C. P. KumarScientist ‘F’

C. P. KumarScientist ‘F’

National Institute of Hydrology

Roorkee – 247667 (Uttaranchal)

India

Email: cpkumar@yahoo.com

Webpage: http://www.angelfire.com/nh/cpkumar/

Introduction to Groundwater Modelling

Presentation OutlineGroundwater in Hydrologic CycleWhy Groundwater Modelling is needed?Mathematical ModelsModelling ProtocolModel DesignCalibration and ValidationGroundwater Flow ModelsGroundwater Modelling Resources

Groundwater in Hydrologic Cycle

Types of Terrestrial WaterTypes of Terrestrial Water

Ground waterGround water

SoilSoilMoistureMoisture

SurfaceWater

Unsaturated Zone / Zone of Aeration / Vadose(Soil Water)

Pores Full of Combination of Air and Water

Zone of Saturation (Ground water)

Pores Full Completely with Water

Groundwater

Important source of clean waterMore abundant than SW

Linked to SW systems

Sustains flows in streams

Baseflow

pollution

Groundwater Concerns?

groundwater miningsubsidence

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• The total volume that may be withdrawn annually from the aquifer.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 theirrates.

• 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.

We should have a CALIBRATED MODEL of the aquifer, especially,we should know the aquifer’s natural replenishment (from precipitation and through aquifer boundaries).

Prior to determining the management scheme for any aquifer:

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 otherparts of the water resources system, economic information, sourcesof pollution, effect of changes on the environment---springs, rivers,...

The model will provide the response of the aquifer (water levels,concentrations, etc.) to the implementation of any managementalternative.

GROUND WATER MODELING

WHY MODEL?

•To make predictions about a ground-water system’s 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 Toolfor furthering our understanding

of hydrogeological systems

Importance of understanding ground water flow modelsConstruct accurate representations of hydrogeological systemsUnderstand the interrelationships between elements of systemsEfficiently develop a sound mathematical representation Make reasonable assumptions and simplificationsUnderstand the limitations of the mathematical representationUnderstand the limitations of the interpretation of the results

Introduction to Ground Water Flow Modelling

Kxqhxh −= 0)(

Predicting heads (and flows) and Approximating parameters

Solutions to the flow equationsMost ground water flow models are solutions of some form of the ground water flow equation

PotentiometricSurface

x

xx

ho

x0

h(x)

x

Kq

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

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

h(x,y,z,t)?

Kxqhhdx

Kqdh

Kq

dxdh xh

h−=−⇒−=⇒−= ∫∫ 000

Darcy’s Law Integrated

The only effective way to test effects of The only effective way to test effects of groundwater management strategiesgroundwater management strategiesTakes time, money to make modelTakes time, money to make modelConceptual modelConceptual model

Steady state modelSteady state modelTransient modelTransient model

The model is only as good as its calibrationThe model is only as good as its calibration

Groundwater ModelingGroundwater Modeling

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 MODELSCONCEPTUAL 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

(Darcy’s law + water balance equation) with head (h) as the dependent variable

• Boundary Conditions

• Initial conditions (for transient problems)

R Δx Δy Q

ΔyΔx

Δz

1. Consider flux (q) through REV2. OUT – IN = - ΔStorage3. Combine with: q = -KK grad h

q

Derivation of the Governing Equation

Law of Mass Balance + Darcy’s Law = Governing Equation for Groundwater Flow

---------------------------------------------------------------

div q = - Ss (∂h ⁄∂t) (Law of Mass Balance)

q = - K grad h (Darcy’s Law)

div (K grad h) = Ss (∂h ⁄∂t)(Ss = S / Δ z)

0)()()( =∂∂

∂∂

+∂∂

∂∂

+∂∂

∂∂

zhK

zyhK

yxhK

xzyx

General governing equationfor steady-state, heterogeneous, anisotropic

conditions, without a source/sink term

*)()()( RzhK

zyhK

yxhK

xzyx −=∂∂

∂∂

+∂∂

∂∂

+∂∂

∂∂

with a source/sink term

*)()()( RthS

zhK

zyhK

yxhK

xszyx −∂∂

=∂∂

∂∂

+∂∂

∂∂

+∂∂

∂∂

General governing equation for transient, heterogeneous, and anisotropic conditions

Specific StorageSs = ΔV / (Δx Δy Δz Δh)

Figures taken from Hornberger et al. (1998)

Unconfined aquiferSpecific yield

Confined aquiferStorativity

S = V / A Δ hS = Ss b

b

ΔhΔh

*)()()( RthS

zhK

zyhK

yxhK

xszyx −∂∂

=∂∂

∂∂

+∂∂

∂∂

+∂∂

∂∂

RthS

yhT

yxhT

xyx −

∂∂

=∂∂

∂∂

+∂∂

∂∂ )()(

RthS

yhhK

yxhhK

xyx −

∂∂

=∂∂

∂∂

+∂∂

∂∂ )()(

2D confined:

2D unconfined:

Storage coefficient (S) is either storativity or specific yield.S = Ss b & T = K b

General 3D equation

Types of Solutions of Mathematical Models

• Analytical Solutions: h= f(x,y,z,t)(example: Theis equation)

• Numerical SolutionsFinite difference methodsFinite element methods

• Analytic Element Methods (AEM)

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

Limitations of Analytical Models

Numerical Methods

hAll numerical methods involve representing the flow domain by a limited number of discrete points called nodes.hA 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 ModelsRequires vertical discretization (or layering) of model

K1K2K3K4

Finite difference modelsmay be solved using:

• a computer program (e.g., a FORTRAN program)

• a spreadsheet (e.g., EXCEL)

Finite Elements: basis functions, variational principle,Galerkin’s method, weighted residuals

• Nodes plus elements; elements defined by nodes

• Nodes located on flux boundaries

• Flexibility in grid design: elements shaped to boundarieselements fitted to capture detail

• Easier to accommodate anisotropy that occurs at anangle to the coordinate axis

• Able to simulate point sources/sinks at nodes

• Properties (K, S) assigned to elements

Involves superposition of analytic solutions. Heads are calculated in continuous space using a computer to do the mathematics involved in superposition.

Hybrid

Analytic Element Method (AEM)

The AE Method was introduced by Otto Strack. A general purpose code, GFLOW, was developed byStrack’s 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 ModelsMathematical Models

AnalyticalNumerical

Modelling ProtocolEstablish the Purpose of the ModelDevelop Conceptual Model of the SystemSelect Governing Equations and Computer CodeModel DesignCalibrationCalibration Sensitivity AnalysisModel VerificationPredictionPredictive Sensitivity AnalysisPresentation of Modeling Design and ResultsPost AuditModel Redesign

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

Prediction; System Interpretation; Generic ModelingWhat 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

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?

ETHICSThere may be a cheaper, more effective approachWarn of limitations

Conceptual Model“Everything should be made as simple as possible, but not simpler.” Albert Einstein

Pictorial representation of the groundwater flow systemWill 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 CodeSelect Computer ModelCode Verification

Comparison to Analytical Solutions; Other Numerical Models

Model DesignDesign of Grid, selecting time steps, boundary and initial conditions, parameter data set

Steady/Unsteady..1, 2, or 3-D; …Heterogeneous/Isotropic…..Instantaneous/Continuous

Steady/Unsteady..1, 2, or 3-D; …Heterogeneous/Isotropic…..Instantaneous/Continuous

CalibrationShow 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 AnalysisUncertainty in Input ConditionsDetermine Effect of Uncertainty on Calibrated Model

Model VerificationUse Model to Reproduce a Second Set of Field Data

PredictionDesired Set of ConditionsSensitivity 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.

PostauditNew field data collected to determine if prediction was correctSite-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 nodeDarcy's LawConservation of Mass

Define Material PropertiesBoundary ConditionsInitial ConditionsStresses

At each node either H or Q is known, the other is unknownn equations & n unknownssolve simultaneously with matrix algebra

Result H at each known Q nodeQ at each known H node

Calibrate Steady StateTransient

Validate

Sensitivity

Predictions

Similar Process for Transport Modeling only Concentration and Flux is unknown

NUMERICAL MODELING

Model Design

MODELs NEED

GeometryMaterial Properties (K, S, T, Φe, R, etc.)

Boundary Conditions (Head, Flux, Concentration etc.)

Stress - changing boundary condition

Model DesignModel Design

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

Concept DevelopmentConcept 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 representationof 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 CodeSelection 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 GeometryModel Geometry

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

BoundariesBoundaries

• 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.)

BoundariesBoundaries

• 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 BOUNDARYNeither HEAD nor FLUX isSpecified. Can represent aPhysical boundary or a flowLine (Groundwater Divide)

SPECIFIED HEAD ORCONSTANT HEAD BOUNDARYh = constantq is determined by the model.And may be +ve or –ve accordingto the hydraulic gradient developed

TYPES OF MODEL BOUNDARY (cont’d)

SPECIFIED FLUX BOUNDARYq = constanth is determined by the model(The common method of simulationis to use one injection well for eachboundary cell)

HEAD DEPENDANT BOUNDARYhb = constantq = c (hb – hm) and c = f (K,L) and is calledCONDUCTANCEhm is determined by the model andits 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 Boundary conditions in ModflowModflow• Constant head boundary• Head dependent flux

– River Package– Drain Package– General-head Boundary Package

• Known Flux– Recharge– Evapotranspiration– Wells– Stream

• No Flow boundaries

Initial ConditionsInitial 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 ParametersModel Parameters

• Time• Space (layer top and bottom)• Hydrogeologic characteristics

(hydraulic conductivity, transmissivity, storage parameters and effective porosity)

TimeTime

• 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

GridGrid

• 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.

GridGrid

• 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

GridGrid

• 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 irregulargrid spacing have a higher associated error than FD equations that use regular grid spacing.

Curvature of the water table

Vertical change in head

Variability of aquifer characteristics (K,T,S)

Variability of hydraulic parameters (R, Q)

Considerations in selecting the size of the grid spacing

Desired detail around sources and sinks (e.g., rivers)

MODEL GRIDS

GridshIt is generally agreed that from a practical

point-of-view the differences between grid types are minor and unimportant.

hUSGS MODFLOW employs a body-centred grid.

Boundary array (cell type)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 Hydraulic conductivity and transmissivitytransmissivity

• 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 porosityEffective porosity

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

Calibration and Validation

Calibration parameters are uncertain parameterswhose values are adjusted during model calibration.

Typical calibration parameters include hydraulic conductivity and recharge rate.

Identify calibration parameters and their reasonable ranges.

Calibration Targets

calibrationvalue

associated error

20.24 m

+/−0.80 m

Target with relativelylarge associated error.

Target with smaller associated error.

In a real-world problem, we need to establish model specific calibration criteria and define targets including associated error.

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

Targets used in Model Calibration

• 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.

H1H2

q = KI

In this example, flux information helps calibrate K.

In this example, discharge information helps calibrate R.

Calibration - Remarks

• Calibrations are non-unique.

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

• Need for an uncertainty analysis to accompanycalibration results and predictions.

• You can never have enough field data.

• Modelers need to maintain a healthy skepticismabout their results.

Uncertainty in the Calibration

Involves uncertainty in:

Parameter values

Conceptual model including boundary conditions,zonation, geometry etc.

Targets

Ways to analyze uncertaintyin 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

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

Reflects uncertainty in the calibration.

Stochastic simulation

Ways to quantify uncertaintyin the prediction

Sensitivity analysis

How do we “validate” a model so thatwe have confidence that it will makeaccurate predictions?

Modeling Chronology

1960’s Flow models are great!

1970’s Contaminant transport models are great!

1975 What about uncertainty of flow models?

1980s Contaminant transport models don’t 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.

Considering 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, arealrecharge, 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 Resourceshttp://www.angelfire.com/nh/cpkumar/hydrology.html

USGS Water Resources Software Pagewater.usgs.gov/software

Richard B. Winston’s Home Pagewww.mindspring.com/~rbwinston/rbwinsto.htm

Geotech & Geoenviron Software Directorywww.ggsd.com

International Ground Water Modeling Centerwww.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 publications, and casestudies.

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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 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.

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HAPPY MODELLING

THANKS