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.     

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.     

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.     

A century of climate and ecosystem change in Western Montana: what do temperature trends portend?

The physical science linking human-induced increases in greenhouse gasses to the warming of the global climate system is well established, but the implications of this warming for ecosystem processes and services at regional scales is still poorly understood. Thus, the objectives of this work were to: (1) describe rates of change in temperature averages and extremes for western Montana, a region containing sensitive resources and ecosystems, (2) investigate associations between Montana temperature change to hemispheric and global temperature change, (3) provide climate analysis tools for land and resource managers responsible for researching and maintaining renewable resources, habitat, and threatened/endangered species and (4) integrate our findings into a more general assessment of climate impacts on ecosystem processes and services over the past century. Over 100 years of daily and monthly temperature data collected in western Montana, USA are analyzed for long-term changes in seasonal averages and daily extremes. In particular, variability and trends in temperature above or below ecologically and socially meaningful thresholds within this region (e.g., ?17.8°C (0°F), 0°C (32°F), and 32.2°C (90°F)) are assessed. The daily temperature time series reveal extremely cold days (≤??17.8°C) terminate on average 20 days earlier and decline in number, whereas extremely hot days (≥32°C) show a three-fold increase in number and a 24-day increase in seasonal window during which they occur. Results show that regionally important thresholds have been exceeded, the most recent of which include the timing and number of the 0°C freeze/thaw temperatures during spring and fall. Finally, we close with a discussion on the implications for Montana’s ecosystems. Special attention is given to critical processes that respond non-linearly as temperatures exceed critical thresholds, and have positive feedbacks that amplify the changes.     

A parallel, implicit, cell‐centered method for two‐phase flow with a preconditioned Newton–Krylov solver

A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective.     

The representer method for two-phase flow in porous media

The representer method is applied to a one-dimensional two-phase flow model in porous media; capillary pressure and gravity are neglected. The Euler–Lagrange equations must be linearized, and one such linearization is presented here. The representer method is applied to the linear system iteratively until convergence, though a rigorous proof of convergence is out of reach. The linearization chosen is easy to calculate but does not converge for certain weights; however, a simple damping restores convergence at the cost of extra iterations. Numerical experiments are performed that illustrate the method, and quick comparison to the ensemble Kalman smoother is made. This research was supported by NSF grant EIA-0121523.