Grantee Research Project Results
Final Report: Mechanistic-based Watershed Modeling for Evaluation of Ecosystem Conditions
EPA Grant Number: R827956Title: Mechanistic-based Watershed Modeling for Evaluation of Ecosystem Conditions
Investigators: Yeh, Gour-Tsyh , Schayek, Lily , Gwo, J. P.
Institution: Pennsylvania State University
EPA Project Officer: Packard, Benjamin H
Project Period: January 10, 2000 through September 30, 2003 (Extended to September 30, 2005)
Project Amount: $888,637
RFA: Computing Technology for Ecosystem Modeling (1999) RFA Text | Recipients Lists
Research Category: Environmental Statistics
Objective:
The objectives of this research project were to: (1) understand, quantify, and model key transport and transformation mechanisms of physical, chemical, and biological processes; (2) develop an integrated modeling system for high priority problems of interest, including sediments, nutrients, industrial chemicals, pesticides, metals, algae, and microbes; and (3) provide a prototype modeling framework covering a full range of computing architectures from personal computers to scalable, parallel machines.
Summary/Accomplishments (Outputs/Outcomes):
This report presents the development of a numerical model simulating density-dependent water flow, thermal transport, and salinity transport and sediment and water quality transport in watershed systems of WAterSHed Systems of 1-D Stream-River Network, 2-D Overland Regime, and 3-D Subsurface Media (WASH123D). WASH123D is an integrated multimedia/control structures/management, multiprocesses, physics-based computational model of various spatial-temporal scales:
Multimedia (Figure 1)
- Dentric streams/rivers/canal/open channel.
- Overland regime (land surface).
- Subsurface media (vadose and saturated zones).
- Ponds, lakes/reservoirs (small/shallow).
Control Structures (Figure 2)
- Weirs, gates, culverts, pumps, levees, and storage ponds.
Management
- Operational rules for pumps and control structures.
Figure 1. Multimedia Included in WASH123D
Weirs Gate
Culverts Pumps
Levees Storage Ponds
Figure 2. Various Types of Control Structures Handled in WASH123D
Multiprocesses (Figures 3 and 4)
- Hydrological cycles (evaporation, evapotranspiration, infiltration, and recharges).
- Fluid flow (surface runoff in land surface, hydraulics and hydrodynamics in river/stream/canal networks, interflow in vadose zones, and groundwater flow in saturated zones).
- Salinity transport and thermal transport (in surface waters and groundwater).
- Sediment transport (in surface waters).
- Water quality transport (any number of reactive constituents).
- Biogeochemical cycles (nitrogen, phosphorous, carbon, oxygen, etc.).
- Biota kinetics (algae, phyotoplankton, zooplankton, coliform, bacteria, plants, etc.).
Figure 3. Flow and Thermal and Salinity Transport Processes of Hydrologic Cycles in WASH123D
Figure 4. Biogeochemical Cycles and Reactive Transport Included in WASH123D.
Theoretical Bases
Theoretical bases of WASH123D are the conservation laws of fluids, energy, mass, and biogeochemical reaction principles with physics-based constitutional relationships. The governing equations and particular features of WASH123D are given as follows:
Fluid Flows
- 1D St. Venant equations for river networks: kinematic, diffusive, and fully dynamic (MOC) waves.
- 2D St. Venant equations for overland regime: kinematic, diffusive, and fully dynamic (MOC) waves, as well as lumped models such as SCS.
- 3D Richard equation for subsurface media (both vadose and saturated zones): saturated-unsaturated conditions.
Salinity, Thermal, and Sediment Transport
- Modified advection-dispersion equations with phenomenological approaches for erosion and deposition.
Water Quality Transport
- Advection-dispersion-reaction equations with reaction-based mechanistic approaches to water-quality modeling, a general paradigm.
Types of Boundary Conditions
To enable the simulation of as wide a range of problems as possible, many types of boundary conditions, including many particular features that can be anticipated in real-world problems, are provided. These include global boundaries, internal boundaries and internal sources/sinks, and media interfaces:
Global Boundaries
- Flows
- For subsurface flow: specify pressure head, fluxes, pressure gradients, radiation conditions or variable boundary conditions.
- For surface flow: specify water depth, flow rate, or rating curve.
- Salinity, sediment, and reactive chemical transport.
- Specify concentration, flux, concentration gradient or variable boundary conditions.
- Thermal transport.
- Specify temperature, heat flux, temperature gradient or variable boundary conditions, and heat and mass budgets at the air-media interface.
Internal Sources/Sinks and Internal Boundary Conditions
- Pumps and operational rules.
- Junctions: explicitly enforced mass balance.
- Control structures: weirs, gates, culverts, levees, and storage ponds.
Media Interfaces
- Continuity of fluxes across media interfaces.
- Continuity of state variables across media interfaces.
- Linkage terms for special cases.
Optional Numerical Methods and Strategies
To provide robust and efficient numerical solutions of the governing equations, many options and strategies are provided in WASH123D so a wide range of application-depending circumstances can be simulated. These options, strategies, and particular features are stated as follows:
Discretization
- Flows
- For subsurface flow: use Galerkin finite element methods (FEM).
- For surface flow: use particle-tracking methods for the kinematic wave approaches; use FEM or particle-tracking methods for the diffusive wave approaches; use Lagrangian-Eluerian FEM or FEM for the fully dynamic wave approaches.
- Salinity, thermal, sediment, and reaction-based water quality transport
- Use FEM or particle-tracking methods.
Solvers
- Direct band matrix; basic point iterations methods; basic line iterations; preconditioned conjugate gradient methods with point iterations, incomplete Cholesky decomposition, and line iterations as preconditioners; multigrid methods.
Coupling strategies between transport and reactive chemistry
- Fully implicit method.
- Mixed prediction/corrector (on kinetic reaction rates) and operator-splitting method (on accumulation rates of immobile species).
- Operator-splitting methods.
To not introduce nonphysics parameters on the media interfaces, rigorous coupling of continuity of fluxes and continuity of state variables or formulations of fluxes when state variables are discontinuous are imposed:
- Continuous of fluxes.
- Continuous of state variables or formulation of fluxes.
To handle vast differences of flow and transport scales in system components of river/stream/canal networks, overland regime, and subsurface media, different time-step sizes are used.
Design Capability of WASH123D
The code consisted of eight modules to deal with multiple media:
- 1-D River/Stream Networks.
- 2-D Overland Regime.
- 3-D Subsurface Media (both vadose and saturated zones).
- Coupled 1-D River/Stream Network and 2-D Overland Regime.
- Coupled 2-D Overland Regime and 3-D Subsurface.
- Coupled 3-D Subsurface and 1-D River Systems.
- Coupled 3-D Subsurface Media, 2-D Overland, and 1-D River Network.
- Coupled 0-D Shallow Water Bodies and 1-D Canal Network.
For any of the above eight modules, flow only, transport only, or coupled flow and transport simulations can be carried out using WASH123D.
Example Problems
A total of 17 flow problems and 15 water quality transport problems are presented in WASH123D. These example problems can serve as templates for users to apply WASH123D to research problems or practical field-scale problems. For the 17 flow examples, the following objectives are achieved: (1) seven to demonstrate the design capability of WASH123D using seven different flow modules; (2) four to the needs of various approaches to simulate various types of flow (critical, subcritical, and supercritical) in river networks and overland regime; and (3) five to illustrate some realistic problems using WASH123D
For the 13 water quality transport problems: six examples for one-dimensional transport, four examples for two-dimensional transport, and three examples for three-dimensional transport. These examples are used to achieve the following objectives: (1) verify the correctness of computer implementation; (2) demonstrate the need of various numerical options and coupling strategies between transport and biogeochemical processes for application-depending circumstances; (3) illustrate how the generality of the water quality modeling paradigm embodies the widely used water quality models as specific examples; and (4) validate the capability of the models to simulate laboratory experiments and indicate its potential applications to field problems.
Significant Results
The significant results of this research follow: (1) WASH123D enables science to move beyond past piecemeal approaches and creates an integrated approach needed to facilitate the evolution to a more comprehensive assessment tool; (2) this model is based on “first principle” and sufficiently complex in the description of the processes that the model becomes virtual realities; (3) the numerical software will provide exposure concentrations from multiple stressors at multiple scales, aiding in selecting indicators and design of a monitoring network, and provides a physics-based tool for watershed assessment; (4) this model provides a mechanistic-based total maximum daily load (TMDL) input for lakes/reservoirs and tidal water bodies; and (5) the model is designed to include thermal and salinity transport so that it can be applied to a larger class of watersheds such as wetland watersheds along coastal areas, like the National Everglades Watershed.
The computer code, WASH123D, has been chosen by the U. S. Army Corps (USACE) as the core computational code to model two watersheds: Lower East Coast Wetland Watershed and CN111 Watershed in South Florida. The code has been interfaced with Groundwater Modeling Systems by USACE. It has also been parallelized computationally by USACE.
The WASH123D model is expected to be applied to ecological problems that have a need to couple both hydrology and water quality measurements in a variety of different spatial scales and along coastal areas. It is currently being applied to construct a Regional Engineering Model for Ecosystem Restoration (REMER) in the Comprehensive Everglades Restoration Program (CERP) in South Florida. The REMER model covers the eastern one-half of Florida south of Lake Okeechobee. The modeling domain includes approximately 25,000 km2. WASH123D is cutting edge and coupled with appropriate computational technology it can be applied to most of the projects being conducted in the $8 billion CERP. It may also be applied to many areas of the nation.
Recommended Further Developments
Further refinements and enhancements can be made of WASH123D in several areas. First, the governing equations for surface water flows and scalar transport should be cast in curvilinear coordinates along river directions for one-dimensional river networks (straightforward) and land surface fitted curvilinear coordinate (not so straightforward) for two-dimensional overland regime. These modifications will make the model applicable to landscapes of steep slopes. Second, high-performance parallel computing (partially done by USACE) should be implemented to make the application of the model to large scale problems computationally more tractable. Third, robust and user friendly graphical interface pre- and postprocessors (almost done by USACE) should be developed to make the learning curves of the model much shorter. Fourth, adaptive local grid refinement algorithms such as LEZOOMPC (Yeh 1990; Yeh, et al., 1992; Yeh, et al., 1995; Cheng, et al., 1996a, 1996b; Cheng et al, 1998a) should be incorporated in the discretization of sharp moving front problems to greatly speed up the computations. Fifth, optimal matrix solvers with computational efforts proportional to N (where N is the number of unknowns) such as algebraic-based multigrid method (Ruge and Stuben, 1985, 1987; Stuben and Trottenberg, 1982; Stuben, 1999a, 1999b) or geometric-based multigrid methods (Brandt, 1984; Bramble, et al., 1988; Xu and Zikatanov, 2000; Cheng, et al., 1998b; Li, et al., 2000, 2005) should be provided to increase greatly the computational speed. The algebraic-based multigrid methods will demand excessive CPU storages and are in general very difficult to achieve optimal performances for matrix equations resulting from generic nonlinear problems. On the other hand, geometric-based multigrid methods require extensive problem specific developments.
References:
Bramble JH, Pasciak JE, Xu J. The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems. Mathematics of Computation 1988;51:389-414.
Brandt A. Multigrid techniques: 1984 guide with applications to fluid dynamics. Presented to Department of Applied Mathematics, The Weizman Institute of Sciences, Rehovot 76100, Israel, 1984.
Cheng JR, Cheng HP, Yeh GT. A Lagrangian-Eulerian method with adaptively local zooming and peak/valley capturing approach to solve two-dimensional advection-diffusion transport equations. International Journal of Numerical Methods in Engineering 1996a;39(6):987-1016.
Cheng HP, Cheng JR, Yeh GT. A particle tracking technique for the Lagrangian-Eulerian finite element method in multi-dimensions. International Journal of Numerical Methods in Engineering 1996b;39(7):1115-1136.
Cheng HP, Cheng JR, Yeh GT. A Lagrangian-Eulerian method with adaptively local zooming and peak/valley capturing approach to solve three-dimensional advection-diffusion transport equations. International Journal of Numerical Methods in Engineering 1998a;41:587-615.
Cheng HP, Yeh GT, Li MH, Xu J, Carsel R. A study of incorporating the multigrid method into the three-dimensional finite element discretization. International Journal of Numerical Methods in Engineering 1998b;41:499-526.
Li MH, Cheng HP, Yeh GT. Solving 3-d subsurface density-dependent flow and transport problems with an adaptive multigrid approach. ASCE Journal of Hydrologic Engineering 2000;5(1):74-81.
Li MH, Cheng HP, Yeh GT. An adaptive multigrid approach for the simulation of contaminant transport in 3D subsurface. Computers and Geosciences 2005;31(8):1028-1041.
Ruge JW, Stuben K. Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG). In: Paddon DJ, Holstein H, eds. Multigrid Methods for Integral and Differential Equations. The Institute of Mathematics and its Applications Conference Series, New Series Number 3. Oxford: Clarenden Press, 1985, pp. 169-212.
Ruge JW, Stuben K. Algebraic multigrid. In: McCormick S-F, ed. Multigrid Methods, Frontiers in applied mathematics. Philadelphia, PA: SIAM, 1987;5:73-130.
Stüben K, Trottenberg U. Multi-grid methods: fundamental algorithms, model problem analysis and applications. In: Hackbusch W, Trottenberg U, eds. Multigrid Methods. Berlin: Springer Verlag, 1982.
Stuben K. Algebraic multigrid (AMG): experiences and comparisons. St. Augustin: GMD Rep. 53, 1999a.
Stuben K. A review of algebraic multigrid. St. Augustin: GMD Rep. 69, 1999b.
Xu J, Zikatanov L. A monotone finite element scheme for convection diffusion equations. Mathematics of Computation 2000;68:1429-1446.
Yeh GT. A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach to solving advection-dispersion equations. Water Resources Research 1990;26(6):1133-1144.
Yeh GT, Chang JR, Short TE. An exact peak capturing and essentially oscillation-free scheme to solve advection-dispersion-reactive transport equations. Water Resources Research 1992;28(11):2937-2951.
Yeh GT, Chang JR, Cheng HP, Sung CH. An adaptive local grid refinement based on the exact peak capturing and oscillation free scheme to solve transport equations. Computers and Fluids 1995;24(3):293-332.
Journal Articles on this Report : 4 Displayed | Download in RIS Format
Other project views: | All 51 publications | 12 publications in selected types | All 7 journal articles |
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Fang Y, Yeh G-T, Burgos WD. A general paradigm to model reaction-based biogeochemical processes in batch systems. Water Resources Research 2003;39(4):HWC21-HWC225. |
R827956 (2003) R827956 (Final) |
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Gwo JP, D’Azevedo EF, Frenzel H, Mayes M, Yeh GT, Jardine PM, Salvage KM, Hoffman FM. HBGC123D: a high-performance computer model of coupled hydrogeological and bigeochemical processes. Computers & Geosciences 2001;27(10):1231-1242. |
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Wang H, Yeh G-T. A characteristic-based semi Lagrangian method for hyperbolic systems for conservation laws. Chinese Journal of Atmospheric Sciences 2005;29(1):21-42. |
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Yeh GT, Siegel MD, Li MH. Numerical modeling of coupled variably saturated fluid flow and reactive transport with fast and slow chemical reactions. Journal of Contaminant Hydrology 2001;47(2-4):379-390. |
R827956 (Final) |
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Supplemental Keywords:
multi-media, water, watersheds, groundwater, land, soil, sediments, precipitation, leachate, adsorption, absorption, chemical transport, exposure, risk assessment, effects, ecological effects, bioavailability, metabolism, vulnerability, organism, enzymes, stressor, metabolism, susceptibility, cumulative effects, chemicals, toxics, particulates, VOC, PAHs, PCBs, Dioxin, metals, heavy metals, solvents, oxidants, nitrogen oxides, sulfates, organics, pathogens, viruses, bacteria, acid rain, effluent, discharge, dissolved solids, intermediates, ecosystem, restoration, scaling, terrestrial, aquatic, integrated assessment, pollution prevention, life-cycle analysis, waste reduction, waste minimization, treatment, remediation, bioremediation, cleanup, oxidation, restoration, environmental chemistry, biology, physics, engineering, ecology, hydrology, geology, mathematics, limnology, modeling, general circulation models, Pacific coast, Atlantic coast, Gulf coast, Pacific Northwest, Chesapeake Bay, Great Lakes, Midwest, midatlantic, Florida,, RFA, Scientific Discipline, Toxics, Water, Waste, Ecosystem Protection/Environmental Exposure & Risk, Nutrients, Ecology, Hydrology, Ecosystem/Assessment/Indicators, Ecosystem Protection, Contaminated Sediments, Environmental Chemistry, Mathematics, pesticides, Chemistry, Fate & Transport, Wet Weather Flows, computing technology, Biology, Ecological Indicators, hydrological stability, aquatic ecosystem, nutrient transport, ecosystem modeling, fate and transport, ecological exposure, high performance computing, computer simulation model, streams, watershed, mechanistic based watershed modeling, ecological modeling, sediment transport, contaminated sediment, ecosystem evaluation, numerical models, sediment, mechanistic-based watershed modeling, watershed modeling, industrial chemicals, tidal influence, computer science, tidal water bodies, microbial pollution, numerical model, bioindicators, subsurface media, component-based software, information technology, water quality, lake ecosystemsProgress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.