An objective replacement method for censored geochemical data

Geochemical data are commonly censored, that is, concentrations for some samples are reported as less than or greater than some value. Censored data hampers statistical analysis because certain computational techniques used in statistical analysis require a complete set of uncensored data. We show that the simple substitution method for creating an uncensored dataset, e.g., replacement by3/4 times the detection limit, has serious flaws, and we present an objective method to determine the replacement value. Our basic premise is that the replacement value should equal the mean of the actual values represented by the qualified data. We adapt the maximum likelihood approach (Cohen, 1961) to estimate this mean. This method reproduces the mean and skewness as well or better than a simple substitution method using3/4 of the lower detection limit or3/4 of the upper detection limit. For a small proportion of less than substitutions, a simple-substitution replacement factor of 0.55 is preferable to3/4; for a small proportion of greater than substitutions, a simple-substitution replacement factor of 1.7 is preferable to4/3, provided the resulting replacement value does not exceed 100%. For more than 10% replacement, a mean empirical factor may be used. However, empirically determined simple-substitution replacement factors usually vary among different data sets and are less reliable with more replacements. Therefore, a maximum likelihood method is superior in general. Theoretical and empirical analyses show that true replacement factors for less thans decrease in magnitude with more replacements and larger standard deviation; those for greater thans increase in magnitude with more replacements and larger standard deviation. In contrast to any simple substitution method, the maximum likelihood method reproduces these variations. Using the maximum likelihood method for replacing less thans in our sample data set, correlation coefficients were reasonably accurately estimated in 90% of the cases for as much as 40% replacement and in 60% of the cases for 80% replacement. These results suggest that censored data can be utilized more than is commonly realized.     

Systematics of xenocrystic contamination: preservation of discrete feldspar populations at McCullough Pass Caldera revealed by Ar/Ar dating

Single crystal ⁴⁰Ar/³⁹Ar dating of K-feldspars from silicic volcanic rocks containing xenocrysts often yields a spectrum of ages slightly older than those of juvenile sanidine phenocrysts. In contrast, feldspars from thin, low-volume units of the Tertiary (14 Ma) McCullough Pass Tuff define discrete age populations at 14 Ma, 15 Ma, and 1.3 Ga, reflecting the time of eruption, xenocrysts from an older ignimbrite exposed in the caldera wall, and Proterozoic basement K-feldspars, respectively. Conductive cooling and diffusion modelling suggests preservation of such discrete populations is likely only when xenocrystic material is incorporated into the magma very near or at the surface, or is engulfed in thin, rapidly cooled pyroclastic flows during emplacement. Incorporation of xenocrysts into the subvolcanic magma chamber, into thick rhyolite domes or lava flows, or into large, welded ignimbrite sheets will result in partial or total resetting of the K/Ar isotopic system. Similarly, petrographic evidence such as exsolution lamellae may be homogenized under these conditions but not in thin ignimbrites. Extremely low diffusion rates for disordering of the Al–Si tetrahedral siting of basement feldspars suggests that they will retain their ordered structural state given rhyolitic magma temperatures. Thus, even when petrographic and K/Ar isotopic evidence for xenocrystic contamination is obscured, it may be preserved in the form of Al–Si ordering.     

Assessment Of A Groundwater Flow Model Of The Bangkok Basin,Thailand, Using Carbon-14-Based Ages And Paleohydrology

A study was undertaken to understand the groundwater flow conditions in the Bangkok Basin, Thailand, by comparing ¹⁴C-based and simulated groundwater ages. ¹⁴C measurements were made on about 50 water samples taken from wells throughout the basin. Simulated ages were obtained using 1) backward-pathline tracking based on the well locations, and 2) results from a three-dimensional groundwater flow model. Comparisons of ages at these locations reveal a large difference between ¹⁴C-based ages and ages predicted by the steady-state groundwater flow model. Mainly, ¹⁴C and ¹³C analyses indicate that groundwater in the Bangkok area is about 20,000 years old, whereas steady-state flow and transport simulations imply that groundwater in the Bangkok area is 50,000-100,000 years old. One potential reason for the discrepancy between simulated and ¹⁴C-based ages is the assumption in the model of steady-state flow. Groundwater velocities were probably greater in the region before about 10,000 years ago, during the last glacial maximum, because of the lower position of sea level and the absence of the surficial Bangkok Clay. Paleoflow conditions were estimated and then incorporated into a second set of simulations. The new assumption was that current steady-state flow conditions existed for the last 8,000 years but were preceded by steady-state conditions representative of flow during the last glacial maximum. This "transient" paleohydrologic simulation yielded a mean simulated age that more closely agrees with the mean ¹⁴C-based age, especially if the ¹⁴C-based age corrected for diffusion into clay layers. Although the uncertainties in both the simulated and ¹⁴C-based ages are nontrivial, the magnitude of the improved match in the mean age using a paleohydrologic simulation instead of a steady-state simulation suggests that flow conditions in the basin have changed significantly over the last 10,000-20,000 years. Given that the valid age range of ¹⁴C-dating methods and the timing of the last glacial maximum are of similar magnitude, adjustments for paleohydrologic conditions may be required for many such studies. RÉSUMÉ: Les conditions d'écoulement souterrain dans le bassin de Bangkok (Thaïlande) ont été étudieés en comparant les âges ¹⁴C mesurés et ceux simulés. Les âges mesurés ont été obtenus à partir d'environ 50 échantillons d'eau de puits dans tout le bassin. Les âges simulés proviennent 1) de la position des puits sur les lignes de flux, et 2) des résultats d'un modèle 3-D d'écoulement de nappe. La comparaison des âges aux positions des puits fait apparaître une grande différence entre les âges mesurés et les prédictions du modèle d'écoulement en régime permanent. Dans l'ensemble, les teneurs en ¹⁴C et en ¹³C indiquent que les eaux souterrains du bassin de Bangkok sont âgées d'environ 20 000 ans, alors que les simulations d'écoulement en régime permanent et de transport prédisent un âge compris entre 50 000 et 100 000 ans. Une raison probable du désaccord entre les âges simulés et ceux mesurés est due à l'hypothèse d'écoulement en régime permanent du modèle. Les vitesses d'écoulement souterrain ont probablement été plus fortes dans cette région jusqu'il y a 10 000 ans, lors du dernier maximum glaciaire, du fait de la position plus basse du niveau marin et de l'absence de la couverture par la formation argileuse de Bangkok. Les conditions des paléo-écoulements ont été estimées, puis introduites dans une seconde série de simulations. La nouvelle hypothèse supposait que les conditions actuelles d'écoulement en régime permanent ont existé au cours des 8 000 dernières années, et qu'elles ont été précédées par des conditions d'écoulement en régime permanent représentatives de l'écoulement au cours du dernier maximum glaciaire. La simulation paléohydrologique "transitoire" a donné un âge moyen simulé qui s'accorde mieux avec les âges ¹⁴C mesurés, particulièrement lorsque l'âge ¹⁴C est corrigé pour tenir compte de la diffusion au travers des niveaux argileux. Bien que les incertitudes sur les âges aussi bien simulés que mesurés ne soient pas négligeables, l'ordre de grandeur de l'âge moyen fourni par la simulation s'appuyant sur la paléohydrologie, au lieu de l'écoulement permanent, laisse supposer que les conditions d'écoulement dans le bassin ont nettement changé au cours des 10 000 à 20 000 dernières années. Etant donné que la gamme d'âges ¹⁴C et la durée du dernier maximum glaciaire sont du m{me ordre de grandeur, les ajustement pour les conditions paléohydrologiques peuvent être nécessaires pour nombre d'études de ce type. RESUMEN: Se llevó a cabo un estudio con el objetivo de caracterizar las condiciones del flujo de agua subterránea en la Cuenca de Bangkok, Tailandia, mediante la comparación entre las edades del agua basadas en medidas de ¹⁴C y las simuladas mediante un modelo. Las medidas de ¹⁴C se tomaron en cerca de 50 muestras de agua, en pozos repartidos por toda la cuenca. Las edades simuladas se obtuvieron utilizando 1) seguimiento de partículas a contracorriente, basado en la situación de los pozos, y 2) resultados de un modelo de flujo tridimensional. La comparación entre las edades en estos puntos revelan una gran diferencia entre las basadas en ¹⁴C y las predichas por el modelo de flujo estacionario. Fundamentalmente, los análisis de ¹⁴C y ¹³C indican que la edad del agua subterránea en el área de Bangkok es de alrededor de 20000 años, mientras que las simulaciones de flujo y transporte en condiciones estacionarias revelan una edad de 50000-100000 años. Una posible razón para la discrepancia entre estas dos edades es la hipótesis de flujo estacionario realizada en el modelo. Las velocidades del agua subterránea eran probablemente mayores en esta región anteriormente a los últimos 10000 años, durante el último máximo glaciar, que en la actualidad, debido a que el nivel del mar era menor y a la ausencia de la capa superficial de Arcilla de Bangkok. Por esta razón, se estimaron las condiciones de paleoflujo y se incorporaron a un segundo grupo de simulaciones. La nueva hipótesis era que las condiciones actuales de flujo se habían mantenido estacionarias durante los últimos 8000 años, pero que fueron precedidas por otras condiciones estacionarias representativas del flujo durante el último máximo glaciar. Esta simulación paleohidrológica "transitoria" da lugar a una edad media simulada que se ajusta mejor a la edad basada en ¹⁴C, especialmente si esta última edad se corrige por difusión hacia las capas de arcilla. Aunque las incertidumbres tanto en las edades simuladas con el modelo como en las basadas en ¹⁴C no son sencillas de evaluar, la magnitud de la mejora en el ajuste de la edad media que se produce al utilizar una simulación paleohidrológica en lugar de una estacionaria sugiere que las condiciones de flujo en la cuenca han cambiado significativamente en los últimos 10000-20000 años. Dado que el rango válido de los métodos de datación de ¹⁴C y que el tiempo transcurrido desde el último máximo glaciar son de magnitud similar, los ajustes debidos a condiciones paleohidrológicas serán necesarios para muchos de estudios como éste.     

Petrologic constraints on rift-zone processes

The Puu Oo eruption in the middle of Kilauea volcano's east rift zone provides an excellent opportunity to utilize petrologic constraints to interpret rift-zone processes. Emplacement of a dike began 24 hours before the start of the eruption on 3 January 1983. Seismic and geodetic evidence indicates that the dike collided with a magma body in the rift zone. Most of the lava produced during the initial episode of the Puu Oo eruption is of hybrid composition, with petrographic and geochemical evidence of mixing magmas of highly evllved and more mafic compositions. Some olivine and plagioclase grains in the hybrid lavas show reverse zoning. Whole-rock compositional variations are linear even for normally compatible elements like Ni and Cr. Leastsquares mixing calculations yield good residuals for major and trace element analyses for magma mixing. Crystal fractionation calculations yield unsatisfactory residuals. The highly evolved magma is similar in composition to the lava from the 1977 eruption and, at one point, vents for these two eruptions are only 200 m apart. Possibly both the 1977 lava and the highly evolved component of the episode 1 Puu Oo lava were derived from a common body of rift-zone-stored magma. The more mafic mixing component may be represented by the most mafic lava from the January 1983 eruption; it shows no evidence of magma mixing. The dike that was intruded just prior to the start of the Puu Oo eruption may have acted as a hydraulic plunger causing mixing of the two rift-zone-stored magmas.     

Influences of Wave Climate and Sea Level on Shoreline Erosion Rates in the Maryland Chesapeake Bay

We investigated spatial correlations between wave forcing, sea level fluctuations, and shoreline erosion in the Maryland Chesapeake Bay (CB), in an attempt to identify the most important relationships and their spatial patterns. We implemented the Simulating WAves Nearshore (SWAN) model and a parametric wave model from the USEPA Chesapeake Bay Program (CBP) to simulate wave climate in CB from 1985 to 2005. Calibrated sea level simulations from the CBP hydrodynamic model over the same time period were also acquired. The separate and joint statistics of waves and sea level were investigated for the entire CB. Spatial patterns of sea level during the high wave events most important for erosion were dominated by local north-south winds in the upper Bay and by remote coastal forcing in the lower Bay. We combined wave and sea level data sets with estimates of historical shoreline erosion rates and shoreline characteristics compiled by the State of Maryland at two different spatial resolutions to explore the factors affecting erosion. The results show that wave power is the most significant influence on erosion in the Maryland CB, but that many other local factors are also implicated. Marshy shorelines show a more homogeneous, approximately linear relationship between wave power and erosion rates, whereas bank shorelines are more complex. Marshy shorelines appear to erode faster than bank shorelines, for the same wave power and bank height. A new expression for the rate of shoreline erosion is proposed, building on previous work. The proposed new relationship expresses the mass rate of shoreline erosion as a locally linear function of the difference between applied wave power and a threshold wave power, multiplied by a structure function that depends on the ratio of water depth to bank height.     

Lateral circulation driven by boundary mixing and the associated transport of sediments in idealized partially mixed estuaries

A three-dimensional, hydrostatic, primitive equation numerical model with modern turbulence closures is used to explore lateral circulation and the associated transport of sediments in idealized, moderately to highly stratified estuaries. The model results suggest that boundary mixing on a sloping bottom can drive a significant amount of lateral circulation. This mechanism has received little attention to date in the estuarine literature. Good agreement with an analytical solution and similar vertical structures of lateral flows to observations from the Hudson River estuary support the importance of the boundary mixing mechanism. Boundary mixing is at least as important as differential advection for the modeled scenarios, when the two mechanisms are evaluated using the salt balance equation for model runs without rotation. Linearly superposing analytical solutions for lagged boundary mixing lateral flow and Ekman-forced lateral flow yields a good representation of the near-bottom lateral flow from the model with rotation. The 2 h lag required for the boundary mixing solution is roughly equal to the vertical diffusion time scale, indicating that lateral flow adjustment depends on development of a bottom mixed layer. Sediment dynamics at cross sections seaward and landward of the salt intrusion are very different. Seaward of the salt intrusion, sediments are eroded in the channel and preferentially deposited on the right slope (looking seaward), mainly due to the combination of high sediment concentration in the channel during flood with strong up-slope transport on that side (tidal pumping). Lateral sediment re-distribution landward of the salt intrusion is negligible due to weak residual lateral circulation.