Grid Design, Finite Difference Grids, and an Introduction to MODFLOW Based on Slides Prepared By Eileen Poeter, Colorado School of Mines

Conceptual Model Defines 1) Dimensions of numerical model 2) How the grid is designed 3) How the grid is oriented

Representation of Numerical Model

DISCRETIZED HYPOTHETICAL AQUIFER Layers may correspond to horizontal geohydrologic intervals ---- Aquifer boundary ● Active cell ○ Inactive cell Δrj Width of cell in row direction (j indicates column number) Δci Width of cell in column direction (i indicates row number) Δvk Thickness of the cell ΔrjΔciΔvk Volume of cell with coordinates (i,j,k)

Representation of Numerical Model Choose numbers to define a conceptual object like the grid shown below to represent the geometry, properties, boundary conditions, initial conditions and stresses on a groundwater system to build a representation of field conditions Videos of Flow (Mojave, Santa Clara Transport Models (Tracy?)

Representation of Numerical Model Divide space into pieces Define one value for each geohydrologic parameter to represent the piece One value defined for each physical property (ie. K and S) One value of head and flow is calculated Complex geologic material distributions are simplified Properties vary Within a layer From layer to layer

Representation of Numerical Model Some of the model pieces are defined as inactive (open circles) Take the rectangular form of the mathematics and create an odd shaped geometry Inactive indicators may continue down through every layer of the grid, or not Example: aquifer is bowl shaped then some pieces that are active in the shallow layers would be specified as inactive in the deeper layers

Grid Design Numerical model needs to be divided into pieces of space and time for which the solution can be linearized and the properties and results averaged Compromise between accuracy, cost, and effort Smaller pieces are more accurate, but require more time and effort

Grid Design Discretize: Space (plan view and cross section) Time Difficult Task Redesign is a major undertaking

Spatial Dimension 2D areal 2D profile (special class) Quasi 3D (confining layers by leakage) Fully 3D Aquifer viewpoint: 2D areal and quasi 3D Flow system viewpoint: 2D profile and 3D

QUASI THREE DIMENSIONAL Flowlines in sand are nearly horizontal Flowlines in clay are nearly vertical Quasi-3d Single model layer maybe used to represent each sand, while the clay may be represented by the vertical conductance between layers Clay layer is represented by six model layers. Use if clay storage is an issue.

Fully 3D Models Simulate confined and unconfined aquifers when vertical head gradients are important Represent transient release of water from storage in confining beds by including confining bed as a layer with storage properties Parameter arrays specified for each layer of the model

Parameters Transmissivity Hydraulic conductivity Thickness Anisotropy Storage properties

Laying out the grid Types of Grids Defining Model Layers Orienting the Grid Spatial Scales

Types of Grids Array of Nodes Grid Structure Finite elements Finite difference cells

Finite Elements Allow more flexibility in designing grid 2D elements Triangles Quadrilaterals 3D elements Tetrahedrons Hexahedrons Prisms Exact representation of boundaries is possible Input of data is generally more laborious than finite difference

Finite difference cells Mesh-centered Block-centered Easier math for boundaries MODFLOW

Defining Model Layers One layer layer represents a single hydrostratigraphic unit or aquifer Quasi-3D Hydrogeologic units horizontal Leakance Fully 3D Dipping units Aquifers and Confining units explicit

Orienting the Grid Grid drawn on an overlay of a map of the area to be modeled If possible orient the grid so that the x and y axes are colinear with Kx and Ky and vertical axis is aligned with Kz For finite difference, try to minimize the number of nodes that fall outside the boundaries of the modeled area Set boundaries far from the area of interest so imposed stresses to the interior of system don’t reach the boundaries

Spatial Scales Critical Step Based on: Size of model area Changes in head (primary) Changes in aquifer properties (secondary) Changes in recharge, pumping, surface-water interaction

Spatial Scales Horizontal Node Spacing: Vertical Node Spacing: Function of expected curvature in the water table or potentiometric surface Variations in aquifer properties in horizontal dimension typically greater than vertical Vertical Node Spacing: Function of change in head in the vertical direction Typically one layer per hydrostratigraphic unit Significant vertical head gradients may want more

Vertical discretization can vary depending on use of the model Halford, 1999

Spatial Scales Overall size of model area also affects the selection of model area Compromise between accuracy and practicality Small number of nodes Minimize data handling, computer storage and computation time Large number of nodes Represent system accurately Meaningful boundaries may require a large area

Variably spaced finite-difference grid allows good discretization of remediation area, while allowing model to go to hydrologic boundaries. Halford, 1999

Assigning Parameter Values Data Needs (Discussed last week) Two Categories Physical framework (geometry including thickness, extent, and properties of units) Hydraulic data (heads and fluxes) Transferring field data to the grid Scale issues Zones (sets of nodes with similar properties) Interpolation algorithms such as kriging Hydrogeologic judgement WHATEVER METHOD, DISTRIBUTIONS MUST BE REASONABLE AND MAKE SENSE!!!!

FINITE DIFFERENCE METHOD The continuous system is replaced by a finite set of discrete points in time and space The partial derivatives are replaced by terms calculated from the differences in head values at these points The discretization process results in a system of simultaneous linear algebraic equations—difference equations The solution to the difference equations yields values of head at specific points and time

Finite Difference Methods See handout taken from Lessons Prepared By Eileen Poeter, Colorado School of Mines Spreadsheet Example MODFLOW

Discretize Time and Space FINITE DIFFERENCE AND MODFLOW Plan View Cross Sectional View Time

Discretize Time and Space Plan View For a finite-difference grid, lines between cells need to orthogonal and extend the entire width of the grid any detail defined in the interior of the grid is extended all the way to the edges most finite-difference codes allow the width of cells along rows to vary

Plan View Grid Considerations Problem Domain External Inactive Grids Flow Direction Anisotropy Minimize Number of Cells Boundaries Between Features Stress Areas Observation Points Symmetry Relative Size of Adjacent Grids (1.5) Orthogonal Directions (100:1) Future Solute Transport

Plan View Grid Considerations Problem Domain Use well-defined, permanent natural boundaries when possible. If a boundary is not permanent (e.g. a ground-water divide) anticipate potential future variations, and either accommodate them from the start or be prepared to monitor appropriately and make adjustments later. Most approaches to grid development require substantial time and effort to make substantial changes to the model grid.

Plan View Grid Considerations External Inactive Grids Rotate grid to allow as few nodes as possible outside the active model domain Minimize input and output file size Make data management easier Flow Direction Orient grid so that the primary flow direction is aligned with the rows and columns Flow calculations are oriented along rows and columns, so diagonal flows are calculated in a stair-step manner, thus orienting the rows and columns in the direction of flow will reduce errors.

Plan View Grid Considerations Anisotropy Orient grid so that the rows and columns of the grid coincide with the major axes of the hydraulic conductivity ellipsoid. Minimize Number of Cells Easier to manage Executes more quickly Tradeoff with accuracy Boundaries Between Features More detailed grid where conditions change abruptly May need gradual transition in parameter values at a contact, which can reduce calculation errors or convergence trouble. If the cells are small, such a gradation is a fairly good approximation of the actual transition.

Plan View Grid Considerations Stress Areas (Steep Gradients) Gradient between cells represented by a straight line. Better solution if many small cells are used. Observation Points / Areas of Interest Head, concentration, or flow rate can be interpolated between cells More accurate and more convenient to have cells at needed locations Symmetry May allow you to cut your model size in half or more Common when simulating engineered features Relative Size of Adjacent Grids (1.5) Orthogonal Directions (100:1) Future Solute Transport

Plan View Grid Considerations Relative Size of Adjacent Grids (1.5) If adjacent grids have substantially different size, then truncation errors may occur in the matrix solution. To avoid problems maintain a maximum size difference of 1.5 for adjacent cells. Orthogonal Directions (100:1) Aspect ratio is less critical than relative size. Acceptable for the ratio of length to width, or width to length, to be 100:1. Future Solute Transport Frequently requires much smaller cells than flow modeling Often advantageous to start with this discretization

Discretize Time and Space 2) Cross Sectional View MODFLOW allows thickness of layers to vary on a cell by cell basis Each layer must extend across the entire model Pinch outs must be dealt with by changing properties of the layer

Layer Considerations One Layer = NO VERTICAL flow, flow parallel to layer Vertical Components = stacks of cells, layers Two layers = upward or downward gradient of one magnitude (cannot calculate convergent flow) Complicated vertical flow patterns = multiple layers

Layer Considerations Purpose of Model Hydrostratigraphic Units Regional vs. Local Partial Penetration Confining Unit Storage Future Transport Modeling Hydrostratigraphic Units Geologic Logs Geophysics Vertical Hydraulic Gradients Dewatering Layer Representation Options Constant layer thickness (variable properties) Variable layer thickness (constant properties) Relative size of adjacent grids is not an issue in vertical direction

Layer Considerations – Purpose of the Model Regional vs. Local Units likely to be grouped or lumped in regional More detail in local Nature of question will influence Partial Penetration Layers to define open interval Additional layers to define head gradients and flow paths Confining Unit Storage Future Transport Modeling

Layer Considerations – Purpose of the Model Confining Unit Storage No layers No storage Leakage Multiple layers Water in storage Long travel times for pressure gradient Future Transport Modeling All of above issues Travel time requires multiple layers No cells for confining unit: Multiple layers for confining unit:

Layer Considerations (cont.) Hydrostratigraphic Units Geologic Logs Build a 3D stratigraphy Determine lumping/simplification Even homogeneous may have vertical gradients because of boundaries Geophysics Use to add to information from geologic logs Vertical Hydraulic Gradients Determine if natural gradients are important to your problem Enough layers to represent variation in gradients

Layer Considerations (cont.) Dewatering The original version of MODFLOW would not allow grid cells to "re-wet" if the head had dropped below the bottom of a cell in a previous iteration. These cells would become impermeable. The modern MODFLOW accommodates this feature. However there are often convergence issues or long run times. If not using rewetting, you may have to make shallow units thick in order to keep them from completely dewatering. Of course, this means that you will not evaluate vertical components of flow in that zone. permanently impermeable zone if re-wetting option is not used, even if the well is turned off:

Layer Considerations (cont.) Relative size of adjacent grids is not an issue in vertical direction MODFLOW connects layers explicitly, consequently you do not need to be concerned about truncation errors in a matrix solution for vertically adjacent cells.

Layer Considerations (cont.) Layer Representation Options Constant layer thickness /variable properties Expedites modeling Rough approximation Compatibility with another function Variable layer thickness /constant properties More representative of field conditions

Discretize Time and Space TIME STEPS: temporal equivalent of grid cells Small when stresses change and increase in length to a constant, convenient size until the stresses change STRESS PERIODS: groups of time steps during which stresses do not change Temporal data compiled at these increments

Time Discretization

Time Discretization Considerations Difficult to decide on initial time step size MODFLOW requires the time period, number of steps and a multiplier to gradually increase steps Multiplier is typically 1.1 to 1.5

How small is small enough? YOU KNOW YOUR DISCRETIZATION IS APPROPRIATE WHEN: THE ANSWER REMAINS THE SAME FOR: SMALLER TIME STEPS, STRESS PERIODS, AND SMALLER CELL SIZES TIME Easy to test smaller time steps Stress periods require recompiling stress data (may be time consuming) and updating any packages with stresses specified SPATIAL Unless you have an automated grid generator / input file creator, then the time requirements and logistics of rebuilding the model with smaller cell sizes renders the task unreasonable Important to use smaller grid sizes from the beginning of numerical model development because you will never be able to test this issue. In reality, few if any modelers check this.

MODFLOW MODFLOW is the world's most used ground-water modeling code Goal was/is to be: easy to understand, use, and modify

Versions of MODFLOW Trescott, Pinder, and Larson codes MODFLOW (much longer name) MODFLOW-88 (first version) MODFLOW-96 MODFLOW-2000 MODFLOW-2005 This class will use the documentation for MODFLOW-2005 as a primary reference. Class projects will be done with this version. The report and program can be downloaded to your computer from USGS web site http://water.usgs.gov/nrp/gwsoftware/modflow2005/modflow2005.html

MODFLOW Originally organized in modules Modules grouped into packages that perform calculations either specific to the behavior of a geohydrologic feature or a numerical modeling task Packages allow examination of specific hydrologic features independently facilitates development of additional capabilities Originally solely a ground-water flow model

MODFLOW Scope broadened to allow capabilities such as transport and parameter estimation Expansion of modular design required (MODFLOW-2000) addition of “Process” MODFLOW-2005 is similar in design to MODFLOW-2000 Incorporates different approach for managing internal data Fortran modules are used to declare data that can be shared among subroutines MODFLOW subroutines were originally called modules generic term module has been eliminated and replaced by the term subroutine

MODFLOW DOCUMENTATION MODFLOW2005 and associated documentation: http://water.usgs.gov/nrp/gwsoftware/modflow2005/modflow2005.html *******FOR MUCH MORE DETAIL visit the USGS Online Guide to MODFLOW******** http://water.usgs.gov/nrp/gwsoftware/modflow2000/MFDOC/guide.html Older versions: MODFLOW88 - http://pubs.usgs.gov/twri/twri6a1/pdf/TWRI_6-A1.pdf MODFLOW96 - http://water.usgs.gov/software/code/ground_water/modflow/doc/ofr96485.pdf MODFLOW2000 and associated documentation : Overview and Ground Water Flow Process - http://water.usgs.gov/nrp/gwsoftware/modflow2000/ofr00-92.pdf

ORIGINAL MODULAR STRUCTURE (1988): BAS - basic package general tasks - gridding, constant head and no-flow boundaries, initial conditions, time stepping OC - output control package controls the information and format of results BCF - block centered flow package layer types, grid dimensions, material properties WEL - well package locations and flow rates of wells RCH - recharge package recharge rates and locations RIV - river package locations, river bed material properties, and river stages DRN - drain package location, material properties surrounding drains, and elevation of drains EVT - evapotranspiration package parameters describing evapotranspiration rate with depth to water table GHB - general head boundary package locations, local material properties, and elevation of specified heads SOLVERS SIP - strongly implicit procedure package SOR - slice-successive over-relaxation package

PACKAGES WRITTEN AFTER ORIGINAL MODFLOW: PCG2 - preconditioned conjugate-gradient 2 package alternative matrix solver STR1 - stream routing package differs from the river package in that the surface water stage varies based on the surface water flow and the Manning equation BCF2 - block-centered flow 2 package allows for re-wetting of cells that have gone dry BCF3 - block-centered flow 3 package a supplement to the BCF2 package, allowing alternative interblock transmissivity formulations HFB1 - horizontal flow barrier package simulation of thin, vertical, low permeability features that impede horizontal flow TLK1 - transient leakage package simulates transient leakage and storage changes in confining units of quasi-3D models GFD1 - general finite difference flow package substitutes for the BCF package, allows user to enter conductance rather than calculating with MODFLOW IBS1 - interbed storage package simulates compaction of compressible, fine-grained units within or adjacent to aquifers in response to pumping CHD1 - time-variant specified head boundary package allows time varying specified head

PACKAGES WRITTEN MODFLOW-2000 and since: rapidly growing long list earlier packages are listed here, refer to the USGS MODFLOW and related programs web page, OR use the USGS OnLine Guide for MODFLOW GWF1 - ground water flow process (GWF in name file) finite difference simulation of saturated porous media flow OBS1 - observation process (OBS in name file) monitors value of head or flow at specified locations SEN1 - sensitivity process (SEN in name file) calculates the change in simulated head and flows at observation locations PES1 - parameter estimation process (PES in name file) estimates values of parameters by nonlinear regression to minimize the weighted sum of squared residuals for observations DIS - discretization package (DIS in name file) gridding, defining division of space and time for the numerical solution MULT - multiplier file (MULT in name file) defines the spatial distribution of multipliers in the grid that act on parameter values specified in those zone

PACKAGES WRITTEN MODFLOW-2000 and since: (continued) ZON - zone file (ZONE in name file) defines the spatial distribution of zones in the grid where specified parameters apply BAS6 - basic package (BAS6 in name file) constant head and no-flow boundary conditions; and initial conditions OC - output control package (OC in name file) controls the information and format of results BCF6 - block centered flow package (BCF6 in name file) defines material properties with some parameters being dependent on grid dimensions (e.g. transmissivity), thus this package ignores the discretization information in DIS for some purposes -- the parameter method of inputting data cannot be used -- method of interblock conductance calculations can be selected LPF1 - layer property flow package (LPFin name file) an alternative to BCF6 defines material properties with all parameters independent of grid dimensions (e.g. hydraulic conductivity) -- the parameter method of inputting data can be used -- method of interblock conductance calculations can be selected HFB6 - horizontal flow barrier package (HBF6 in name file) represents thin barriers that occur between model cells by defining their hydraulic conductivity divided by their thickness and specifying where they occur

PACKAGES WRITTEN MODFLOW-2000 and since: (continued) WEL6 - well package (WEL in name file) locations and flow rates of wells RCH6 - recharge package (RCH in name file) recharge rates and locations RIV6 - river package (RIV in name file) locations, river bed material properties, and river stages STR6 - stream routing package (STR in name file) differs from the river package in that the surface water stage varies based on the surface water flow (calculated as specified flow and ground water flux to/from stream) and the Manning equation DRN6 - drain package (DRN in name file) location, material properties surrounding drains, and elevation of drains (this update allows a fraction [0-1] of the drain outflow to be returned to a specified cell) EVT6 - evapotranspiration package (EVT in name file) parameters describing evapotranspiration rate with depth to water table GHB6 - general head boundary package (GHB in name file) locations, local material properties, and elevation of specified heads CHD6 - time-variant specified head boundary package (CHD in name file) allows time varying specified head

PACKAGES WRITTEN MODFLOW-2000 and since: (continued) SOLVERS (SIP SOR PCG DE4 LMG in name file) SIP5 - strongly implicit procedure package SOR5 - slice-successive over-relaxation package PCG2 - preconditioned conjugate gradient package   DE45 - direct solution by alternating diagonal ordering package   LMG1 - multigrid solver speeds execution for large grids and high degree of heterogeneity ADV2 - advective transport observation package (ADV2 in name file) allows use of travel time observations for parameter observations RES1 - reservoir package (RES in name file) simulates leakage between reservoir and aquifer as reservoir area changes in response to stage changes FHB1 - flow and head boundary package (FHB in name file) allows flow and head boundary conditions that vary at times other than starting and ending times of stress periods IBS6 - interbed storage (subsidence) (IBS in name file) simulates compaction related to hydraulic head decline HUF1 - hydrologic-unit flow package (HUF in name file) calculates effective hydraulic properties for cells based on geometric description of hydrologic units

PACKAGES WRITTEN MODFLOW-2000 and since: (continued) LAK3 - lake package (LAK in name file) allows variation of lake stage based on water budgets ETS1 - evapotranspiration package with segment ET function (ETS in name file) allows function describing evapotranspiration rate with depth to water table to be piece-wise linear DRT1 - drain package with return flows (DRT in name file) allows user to allocate proportions of drain flow to be recharge to specified cells LMT6 - link to MT3D (LMT in name file) allows printing of file to be read by MT3D for contaminant transport SFR - Streamflow-Routing package (SFR in name file) is used to simulate streams in a model (provides greater flexibility in how streams are specified than STR) UZF - Unsaturated Zone Flow Package (UZF in name file) simulates vertical flow of water through the unsaturated zone to the saturated zone

MODFLOW DOCUMENTATION Documentation for MODFLOW-96 and MODFLOW-2000 was not complete by itself and referred extensively to the MODFLOW-88 documentation MODFLOW-2005 is similar to MODFLOW-88 documentation details entirely contained in one report fundamental concepts, programmer information, and user input instructions for ground-water flow additional reports for added capabilities Processes Capabilities to simulate additional hydrologic features

MODFLOW-2005 DOCUMENTATION Purpose is to describe the mathematical concepts used in the GWF Process program design, input needed to use it, and programming details Outline: Chapter 1. Introduction Chapter 2. Derivation of the Finite-Difference Equation Chapter 3. Design of the Ground-Water Flow Process Chapter 4. Basic Package Chapter 5. Internal Flow Packages Chapter 6. Conceptualization and Implementation of Stress Packages Chapter 7. Solver Packages Chapter 8. Input Instructions Chapter 9. Programmer Documentation

MODFLOW-2005 DOCUMENTATION Get familiar with the MODFLOW code through its Documentation: Read Chapters 1 through 3 Describes overall program Look over the core chapters (Chapters 4 -7) 4) Basic Package – administrative tasks and program design 5) Internal Flow Packages – how flow is simulated 6) Stress Packages – physical and mathematical concepts 7) Numerical Solvers Each time you use a new package, stop and read the theory section for that package before proceeding Become familiar with input instructions for packages including utility subroutines (Chapter 8)

MODFLOW Get an overview of the numerical model Note unusual coordinate system Sequence of cells = rows, columns, and layers Origin of numbering = top, back, left corner Chapters 4-7 discuss theory Chapter 8 includes a step by step description of the file setup

MODFLOW MODFLOW-88 MODFLOW-96 MODFLOW-2000 MODFLOW-2005 Versions of MODFLOW MODFLOW MODFLOW-88 MODFLOW-96 MODFLOW-2000 MODFLOW-2005 This class will use the documentation for MODFLOW-2005 as a primary reference. Class projects will be done with this version. The report and program can be downloaded to your computer from USGS web site http://water.usgs.gov/nrp/gwsoftware/modflow2005/modflow2005.html

MODFLOW -2005 Supports multiple grids so that it is possible to incorporate local grid refinement. Uses parameter structure to ease the modification of data input values. Provides expanded data input capabilities. Program is designed to minimize changes that would impact existing MODFLOW users.

MODFLOW -2005 PROCESSES Previous MODFLOW tasks (prior to MF2K) are now defined as the: Global Process GLO – Controls Overall Program Operation Equation Solving Processes GWF – Ground-water Flow Process

MODFLOW 2005 PROCESSES As Initially released, MODFLOW also includes other processes: OBS - Observation Process SEN - Sensitivity Process PES - Parameter Estimation Process GWT - Ground-water Transport Process Other Processes being developed including: FMP – Farm Process We are going to concentrate on the GWF – Ground-water Flow Process and discuss the others later in the class

The Global Process does not solve an equation Controls overall program flow Activates capabilities (Packages) Opens package data files (Input and Output) Reads data for space and time discretization (DIS file) Reads parameter files (Multplier and Zone) Has a global level listing file The Global Process does not solve an equation

GROUNDWATER FLOW PROCESS (abbreviated list) GWF Process Packages – User Prospective BAS6 Basic Package Hydrologic Packages BCF6 Block Centered Flow Package LPF Layer Property Flow Package RCH Recharge Package RIV River Package WEL Well Package DRN Drain Package GHB General Head Boundary Package EVT Evapotranspiration Package STR Stream/Aquifer Package HFB6 Horizontal Flow Barrier Package CHD Constant-Head Package Solution Packages SOR Slice-Successive Over-relaxation SIP Strongly Implicit Procedure PCG Preconditioned Conjugate Gradient

GROUNDWATER FLOW PROCESS GWF Process Procedures – Programmer Prospective DF Define AL Allocate RP Read and Prepare ST Stress AD Advance FM Formulate AP Solve Equations OC Output Control BD Calculate Water Budget OT Output

GROUNDWATER FLOW PROCESS Primary Modules Example RIV6FM The first three characters designate the package (river) The fourth character is the version number (6) The last two characters represent the procedure (formulate)

Example Module Flowchart And Code

MODFLOW – user perspective Input Data ASCII text files Output Data Binary files Graphical user interface (GUI) Code Execution

MODFLOW – user perspective BASIC INPUT ITEMS: Grid Time stepping Solution parameters Hydraulic parameters (includes material properties) Boundary Conditions Stresses (source-sinks) Output options BASIC OUTPUT ITEMS: Hydraulic Heads Drawdown Flow rates Mass Balance Optional info at specified times Iteration information Binary files containing heads, drawdowns and flow rates in compressed form

GUI Allows you to develop a nice image of model features on the computer screen and manipulate the model inputs graphically Creates the text files and executes MODFLOW. You never need to see the text files or know the commands that are necessary to run MODFLOW ... until something goes wrong!

GUI Pros and Cons Inevitably something does not work correctly Need to have the ability to look at and understand the content of the model files and control the commands. Likely to dislike the tedium associated with the portion of the course where we work with text files

File formats Original code MODFLOW88 expects to have FORMATTED DATA SETS exact about placement of data in columns of the file Occasionally see files in an old format (may have no spaces) MODFLOW96 provides the option of using either FREE or FORMATTED DATA SETS Translator was released with MODFLOW-2000 Takes MODFLOW88 or MODFLOW96 files and convert them to MODFLOW-2000 HUF package – allows geometry of the geology defined separately from the layers and have code simplify it to individual values for each model cell

File formats Prior to MODFLOW-2000, MODFLOW required a different number in each model cell, now have flexibility in populating the cells with parameter values Parameters MODFLOW calculates value for each cell based on Parameter file (PVAL) – defines values used to replace parameters specified in the files where parameters are defined (can use SEN in 2000) Multiplier files (MULT) - specify multiplier arrays which can be used to calculate layer variables Zone files (ZONE) – specify the cells in a layer (arrays) that are associated with a parameter

Next: LEARNING MODFLOW Global Process Overview of Common Packages Basic Utility Module Output Control BCF WEL RIV RCH EVT STR DRN GHB LPF Once use to input for several packages, others are the same Best way to learn is to build a model In class, we will build a model for a simple problem Work on class project