An Introduction to MODFLOW

What is MODFLOW? Widely used ground-water flow simulation program that runs on any

platform (Windows, Sun, Unix, Linux,…). Mostly written in standard FORTRAN (GMG is C++) Solves the ground-water flow equation with different possible properties,

boundary conditions, and initial conditions First version, 1983, McDonald and Harbaugh. Written to serve USGS

needs. Education emphasized. MODFLOW escaped! Public domain (Free) Open source (Anyone can check and change the source code) Changed versions are sometimes commercial – it’s up to the developer Well documented Modularly constructed (More later) Latest version: MODFLOW-2005 (Harbaugh, 2005)

What is MODFLOW? Cited in statutes, legally tested 250,000 hits on Google for MODFLOW Many other programs use results from or are based

on MODFLOW: Public domain/open source

MT3DMS (multi-species solute or heat transport, some reactions, dual porosity) (Chunmiao Zheng, U Alabama)

MODPATH (particle tracking) (Dave Pollock, USGS) SEAWAT (density-dependent transport using MODFLOW and

MT3DMS) (Chris Langevin, USGS) Phreeqc connections (PHT3D) (Henning Prommer)

Commercial MODHMS-Surfact (Integrated sw/gw/unsat) GUI’s: Visual MODFLOW, Groundwater Vistas, GMS, PMWin, …

Program organized into MODules Activate the capabilities you need; no overhead

from other capabilities (execution time, RAM) The structure is clear and documented for adding

additional capabilities such as new equations Modularity in ‘Processes’ and ‘Packages’

What is MODFLOW?

What is MODFLOW-2005? Latest release of USGS MODFLOW Internal computer storage redesigned to support

storage of multiple models necessary for local grid refinement and facilitate linkages to other models (GSFLOW = MODFLOW + PRMS).

Parameter-estimation, sensitivity analysis, uncertainty now from UCODE_2005

Who is MODFLOW? Collaborative open-source development with roots at the USGS Some USGS developers

Arlen Harbaugh (MODFLOW, Reston, Virginia, USA) Ned Banta (MODFLOW-2000, Lakewood, Colorado, USA) Mary Hill (SA/PE/UA, MODFLOW-2000, UCODE, MMA, Boulder, Colorado, USA) Steffen Mehl (local grid refinement (LGR), SA/PE/UA, now at CalSU-Chico, USA) Stan Leake (compaction and subsidence, TMR, Tucson, Arizona, USA) John Hoffman (compaction and subsidence, TMR, Tucson, Arizona, USA) Dave Prudic (gw/sw interaction, STR, SFR, GSFLOW, Carson City, Nevada, USA) Rick Niswonger (gw/sw interactions, SFR, GSFLOW, Carson City, Nevada. USA) Paul Barlow (ground-water management, MODMAN, Reston, VA, USA) Randy Hanson (FARM Process, MNW, San Diego, USA) Alden Provost (HUF, Reston, VA) Dave Pollock (particle tracking, MODPATH, Reston, Virginia, USA) Chris Langevin (transport, saltwater intrusion, SEAWAT, Miami, Florida, USA) Lennie Konikow (transport extended from MOC3D, GWT, Reston, Virginia, USA) George Hornberger (transport extended from MOC3D, GWT, Reston, Virginia, USA)

Some non-USGS developers Chunmiao Zheng (transport, MT3DMS, University of Alabama, USA) Eileen Poeter (UCODE, MMA, Colorado School of Mines, IGWMC, Golden, CO, USA) Evan Anderman (ADV, HUF, now at EvanAnderman.com, photography) Henning Prommer (MODFLOW+PHREEQC, CSIRO, Perth, Australia) Wolfgang Schmid (FARM Process, U. of Arizona, USA) David Ahlfeld (ground-water management, GWM, U. of Massachusetts, USA) You…???

MODFLOW-2005 Processes

Processes each solve a fundamental equation. Of importance in this class are

Ground-water Flow (GWF) Kh = S(h/t) …

Observation (OBS) y = y′ + e

GWF Packages Packages each represent a type of system

feature. Of importance in this class arePackage that defines model layers and properties:

Layer-Property Flow (LPF) Package

Packages used to add/remove water at a specified rate: Well (WEL) Recharge (RCH)

Packages that add/remove water based on head in the aquifer: General-Head Boundary (GHB) River (RIV)

How Processes and Packages Interact

GWF Process OBS Process

LPF Package

Define K and S properties, possibly using parameters. Calculate contributions to the matrix equations

No observations are now defined for the LPF Package. Possible observations are internal flows.

RIV Package

Define ricer properties, possibly using parameters.

Calculate contributions to the matrix equations.

River gain and loss observations can be defined.

In MODFLOW, subroutines are named using the three-letter identifiers for processes and packages. For example, GWF1LPF6RP

Back to the world of users instead of programmers --

What is required for a simulation?

Tell the program what capabilities to use Name file (NAM)

Package input files for each process (only the GWF Process is always required) Basic (BAS6) (can define constant head BC’s here)

Discretization (DIS) Hydrogeologic info (here, LPF)

Solver. Here we use Preconditioned Conjugate Gradient (PCG)

Turn Packages on and define input files using the NAME file

Example: # GW Flow process input files

bas6 41 tc1.bas

lpf 42 tc1.lpf

wel 43 tc1.wel

pcg 44 ../data/tc1.pcg

.

.

.

Activating capabilities

Basics of Data Input

List data Data input using lists

of cells

layer row column ……

Example:

1 3 43 …….

2 62 53 …….

Array data Data input in arrays with

one row for each row of the model grid and one column for each column of the model grid. Sometimes repeat one array for each model layer.

# # # # # ……… # # # # # ……… # # # # # ……… # # # # # ……… . . .

What is MODFLOW?

Input files(plain textor binary)

MODFLOWis a

calculationprogram

Output files(plain text or binary)

Often use MODFLOW through a (Graphical) User Interface

Maps

Model

Results

MODFLOW capabilities used in class

Class exercise MODFLOW Packages used

Layer-Property Flow (LPF)Recharge (RCH)River (RIV)General-Head Boundary (GHB)Advective Transport (ADV) Preconditioned-Conjugate Gradient

(PCG) MODFLOW Processes used

Ground-Water Flow (GWF)Observations (OBS)

UCODE_2005 capabilities usedSensitivityParameter-Estimation

Aspects of flow model creation Conceptual model Base map Grid design

Areal Model layers (thickness can be variable)

Boundary conditions Aquifer properties Pumping wells Recharge Time

Here, describe selected aspects of capabilities used in class

Head-dependent boundaries

From Hill+, 2000

Generally use many cells to define a feature. Here, shaded cells are used to simulate flow to compare to measured flow Q2-Q1. Other cells would be used to define the rest of the river.

Head-dependent boundaries

Cell center

(KA/M)n = Cn = conductance of assumed distinct streambed

Often define Cn with parameters Cn=FnP1

Additive:

Cn= Fn1P1 + Fn2P2

Hn= water-body stage

hn= simulated head

For each finite-difference cell n:

Qn = (KA/M)n (Hn – hn)

A Areal view of typical cell n

Cross-section of typical cell n

Packages that represent head-dependent boundaries q=C(H-h) Important

here: GHB:

General-Head Boundary

RIV: River

GHB

DRN RIV

Positive qn indicates flow into

the subsurface

Negative qn indicates

flow out of the

subsurface Hn

qn = 0

Slope = -Cn = -(KnAn)/Dn

Positive qn indicates flow into

the subsurface

Negative qn indicates

flow out of the

subsurface En Hn

qn = 0

Slope = -Cn = -(KnAn)/Dn

Slope = -Cn = -(KnAn)/Dn

Hn

Negative qn indicates

flow out of the

subsurface

qn

qn

qn

hn

hn

hn

(C)

(A)

(B)

EXPLANATION

qn the simulated flow rate at one cell (L3/T)

(negative for flow out of the ground-water system)

Kn the hydraulic conductivity (L/T) of, for

example, the riverbed or lakebed

Dn the thickness (L) of, for example, the riverbed

or lakebed

An the area of the water body within the finite-

difference cell (L2)

Cn the conductance calculated using Kn, Dn, and An.

hn is the simulated hydraulic head in the ground-

water system adjacent to the head-dependent boundary (L); and

Hn is the water level in the water body or the

elevation of the drain (L)

En is the bottom of the streambed

(C)

qn = 0

GHB

RIV

RIV Package with hn below RBOTn (hn<RBOTn)

Cell center

Pumping wells

Well (WEL) Package List input: layer, row , column, rate (negative means

flow out of the ground-water system) Rate can be defined using parameters Problem: If a well intersects many model layers, how

much water comes from each layer?

Flow model creation: Time Steady state

Inputs = outputs. No change in storage No time dimension: easier to visualize Errors in model setup more clear in results

Transient Requires (often steady-state) initial conditions Requires a value for storage Stresses are defined using stress periods (time interval of input) Each stress period is divided into time steps (time interval of head

calculation).

Lengthy calculation times can produce large output files

For some tips on when to “go transient”, see H.M.Haitjema (2006) Role of Hand Calculations in Ground Water Flow Modeling, Ground Water.

Parameters In the MODFLOW model for the class problem,

parameters are used to define the following model inputs Layer-Property Flow (LPF) Package

Horizontal hydraulic conductivity of model layers (HK)Vertical hydraulic conductivity of an implicit confining unit

(VKCB) Recharge (RCH) Package

Recharge rate (RCH) River (RIV) Package

Riverbed conductance (RIV)

Values of defined parameters can be controlled using the PVAL file. This makes it easy for users of UCODE_2005, etc.

Parameters Model Input River Package input filePARAMETER 1 18 18 54 MXACTR IRIVCBK_RB RIV 1.200000E-03 18 1 1 1 100. 1000. 90. . . . 1 18 1 100. 1000. 90. 0 1 ITMP NP -- Stress Period 1K_RB

C of river bed equals the value in the package input file times the factor in the package input file. Here, the factor is 1000. C of river bed = 1000 × 0.0012The factor can be different for different cells.

Parameters and PVAL file River Package input file

PVAL file 6HK_2 1.523554700000E-5 HK_1 4.619000000000E-4 VK_CB 9.903220000000E-8 K_RB .0011699900000000 RCH_2 38.39840000000000 RCH_1 47.55430000000000

PARAMETER 1 18 18 54 MXACTR IRIVCBK_RB RIV 1.200000E-03 18 1 1 1 100. 1000. 90. . . . 1 18 1 100. 1000. 90. 0 1 ITMP NP -- Stress Period 1K_RB

C of river bed equals the value in PVAL times the factor in the package input file. Here, the factor is 1000. C of river bed = 1000 × 0.00116999The factor can be different for different cells.

Easy to use UCODE_2005 to change parameter values in PVAL file.

Flow model creation: Observations

MODFLOW’s Observation Process allows simulated values to be compared to

observations. Here, use it for the following observations

Head observationsAt a cellChanges in head over time

Flow observationsOver the reach of a feature represented by the RIV

Package

Observations Heads (HOB in name file)

River Gain(RVOB in

name file)

Output file (“data 50 ex8._os” in name file)"SIMULATED EQUIVALENT" "OBSERVED VALUE" "OBSERVATION NAME" 100.209701538086 101.800003051758 hd01.ss 126.954444885254 128.119995117188 hd02.ss . . . -4.41627883911133 -4.40000009536743 flow01.ss

10 0 0 50 1.E+30 NH,MOBS,MAXM,IUHOBSV,HOBDRY 1. TOMULTH (below, lay,r,c,ts,roff,coff,toff,obs)hd01.ss 1 3 1 1 0.0 0.0 0.0 101.80 hd02.ss 1 4 4 1 0.0 0.0 0.0 128.12 hd03.ss 1 10 9 1 0.0 0.0 0.0 156.68. . .hd10.ss 2 18 6 1 0.0 0.0 0.0 142.02

1 18 1 50 NQxx,NQCxx,NQTx 1.00000E+00 TOMULTxx 1 18 NQOBxx,NQCLxxflow01.ss 1 0.0 -4.4 ts,toff,obs 1 1 1 1.00 lay,r,c,factor . . . 1 18 1 1.00

Constructing input files

In class we will either use 00-MFI2005.exe or the files will be constructed already.

Instructions for using 00_MFI2005.bat are provided in class.

Execute MODFLOW

Here, we will use 00-MFI2005.exe or already constructed batch files. Detailed instructions are provided in the exercise

instructions.

Basically, need to provide the name file filename on the same line (this is often done in a batch file) MODFLOW test.nam

Model results

Possible results for class problem (depends on options chosen) Global budget (check for overall solution accuracy) Heads at each active cell in the grid at each time step Flows at each cell face Simulated equivalents to observations

Often use software to visualize results. In class, use ModelViewer

Pathline Modeling

Advective transport. Used here as a first investigation of transport predictions

Requires: Flow solution Porosity – to determine velocity Starting locations

The particle tracking is calculated using MODPATH, which uses results produced by MODFLOW.