Introduction to Groundwater Modelling

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Introduction to Groundwater Modelling
C. P. Kumar Scientist E1
National Institute of Hydrology Roorkee 247667
(Uttaranchal) India Email cpkumar_at_yahoo.com Webp
age http//www.angelfire.com/nh/cpkumar/
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Presentation Outline

• Groundwater in Hydrologic Cycle
• Why Groundwater Modelling is needed?
• Mathematical Models
• Modelling Protocol
• Model Design
• Calibration and Validation
• Groundwater Flow Models
• Groundwater Modelling Resources

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Groundwater in Hydrologic Cycle
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Types of Terrestrial Water
Surface Water
Soil Moisture
Ground water
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Pores Full of Combination of Air and Water
Unsaturated Zone / Zone of Aeration / Vadose
(Soil Water)
Zone of Saturation (Ground water)
Pores Full Completely with Water
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Groundwater
Important source of clean water More abundant
than SW
Baseflow
Linked to SW systems Sustains flows in streams
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Groundwater Concerns?
pollution
groundwater mining subsidence
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• Problems with groundwater
• Groundwater overdraft / mining / subsidence
• Waterlogging
• Seawater intrusion
• Groundwater pollution

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Why Groundwater Modelling is needed?
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• Groundwater
• An important component of water resource systems.
  
• Extracted from aquifers through pumping wells and
  supplied for domestic use, industry and
  agriculture.
• With increased withdrawal of groundwater, the
  quality of groundwater has been continuously
  deteriorating.
• Water can be injected into aquifers for storage
  and/or quality control purposes.

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• Management of a groundwater system, means making
  such decisions as
• The total volume that may be withdrawn annually
  from the aquifer.
• The location of pumping and artificial recharge
  wells, and their rates.
• Decisions related to groundwater quality.
• Groundwater contamination by
• Hazardous industrial wastes
• Leachate from landfills
• Agricultural activities such as the use of
  fertilizers and pesticides

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• MANAGEMENT means making decisions to achieve
  goals without violating specified constraints.
• Good management requires information on the
  response of the managed system to the proposed
  activities.
• This information enables the decision-maker, to
  compare alternative actions and to ensure that
  constraints are not violated.
• Any planning of mitigation or control measures,
  once contamination has been detected in the
  saturated or unsaturated zones, requires the
  prediction of the path and the fate of the
  contaminants, in response to the planned
  activities.
• Any monitoring or observation network must be
  based on the anticipated behavior of the system.

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• A tool is needed that will provide this
  information.
• The tool for understanding the system and its
  behavior and for predicting this response is the
  model.
• Usually, the model takes the form of a set of
  mathematical equations, involving one or more
  partial differential equations. We refer to such
  model as a mathematical model.
• The preferred method of solution of the
  mathematical model of a given problem is the
  analytical solution.

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• The advantage of the analytical solution is that
  the same solution can be applied to various
  numerical values of model coefficients and
  parameters.
• Unfortunately, for most practical problems,
  because of the heterogeneity of the considered
  domain, the irregular shape of its boundaries,
  and the non-analytic form of the various
  functions, solving the mathematical models
  analytically is not possible.
• Instead, we transform the mathematical model into
  a numerical one, solving it by means of computer
  programs.

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Prior to determining the management scheme for
any aquifer
We should have a CALIBRATED MODEL of the aquifer,
especially, we should know the aquifers natural
replenishment (from precipitation and through
aquifer boundaries).
The model will provide the response of the
aquifer (water levels, concentrations, etc.) to
the implementation of any management alternative.
We should have a POLICY that dictates management
objectives and constraints.
Obviously, we also need information about the
water demand (quantity and quality, current and
future), interaction with other parts of the
water resources system, economic information,
sources of pollution, effect of changes on the
environment---springs, rivers,...
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• GROUND WATER MODELING
• WHY MODEL?
• To make predictions about a ground-water
• systems response to a stress
• To understand the system
• To design field studies
• Use as a thinking tool

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Use of Groundwater models

• Can be used for three general purposes
• To predict or forecast expected artificial or
  natural changes in the system. Predictive is more
  applied to deterministic models since it carries
  higher degree of certainty, while forecasting is
  used with probabilistic (stochastic) models.

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Use of Groundwater models

• To describe the system in order to analyse
  various assumptions
• To generate a hypothetical system that will be
  used to study principles of groundwater flow
  associated with various general or specific
  problems.

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ALL GROUND-WATER HYDROLOGY WORK IS MODELING A
Model is a representation of a system. Modeling
begins when one formulates a concept of a
hydrologic system, continues with application
of, for example, Darcy's Law to the problem,
and may culminate in a complex numerical
simulation.
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Ground Water Flow Modelling

• A Powerful Tool
• for furthering our understanding of
  hydrogeological systems

• Importance of understanding ground water flow
  models
• Construct accurate representations of
  hydrogeological systems
• Understand the interrelationships between
  elements of systems
• Efficiently develop a sound mathematical
  representation
• Make reasonable assumptions and simplifications
• Understand the limitations of the mathematical
  representation
• Understand the limitations of the interpretation
  of the results

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Introduction to Ground Water Flow Modelling

• Predicting heads (and flows) and
• Approximating parameters

• Solutions to the flow equations
• Most ground water flow models are solutions of
  some form of the ground water flow equation

• The partial differential equation needs to be
  solved to calculate head as a function of
  position and time, i.e., hf(x,y,z,t)

• e.g., unidirectional, steady-state flow within a
  confined aquifer

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Groundwater Modeling

• The only effective way to test effects of
  groundwater management strategies
• Takes time, money to make model
• Conceptual model Steady state model
  Transient model
• The model is only as good as its calibration

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• Processes we might want to model
• Groundwater flow
• calculate both heads and flow
• Solute transport requires information on flow
  (velocities)
• calculate concentrations

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MODELING PROCESS ALL IMPORTANT
MECHANISMS PROCESSES MUST BE INCLUDED IN THE
MODEL, OR RESULTS WILL BE INVALID.
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TYPES OF MODELS CONCEPTUAL MODEL QUALITATIVE
DESCRIPTION OF SYSTEM "a cartoon of the system
in your mind" MATHEMATICAL MODEL MATHEMATICAL
DESCRIPTION OF SYSTEM SIMPLE - ANALYTICAL
(provides a continuous solution over the model
domain) COMPLEX - NUMERICAL (provides a discrete
solution - i.e. values are calculated at only a
few points) ANALOG MODEL e.g. ELECTRICAL
CURRENT FLOW through a circuit board with
resistors to represent hydraulic conductivity and
capacitors to represent storage
coefficient PHYSICAL MODEL e.g. SAND TANK which
poses scaling problems
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Mathematical Models
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• Mathematical model
• simulates ground-water flow and/or solute fate
  and transport indirectly by means of a set of
  governing equations thought to represent the
  physical processes that occur in the system.
• (Anderson and Woessner, 1992)

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• Components of a Mathematical Model
• Governing Equation
• (Darcys law water balance equation) with head
  (h) as the dependent variable
• Boundary Conditions
• Initial conditions (for transient problems)

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Derivation of the Governing Equation
Q
R ?x ?y
q
?z
?x
?y

• Consider flux (q) through REV
• OUT IN - ?Storage
• Combine with q -K grad h

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Law of Mass Balance Darcys Law
Governing Equation for Groundwater Flow
-------------------------------------------------
-------------- div q - Ss (?h ??t)
(Law of Mass Balance) q - K grad h
(Darcys Law) div (K grad h)
Ss (?h ??t)
(Ss S / ? z)
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General governing equation for steady-state,
heterogeneous, anisotropic conditions, without a
source/sink term
with a source/sink term
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General governing equation for transient,
heterogeneous, and anisotropic conditions
Specific Storage Ss ?V / (?x ?y ?z ?h)
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?h
?h
b
S V / A ? h S Ss b
Confined aquifer
Unconfined aquifer
Storativity
Specific yield
Figures taken from Hornberger et al. (1998)
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General 3D equation
2D confined
2D unconfined
Storage coefficient (S) is either storativity or
specific yield. S Ss b T K b
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• Types of Solutions of Mathematical Models
• Analytical Solutions h f(x,y,z,t)
• (example Theis equation)
• Numerical Solutions
• Finite difference methods
• Finite element methods
• Analytic Element Methods (AEM)

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Limitations of Analytical Models

• The flexibility of analytical modeling is limited
  due to simplifying assumptions
• Homogeneity, Isotropy, simple geometry, simple
  initial conditions
• Geology is inherently complex
• Heterogeneous, anisotropic, complex geometry,
  complex conditions

• This complexity calls for a more
• powerful solution to the flow equation ?
  Numerical modeling

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Numerical Methods

• All numerical methods involve representing the
  flow domain by a limited number of discrete
  points called nodes.
• A set of equations are then derived to relate the
  nodal values of the dependent variable such that
  they satisfy the governing PDE, either
  approximately or exactly.

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• Numerical Solutions
• Discrete solution of head at selected nodal
  points.
• Involves numerical solution of a set of
  algebraic
• equations.

Finite difference models (e.g., MODFLOW) Finite
element models (e.g., SUTRA)
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Finite Difference Modelling

• 3-D Finite Difference Models
• Requires vertical discretization (or layering) of
  model

K1
K2
K3
K4
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• Finite difference models
• may be solved using
• a computer program
• (e.g., a FORTRAN program)
• a spreadsheet (e.g., EXCEL)

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Finite Elements basis functions, variational
principle,
Galerkins method, weighted residuals

• Nodes plus elements elements defined by nodes

• Properties (K, S) assigned to elements

• Nodes located on flux boundaries

• Able to simulate point sources/sinks at nodes

• Flexibility in grid design
• elements shaped to boundaries
• elements fitted to capture detail

• Easier to accommodate anisotropy that occurs at
  an
• angle to the coordinate axis

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Hybrid Analytic Element Method (AEM)
Involves superposition of analytic solutions.
Heads are calculated in continuous space using a
computer to do the mathematics involved in
superposition.
The AE Method was introduced by Otto Strack. A
general purpose code, GFLOW, was developed
by Stracks student Henk Haitjema, who also wrote
a textbook on the AE Method Analytic Element
Modeling of Groundwater Flow, Academic Press,
1995.
Currently the method is limited to
steady-state, two-dimensional, horizontal flow.
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Modelling Protocol
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What is a model?

• Any device that represents approximation to
  field system
• Physical Models
• Mathematical Models
• Analytical
• Numerical

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Modelling Protocol

• Establish the Purpose of the Model
• Develop Conceptual Model of the System
• Select Governing Equations and Computer Code
• Model Design
• Calibration
• Calibration Sensitivity Analysis
• Model Verification
• Prediction
• Predictive Sensitivity Analysis
• Presentation of Modeling Design and Results
• Post Audit
• Model Redesign

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Purpose - What questions do you want the model to
answer?

• Prediction System Interpretation Generic
  Modeling
• What do you want to learn from the model?
• Is a modeling exercise the best way to answer the
  question? Historical data?
• Can an analytical model provide the answer?

System Interpretation Inverse Modeling
Sensitivity Analysis Generic Used in a
hypothetical sense, not necessarily for a real
site
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Model Overkill?

• Is the vast labor of characterizing the system,
  combined with the vast labor of analyzing it,
  disproportionate to the benefits that follow?

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ETHICS

• There may be a cheaper, more effective approach
• Warn of limitations

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Conceptual ModelEverything should be made as
simple as possible, but not simpler. Albert
Einstein

• Pictorial representation of the groundwater flow
  system
• Will set the dimensions of the model and the
  design of the grid
• Parsimony.conceptual model has been simplified
  as much as possible yet retains enough complexity
  so that it adequately reproduces system behavior.

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Select Computer Code

• Select Computer Model
• Code Verification
• Comparison to Analytical Solutions Other
  Numerical Models
• Model Design
• Design of Grid, selecting time steps, boundary
  and initial conditions, parameter data set

Steady/Unsteady..1, 2, or 3-D
Heterogeneous/Isotropic..Instantaneous/Continuou
s
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Calibration

• Show that Model can reproduce field-measured
  heads and flow (concentrations if contaminant
  transport)
• Results in parameter data set that best
  represents field-measured conditions.

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Calibration Sensitivity Analysis

• Uncertainty in Input Conditions
• Determine Effect of Uncertainty on Calibrated
  Model

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Model Verification

• Use Model to Reproduce a Second Set of Field Data
• Prediction
• Desired Set of Conditions
• Sensitivity Analysis
• Effect of uncertainty in parameter values and
  future stresses on the predicted solution

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Presentation of Modelling Design and Results

• Effective Communication of Modeling Effort
• Graphs, Tables, Text etc.

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Postaudit

• New field data collected to determine if
  prediction was correct
• Site-specific data needed to validate model for
  specific site application
• Model Redesign
• Include new insights into system behavior

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NUMERICAL MODELING DISCRETIZE Write equations
of GW Flow between each node Darcy's
Law Conservation of Mass Define Material
Properties Boundary Conditions Initial
Conditions Stresses At each node either H or Q
is known, the other is unknown n equations n
unknowns solve simultaneously with matrix
algebra Result H at each known Q node Q at
each known H node Calibrate Steady
State Transient Validate Sensitivity Pr
edictions Similar Process for Transport Modeling
only Concentration and Flux is unknown
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NUMERICAL MODELING
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Model Design
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MODELs NEED Geometry Material Properties (K, S,
T, Fe, R, etc.) Boundary Conditions (Head, Flux,
Concentration etc.) Stress - changing boundary
condition
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Model Design

• Conceptual Model
• Selection of Computer Code
• Model Geometry
• Grid
• Boundary array
• Model Parameters
• Boundary Conditions
• Initial Conditions
• Stresses

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Concept Development

• Developing a conceptual model is the initial and
  most important part of every modelling effort. It
  requires thorough understanding of hydrogeology,
  hydrology and dynamics of groundwater flow.

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Conceptual Model A descriptive representation of
a groundwater system that incorporates an
interpretation of the geological hydrological
conditions. Generally includes information about
the water budget. May include information on
water chemistry.
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Selection of Computer Code

• Which method will be used depends largely on the
  type of problem and the knowledge of the model
  design.
• Flow, solute, heat, density dependent etc.
• 1D, 2D, 3D

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Model Geometry

• Model geometry defines the size and the shape of
  the model. It consists of model boundaries, both
  external and internal, and model grid.

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Boundaries

• Physical boundaries are well defined geologic and
  hydrologic features that permanently influence
  the pattern of groundwater flow (faults, geologic
  units, contact with surface water etc.)

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Boundaries

• Hydraulic boundaries are derived from the
  groundwater flow net and therefore artificial
  boundaries set by the model designer. They can be
  no flow boundaries represented by chosen stream
  lines, or boundaries with known hydraulic head
  represented by equipotential lines.

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HYDRAULIC BOUNDARIES
A streamline (flowline) is also a hydraulic
boundary because by definition, flow is ALWAYS
parallel to a streamflow. It can also be said
that flow NEVER crosses a streamline therefore
it is similar to an IMPERMEABLE (no flow)
boundary BUT Stress can change the flow pattern
and shift the position of streamlines therefore
care must be taken when using a streamline as the
outer boundary of a model.
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TYPES OF MODEL BOUNDARY
NO-FLOW BOUNDARY Neither HEAD nor FLUX
is Specified. Can represent a Physical boundary
or a flow Line (Groundwater Divide)
SPECIFIED HEAD OR CONSTANT HEAD BOUNDARY h
constant q is determined by the model. And may be
ve or ve according to the hydraulic gradient
developed
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TYPES OF MODEL BOUNDARY (contd)
SPECIFIED FLUX BOUNDARY q constant h is
determined by the model (The common method of
simulation is to use one injection well for
each boundary cell)
HEAD DEPENDANT BOUNDARY hb constant q c (hb
hm) and c f (K,L) and is called CONDUCTANCE hm
is determined by the model and its interaction
with hb
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Boundary Types Specified Head/Concentration a
special case of constant head (ABC, EFG)
Constant Head /Concentration could replace
(ABC, EFG) Specified Flux could be recharge
across (CD) No Flow (Streamline) a special
case of specified flux (HI) Head Dependent
Flux could replace (ABC, EFG) Free Surface
water-table, phreatic surface (CD) Seepage
Face pressure atmospheric at ground surface
(DE)
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Boundary conditions in Modflow

• Constant head boundary
• Head dependent flux
• River Package
• Drain Package
• General-head Boundary Package
• Known Flux
• Recharge
• Evapotranspiration
• Wells
• Stream
• No Flow boundaries

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Initial Conditions

• Values of the hydraulic head for each active and
  constant-head cell in the model. They must be
  higher than the elevation of the cell bottom.
• For transient simulation, heads to resemble
  closely actual heads (realistic).
• For steady state, only hydraulic heads in
  constant head-cell must be realistic.

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Model Parameters

• Time
• Space (layer top and bottom)
• Hydrogeologic characteristics (hydraulic
  conductivity, transmissivity, storage parameters
  and effective porosity)

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Time

• Time parameters are specified when modelling
  transient (time dependent) conditions. They
  include time unit, length and number of time
  steps.
• Length of stress periods is not relevant for
  steady state simulations

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Grid

• In Finite Difference model, the grid is formed by
  two sets of parallel lines that are orthogonal.
  The blocks formed by these lines are called
  cells. In the centre of each cell is the node
  the point at which the model calculates hydraulic
  head. This type of grid is called block-centered
  grid.

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Grid

• Grid mesh can be uniform or custom, a uniform
  grid is better choice when
• Evenly distributed aquifer characteristics data
• The entire flow field is equally important
• Number of cells and size is not an issue

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Grid

• Grid mesh can be custom when
• There is less or no data for certain areas
• There is specific interest in one or more smaller
  areas
• Grid orientation is not an issue in isotropic
  aquifers. When the aquifer is anisotropic, the
  model coordinate axes must be aligned with the
  main axes of the hydraulic conductivity.

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• Regular vs irregular grid spacing

Irregular spacing may be used to obtain detailed
head distributions in selected areas of the grid.
Finite difference equations that use
irregular grid spacing have a higher associated
error than FD equations that use regular grid
spacing.
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Considerations in selecting the size of the grid
spacing
Variability of aquifer characteristics (K,T,S)
Variability of hydraulic parameters (R, Q)
Curvature of the water table
Vertical change in head
Desired detail around sources and sinks (e.g.,
rivers)
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MODEL GRIDS
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Grids

• It is generally agreed that from a practical
  point-of-view the differences between grid types
  are minor and unimportant.
• USGS MODFLOW employs a body-centred grid.

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Boundary array (cell type)

• Three types of cells
• Inactive cells through which no flow into or out
  of the cells occurs during the entire time of
  simulation.
• Active, or variable-head cells are free to vary
  in time.
• Constant-head cell, model boundaries with known
  constant head.

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Hydraulic conductivity and transmissivity

• Hydraulic conductivity is the most critical and
  sensitive modelling parameter.
• Realistic values of storage coefficient and
  transmissivity, preferably from pumping test,
  should be used.

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Effective porosity

• Required to calculate velocity, used mainly in
  solute transport models

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Calibration and Validation
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Calibration parameters are uncertain
parameters whose values are adjusted during model
calibration.
Identify calibration parameters and their
reasonable ranges.
Typical calibration parameters include hydraulic
conductivity and recharge rate.
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In a real-world problem, we need to establish
model specific calibration criteria and define
targets including associated error.
Calibration Targets
associated error
calibration value
???0.80 m
20.24 m
Target with smaller associated error.
Target with relatively large associated error.
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Targets used in Model Calibration

• Head measured in an observation well is known
  as a target.

• The simulated head at the node representing the
  observation well is compared with the measured
  head.

• During model calibration, parameter values are
  adjusted until the simulated head matches the
  observed value.

• Model calibration solves the inverse problem.

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Calibration to Fluxes

• When recharge rate (R) is a calibration
  parameter, calibrating to fluxes can help in
  estimating K and/or R.

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In this example, flux information helps calibrate
K.
q KI
K ?
H1
H2
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In this example, discharge information helps
calibrate R.
R ?
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Calibration - Remarks

• Calibrations are non-unique.

• A good calibration does not ensure that the
  model will make good predictions.

• You can never have enough field data.

• Modelers need to maintain a healthy skepticism
• about their results.

• Need for an uncertainty analysis to accompany
• calibration results and predictions.

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Uncertainty in the Calibration
Involves uncertainty in

• Targets

• Parameter values

• Conceptual model including boundary conditions,
• zonation, geometry etc.

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Ways to analyze uncertainty in the calibration
Sensitivity analysis is used as an uncertainty
analysis after calibration.
Use an inverse model (automated calibration) to
quantify uncertainties and optimize the
calibration.
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Uncertainty in the Prediction

• Reflects uncertainty in the calibration.

• Involves uncertainty in how parameter values
• (e.g., recharge) will vary in the future.

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Ways to quantify uncertainty in the prediction
Sensitivity analysis
Stochastic simulation
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Model Validation
How do we validate a model so that we have
confidence that it will make accurate predictions?
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Modeling Chronology
1960s Flow models are great! 1970s
Contaminant transport models are great!
1975 What about uncertainty of flow models?
1980s Contaminant transport models dont work.
(because of failure to account for
heterogeneity)
1990s Are models reliable?
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The objective of model validation is to
determine how well the mathematical
representation of the processes describes the
actual system behavior in terms of the degree of
correlation between model calculations and actual
measured data.
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How to build confidence in a model Calibration
(history matching) Verification
requires an independent set of field
data Post-Audit requires waiting for
prediction to occur Models as interactive
management tools
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KEEPING AN OPEN MIND Consider all dimensions of
the problem before coming to a conclusion. Consid
ering all the stresses that might be imposed and
all the possible processes that might be involved
in a situation before reaching a
conclusion. KEEPING AN OPEN MIND is spending 95
of your TIME DETERMINING WHAT YOU THINK IS
HAPPENING and only 5 of your TIME DEFENDING YOUR
OPINION. AVOID the common human TRAP of
REVERSING THOSE PERCENTAGES.
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Groundwater Flow Models
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• Groundwater Flow Models
• The most widely used numerical groundwater flow
  model is MODFLOW which is a three-dimensional
  model, originally developed by the U.S.
  Geological Survey.
• It uses finite difference scheme for saturated
  zone.
• The advantages of MODFLOW include numerous
  facilities for data preparation, easy exchange of
  data in standard form, extended worldwide
  experience, continuous development, availability
  of source code, and relatively low price.
• However, surface runoff and unsaturated flow are
  not included, hence in case of transient
  problems, MODFLOW can not be applied if the flux
  at the groundwater table depends on the
  calculated head and the function is not known in
  advance.

107

• MODFLOW
• ? USGS code
• ? Finite Difference Model
• MODFLOW 88
• MODFLOW 96
• MODFLOW 2000

108

• MODFLOW
• (Three-Dimensional Finite-Difference
  Ground-Water Flow Model)
• When properly applied, MODFLOW is the recognized
  standard model.
• Ground-water flow within the aquifer is simulated
  in MODFLOW using a block-centered
  finite-difference approach.
• Layers can be simulated as confined, unconfined,
  or a combination of both.
• Flows from external stresses such as flow to
  wells, areal recharge, evapotranspiration, flow
  to drains, and flow through riverbeds can also be
  simulated.

109

• MT3D
• (A Modular 3D Solute Transport Model)
• MT3D is a comprehensive three-dimensional
  numerical model for simulating solute transport
  in complex hydrogeologic settings.
• MT3D is linked with the USGS groundwater flow
  simulator, MODFLOW, and is designed specifically
  to handle advectively-dominated transport
  problems without the need to construct refined
  models specifically for solute transport.

110
FEFLOW (Finite Element Subsurface Flow
System) FEFLOW is a finite-element package for
simulating 3D and 2D fluid density-coupled flow,
contaminant mass (salinity) and heat transport in
the subsurface. HST3D (3-D Heat and Solute
Transport Model) The Heat and Solute Transport
Model HST3D simulates ground-water flow and
associated heat and solute transport in three
dimensions.
111

• SEAWAT
• (Three-Dimensional Variable-Density Ground-Water
  Flow)
• The SEAWAT program was developed to simulate
  three-dimensional, variable- density, transient
  ground-water flow in porous media.
• The source code for SEAWAT was developed by
  combining MODFLOW and MT3D into a single program
  that solves the coupled flow and solute-transport
  equations.

112

• SUTRA
• (2-D Saturated/Unsaturated Transport Model)
• SUTRA is a 2D groundwater saturated-unsaturated
  transport model, a complete saltwater intrusion
  and energy transport model.
• SUTRA employs a two-dimensional hybrid
  finite-element and integrated finite-difference
  method to approximate the governing equations
  that describe the two interdependent processes.
• A 3-D version of SUTRA has also been released.

113

• SWIM
• (Soil water infiltration and movement model)
• SWIMv1 is a software package for simulating water
  infiltration and movement in soils.
• SWIMv2 is a mechanistically-based model designed
  to address soil water and solute balance issues.
• The model deals with a one-dimensional vertical
  soil profile which may be vertically
  inhomogeneous but is assumed to be horizontally
  uniform.
• It can be used to simulate runoff, infiltration,
  redistribution, solute transport and
  redistribution of solutes, plant uptake and
  transpiration, evaporation, deep drainage and
  leaching.

114

• VISUAL HELP
• (Modeling Environment for Evaluating and
  Optimizing Landfill Designs)
• Visual HELP is an advanced hydrological modeling
  environment available for designing landfills,
  predicting leachate mounding and evaluating
  potential leachate contamination.
• Visual MODFLOW
• (Integrated Modeling Environment for MODFLOW and
  MT3D)
• Visual MODFLOW provides professional 3D
  groundwater flow and contaminant transport
  modeling using MODFLOW and MT3D.

115
Groundwater Modelling Resources
116
Groundwater Modeling Resources

• Kumar Links to Hydrology Resources
• http//www.angelfire.com/nh/cpkumar/hydrology.html
  
• USGS Water Resources Software Page
• water.usgs.gov/software
• Richard B. Winstons Home Page
• www.mindspring.com/rbwinston/rbwinsto.htm
• Geotech Geoenviron Software Directory
• www.ggsd.com
• International Ground Water Modeling Center
• www.mines.edu/igwmc

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Ground Water Modelling Discussion Group An
email discussion group related to ground water
modelling and analysis. This group is a forum for
the communication of all aspects of ground water
modelling including technical discussions
announcement of new public domain and commercial
softwares calls for abstracts and papers
conference and workshop announcements and
summaries of research results, recent
publications, and case studies. Group home page
http//groups.yahoo.com/group/gwmodel/ Post
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118
Visual MODFLOW Users Group Visual MODFLOW is a
proven standard for professional 3D groundwater
flow and contaminant transport modeling using
MODFLOW-2000, MODPATH, MT3DMS AND RT3D. Visual
MODFLOW seamlessly combines the standard Visual
MODFLOW package with Win PEST and the Visual
MODFLOW 3D-Explorer to give a complete and
powerful graphical modeling environment. This
group aims to provide a forum for exchange of
ideas and experiences regarding use and
application of Visual MODFLOW software. Group
home page http//in.groups.yahoo.com/group/visu
al-modflow/ Post message
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THANKS
HAPPY MODELLING