Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow

We present a locally mass conservative scheme for the approximation of two-phase flow in a porous medium that allows us to obtain detailed fine scale solutions on relatively coarse meshes. The permeability is assumed to be resolvable on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We define a two-scale mixed finite element space and resulting method, and describe in detail the solution algorithm. It involves a coarse scale operator coupled to a subgrid scale operator localized in space to each coarse grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid scale problems independently of the coarse grid approximation. The coarse grid problem is modified to take into account the subgrid scale solution and solved as a large linear system of equations posed over a coarse grid. Finally, the coarse scale solution is corrected on the subgrid scale, providing a fine grid representation of the solution. Numerical examples are presented, which show that near-well behavior and even extremely heterogeneous permeability barriers and streaks are upscaled well by the technique.     

Postshield volcanism and catastrophic mass wasting of the Waianae Volcano, Oahu, Hawaii

 The 3.9- to 2.9-Ma Waianae Volcano is the older of two volcanoes making up the island of Oahu, Hawaii. Exposed on the volcanic edifice are tholeiitic shield lavas overlain by transitional and alkalic postshield lavas. The postshield "alkalic cap" consists of aphyric hawaiite of the Palehua Member of the Waianae Volcanics, overlain unconformably by a small volume of alkalic basalt of the Kolekole Volcanics. Kolekole Volcanics mantle erosional topography, including the uppermost slopes of the great Lualualei Valley on the lee side of the Waianae Range. Twenty new K–Ar dates, combined with magnetic polarity data and geologic relationships, constrain the ages of lavas of the Palehua member to 3.06–2.98 Ma and lavas of the Kolekole Volcanics to 2.97–2.90 Ma. The geochemical data and the nearly contemporaneous ages suggest that the Kolekole Volcanics do not represent a completely independent or separate volcanic event from earlier postshield activity; thus, the Kolekole Volcanics are reduced in rank, becoming the Kolekole Member of the Waianae Volcanics. Magmas of the Palehua and Kolekole Members have similar incompatible element ratios, and both suites show evidence for early crystallization of clinopyroxene consistent with evolution at high pressures below the edifice. However, lavas of the Kolekole Member are less fractionated and appear to have evolved at greater depths than the earlier Palehua hawaiites. Postshield primary magma compositions of the Palehua and Kolekole Members are consistent with formation by partial melting of mantle material of less than 5–10% relative to Waianae shield lavas. Within the section of Palehua Member lavas, an increase with respect to time of highly incompatible to moderately incompatible element ratios is consistent with a further decrease in partial melting by approximately 1–2%. This trend is reversed with the onset of eruption of Kolekole Member lavas, where an increase in extent of partial melting is indicated. The relatively short time interval between the eruption of Palehua and Kolekole Member lavas appears to date the initial formation of Lualualei Valley, which was accompanied by a marked change in magmatic conditions. We speculate that the mass-wasting event separating lavas of the Palehua and Kolekole Members may be related to the formation of a large submarine landslide west and southwest of Waianae Volcano. Enhanced decompression melting associated with removal of the equivalent volume of this landslide deposit from the edifice is more than sufficient to produce the modeled increase of 1–2% in extent of melting between the youngest Palehua magmas and the posterosional magmas of the Kolekole Member. The association between magmatic change and a giant landsliding event suggests that there may be a general relationship between large mass-wasting events and subsequent magmatism in Hawaiian volcano evolution. Received: 1 September 1996 / Accepted: 26 November 1996     

A review of inlet bypassing solutions with nomographs

Bypassing of the coastal sediment at inlets is required to prevent downdrift erosion or the filling in of navigation channels. When coastal structures such as jetties or terminal groins are placed along the inlet boundaries, bypassing is reduced but not eliminated. Bypassing solutions such as Pelnard-Considere (1956) [Pelnard-Considere, R., 1956. Essai de Theorie de l'Evolution des Forms de Rivages en Plage de Sable et de Galets, Fourth Journess de l'Hydralique, les energies de la Mer, Question III, Rapport No. 1, pp. 289–298.] are known although the effect of existing background erosion on such bypassing is not so well known. The occurrence of existing erosion due to offshore sand loss complicates the bypassing situation. The following note reviews existing analytical bypassing solutions and presents a solution and nomograms for solving a bypassed amount when existing erosion occurs along a shoreline and the sand which bypasses the updrift structure is assumed to reach the downdrift shoreline without being trapped in shoals or inlet channel.     

Defining probability of saturation with indicator kriging on hard and soft data

In humid, well-vegetated areas, such as in the northeastern US, runoff is most commonly generated from relatively small portions of the landscape becoming completely saturated, however, little is known about the spatial and temporal behavior of these saturated regions. Indicator kriging provides a way to use traditional water table data to quantify probability of saturation to evaluate predicted spatial distributions of runoff generation risk, especially for the new generation of water quality models incorporating saturation excess runoff theory. When spatial measurements of a variable are transformed to binary indicators (i.e., 1 if above a given threshold value and 0 if below) and the resulting indicator semivariogram is modeled, indicator kriging produces the probability of the measured variable to exceed the threshold value. Indicator kriging gives quantified probability of saturation or, consistent with saturation excess runoff theory, runoff generation risk with depth to water table as the variable and the threshold set near the soil surface. The probability of saturation for a 120 m × 180 m hillslope based upon 43 measurements of depth to water table is investigated with indicator semivariograms for six storm events. The indicator semivariograms show high spatial structure in saturated regions with large antecedent rainfall conditions. The temporal structure of the data is used to generate interpolated (soft) data to supplement measured (hard) data. This improved the spatial structure of the indicator semivariograms for lower antecedent rainfall conditions. Probability of saturation was evaluated through indicator kriging incorporating soft data showing, based on this preliminary study, highly connected regions of saturation as expected for the wet season (April through May) in the Catskill Mountain region of New York State. Supplementation of hard data with soft data incorporates physical hydrology of the hillslope to capture significant patterns not available when using hard data alone for indicator kriging. With the need for water quality models incorporating appropriate runoff generation risk estimates on the rise, this manner of data will lay the groundwork for future model evaluation and development.     

Underground Storage Tank Monitoring: Observation Well Based Systems

A growing number of state and local governments and petroleum-related companies require the use of release detection systems for underground petroleum storage tanks. This has resulted in a confusing array of commercially available petroleum product detection devices, many of which have not been extensively field-tested. These systems, which are installed in ground water observation wells, vapor wells or U-tubes, include hydrocarbon-detecting paste, bailers, interface probes, electrical resistivity sensors, thermal-conductivity sensors, hydrocarbon-soluble devices, hydrocarbon-permeable materials and vapor detectors. This paper describes the available state-of-the-art technology for leak detection and the application for which each system is best suited.     

The extension of the magnetic time scale in sediments of the Central Pacific Ocean

The extension of the magnetic reversal record back to the early Miocene is presented. This record is pieced together with the aid of microfloral analysis from three low sedimentation rate siliceous deep sea cores from the Equatorial Pacific.Nineteen Magnetic Epochs are now recognized from the earliest Miocene to the Present. By correlating the micropaleontological data in our cores with selected foraminiferal datums from DSDP Leg IX we correlate these datums with the following magnetic epochs: the Pulleniatina Datum occurs in the lower part of Epoch 5, the G. acostaensis Datum occurs in Epoch 11, the G. nepenthes Datum occurs in Epoch 12, the Orbulina Datum at the Epoch 15/16 boundary and the G. dissimilis Datum in the lower part of Epoch 16. The Early/Middle Miocene boundary (Orbulina Datum) is tentatively placed at the top of Epoch 16.     

Microhabitat influences on stream insect emergence

Understanding the factors controlling insect emergence from streams has applications to ecological theory regarding cross-boundary flux, along with practical value for monitoring stream function after restoration projects. We hypothesized that stream microhabitat would have effects on emergence that were independent of those mediated by the local stock of benthic macroinvertebrates. We set 50 emergence traps in a third-order stream in northern Minnesota, USA, during two study periods and used structural equation modeling to examine direct and indirect effects of benthic stock and microhabitat features on emergence. Emergence by biomass showed direct positive relationships to substrates of fines and detritus in the first sampling period, and to shallow depth and wood area in the second period. Emergence by abundance had direct positive relationships with benthic stock, CPOM, and fewer macrophytes in the first period, and with benthic stock and periphyton in the second period. Fine substrates may act to concentrate burrowing larvae, whereas CPOM and particularly wood may intercept drifting pre-emergent insects and provide exiting surfaces. Shallow depths may reduce the extent to which resident insects drift downstream (and leave the sample area) while emerging. Periphyton may be an indicator for patches with greater illumination, which itself attracts emergers. Our results suggest emergence is sensitive to environmental conditions at the microhabitat scale, and that stream restoration activities should consider habitat for emerging insects when designing projects.