plagioclase, and hornblende) were stored at a temperature between 950–975 °C, at a pressure between 700–1500 bars, and with a water content of 3.0–5.0 wt%. A hornblende andesite (spessartite) from Mascota, of nearly identical composition but with only amphibole phenocrysts, had a similar temperature but equilibrated at a minimum of 2000 bars pressure with a dissolved water content of at least 5.5 wt% in the liquid. Experiments on the basaltic andesite show that the most common natural phenocryst assemblages (olivine, ±augite, ±plagioclase) could have precipitated at temperatures from 1000–1150 °C, in liquids with a wide range of dissolved water content (∼2.0–6.0 wt%) and a corresponding pressure range. A lava of the same bulk composition with phenocrysts of hornblende, olivine, plagioclase, and augite is restricted to temperatures below 1000 °C and pressures below 2500 bars, corresponding to <5.5 wt% water in the residual liquid. Although there is some evidence for mixing in the andesites (sporadic olivine phenocrysts), the broad theme of the history of both lava types is that the phenocryst assemblages for both the andesitic magmas and basaltic andesitic magmas are generated from degassing and reequilibration on ascent of initially hydrous parents containing greater than 6 wt% water. Indeed andesitic magmas could be related to a basaltic andesite parent by hornblende-plagioclase fractionation under the same hydrous conditions. Received: 10 December 1996 / Accepted: 21 August 1997     

Warm-Season Annual to Decadal Temperature Variability for Hokkaido, Japan, Inferred from Maximum Latewood Density and Ring Width Data

We present a warm season (April–September) temperature reconstructionfor Asahikawa, north central Hokkaido, Japan for AD 1557–1990. The reconstruction, which accounts for 34% of the temperature variancefrom 1925–1990, is based on maximum latewood density data from Saghalinspruce (Picea glehnii) growing at timberline (1340–1390 m) at MountAsahidake, Hokkaido. We only present a high frequency (prewhitened or white noise) version of the reconstruction because there is an unexplained offset in the mean between the actual and estimated temperature data for an earlier period of overlap from 1891–1924. The coldest summer in the reconstruction is 1718, forwhich the estimated value is 12.89 ° C, nearly four standard deviations (SD) below the mean. A colder-than-average year is reconstructed for 1641 (13.30° C, nearly 3 SD below mean), following the eruption of Komagatake, Hokkaido which began in July, 1640. The Asahikawa density chronology, shows decadal modes of variation with statistically significant spectral peaks prior to around 1850. A tree-ring width chronology for this same site (AD 1532–1990) is in phase with a tree-ring width record from centralKamchatka prior to around 1850, but out of phase since that time. This pattern suggests, as has been hypothesized for temperature-sensitive tree-ring records from the eastern Pacific sector (Alaska and Patagonia), that a decadal mode of climate variation was more dominant in the Pacific sector prior to about 1850, after which a higher frequency (ENSO-type) mode may have become more pronounced, at least until recent decades. Additional data from the northwestern Pacific is needed to compare to these findings.     

In situ determination of long-term basaltic glass dissolution in the unsaturated zone

Maximum in situ weathering rates of basaltic glass measured at the El Malpais National Monument in New Mexico are on the order of 2–5×10⁻¹⁹ mol/cm² s. Rates were calculated from backscattered electron (BSE) imaging of weathered porosity and are equivalent to 1.7–5% of the surface per 1000 years. Weathering is independent of glass composition but appears to increase with flow elevation at El Malpais. Measured rates represent weathering over 3000 years and are substantially lower than glass dissolution rates measured in the laboratory over much shorter time spans. Basaltic glass is a close chemical analogue to glass hosts proposed for encapsulation of high-level nuclear wastes. Radionuclide release rates predicted from the basis of in situ field rates are substantially less than those predicted from short-term laboratory experiments.     

Structure of mineral glasses—I. The feldspar glasses NaAlSi3O8, KAlSi3O8, CaAl2Si2O8

The short range distribution of interatomic distances in three feldspar glasses has been determined by X-ray radial distribution analysis. The resulting radial distribution functions (RDF's) are interpreted by comparison with RDF's calculated for various quasi-crystalline models of the glass structure.The experimental RDF's of the alkali feldspar glasses were found to be inconsistent with the four-membered rings of tetrahedra associated with crystalline feldspars; the structures of these glasses are probably based on interconnected six-membered rings of the type found in tridymite, nepheline, or kalsilite. In contrast, the RDF of calcic feldspar glass is consistent with a four-membered ring structure of the type found in crystalline anorthite. T-O bond lengths (T = Si,Al) increase from 1.60 Å in SiO₂ glass [J. H. Konnert and J. Karle (1973) Acta Cryst.A29, 702–710] to 1.63 Å in the alkali feldspar glasses to 1.66 Å in the calcic feldspar glass due to the substitution of Al for Si in the tetrahedra] sites. The T-O-T bond angles inferred from the RDF peak positions are 151° in SiO₂ glass (see reference above), 146° in the alkali feldspar glasses, and 143° in the calcic feldspar glass. Detail in the RDF at distances greater than 5 Å suggests that the alkali feldspar glasses have a higher degree of long range order than the calcic feldspar glasses.Assuming that the structural details of our feldspar glasses are similar to those of the melts, the observed structural differences between the alkali feldspar and calcic feldspar glasses helps explain the differences in crystallization kinetics of anhydrous feldspar composition melts. Structural interpretations of some thermodynamic and rheologic phenomena associated with feldspar melts are also presented based on these results.     

Occurrence ofSpartina macrodetritus in Bay of Fundy waters

Suspended macrodetritus (>600 μm) from extensiveSpartina alterniflora marshes is widespread in the Cumberland Basin region of the macrotidal upper Bay of Fundy. The average concentration is about 5 mg C per m³ and most is found in the lower two-thirds of the water column. The total amount in the Basin at high tide is approximately 8 metric tonnes of organic carbon which is less than 1% of the annual net aerial primary production of the fringingS. alterniflora marshes. The high visibility ofSpartina detritus in Cumberland Basin is caused by the extreme tides (average tidal range about 11 m) which export marsh vegetation and distribute it widely about the estuary, and by the pronounced turbidity which has been shown to limit phytoplankton growth.     

Activity of Hawaiian Volcanoes during the years 1940–1950

Summit eruptions of Mauna Loa, on the Island of Hawaii, occurred in 1940 and 1949, and flank eruptions in 1942 and 1950. Lava poured out in 1940 and 1942 was about equal in amount, totaling approximately 76 million cubic meters in each eruption. The 1949 eruption was somewhat smaller, liberating approximately 59 million cubic meters. The 1950 eruption was one of the largest on record, producing five large lava flows and several smaller ones, totaling approximately 459 million cubic meters. Three of the 1950 flows entered the sea. In 1942 a lava flow threatened the city of Hilo, and was bombed from the air in an effort to divert it. Calculations indicate that the gas content of the lava extruded during the 1940 eruption probably was in the vicinity of one percent by weight of the total magma. Other calculations indicate the viscosity of fluid Hawaiian lava to be in the range of 10³ to 10⁵ poises. Temperature readings on the 1950 lava ranged from 1090⁰ to 900⁰ C. Kilauea Volcano showed signs of uneasiness in 1944, with an apparent increase of magmatic pressure indicated by outward tilting of the moutain flanks and a series of earthquakes progressing toward the surface. In December 1950 a series of earthquakes accompanied a subsidence of the summit of Kilauea Volcano.