A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow

We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical and numerical aspects of surface–subsurface flow modeling are presented. This work was supported by National Science Foundation grant DMS-0411413.     

Holocene lake-level fluctuations and beach-ridge development along the northern shore of Lake Michigan, USA

Geomorphology of a beach-ridge complex and adjacent lake basins along the northern shore of Lake Michigan records fluctuations in the level of Lake Michigan for the last 8000 to 10 000 ¹⁴C yr B.P. (radiocarbon years Before Present). A storm berm at 204.7–206 m (671.6–675.9 ft) exposed in a sandpit provides evidence of a pre-Chippewa Low lake level that is correlated with dropping water levels of Glacial Lake Algonquin (c. 10 300–10 100 ¹⁴C yr B.P.). Radiocarbon dates from organic material exposed in a river cutbank and basal sediments from Elbow Lake, Mackinac Co., Michigan, indicate a maximum age of a highstand of Lake Michigan at 6900 ¹⁴C yr B.P., which reached as high as 196.7 m (645 ft), during the early-Nipissing transgression of Lake Michigan. Basal radiocarbon dates from beach swales and a second lake site (Beaverhouse Lake, Mackinac Co.) provide geomorphic evidence for a subsequent highstand which reached 192.6 m (632 ft) at 5390±70 ¹⁴C yr B.P.Basal radiocarbon dates from a transect of sediment cores, along with tree-ring data, and General Land Office Surveyor notes of a shipwreck, c. A.D. 1846, reveal a late-Holocene rate for isostatic rebound of 22.6 cm/100 radiocarbon years (0.74 ft/100 radiocarbon years) for the northern shore of Lake Michigan, relative to the Lake Michigan-Lake Huron outlet at Port Huron, Michigan. Changes in sediment stratigraphy, inter-ridge distance, and sediment accumulation rates document a mid- to late-Holocene retreat of the shoreline due to isostatic rebound. This regression sequence was punctuated by brief, periodic highstands, resulting in progressive development over the past 5400 ¹⁴C yr of 75 pairs of dune ridges and swales each formed over an interval of approximately 72 years. Times of lake-level fluctuation were identified at 3900, 3200, and 1000 ¹⁴C yr B.P. based on changes in inter-ridge spacing, shifts in the course of Millecoquins River, and reorientation of beach-ridge lineation. Soil type, dune development, and selected pollen data provide supporting evidence for this chronology. Late-Holocene beach-ridge development and lake-level fluctuations are related to a retreat of the dominant Pacific airmass and the convergence of the Arctic and Tropical airmasses resulting in predominantly meridional rather than zonal air flow across the Great Lakes region.This is the 13th in a series of papers published in this special AMQUA issue. These papers were presented at the 1994 meeting of the American Quaternary Association held 19–22 June, 1994, at the University of Minnesota, Minneapolis, Minnesota, USA. Dr Linda C. K. Shane served as guest editor for these papers.     

Planning for Tsunami-Resilient Communities

The National Tsunami Hazard Mitigation Program (NTHMP) Steering Committee consists of representatives from the National Oceanic and Atmospheric Administration (NOAA), the Federal Emergency Management Agency (FEMA), the U.S. Geological Survey (USGS), and the states of Alaska, California, Hawaii, Oregon, and Washington. The program addresses three major components: hazard assessment, warning guidance, and mitigation. The first two components, hazard assessment and warning guidance, are led by physical scientists who, using research and modeling methods, develop products that allow communities to identify their tsunami hazard areas and receive more accurate and timely warning information. The third component, mitigation, is led by the emergency managers who use their experience and networks to translate science and technology into user-friendly planning and education products. Mitigation activities focus on assisting federal, state, and local officials who must plan for and respond to disasters, and for the public that is deeply affected by the impacts of both the disaster and the pre-event planning efforts. The division between the three components softened as NTHMP scientists and emergency managers worked together to develop the best possible products for the users given the best available science, technology, and planning methods using available funds.     

Application of the Kalman filter to light curves of eclipsing binaries

Recently Kopal (1975a, b, c, d) initiated a new approach to the analysis of the light curves of eclipsing binary systems in which the solution is based on transforming the problem from the conventional time-domain into the frequency-domain. Irrespective of the type of eclipse, the present formulation of the frequency approach requires that a set of quantitiesA _2m, called moments, be determined from the observations.It is the purpose of the present paper to describe a data interpolation and smoothing technique based on a version of the Kalman filter to pre-process observations and to determine the quantitiesA _2m in an optimal sense.     

Use of Rhodamine water tracer in the marshland upwelling system

Rhodamine water tracer (RWT) was used to characterize the migration of waste water within the saline subsurface of a marshland upwelling system (MUS), which is an alternative on-site waste water treatment system for coastal areas. Field tracer studies were performed to investigate the fresh waste water plume movement within the saline ground water. Pore velocities were calculated using first detection times and ranged from 0.68 to 10.7 x 10(-4) cm/sec for the loamy sandy soil matrix present at the site. Use of RWT in the field also allowed determination of main and preferential flowpaths. One- and two-dimensional laboratory experiments were performed using silica sand to investigate the interactions of the organically rich waste water with RWT within the zone surrounding the point of injection (one-dimensional) and the impact of background salinity on plume movement (two-dimensional). The results from these studies were used to help explain the field data. One-dimensional breakthrough curves revealed retardation factors for the RWT in the waste water mixture of 1.73 to 1.90. These results were similar to other researchers, indicating little interaction between the waste water and RWT. Variations in pore water salinity (5, 15, 25, and 35 ppt) were found to have a significant effect on pore water velocities of the fresh water plume (two-dimensional), indicating the need to incorporate background salinities into the design process for MUS.     

Reservoir construction from the Newberry Volcano EGS Demonstration

The Newberry Volcano EGS Demonstration in central Oregon tests recent technological advances designed to reduce the cost of power generated by EGS in a hot, dry well (NWG 55-29) drilled in 2008. An EGS reservoir was created by injecting large volumes of cold water, causing existing fractures to slip in shear (known as hydroshearing) generating the seismic waves that can be used to map fracture location and size. At the Newberry Demonstration the final injectivity ranged between 1.4 and 1.7 L/s/MPa a ~6x improvement over the initial injectivity of the well. The injectivity improvement and seismic analysis indicate that previously impermeable fractures were enhanced during the NWG 55-29 stimulation.     

Climate change links fate of glaciers and an endemic alpine invertebrate

Climate warming in the mid- to high-latitudes and high-elevation mountainous regions is occurring more rapidly than anywhere else on Earth, causing extensive loss of glaciers and snowpack. However, little is known about the effects of climate change on alpine stream biota, especially invertebrates. Here, we show a strong linkage between regional climate change and the fundamental niche of a rare aquatic invertebrate—the meltwater stonefly Lednia tumana—endemic to Waterton-Glacier International Peace Park, Canada and USA. L. tumana has been petitioned for listing under the U.S. Endangered Species Act due to climate-change-induced glacier loss, yet little is known on specifically how climate impacts may threaten this rare species and many other enigmatic alpine aquatic species worldwide. During 14 years of research, we documented that L. tumana inhabits a narrow distribution, restricted to short sections (~500 m) of cold, alpine streams directly below glaciers, permanent snowfields, and springs. Our simulation models suggest that climate change threatens the potential future distribution of these sensitive habitats and the persistence of L. tumana through the loss of glaciers and snowfields. Mountaintop aquatic invertebrates are ideal early warning indicators of climate warming in mountain ecosystems. Research on alpine invertebrates is urgently needed to avoid extinctions and ecosystem change.     

Discontinuous Galerkin methods for modeling Hurricane storm surge

Storm surge due to hurricanes and tropical storms can result in significant loss of life, property damage, and long-term damage to coastal ecosystems and landscapes. Computer modeling of storm surge can be used for two primary purposes: forecasting of surge as storms approach land for emergency planning and evacuation of coastal populations, and hindcasting of storms for determining risk, development of mitigation strategies, coastal restoration and sustainability.Storm surge is modeled using the shallow water equations, coupled with wind forcing and in some events, models of wave energy. In this paper, we will describe a depth-averaged (2D) model of circulation in spherical coordinates. Tides, riverine forcing, atmospheric pressure, bottom friction, the Coriolis effect and wind stress are all important for characterizing the inundation due to surge. The problem is inherently multi-scale, both in space and time. To model these problems accurately requires significant investments in acquiring high-fidelity input (bathymetry, bottom friction characteristics, land cover data, river flow rates, levees, raised roads and railways, etc.), accurate discretization of the computational domain using unstructured finite element meshes, and numerical methods capable of capturing highly advective flows, wetting and drying, and multi-scale features of the solution.The discontinuous Galerkin (DG) method appears to allow for many of the features necessary to accurately capture storm surge physics. The DG method was developed for modeling shocks and advection-dominated flows on unstructured finite element meshes. It easily allows for adaptivity in both mesh (h) and polynomial order (p) for capturing multi-scale spatial events. Mass conservative wetting and drying algorithms can be formulated within the DG method.In this paper, we will describe the application of the DG method to hurricane storm surge. We discuss the general formulation, and new features which have been added to the model to better capture surge in complex coastal environments. These features include modifications to the method to handle spherical coordinates and maintain still flows, improvements in the stability post-processing (i.e. slope-limiting), and the modeling of internal barriers for capturing overtopping of levees and other structures. We will focus on applications of the model to recent events in the Gulf of Mexico, including Hurricane Ike.