Results for “Mathematical and Computer Modelling” — Page 8

USGS2002

SUTRA: A model for 2D or 3D saturated-unsaturated, variable-density ground-water flow with solute or energy transport

SUTRA (Saturated-Unsaturated Transport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. This upgraded version of SUTRA adds the capability for three-dimensional simulation to the former code (Voss, 1984), which allowed only two-dimensional simulation. The code employs a two- or three-dimensional finite-element and finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated: 1) fluid density-dependent saturated or unsaturated ground-water flow; and 2) either (a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay; or (b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA may also be used to simulate simpler subsets of the above processes. A flow-direction-dependent dispersion process for anisotropic media is also provided by the code and is introduced in this report. As the primary calculated result, SUTRA provides fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA flow simulation may be employed for two-dimensional (2D) areal, cross sectional and three-dimensional (3D) modeling of saturated ground-water flow systems, and for cross sectional and 3D modeling of unsaturated zone flow. Solute-transport simulation using SUTRA may be employed to model natural or man-induced chemical-species transport including processes of solute sorption, production, and decay. For example, it may be applied to analyze ground-water contaminant transport problems and aquifer restoration designs. In addition, solute-transport simulation with SUTRA may be used for modeling of variable-density leachate movement, and for cross sectional modeling of saltwater intrusion in aquifers at near-well or regional scales, with either dispersed or relatively sharp transition zones between freshwater and saltwater. SUTRA energy-transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal-energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems. Mesh construction, which is quite flexible for arbitrary geometries, employs quadrilateral finite elements in 2D Cartesian or radial-cylindrical coordinate systems, and hexahedral finite elements in 3D systems. 3D meshes are currently restricted to be logically rectangular; in other words, they are similar to deformable finite-difference-style grids. Permeabilities may be anisotropic and may vary in both direction and magnitude throughout the system, as may most other aquifer and fluid properties. Boundary conditions, sources and sinks may be time dependent. A number of input data checks are made to verify the input data set. An option is available for storing intermediate results and restarting a simulation at the intermediate time. Output options include fluid velocities, fluid mass and solute mass or energy budgets, and time-varying observations at points in the system. Both the mathematical basis for SUTRA and the program structure are highly general, and are modularized to allow for straightforward addition of new methods or processes to the simulation. The FORTRAN-90 coding stresses clarity and modularity rather than efficiency, providing easy access for later modifications.

Water-Resources Investigations Report↗

USGS2007

Yellowstone grizzly bear investigations: Annual report of the Interagency Grizzly Bear Study Team, 2006

The contents of this Annual Report summarize results of monitoring and research from the 2006 field season. The report also contains a summary of nuisance grizzly bear ( Ursus arctos horribilis ) management actions. The Interagency Grizzly Bear Study Team (IGBST) continues to work on issues associated with counts of unduplicated females with cubs-of- the-year (COY). These counts are used to establish a minimum population size, which is then used to establish mortality thresholds for the Recovery Plan (U.S. Fish and Wildlife Service [USFWS] 1993). After considerable delays due to programming issues, a computer program that defines the rule set used by Knight et al. (1995) to differentiate unique family groups was development and tested in 2005 and 2006. Simulations using observations of collared females with COY were randomly sampled to generate datasets of observations of random females with COY. These datasets were then run though the simulations program to test the accuracy of the rules. Data are currently being summarized. This project has been completed and a manuscript was submitted to the Journal of Wildlife Management. The grizzly bear recovery plan (USFWS 1993) established human-caused mortality quotas. We used the latest information on reproduction and survival to estimate population trajectory in the same simulation model originally used by Harris (1984). A Wildlife Monographs was published in 2006. Additionally, the study team, in cooperation with several quantitative experts, reassessed how population size is indexed and how sustainable mortality rates are established. A draft report was presented to the Yellowstone Ecosystem Subcommittee in spring 2005. It was published as part of the USFWS Delisting Rule (Federal Register Vol. 70, No. 221, Nov. 17, 2005, 69853–69884) and subjected to public comment. This workshop document can be found at http://www.fws.gov/mountain-prairie/species/mammals/grizzly/yellowstone.htm. During the summer of 2006, a second workshop was held to address public comment and professional peer review. The result of this workshop was a supplement to the 2005 workshop document. This supplement can be found at http://www.fws.gov/mountain-prairie/species/mammals/grizzly/yellowstone.htm under the link Revised Methods to Estimate Population Size and Sustainable Mortality Limits. Results of those estimates are provided in Appendix A. Our project addressing the potential application of stable isotopes and trace elements to quantify consumption rates of whitebark pine ( Pinus albicaulis ) and cutthroat trout ( Oncorhynchus clarki ) by grizzly bears was completed. Our manuscript on consumption rates of whitebark pine was published in the Canadian Journal of Zoology 81:763-770. Results of the mercury studies were also published in the Canadian Journal of Zoology 82:493–501. Copies can be found on the IGBST website http://www.nrmsc.usgs.gov/research/igbst-home.htm. Based upon this work, we submitted a proposal to analyze all historic tissue samples from grizzly bears in the ecosystem. That proposal was funded and samples have been sent to a lab for isotopic analysis. We hope to have those results in early 2008. Results of DNA hair snaring work conducted on Yellowstone Lake were submitted and published in the Journal Ursus (Haroldson et al. 2005). Results of this study conducted from 1997–2000 showed a decline in fish use by grizzly bears when compared to earlier work conducted by Reinhart (1990) in 1985–1987. As a consequence, the IGBST submitted a proposal to the National Park Service and received 3 years funding to repeat that work. This project began in 2007. There are 2 graduate students and several field technicians working on the program. We completed the final field season in Grand Teton National Park evaluating habitat use both temporally and spatially between grizzly and black bears ( Ursus americanus ). We continue to use GPS technology that incorporates a spread spectrum communication system. Spread spectrum allows for transfer of stored GPS locations from the collar to a remote receiving station. Results of the 2006 field season are reported here. We plan to complete the final report in late 2007. We continued to monitor the health of whitebark pine in the Greater Yellowstone Ecosystem (GYE) in cooperation with the Greater Yellowstone Whitebark Pine Monitoring Working Group. A summary of the 2006 monitoring is also presented (Appendix B). The IGBST uses counts of winter-killed ungulates to index spring carcass abundance for grizzly bears. Likewise, we use wier counts and stream surveys to index cutthroat trout abundance. We ask Dr. Steve Cherry, Department of Mathematical Sciences, Montana State University-Bozeman, to review the protocols and make recommendations for improving them. That review and recommendations are presented in Appendix C. Finally, the state of Wyoming, following recommendations from the Yellowstone Ecosystem Subcommittee and the IGBST, launched the Bear Wise Community Effort. The focus is to minimize human/bear conflicts, minimize human-caused bear mortalities associated with conflicts, and safeguard the human community. Results of these efforts are detailed in Appendix D. The annual reports of the IGBST summarize annual data collection. Because additional information can be obtained after publication, data summaries are subject to change. For that reason, data analyses and summaries presented in this report supersede all previously published data. The study area and sampling techniques are reported by Blanchard (1985), Mattson et al. (1991 a), and Haroldson et al. (1998).

Idaho, Montana, Wyoming↗