 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  Zhang, Fan  An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 8 – Reactive Chemical Transport in Subsurface Media    

Abstract  A watershed system includes river/stream networks, overland regions, and subsurface
media. This paper presents a reactionbased numerical model of reactive chemical
transport in subsurface media of watershed systems. Transport of M chemical species
with a variety of chemical and physical processes is mathematically described by M
partial differential equations (PDEs). Decomposition via GaussJordan column
reduction of the reaction network transforms M species reactive transport equations
into M reaction extenttransport equations (a reaction extent is a linear
combination of species concentrations), each involves one and the only one linearly
independent reaction. Thus, the reactive transport problem is viewed from two
different points of view. Descirbed with a speciestransport equation, the
transport of a species is balanced by a linear combinations of rates of all
reactions. Described by a reaction extenttransport equation, the rate of a linear
independent reaction is balanced by the transport of the linear combination of
species. The later description facilitates the decoupling of fast reactions from
slow reactions and circumvent the stiffness of reactive transport problems. This
is so because the M reaction extenttransport equations can be approximated with
three subsets of equations: NE algebraic equations describing NE fast reactions
(where NE is the set of linearly independent fast/equilibrium reactions), NKI
reactive transport equations of kineticvariables involving no fast reactions
(where NKI is the number of linearly independent slow/kinetic reactions), and NC
transport equations of components involving no reaction at all (where NC = M – NE –
NKI is the number of components). The elimination of fast reactions from reactive
transport equations allows robust and efficient numerical integration. The model
solves the PDEs of kineticvariables and components rather than individual chemical
species, which reduces the number of reactive transport equations and simplifies
the reaction terms in the equations. Two validation examples involving simulations
of uranium transport in soil columns are presented to evaluate the ability of the
model to simulate reactive transport with reaction networks involving both kinetic
and equilibrium reactions. A hypothetical threedimensional example is presented to
demonstrate the model application to a fieldscale problem involving reactive
transport with a complex reaction network. 
Track/Session  General Sessions / General 
Author(s)  Fan Zhang^{1}; GourTsyh Yeh^{2}; Jack Parker^{1}; Scott Brooks^{1}; Molly Pace^{1}; YoungJin Kim^{1}; Philip Jardine^{1}; Fan Zhang^{1} 
Organisation(s)  ^{1}Oak Ridge National Laboratory, USA; ^{2}2Dept of Civil and Environ. Eng., Univ. of Central Florida 
Dates  20060618 
DOI  10.4122/1.1000000716 

 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  Zhang, Fan  An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 6 – Sediment and Reactive Chemical Transport in Stream/River Networks    

Abstract  A watershed system includes river/stream networks, overland regions, and subsurface
media. This paper presents a numerical model of sediment and reactive chemical
transport in river/stream networks of watershed systems. The distribution of
mobile suspended sediments and immobile bed sediments is controlled by hydrological
transport as well as erosion and deposition processes. The distribution and fate of
chemical species with a variety of chemical and physical processes is
mathematically described by a system of advectivedispersivereactive species
transport equations. Each equation in the system simply states that the rate of
increase of a species is due to hydrology transport and the production rate from
all reactions contributing to the species. The system is very stiff if some of
reactions are very fast; in the limit with infinite rates. To circumvent the stiff
problem, fast reactions must be decoupled from slow reactions. A matrix
decomposition procedure is performed via the GaussJordan column reduction of the
reaction network. After matrix decomposition, the system of speciestransport
equations is transformed to a system of reaction extenttransport equations, in
which one and only one linearly independent reaction rate appears in any reaction
extent equation. This facilitates the decoupling of fast reactions from slow
reactions. Each of the reactionextent transport equations with the one and only
one fast reaction is then approximated with an algebraic equation and its reaction
extent is called an equilibrium variable. Thus the system of reactionextent
transport equations is reduced three subsets: (1) algebraic equations, (2) kinetic
variable transport equations, and (3) component transport equations. A variety of
numerical methods are investigated for solving the mixed differential and algebraic
equations (DAE). Two verification examples are compared with analytical solutions
to demonstrate the correctness of and to emphasize the need of implementing various
numerical options and coupling strategies for applicationdependent simulations. A
hypothetical example is employed to demonstrate the capability of the model to
simulate both sediment and reactive chemical transport and to handle complex
reaction networks involving both slow and fast reactions. 
Track/Session  General Sessions / General 
Author(s)  Fan Zhang^{1}; GourTsyh Yeh^{2}; Fan Zhang^{1} 
Organisation(s)  ^{1}Oak Ridge National Laboratory, USA; ^{2}2Dept of Civil and Environ. Eng., Univ. of Central Florida 
Dates  20060618 
DOI  10.4122/1.1000000720 

 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  Zhang, Fan  An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 7 – Sediment and Reactive Chemical Transport in Surface Runoff    

Abstract  A watershed system includes river/stream networks, overland regime, and subsurface
media. This paper presents a numerical model of sediment and reactive chemical
transport in surface runoff of watershed systems. The distribution of mobile
suspended sediments and immobile bed sediments is controlled through hydrological
transport as well as erosion and deposition processes. Transport of chemical
species with a variety of chemical and physical processes is mathematically
described by system of M advectivedispersivereactive transport equations (where M
is the number of species). Decomposition via GaussJordan column reduction of the
reaction network transforms M speciestransport equations into three sets of
equations: a set of thermodynamic equilibrium equations representing NE equilibrium
reactions, a set of reactive transport equations of NKI kineticvariables involving
no equilibrium reactions (where NKI is the number of linearly independent kinetic
reactions), and a sent of NC component transport equations (where NC is the number
of components). The elimination of fast reactions from reactive transport equations
allows robust and efficient numerical integration. The model solves the PDEs of
kineticvariables and components rather than individual chemical species, which
reduces the number of reactive transport equations and simplifies the reaction
terms in the equations. A hypothetical example was used to demonstrate the
capability of the model in simulating sediment and reactive chemical transport
subject to a complex reaction network involving both slow and fast reactions, under
the effect of temperature. Based on the application of an eutrophication example,
the deficiency of current practices in the water quality modeling is discussed and
potential improvements over current practices using this model are addressed. 
Track/Session  General Sessions / General 
Author(s)  Fan Zhang^{1}; GourTsyh Yeh^{2}; Fan Zhang^{1} 
Organisation(s)  ^{1}Oak Ridge National Laboratory, USA; ^{2}2Dept of Civil and Environ. Eng., Univ. of Central Florida 
Dates  20060618 
DOI  10.4122/1.1000000718 

 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  HUANG, GUOBIAO  An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 2 – Simulating surface water flows with different water wave models    

Abstract  The complete Saint Venant equations/2D shallow water equations (dynamic wave
equations) and the kinematic wave or diffusion wave approximations were implemented
for 1D channel network flow and 2D overland flow in a watershed model, WASH123D.
Careful choice of numerical methods is needed even for the simple kinematic wave
model. Motha and Wigham (1995) reported numerical oscillation in Galerkin finite
element of kinematic wave overland flow. Since the kinematic wave equation is of
pure advection, the backward method of characteristics is used for kinematic wave
model. A characteristic based finite element method is chosen for the hyperbolic
type dynamic wave model. And the Galerkin finite element method is used to solve the
diffusion wave model.
Diffusion wave and kinematic wave approximations are found in many overland runoff
routing models. The error in these models has been characterized for some cases of
overland flow over simple geometry (e.g. Ponce 1978; Singh 2000 and Parlange 1990).
However, the nature and propagation of these approximation errors under more complex
2D flow conditions are not well known. These issues are evaluated within WASH123D
by comparison of simulation results on several example problems. The accuracy of the
three wave models for 1D channel flow was evaluated with several nontrivial (trans
critical flow; varied bottom slopes with frictions and nonprismatic crosssection)
benchmark problems (MacDonnell et al., 1997). The test examples for 2D overland
flow include: (1) a simple rainfallrunoff process on a single plane with constant
rainfall excess that has a kinematic analytical solution under steep slope
condition. A range of bottom slopes (mild, average and steep slope) are numerically
solved by the three wave models and compared; (2) Iwagaki (1955) overland flow
experiments on a cascade of three planes with shock waves; (3) overland flow in a
hypothetical wetland (infiltration bed). The applicability of dynamicwave,
diffusionwave and kinematicwave models to real watershed modeling is discussed
with simulation results from these numerical experiments. It was concluded that
kinematic wave model could lead to significant errors in most applications. On the
other hand, diffusion wave model is adequate for modeling overland flow in most
natural watersheds. The complete dynamic wave equations are required in lowterrain
areas such as flood plains or wetlands and many transient fast flow situations. 
Track/Session  General Sessions / General 
Author(s)  GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GUOBIAO HUANG^{1} 
Organisation(s)  ^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Dates  20060618 
DOI  10.4122/1.1000000641 

 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  HUANG, GUOBIAO  An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 4 – A characteristicsbased finite element method for 2D overland flow    

Abstract  The Method of Characteristics (MOC) in the context of finite element method was
applied to the complete 2D shallow water equations for 2D overland flow. For two
dimensional overland flow, finite element or finite volume methods are more flexible
in dealing with complex boundary. Recently, finite volume methods have been very
popular in numerical solution of the shallow water equations. Some have pointed out
that finite volume methods for 2D flow are fundamentally onedimensional (normal to
the cell interface). The results may rely on the grid orientation. The search for
genuinely multidimensional numerical schemes for 2D flow is an active topic. We
consider the Method of Characteristics (MOC) in the context of finite element method
as a good alternative. Many researchers have pointed out the advantage of MOC in
solving 2D shallow water equations that are of the hyperbolic type that has wave
like solutions and at same time, considered MOC for 2D overland flow being non
tractable on complex topography. The intrinsic difficulty in implementing MOC for 2
D overland flow is that there are infinite numbers of wave characteristics in the 2
D context, although there only three independent wave directions are needed for a
wellposed solution to the characteristic equations. We have implemented a numerical
scheme that attempts to diagonalize the characteristic equations based on pressure
and velocity gradient relationship. This new scheme was evaluated by comparison with
other choice of wave characteristic directions in the literature. Example problems
of mixed subcritical flow/supercritical flow in a channel with approximate
analytical solution was used to verify the numerical algorithm. Then experiments of
overland flow on a cascade of three planes (Iwagaki 1955) were solved by the new
method. The circular dam break problem was solved with different selections of wave
characteristic directions and the performance of each selection was evaluated based
on accuracy and numerical stability. Finally, 2D overland flow over complex
topography in a wetland setting with very mild slope was solved by the new numerical
method to demonstrate its applicability. 
Track/Session  General Sessions / General 
Author(s)  GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GUOBIAO HUANG^{1} 
Organisation(s)  ^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Dates  20060618 
DOI  10.4122/1.1000000637 

 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  HUANG, GUOBIAO  An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 3 –a comparative study on different surface water/groundwater coupling approaches    

Abstract  In the core of an integrated watershed model is the coupling among surface water and
subsurface water flows. Recently, there is a tendency of claiming the fully coupled
approach for surface water and groundwater interactions in the hydrology literature.
One example is the assumption of a gradient type flux equation based on Darcy’s Law
(linkage term) and the numerical solution of all governing equations in a single
global matrix. We argue that this is only a special case of all possible coupling
combinations and if not applied with caution, the nonphysical interface parameter
becomes a calibration tool. Generally, there are two cases based on physical
nature of the interface: continuous or discontinuous assumption, when a sediment
layer exists at the interface, the discontinuous assumption may be justified. As for
numerical schemes, there are three cases: timelagged, iterative and simultaneous
solutions. Since modelers often resort to the simplest, fastest schemes in
practical applications, it is desirable to quantify the potential error and
performance of different coupling schemes. We evaluate these coupling schemes in a
finite element watershed model, WASH123D. Numerical experiments are used to compare
the performance of each coupling approach for different types of surface water and
groundwater interactions. These are in term of surface water and subsurface water
solutions and exchange flux (e.g. infiltration/seepage rate). It is concluded that
different coupling approaches are justified for flow problems of different spatial
and temporal scales and the physical setting of the interface. 
Track/Session  General Sessions / General 
Author(s)  GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GUOBIAO HUANG^{1} 
Organisation(s)  ^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Dates  20060618 
DOI  10.4122/1.1000000639 

 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  HUANG, GUOBIAO  An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 5 – Integrated modeling of surface water and groundwater interactions in a constructed wetland    

Abstract  A pilot constructed wetland in south Florida, USA, the Everglades Nutrient Removal
(ENR) project was modeled with a physicsbased integrated approach by WASH123D.
Stormwater is routed into the treatment wetland for phosphorus removal by plant and
sediment intake. It overlies a highly permeable surficial groundwater aquifer.
Strong surface water and groundwater interactions are a key component of the
hydrologic processes. The site has extensive field measurement and monitoring that
provide point scale and distributed data on surface water levels, groundwater levels
and physical range of hydraulic parameters and hydrologic fluxes. Previous
hydrologic and hydrodynamic modeling studies have treated seepage losses empirically
by some simple regression equations and only surface water flows are modeled in
detail. Several years of operational data are available and were used in model
calibration and validation. The validity of diffusion wave approximation for 2D
overland flow in the region with very flat topography was also tested. The
uniqueness of this modeling study includes (1) the point scale and distributed
comparison of model results with observed data; for example, the spatial
distribution of measured vertical flux in the wetland is available. (2) Model
parameters are based on available field test data. (3) Water flows in the study area
consist of 2D overland flow, hydraulic structures/levees, 3D subsurface flow and 1
D canal flow and their interactions. This study demonstrates the need and the
utility of a physicsbased modeling approach for strong surface water and
groundwater interactions. 
Track/Session  General Sessions / General 
Author(s)  GUOBIAO HUANG^{1}; GourTsyh Yeh^{2}; GourTsyh Yeh^{2} 
Organisation(s)  ^{1}Sutron Corporation, West Palm Beach, FL, USA; ^{2}Dept of Civil and Environ. Eng., Univ. of Central Florida, Orlando, FL, USA 
Dates  20060618 
DOI  10.4122/1.1000000635 

 2006  XVI International Conference on Computational Methods in Water Resources (CMWRXVI)  Cheng, HwaiPing  Numerical Strategies to Model Surface and Groundwater Interactions for the Biscayne Bay Coastal Wetlands Project Alternatives    

Abstract  WASH123D is a firstprinciple, physicsbased numerical model that computes flow and
transport in a watershed system that is conceptualized as a combination of 1D
channel network, 2D overland regimes, and 3D subsurface media. It has been
selected as the tool to help evaluate the proposed alternatives of the Biscayne Bay
Coastal Wetlands project that is one of the 40 projects included in the Florida
Comprehensive Everglade Restoration Plan. In order to best rehydrate wetlands and
reduce point source discharge to Biscayne Bay, rulecontrolled coastal canal
structures, rulecontrolled pump stations, spreader swales, stormwater treatment
areas, flowways, levees, culverts, roads, and backfilling canals are included in
these project alternatives. Specified target freshwater flows for Biscayne Bay and
the wetlands within the redistribution system are to be computed in each
alternative, which will be used in performance measurement to determine the most
adequate alternative for further investigation. In this paper, the numerical
strategies to incorporate all the aforementioned hydrological features and
processes included in the alternatives are presented. An example alternative will
be used for demonstration. 
Track/Session  General Sessions / General 
Author(s)  HwaiPing Cheng^{1}; JingRu cheng^{1}; David Richards^{1}; GourTsyh Yeh^{2}; HwaiPing Cheng^{1}; David Richards^{1} 
Organisation(s)  ^{1}US Army Engineer Research and Development Center; ^{2}University of Central Florida 
Dates  20060618 
DOI  10.4122/1.1000000505 
