5Types of Terrestrial Water SurfaceWaterSoilMoistureGround water
6Unsaturated Zone / Zone of Aeration / Vadose Pores Full of Combination of Air and WaterUnsaturated Zone / Zone of Aeration / Vadose(Soil Water)Zone of Saturation (Ground water)Pores Full Completely with Water
7Important source of clean water GroundwaterImportant source of clean waterMore abundant than SWBaseflowLinked to SW systemsSustains flowsin streams
12Groundwater 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.
13Management of a groundwater system, means making such decisions as: The total volume that may be withdrawn annually from the aquifer.The location of pumping and artificial recharge wells, and their rates.Decisions related to groundwater quality.Groundwater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 wastesLeachate from landfillsAgricultural activities such as the use of fertilizers and pesticides
14MANAGEMENT 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.
15A 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.
16The 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.
17Prior to determining the management scheme for any aquifer: We should have a CALIBRATED MODEL of the aquifer, especially,we should know the aquifer’s natural replenishment (fromprecipitation and through aquifer boundaries).The model will provide the response of the aquifer (water levels,concentrations, etc.) to the implementation of any managementalternative.We should have a POLICY that dictates management objectivesand 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,...
18GROUND WATER MODELINGWHY MODEL?To make predictions about a ground-watersystem’s response to a stressTo understand the systemTo design field studiesUse as a thinking tool
19Use 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.
20Use of Groundwater models To describe the system in order to analyse various assumptionsTo generate a hypothetical system that will be used to study principles of groundwater flow associated with various general or specific problems.
21ALL 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 mayculminate in a complex numerical simulation.
22Ground Water Flow Modelling A Powerful Toolfor furthering our understanding of hydrogeological systemsImportance of understanding ground water flow modelsConstruct accurate representations of hydrogeological systemsUnderstand the interrelationships between elements of systemsEfficiently develop a sound mathematical representationMake reasonable assumptions and simplificationsUnderstand the limitations of the mathematical representationUnderstand the limitations of the interpretation of the resultsI want to show you how to use the power of hydrogeological modelingYou should be able to do more than just go through the motions of hydrogeological modeling, you should to be able to use the modeling process to further your understanding of the hydrogeological system that you are investigating.This will hinge on the development of a sound conceptual model, a concept in your mind of how the plumbing works and how it relates to the problem to be addressedWe will use mathematical models (analytical and numerical) as tools to address these problemsThe next step is to learn how to convert your conceptual model into a mathematical model. This could be as simple as applying 1-D Darcy’s Law and as complex as setting up and calibrating a 3-D, transient numerical model.In any case the procedure is the same: 1) Define the problem in lay-terms (demonstrate the significance to your audience), 2) define the specific objectives in technical (hydrogeological) terms, 3) Develop a conceptual model [site description and general hydrogeology], 4) convert the conceptual model into mathematical models that will address the objectives [methodology] 5) determine specifically where you will get the information from to set up your model [more methodology], 6) set up your model, calibrate and use it to address the objective [results]This will also help write the documentation which you should be writing all along
23Introduction to Ground Water Flow Modelling Predicting heads (and flows) andApproximating parametersPotentiometricSurfaceh(x,y,z,t)?Solutions to the flow equationsMost ground water flow models are solutions of some form of the ground water flow equationxhoh(x)KqThe 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)“e.g., unidirectional, steady-state flow within a confined aquiferDarcy’s Law Integrated
24Groundwater ModelingThe only effective way to test effects of groundwater management strategiesTakes time, money to make modelConceptual model Steady state model Transient modelThe model is only as good as its calibration
25Processes we might want to model Groundwater flowcalculate both heads and flowSolute transport – requires information on flow (velocities)calculate concentrations
26MODELING PROCESSALL IMPORTANT MECHANISMS & PROCESSES MUST BE INCLUDED IN THE MODEL, OR RESULTS WILL BE INVALID.
27TYPES OF MODELS CONCEPTUAL MODEL QUALITATIVE DESCRIPTION OF SYSTEM "a cartoon of the system in your mind"MATHEMATICAL MODEL MATHEMATICAL DESCRIPTION OF SYSTEMSIMPLE - 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 coefficientPHYSICAL MODEL e.g. SAND TANK which poses scaling problems
29Mathematical 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)
30Components of a Mathematical Model Governing Equation(Darcy’s law + water balance equation) with head (h) as the dependent variableBoundary ConditionsInitial conditions (for transient problems)
31Derivation of the Governing Equation R x yqzxyConsider flux (q) through REVOUT – IN = - StorageCombine with: q = -K grad h
32div (K grad h) = Ss (h t) Law of Mass Balance + Darcy’s Law =Governing Equation for Groundwater Flowdiv q = - Ss (h t) (Law of Mass Balance)q = - K grad h (Darcy’s Law)div (K grad h) = Ss (h t)(Ss = S / z)
33General governing equation for steady-state, heterogeneous, anisotropic conditions, without a source/sink termwith a source/sink term
34General governing equation for transient, heterogeneous, and anisotropic conditions Specific StorageSs = V / (x y z h)
35h h b S = V / A h S = Ss b Confined aquifer Unconfined aquifer StorativitySpecific yieldFigures taken from Hornberger et al. (1998)
36Storage coefficient (S) is either storativity or specific yield. General 3D equation2D confined:2D unconfined:Storage coefficient (S) is either storativity or specific yield.S = Ss b & T = K b
37Types of Solutions of Mathematical Models Analytical Solutions: h= f(x,y,z,t)(example: Theis equation)Numerical SolutionsFinite difference methodsFinite element methodsAnalytic Element Methods (AEM)
38Limitations 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 morepowerful solution to the flow equation Numerical modeling
39Numerical MethodsAll 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.
40Numerical SolutionsDiscrete solution of head at selected nodal points.Involves numerical solution of a set of algebraicequations.Finite difference models (e.g., MODFLOW)Finite element models (e.g., SUTRA)
42Finite difference models may be solved using:a computer program(e.g., a FORTRAN program)a spreadsheet (e.g., EXCEL)
43Finite Elements: basis functions, variational principle, Galerkin’s method, weighted residualsNodes plus elements; elements defined by nodesProperties (K, S) assigned to elementsNodes located on flux boundariesAble to simulate point sources/sinks at nodesFlexibility in grid design:elements shaped to boundarieselements fitted to capture detailEasier to accommodate anisotropy that occurs at anangle to the coordinate axis
44HybridAnalytic 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 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.
48Modelling Protocol Establish the Purpose of the Model Develop Conceptual Model of the SystemSelect Governing Equations and Computer CodeModel DesignCalibrationCalibration Sensitivity AnalysisModel VerificationPredictionPredictive Sensitivity AnalysisPresentation of Modeling Design and ResultsPost AuditModel Redesign
49Purpose - 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 AnalysisGeneric: Used in a hypothetical sense, not necessarily for a real site
50Model “Overkill”?Is the vast labor of characterizing the system, combined with the vast labor of analyzing it, disproportionate to the benefits that follow?
51ETHICS There may be a cheaper, more effective approach Warn of limitations
52Conceptual 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.
53Select Computer Code Select Computer Model Code Verification Comparison to Analytical Solutions; Other Numerical ModelsModel DesignDesign of Grid, selecting time steps, boundary and initial conditions, parameter data setSteady/Unsteady..1, 2, or 3-D; …Heterogeneous/Isotropic…..Instantaneous/Continuous
54CalibrationShow that Model can reproduce field-measured heads and flow (concentrations if contaminant transport)Results in parameter data set that best represents field-measured conditions.
55Calibration Sensitivity Analysis Uncertainty in Input ConditionsDetermine Effect of Uncertainty on Calibrated Model
56Model Verification Prediction Use Model to Reproduce a Second Set of Field DataPredictionDesired Set of ConditionsSensitivity AnalysisEffect of uncertainty in parameter values and future stresses on the predicted solution
57Presentation of Modelling Design and Results Effective Communication of Modeling EffortGraphs, Tables, Text etc.
58Postaudit Model Redesign New field data collected to determine if prediction was correctSite-specific data needed to validate model for specific site applicationModel RedesignInclude new insights into system behavior
59NUMERICAL MODELING DISCRETIZE Write equations of GW Flow between each nodeDarcy's LawConservation of MassDefine Material PropertiesBoundary ConditionsInitial ConditionsStressesAt each node either H or Q is known, the other is unknownn equations & n unknownssolve simultaneously with matrix algebraResult H at each known Q nodeQ at each known H nodeCalibrate Steady StateTransientValidateSensitivityPredictionsSimilar Process for Transport Modeling only Concentration and Flux is unknown
63Model Design Conceptual Model Selection of Computer Code Model GeometryGridBoundary arrayModel ParametersBoundary ConditionsInitial ConditionsStresses
64Concept DevelopmentDeveloping 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.
65Conceptual ModelA 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.
66Selection 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
67Model GeometryModel geometry defines the size and the shape of the model. It consists of model boundaries, both external and internal, and model grid.
68BoundariesPhysical boundaries are well defined geologic and hydrologic features that permanently influence the pattern of groundwater flow (faults, geologic units, contact with surface water etc.)
69BoundariesHydraulic 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.
70HYDRAULIC BOUNDARIESA 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) boundaryBUTStress 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.
71TYPES 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
72TYPES 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
73Boundary TypesSpecified 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)
74Boundary conditions in Modflow Constant head boundaryHead dependent fluxRiver PackageDrain PackageGeneral-head Boundary PackageKnown FluxRechargeEvapotranspirationWellsStreamNo Flow boundaries
75Initial ConditionsValues 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.
76Model Parameters Time Space (layer top and bottom) Hydrogeologic characteristics (hydraulic conductivity, transmissivity, storage parameters and effective porosity)
77TimeTime 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
78GridIn 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.
79GridGrid mesh can be uniform or custom, a uniform grid is better choice whenEvenly distributed aquifer characteristics dataThe entire flow field is equally importantNumber of cells and size is not an issue
80Grid Grid mesh can be custom when There is less or no data for certain areasThere is specific interest in one or more smaller areasGrid 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.
81Regular 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 errorthan FD equations that use regular grid spacing.
82Considerations 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 tableVertical change in headDesired detail around sources and sinks (e.g., rivers)
84GridsIt 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.
85Boundary array (cell type) Three types of cellsInactive 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.
86Hydraulic 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.
87Effective porosityRequired to calculate velocity, used mainly in solute transport models
89Calibration 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.
90In a real-world problem, we need to establish model specific calibration criteria and define targets including associated error.Calibration Targetsassociated errorcalibrationvalue0.80 m20.24 mTarget with smaller associated error.Target with relativelylarge associated error.
91Targets 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.
92Calibration to FluxesWhen recharge rate (R) is a calibration parameter, calibrating to fluxes can help in estimating K and/or R.
93In this example, flux information helps calibrate K. q = KIK = ?H1H2
94In this example, discharge information helps calibrate R.
95Calibration - 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 skepticismabout their results.Need for an uncertainty analysis to accompanycalibration results and predictions.
96Uncertainty in the Calibration Involves uncertainty in:TargetsParameter valuesConceptual model including boundary conditions,zonation, geometry etc.
97Ways to analyze uncertainty in the calibrationSensitivity analysis is used as an uncertainty analysis after calibration.Use an inverse model (automated calibration) to quantify uncertainties and optimize the calibration.
98Uncertainty in the Prediction Reflects uncertainty in the calibration.Involves uncertainty in how parameter values(e.g., recharge) will vary in the future.
99Ways to quantify uncertainty in the predictionSensitivity analysisStochastic simulation
100Model Validation How do we “validate” a model so that we have confidence that it will makeaccurate predictions?
101Modeling Chronology 1960’s Flow models are great! 1970’s Contaminant transport models are great!What about uncertainty of flow models?1980s Contaminant transport models don’t work.(because of failure to account for heterogeneity)1990s Are models reliable?
102“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”.
103How to build confidence in a model Calibration (history matching)“Verification”requires an independent set of field dataPost-Audit: requires waiting for prediction to occurModels as interactive management tools
104Consider all dimensions of the problem before coming to a conclusion. KEEPING AN OPEN MINDConsider 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.
106Groundwater 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.
108MODFLOW (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.
109MT3D (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.
110FEFLOW HST3D (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.
111SEAWAT (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.
112SUTRA (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.
113SWIM (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.
114VISUAL HELP Visual MODFLOW (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.
116Groundwater Modeling Resources Kumar Links to Hydrology ResourcesUSGS Water Resources Software Pagewater.usgs.gov/softwareRichard B. Winston’s Home PageGeotech & Geoenviron Software DirectoryInternational Ground Water Modeling Center
117Ground Water Modelling Discussion Group An 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 :Post message :Subscribe :Unsubscribe :List owner :
118Visual 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 :Post message :Subscribe :Unsubscribe :List owner :