Introduction to Groundwater Modelling

C. P. Kumar Scientist F

National Institute of Hydrology Roorkee 247667

(Uttaranchal) India Email cpkumar_at_yahoo.com Webp

age http//www.angelfire.com/nh/cpkumar/

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

Groundwater in Hydrologic Cycle

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Types of Terrestrial Water

Surface Water

Soil Moisture

Ground water

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

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

- Problems with groundwater
- Groundwater overdraft / mining / subsidence
- Waterlogging
- Seawater intrusion
- Groundwater pollution

Why Groundwater Modelling is needed?

- 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.

- 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such decisions as - The total volume that may be withdrawn annually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

- 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.

- 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.

- 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.

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,...

- 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

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.

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.

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.

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

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

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

- Processes we might want to model
- Groundwater flow
- calculate both heads and flow
- Solute transport requires information on flow

(velocities) - calculate concentrations

MODELING PROCESS ALL IMPORTANT

MECHANISMS PROCESSES MUST BE INCLUDED IN THE

MODEL, OR RESULTS WILL BE INVALID.

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

Mathematical Models

- 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)

- 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)

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

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)

General governing equation for steady-state,

heterogeneous, anisotropic conditions, without a

source/sink term

with a source/sink term

General governing equation for transient,

heterogeneous, and anisotropic conditions

Specific Storage Ss ?V / (?x ?y ?z ?h)

?h

?h

b

S V / A ? h S Ss b

Confined aquifer

Unconfined aquifer

Storativity

Specific yield

Figures taken from Hornberger et al. (1998)

General 3D equation

2D confined

2D unconfined

Storage coefficient (S) is either storativity or

specific yield. S Ss b T K b

- 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)

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

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.

- 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)

Finite Difference Modelling

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

model

K1

K2

K3

K4

- Finite difference models
- may be solved using
- a computer program
- (e.g., a FORTRAN program)
- a spreadsheet (e.g., EXCEL)

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

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.

Modelling Protocol

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

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

Model Overkill?

- Is the vast labor of characterizing the system,

combined with the vast labor of analyzing it,

disproportionate to the benefits that follow?

ETHICS

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

Conceptual Model Everything 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.

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

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.

Calibration Sensitivity Analysis

- Uncertainty in Input Conditions
- Determine Effect of Uncertainty on Calibrated

Model

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

Presentation of Modelling Design and Results

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

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

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

NUMERICAL MODELING

Model Design

MODELs NEED Geometry Material Properties (K, S,

T, Fe, R, etc.) Boundary Conditions (Head, Flux,

Concentration etc.) Stress - changing boundary

condition

Model Design

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

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.

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.

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

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.

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.)

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.

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.

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

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

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)

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

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.

Model Parameters

- Time
- Space (layer top and bottom)
- Hydrogeologic characteristics (hydraulic

conductivity, transmissivity, storage parameters

and effective porosity)

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

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.

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

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.

- 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.

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)

MODEL GRIDS

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.

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.

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.

Effective porosity

- Required to calculate velocity, used mainly in

solute transport models

Calibration and Validation

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.

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.

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.

Calibration to Fluxes

- When recharge rate (R) is a calibration

parameter, calibrating to fluxes can help in

estimating K and/or R.

In this example, flux information helps calibrate

K.

q KI

K ?

H1

H2

In this example, discharge information helps

calibrate R.

R ?

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.

Uncertainty in the Calibration

Involves uncertainty in

- Targets

- Parameter values

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

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.

Uncertainty in the Prediction

- Reflects uncertainty in the calibration.

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

Ways to quantify uncertainty in the prediction

Sensitivity analysis

Stochastic simulation

Model Validation

How do we validate a model so that we have

confidence that it will make accurate predictions?

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?

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.

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

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.

Groundwater Flow Models

- 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.

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

- 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.

- 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.

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.

- 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.

- 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.

- 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.

- 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.

Groundwater Modelling Resources

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

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

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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

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THANKS

HAPPY MODELLING