U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5205

Prepared in cooperation with the city of Rapid City

Numerical Groundwater-Flow Model of the Minnelusa 

and Madison Hydrogeologic Units in the Rapid City Area, 

South Dakota
Front cover. Swallow hole in Madison Limestone in Spring Creek Canyon (photograph by Ingrid E. Arlton).

Back cover. Doty Spring discharging from the Madison Limestone to Boxelder Creek (photograph by Ingrid E. Arlton).

Numerical Groundwater-Flow Model of 

the Minnelusa and Madison Hydrogeologic 

Units in the Rapid City Area, South Dakota

By Larry D. Putnam and Andrew J. Long

Prepared in cooperation with the city of Rapid City

Scientific Investigations Report 2009–5205

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

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Suggested citation:

Putnam, L.D., and Long, A.J., 2009, Numerical groundwater-flow model of the Minnelusa and Madison hydrogeologic 

units in the Rapid City area, South Dakota: U.S Geological Survey Scientific Investigations Report 2009–5205, 81 p.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................2

Previous Investigations........................................................................................................................2

Acknowledgments................................................................................................................................2

Description of Study Area ............................................................................................................................4

Physiography and Climate...................................................................................................................4

Hydrogeologic Setting .........................................................................................................................4

Minnelusa Hydrogeologic Unit..................................................................................................8

Madison Hydrogeologic Unit .....................................................................................................8

Numerical Groundwater-Flow Model.........................................................................................................9

Finite-Difference Grid and Boundary Conditions ..........................................................................10

Calibration and Simulated Stress Periods......................................................................................14

Representation of Flow-System Components................................................................................18

Recharge.....................................................................................................................................19

Streamflow Recharge ......................................................................................................19

Areal Recharge .................................................................................................................20

Upward Flow from Deadwood Aquifer..........................................................................23

Discharge....................................................................................................................................23

Springflow..........................................................................................................................23

Water Use ..........................................................................................................................26

Flow to Overlying Units ....................................................................................................26

Regional Outflow...............................................................................................................28

Hydraulic Properties .................................................................................................................28

Horizontal Hydraulic Conductivity..................................................................................28

Vertical Hydraulic Conductivity ......................................................................................33

Horizontal Flow Barriers..................................................................................................37

Storage Properties ...........................................................................................................37

Steady-State Calibration ...................................................................................................................39

Sensitivity Analysis....................................................................................................................39

Comparison of Simulated and Observed Steady-State Hydraulic Head Values .............43

Comparison of Simulated and Estimated Steady-State Flow.............................................43

Transient Calibration ..........................................................................................................................43

Comparison of Simulated and Observed Transient Hydraulic Head Values....................47

Comparison of Simulated and Observed Transient Springflow .........................................53

Comparison of Simulated and Estimated Transient Regional Outflow..............................53

Calibrated Hydraulic Properties.......................................................................................................53

Response to Stress......................................................................................................................................58

Model Limitations.........................................................................................................................................58

Summary........................................................................................................................................................60

References Cited..........................................................................................................................................64

Supplemental Information..........................................................................................................................67
iv

Figures

1. Map showing location of study area.........................................................................................3

2. Stratigraphic section for the study area...................................................................................5

3. Schematic showing conceptual hydrogeologic section of the study area ........................6

4. Generalized diagram with vertical exaggeration of a confined 

aquifer recharged at the updip end...........................................................................................7

5. Generalized diagram showing recharge conditions and vertical 

gradients in the Minnelusa and Madison hydrogeologic units ............................................8

6. Conceptual schematic of model layers in relation to hydrogeology .................................10

7–12. Maps showing:

7. Location of finite-difference grid ....................................................................................11

8. Active model cells and boundary conditions for layers 1 and 2 

(Minnelusa hydrogeologic unit) ......................................................................................12

9. Active model cells and boundary conditions for layers 3 and 4 

(Madison hydrogeologic unit)..........................................................................................13

10. Specified-flow cells representing streamflow recharge............................................15

11. Model cells representing upward flow from the Deadwood aquifer 

to layer 4, flow from the Minnelusa hydrogeologic unit to overlying 

units, and discharge to Elk Spings..................................................................................16

12. Locations of head-dependent flow cells representing springs in the 

detailed study area............................................................................................................17

13. Graph showing total transient streamflow recharge rates for twenty 

6-month stress periods by model layer...................................................................................21

14. Map showing locations of areal recharge zones..................................................................22

15. Graph showing total transient areal recharge rates for twenty 6-month 

stress periods by model layer and spatially averaged precipitation on 

outcrops of the Minnelusa and Madison hydrogeologic units ...........................................24

16–26. Maps showing:

16. Locations of specified-flow cells representing water use in model 

layers 1 and 3......................................................................................................................27

17. Horizontal hydraulic conductivity parameter groups and zones for 

model layer 1 ......................................................................................................................29

18. Horizontal hydraulic conductivity multiplier zones for model layer 2.......................30

19. Horizontal hydraulic conductivity parameter groups and zones for 

model layer 3 ......................................................................................................................31

20. Horizontal hydraulic conductivity parameter groups and zones for 

model layers 3 in the detailed study area......................................................................32

21. Horizontal hydraulic conductivity multiplier zones for model layer 4.......................34

22. Horizontal hydraulic conductivity parameter group for model 

layer 5 and horizontal flow barriers for layers 1 to 5 ...................................................35

23. Vertical hydraulic conductivity parameter groups and zones for 

model layer 2, transition zone for sulfate concentrations in Minnelusa 

hydrogeologic unit, and location of aquifer tests in Madison aquifer......................36

24. Model cells with storage represented by unconfined storage 

coefficient...........................................................................................................................38
v

25. Comparison of simulated steady-state potentiometric surface for 

model layer 1 to the average potentiometric surface of the Minnelusa 

aquifer, water years 1988–97 ...........................................................................................40

26. Comparison of simulated steady-state potentiometric surface for 

model layer 3 and western part of layer 4 to the average 

potentiometric surface of the Madison aquifer, water years 1988–97 .....................41

27–29. Graphs showing:

27. Composite-scaled sensitivities for parameter values that were 

determined with inverse modeling in steady-state simulation..................................43

28. Residuals between simulated steady-state and observed hydraulic 

head values and their relation to average (water years 1988–97) 

hydraulic head values.......................................................................................................44

29. Histograms of residuals between simulated steady-state and 

observed (average for water years 1988–97) hydraulic head values .......................44

30–32. Maps showing:

30. Differences between simulated steady-state and observed (average 

for water years 1988–97) hydraulic head values for the Minnelusa 

hydrogeologic unit in the detailed study area ..............................................................45

31. Differences between simulated steady-state and observed (average 

for water years, 1988–97) hydraulic head values for the Madison 

hydrogeologic unit in the detailed study area ..............................................................46

32. Locations of observation wells with transient hydraulic head values .....................48

33–34. Graphs showing:

33. Simulated and observed hydraulic head values for model layers 1 

and 3.....................................................................................................................................50

34. Simulated and observed or estimated springflow values ..........................................55

35. Map showing simulated extent of drawdown resulting from hypothetical 

increases in pumping rates from the Madison hydrogeologic unit ...................................59

36. Graph showing simulated decrease in springflow from Jackson-Cleghorn 

Springs in response to hypothetical increases in pumping rates from the 

Madison hydrogeologic unit.....................................................................................................60

37. Map showing locations of production and observation wells for Madison 

aquifer test at well 49.................................................................................................................61

38. Graph showing simulated and observed drawdown for Madison aquifer 

test at well 49...............................................................................................................................62

Tables

1. Stress periods for transient simulations.................................................................................18

2. Estimated water-budget components for steady-state simulation....................................19

3. Steady-state streamflow recharge rates distributed by model layer................................20

4. Areal recharge zones and average annual precipitation on outcrops of 

the Minnelusa and Madison hydrogeologic units.................................................................21

5. Areal recharge zones and steady-state areal recharge rates distributed 

by model layer.............................................................................................................................23

6. Steady-state springflow ............................................................................................................25

7. Water-use rates for steady-state and transient simulations ..............................................26
vi

8. Sites used as basis for delineation of hydraulic conductivity parameter 

zones for model layer 3..............................................................................................................33

9. Horizontal barrier hydraulic characteristic for City Springs fault, City 

Springs monocline, and Victoria Creek fault..........................................................................37

10. Composite-scaled sensitivities for hydraulic properties represented as 

parameters...................................................................................................................................42

11. Steady-state springflow estimates and simulated springflow ...........................................47

12. Difference between simulated and observed hydraulic head values for 

transient simulation....................................................................................................................49

13. Estimated and simulated transient springflow ......................................................................54

14. Jackson-Cleghorn springflow estimated from streamflow measurements 

on Rapid Creek ............................................................................................................................56

15. Simulated transient regional outflow from Minnelusa and Madison 

hydrogeologic units at the eastern model boundary............................................................56

16. Calibrated horizontal hydraulic conductivity for parameters representing 

zones of hydraulic conductivity in model layers 1, 3, and 5.................................................57

17. Conductance for head-dependent cells representing springs...........................................57

18. Transient streamflow recharge rates for the Minnelusa and Madison 

hydrogeologic units....................................................................................................................68

19. Transient areal recharge rates for the Minnelusa and Madison 

hydrogeologic units by zones ...................................................................................................70

20. Observed and simulated hydraulic head values for the Minnelusa 

hydrogeologic unit in steady-state simulation.......................................................................71

21. Observed and simulated hydraulic head values for the Madison 

hydrogeologic unit in steady-state simulation.......................................................................77

22. Supplemental interpolated hydraulic head values for the Minnelusa and 

Madison hydrogeologic units in steady-state simulation....................................................80
vii

Conversion Factors and Datums

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 3.785 liter (L) 

gallon (gal) 0.003785 cubic meter (m3) 

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

gallon per minute (gal/min) 0.06309 liter per second (L/s)

inch per year (in/yr) 25.4 millimeter per year (mm/yr)

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Conductance

feet squared per day (ft2/d) 0.0929 Meter squared per day (m2/d)

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29).

Horizontal coordinate information is referenced to the North American Datum of 1927 (NAD 27).

Altitude, as used in this report, refers to distance above the vertical datum.

Water year (WY) is the 12-month period, October 1 through September 30, and is designated by 

the calendar year in which it ends.

Abbreviations and Acronyms

SDDENR South Dakota Department of Environment and Natural Resources

SDME standard deviation of measurement error

USGS U.S. Geological Survey

WY water year

Numerical Groundwater-Flow Model of the Minnelusa 

and Madison Hydrogeologic Units in the Rapid City Area, 

South Dakota

By Larry D. Putnam and Andrew J. Long

Abstract

The city of Rapid City and other water users in the 

Rapid City area obtain water supplies from the Minnelusa and 

Madison aquifers, which are contained in the Minnelusa and 

Madison hydrogeologic units. A numerical groundwater-flow 

model of the Minnelusa and Madison hydrogeologic units in 

the Rapid City area was developed to synthesize estimates 

of water-budget components and hydraulic properties, and 

to provide a tool to analyze the effect of additional stress on 

water-level altitudes within the aquifers and on discharge to 

springs. This report, prepared in cooperation with the city of 

Rapid City, documents a numerical groundwater-flow model 

of the Minnelusa and Madison hydrogeologic units for the 

1,000-square-mile study area that includes Rapid City and the 

surrounding area. 

Water-table conditions generally exist in outcrop areas of 

the Minnelusa and Madison hydrogeologic units, which form 

generally concentric rings that surround the Precambrian core 

of the uplifted Black Hills. Confined conditions exist east of 

the water-table areas in the study area. 

The Minnelusa hydrogeologic unit is 375 to 800 feet (ft) 

thick in the study area with the more permeable upper part 

containing predominantly sandstone and the less permeable 

lower part containing more shale and limestone than the upper 

part. Shale units in the lower part generally impede flow 

between the Minnelusa hydrogeologic unit and the underlying 

Madison hydrogeologic unit; however, fracturing and weathering may result in hydraulic connections in some areas. The 

Madison hydrogeologic unit is composed of limestone and 

dolomite that is about 250 to 610 ft thick in the study area, 

and the upper part contains substantial secondary permeability 

from solution openings and fractures. Recharge to the Minnelusa and Madison hydrogeologic units is from streamflow 

loss where streams cross the outcrop and from infiltration of 

precipitation on the outcrops (areal recharge).

MODFLOW–2000, a finite-difference groundwaterflow model, was used to simulate flow in the Minnelusa 

and Madison hydrogeologic units with five layers. Layer 1 

represented the fractured sandstone layers in the upper 250 ft 

of the Minnelusa hydrogeologic unit, and layer 2 represented 

the lower part of the Minnelusa hydrogeologic unit. Layer 3 

represented the upper 150 ft of the Madison hydrogeologic 

unit, and layer 4 represented the less permeable lower part. 

Layer 5 represented an approximation of the underlying Deadwood aquifer to simulate upward flow to the Madison hydrogeologic unit. The finite-difference grid, oriented 23 degrees 

counterclockwise, included 221 rows and 169 columns with 

a square cell size of 492.1 ft in the detailed study area that 

surrounded Rapid City. The northern and southern boundaries for layers 1–4 were represented as no-flow boundaries, 

and the boundary on the east was represented with headdependent flow cells. Streamflow recharge was represented 

with specified-flow cells, and areal recharge to layers 1–4 was 

represented with a specified-flux boundary. Calibration of the 

model was accomplished by two simulations: (1) steady-state 

simulation of average conditions for water years 1988–97 and 

(2) transient simulations of water years 1988–97 divided into 

twenty 6-month stress periods.

Flow-system components represented in the model 

include recharge, discharge, and hydraulic properties. The 

steady-state streamflow recharge rate was 42.2 cubic feet per 

second (ft3/s), and transient streamflow recharge rates ranged 

from 14.1 to 102.2 ft3/s. The steady-state areal recharge rate 

was 20.9 ft3/s, and transient areal recharge rates ranged from 

1.1 to 98.4 ft3/s. The upward flow rate from the Deadwood 

aquifer to the Madison hydrogeologic unit was 6.3 ft3/s. 

Discharge included springflow, water use, flow to overlying 

units, and regional outflow. The estimated steady-state springflow of 32.8 ft3

/s from seven springs was similar to the simulated springflow of 31.6 ft3

/s, which included 20.5 ft3/s from 

Jackson-Cleghorn Springs. Simulated transient springflow 

ranged from 25.7 to 42.3 ft3/s. Steady-state water-use rates for 

the Minnelusa and Madison hydrogeologic units were 3.4 and 

6.7 ft3/s, respectively. Total transient water-use rates ranged 

from 3.4 to 19.1 ft3/s. Flow from the Minnelusa hydrogeologic 

unit to overlying units was 2.0 ft3/s. Steady-state and transient 

regional outflows from the Minnelusa and Madison hydrogeologic units were 12.9 and 12.8 ft3

/s, respectively. 

Linear regression of the 252 simulated and observed 

hydraulic head values for the steady-state simulation had a 

coefficient of determination (R2 value) of 0.92 with an average 
2 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

absolute difference of 37.6 ft. For the transient simulation, the 

average absolute difference between simulated and observed 

hydraulic head values for 19 observation wells ranged from 

3.5 to 65.1 ft with a median value of 18.3 ft.

Calibrated horizontal hydraulic conductivity values 

for model layer 1 ranged from 1.0 to 5.2 feet per day (ft/d). 

Horizontal hydraulic conductivity values for model layer 3 

ranged from 0.1 to 388.8 ft/d. Horizontal hydraulic conductivity for layers 2 and 4 were 10 percent of hydraulic conductivity values for layers 1 and layer 3, respectively, except near the 

outcrop where it was 50 percent of the values for layers 1 and 

3, respectively. Vertical hydraulic conductivity for layers 1, 3, 

4, and 5 was 10 percent of the respective horizontal hydraulic 

conductivity for those layers. Vertical hydraulic conductivity 

for layer 2 ranged from 0.000001 to 0.25 ft/d. Conductance for 

head-dependent cells representing springs ranged from 3,000 

to 86,400 feet squared per day.

Simulation of increased hypothetical pumping of more 

than about 10 ft3/s may require modification of the boundaries 

to allow flow into the model. The model is limited by simplifying assumptions necessary to represent material having 

secondary porosity as a porous media. With additional data, 

further refinement of the model would be possible, which 

could improve the accuracy of model estimates of the effects 

of additional stresses on the system, such as increased withdrawals or drought. The model can yield simulations of future 

conditions, which can guide management decisions and planning. The model provides a useful tool for general characterization of the effects of stresses and management alternatives 

on a regional basis.

Introduction

The city of Rapid City, South Dakota (fig. 1), obtains 

more than one-half of its municipal water supplies from the 

Minnelusa and Madison aquifers through deep wells and 

springs, predominantly from the Madison aquifer. Numerous 

additional users in the Rapid City area obtain water from these 

aquifers for domestic, commercial, industrial, and irrigation 

usage. Groundwater flow within the Minnelusa and Madison 

aquifers is complex with extensive secondary porosity from 

fracturing, solution enhancement, and brecciation. The Minnelusa and Madison aquifers are contained within the Minnelusa and Madison hydrogeologic units, which include layers 

with less permeability.

The U.S. Geological Survey (USGS), as part of a 

long-term cooperative study with the city of Rapid City, has 

compiled numerous datasets designed to better understand 

groundwater flow in the Minnelusa and Madison hydrogeologic units. A numerical groundwater-flow model of the 

Minnelusa and Madison hydrogeologic units in the Rapid City 

area was developed to synthesize estimates of water-budget 

components and hydraulic properties, and to provide a tool to 

analyze the effect of additional stress on water-level altitudes 

within the aquifers and on discharge to springs.

Purpose and Scope

 The purposes of this report are to (1) document the 

development of a numerical groundwater-flow model of the 

Minnelusa and Madison hydrogeologic units, which contain 

the Minnelusa and Madison aquifers, in the Rapid City area 

in South Dakota, and (2) present simulated responses to stress 

and describe model limitations. The report describes the calibrated numerical groundwater-flow model including estimates 

of recharge, discharge, and hydraulic properties that characterize the Minnelusa and Madison hydrogeologic units.

Previous Investigations

This numerical modeling effort utilized datasets compiled 

in a report by Long and Putnam (2002) that documents a 

conceptual model of the Madison and Minnelusa aquifers. 

The concepts and datasets from that report were used extensively in constructing the numerical groundwater-flow model. 

Detailed description of the methods and interpretations that 

were used in compiling these datasets is available in Long 

and Putnam (2002). The conceptual-model report by Long 

and Putnam (2002) describes previous investigations pertinent to this report. Previous investigations include several 

publications from the Black Hills hydrology study (Hortness 

and Driscoll, 1998; Carter and Redden, 1999a, 1999b, 1999c; 

Strobel and others, 1999; Driscoll, Bradford, and Moran, 

2000; Driscoll, Hamade, and Kenner, 2000; Carter and others, 

2001) and studies specific to the Rapid City area (Greene, 

1993, 1999; Anderson and others, 1999; Long, 2000; Long 

and Putnam, 2002).

Recent studies of the Minnelusa and Madison aquifers 

include linear modeling of three components of flow in karst 

aquifers by using oxygen isotopes (Long and Putnam, 2004). 

Hargrave (2005) described the vulnerability of the Minnelusa 

aquifer to contamination. Miller (2005) described the influences of geologic structures and stratigraphy on groundwater 

flow in the karstic Madison hydrogeologic unit in the study 

area. Putnam and Long (2007) characterized karst groundwater flow in the Rapid City area by using fluorescent dyes. 

Long and others (2008) described the use of age-determining 

tracers in conjunction with other tracers to characterize 

groundwater flow paths in the Madison aquifer. 

Acknowledgments

The authors acknowledge the extensive support from the 

city of Rapid City for numerous studies from which datasets used in this modeling effort have been developed. West 

Dakota Water Development District and the South Dakota 

School of Mines and Technology participated in numerous 
Figure 1. Location of study area.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

SOUTH DAKOTA

Study area

Black Hills

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Outcrop of Minnelusa hydrogeologic unit

Outcrop of Madison hydrogeologic unit

Fault—Dashed where approximated. Bar and ball on downthrown side

Anticline—Showing trace of axial plane and direction of plunge. Dashed where 

 approximated

Syncline—Showing trace of axial plane and direction of plunge. Dashed where 

 approximated

Monocline—Showing trace of axial plane. Dashed where approximated

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Geologic outcrops modified from Strobel 

and others, 1999

Structural features modified from Strobel 

and others, 1999, and Miller, 2005

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

43°55’

44°15’

44°05’

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44

79

79

Introduction 3
4 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

studies to better understand the complex hydrogeology in 

the Rapid City area. The Water Rights Program of the South 

Dakota Department of Environment and Natural Resources 

(SDDENR) provided compilations of water-level data for 

numerous observation wells they operate in the study area. 

The SDDENR also provided water-use data. 

Description of Study Area

The approximately 1,000-square-mile (mi2) study area 

(fig. 1) on the eastern flank of the Black Hills includes Rapid 

City and the surrounding area. The study area extends from 

Elk Creek on the north to Battle Creek on the south, and from 

the outcrop of the Madison hydrogeologic unit on the west to 

Farmingdale and Box Elder on the east (fig. 1). The population 

of Rapid City in the 2000 census was 59,607 (U.S. Census 

Bureau, 2000). The area around Rapid City includes numerous suburban subdivisions and smaller towns. The study area 

includes parts of Lawrence, Meade, Pennington, and Custer 

Counties. The Minnelusa and Madison aquifers are important 

sources of water for many of the smaller communities and 

subdivisions in these counties.

Physiography and Climate

Land-surface altitudes range from more than 

5,000 feet (ft) above the National Geodetic Vertical Datum of 

1929 on the western side of the study area to about 2,800 ft 

near Farmingdale. The western extent of the study area is 

characterized by high relief covered predominantly by pine 

and spruce forests. The eastern lowlands are characterized by 

rolling prairies with bottom lands along stream channels. The 

Minnelusa and Madison hydrogeologic units crop out in the 

western part of study area along the eastern flank of the Black 

Hills uplift. These outcrops are characterized by high-relief 

forested areas cut by deep canyons with entrenched meanders 

and steep cliffs formed by resistant limestone and sandstone.

Average (water years 1961–90) precipitation rates range 

from about 24 inches per year (in/yr) in the northwest to about 

16 in/yr in the eastern lowlands with most precipitation occurring in March, April, May, and June (Driscoll, Hamade, and 

Kenner, 2000). The average (1960–90) temperature at Rapid 

City is about 22 degrees Fahrenheit in January and about 

72 degrees Fahrenheit in July (National Oceanic and Atmospheric Administration, 1996).

Hydrogeologic Setting

Uplift at the end of the Cretaceous period followed by 

erosion has created the dome-like structure and geomorphology of the Black Hills. Metamorphic and igneous rocks of 

Precambrian age are exposed in the Black Hills’ central core, 

whereas stratigraphic layers (figs. 2 and 3) of Paleozoic age 

and younger are exposed on its flanks. The outcrops of Paleozoic units form generally concentric rings surrounding the 

Precambrian core and dip radially outward.

The Minnelusa and Madison hydrogeologic units dip 

away from the uplifted Black Hills at angles that can approach 

or exceed 15 to 20 degrees near the outcrops and decrease 

with distance from the uplift to less than 1 degree (Carter and 

Redden, 1999a, 1999b, 1999c). The Minnelusa and Madison 

aquifers are contained within the Minnelusa and Madison 

hydrogeologic units, and many studies refer to the aquifers as being the upper part of the hydrogeologic units. The 

Minnelusa hydrogeologic unit is composed of the Minnelusa 

Formation. The Madison hydrogeologic unit includes the 

Madison Limestone and the underlying Englewood Formation because the Englewood Formation is hydrogeologically 

similar to the lower part of the Madison Limestone. The 

outcrop areas for the Minnelusa and Madison hydrogeologic 

units in the study area are about 39 square miles (mi2) and 

52 mi2, respectively (fig. 1). Anticlines and synclines (fig. 1) 

result in local variations in the dip of beds near the outcrops.

A conceptual illustration of groundwater-flow components in an aquifer with hydrogeology similar to the Minnelusa and Madison aquifers is shown in figure 4. Infiltrating 

precipitation or streamflow losses may have an easterly 

flow component rather than a strictly vertical one because 

of the greater hydraulic conductivity parallel to easterly 

dipping bedding planes. The hydraulic head in the recharge 

area fluctuates with the changing recharge rate and causes 

a pressure wave to propagate through the confined part of 

the aquifer. This wave decreases in amplitude with distance 

traveled because of head losses in the aquifer. For this reason, 

hydraulic head fluctuations in downgradient locations east of 

the recharge area generally are less than in the recharge area 

unless other stresses, such as pumping, are introduced. Springs 

discharge through breccias pipes, fractures, and enlarged solution openings.

Water-table conditions generally exist in outcrop areas; 

however, the water table in the updip parts of the outcrops 

(approximately 1 to 2 miles along western edge) may be 

perched above the regional water table because of the higher 

altitudes. Recharge water may be stored under perched conditions before percolating downward to the regional water table. 

Water perched on discontinuous layers of low permeability 

material may exist in the Minnelusa Formation, and pools of 

perched water can be found in Madison Limestone caves. The 

unconfined area extends beyond the outcrop areas to the east 

a few hundred feet, where the dip is steepest, to more than 

1 mile (mi), where the dip is less steep (Long and Putnam, 

2002). Structural features near the outcrops (fig. 1) influence 

the shape and extent (described in the subsequent “Storage 

Properties” section) of the unconfined area. The estimated 

unconfined area is 36.3 mi2 for the Minnelusa hydrogeologic 

unit and 52.9 mi2 for the Madison hydrogeologic unit (Long 

and Putnam, 2002). East of the water-table areas, hydraulic 

head is above the tops of the hydrogeologic units owing to 

their easterly dip, and confined conditions exist. In some areas, 
Figure 2. Stratigraphic section for the study area.

STRATIGRAPHIC UNIT DESCRIPTION THICKNESS IN FEET

ABBREVIATION

FOR

STRATIGRAPHIC

INTERVAL

ERATHEM SYSTEM

QUATERNARY

& TERTIARY (?)

UNDIFFERENTIATED SANDS AND GRAVELS 0–50 Sand, gravel, and boulders

1,200–2,000

Light colored clays with sandstone channel fillings and local limestone leIncludes rhyolite, latite, trachyte, and phondite.

WHITE RIVER GROUPINTRUSIVE IGNEOUS ROCKS

Tw

TERTIARY Tui

QTu

Principal horizon of limestone lenses giving teepee buttes. Dark-gray shale containing scattered concretions. Widely scattered limestone masses, giving small teepee buttes. Black fissile shale with concretions. 

PIERRE SHALENIOBRARA FORMATION 100–225 Impure chalk and calcareous shale.CARLILE FORMATION Turner Sand Member

Wall Creek Sands

400–750

Light-gray shale with numerous large concretions and sandy layers.Dark-gray shale.

GRANEROS GROUP

GREENHORN FORMATION

Kps

25–380

Impure slabby limestone. Weathers buff.Dark-gray calcareous shale, with thin Orman Lake limestone at base.

BELLE FOURCHE SHALE

MOWRY SHALE

NEWCASTLE

SANDSTONE

SKULL CREEK SHALE

300–550

Gray shale with scattered limestone concretions.Clay spur bentonite at base.

150–250

20–60

Light-gray siliceous shale. Fish scales and thin layers of bentonite.Brown to light-yellow and white sandstone.

170–270 Dark-gray to black siliceous shale.

CRETACEOUS

FALL RIVER FORMATIONLAKOTA FORMATION

INYAN KARA

GROUP

10–200 Massive to slabby sandstone.

Coarse gray to buff crossbedded conglomeratic sandstone, interbedded w and gray clay, especially toward top. Local fine-grained limestone. 35–700

0–2200–225

Green to maroon shale. Thin sandstone.Massive fine-grained sandstone.

250–450

0–45

Greenish-gray shale, thin limestone lenses.Glauconitic sandstone; red sandstone near middle.Red siltstone, gypsum, and limestone.

MORRISON FORMATION

UNKPAPA SS Redwater Member

Lak MemberHulett MemberStockade Beaver Mem.Canyon Spr Member

SUNDANCEFORMATIONGYPSUM SPRING FORMATION

Kik

Ju JURASSIC

Goose Egg Equivalent

SPEARFISH FORMATION T Ps R TRIASSIC

MINNEKAHTA LIMESTONE

Po OPECHE SHALE

Pmk

250–700

125–65

Red sandy shale, soft red sandstone and siltstone with gypsum and thin liGypsum locally near the base.Thin to medium-bedded finely crystalline, purplish-gray laminated limesto

50-135 Red shale and sandstone.

1,2375–800

2250–550

30–60

0–60

0–100

375–400

Yellow to red crossbedded sandstone, limestone, and anhydrite locally at Red shale with interbedded limestone and sandstone at base.Massive light-colored limestone. Dolomite in part. Cavernous in upper paPink to buff limestone. Shale locally at base.Buff dolomite and limestone.Green shale with siltstone.Massive to thin-bedded buff to purple sandstone. Greenish glauconitic sh dolomite, and flat-pebble limestone conglomerate. Sandstone, with co locally at the base.Schist, slate, quartzite, and arkosic grit. Intruded by diorite, metamorphos to amphibolite, and by granite and pegmatite.

PERMIAN

PENNSYLVANIAN

MISSISSIPPIAN

MINNELUSA FORMATIONMADISON (PAHASAPA) LIMESTONEENGLEWOOD FORMATION

MDme

Ou

DEVONIAN

WHITEWOOD (RED RIVER) FORMATIONWINNIPEG FORMATIONDEADWOOD FORMATIONUNDIFFERENTIATED METAMORPHICAND IGNEOUS ROCKS

OCd

pCu

ORDOVICIAN

CAMBRIAN

PRECAMBRIAN

PALEOZOIC MESOZOIC CENOZOIC

Modified from information furnished by the Department of Geology and GeoSouth Dakota School of Mines and Technology (written commun., January 

0–600

Interbedded sandstone, limestone, dolomite, shale, and anhydrite.

1 Modified on the basis of drill-hole data.3 Based on Carter and others, 2001.2 Thickness based on structure contours of Minnelusa Formation,

Madison Limestone, and Deadwood Formation tops (Carter andRedden, 1999a, 1999b, 1999c).

MUDDY

SANDSTONE

P Pm

Unknown
Figure 3. Conceptual hydrogeologic section of the study area (modified from Hayes, 1999). Each 

aquifer shown is separated from other aquifers by confining units. Hydraulic connection between 

aquifers is increased by vertical breccia pipes and fractures. The schematic shows (1) exposed 

breccia pipe above hydraulic head in Madison aquifer, (2) exposed breccia pipe with hydraulic head 

below land surface, (3) breccia pipe at active spring-discharge point, (4) developing breccia pipe, 

(5) fractures in confining unit, (6) breccia pipe originating in the Madison Limestone, (7) breccia pipe 

extending from Minnelusa Formation to the Inyan Kara Group, and (8) discontinuous residual clay soil. 

Arrows show general areal leakage, focused leakage at breccia pipes, or groundwater-flow directions.

West

East

Potentiometric surface

of Madison aquifer

Alluvium

Dip of sedimentary rocks greatly exaggerated

Precambrian metamorphic

and igneous rocks

Deadwood

Inyan Kara Group

Thicknesses not to scale

Madison

Minnelusa

Minnekahta

Limestone

Aquifer Cave

Breccia pipe

Residual clay soil

 (collapsed area)

Confining unit

EXPLANATION

Formation

Formation

Water

table

(1)

(2)

(3)

(4)

(5)

(6)

(8)

(7) Limestone

Spring

Englewood 

Formation

6 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

the hydraulic head is above the land surface, and flowing wells 

may exist in these areas. Hydraulic connection to the overlying Minnekahta Limestone and Inyan Kara Group is limited 

by intervening shale layers.

Movement of groundwater between the Minnelusa and 

Madison aquifers is influenced by vertical hydraulic gradients, 

hydraulic properties of the intervening confining unit, and 

recharge rates (fig. 5; Long and Putnam, 2002). Although the 

confining units generally do not transmit water at a high rate, 

their capacity to store water could have substantial effects on 

the hydraulics of the groundwater-flow system. Water that 

flows between the Minnelusa and Madison aquifers must pass 

through a confining unit that is several hundred feet thick with 

variable porosity and potentially a substantial amount of water 

held in storage. The confining units contain more secondary 

porosity in the western side of the study area where fracturing from the Black Hills uplift is more prevalent than in the 

eastern side of the study area. East of Rapid City, the hydraulic 

head is higher in the Minnelusa aquifer than in the Madison 

aquifer.
Figure 4. Generalized diagram with vertical exaggeration of a confined aquifer recharged at the updip end (from Long and 

Putnam, 2002). The diagram shows (1) recharge infiltrates and moves downward vertically or diagonally parallel to bedding 

planes, (2) near horizontal flow with head losses resulting from resistance from aquifer material, (3) sloping potentiometric 

surface results from head losses, (4) artesian spring discharges through high-conductivity breccia pipe or fracture because 

hydraulic head is above the land surface, (5) spring causes depression in the potentiometric surface, (6) outflow rate is 

controlled by hydraulic gradient and transmissivity, (7) hydraulic head fluctuation at recharge area is controlled by changes 

in recharge rate, and (8) smaller hydraulic head fluctuation downgradient is in response to larger fluctuation at recharge 

area.

Water table

4

5

3

2

1

7

Areal recharge or

 infiltration

Unsaturated zone

Bedding plane

EXPLANATION

Aquifer

Confining unit

Confining unit

Outcrop

unsaturated

area

Outcrop area

Unconfined

area Confined area

Direction of flow

Breccia pipe

8

6

Land surface

Losingstream

West East

Potentiometric surface

Description of Study Area 7
Figure 5. Recharge conditions and vertical gradients in the Minnelusa and Madison hydrogeologic units (from Long 

and Putnam, 2002). The diagram shows (1) perched water, (2) part of the recharge on the Minnelusa outcrop infiltrates to 

the Madison aquifer, (3) hydraulic head in Madison aquifer greater than in Minnelusa aquifer creating upward hydraulic 

gradient, and (4) hydraulic head greater in Minnelusa aquifer than in Madison aquifer creating downward hydraulic gradient.

West East

Minnelusa aquifer

potentiometric surface

(water table in unconfined area)

Madison aquifer

potentiometric surface

(water table in unconfined area)

4 3

1

Areal recharge

 or infiltration

Leakage

Perched water

Bedding plane

EXPLANATION

Aquifer

Aquifer

Confining unit

Confining unit

Confining unit

Madison

hydrogeologic unit

Minnelusa

hydrogeologic unit

Upward

hydraulic gradient

Madison > Minnelusa

Downward

hydraulic gradient

Minnelusa > Madison

Greater than

2

>

8 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Minnelusa Hydrogeologic Unit

The Pennsylvanian- and Permian-age Minnelusa Formation, which composes the Minnelusa hydrogeologic unit, is 

375 to 800 ft thick (fig. 2) east of its outcrop. Bowles and 

Braddock (1963) described the upper part of the Minnelusa 

hydrogeologic unit as thick sandstone with thin limestone, 

dolomite, and mudstone, and the lower part as having less 

sandstone and more shale, limestone, and dolomite than the 

upper part. Siltstone, gypsum, and anhydrite also can be 

present. The upper 200 to 300 ft of the Minnelusa hydrogeologic unit is more permeable, because of the coarser sandstone, solution openings, breccias, and other karst features, 

than the lower part of the unit (Peter and others, 1988; Greene, 

1993). At the base of the Minnelusa hydrogeologic unit is a 

red clay shale that ranges in thickness from 0 to 50 ft (Cattermole, 1969; Greene, 1993). This shale, which is discontinuous 

in the study area, is an ancient residual soil developed on the 

surface of the Madison Limestone (Gries, 1996). The lower 

part of the Minnelusa hydrogeologic unit is less permeable 

than the upper part and generally is an aquitard that impedes 

flow between the Minnelusa and Madison aquifers (Kyllonen 

and Peter, 1987; Peter and others, 1988; Greene, 1993). Near 

outcrop areas, however, the lower part can have greater permeability than in other areas owing to fracturing and weathering in outcrop areas. The hydraulic connection between the 

Minnelusa and Madison aquifers is highly varied with strong 

connections possible in areas with breccia pipes (fig. 3) and 

structural features; however, over most of the area, the shale 

in the lower Minnelusa hydrogeologic unit limits the hydraulic 

connection.

Recharge to the Minnelusa hydrogeologic unit is from 

streamflow where streams cross the outcrop and from infiltration of precipitation on the outcrops (areal recharge). Most 

Black Hills streams lose their flow to various sedimentary 

rocks that are exposed around the periphery of the Black Hills 

(Hortness and Driscoll, 1998). When streamflow from the 

central core of the Black Hills is low, most streamflow is lost 

to the outcrop of the Madison hydrogeologic unit, which is 

upstream from the outcrop of the Minnelusa hydrogeologic 

unit.

Wells completed in the Minnelusa hydrogeologic unit in 

the study area range in depth from 80 ft near the outcrop to 

about 3,000 ft in the eastern part and are capable of producing 

from 5 to 700 gallons per minute (gal/min; Long and Putnam, 

2002). Wells completed in the Minnelusa hydrogeologic unit 

are used extensively by small suburban developments and 

domestic households surrounding Rapid City.

Madison Hydrogeologic Unit

The Madison hydrogeologic unit includes the 

Mississippian-age Madison Limestone and the Devonian-age 

Englewood Formation and is 250 to 610 ft thick in the study 
Numerical Groundwater-Flow Model 9

50 gal/min, 11 percent yield 50 to 200 gal/min, and 25 percent 

yield 200 to 2,500 gal/min. The depth of wells ranges from 

20 to 4,600 ft, with 78 percent of the wells less than 1,000 ft 

and 41 percent less than 500 ft (Long and Putnam, 2002). The 

deepest wells are on the eastern side of the study area, where 

the water level may be only a few hundred feet below the land 

surface owing to artesian pressure. The varied well yields are 

influenced by karst features, with the larger production wells 

connected to substantial solution openings.

Numerical Groundwater-Flow Model

MODFLOW–2000, a numerical, three-dimensional, 

finite-difference groundwater-flow model (Harbaugh and 

others, 2000), was used to simulate flow in the hydrogeologic units within the study area. Detailed descriptions of 

MODFLOW–2000 packages that were used in the model are 

presented in McDonald and Harbaugh (1988) and Harbaugh 

and others (2000). The MODFLOW–2000 parameter estimation process (Hill and others, 2000) was used to optimize 

estimates of hydraulic properties for calibration.

The design of the numerical groundwater-flow model was 

based on the conceptual model described in Long and Putnam 

(2002) and includes five model layers (fig. 6). The Minnelusa 

and Madison hydrogeologic units were each represented by 

two model layers. Although the entire thickness of these units 

may include secondary porosity, the more permeable parts 

of the hydrogeologic units generally occur in the upper part 

of both units (Long and Putnam, 2002). Layer 1 represents 

the fractured sandstone layers in the upper part of the Minnelusa hydrogeologic unit. The Minnelusa aquifer generally is 

contained in the upper 200 to 300 ft of the unit (Greene, 1993). 

Layer 2 represents the fractured limestone, minor sandstone 

layers, and shale units in the lower part of the Minnelusa 

hydrogeologic unit. Layer 3 represents the secondary porosity 

and karstic features of the Madison hydrogeologic unit that 

are more prevalent in the upper part than in the lower part. 

This layer approximates the upper two geomorphic units of the 

Madison Limestone described by Miller (2005) and described 

by Greene (1993) as being 100 to 200 ft thick in total. Layer 4 

represents the less permeable lower part of the Madison 

hydrogeologic unit. Layer 5 represents the western part of 

the Deadwood aquifer to approximate upward flow to the 

Madison hydrogeologic unit from the underlying Deadwood 

aquifer. The Whitewood and Winnipeg Formations shown in 

figure 2 are absent throughout most of the study area (Long 

and Putnam, 2002).

Arrays representing the altitude of the tops of model 

layers 1, 3, and 5 were constructed from maps of the structural tops of the Minnelusa Formation, Madison Limestone, 

and Deadwood Formation (Carter and Redden, 1999a, 1999b, 

1999c; Long and Putnam, 2002). A uniform thickness of 250 ft 

was assumed for layer 1 with the remainder of the Minnelusa 

hydrogeologic unit represented as layer 2. The upper 250 ft 

area. The Madison Limestone is composed of limestone and 

dolomite and is 250 to 550 ft thick east of the outcrop of the 

Madison hydrogeologic unit (fig. 2). The Englewood Formation, which underlies the Madison Limestone, is less than 

60 ft thick, is composed of argillaceous, dolomitic limestone, 

and probably could logically be considered a member of the 

Madison Limestone because of its lithology (Gries and Martin, 

1985).

The upper surface of the Madison Limestone is a 

weathered karst surface and is unconformably overlain by the 

Minnelusa Formation (Cattermole, 1969). The upper 150 ft of 

the Madison hydrogeologic unit contains substantial secondary 

permeability from solution openings and fractures (Greene, 

1993), and solution enlargement of fractures has resulted in 

a predominance of conduit flow. Secondary permeability in 

the lower part of the Madison hydrogeologic unit generally is 

smaller than in the upper part (Greene, 1993); however, the 

lower unit can have greater permeability near outcrop areas 

than in the eastern part, especially along stream channels.

The Madison Limestone was divided into four cliffforming geomorphic units by Miller (2005) through detailed 

mapping of the canyons in the Spring, Rapid, and Boxelder 

Creek Basins that are on the west-central edge of the study 

area (fig. 1). The thickness of the units from bottom to top 

are 130 to 165 ft for unit 1, 81 to 120 ft for unit 2, 140 to 

150 ft for unit 3, and 0 to 85 ft for unit 4. Late Mississippian 

erosion removed the upper part of unit 4 in the Boxelder and 

Spring Creek canyons and all of unit 4 and part of unit 3 in 

the Rapid Creek canyon. Unit 1 is highly resistant to erosion, 

having thickly bedded sections and forming nearly vertical 

cliffs. Unit 2 is similar; however, the bedding is thinner and 

cliff faces tend to be more irregular. Unit 3 is characterized 

by massive collapse brecciation with large angular blocks 

and poorly preserved bedding. Caves are numerous in unit 3 

and commonly are filled with cemented solution breccias and 

cave fill. Unit 4, where present, is characterized by collapse 

brecciation with angular blocks. Upper cliff surfaces in unit 4 

are rounded off because of low resistance to erosion. Karst 

features are located throughout the Madison Limestone; 

however, they tend to be more common along the contacts 

between these geomorphic units (Miller, 2005).

Recharge to the Madison hydrogeologic unit is from 

streamflow loss where streams cross the outcrops and from 

infiltration of precipitation on the outcrops. The streamflow 

loss threshold represents the maximum amount of streamflow 

loss that can occur when water is available in the stream. Loss 

thresholds for the major streams in the study area (Hortness 

and Driscoll, 1998) for the Madison hydrogeologic unit range 

from about 10 to 25 cubic feet per second (ft3/s). Because the 

Madison hydrogeologic unit outcrop is the most upstream unit 

with large loss thresholds, streamflow recharge is substantial 

and usually greater than areal recharge to the Madison hydrogeologic unit in the study area.

Wells completed in the Madison hydrogeologic 

unit in the study area are capable of producing from 5 to 

2,500 gal/min. About 64 percent of the wells yield 5 to 
Figure 6. Conceptual schematic of model layers in relation to hydrogeology.

Deadwood aquifer

Madison confining unit 

(includes Englewood Formation)

Minnelusa

confining

unit

Minnelusa aquifer

Madison aquifer

Spring Wells

Water use Discharge to

overlying units

Discharge by regional outflow

EXPLANATION

Aquifer

Confining unit

Well

Breccia pipe

Flow direction Areal recharge

Streamflow recharge

Model 

layer

2

1

3

4

5

Madison hydrogeologic

unit 

Minnelusa hydrogeologic

unit

10 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

generally contains the sandstone layers. The thickness of layer 

2 ranged from 106 to 590 ft with a mean of 293 ft. A uniform 

thickness of 150 ft was assumed for layer 3 with the remainder 

of the Madison hydrogeologic unit represented in layer 4. The 

thickness of layer 4 ranged from 139 to 599 ft with a mean of 

341 ft.

Finite-Difference Grid and Boundary Conditions

The finite-difference grid defining the model area 

consisted of 221 rows and 169 columns (fig. 7). The cell size 

was 492.1 ft (150 meters) by 492.1 ft in the detailed study 

area that surrounded Rapid City. Cell sizes increased from the 

detailed area to 1,640 ft in width at the boundaries on the north 

and south and to 6,562 ft in width at the boundary on the east 

(fig. 7). The model was oriented 23 degrees counterclockwise 

so that the orientation of finite-difference cells approximated 

the orthogonal patterns in cave passageways and fracture 

patterns (Greene and Rahn, 1995). This orientation allowed for 

simulation of horizontal anisotropy if necessary. Miller (2005) 

mapped a major trend in fractures and joints in the study area 

as north 65 degrees east with a less dominant trend of north 

35 degrees west. The general pattern of structural features 

(fig. 1; Strobel and others, 1999) in the study area was about 

23 degrees.

The boundary conditions used in the model are described 

in general terms in this section with quantitative descriptions 

presented in the subsequent “Representation of Flow System 

Components” section. The mathematical concepts for various 

types of cells used to represent boundaries are described in 

detail in McDonald and Harbaugh (1988), and the specific 

MODFLOW–2000 packages that were used are included with 

the model cell descriptions that follow.

Boundaries on the north and south for layers 1–4 were 

represented as no-flow boundaries (figs. 8 and 9) because 

the northern and southern boundaries generally occur along 

flow lines. The boundaries on the east for layers 1–4 were 

represented with head-dependent flow cells (Drain Package, 

McDonald and Harbaugh, 1988). With this type of boundary cell, flow across the boundary changes in relation to the 

hydraulic head in the aquifer. The calculated flow is the difference between a specified head and the head in the model cell 

multiplied by the area of the cell multiplied by the assigned 
Figure 7. Location of finite-difference grid.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

16

I-90

I-90

Creek

Creek

Creek

Creek

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Hisega

43°55’

44°15’

44°05’

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44

79

79

1

20

40

60

80

100

120

140

160

180

200

221

1

60

20

80

40

169

120

140

160

100

EXPLANATION

Outcrop of Minnelusa hydrogeologic unit

Outcrop of Madison hydrogeologic unit

Boundary of detailed study area—Cell dimensions within this area are 492.1 by 492.1 feet

Selected grid lines—Adjacent number is row or column number

Geologic outcrops modified from Strobel 

and others, 1999

Numerical Groundwater-Flow Model 11
Figure 8. Active model cells and boundary conditions for layers 1 and 2 (Minnelusa hydrogeologic unit).

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid

City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

16

I-90

I-90

Creek

Creek

Creek

Creek

Base from U.S. Geological Survey digital 

data, 1977, 1:100,000, and Rapid City, 

Office of City Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

43°55’

44°15’

44°05’

79

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

EXPLANATION

Part of Minnelusa hydrogeologic unit estimated as unsaturated (inactive cells)

Active cells in layers 1 and 2

Active cells in layer 2

No-flow boundary

Head-dependent flow boundary representing outflow from layers 1 and 2

Specified-flux boundary representing areal recharge to layer 2 (applied to 

 westernmost active cell in layer 2)

Specified-flux boundary representing areal recharge to layer 1 (applied to 

 westernmost active cell in layer 1)

Minnelusa aquifer potentiometric contour (average for water years 1988–97; 

 Long and Putnam, 2002)—Shows altitude at which water would have stood in 

 tightly cased, nonpumped well. Contour interval 100 feet. Datum is National 

 Geodetic Vertical Datum of 1929

3,500

2,600

2,700

2,800

2,900

3,000

3,100

3,200

3,3,00

3,500

3,400

3,600

3,700

3,800

2,900

3,000

3,100

3,200

3,3,00

3,500

3,400

12 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Figure 9. Active model cells and boundary conditions for layers 3 and 4 (Madison hydrogeologic unit).

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid

City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

Base from U.S. Geological Survey digital 

data, 1977, 1:100,000, and Rapid City, 

Office of City Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

79

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

EXPLANATION

Part of Madison hydrogeologic unit estimated as unsaturated (inactive cells)

Active cells in layers 3 and 4

Active cells in layer 4

No-flow boundary

Head-dependent flow boundary representing outflow from layers 3 and 4

Specified-flux boundary representing areal recharge to layer 4 (applied to 

 westernmost active cell in layer 4)

Specified-flux boundary representing areal recharge to layer 3 (applied to 

 westernmost active cell in layer 3)

Madison aquifer potentiometric contour (average for water years 1988–97; 

 Long and Putnam, 2002)—Shows altitude at which water would have stood in 

 tightly cased, nonpumped well. Contour interval 100 feet. Datum is National 

 Geodetic Vertical Datum of 1929

3,500

3,500

3,400

3,300

3,200

3,100

3,000

2,900

2,800

2,700

2,600

3,900

4,100

3,800

2,500

3,700

3,600

3,500

3,400

3,300

3,200

3,100

3,000

2,900

2,800

2,700

2,600

3,600

3,500

4,000

Numerical Groundwater-Flow Model 13
14 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

boundary conductance. Conductance is a term that represents 

the hydraulic conductivity multiplied by a unit of length, and 

is expressed in units of feet squared per day (ft2/d). The boundaries on the north, east, and south perimeters were located 

about 12 mi from the detailed study area to minimize their 

influence on analysis of groundwater flow in the detailed study 

area (fig. 7).

Areal recharge to layers 1–4 (figs. 8 and 9) was represented with a specified-flux boundary (Recharge Package, 

McDonald and Harbaugh, 1988) with the recharge flux 

assigned to the westernmost active cell. Groundwater flow in 

the western part of the outcrops of the Minnelusa and Madison 

hydrogeologic units was not simulated for the unsaturated 

areas (figs. 8 and 9). In these areas near the outcrops, groundwater flow includes unsaturated areas, perched water, and 

caves intermittently filled with water that spills and moves 

downgradient. This non-Darcian flow was not simulated; 

therefore, accumulated infiltration of precipitation on the 

outcrop was assigned to the first downgradient (westernmost) 

active model cells in layers 1–4. Streamflow recharge was 

represented with specified-flow cells assigned to selected 

cells in layers 1–4 to represent streamflow loss that occurred 

when streams crossed the outcrops of the Minnelusa and 

Madison hydrogeologic units (fig. 10). Streamflow loss for 

the larger streams was gaged and described in Hortness and 

Driscoll (1998). The streamflow recharge cells were located 

approximately where streamflow loss was observed for the 

larger streams. For some streams, the specified-flow cells 

were moved downstream to the westernmost active cell in the 

model layer.

A specified-flux boundary (Recharge Package, McDonald and Harbaugh, 1988) representing the source of water 

for upward flow from the Deadwood aquifer (layer 5) to 

layer 4 was assigned to the westernmost active cells in layer 5 

(fig. 11). Active cells for layer 5 extend from one cell west 

of active cells in layer 4 to the east beyond the start of active 

cells in layer 3 (fig. 11) with no-flow boundaries on the north, 

east, and south. The purpose of layer 5 was to approximate 

the distribution of upward flow from underlying units to the 

Madison hydrogeologic unit and not to simulate groundwater flow in the Deadwood aquifer. Upward flow from the 

Minnelusa hydrogeologic unit to overlying units, which was 

assumed to be small, was represented with specified-flux cells 

(Recharge Package, McDonald and Harbaugh, 1988) in the 

western part of the model where more fracturing was likely 

(Long and Putnam, 2002; fig. 11).

Springs discharging from the Minnelusa and Madison 

hydrogeologic units (figs. 11 and 12) were represented with 

head-dependent flow cells (Drain package or River Package, 

McDonald and Harbaugh, 1998). The user-specified hydraulic head at the cell or cells was set at the altitude of the 

land surface at the spring. The springs generally appear as 

seepage from the alluvium along streams; therefore, springflow through the bedrock openings could emerge somewhat 

upgradient from observed flow in the streams. A more detailed 

description of individual springs and estimates of spring 

discharge is included in the subsequent “Springflow” section.

Calibration and Simulated Stress Periods

Calibration of the model was accomplished by two simulations: (1) steady-state simulation of average conditions for 

water years (WY) 1988–97 and (2) transient simulations for 

WY 1988–97 divided into twenty 6-month stress periods. The 

model was calibrated with both the steady-state and transient 

simulations by comparison of hydraulic head values and flows. 

Average hydraulic heads for water years 1988–97 (Long 

and Putnam, 2002) were assumed to approximate hydraulic 

heads for the steady-state simulation because the 10-year 

period included a range of hydrologic conditions. Hydraulic 

heads from the steady-state simulation were used as starting 

heads for the transient simulation. The transient stress periods 

(table 1) include a dry period in the late 1980s and early 1990s 

(stress periods 1–11) and a wet period in the late 1990s (stress 

periods 12–20). Most recharge occurred during the summer 

stress periods from April through September, and water use 

from the Madison aquifer also increased substantially during 

the summer stress periods. Recharge and other model components are described with more detail in the subsequent “Representation of Flow-System Components” section.

Inverse modeling with the MODFLOW–2000 parameter estimation process (Hill and others, 2000) was used to 

calibrate the steady-state model, and trial-and-error methods 

were used to conjunctively calibrate the transient model. 

The term “parameter” in this report is used to describe any 

physical property that was estimated by model calibration. An 

“observation” is a direct measurement or an estimate based on 

measured data. A parameter can represent a particular property 

for a single cell or group of model cells. Simulated results 

were compared to measured or estimated hydraulic heads or 

flow rates and optimized.

In inverse modeling, simulated values of hydraulic head 

and flows are statistically compared to observed values. The 

program adjusts parameter values in an iterative process to 

produce the best possible match between the observed and 

simulated values. Parameterization is the process of identifying the aspects of the simulated system that can be optimized 

with these statistical algorithms. The number of parameters 

that can be estimated is limited by the amount and distribution 

of observed data (Hill, 1998). Some parameters may be insensitive to the observed data, or some parameters may be highly 

correlated with each other and cannot be optimized. The 

selection of parameters that could be estimated with statistical 

confidence by inverse modeling is described in the subsequent 

“Steady-State Calibration” section.

Transient simulations were calibrated by comparison of 

observed and simulated hydraulic head values and flows using 

a trial-and-error evaluation. Simulated steady-state hydraulic 

head values were used as the starting hydraulic head values 

for the transient simulation. Parameters that were not sensitive 
Figure 10. Specified-flow cells representing streamflow recharge.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Outcrop of Minnelusa hydrogeologic unit

Outcrop of Madison hydrogeologic unit

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

Specified-flow cell representing streamflow recharge to layer 1

Specified-flow cell representing streamflow recharge to layer 2

Specified-flow cell representing streamflow recharge to layer 3

Specified-flow cell representing streamflow recharge to layer 4

Geologic outcrops modified from Strobel 

and others, 1999

Numerical Groundwater-Flow Model 15
Figure 11. Model cells representing upward flow from the Deadwood aquifer to layer 4, flow from the Minnelusa hydrogeologic 

unit to overlying units, and discharge to Elk Spings.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

Elk Springs

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

79

Specified-flux cells representing upward flow from the Minnelusa hydrogeologic 

 unit to overlying units

Active cells in layer 5 representing distribution of upward flow from the 

 Deadwood aquifer

Specified-flux boundary representing upward flow from the Deadwood aquifer 

 (applied to westernmost active cell in layer)

Head-dependent flow cell (Drain Package) representing discharge from layers 1 

 and 3 to Elk Springs

EXPLANATION

16 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Figure 12. Locations of head-dependent flow cells representing springs in the detailed study area.

44°05’

I-90

44

79

Rapid

16

Creek

Boxelder

Spring

Creek

Creek

MEADE CO

PENNINGTON CO

T. 1 N.

T. 1 S.

R. 7 E.

R. 6 E.

R. 5 E.

103°22’30”

103°15’

44°00’

T. 3 N.

T. 2 N.

Base fom U.S. Geological Survey 

digital data, 1977, 1:100,000 

Rapid City, Office of City Engineer map, 

2005, 1:18,000

Unversal Transverse Mercator projection

Zone 13 0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

Rapid City

79

44

16

Rapid

Creek

440321103181101

06412900

Canyon Lake

City Springs

Jackson-Cleghorn 

Springs

Boxelder 

Springs

Infiltration Gallery Springs

Deadwood 

Avenue 

Springs

Canyon Lake

City Springs

Jackson-Cleghorn 

Springs

Infiltration Gallery Springs

Deadwood 

Avenue 

Springs

EXPLANATION

Head-dependent flow cell (Drain Package) representing discharge from 

 model layer 1 to Boxelder and Infiltration Gallery Springs

Head-dependent flow cell (River Package) representing hydraulic

 connection of model layer 1 to Canyon Lake

Head-dependent flow cell (River Package) representing discharge from 

 model layer 1 to Jackson-Cleghorn Springs

Head-dependent flow cell (Drain Package) representing discharge from 

 model layer 3 to Jackson-Cleghorn Springs

Head-dependent flow cell (Drain Package) representing discharge from 

 model layers 1 and 3 to City and Deadwood Avenue Springs

Streamflow-gaging station—Number is station identification

Numerical Groundwater-Flow Model 17
Table 1. Stress periods for transient simulations.

[Stress period identifiers: “W” represents the 6-month stress period from October through March, and “S” represents the 6-month period from April through 

October. Total recharge and water-use rates from Long and Putnam (2002)]

Stress period 

number

Stress period 

identifier Time period

Total recharge rate to Minnelusa 

and Madison hydrogeologic units 

(cubic feet per second)

Water-use rate for Minnelusa 

and Madison hydrogeologic units 

(cubic feet per second)

1 W–88 October 1, 1987–March 31, 1988 18.7 1.9

2 S–88 April 1, 1988–September 30, 1988 23.6 4.7

3 W–89 October 1, 1988–March 31, 1989 16.3 1.7

4 S–89 April 1, 1989–September 30, 1989 34.1 3.4

5 W–90 October 1, 1989–March 31, 1990 22.7 1.8

6 S–90 April 1, 1990–September 30, 1990 50.0 4.2

7 W–91 October 1, 1990–March 31, 1991 19.8 3.0

8 S–91 April 1, 1991–September 30, 1991 135.2 7.2

9 W–92 October 1, 1991–March 31, 1992 32.9 5.4

10 S–92 April 1, 1992–September 30, 1992 40.3 12.5

11 W–93 October 1, 1992–March 31, 1993 25.6 3.7

12 S–93 April 1, 1993–September 30, 1993 149.4 13.6

13 W–94 October 1, 1993–March 31, 1994 46.9 6.2

14 S–94 April 1, 1994–September 30, 1994 59.6 15.0

15 W–95 October 1, 1994– March 31, 1995 43.0 5.8

16 S–95 April 1, 1995–September 30, 1995 180.7 11.0

17 W–96 October 1, 1995–March 31, 1996 57.0 3.2

18 S–96 April 1, 1996–September 30, 1996 131.6 11.4

19 W–97 October 1, 1996–March 31, 1997 82.3 5.5

20 S–97 April 1, 1997–September 30, 1997 181.8 11.9

18 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

to the observed data in inverse modeling or by trial-and-error 

methods were assigned fixed values that were considered to 

be within the range of values expected for the parameters. The 

following section describes the properties that were represented with parameters and the remaining properties that were 

assigned values on the basis of previous estimates.

Representation of Flow-System Components

Flow-system components represented in the model 

include recharge, discharge, and hydraulic properties. 

Recharge includes streamflow recharge, areal recharge, 

and upward flow from the Deadwood aquifer. Upward flow 

from other underlying units was assumed to be small and 

included in upward flow represented in layer 5. Recharge to 

the hydrogeologic units occurs by two processes: streamflow 

recharge and areal recharge. Streamflow recharge originates 

from precipitation runoff in the central Black Hills upstream 

from the outcrops of the Minnelusa and Madison hydrogeologic units. These streams lose flow to swallow holes and 

fractures as they cross the outcrops. Areal recharge occurs 

from infiltration of precipitation on the outcrops. Because 

of the fractures and openings on the outcrop, any precipitation that exceeds evapotranspiration is assumed to infiltrate. 

Discharge includes springflow, water use, flow to overlying 

units, and regional outflow. Hydraulic properties and model 

features include horizontal and vertical hydraulic conductivity, 

horizontal flow barriers, and storage properties.

A steady-state water budget (table 2) was estimated by 

modifying the water-balance analysis by Long and Putnam 

(2002). The water-balance analysis quantified budget components for twenty 6-month time steps for water years (WY) 

1988–97 (table 1). The average water budget for that 10-year 

period included varied hydrologic conditions that collectively 

were assumed to approximate steady-state conditions. That 

water-balance analysis is described with more detail in the 

following subsections for each budget component.

Recharge and discharge were adjusted slightly to account 

for the change in storage that was included in the 10-year 

average water budget (1988–97) from Long and Putnam 

(2002). Inflow (recharge) was decreased by 4.4 ft3/s, and 

outflow was increased by 4.3 ft3/s to account for the change 

in storage of 8.7 ft3/s. Streamflow recharge was reduced by 
Table 2. Estimated water-budget components for steady-state simulation.

Component

Water-budget rate (cubic feet per second)

Minnelusa hydrogeologic unit Madison hydrogeologic unit

Model 

total Model layer Total Model layer Total

1 2 3 4

Inflow

Streamflow recharge 3.4 2.6 6.0 23.8 12.4 36.2 42.2

Areal recharge 2.9 2.9 5.8 7.6 7.5 15.1 20.9

Upward flow from Deadwood aquifer (1) (1) (1) (1) 6.3 6.3 6.3

Total inflow 69.4

Outflow

Springflow (2) (2) (2) (2) (2) (2) 32.8

Water use 3.4 (3) 3.4 6.7 (3) 6.7 10.1

Flow to units overlying the Minnelusa 

hydrogeologic unit 2.0 (

4

) 2.0 (4) (

4

) (4) 2.0

Regional outflow (5) (5) 12.3 (5) (5) 12.2 24.5

Total outflow 69.4

1

Upward flow from the Deadwood aquifer only occurred to layer 4.

2

Distribution among layers was determined by model calibration; springflow measurements are described in the “Springflow” section.

3

Because layers 1 and 3 represented the more permeable parts of the Minnelusa and Madison hydrogeologic units, water use from wells was simplified to a 

specified flow from cells in layer 1 or 3, respectively.

4

Discharge from the model as upward flow only occurred from layer 1.

5

Distribution of discharge among model layers was determined in model calibration.

Numerical Groundwater-Flow Model 19

3.1 ft3/s, and areal recharge was reduced by 1.3 ft3/s. Streamflow recharge for the Minnelusa hydrogeologic unit was 

distributed between model layers 1 and 2 with a larger portion 

assigned to model layer 1 because of its higher permeability. 

Streamflow recharge for the Madison hydrogeologic unit was 

distributed between model layers 3 and 4 with a larger portion 

assigned to model layer 3 because of its higher permeability. 

Areal recharge was distributed equally between model layers 1 

and 2 for the Minnelusa hydrogeologic unit and between 

layers 3 and 4 for the Madison hydrogeologic unit. Although 

layers 1 and 3 represented more permeable parts of the units, 

the outcrop area associated with these layers was smaller than 

the outcrop areas for layers 2 and 4; therefore, areal recharge 

was distributed equally between the layers for each hydrogeologic unit. The estimated springflow was increased by 2.0 ft3

/s, 

and regional outflow from the Minnelusa and Madison 

hydrogeologic units was increased by 1.3 ft3/s and 1.0 ft3/s, 

respectively.

Recharge

Recharge assigned in the model was based on rates calculated by Long and Putnam (2002) and was not adjusted during 

calibration (tables 18 and 19, in the “Supplemental Information” section). The calculated streamflow recharge rate was 

determined from streamflow-gaging records and loss thresholds for the major streams (Hortness and Driscoll, 1998). 

Recharge rates for the small ungaged streams were estimated 

by making correlations with data from adjacent gaged streams 

(Long and Putnam, 2002).

Areal recharge from infiltration of precipitation on the 

outcrops of the Minnelusa and Madison hydrogeologic units 

was estimated by a stream-catchment-runoff-yield method 

applied in the Black Hills hydrology study (Carter and others, 

2001) and applicable in mountainous areas with large variability in precipitation (Carter and Driscoll, 2005). Application of this method to determine areal recharge for the twenty 

6-month time steps for WY 1988–97 is presented in Long 

and Putnam (2002). Because of fractures and openings in the 

exposed outcrops, any precipitation that exceeded evapotranspiration was assumed to infiltrate to the aquifers. The amount 

of precipitation that exceeded evapotranspiration was determined by analyzing runoff from adjacent drainage basins in 

the Precambrian rocks upgradient from the outcrops.

Streamflow Recharge

 Drainage areas that contribute flow to the streams that 

cross the outcrops of the Minnelusa and Madison hydrogeologic units were delineated, and streamflow recharge rates 

were calculated for the 10 streams (table 3 and fig. 10) that 

cross these outcrops (Long and Putnam, 2002). Daily streamflow records were available for the larger streams that lose 

flow when crossing the outcrops, including Battle, Spring, 

Rapid, Boxelder, and Elk Creeks (fig. 10), and loss thresholds 
Table 3. Steady-state streamflow recharge rates distributed by model layer.

Stream

Streamflow recharge rate (cubic feet per second)

 Minnelusa hydrogeologic unit Madison hydrogeologic unit 

Total 

model Model layer Total Model layer Total 

1 2 3 4

Elk Creek 0.4 0.4 0.8 1.2 1.2 2.4 3.2

Little Elk Creek .3 .3 .6 .3 .3 .6 1.2

Boxelder Creek 1.4 .6 2.0 9.1 2.8 11.9 13.9

Unnamed tributary on Rapid Creek .0 .0 .0 .1 .1 .2 .2

Rapid Creek .9 .9 1.8 4.5 3.0 7.5 9.3

Victoria Gulch (1) (1) (1) (1) .8 .8 .8

Spring Creek .4 .4 .8 6.9 2.3 9.2 10.0

Rockerville Gulch .0 .0 .0 .4 .4 .8 .8

Deadman Gulch .0 .0 .0 .0 .2 .2 .2

Battle Creek (

2

) (2) (2) 1.3 1.3 2.6 2.6

Total 3.4 2.6 6.0 23.8 12.4 36.2 42.2

1

The stream did not cross the part of the hydrogeologic unit represented by layers 1, 2, or 3.

2

Streamflow loss was offset by reemerging springs.

20 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

for all but 2 of the 10 streams were determined by Hortness 

and Driscoll (1998). For the other two streams (Rockerville 

Gulch and Deadman Gulch), loss thresholds were estimated 

by Long and Putnam (2002). For the small ungaged streams, 

flow was estimated by correlation with flow at adjacent gaged 

streams as described in Long and Putnam (2002), and the 

distribution of recharge among the model layers was approximated. Measured or estimated daily streamflow less than or 

equal to the loss threshold recharged the Madison hydrogeologic unit, and once that threshold flow was exceeded, 

streamflow recharged the Minnelusa hydrogeologic unit at a 

rate equal to the loss threshold for this unit.

Streamflow recharge was represented with specifiedflow cells (Well Package, McDonald and Harbaugh, 1998) 

in model layers 1–4 (fig. 10). The recharge was distributed 

between the four layers with larger amounts assigned to 

layers 1 and 3, which represented the more permeable parts of 

each hydrogeologic unit. Streamflow recharge rates assigned 

to the steady-state simulation (table 3) show the relatively 

large contributions from Boxelder, Rapid, and Spring Creeks. 

Because Battle Creek and Elk Creek were on the southern and 

northern boundaries of the model, respectively, it was assumed 

that one-half of the streamflow recharge for these streams 

entered the model area. When streamflow was adequate to 

flow through the loss zones, the more permeable layers 1 and 

3 were assigned a larger portion of the recharge calculated 

for each hydrogeologic unit. When streamflow was less than 

the loss threshold, layer 4 had the first opportunity to receive 

recharge; therefore, for stress periods with relatively small 

streamflow, the recharge to layers 3 and 4 was about equal. 

As streamflow increased, layer 4 could not accept any more 

recharge and layer 3 received the increase in streamflow. A 

similar scenario occurred for layers 1 and 2; however, available flow was reduced by the upstream loss to layers 3 and 4. 

Spring Creek and Boxelder Creek had the largest streamflow 

loss thresholds; thus, the largest streamflow recharge to layer 3 

occurred along these two streams. Rapid Creek almost always 

exceeded the loss threshold because streamflow was regulated 

by releases from an upstream dam; therefore, the distribution 

of streamflow recharge for this stream was the same for all 

stress periods.

Transient streamflow recharge rates for the Minnelusa 

and Madison hydrogeologic units are presented in table 18 

in the “Supplemental Information” section for each of the 

10 streams. Total transient streamflow recharge rates for 

all streams by stress period for the Minnelusa and Madison 

hydrogeologic units ranged from 14.1 ft3/s (stress period 3, 

winter WY 1989) to 102.2 ft3/s (stress period 20, summer 

WY 1997). Distribution of transient streamflow recharge rates 

for 20 stress periods by model layer (fig. 13) shows the relatively large rates during wet periods (stress periods 12–20). 

Because the Minnelusa hydrogeologic unit receives recharge 

only when streamflow exceeds the loss threshold for the 

Madison hydrogeologic unit, streamflow recharge rates to 

model layers 1 and 2 were substantially less than streamflow 

recharge rates to model layers 3 and 4.

Areal Recharge

 The methods used for calculating the areal recharge are 

described in detail in Long and Putnam (2002) and summarized here. The outcrop area of the Minnelusa and Madison 
Figure 13. Total transient streamflow recharge rates for twenty 6-month stress periods by model layer.

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

STREAMFLOW RECH

ARGE RATE, IN CUBIC FEET PER SECOND 

TRANSIENT 6-MONTH STRESS PERIODS FOR WATER YEARS 1988−97

Layer 1

Layer 2

Layer 3

Layer 4

Table 4. Areal recharge zones and average annual precipitation on outcrops of the Minnelusa and Madison hydrogeologic units.

[From Long and Putnam (2002). Outcrop zone represents extent of hydrogeologic unit outcrop bounded by streams crossing the outcrop. Average annual precipitation by hydrogeologic unit was calculated from precipitation data for water years 1961–98 by Driscoll, Hamade, and Kenner (2000). NA, not applicable]

Outcrop zone

Outcrop zone 

number 

shown on 

fig. 14

Outcrop area by 

hydrogeologic unit

 (square miles)

Average annual 

precipitation by 

hydrogeologic unit

(inches)

Average annual 

precipitation rate by 

hydrogeologic unit 

(cubic feet per second)

Minnelusa Madison Minnelusa Madison Minnelusa Madison 

Elk Creek to Little Elk Creek 1 3.6 10.1 22.3 24.0 5.9 17.9

Little Elk Creek to Boxelder Creek 2 15.2 27.3 19.2 20.0 21.5 40.2

Boxelder Creek to Rapid Creek 3 12.5 9.8 18.9 19.6 17.4 14.2

Rapid Creek to Spring Creek 4 7.1 4.6 18.6 19.1 9.7 6.5

Spring Creek to Battle Creek 5 15.1 6.6 19.4 19.9 21.6 9.7

Total NA 53.5 58.4 NA NA 76.1 88.5

Numerical Groundwater-Flow Model 21

hydrogeologic units was subdivided into five zones for 

calculation of areal recharge from infiltration of precipitation 

on the outcrops (table 4 and fig. 14). The zones represented 

infiltration of precipitation on the outcrop areas between major 

streams. The fraction of precipitation that was available for 

recharge after evapotranspiration was represented by runoff 

in gaged stream basins in Precambrian rocks adjacent to the 

outcrop areas. Most of the groundwater infiltration in these 

Precambrian basins with high relief returns to the basins as 

springflow; therefore, the runoff per unit area was assumed to 

represent the fraction of precipitation that was available for 

infiltration on the adjacent outcrops.

The areal recharge was distributed equally between 

the two model layers representing each hydrogeologic unit. 

The distribution was assumed to be equal because the more 

permeable layers 1 and 3 represented a smaller percentage 

of the total outcrop area than the thicker layers 2 and 4. The 

recharge flux for each model layer was assigned to the first 

downgradient (westernmost) active model cell. Steady-state 

areal recharge by zone and model layer (table 5) shows larger 

recharge rates for the northern zones because of greater precipitation and larger outcrop areas for these zones than for the 

southern zones. Calculated areal recharge rates for the Minnelusa hydrogeologic unit were less than rates for the Madison 
Figure 14. Locations of areal recharge zones.

MEADE CO

PENNINGTON CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44 79

44

Outcrop of Minnelusa hydrogeologic unit

Outcrop of Madison hydrogeologic unit

1

2

3

4

5

Areal recharge zone (tables 5 and 19)

Geologic outcrops modified from Strobel 

and others, 1999

22 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Table 5. Areal recharge zones and steady-state areal recharge rates distributed by model layer.

[Outcrop zone represents extent of hydrogeologic unit outcrop bounded by streams crossing the outcrop. NA, not applicable]

Outcrop zone

Outcrop 

zone number 

shown on 

fig. 14

Areal recharge rate (cubic feet per second)

Minnelusa hydrogeologic unit Madison hydrogeologic unit

Total 

model Model layer Total Model layer Total

1 2 3 4

Elk Creek to Little Elk Creek 1 0.3 0.3 0.6 1.6 1.6 3.2 3.8

Little Elk Creek to Boxelder Creek 2 1.1 1.1 2.2 3.8 3.7 7.5 9.7

Boxelder Creek to Rapid Creek 3 .6 .6 1.2 1.2 1.2 2.4 3.6

Rapid Creek to Spring Creek 4 .2 .2 .4 .4 .4 .8 1.2

Spring Creek to Battle Creek 5 .7 .7 1.4 .6 .6 1.2 2.6

Total NA 2.9 2.9 5.8 7.6 7.5 15.1 20.9

Numerical Groundwater-Flow Model 23

hydrogeologic unit because 50 percent of the precipitation that 

fell on the thin western part of the Minnelusa hydrogeologic 

unit outcrop was assumed to have infiltrated downward to the 

Madison hydrogeologic unit.

Transient areal recharge rates for the Minnelusa and 

Madison hydrogeologic units (Long and Putnam, 2002) are 

presented in table 19 in the “Supplemental Information” 

section. Total transient areal recharge by stress period (fig. 15) 

shows the substantially larger areal recharge during wet stress 

periods (stress periods 12–20) compared to recharge during 

dry periods (stress periods 1–11). During the stress periods 

with large precipitation, a greater fraction of precipitation 

becomes recharge. During the summer stress periods 8, 12, 

16, and 20, areal recharge was about the same as streamflow 

recharge (fig. 13); however, during the winter stress periods 

and drier summer stress periods, streamflow recharge was 

larger than areal recharge. Total transient areal recharge rates 

by stress period for the Minnelusa and Madison hydrogeologic 

units (table 19) ranged from 1.1 ft3/s (stress period 1, winter 

WY 1988) to 98.4 ft3/s (stress period 16, summer WY 1995). 

Most of the steady-state areal recharge occurred during the wet 

summer periods. The steady-state areal recharge rate (table 5) 

was largest for the Little Elk Creek to Boxelder Creek zone 

(zone 2) because of the relatively large outcrop area and 

greater precipitation in this zone than in the southern zones.

Upward Flow from Deadwood Aquifer

Layer 5 represented an approximation of the underlying 

Deadwood aquifer to simulate upward flow to the Madison 

hydrogeologic unit. The average upward flow from the Deadwood aquifer to the Madison hydrogeologic unit was estimated by Long and Putnam (2002) to be 6.3 ft3

/s in the study 

area, representing about 9 percent of the total average inflow 

to the model. This upward flow was assumed to be constant 

during transient simulations. Although the hydraulic head in 

the Deadwood aquifer and the Madison hydrogeologic unit 

changed over time, it was assumed that the vertical gradient 

between the two units did not change substantially. Input to 

model layer 5 was accomplished by a specified flux (fig. 11) 

equally distributed to the westernmost cells in layer 5.

Discharge

Springflow, water use, flow to overlying units, and 

regional outflow were estimated by Long and Putnam (2002). 

Water use was assigned to the model by using specified-flow 

cells. Flow to overlying units was assumed to be small and 

assigned a value that did not change in transient simulations. 

Simulated springflow and regional outflow rates were dependent on the conductance of head-dependent cells, which was 

estimated by model calibration.

Springflow

Discharge from springs (figs. 11 and 12) calculated 

by model simulation was the difference between the userspecified hydraulic head of the spring and the simulated 

hydraulic head multiplied by the conductance for the cell. 

Conductance is a term that groups the hydraulic conductivity and the length of flow path. The conductance term for 

springs was represented as a parameter that was adjusted in 

model calibration (described in the subsequent “Steady-State 

Calibration” section and “Transient Calibration” section) to 

produce the best fit with estimated flows and hydraulic head 

values. Generally, the Madison hydrogeologic unit has been 

interpreted as the major source of water for large springs 

in the model area on the basis of hydrochemistry and the 

presence of conduits (Anderson and others, 1999; Long and 

Putnam, 2002). Although the Madison hydrogeologic unit is 

the predominant source of water for the springs, substantial 

interaction between the upward flow and the Minnelusa hydrogeologic unit is possible. In representing discharge from these 

springs, both the Minnelusa and Madison hydrogeologic units 
Figure 15. Total transient areal recharge rates for twenty 6-month stress periods by model layer and 

spatially averaged precipitation on outcrops of the Minnelusa and Madison hydrogeologic units.

0

5

10

15

20

25

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

SPATIALLY AVERAGED PRECIPITATION, IN INCHES

AREAL RECHARGE RATE, IN CUBIC FEET PER SECOND

TRANSIENT 6-MONTH STRESS PERIODS FOR WATER YEARS 1988−97

Recharge rate to layer 1

Recharge rate to layer 2

Recharge rate to layer 3

Recharge rate to layer 4

Precipitation

24 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

were considered as potential sources. Steady-state springflow 

(table 6) was estimated by Anderson and others (1999) and 

Long and Putnam (2002).

The springflow of Jackson-Cleghorn Springs, the largest 

spring in the study area, was estimated as 21.6 ft3/s by a waterbudget analysis of a Rapid Creek stream reach that extended 

through the Jackson-Cleghorn complex (Anderson and others, 

1999). On the basis of stable isotope data, they concluded 

that the springs were a regional discharge point from the 

Madison aquifer. The spring’s discharge from the Madison 

hydrogeologic unit in the current model was represented with 

two head-dependent flow cells (Drain Package, McDonald 

and Harbaugh, 1998) in layer 3 (fig. 12) with hydraulic head 

set equal to the hydraulic head in the alluvium (Anderson 

and others, 1999), and the conductance was represented with 

parameter CLEGmdsn that was estimated in model calibration. Although assumed to be small, a contribution to spring 

discharge from the Minnelusa hydrogeologic unit also is 

possible. The component of discharge from Jackson-Cleghorn 

Springs from the Minnelusa hydrogeologic unit was represented with five head-dependent cells in layer 1 located 

along the Rapid Creek reach near Jackson-Cleghorn Springs 

(fig. 12). This hydraulic connection was represented with 

special head-dependent flow cells (River Package, McDonald 

and Harbaugh, 1998) that allowed both outflow and inflow 

to the model depending on the relation between the hydraulic head of the water body and the hydraulic head in the cell. 

Conductance was represented with parameter CLEGmnls that 

was estimated in calibration. This Rapid Creek stream reach 

and associated alluvium overlies the outcrop of the Minnelusa hydrogeologic unit and was assumed to be hydraulically 

connected to the unit.

Comparison of hydraulic head values in the Minnelusa and Madison hydrogeologic units and Rapid Creek at 

Jackson Springs, located in the southwest part of the JacksonCleghorn springs area provides some insight on the potential 

for interaction between the Minnelusa and Madison hydrogeologic units. On September 8, 1999, hydraulic head in 

the Minnelusa hydrogeologic unit in the observation well at 

site 231 (well JS–1B; table 20 in “Supplemental Information” 

section), which is located near Jackson-Cleghorn Springs, 

was about 17 ft above Rapid Creek. At site 52, a nested well 

completed in the Madison hydrogeologic unit (well JS–1A; 

table 21 in “Supplemental Information” section), hydraulic 

head was about 40 ft above Rapid Creek. Hydraulic head in 

the Minnelusa hydrogeologic unit was about 10 ft higher at 

site 231 than it was in the observation well at site 233 (well 

CHLN–1; table 20), which is located about 0.5 mi south of 

site 231. This higher hydraulic head indicted the possibility 

of a mound created in the Minnelusa hydrogeologic unit from 
Table 6. Steady-state springflow.

[NA, not applicable]

Spring name Conductance parameter 

names

Steady-state springflow 

(cubic feet per second)

Jackson-Cleghorn Springs CLEGmdsn, CLEGmnls 121.6

City Springs CITYSPR 21.7

Deadwood Avenue Springs DWSPR 22.8

Boxelder Springs BESPR 21.0

Elk Springs ELKSPR 23.7

Infiltration Gallery Springs GAL 11.5

Canyon Lake CLAKE 3.5

Total NA 32.8

1

From Anderson and others, 1999.

2

From Long and Putnam, 2002.

3

No quantitative measurements were available; small discharge was assumed because of hydraulic 

connection.

Numerical Groundwater-Flow Model 25

water moving upward from the Madison hydrogeologic unit. 

The vertical hydraulic conductivity for cells in layer 2 in the 

Jackson-Cleghorn Springs area was assumed to be substantially higher than surrounding areas because of collapse 

features and solution enhanced openings. The multiplier for 

layer 2 vertical hydraulic conductivity was determined in 

model calibration.

Discharge at City Springs was represented by headdependent cells (Drain Package, McDonald and Harbaugh, 

1998) in layers 1 and 3 (fig. 12), and the conductance was 

assumed to be similar for the two cells and was represented 

with parameter CITYSPR. Because of the structural features 

in this area (fig. 1), vertical hydraulic conductivity for layer 2 

in the City Springs area was assumed to be substantially 

higher than for other parts of layer 2. During dry periods, flow 

from this spring decreased to near zero (Long and Putnam, 

2002).

Discharge at Deadwood Avenue Springs was represented 

with head-dependent cells (Drain Package, McDonald and 

Harbaugh, 1998) in both layers 1 and 3 (fig. 12). In the Deadwood Avenue Springs area, the average hydraulic head (Long 

and Putnam, 2002) was about 100 ft above the land surface 

in the Madison hydrogeologic unit and near the land surface 

in the Minnelusa hydrogeologic unit. Therefore, most spring 

discharge probably occurred from the Madison hydrogeologic 

unit. Conductance was assumed similar for both cells and was 

estimated with parameter DWSPR in model calibration.

Boxelder Springs was assumed to increase from no flow 

in dry periods to estimated flows of about 7 ft3/s in wet periods 

(Carter and others, 2001; Long and Putnam, 2002). Because 

the hydraulic head in the Madison hydrogeologic unit was 

always well above the land surface even during periods when 

there was no observed spring discharge, Boxelder Springs 

was assumed to discharge from the Minnelusa hydrogeologic 

unit and was represented with a head-dependent cell (Drain 

Package, McDonald and Harbaugh, 1998) in layer 1 (fig. 12), 

and conductance was estimated with parameter BESPR in 

model calibration.

Elk Springs was represented by five head-dependent 

cells (Drain Package, McDonald and Harbaugh, 1998) in 

both layers 1 and 3 (fig. 11) upstream on Elk Creek from 

the point identified as the spring on the map in Long and 

Putnam (2002). During the wet periods (late 1990s), flow was 

observed to increase in the downstream direction in this reach. 

Flow was very low during the dry periods, but increased 

dramatically during the wet periods. On the basis of hydraulic 

head values, the source potentially could be both the Minnelusa and Madison hydrogeologic units. Conductance was 

assumed to be similar for each layer and was estimated with 

parameter ELKSPR in model calibration.

Anderson and others (1999) estimated a small discharge 

contribution of about 1.5 ft3/s from bedrock units to two 

infiltration galleries along Rapid Creek about 0.7 mi and 

1.2 mi downstream, respectively, from Canyon Lake. This 

discharge was represented by two head-dependent cells (Drain 

Package, McDonald and Harbaugh, 1998) in layer 1 (fig. 12), 

and conductance was estimated with parameter GAL in model 

calibration.

When Canyon Lake was drained in the winter of 1995–

96, hydraulic head in an observation well completed in the 

Minnelusa hydrogeologic unit near Canyon Lake (site 229, 

table 20) responded with a similar decline in hydraulic head 

(Driscoll, Bradford, and Moran, 2000). Canyon Lake was 

represented with six head-dependent cells (River Package, 

McDonald and Harbaugh, 1998) in layer 1 (fig. 12) that 

allowed inflow or outflow from the model depending on the 

hydraulic head relation, and conductance was estimated with 

parameter CLAKE in model calibration.
Table 7. Water-use rates for steady-state and transient simulations.

[From Long and Putnam (2002). W, winter; S, summer (W–88 = winter, water year 1988)]

Stress 

period

Other 

stress 

period 

identifier

Water-use rate (cubic feet per second)

Model layer 1 

(Minnelusa hydrogeologic unit)

Model layer 3

 (Madison hydrogeologic unit)

Total 

model

Rapid City

Other 

domestic 

and public 

water 

supplies

Industrial 

and 

irrigation 

use

Total

layer 1 Rapid City

Other 

domestic 

and public 

water 

supplies

Industrial 

and 

irrigation 

use

Total 

layer 3

1 W–88 1.5 1.2 0.2 2.9 0.0 1.3 0.6 1.9 4.8

2 S–88 1.4 3.1 1.2 5.7 .0 3.4 1.3 4.7 10.4

3 W–89 .5 1.0 .2 1.7 .0 1.1 .6 1.7 3.4

4 S–89 .7 1.8 1.2 3.7 .1 2.0 1.3 3.4 7.1

5 W–90 1.6 1.1 .2 2.9 .0 1.2 .6 1.8 4.7

6 S–90 1.9 1.8 1.2 4.9 .9 2.0 1.3 4.2 9.1

7 W–91 1.8 1.3 .2 3.3 1.0 1.4 .6 3.0 6.3

8 S–91 1.6 2.0 1.0 4.6 3.3 2.2 1.7 7.2 11.8

9 W–92 1.3 1.1 .2 2.6 3.6 1.2 .6 5.4 8.0

10 S–92 1.2 1.9 1.2 4.3 9.1 2.1 1.3 12.5 16.8

11 W–93 1.1 1.3 .2 2.6 1.7 1.4 .6 3.7 6.3

12 S–93 1.1 1.8 1.1 4.0 10.6 1.9 1.1 13.6 17.6

13 W–94 .6 1.3 .2 2.1 4.2 1.4 .6 6.2 8.3

14 S–94 .3 2.6 1.2 4.1 10.9 2.8 1.3 15.0 19.1

15 W–95 .8 1.3 .2 2.3 3.7 1.4 .7 5.8 8.1

16 S–95 .6 2.1 1.0 3.7 7.5 2.3 1.2 11.0 14.7

17 W–96 .5 1.4 .2 2.1 .9 1.6 .7 3.2 5.3

18 S–96 .6 2.4 1.0 4.0 7.6 2.6 1.2 11.4 15.4

19 W–97 .8 1.5 .2 2.5 3.2 1.6 .7 5.5 8.0

20 S–97 .9 2.2 1.0 4.1 8.4 2.3 1.2 11.9 16.0

Average (steady state) 1.0 1.7 .7 3.4 3.8 1.9 1.0 6.7 10.1

26 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Water Use

Water-use estimates (table 7) from Long and Putnam 

(2002) were used in model simulations. All water use was 

represented by specified-flow cells (Well Package, McDonald 

and Harbaugh, 1998) in layer 1 for pumping in the Minnelusa 

hydrogeologic unit and in layer 3 for pumping in the Madison 

hydrogeologic unit (fig. 16). The average water-use rates 

for the Minnelusa and Madison hydrogeologic units for the 

10-year period were 3.4 and 6.7 ft3/s, respectively. The average 

combined pumping rates were 6.3 ft3/s for the October–March 

(W) stress periods and 13.8 ft3/s for the April–September (S) 

stress periods. The highest average pumping rate of 19.1 ft3/s 

was for stress period 14 (S–94).

Flow to Overlying Units

Groundwater under confined pressure in the Minnelusa 

hydrogeologic unit probably flows into overlying units (figs. 2 

and 3) including aquifers in the Minnekahta Limestone and 

Inyan Kara Group through fractures or breccia pipes. Because 

very little information was available to calculate the upward 

flow from the Minnelusa hydrogeologic unit, the estimate 

of 2.0 ft3/s from the water-budget calculation in Long and 

Putnam (2002) was uniformly assigned to the specified-flux 

cells (Recharge Package, McDonald and Harbaugh, 1998; 

fig. 11). Evidence supporting the potential upward flow is 

presented in Long and Putnam (2002).
Figure 16. Locations of specified-flow cells representing water use in model layers 1 and 3.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Creek

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44

79

Specified-flow cell representing production wells in layer 1

Specified-flow cell representing production wells in layer 3

Geologic outcrops modified from Strobel 

and others, 1999

EXPLANATION

Outcrop of Minnelusa hydrogeologic unit

Outcrop of Madison hydrogeologic unit

Numerical Groundwater-Flow Model 27
28 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Regional Outflow

Regional outflow to the east was estimated by Long 

and Putnam (2002) to be 22.2 ft3/s. The model boundary was 

extended about 6 mi farther east than the eastern boundary 

used to define the aquifer analysis area in Long and Putnam 

(2002) to minimize the effect of the boundary on the detailed 

study area. Head-dependent flow cells (Drain Package, 

McDonald and Harbaugh, 1998) represented the boundary 

(figs. 8 and 9) with the hydraulic head extrapolated from Long 

and Putnam (2002). Conductance for head-dependent cells in 

layers 1 and 2 at the eastern boundary was represented with 

parameter MnlsEB, and conductance for head-dependent cells 

in layers 3 and 4 was represented with parameter MdsnEB. 

Steady-state discharge was estimated as 12.3 ft3/s from the 

Minnelusa hydrogeologic unit and 12.2 ft3/s from the Madison 

hydrogeologic unit. 

Hydraulic Properties

Hydraulic properties represented include horizontal 

hydraulic conductivity, vertical hydraulic conductivity, 

conductance of horizontal flow barriers, and storage coefficients. Hydraulic properties were represented by parameters 

that included cells grouped into zones.

Horizontal Hydraulic Conductivity

Horizontal hydraulic conductivity values for active 

cells in layer 1 were estimated by using three parameters 

named HK1_1, HK1_2, and HK1_3 (fig. 17) and multiplier 

arrays. Parameter group HK1_1 represented zones where the 

relatively gradual hydraulic gradient is attributable to larger 

hydraulic conductivity. Parameter group HK1_3 represented 

a zone where the relatively steep hydraulic gradient indicated 

potentially lower hydraulic conductivity. Parameter group 

HK1_2 represented a zone where the hydraulic conductivity 

was assumed to be between the values in zones HK1_1 and 

HK1_3. Areas near streamflow loss zones included subzones 

with large hydraulic conductivity that were assigned values by 

using a multiplier of five times the hydraulic conductivity in 

each respective zone. These small areas are near streams with 

substantial streamflow recharge where solution and collapse 

features cause increased permeability. 

Hydraulic conductivity for layer 2 was represented as the 

product of the hydraulic conductivity of layer 1 times a multiplier. The multiplier was set as 0.1 for most of the active cells 

in layer 2. The multiplier for active cells in layer 2 near the 

western boundary was set as 0.5 (fig. 18); this higher multiplier accounted for the enhanced permeability in layer 2 near 

the outcrop area of the Minnelusa hydrogeologic unit resulting 

from fracturing, weathering, and dissolution.

Hydraulic properties for active cells in layer 3 were represented with seven parameters named HK3_1, HK3_2, HK3_3, 

HK3_4, and HK3_5, HK3_6, and HK3_7 (fig. 19). Most of 

the discharge from Jackson-Cleghorn Springs represents a 

regional discharge point from the Madison hydrogeologic 

unit (Anderson and others, 1999), and substantially enlarged 

solution openings probably exist in the vicinity of the spring. 

The zone surrounding Jackson-Cleghorn Springs (fig. 19) was 

grouped in parameter HK3_6. Parameter group HK3_7 represented a zone of large hydraulic conductivity in the general 

areas of conduit flow paths from Spring Creek (Putnam and 

Long, 2007; Long and others, 2008) and the area surrounding zone HK3_6. Parameter group HK3_4 represented the 

western area of Boxelder Creek that had a relatively gradual 

hydraulic gradient. Parameter group HK3_5 represented 

the areas near the outcrop that were assumed to have lower 

hydraulic conductivity than the areas near streams. Parameter 

group HK3_5 also represented other areas where the hydraulic 

gradient transitioned from gradual to steep. Parameter group 

HK3_3 represented an area where the hydraulic gradient was 

much steeper than for the surrounding areas and hydraulic 

conductivity was assumed to be substantially lower. Parameter 

group HK3_1 represented a high transmissivity zone described 

by Downey (1986). The horizontal hydraulic conductivity for 

the parameter group HK3_1 area included anisotropy represented by parameter HANI3_2. The hydraulic conductivity for 

parameter group HK3_1 was greater in the direction of model 

rows than in the direction of model columns. Parameter group 

HK3_2 represented the remaining areas that had relatively 

gradual hydraulic gradients.

Additional information was available to characterize 

hydraulic conductivity in the detailed study area (fig. 20). 

Wells completed in the Madison hydrogeologic unit that were 

used as the basis for the characterization are listed in table 8. 

Hydraulic conductivity parameter groups HK3_4, HK3_6, 

and HK3_7 in model layer 3 represented areas that probably 

include substantial solution enlargement. Parameter group 

HK3_4 included wells 32, 35, 36, and 40 (fig. 20) where dye 

was detected following injection of dye in Boxelder Creek 

(Greene, 1999). The relatively large recharge from Boxelder 

Creek and the dispersed detection of dye indicated the likelihood of a relatively large hydraulic conductivity. This zone 

also contains structural features that could have contributed to 

enlargement of solution openings in the Madison hydrogeologic unit. A small area south of this zone that includes well 44 

was represented with parameter group HK3_5 because of a 

steep hydraulic gradient in the area. The difference in hydraulic head between wells 40 and 44, which are about 2,000 ft 

apart, was about 100 ft (table 21).

Parameter group HK3_7 represented an area that was 

assumed to have relatively high hydraulic conductivity 

because of preferential flow paths, structural features, and 

relatively gradual hydraulic gradient. The parameter zone 

includes a potential flow path from the Spring Creek loss zone 

towards Jackson-Cleghorn Springs. Dye injected in Spring 

Creek was detected at sites CRO, NON, 66 (HH), and NAY 

(Putnam and Long, 2007). Analysis of a time-series of oxygen 

isotope values for Spring Creek streamflow recharge and water 

samples from site 71 (HR–2), also indicated a potential flow 

path from Spring Creek toward site 71 (Long and Putnam, 
Figure 17. Horizontal hydraulic conductivity parameter groups and zones for model layer 1.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

44

44 79

3,200

3,300

3,100

3,400

3,000

2,900

2,800

2,700

3,500

2,600

3,700

3,600

3,800

3,600

3,500

3,500

3,400

3,000

2,900

2,800

3,100

3,300

3,200

Horizontal hydraulic conductivity parameter groups and zones

HK1_1

HK1_2

HK1_3

Hydraulic conductivity multiplier zone within parameter groups 

 representing areas near streamflow loss zones (multiplier of 5)

Minnelusa aquifer potentiometric contour (average for water 

 years 1988–97; Long and Putnam, 2002)—Contour interval

 100 feet. Datum is National Geodetic Vertical Datum of 1929

3,400

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

Numerical Groundwater-Flow Model 29
MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

Layer 2 hydraulic conductivity equals hydraulic conductivity for 

 layer 1 parameter group multiplied by 0.5

Layer 2 hydraulic conductivity equals hydraulic conductivity for 

 layer 1 parameter group multiplied by 0.1

Figure 18. Horizontal hydraulic conductivity multiplier zones for model layer 2.

30 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid

City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

3,100

3,200

3,600 3,700

3,000

2,900

2,800

3,700

2,600

3,800

3,800 3,900

2,500

4,100

4,200

4,300

4,000

3,700

4,000 3,900

3,900

3,600

3,500

3,400

3,300

3,200

3,000

3,800

3,600

2,800

2,700

2,600

2,700

2,900

3,100

3,300

3,500

3,400

Horizontal hydraulic conductivity parameter groups 

 and zones

HK3_1

HK3_2

HK3_3

HK3_4

HK3_5

HK3_6

HK3_7

Detailed study area

Madison aquifer potentiometric contour (average for 

 water years 1988–97; Long and Putnam, 2002)—

 Contour interval 100 feet. Datum is National 

 Geodetic Vertical Datum of 1929

JacksonCleghorn 

Springs

3,400

Figure 19. Horizontal hydraulic conductivity parameter groups and zones for model layer 3.

Numerical Groundwater-Flow Model 31
44°05’

I-90

44

79

Rapid

16

Creek

Boxelder

Spring

Creek

Creek

MEADE CO

PENNINGTON CO

T. 1 N.

T. 1 S.

R. 7 E.

R. 6 E.

R. 5 E.

103°22’30”

103°15’

44°00’

T. 3 N.

T. 2 N.

Base fom U.S. Geological Survey 

digital data, 1977, 1:100,000 

Rapid City, Office of City Engineer map, 

2005, 1:18,000

Unversal Transverse Mercator projection

Zone 13

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

79

44

16

Rapid Creek

EXPLANATION

Rapid City

3,500

3,300

3,400

3,200

3,100

3,000

2,900

2,800

3,800

3,900

3,700

2,700

4,000

3,700

3,800

3,900

3,600

2,600

3,500

3,600

47

71

51

44

36

32

40

35

66 NON

NAY

CRO

71

40

NON

Jackson-Cleghorn 

Springs

Horizontal hydraulic 

 conductivity para-

 meter group and 

 zone

HK3_2

HK3_3

HK3_4

HK3_5

HK3_6

HK3_7

Well where dye was detected when dye 

 was injected in Boxelder Creek 

 (Greene, 1999) and number

Well where dye was detected when dye 

 was injected in Spring Creek (Putnam 

 and Long, 2007) and identifier

Selected observation well completed in 

 Madison hydrogeologic unit and 

 number

Madison aquifer potentiometric contour 

 (average for water years 1988–97; Long 

 and Putnam, 2002)—Contour interval 

 100 feet. Datum is National Geodetic 

 Vertical Datum of 1929

3,600 Fault—Dashed where approximated. Bar 

 and ball on downthrown side

Anticline—Showing trace of axial plane 

 and direction of plunge. Dashed where 

 approximated

Syncline—Showing trace of axial plane 

 and direction of plunge. Dashed where 

 approximated

Monocline—Showing trace of axial 

 plane. Dashed where approximated

Structural features modified from Strobel 

and others, 1999, and Miller, 2005

Figure 20. Horizontal hydraulic conductivity parameter groups and zones for model layers 3 in the detailed study area.

32 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Table 8. Sites used as basis for delineation of hydraulic conductivity parameter zones for model layer 3.

[Site numbers from table 20 in Long and Putnam (2002). Other identifier from Long and Putnam (2002) unless otherwise noted. NA, not applicable; gal/min, 

gallons per minute]

Site number

(fig. 20)

Station identification 

number

Other 

identifier Description

40 440500103193601 WT–2 Dye injected in Boxelder Creek was detected in well.

44 440441103193301 NA Hydraulic head measurements indicate an area of steep hydraulic gradient.

32 440612103152001 RC–10 Dye injected in Boxelder Creek was detected in well; approximate well yield of 

1,790 gal/min (Anderson and others, 1999).

35 440526103173001 RC–6 Dye injected in Boxelder Creek was detected in well; approximate well yield of 

770 gal/min (Anderson and others, 1999).

36 440523103155701 BHPL Dye injected in Boxelder Creek was detected in well.

47 440427103131701 RC–7 Approximate well yield of 150 gal/min (Anderson and others, 1999). Hydraulic 

head indicates steep hydraulic gradient.

51 440334103095601 RV–4 Hydraulic head measurements indicate an area of steep hydraulic gradient.

NA 440037103174401 CRO1 Dye injected in Spring Creek was detected in well.

NA 440017103174301 NON1 Dye injected in Spring Creek was detected in well.

66 440004103174001 HH Dye injected in Spring Creek was detected in well.

NA 440007103175301 NAY1 Dye injected in Spring Creek was detected in well.

71 435851103143501 HR–21 Analysis of stable isotope tracers indicates conduit flow from Spring Creek 

(Long and Putnam, 2004).

1

From Putnam and Long, 2007.

Numerical Groundwater-Flow Model 33

2004; Long and others, 2008). Parameter zone HK3_7 was 

extended toward site 71 and included the anticline-syncline 

structural feature oriented towards Jackson-Cleghorn Springs. 

Anderson and others (1999) estimated that more than 

50 percent of the discharge from Jackson-Cleghorn Springs 

originated from the area south of Jackson-Cleghorn Springs.

Potentiometric contours for the Madison aquifer (Long 

and Putnam, 2002) show the relatively steep hydraulic 

gradient in the area represented by parameter group HK3_3 

(fig. 20). The decline in hydraulic head from site 36 to site 51 

was about 800 ft (table 21) in approximately 5 miles.

Similarly to hydraulic conductivity for layer 2, hydraulic 

conductivity for layer 4 was set as 0.1 times that of layer 3. 

The multiplier for active cells in layer 4 near the western 

boundary was set as 0.5 times those in layer 3 (fig. 21); this 

higher multiplier accounted for enhanced permeability near 

the outcrop area of the Madison hydrogeologic unit in layer 4.

Horizontal hydraulic conductivity for layer 5 was represented by parameter group HK5_1. The active cells in model 

layer 5 (fig. 22) facilitated the distribution of flow to layer 4 

from the underlying Deadwood aquifer.

Vertical Hydraulic Conductivity

The vertical hydraulic conductivity for model layer 2 

was important in the model because it controls the hydraulic 

connection between the Minnelusa and Madison hydrogeologic units. Layer 2 represented the lower part of the Minnelusa hydrogeologic unit, which because of shale layers had a 

lower vertical hydraulic conductivity than other model layers. 

Vertical hydraulic conductivity determined from aquifer tests 

(Greene, 1993; Long and Putnam, 2002) conducted in the 

western part of the model area (fig. 23) ranged from 0.0053 to 

2.7 feet per day (ft/d). Regional estimates of vertical conductivity for the lower part of the Minnelusa hydrogeologic unit 

are several orders of magnitude smaller (Long and Putnam, 

2002). Collapse features related to dissolution of gypsum 

(hydrated calcium sulfate) in the Minnelusa hydrogeologic 

unit probably has resulted in greater vertical hydraulic 

conductivity on the western side of the model area than on the 

eastern side. A transition zone of increasing sulfate concentrations from west to east in the Minnelusa hydrogeologic unit 

(Williamson and Carter, 2001) provides an estimate of the 
Figure 21. Horizontal hydraulic conductivity multiplier zones for model layer 4.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Hisega

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

Layer 4 hydraulic conductivity equals hydraulic conductivity for 

 layer 3 parameter group multiplied by 0.5

Layer 4 hydraulic conductivity equals hydraulic conductivity for 

 layer 3 parameter group multiplied by 0.1

JacksonCleghorn 

Springs

34 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Figure 22. Horizontal hydraulic conductivity parameter group for model layer 5 and horizontal flow barriers for layers 1 to 5.

Horizontal hydraulic conductivity parameter group for layer 5 (HK5_1)

Horizontal flow barrier representing City Springs monocline

Horizontal flow barrier representing City Springs and Victoria Creek faults

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Fault—Dashed where approximated. Bar and ball on downthrown side

Anticline—Showing trace of axial plane and direction of plunge. Dashed where 

 approximated

Syncline—Showing trace of axial plane and direction of plunge. Dashed where 

 approximated

Monocline—Showing trace of axial plane. Dashed where approximated

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Hisega

Structural features modified from Strobel 

and others, 1999, and Miller, 2005 0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

Numerical Groundwater-Flow Model 35
Figure 23. Vertical hydraulic conductivity parameter groups and zones for model layer 2, transition zone for sulfate concentrations in 

Minnelusa hydrogeologic unit, and location of aquifer tests in Madison aquifer.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid

City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Hisega

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

Outline of vertical hydraulic conductivity parameter group 

 (VKA2_1, label is parameter name)

VKA2_1

VKA2_2

Vertical hydraulic conductivity multiplier zone—Number is multiplier 

10 (areas near structural features and Elk Springs)

100 (area near City Springs)

1,000 (area near Jackson-Cleghorn Springs)

Transition of sulfate concentrations from 250 to 1,000 milligrams per 

 liter in Minnelusa aquifer (Williamson and Carter, 2001)

Location of production wells for aquifer tests that were used to estimate 

 vertical hydraulic conductivity (Greene, 1993; Long and Putnam 2002)

Base from U.S. Geological Survey digital 

data, 1977, 1:100,000, and Rapid City, 

Office of City Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

103°18' 103°17'20"

44°03'40"

44°03'20"

Rapid

Canyon 

Lake

Inset map

0 500 1,000 METERS

0 2,000 4,000 FEET

44

Creek

Inset map area

36 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Table 9. Horizontal barrier hydraulic characteristic for City Springs fault, City Springs monocline, and Victoria Creek fault.

[Hydraulic characteristic is hydraulic conductivity of the barrier divided by the width of the barrier. NA, not applicable]

Barrier name

Barrier hydraulic characteristic (feet per day per foot)

Model layer

1 2 3 4 5

City Springs fault 0.0005 0.0005 0.0005 0.0005 NA

City Springs monocline .01 .01 .001 .001 0.01

Victoria Creek fault NA NA .0005 .0005 NA

Numerical Groundwater-Flow Model 37

extent of this area of greater vertical hydraulic conductivity 

(fig. 23); areas to the west of the transition zone indicate areas 

where gypsum has been dissolved in the Minnelusa hydrogeologic unit and collapse features exist, and areas within 

the zone indicate areas of active dissolution of gypsum. The 

transition zone of increasing sulfate concentrations was used 

as the basis for dividing the vertical hydraulic conductivity for 

layer 2 into parameter groups VKA2_1 and VKA2_2 (fig. 23), 

with group VKA2_2 having higher vertical hydraulic conductivity than group VKA2_1. Parameter group VKA2_2 includes 

multiplier zones of a factor of 10 near structural features and 

Elk Springs. The area near City Springs had a multiplier of 

100 times the vertical hydraulic conductivity of the surrounding area (fig. 23) on the basis of upward flow from the 

Madison hydrogeologic unit through the Minnelusa hydrogeologic unit. The vertical hydraulic conductivity multiplier 

at Jackson-Cleghorn Springs was set as 1,000 because of the 

large volume of upward flow. Additional information about the 

potential variability in vertical hydraulic conductivity can be 

found in Long and Putnam (2002).

The vertical hydraulic conductivity of the other model 

layers was assumed to be larger than that of layer 2 and 

was represented by ratios of vertical to horizontal hydraulic conductivity. The ratios for layers 1, 3, 4, and 5 were 

represented by a single parameter for each layer (VANI1_1, 

VANI3_1, VANI4_1, and VANI5_1, respectively).

Horizontal Flow Barriers

Horizontal flow barriers restrict lateral flow between 

adjacent cells in a layer and are simulated by a parameter 

called the “barrier hydraulic characteristic,” which is the 

value of the hydraulic conductivity of the barrier divided by 

the width of the barrier. Horizontal flow barriers were used 

to simulate the hydraulic effect of the City Springs fault, the 

City Springs monocline, and the Victoria Creek fault (fig. 22). 

The offset along the faults placed impermeable areas against 

permeable areas with increased solution openings probable 

along the axis of the faults and monoclines. These barriers 

were assumed to extend vertically through all model layers 

having active cells in the area. Values used for the hydraulic 

characteristic assigned to the barriers by model layer (table 9) 

ranged from 0.0005 to 0.01 foot per day per foot. The Victoria 

Creek fault was present only in layers 3 and 4.

In layers 1 and 2, the City Springs monocline was interpreted to have little effect on horizontal flow in the sandstone 

layers of the Minnelusa hydrogeologic unit; therefore, the 

barrier hydraulic characteristic was set as 0.01 foot per day per 

foot. The barrier hydraulic characteristic for the City Springs 

and Victoria Creek faults for all layers was assumed to be less 

than for the City Springs monocline and was assigned a value 

of 0.0005. The maximum offset along the City Springs fault 

is about 500 ft, downthrown to the south, and the maximum 

offset for the Victoria Creek fault is about 350 ft, downthrown 

to the north (Miller, 2005). The hydraulic characteristic for the 

barrier representing the City Springs monocline in layers 3 and 

4 was assigned a value of 0.001 to approximate the effects of 

preferential solution openings along the axis of the monocline. 

The hydraulic characteristic for the barriers in layer 5 were 

estimated as 0.01 where cells in layer 5 were active.

Storage Properties

A general definition of specific yield for the unconfined 

part of the Minnelusa and Madison hydrogeologic units 

(figs. 2 and 3) is the ratio of the volume of water that the rock, 

after being saturated, will yield by gravity to the volume of the 

rock (Lohman and others, 1972). A definition of storage coefficient for the confined part of the aquifer is the volume of water 

an aquifer releases from or takes into storage per unit surface 

area of the aquifer per unit change in hydraulic head (Lohman 

and others, 1972). Smaller changes in storage occur in a 

confined aquifer compared to an unconfined aquifer because 

storage changes in a confined aquifer result from the slight 

expansion or contraction of the aquifer material and water due 

to hydraulic head changes.

The unconfined areas (fig. 24) for the Minnelusa and 

Madison hydrogeologic units were delineated for average 

conditions for WY 1988–97 by Long and Putnam (2002). 

In MODFLOW–2000, a layer can be simulated as confined 

(constant saturated thickness), unconfined (variable saturated thickness), or convertible, in which cells convert from 

confined to unconfined depending on hydraulic head and 

layer thickness. To maintain numerical stability, convertible 

layers were not used in this simulation, and all layers were 

simulated as confined, except that storage coefficients for 

unconfined areas were set equal to estimated values of specific 

yield. Thus, the compromise between numerical stability, 
Figure 24. Model cells with storage represented by unconfined storage coefficient.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Creek

EXPLANATION

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Hisega

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

Model cells represented with unconfined storage coefficient

Layer 1 (storage coefficient = 0.09)

Layer 2 (storage coefficient = 0.03)

Layer 3 (storage coefficient = 0.09)

Layer 4 (storage coefficient = 0.03)

White area to the east is continuation of layers 1–4, with a confined 

 storage coefficient of 0.0003.

38 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Numerical Groundwater-Flow Model 39

particularly for inverse modeling, and physical accuracy was 

to assume that hydraulic conductivity did not change with 

hydraulic head in unconfined areas. Also, the actual unconfined areas move up and down dip as water levels fluctuate, 

but their general shape and total areal coverage change negligibly. Therefore, unconfined areas were simulated as spatially 

fixed. Unconfined areas for layers 1–4 were represented in the 

simulation by assigning storage coefficient values that were 

much higher than for the confined areas to the east. As estimated by Long and Putnam (2002), the storage coefficient in 

unconfined areas (specific yield) was 0.09 for the upper parts 

of the hydrogeologic units (layers 1 and 3) and 0.03 for the 

lower parts of the hydrogeologic units (layers 2 and 4). The 

storage coefficient for all confined areas was 0.0003.

Specific storage, which is the storage coefficient divided 

by the aquifer thickness, is the required storage property in 

MODFLOW–2000. Therefore, the storage coefficients were 

divided by arrays of thickness for each model layer to create 

the required specific storage input.

Steady-State Calibration

The steady-state model was calibrated by using a 

hypothetical simulation of estimated average conditions with 

no changes in storage. A sensitivity analysis showed model 

parameters that were most sensitive to steady-state observations, and these parameters were optimized with inverse 

modeling as described in the following section. Comparisons 

of simulated steady-state hydraulic head values and flows to 

observed values and estimated flows were used to calibrate the 

model. The observed hydraulic head values used for steadystate calibration were based on 10-year average hydraulic 

head values for WY1988–97 for 176 wells completed in the 

Minnelusa hydrogeologic unit and 76 wells completed in 

the Madison hydrogeologic unit (Long and Putnam, 2002); 

selected information for these wells is presented in tables 20 

and 21 in the “Supplemental Information” section. Forty 

interpolated hydraulic head values, 20 for model layer 1 and 

20 for model layer 3 (table 22 in “Supplemental Information” section), were added to constrain the model in locations 

where information was sparse. These hydraulic head values 

were interpolated from the estimated average potentiometric 

contours for WY 1988–97 for the Minnelusa and Madison 

aquifers (Long and Putnam, 2002). The observed (measured) 

hydraulic head values (figs. 25 and 26) predominantly were 

available near the outcrops of the Minnelusa and Madison 

hydrogeologic units, whereas the interpolated hydraulic heads 

were used in areas east of the outcrops where measured waterlevel data were sparse. Estimated springflow and regional 

outflow (Anderson and others, 1999; Long and Putnam, 2002) 

also were used for steady-state flow calibration. 

Standard deviation of measurement error (SDME) was 

used in the MODFLOW–2000 observation process for weighting observations and estimates for inverse modeling, in which 

the weight assigned to an observation or estimate was the 

inverse of the implied accuracy. The implied accuracy was 1 ft 

for observation wells with surveyed altitudes and continuous 

water-level records, 5 ft for wells with multiple measurements, 

and 10 ft for wells with water levels estimated from well 

driller’s completion reports or potentiometric surfaces. The 

implied accuracy was 0.1 ft3/s for discharge from JacksonCleghorn Springs, City Springs, and Deadwood Avenue 

Springs, and 0.2 ft3/s for discharge from other springs. Implied 

accuracy for discharge at the eastern boundary was 0.1 ft3/s.

Sensitivity Analysis

Composite-scaled sensitivity is the square root of the 

sum of squared scaled sensitivity values for all observations 

divided by the number of observations. Composite-scaled 

sensitivity indicates the information content of all of the 

observations for the estimation of the parameter (Hill and 

others, 2000). The composite-scaled sensitivities for hydraulic properties represented as parameters (table 10) indicated 

the parameters most sensitive to steady-state observations. 

Parameters with composite-scaled sensitivities greater than 1.2 

were selected for optimization with inverse modeling. If some 

parameters have composite-scaled sensitivities that are less 

than about 0.01 times the largest composite-scaled sensitivity, 

the regression has trouble converging (Hill, 1998). Optimization for parameters that had composite-scaled sensitivity 

values less than 1.2 did not converge with reasonable values 

for the less-sensitive parameters.

The sensitivity of a parameter is related to the amount 

of information that is available to constrain the parameter. 

The ratio of the smallest to the largest composite-scaled 

sensitivities for the 12 parameters selected for optimization 

with parameter estimation (fig. 27) was 0.06 (ratio of sensitivities of DWSPR to HK3_2). The model was sensitive to 

most horizontal hydraulic conductivity parameters except 

parameter HK3_3, which represented the area in model 

layer 3 where the hydraulic gradient was very steep. Sensitivity to vertical hydraulic conductivity parameters was low 

except for VKA2_2 (fig. 23 and table 10), which represents 

an area in model layer 2 that extends east about 2 to 4 mi 

from the outcrop of the Minnelusa hydrogeologic unit. The 

model was substantially more sensitive to conductance for 

the cells in layer 3 that represented Jackson-Cleghorn Springs 

(CLEGmdsn) than conductance for other springs. The model 

was relatively insensitive to conductance parameters for headdependent cells representing the eastern boundary (MnlsEB 

and MdsnEB; table 10).
Figure 25. Comparison of simulated steady-state potentiometric surface for model layer 1 to the average potentiometric surface of 

the Minnelusa aquifer, water years 1988–97.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hayward

Tilford

Piedmont

Box 

Elder

Blackhawk

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Creek

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

EXPLANATION

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Hisega

Rockerville

Victoria Creek

44

44

79

2,900

2,800

3,000

3,100

3,300

3,200

2,700

2,600

3,400

3,500

2,500

3,600

3,400

3,500

3,500

2,900

3,000

3,200

3,300

3,100

2,800

2,700

2,600

3,400

3,200

3,100

3,300

2,900

2,800

3,400

2,700

3,500

2,600

3,500

3,000

3,300

3,600

2,900

3,000

3,100

3,200

2,800

Simulated steady-state potentiometric surface for layer 1—Shows altitude at 

 which water would have stood in tightly cased, nonpumped well. Contour 

 interval 100 feet. Datum is National Geodetic Vertical Datum of 1929

Average potentiometric surface of the Minnelusa aquifer, water years 1988–97 

 (Long and Putnam, 2002)—Shows altitude at which water would have stood in 

 tightly cased, nonpumped well. Contour interval 100 feet. Datum is National 

 Geodetic Vertical Datum of 1929. Dashed where approximately located

Location of observation; value interpolated from average potentiometric 

 surface, water years 1988–97 (Long and Putnam, 2002)

Location of well completed in the Minnelusa hydrogeologic unit for which 

 hydraulic head value was measured

Boundary of model layer 1

3,500

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

3,200

40 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Figure 26. Comparison of simulated steady-state potentiometric surface for model layer 3 and western part of layer 4 to the average 

potentiometric surface of the Madison aquifer, water years 1988–97.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Box Elder

Blackhawk

Rockerville

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid

 City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

Creek

Creek

Creek

Creek

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

79

Tilford

Piedmont

Farmingdale

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44

2,500

2,600

2,700

2,800

2,900

3,000

3,100

3,200

3,300

3,400

3,500

3,600

3,800

4,000

2,600

2,700

2,900

3,000

3,100

3,300

3,200

3,300

3,400

3,500

3,600

3,700

2,800

3,100

3,200

3,600

3,000

2,900

2,800

3,700

2,600

3,800

3,900

2,500

4,100

4,200

4,000

4,000 3,900

3,900

3,500

3,600

3,400

3,300

3,200

3,000

3,600

2,800

2,700

2,600

2,700

2,900

3,100

3,300

3,400

3,500

Simulated steady-state potentiometric surface for layer 3 and for layer 4 where layer 3 was 

 inactive—Shows altitude at which water would have stood in tightly cased, nonpumped 

 well. Contour interval 100 feet. Datum is National Geodetic Vertical Datum of 1929

Average potentiometric surface of the Madison aquifer, water years 1988–97 (Long and 

 Putnam, 2002)—Shows altitude at which water would have stood in tightly cased, nonpumped 

 well. Contour interval 100 feet. Datum is National Geodetic Vertical Datum of 1929. Dashed 

 where approximately located

Location of observation; value interpolated from average potentiometric surface, water 

 years 1988–97 (Long and Putnam, 2002)

Location of well completed in the Madison hydrogeologic unit for which hydraulic head 

 value was measured

3,100

Boundary of model layer 4

EXPLANATION

2,900

Numerical Groundwater-Flow Model 41
Table 10. Composite-scaled sensitivities for hydraulic properties represented as parameters.

[Shading indicates that parameter values were estimated by inverse modeling. Composite-scaled sensitivity calculated for final parameter values]

Parameter name Location map Parameter description Composite-scaled 

sensitivity

CLEGmdsn Jackson-Cleghorn Springs, fig. 12 Conductance parameter is the hydraulic conductivity of the 

interface between the head-dependent cells times the cell 

area divided by the thickness

4.63

CLEGmnls Jackson-Cleghorn Springs, fig. 12 .39

CITYSPR City Springs, fig. 12 .19

DWSPR Deadwood Avenue Springs, fig. 12 1.25

BESPR Boxelder Springs, fig. 12 .15

ELKSPR Elk Springs, fig. 11 .05

GAL Infiltration Gallery Springs, fig. 12 .03

CLAKE Canyon Lake, fig. 12 .16

HK1_1 Fig. 17 Horizontal hydraulic conductivity parameters for model 

layer 1

2.38

HK1_2 Fig. 17 16.96

HK1_3 Fig. 17 5.98

HK3_1 Fig. 19 Horizontal hydraulic conductivity parameters for model 

layer 3

1.29

HK3_2 Fig. 19 21.42

HK3_3 Fig. 19 1.13

HK3_4 Fig. 19 15.51

HK3_5 Fig. 19 8.63

HK3_6 Fig. 19 2.24

HK3_7 Fig. 19 5.70

HANI3_2 Fig. 19 Anisotropy for area represented by parameter group HK3_1 .03

HK5_1 Fig. 22 Horizontal hydraulic conductivity for layer 5 .83

VANI1_1 Active cells in model layer 1, fig. 8 Ratio of vertical to horizontal hydraulic conductivity for 

model layer 1

.01

VKA2_1 Fig. 23 Vertical hydraulic conductivity for model layer 2 .20

VKA2_2 Fig. 23 4.13

VANI3_1 Active cells in model layer 3, fig. 9 Ratio of vertical to horizontal hydraulic conductivity for 

model layer 3

.01

VANI4_1 Active cells in model layer 4, fig. 9 Ratio of vertical to horizontal hydraulic conductivity for 

model layer 4

.04

VANI5_1 Fig. 22 Ratio of vertical to horizontal hydraulic conductivity for 

model layer 5

.01

MnlsEB Fig. 8 Conductance parameter is the hydraulic conductivity of the 

interface between the head-dependent cell at the eastern 

boundary times the area divided by the thickness

.01

MdsnEB Fig. 9 .01

42 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Figure 27. Composite-scaled sensitivities for parameter values that were determined with inverse 

modeling in steady-state simulation.

0

5

10

15

20

25

HK1_1HK1_2HK1_3HK3_1HK3_2HK3_4HK3_5HK3_6HK3_7

VKA2_2

CLEGmdsn

DWSPR

COMPOSITE-SCALED SENSITIVITY

PARAMETER (SEE TABLE 10 FOR DESCRIPTION)

Numerical Groundwater-Flow Model 43

Comparison of Simulated and Observed SteadyState Hydraulic Head Values

Linear regression between the 252 simulated and 

observed hydraulic head values for the steady-state simulation had a coefficient of determination (R2 value) of 0.92 with 

an average arithmetic difference of -7.6 ft and an average 

absolute difference of 37.6 ft. Most of the observed hydraulic 

heads used for comparison with simulated hydraulic heads 

were between 3,400 and 3,600 ft above NGVD 29 (fig. 28). 

A histogram of residuals between the 252 simulated and 

observed hydraulic head values (fig. 29) shows that about 

65 percent of the residuals were less than ±40 ft.

The simulated potentiometric surface for model 

layer 1 overlain on the average potentiometric surface for 

WY 1988–97 generally shows similar gradients in hydraulic head values, with the largest differences near the model 

boundaries (fig. 25). The differences between simulated and 

observed (average for WY 1988–97) hydraulic head values 

for the Minnelusa hydrogeologic unit in the detailed study 

area were within ±30 ft for 73.7 percent of the observation 

wells (fig. 30). The difference between observed and simulated 

hydraulic head values that were not within ±30 ft for some 

of the wells could be related to the effect of unknown breccia 

pipes or karst features that were not represented in the model.

The simulated potentiometric surface for model layer 3 

matched the observed steep hydraulic gradients in eastern 

Rapid City (fig. 26). The differences between simulated and 

observed hydraulic head values for the Madison hydrogeologic unit in the detailed study area were within ±30 ft for 

76.9 percent of the observation wells (fig. 31). Wells with a 

hydraulic head difference that was not within ±30 ft generally 

were near the western model boundary. 

Comparison of Simulated and Estimated SteadyState Flow

Total simulated steady-state springflow of 31.6 ft3/s 

was similar to the sum of estimated springflow of 32.8 ft3/s 

(table 11). Simulated discharge from Jackson-Cleghorn 

Springs was 20.5 ft3/s compared to the estimated value of 

21.6 ft3/s. Simulated regional outflow from model layers 1 

and 2 at the eastern boundary of 12.9 ft3/s was slightly larger 

than the estimated value of 12.3 ft3/s from Long and Putnam 

(2002). Simulated regional outflow from model layers 3 and 

4 of 12.8 ft3/s was slightly larger than the estimated value of 

12.2 ft3/s from Long and Putnam (2002).

Transient Calibration

The transient calibration was accomplished by simulating transient conditions for WY 1988–97 divided into twenty 

6-month stress periods. Comparisons of simulated transient 

hydraulic head values and flows to observed values and 

estimated flows were used to calibrate the model. Simulated 

transient hydraulic head values were compared to observed 

(measured) hydraulic head values for 19 observation wells 

completed in the Minnelusa and Madison hydrogeologic units 

(fig. 32); water-level records were available for these 19 observation wells for all or parts of the transient simulation. Transient springflow was calibrated to springflow measurements 
Figure 29. Histograms of residuals between simulated steady-state and observed (average for water 

years 1988–97) hydraulic head values.

Figure 28. Residuals between simulated steady-state and observed hydraulic head values and their relation to 

average (water years 1988–97) hydraulic head values.

0

50

100

150

200

2,500 3,000 3,500 4,000 4,500

HYDRAULIC HEAD RESIDIUAL, IN FEET

AVERAGE HYDRAULIC HEAD, WATER YEARS 1988−97 IN FEET ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929

Minnelusa hydrogeologic unit

Madison hydrogeologic unit

-200

-150

-100

-50

0

5

10

15

20

25

0 40 80 120 160 200

FREQUENCY, IN PERCENT

HYDRAULIC HEAD RESIDUAL, IN FEET

-200 -160 -120 -80 -40

44 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Figure 30. Differences between simulated steady-state and observed (average for water years 1988–97) hydraulic head 

values for the Minnelusa hydrogeologic unit in the detailed study area.

44°05’

I-90

44

79

Rapid

16

Creek

Boxelder

Spring

Creek

Creek

MEADE CO

PENNINGTON CO

T. 1 N.

T. 1 S.

R. 7 E.

R. 6 E.

R. 5 E.

103°22’30”

103°15’

44°00’

T. 3 N.

T. 2 N.

Base fom U.S. Geological Survey 

digital data, 1977, 1:100,000 

Rapid City, Office of City Engineer map, 

2005, 1:18,000

Unversal Transverse Mercator projection

Zone 13

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

79

44

16

Rapid

Creek

Boundary of model layer 1

3,350

3,300

3,150

3,400

3,450

3,500

3,000

3,400

3,450

3,200

3,100

3,300

3,250

3,200

3,100

3,050

3,150

3,250

3,350

3,400

 1.0

 4.1

 8.1

34.3

39.4

 9.1

 3.0

 1.0

90 to less than 120

60 to less than 90

30 to less than 60

0 to less than 30

Less than 0 to greater than -30

-30 to greater than -60

-60 to greater than -90

-90 to greater than -120

Frequency of

difference

category Difference, in feet

Simulated steady-state potentiometric surface for model layer 1—Shows 

 altitude at which water would have stood in tightly cased, nonpumped well. 

 Contour interval 50 feet. Datum is National Geodetic Vertical Datum of 1929

3,500

EXPLANATION

Rapid City

Numerical Groundwater-Flow Model 45
Figure 31. Differences between simulated steady-state and observed (average for water years, 1988–97) hydraulic head 

values for the Madison hydrogeologic unit in the detailed study area.

44°05’

I-90

44

79

Rapid

16

Creek

Boxelder

Spring

Creek

Creek

MEADE CO

PENNINGTON CO

T. 1 N.

T. 1 S.

R. 7 E.

R. 6 E.

R. 5 E.

103°22’30”

103°15’

44°00’

T. 3 N.

T. 2 N.

Base fom U.S. Geological Survey 

digital data, 1977, 1:100,000 

Rapid City, Office of City Engineer map, 

2005, 1:18,000

Unversal Transverse Mercator projection

Zone 13

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

79

44

16

Rapid

Creek

Rapid City

3,425

3,475

3,475

3,425

3,450

3,450

3,425

3,200

3,100

3,300

3,400

3,000

2,900

2,800

2,700

3,500

3,600

3,700

3,600

3,500

3,500

3,600

3,200

3,100

3,000

2,900

2,800

2,700

3,400 3,400

3,300

3,400

2,600

3,475 Supplemental contours 3,425, 3,450, and 3,475

Difference, in feet

 1.9

 .0

 7.7

30.8

46.1

 5.8

 5.8

 1.9

90 to less than 120

60 to less than 90

30 to less than 60

0 to less than 30

Less than 0 to greater than -30

-30 to greater than -60

-60 to greater than -90

-90 to greater than -120

Simulated steady-state potentiometric surface for model layer 3—Shows 

 altitude at which water would have stood in tightly cased, nonpumped well. 

Contour interval 100 feet. Datum is National Geodetic Vertical Datum of 1929

3,600

EXPLANATION

Boundary of model layer 3

Frequency of

difference

category

46 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Table 11. Steady-state springflow estimates and simulated springflow.

[Springflow rates in cubic feet per second]

Spring name Steady-state springflow 

(from table 6) 

Simulated 

springflow

Arithmetic 

difference

Jackson-Cleghorn Springs 121.6 20.5 -1.1

City Springs 21.7 1.4 -.3

Deadwood Avenue Springs 22.8 2.6 -.2

Boxelder Springs 21.0 1.8 .8

Elk Springs 23.7 4.2 .5

Infiltration Gallery Springs 11.5 .5 -1.0

Canyon Lake 3.5 .6 .1

Total 32.8 31.6 -1.2

1

Anderson and others, 1999.

2

Long and Putnam, 2002.

3

No quantitative measurements were available; small discharge was assumed because of hydraulic connection.

Numerical Groundwater-Flow Model 47

or estimated springflow for seven springs (figs. 11 and 12). 

The estimated springflow for some of the springs represented 

an average discharge. Regional outflow at the eastern model 

boundary was calibrated to estimated average regional outflow 

used in the steady-state simulation. The regional outflow 

was assumed to be relatively constant because the boundary 

was about 20 mi east of most recharge, spring discharge, and 

pumping areas.

Comparison of Simulated and Observed 

Transient Hydraulic Head Values

The average absolute difference between simulated and 

observed hydraulic head values for the 19 observation wells 

ranged from 3.5 to 65.1 ft with a median value of 18.3 ft 

(table 12). Hydrographs of simulated and observed hydraulic 

head values for 18 of the wells (fig. 33) show the response 

of the heads to stresses. Hydrographs for the nested wells 

completed in both the Minnelusa and Madison hydrogeologic units at six sites are presented adjacent to each other. In 

general, the magnitude of changes in simulated hydraulic head 

values were less than the observed changes.

The changes in simulated hydraulic head values for 

wells 104 and 1 between stress periods are much less than 

observed changes. The simulated hydraulic head for well 104 

does not increase as quickly as the observed hydraulic head 

during the wet period (late 1990s; stress periods 12–20). 

Wells 104 and 1 are located at the northern no-flow boundary 

(figs. 32, 8, and 9), which may have damped hydraulic head 

response. Simulated hydraulic head values for wells 124 and 3 

were similar in trend; however, the simulated hydraulic head 

values for well 3 were about 50 ft higher than observed values. 

Simulated hydraulic head values for wells 200 and 33 were 

similar to observed hydraulic head values; however, declines 

during the dry period and increases during the wet period were 

less for the simulated values.

Simulated hydraulic head values for wells 223 and 46 

were similar to observed hydraulic head values; however, the 

influence of pumping resulted in some fluctuations in observed 

hydraulic head that were not matched in the simulated values, 

probably because of smoothing from using 6-month stress 

periods. Simulated hydraulic head values for wells 229 and 

50 were similar to observed hydraulic head values. Simulated 

hydraulic head values for well 272 were similar in trend but 

consistently about 50 ft below observed values. Simulated and 

observed hydraulic head values for well 68 were very similar.

Simulated hydraulic head values for well 181 were 

similar in trend and consistently about 20 ft above observed 

values. Simulated hydraulic head values for well 209 were 

similar to observed hydraulic head values; however, simulated 

hydraulic head values were smoothed compared to observed 

values. Simulated hydraulic head values for wells 224 and 

233 were similar to observed values. The simulated hydraulic head values for well 15 (table 12) were about 60 ft below 

observed values. Well 15 had only four observations (not 

shown in fig. 33) and is located near the western model boundary. Simulated hydraulic head values for well 47 were about 

35 ft above observed values and were steady in comparison to 

observed values. Simulated hydraulic head values for well 43 

were influenced by pumping in a nearby well, resulting in 

large fluctuation in observed hydraulic head values; however, 

the simulated values were similar to the recovered hydraulic 

head values.
Figure 32. Locations of observation wells with transient hydraulic head values.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Creek

Hisega

Rockerville

Victoria Creek

0 2 4 6 8 MILES

0 2 4 6 8 KILOMETERS

44

44 79

209

229, 50 233

224

200, 33

47

181

272, 68

124, 3

15

223, 46

104, 1

43

272, 68

272, 68

EXPLANATION

Outcrop of Minnelusa hydrogeologic unit

Outcrop of Madison hydrogeologic unit

Observation well completed in Minnelusa hydrogeologic unit and 

 number (table 20)

Observation well completed in Madison hydrogeologic unit and 

 number (table 21)

Note: comma-separated site numbers indicate nested wells in 

 Minnelusa (first number) and Madison (second number) 

 hydrogeologic units

Geologic outcrops modified from Strobel 

and others, 1999

48 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Table 12. Difference between simulated and observed hydraulic head values for transient simulation.

[Site numbers listed in tables 20 and 21; number corresponds to site number in tables 28 and 29 and plates 1 and 2 of Long and Putnam (2002). Smallest, largest, 

and average difference calculated by subtracting observed value from simulated value]

Station 

identification 

number

Model 

layer

Site 

number

Other 

identifier

Number of 

observations

Smallest 

difference

(feet)

Largest 

difference

(feet)

Average 

difference

(feet)

Average 

absolute 

difference 

(feet)

441759103261201 1 104 TF–1 20 1.5 52.4 -8.3 19.0

441337103225001 1 124 PDMT–1 15 16.3 31.6 23.8 23.8

440818103180801 1 181 BLHK–1 20 5.0 30.5 19.5 19.5

440544103180001 1 200 CQ–1 16 1.6 25.4 -7.1 13.5

440528103161001 1 209 CP 16 2.9 37.1 -10.8 11.7

440430103160201 1 223 SP–1 15 8.9 26.9 -18.3 18.3

440423103180501 1 224 WCR-3 16 .8 6.8 .2 3.5

440338103173301 1 229 CL–1 16 3.6 6.7 5.4 5.4

440310103173801 1 233 CHLN–1 13 2.1 7.3 -4.4 4.4

435916103161802 1 272 RG–2 6 34.9 53.3 -47.3 47.3

441759103261202 3 1 TF–2 13 20.3 83.6 49.4 49.4

441337103225002 3 3 PDMT–2 6 48.5 66.4 -57.1 57.1

440544103180002 3 33 CQ–2 16 2.1 25.6 -4.1 14.2

440446103161701 3 43 LC 15 8.3 64.6 13.4 30.6

440430103160202 3 46 SP–2 16 2.6 27.6 -14.1 16.2

440427103131701 3 47 RC–7 14 28.6 52.4 39.0 39.0

440338103173302 3 50 CL–2 16 2.6 13.5 -9.1 9.1

435916103161801 3 68 RG 20 .2 21.2 -6.6 11.7

440811103222201 4 15 DOTY 4 58.4 76.1 -65.1 65.1

Numerical Groundwater-Flow Model 49
Figure 33. Simulated and observed hydraulic head values for model layers 1 and 3.

3,560

3,580

3,600

3,620

3,640

3,660

3,680

3,700

Site 1 (TF−2) MADISON

3,560

3,580

3,600

3,620

3,640

3,660

3,680

3,700

HYDRAULIC HEAD, IN FEET ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929

Site 104 (TF−1) MINNELUSA

3,440

3,460

3,480

3,500

3,520

3,540

3,560

3,580

Site 124 (PDMT−1) MINNELUSA

3,500

3,520

3,540

3,560

3,580

3,600

3,620

3,640

Site 3 (PDMT−2) MADISON

3,400

3,420

3,440

3,460

3,480

3,500

3,520

3,540

WATER YEAR

Site 200 (CQ−1) MINNELUSA

3,400

3,420

3,440

3,460

3,480

3,500

3,520

3,540

Site 33 (CQ−2) MADISON

Simulated

EXPLANATION

Observed

1987 1989 1991 1993 1995 1997

WATER YEAR

1987 1989 1991 1993 1995 1997

50 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Figure 33. Simulated and observed hydraulic head values for model layers 1 and 3.—Continued

WATER YEAR

Simulated

EXPLANATION

Observed

1987 1989 1991 1993 1995 1997

WATER YEAR

1987 1989 1991 1993 1995 1997

3,340

3,360

3,380

3,400

3,420

3,440

3,460 Site 46 (SP−2) MADISON

3,340

3,360

3,380

3,400

3,420

3,440

3,460

Site 223 (SP−1) MINNELUSA

Site 229 (CL−1) MINNELUSA

3,340

3,360

3,380

3,400

3,420

3,440

3,460

3,480

Site 50 (CL−2) MADISON

3,440

3,460

3,480

3,500

3,520

3,540

3,560

3,580

Site 272 (RG−2) MINNELUSA

3,440

3,460

3,480

3,500

3,520

3,540

3,560

3,580

Site 68 (RG) MADISON

3,480 3,480

3,340

3,360

3,380

3,400

3,420

3,440

3,460

3,480

HYDRAULIC HEAD, IN FEET ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929

Numerical Groundwater-Flow Model 51
Figure 33. Simulated and observed hydraulic head values for model layers 1 and 3.—Continued

WATER YEAR

Simulated

EXPLANATION

Observed

1987 1989 1991 1993 1995 1997

WATER YEAR

1987 1989 1991 1993 1995 1997

3,340

3,360

3,380

3,400

3,420

3,440

3,460

3,480

3,380

3,400

3,420

3,440

3,460

3,480

3,500

3,520

3,340

3,360

3,380

3,400

3,420

3,440

3,460

3,480

3,340

3,360

3,380

3,400

3,420

3,440

3,460

3,480

3,100

3,120

3,140

3,160

3,180

3,200

3,220

3,240

3,320

3,340

3,360

3,380

3,400

3,420

3,440

3,460

Site 181 (BLHK−1) MINNELUSA Site 209 (CP) MINNELUSA

Site 224 (WCR−3) MINNELUSA Site 233 (CHLN−1) MINNELUSA

Site 47 (RC−7) MADISON Site 43 (LC) MADISON

HYDRAULIC HEAD, IN FEET ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929

52 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Numerical Groundwater-Flow Model 53

Comparison of Simulated and Observed 

Transient Springflow

Total simulated transient springflow ranged from 25.7 

to 42.3 ft3/s (table 13). Simulated springflow for JacksonCleghorn Springs ranged from 17.0 to 23.6 ft3

/s and averaged 

20.0 ft3/s (table 13 and fig. 34) compared to an estimate of 

21.6 ft3/s (Anderson and others, 1999). The Jackson-Cleghorn 

springflow from model layer 1 ranged from 1.5 to 2.7 ft3/s 

and averaged 2.2 ft3/s. Simulated springflow from model 

layer 3 ranged from 15.4 to 20.9 ft3/s and averaged 17.7 ft3/s. 

Measurements of Jackson-Cleghorn springflow during the 

transient simulation period were not available to compare 

to simulated transient springflow; however, measurements 

made during a dry period during WY 2005–07 (table 14) 

with pumping stresses indicated that the simulated range in 

transient springflow was plausible. Discharge from JacksonCleghorn Springs was most sensitive to the conductance of the 

head-dependent cells (CLEGmdsn; table 10; fig. 12) representing the spring followed by horizontal hydraulic conductivity 

for parameter group HK3_2 (table 10; fig. 19).

Observed and simulated springflow for six smaller 

springs also are listed in table 13. Simulated springflow 

for City Springs had similar trends to observed springflow 

(fig. 34); however, changes in simulated values generally were 

less than changes in observed values. Simulated springflow for 

Deadwood Avenue Springs was slightly less than the estimated average springflow (fig. 34). Simulated springflow for 

Boxelder Springs had similar trends to estimated springflow; 

however, the increase during the wet period (late 1990s) was 

less for simulated values than for estimated values (fig. 34).

The averages of estimated and simulated springflow for 

Elk Springs were about the same (table 13); however, simulated values had a much smaller range (fig. 34). Elk Springs is 

near the northern no-flow boundary, which influences simulated springflow. During very wet conditions, groundwater 

may flow into the study area because of recharge on the large 

outcrop of the Minnelusa and Madison hydrogeologic units 

northwest of the model area near the Vanocker Laccolith 

(Strobel and others, 1999). During extremely wet periods, 

the assumption of a no-flow boundary may not be the best 

approximation. Also, representation of conduits and heterogeneity associated with this spring may be difficult to approximate with the larger cell size near the northern boundary of the 

model.

Simulated springflow representing the combined bedrock 

contributions to the Meadowbrook and Girl Scout galleries 

(Infiltration Gallery Springs) was smaller than the springflow 

estimated by Anderson and others (1999). The potential error 

in the estimated springflow was relatively large (Anderson 

and others (1999). The simulated springflow to Canyon Lake 

ranged from 0.3 to 0.9 ft3/s. No measured or estimated springflow information was available for Canyon Lake; however, 

a response in hydraulic head at a nearby observation well 

completed in the Minnelusa hydrogeologic unit (well 229) was 

evident when Canyon Lake was drained from December 1995 

through January 1996 (Driscoll, Bradford, and Moran, 2000).

Comparison of Simulated and Estimated 

Transient Regional Outflow

Simulated transient regional outflow from the Minnelusa 

and Madison hydrogeologic units at the eastern model boundary (table 15) was steady and slightly higher than the average 

outflow of 12.3 ft3/s for the Minnelusa hydrogeologic unit 

and 12.2 ft3/s for the Madison hydrogeologic unit estimated 

by Long and Putnam (2002). The eastern boundary was far 

enough east so that changes in recharge and pumping did not 

affect regional outflow at the boundary.

Calibrated Hydraulic Properties

Horizontal hydraulic conductivity for zones in layers 1 

and 3, vertical conductivity for part of layer 2, and conductance for head-dependent cells representing selected springs 

were optimized with steady-state parameter estimation and 

trial-and-error transient simulations. Horizontal hydraulic conductivity for layers 2 and 4 was set to 0.1 times the 

hydraulic conductivity for layers 1 and 3, respectively, except 

near the outcrops, where it was set to 0.5 times the hydraulic conductivity for layers 1 and 3. The horizontal hydraulic 

conductivity for layers 2 and 4 was assumed to be smaller than 

for layers 1 and 3, respectively; however, the values selected 

are arbitrary. Vertical conductivity was assigned for layers 1, 

3, 4, and 5 as 0.1 times the horizontal hydraulic conductivity 

for the respective layer. The model was not sensitive to these 

parameters for vertical conductivity; therefore, the assigned 

value was assumed.

Calibrated horizontal hydraulic conductivity values for 

model layer 1 parameter groups (fig. 17) ranged from 1.0 to 

5.2 ft/d (table 16). The largest horizontal hydraulic conductivity (parameter group HK1_1) represented the zone near the 

outcrop of the Minnelusa hydrogeologic unit from Boxelder 

Creek south to the Jackson-Cleghorn Springs area. The smallest hydraulic conductivity (parameter group HK1_3) represented the north and central part of the study area where the 

hydraulic gradient generally was the steepest.

Horizontal hydraulic conductivity values for model 

layer 3 parameter groups (figs. 19 and 20) ranged from 0.1 to 

388.8 ft/d (table 16). The largest value of hydraulic conductivity of 388.8 ft/d (zone HK3_6) represented the zone around 

Jackson-Cleghorn Springs where converging enlarged solution openings are likely. Zone HK3_7, which approximated 

conduit zones beginning at the Spring Creek loss zone and 

surrounding zone HK3_6, had a hydraulic conductivity of 

22.9 ft/d. Hydraulic conductivity values determined from 

large-scale aquifer tests that overlap zones HK3_6 and HK3_7 

were about 57 and 93 ft/d (Greene, 1993; Long and Putnam, 

2002). Zone H3_4, which approximates the conduit zone 
Table 13. Estimated and simulated transient springflow.

[Springflow in cubic feet per second. Springflow for Jackson-Cleghorn and Infiltration Gallery Springs from Anderson and others (1999); estimate was made for water years 198stress periods were assumed to be similar. Springflow for City Springs from Long and Putnam (2002); flow from City Springs and some unnamed springs about 0.3 mi to the easflow record. Springflow for Deadwood Avenue, Boxelder, and Elk Springs from Long and Putnam (2002); an average value was estimated for Deadwood Avenue Springs on the water years 1988–90. No quantitative measurements were available for Canyon Lake; small discharge was assumed]

Stress 

period

Jackson-Cleghorn 

Springs City Springs Deadwood Avenue Springs Boxelder Springs Elk Springs Infiltration Gallery Springs Canyon La

Estimated Sim- ulated Estimated Sim- ulated Estimated Sim- ulated Estimated Sim- ulated Estimated Sim- ulated Estimated Sim- ulated Estimated 

u

1 21.6 20.9 1.9 1.8 2.8 3.2 0.0 1.3 0.3 6.2 1.5 0.5 0.5 2 21.6 20.0 1.0 1.6 2.8 2.8 .0 1.0 .3 5.9 1.5 .5 .5 3 21.6 19.8 1.0 1.7 2.8 3.1 .0 .9 .0 5.7 1.5 .5 .5 4 21.6 19.7 .7 1.5 2.8 2.8 .0 .8 .0 5.4 1.5 .5 .5 5 21.6 19.1 .8 1.5 2.8 2.9 .0 .7 .0 5.3 1.5 .5 .5 6 21.6 19.1 .8 1.2 2.8 2.5 .0 .6 .0 5.0 1.5 .4 .5 7 21.6 18.9 .3 1.0 2.8 2.7 .0 .6 .1 4.8 1.5 .4 .5 8 21.6 20.8 1.3 .7 2.8 2.1 .0 1.4 .1 5.1 1.5 .4 .5 9 21.6 19.5 .6 .9 2.8 1.9 .0 .9 .0 5.1 1.5 .4 .5 

10 21.6 17.0 .4 .4 2.8 1.8 .0 .6 .0 5.0 1.5 .4 .5 

11 21.6 18.4 .3 .9 2.8 2.0 .2 .5 .1 4.8 1.5 .4 .5 

12 21.6 18.1 2.1 .3 2.8 1.5 .2 2.1 .1 5.1 1.5 .4 .5 13 21.6 20.0 1.5 .5 2.8 1.7 .0 1.3 .4 5.2 1.5 .5 .5 14 21.6 17.6 1.4 .1 2.8 1.3 .0 1.9 .4 5.1 1.5 .4 .5 15 21.6 19.3 1.3 .8 2.8 1.9 .5 1.1 8.6 5.1 1.5 .5 .5 16 21.6 20.8 3.3 .7 2.8 2.0 .5 3.1 8.6 5.8 1.5 .5 .5 17 21.6 21.9 2.8 1.3 2.8 2.4 2.5 1.9 8.2 6.1 1.5 .5 .5 18 21.6 21.5 4.0 .7 2.8 1.9 2.5 3.7 8.2 6.5 1.5 .5 .5 19 21.6 23.0 3.5 1.5 2.8 2.5 6.8 2.7 18.9 6.6 1.5 .5 .5 20 21.6 23.6 4.9 1.5 2.8 2.8 6.8 5.9 18.9 7.2 1.5 .5 .5 

Average 21.6 20.0 1.7 1.0 2.8 2.3 1.0 1.7 3.7 5.6 1.5 .5 .5 
Figure 34. Simulated and observed or estimated springflow values.

EXPLANATION

1987 1989 1991 1993 1995 1997

WATER YEAR

1987 1989 1991 1993 1995 1997

WATER YEAR

0

2

4

6

8

10

10

15

20

25

30

0

2

4

6

8

10

SPRINGFLOW, IN CUBIC FEET PER SECOND

0

2

4

6

8

10

0

5

10

15

20

0

2

4

6

8

10

JACKSON-CLEGHORN SPRINGS CITY SPRINGS

DEADWOOD AVENUE SPRINGS BOXELDER SPRINGS

ELK SPRINGS INFILTRATION GALLERY SPRINGS

Simulated springflow from model layers 1 and 3 

Observed springflow (Long and Putnam, 2002) 

Numerical Groundwater-Flow Model 55
Table 14. Jackson-Cleghorn springflow estimated from streamflow measurements on Rapid Creek.

[Upstream station is Rapid Creek at Braeburn Addition (fig. 12). Downstream station is Rapid Creek below Cleghorn Springs (fig. 12). Pumping withdrawal rate 

from Jackson Springs Gallery from Ron Barber, Rapid City Water Department, oral commun. (2004–05). Estimated Jackson-Cleghorn springflow calculated by 

subtracting streamflow at upstream station from downstream station and adding pumping withdrawal from Jackson Springs Gallery]

Date of paired 

streamflow 

measurements

Streamflow (cubic feet per second) Pumping withdrawal rate from 

Jackson Springs Gallery

(cubic feet per second)

Estimated Jackson-Cleghorn 

springflow 

(cubic feet per second) Upstream station

(440321103181101)

Downstream station 

(06412900)

10/19/2004 10.3 26.2 0.0 15.9

10/19/2004 10.7 25.2 .0 14.5

10/19/2004 11.0 28.6 .0 17.6

10/19/2004 10.2 26.5 .0 16.3

10/26/2004 9.9 22.8 4.0 16.9

10/26/2004 10.3 23.0 4.0 16.7

11/04/2004 10.1 24.8 4.0 18.7

11/04/2004 10.7 26.4 4.0 19.7

10/11/2005 8.3 16.6 10.0 18.3

10/11/2005 8.7 16.4 10.0 17.7

11/07/2005 6.4 19.6 4.0 17.2

11/07/2005 7.6 21.2 4.0 17.6

10/02/2006 6.3 21.2 .0 14.9

03/15/2007 8.5 25.2 .0 16.7

03/15/2007 7.9 23.5 .0 15.6

03/16/2007 7.2 23.2 .0 16.0

03/16/2007 7.0 22.0 .0 15.0

Table 15. Simulated transient regional outflow from Minnelusa and Madison hydrogeologic units at the eastern model boundary.

Stress 

period

Simulated regional outflow 

(cubic feet per second)

Minnelusa 

hydrogeologic unit

Madison 

hydrogeologic unit

1 12.9 12.9

2 12.9 12.6

3 12.9 12.9

4 12.8 12.8

5 12.9 12.9

6 12.8 12.8

7 12.9 12.9

8 12.8 12.7

9 12.8 12.8

10 12.8 12.7

Stress 

period

Simulated regional outflow 

(cubic feet per second)

Minnelusa 

hydrogeologic unit

Madison 

hydrogeologic unit

11 12.8 12.7

12 12.7 12.6

13 12.8 12.7

14 12.7 12.5

15 12.8 12.6

16 12.7 12.5

17 12.7 12.6

18 12.7 12.5

19 12.8 12.6

20 12.8 12.5

56 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.
Table 16. Calibrated horizontal hydraulic conductivity for parameters representing zones of hydraulic 

conductivity in model layers 1, 3, and 5.

[Location of area represented by the parameter group name is shown in figures 17, 19, 20, and 22]

Parameter 

group name Model layer Area of parameter zone (square miles)

Effective horizontal hydraulic conductivity 

(feet per day)

HK1_1 1 67.9 5.2

HK1_2 1 566.0 3.3

HK1_3 1 153.2 1.0

1

HK3_1 3 46.8 16.0

HK3_2 3 596.3 5.4

HK3_3 3 56.8 .1

HK3_4 3 28.9 39.3

HK3_5 3 91.5 1.4

HK3_6 3 6.9 388.8

HK3_7 3 16.7 22.9

HK5_1 5 59.4 .1

1

Hydraulic conductivity represented by this parameter included anisotropy of 0.1; hydraulic conductivity along rows (Kx) = 

50.5 feet per day and columns (Ky) = 5.05 feet per day; effective hydraulic conductivity equals the square root of (Kx*Ky).

Table 17. Conductance for head-dependent cells representing 

springs.

Parameter 

name

Spring name

 (location on fig. 11 or 12)

Conductance 

(feet squared per day)

CLEGmdsn Jackson-Cleghorn Springs 32,000

CLEGmnls Jackson-Cleghorn Springs 8,600

CITYSPR City Springs 35,000

DWSPR Deadwood Avenue Springs 3,000

BESPR Boxelder Springs 35,000

ELKSPR Elk Springs 86,400

GAL Infiltration Gallery Springs 6,000

CLAKE Canyon Lake 3,400

Numerical Groundwater-Flow Model 57

extending from Boxelder Creek that included an eastward 

bulge in the potentiometric surface, had a hydraulic conductivity of 39.3 ft/d. Substantial heterogeneity within this zone 

is likely on the basis of tracer tests and the prevalence of 

numerous structural features. Calibrated hydraulic conductivity for zone HK3_5 was 1.4 ft/d, which represented areas near 

the outcrop of the Madison hydrogeologic unit with relatively 

steep hydraulic gradients and areas that transition from gradual 

to steep hydraulic gradients. Calibrated hydraulic conductivity for zone HK3_2 was 5.4 ft/d, which is consistent with 

the assumption of higher hydraulic conductivity where the 

hydraulic gradient is relatively gradual.

Zone HK3_3, which represents the area where the 

hydraulic gradient is relatively steep, was assigned a hydraulic conductivity of 0.1 ft/d. In model calibration, hydraulic 

conductivity for this area converged towards a very small 

value. The parameter group HK3_3 became relatively insensitive at these small values; therefore, a small value was 

assigned. The effective hydraulic conductivity for zone HK3_1 

was 16.0 ft/d with anisotropy of 0.1 (10 times greater along 

model rows than columns). This parameter group approximated the area with large hydraulic conductivity identified in 

regional modeling (Downey, 1986). The hydraulic properties 

represented by zones HK3_1 and HK3_3 are based on sparse 

information, and the areas probably include a combination 

of massive impermeable limestone and karst features that are 

poorly characterized.

Calibrated vertical hydraulic conductivity for layer 2 

(fig. 23) was 0.0025 ft/d for parameter VKA2_2. Vertical 

hydraulic conductivity was 0.025 ft/d for the areas within 

VKA2_2 near structural features and 0.25 ft/d for the area near 

Jackson-Cleghorn Springs. Parameter VKA2_2 was relatively 

sensitive to the concentration of observations in this parameter 

zone. The model was insensitive to parameter VKA2_1, and 

therefore a small value of 0.000001 ft/d was assigned.

The conductance term for head-dependent cells representing springs was calibrated using parameters CLEGmdsn 

and DWDSPR. The sensitivity of the conductance parameters 

for the remaining springs to observed data was low and values 

were estimated. Conductance for head-dependent cells representing springs ranged from 3,000 to 86,400 feet squared per 

day (table 17).
58 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Response to Stress

In calibration of the transient model, the largest annual 

average pumping rate for large production wells in the 

Madison hydrogeologic unit was about 7 ft3/s. To test the 

relation between pumping stresses and boundary conditions, 

the 10-year transient simulation was made with production of 

7 ft3/s from the large production wells in the Madison hydrogeologic unit. The hydraulic head values at the end of this 

simulation were saved, and the same simulation was made 

with pumping increased by 2-ft3/s increments for the same 

wells. Simulations were made for hypothetical pumping rates 

of 7, 9, 11, 13, 15 and 17 ft3/s. The increases in pumping were 

distributed to the production wells as a fraction of the productive capacity of each well relative to the total pumping from 

all the wells. The outline of the area where drawdown from the 

additional pumping exceeded 2 ft was calculated for each of 

these simulations (fig. 35). 

When pumping was increased from 7 to 17 ft3/s, drawdown of 2 feet approached the northern and southern boundaries of the model (fig. 35). Simulation of increased hypothetical 

pumping rates of more than 10 ft3/s (total of about 17 ft3/s) 

may require modification to the no-flow boundaries to allow 

flow into the model. Outflow at the eastern boundary did not 

change with increases in pumping from 7 to 17 ft3/s. The 

drawdown at observation well 46 (SP–2; fig. 35) increased 

from 5.3 ft with an increase in pumping of 2 ft3/s to 27.1 ft 

with an increase in pumping of 10 ft3/s.

The influence of potential pumping stresses on springflow is an important consideration in evaluating management 

alternatives. Although some error may be associated with 

estimating the magnitude of decreases in springflow, transient 

simulation of pumping rates provides an assessment of how 

increased pumping could influence springflow. Compilation 

of the simulated springflows for Jackson-Cleghorn Springs 

(fig. 36) for each of the six previous hypothetical increases 

in pumping rates gives an indication of how springflow may 

decrease with time. The simulated effect of increased pumping 

from existing production wells on springflow from JacksonCleghorn Springs was a decrease in springflow equal to about 

30 percent of the increase in pumping rate at 6 months increasing to about 50 percent of the increase in pumping rate after 

10 years of pumping.

The drawdown in four observation wells during a 6-day 

aquifer test for production well 49 pumped at 2,550 gal/min 

(RC–9; Long and Putnam, 2002) was simulated to illustrate 

limitations of the model in representing the site-specific effect 

of pumping stresses. The locations of well 49 and the four 

observation wells in relation to layer 3 hydraulic conductivity 

zones are shown in figure 37. Comparison of the simulated 

and observed drawdown for the four wells (fig. 38) shows that 

the model approximates the average drawdown; however, the 

response at specific sites may not be matched. This probably 

results from generalization of heterogeneous hydraulic properties. The confined storage coefficient used in the model was 

0.0003, whereas estimates from the aquifer test ranged from 

0.000014 to 0.00027 (Long and Putnam, 2002). Additional 

model limitations are described in the following section.

Model Limitations

The model was developed to evaluate groundwater 

flow on a large scale and is limited by numerous simplifying 

assumptions. One of the most important simplifying assumptions is representation of a hydrogeologic system that contains 

substantial secondary porosity as a porous media. A bulk 

parameter that represents the average for a given model cell 

area provides only a generalized approximation of hydraulic 

properties, especially for the karstic Madison hydrogeologic 

unit. Representation of vertical heterogeneity also is very 

generalized, especially for the Minnelusa hydrogeologic unit, 

which contains many layers of different consolidated sediments. These simplifications probably result in a simulated 

hydraulic head response to stress that is more damped than 

observed responses. Site specific responses in some areas 

could be substantially in error.

An additional limitation is the influence of boundary 

conditions. Model boundaries were extended away from 

the detailed study area to limit the influence of errors in 

approximating boundary conditions; however, the potential for 

boundary conditions to influence simulation results increases 

as simulated stresses are increased. No-flow boundaries on 

the north and south may approximate average conditions; 

however, the boundaries may not represent extreme recharge 

conditions as well.

Estimates of streamflow recharge, which makes up 

a substantial portion of the total recharge, were based on 

measured values; however, the distribution of that recharge 

between model layers is more uncertain. Areal recharge 

was estimated by more indirect methods, and storage in the 

partially saturated zones near the outcrops is poorly understood. Regional outflow at the eastern boundary is based on a 

water balance, and adequate information was not available for 

the horizontal distribution among model layers. The distribution between hydrogeologic units was assumed to be about 

equal. Few springflow measurements were available, and 

many of the calibration constraints were based on estimates. 

Available aquifer tests represent only a small part of the model 

area, and interpretation of hydraulic properties from aquifer 

tests is difficult because of the complex hydrogeology.

With additional data, further refinement of the model 

would be possible, which could improve the accuracy of 

model estimates of the effects of additional stresses on the 

system, such as increased withdrawals or drought. The model 

can yield simulations of future conditions, which can guide 

management decisions and planning. The model provides 

a useful tool for general characterization of the effects of 

stresses and management alternatives on a regional basis.
Figure 35. Simulated extent of drawdown resulting from hypothetical increases in pumping rates from the Madison hydrogeologic 

unit.

MEADE CO

LAWRENCE CO

PENNINGTON CO

MEADE CO

PENNINGTON CO

CUSTER CO

Nemo

Caputa

Hisega

Hayward

Tilford

Piedmont

Box Elder

Blackhawk

Rockerville

Farmingdale

R. 8 E.

Elk

Boxelder

Rapid

Spring

Rapid City

Gulch

Creek

T. 5 N.

T. 3 N.

T. 4 N.

T. 1 S.

T. 2 N.

T. 1 N.

T. 2 S.

R. 6 E. R. 7 E.

R. 9 E.

R. 10 E.

103°07’30”

103°22’30”

43°55’

44°15’

44°05’

16

I-90

I-90

Creek

Creek

Creek

Base from U.S. Geological Survey digital data, 

1977, 1:100,000, and Rapid City, Office of City 

Engineer map, 2005, 1:18,000 

Universal Transverse Mercator projection, 

Zone 13

Victoria Creek

Deadman

Battle Creek

Little Elk

Rockerville

Gulch

79

Creek

0 2 4 6 8 MILES

0 3 6 8 KILOMETERS

44

44 79

EXPLANATION

Increase in pumping from 7 to 9 cubic feet per second

Increase in pumping from 7 to 11 cubic feet per second

Increase in pumping from 7 to 13 cubic feet per second

Increase in pumping from 7 to 15 cubic feet per second

Increase in pumping from 7 to 17 cubic feet per second

Selected production wells completed in Madison hydrogeologic unit

Observation well 46 (SP−2)

Extent of at least 2 feet of drawdown resulting from hypothetical 

 pumping rate increases greater than 7 cubic feet per second

Boundary of model layer 3

Model Limitations 59
Figure 36. Simulated decrease in springflow from Jackson-Cleghorn Springs in response to hypothetical 

increases in pumping rates from the Madison hydrogeologic unit.

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

SI

MULATED DECREASE IN SPRINGFLO

W FRO

M JACKSON-CLEGHORN

SPRINGS, IN CUBIC FEET PER SECOND

STRESS PERIODS (6-MONTH INTERVAL FOR 10 YEARS, WATER YEARS 1987−97)

2 4 6 8 10

Hypothetical increase in pumping rate from Madison production wells by 

increments of 2 cubic feet per second (7 to 17 cubic feet per second) 

60 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Summary

The city of Rapid City, South Dakota, obtains more 

than one-half of its municipal water supplies from the Minnelusa and Madison aquifers through deep wells and springs, 

predominantly from the Madison aquifer. Numerous additional users in the Rapid City area obtain water from the 

Minnelusa and Madison aquifers for domestic, commercial, 

industrial, and irrigation usage. The U.S. Geological Survey, 

as part of a long-term cooperative study with the city of Rapid 

City, has compiled numerous datasets designed to better 

understand groundwater flow in the Minnelusa and Madison 

hydrogeologic units. A numerical groundwater-flow model 

was developed of the Minnelusa and Madison hydrogeologic 

units in the Rapid City area to synthesize estimates of waterbudget components and hydraulic properties, and to provide 

a tool to analyze the effect of additional stress on water-level 

altitudes within the aquifers and on discharge to springs. The 

purposes of this report are to (1) document the development 

of a numerical groundwater-flow model of the Minnelusa and 

Madison hydrogeologic units, which contain the Minnelusa 

and Madison aquifers, in the Rapid City area in South Dakota, 

and (2) present simulated responses to stress and describe 

model limitations.

The 1,000-square-mile study area on the eastern flank of 

the Black Hills includes Rapid City and the surrounding area. 

Land-surface altitudes range from more than 5,000 feet (ft) 

on the western side of the study area to about 2,800 ft in the 

eastern lowlands. Average precipitation rates range from about 

24 inches per year (in/yr) in the northwest to about 16 in/yr 

in the eastern lowlands. The outcrops of the Minnelusa and 

Madison hydrogeologic units, which are characterized by 

high-relief forested areas cut by deep canyons, form generally concentric rings surrounding the Precambrian core of the 

uplifted Black Hills. Water-table conditions generally exist 

in outcrop areas and extend to more than 1 mile east of the 

outcrop areas in parts of the Minnelusa and Madison hydrogeologic units in the study area. Confined conditions exist 

east of the water-table areas because of the easterly dip of the 

hydrogeologic units.

The Minnelusa hydrogeologic unit is 375 to 800 ft thick 

in the study area with the more permeable upper part containing predominantly sandstone, and the less permeable lower 

part containing more shale and limestone than the upper part. 

Siltstone, gypsum, and anhydrite also can be present. The 

shale units in the lower part generally impede flow between 

the Minnelusa hydrogeologic unit and underlying Madison 

hydrogeologic unit; however, fracturing and weathering may 

result in hydraulic connections in some areas. Recharge to 

the Minnelusa hydrogeologic unit is from streamflow loss 

that occurs where streams cross the outcrop and from infiltration of precipitation on the outcrops. Wells completed in the 

Minnelusa hydrogeologic unit are used extensively by small 

suburban developments and for domestic supplies surrounding 

Rapid City.
Figure 37. Locations of production and observation wells for Madison aquifer test at well 49.

44°05’

I-90

44

79

Rapid

16

Creek

Boxelder

Spring

Creek

Creek

MEADE CO

PENNINGTON CO

T. 1 N.

T. 1 S.

R. 7 E.

R. 6 E.

R. 5 E.

103°22’30”

103°15’

44°00’

T. 3 N.

T. 2 N.

Base fom U.S. Geological Survey 

digital data, 1977, 1:100,000 

Rapid City, Office of City Engineer map, 

2005, 1:18,000

Unversal Transverse Mercator projection

Zone 13

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

79

44

16

Rapid

Creek

Rapid City

EXPLANATION

Parameter group and hydraulic conductivity

HK3_2 (5.6 feet per day)

HK3_3 (0.1 feet per day)

HK3_4 (31.9 feet per day)

HK3_5 (1.0 feet per day)

HK3_6 (660 feet per day

HK3_7 (100 feet per day)

Production well (site 49, table 20)

Well where drawdown was monitored 

 during aquifer test (number is site number 

 in table 20; Long and Putnam, 2002)

50

46

62

56

49

62

49

Summary 61
0

2

4

6

8

10

12

Drawdown in well CHLN–2

Site 56

Distance from production well = 7,562 feet 

Drawdown in well CL–2

Site 50

Distance from production well = 6,290 feet

Drawdown in well RC–11

Site 62

Distance from production well = 8,603 feet

Drawdown in well SP–2

Site 46

Distance from production well = 4,564 feet

0

2

4

6

8

10

12

0 2,000 4,000 6,000 8,000 10,000

DRAWDOWN, IN FEET

ELAPSED TIME, IN MINUTES

0 2,000 4,000 6,000 8,000 10,000

ELAPSED TIME, IN MINUTES

SIMULATED

OBSERVED

0

2

4

6

8

10

12

0

2

4

6

8

10

12

EXPLANATION

Figure 38. Simulated and observed drawdown for Madison aquifer test at well 49.

62 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

The Madison hydrogeologic unit, which includes the 

Englewood Formation, is composed of limestone and dolomite that is about 250 to 610 ft thick in the study area. The 

upper 150 ft of the Madison hydrogeologic unit contains 

substantial secondary permeability from solution openings 

and fractures, and permeability is smaller in the lower part 

of the unit. Karst features are found throughout the Madison 

Limestone; however, they tend to be more common along the 

contacts between mapped geomorphic units. Recharge to the 

Madison hydrogeologic unit is from streamflow loss where 

streams cross the outcrop and from infiltration of precipitation 

on the outcrops (areal recharge). The amount of streamflow 

loss to the Madison hydrogeologic unit outcrops can be as 

much as 25 cubic feet per second (ft3/s) for some streams, and 

streamflow recharge usually is greater than areal recharge in 

the study area. Wells completed in the Madison hydrogeologic 

unit are capable of producing from 5 to 2,500 gallons per 

minute.

MODFLOW–2000, a numerical, three-dimensional, 

finite-difference groundwater-flow model, was used to simulate flow in the Minnelusa and Madison hydrogeologic units, 

and the MODFLOW–2000 parameter estimation process was 

used to optimize estimates of hydraulic properties. The model 

includes five layers with layer 1 representing the fractured 

sandstone layers in the upper part of the Minnelusa hydrogeologic unit. Layer 2 represented the fractured limestone, minor 

sandstone layers, and shale units in the lower part of the Minnelusa hydrogeologic unit. Layer 3 represented the upper part 
Summary 63

of the Madison hydrogeologic unit, and layer 4 represented the 

less permeable lower part of the Madison hydrogeologic unit. 

Layer 5 represented an approximation of the underlying Deadwood aquifer to simulate upward flow to the Madison hydrogeologic unit. Arrays representing the altitude of the tops of 

layers 1, 3, and 5 were constructed from maps of the structural 

tops of the Minnelusa Formation, the Madison Limestone, 

and the Deadwood Formation. A uniform thickness of 250 ft 

was assumed for layer 1 with the remainder of the Minnelusa 

hydrogeologic unit represented as layer 2. A uniform thickness 

of 150 ft was assumed for layer 3 with the remainder of the 

Madison hydrogeologic unit represented in layer 4.

The finite-difference grid included 221 rows and 

169 columns with a square cell size of 492.1 ft in the detailed 

study area that surrounded Rapid City. Cell sizes increased 

outward from the detailed area to 1,640 ft at boundaries on 

the north and south and to 6,562 ft at the eastern boundary. 

The model was oriented 23 degrees counterclockwise to 

approximate orthogonal directions observed in cave passageways and fractures. The northern and southern boundaries for 

layers 1–4 were represented as no-flow boundaries, and the 

eastern boundary was represented with head-dependent flow 

cells. Streamflow recharge was represented with specifiedflow cells. Areal recharge to layers 1–4 was represented with a 

specified-flux boundary with the recharge flux assigned to the 

westernmost active cells. A specified-flux boundary assigned 

to the western-most active cells in layer 5 represented the 

source of upward flow from the Deadwood aquifer to layer 4. 

Calibration of the model was accomplished by two simulations: (1) steady-state simulation of average conditions for 

water years 1988–97 and (2) transient simulations of water 

years 1988–97 divided into twenty 6-month stress periods.

Flow-system components represented in the model 

include recharge, discharge, and hydraulic properties. The 

steady-state streamflow recharge rate was 42.2 ft3/s for 

five major streams and five minor tributaries with 36.2 ft3/s 

recharging the Madison hydrogeologic unit. Total transient 

streamflow recharge rates by stress period for the Minnelusa and Madison hydrogeologic units ranged from 14.1 to 

102.2 ft3/s. The steady-state areal recharge rate was 20.9 ft3/s 

and was distributed among five zones from north to south 

delineated by the major streams where they crossed the 

outcrops. Total transient areal recharge rates by stress period 

for the Minnelusa and Madison hydrogeologic units ranged 

from 1.1 to 98.4 ft3/s. The upward flow rate from the Deadwood aquifer to the Madison hydrogeologic unit was 6.3 ft3

/s.

Discharge included springflow, water use, flow to overlying units, and regional outflow. The estimated steady-state 

springflow was 32.8 ft3/s from seven springs. Steady-state 

water-use rates for the Minnelusa and Madison hydrogeologic 

units for the 10-year period were 3.4 and 6.7 ft3/s, respectively. 

Total transient water-use rates ranged from 3.4 to 19.1 ft3/s. 

Steady-state flow from the Minnelusa hydrogeologic unit to 

overlying units was 2.0 ft3/s.

The hydraulic properties that the model was most 

sensitive to were horizontal hydraulic conductivity, vertical 

hydraulic conductivity for layer 2 near the outcrop of the 

Minnelusa hydrogeologic unit, and conductance for JacksonCleghorn Springs. Linear regression of the 252 simulated 

and observed hydraulic heads for the steady-state simulation 

had a coefficient of determination (R2 value) of 0.92 with 

an average arithmetic difference of -7.6 ft and an average 

absolute difference of 37.6 ft. The estimated steady-state 

springflow of 32.8 ft3/s from seven springs was similar to the 

simulated springflow of 31.6 ft3/s, which included springflow of 20.5 ft3

/s from Jackson-Cleghorn Springs. Simulated 

steady-state regional outflow of 12.9 ft3/s from the Minnelusa 

hydrogeologic unit at the eastern boundary was slightly larger 

than the estimated outflow of 12.3 ft3/s. Simulated steadystate regional outflow from the Madison hydrogeologic unit 

of 12.8 ft3/s was slightly larger than the estimated outflow of 

12.2 ft3/s.

For the transient simulation, the average absolute difference between simulated and observed hydraulic heads for the 

19 observation wells ranged from 3.5 to 65.1 ft with a median 

value of 18.3 ft. Simulated transient springflow ranged from 

25.7 to 42.3 ft3/s.

Horizontal hydraulic conductivity for layers 2 and 4 were 

10 percent of horizontal hydraulic conductivity for layers 1 

and 3, respectively, except near the outcrops where it was 

50 percent of the conductivity for layers 1 and 3, respectively. 

Calibrated horizontal hydraulic conductivities for model 

layer 1 ranged from 1.0 to 5.2 feet per day (ft/d). Horizontal 

hydraulic conductivities for model layer 3 ranged from 0.1 to 

388.8 ft/d. Vertical hydraulic conductivity for layers 1, 3, 4, 

and 5 was 10 percent of the respective horizontal hydraulic 

conductivity for those layers. Vertical hydraulic conductivity 

for layer 2 ranged from 0.000001 to 0.25 ft/d. Conductance for 

head-dependent cells representing springs ranged from 3,000 

to 86,400 feet squared per day.

Simulation of increased hypothetical pumping of more 

than about 10 ft3/s may require modification to the no-flow 

boundaries to allow flow into the model. The simulated effect 

of increased pumping from existing production wells on 

springflow from Jackson-Cleghorn Springs was a decrease 

in springflow equal to about 30 percent of the increased 

pumping rate at 6 months increasing to about 50 percent of the 

increased pumping rate after 10 years of pumping. Simulation 

of a large-scale aquifer test indicated that the model is limited 

in describing pumping stresses with detail.

The model is limited by simplifying assumptions 

necessary to represent a hydrogeologic system that contains 

substantial secondary porosity as a porous media. A bulk 

parameter that represents the average for a given model cell 

area provides only a generalized approximation of hydraulic properties. Adequate information was not available for 

distribution of estimates of recharge and discharge among 

model layers. With additional data, further refinement of the 

model would be possible, which could improve the accuracy 

of model estimates of the effects of additional stresses on the 

system, such as increased withdrawals or drought. The model 

can yield simulations of future conditions, which can guide 
64 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

management decisions and planning. The model provides 

a useful tool for general characterization of the effects of 

stresses and management alternatives on a regional basis.

References Cited

Anderson, M.T., Driscoll, D.G., and Williamson, J.E., 1999, 

Ground-water and surface-water interaction along Rapid 

Creek near Rapid City, South Dakota: U.S. Geological Survey Water-Resources Investigations Report 98–4214, 99 p.

Bowles, C.G., and Braddock, W.A., 1963, Solution breccias of 

the Minnelusa Formation in the Black Hills, South Dakota 

and Wyoming, in Geological Survey Research 1963—short 

papers in geology and hydrology, Articles 60–121: U.S. 

Geological Survey Professional Paper 475–C, art. 83, 

p. C91–C95.

Carter, J.M., and Driscoll, D.G., 2005, Estimating recharge 

using relations between precipitation and yield in a mountainous area with large variability in precipitation: Journal 

of Hydrology, v. 316, p. 71–83.

Carter, J.M., Driscoll, D.G., and Hamade, G.R., 2001, Estimated recharge to the Madison and Minnelusa aquifers in 

the Black Hills area, South Dakota and Wyoming, water 

years 1931–98: U.S. Geological Survey Water-Resources 

Investigations Report 00–4278, 66 p.

Carter, J.M., and Redden, J.A., 1999a, Altitude of the top of 

the Minnelusa Formation in the Black Hills area, South 

Dakota: U.S. Geological Survey Hydrologic Investigations 

Atlas HA–744–C, 2 sheets, scale 1:100,000.

Carter, J.M., and Redden, J.A., 1999b, Altitude of the top 

of the Madison Limestone in the Black Hills area, South 

Dakota: U.S. Geological Survey Hydrologic Investigations 

Atlas HA–744–D, 2 sheets, scale 1:100,000.

Carter, J.M., and Redden, J.A., 1999c, Altitude of the top of 

the Deadwood Formation in the Black Hills area, South 

Dakota: U.S. Geological Survey Hydrologic Investigations 

Atlas HA–744–E, 2 sheets, scale 1:100,000.

Cattermole, J.M., 1969, Geologic map of the Rapid City 

west quadrangle, Pennington County, South Dakota: U.S. 

Geological Survey Geologic Quadrangle Map GQ–828, 

scale 1:24,000.

Downey, J.S., 1986, Geohydrology of bedrock aquifers in the 

northern Great Plains in parts of Montana, North Dakota, 

South Dakota, and Wyoming: U.S. Geological Survey Professional Paper 1402–E, 87 p., 3 pls.

Driscoll, D.G., Bradford, W.L., and Moran, M.J., 2000, 

Selected hydrologic data, through water year 1998, Black 

Hills Hydrology Study, South Dakota: U.S. Geological 

Survey Open-File Report 00–70, 284 p.

Driscoll, D.G., Hamade, G.R., and Kenner, S.J., 2000, Summary of precipitation data for the Black Hills area of South 

Dakota, water years 1931–98: U.S. Geological Survey 

Open-File Report 00–329, 151 p.

Greene, E.A., 1993, Hydraulic properties of the Madison aquifer system in the western Rapid City area, South Dakota: 

U.S. Geological Survey Water-Resources Investigations 

Report 93–4008, 56 p.

Greene, E.A.,1999, Characterizing recharge to wells in 

carbonate aquifers using environmental and artificially 

recharged tracers, in Morganwalp, D.W., and Buxton, H.T., 

eds., Proceedings of the Technical Meeting, Charleston, 

S.C., March 8–12, 1999, Toxic Substances Hydrology Program: U.S. Geological Survey Water-Resources Investigations Report 99–4018–C, p. 803–808. 

Greene, E.A., and Rahn, P.H., 1995, Localized anisotropic 

transmissivity in a karst aquifer: Ground Water, v. 33, no. 5, 

p. 806–816.

Greene, E.A., Shapiro, A.M., and Carter, J.M., 1998, Hydrologic characterization of the Minnelusa and Madison aquifers near Spearfish, South Dakota: U.S. Geological Survey 

Water-Resources Investigations Report 98–4156, 64 p.

Gries, J.P., 1996, Roadside geology of South Dakota: Missoula, Mont., Mountain Press Publishing Co., 358 p.

Gries, J.P., and Martin, J.E., 1985, Composite outcrop section 

of the Paleozoic and Mesozoic strata in the Black Hills and 

surrounding areas, in Rich, F.J., ed., Geology of the Black 

Hills, South Dakota and Wyoming (2d ed.): Field Trip 

Guidebook for the annual meeting of the Rocky Mountain 

Section of the Geological Society of America, Rapid City, 

S. Dak., April 1981, p. 261–292.

Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, 

M.G., 2000, MODFLOW–2000, The U.S. Geological Survey Modular Ground-Water Model—user guide to modularization concepts and the ground-water flow process: U.S. 

Geological Survey Open-File Report 00–92, 121 p.

Hargrave, R.G., 2005, Vulnerability of the Minnelusa aquifer 

to contamination in the Rapid City West quadrangle, Pennington County, South Dakota: Rapid City, South Dakota 

School of Mines and Technology, unpublished M.S. thesis, 

80 p.
References Cited 65

Hayes, T.S., 1999, Episodic sediment-discharge events in 

Cascade Springs, southern Black Hills, South Dakota: 

U.S. Geological Survey Water-Resources Investigations 

Report 99–4168, 34 p.

Hill, M.C., 1998, Methods and guidelines for effective model 

calibration: U.S. Geological Survey Water-Resources Investigations Report 98–4005, 90 p.

Hill, M.C., Banta, E.R., Harbaugh, A.W., and Anderman, E.R., 

2000, MODFLOW–2000, The U.S. Geological Survey 

Modular Ground-Water Model—user guide to the observation, sensitivity, and parameter-estimation processes and 

three post-processing programs: U.S. Geological Survey 

Open-File Report 00–184, 209 p.

Hortness, J.E., and Driscoll, D.G., 1998, Streamflow losses in 

the Black Hills of western South Dakota: U.S. Geological 

Survey Water-Resources Investigations Report 98–4116, 

99 p.

Kyllonen, D.P., and Peter, K.D., 1987, Geohydrology and 

water quality of the Inyan Kara, Minnelusa, and Madison aquifers of the northern Black Hills, South Dakota 

and Wyoming, and Bear Lodge Mountains, Wyoming: 

U.S. Geological Survey Water-Resources Investigations 

Report 86–4158, 61 p.

Lohman, S.W., and others, 1972, Definitions of selected 

ground-water terms—revisions and conceptual refinements: 

U.S. Geological Survey Water-Supply Paper 1988, 21 p.

Long, A.J., 2000, Modeling techniques for karst aquifers—

anisotropy, dual porosity, and linear systems analysis: 

Rapid City, South Dakota School of Mines and Technology, 

unpublished Ph.D. dissertation, 59 p.

Long, A.J., and Putnam, L.D., 2002, Flow-system analysis of 

the Madison and Minnelusa aquifers in the Rapid City area, 

South Dakota—conceptual model: U.S. Geological Survey 

Water-Resources Investigations Report 02–4185, 100 p., 

3 pls.

Long, A.J., and Putnam, L.D., 2004, Linear model describing 

three components of flow in karst aquifers using 18O data: 

Journal of Hydrology, v. 296, p. 254–270.

Long, A.J., Sawyer, J.F., and Putnam, L.D., 2008, Environmental tracers as indicators of karst conduits in groundwater 

in South Dakota, USA: Hydrogeology Journal, v. 16, no. 2, 

p. 263–280.

McDonald, M.G., and Harbaugh, A.W., 1988, A modular 

three-dimensional finite-difference ground-water flow 

model: U.S. Geological Survey Techniques of WaterResources Investigations, book 6, chap. A1, 600 p.

Miller, S.L, 2005, Influences of geologic structures and stratigraphy on ground-water flow paths in the karstic Madison 

aquifer in the Rapid City area: Rapid City, South Dakota 

School of Mines and Technology, unpublished Ph.D. dissertation, 191 p.

National Oceanic and Atmospheric Administration, 1996, Climatological data annual summary, South Dakota: National 

Oceanic and Atmospheric Administration, v. 101, no. 13, 

ISSN 0364–5045, 31 p.

Peter, K.D., Kyllonen, D.P., and Mills, K.R., 1988, Geologic 

structure and altitude of the top of the Minnelusa Formation, 

northeastern Black Hills, South Dakota: U.S. Geological 

Survey Water-Resources Investigations Report 85–4233, 

1 sheet, scale 1:100,000.

Putnam, L.D., and Long, A.J., 2007, Analysis of ground-water 

flow in the Madison aquifer using fluorescent dyes injected 

in Spring Creek and Rapid Creek near Rapid City, South 

Dakota, 2003–04: U.S. Geological Survey Scientific Investigations Report 2007–5137, 27 p.

Strobel, M.L., Jarrell, G.J., Sawyer, J.F., Schleicher, J.R., and 

Fahrenbach, M.D., 1999, Distribution of hydrogeologic 

units in the Black Hills area, South Dakota: U.S. Geological 

Survey Hydrologic Investigations Atlas HA–743, 3 sheets, 

scale 1:100,000.

U.S. Census Bureau, 2000, United States census 2000: 

accessed August 2008, at http://www.census.gov

Williamson, J.E., and Carter, J.M., 2001, Water-quality 

characteristics in the Black Hills area, South Dakota: 

U.S. Geological Survey Water-Resources Investigations 

Report 01–4194, 196 p.

Supplemental Information
Table 18. Transient streamflow recharge rates for the Minnelusa and Madison hydrogeologic units. [From Long and Putnam (2002). W, winter; S, summer (for example, W–88 = winter, water year 1988); Mnls, Minnelusa hydrogeologic unit; Mdsn, Madislogic unit] Stress period Other stress period identifier Streamflow recharge (cubic feet per second) Elk Creek Little Elk Creek Boxelder Creek Unnamed tributary on Rapid Creek Rap

Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls 

1 W–88 0.0 1.2 0.0 0.4 0.0 4.2 0.0 0.0 2.0 2 S–88 .0 1.5 .2 .4 .0 5.7 .0 .1 2.0 3 W–89 .0 .8 .1 .3 .0 2.8 .0 .0 1.7 4 S–89 .0 1.5 .1 .5 .0 5.3 .0 .0 2.0 5 W–90 .0 1.2 .1 .4 .0 4.3 .0 .0 1.9 6 S–90 .0 2.1 .3 .6 .0 7.7 .0 .1 2.0 7 W–91 .0 .7 .0 .3 .0 2.4 .0 .0 1.8 8 S–91 1.0 3.8 .9 .9 2.7 17.1 .0 .2 2.0 9 W–92 .0 1.9 .2 .7 .0 7.8 .0 .1 2.0 

10 S–92 .1 2.9 .1 .6 .0 6.9 .0 .1 2.0 

11 W–93 .1 1.3 .1 .5 .1 5.0 .0 .0 1.9 

12 S–93 2.3 4.8 1.6 1.1 5.5 25.3 .0 .4 2.0 13 W–94 .7 3.0 .5 .8 .5 11.2 .0 .1 2.0 14 S–94 1.6 4.1 1.1 .9 3.8 19.2 .0 .3 2.0 15 W–95 .2 3.5 .3 .8 .1 9.7 .0 .1 2.0 16 S–95 2.0 4.6 1.6 1.1 6.7 25.5 .1 .5 2.0 17 W–96 .5 4.2 .7 .9 .5 14.1 .0 .1 2.0 18 S–96 3.4 3.4 1.9 1.1 7.6 28.8 .0 .5 2.0 19 W–97 1.9 3.1 1.4 1.0 2.1 21.5 .0 .2 2.0 20 S–97 3.9 3.0 2.1 1.2 12.6 32.3 .1 .7 2.0 

Average .9 2.6 .7 .7 2.1 12.8 .0 .2 2.0 
Table 18. Transient streamflow recharge rates for the Minnelusa and Madison hydrogeologic units.—Continued[From Long and Putnam (2002). W, winter; S, summer (for example, W–88 = winter, water year 1988); Mnls, Minnelusa hydrogeologic unit; Mdsn, Madishydrogeologic unit]

Stress 

period

Other 

stress period 

identifier

Streamflow recharge (cubic feet per second)

Victoria Creek Spring Creek Rockerville Gulch Deadman Gulch Battle Creek Total of a

streams 

Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls Md

1 W–88 0.0 0.1 0.0 1.1 0.0 0.2 0.0 0.1 0.0 0.3 2.0 152 S–88 .0 .2 .0 2.5 .0 .1 .0 .0 .0 .5 2.2 19

3 W–89 .0 .0 .0 .2 .0 .1 .0 .0 .0 .2 1.8 124 S–89 .0 .1 .0 1.8 .0 .1 .0 .0 .0 .7 2.1 18

5 W–90 .0 .1 .0 1.3 .0 .1 .0 .0 .0 1.1 2.0 16

6 S–90 .0 .9 .9 11.2 .0 .4 .0 .2 .0 4.1 3.2 357 W–91 .0 .2 .0 3.1 .0 .1 .0 .1 .0 .8 1.8 15

8 S–91 .0 1.4 1.9 16.8 .2 1.2 .1 .6 .0 4.4 8.8 549 W–92 .0 .4 .0 6.7 .0 .3 .0 .1 .0 1.5 2.2 27

10 S–92 .0 .5 .0 8.2 .0 .3 .0 .1 .0 2.3 2.2 29

11 W–93 .0 .3 .1 4.1 .0 .2 .0 .1 .0 1.1 2.3 20

12 S–93 .0 1.7 2.6 19.9 .1 1.7 .0 .8 .0 5.7 14.1 6913 W–94 .0 .8 .2 11.1 .0 .9 .0 .4 .0 3.3 3.9 3914 S–94 .0 .9 .9 11.0 .0 .5 .0 .2 .0 2.1 9.4 4715 W–95 .0 .5 .1 7.1 .0 .4 .0 .2 .0 2.0 2.7 3216 S–95 .0 1.5 2.1 18.0 .3 2.1 .1 1.1 .0 5.0 14.9 6717 W–96 .0 .9 .1 13.1 .0 1.2 .0 .5 .0 3.1 3.8 4618 S–96 .0 1.7 2.5 20.3 .1 1.7 .0 .8 .0 5.2 17.5 719 W–97 .0 1.4 1.5 18.5 .0 1.6 .0 .7 .0 4.6 8.9 6020 S–97 .0 1.9 3.4 21.0 .2 2.5 .1 1.2 .0 6.0 24.4 77

Average .0 .8 .8 9.9 .0 .8 .0 .4 .0 2.7 6.5 38
Table 19. Transient areal recharge rates for the Minnelusa and Madison hydrogeologic units by zones. [From Long and Putnam (2002). Areal recharge zones shown in figure 14. W, winter; S, summer (for example, W–88 = winter, water year 1988); Mnls, Minnelusunit; Mdsn, Madison hydrogeologic unit] Stress period Other stress period identifier Areal recharge by zones (cubic feet per second) Total ar

(cubic fee

Elk Creek to Little Elk Creek (Zone 1) Little Elk Creek to Boxelder Creek (Zone 2) Boxelder Creek to Rapid Creek (Zone 3) Rapid Creek to Spring Creek (Zone 4) Spring Creek to Battle Creek (Zone 5) Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls Mdsn Mnls M

1 W–88 0.1 0.5 0.1 0.3 0.0 0.3 0.0 0.0 0.0 0.0 0.2 2 S–88 .1 .9 .1 .6 .1 .6 .0 .1 .2 .2 .5 3 W–89 .1 .5 .2 .6 .2 .6 .0 .1 .1 .1 .6 4 S–89 .3 2.4 .9 3.1 1.0 3.1 .8 1.6 1.0 .9 4.0 5 W–90 .2 1.5 .3 1.1 .2 1.1 .1 .1 .2 .2 1.0 6 S–90 .1 .9 .7 2.2 .6 2.2 .5 .8 2.2 2.3 4.1 7 W–91 .1 .8 .2 .6 .1 .6 .0 .1 .1 .1 .5 8 S–91 1.3 7.5 6.4 24.0 4.9 24.0 2.6 5.5 4.3 4.5 19.5 9 W–92 .1 .9 .2 .8 .1 .8 .1 .1 .3 .3 .8 

10 S–92 .2 1.0 .9 3.1 .4 3.1 .2 .4 .6 .5 2.3 

11 W–93 .1 1.1 .2 .7 .1 .7 .0 .1 .1 .1 .5 

12 S–93 1.7 10.0 5.3 19.6 3.5 19.6 2.3 4.0 7.1 6.2 19.9 13 W–94 .2 1.8 .2 .8 .1 .8 .0 .0 .0 .1 .5 14 S–94 .1 .4 .3 .8 .1 .8 .1 .1 .4 .4 1.0 15 W–95 .4 3.1 .6 2.4 .3 2.4 .0 .1 .2 .3 1.5 16 S–95 2.9 18.4 11.6 35.8 4.6 35.8 1.1 2.1 5.5 5.5 25.7 17 W–96 .3 2.8 .5 2.2 .2 2.2 .1 .1 .2 .2 1.3 18 S–96 1.1 4.5 4.4 17.8 2.1 17.8 .9 1.5 3.0 3.0 11.5 19 W–97 .6 2.6 1.2 4.8 .7 4.8 .2 .4 .5 .5 3.2 20 S–97 1.4 5.8 11.6 35.0 5.9 35.0 1.1 1.8 3.3 3.1 23.3 

Average .6 3.4 2.3 7.8 1.3 7.8 .5 1.0 1.5 1.4 6.1 
Supplemental Information 71

Table 20. Observed and simulated hydraulic head values for the Minnelusa hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Observed hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME)2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series 

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Observed 

hydraulic 

head

 (feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

 Difference 

between 

simlated 

and 

observed 

hydraulic 

head 

(feet)

Implied 

accuracy of 

hydraulic 

head

(feet)

Station 

identification 

number

Other 

identifier Layer Row Column

102 1 2 89 3,454 3,486 32 10 441812103230501 --

103 1 1 75 3,564 3,574 10 10 441826103263301 --

104 1 1 70 3,610 3,602 -8 1 441759103261201 TF–1

105 1 5 74 3,515 3,573 58 10 441701103251101 PDMT-East

106 1 4 65 3,592 3,653 61 10 441656103261601 --

107 1 4 65 3,593 3,652 59 10 441649103262401 --

108 1 6 65 3,529 3,624 95 10 441620103255301 --

109 1 7 68 3,532 3,591 59 10 441612103252801 --

110 1 8 68 3,557 3,586 29 10 441606103252501 --

111 1 8 66 3,514 3,591 77 10 441556103253201 --

112 1 13 79 3,428 3,486 58 10 441504103230301 --

113 1 13 74 3,422 3,524 102 10 441500103240601 --

114 1 13 69 3,486 3,563 77 10 441453103243801 --

115 1 12 66 3,527 3,582 55 10 442221103245501 --

116 1 16 83 3,412 3,458 46 10 441314103233301 --

117 1 14 67 3,506 3,583 77 10 441424103243601 --

118 1 15 68 3,510 3,576 66 10 441421103242302 --

119 1 17 79 3,478 3,491 13 10 441400103231501 --

120 1 16 67 3,526 3,594 68 10 441358103241801 --

121 1 18 73 3,490 3,547 57 10 441643103232801 --

122 1 18 73 3,530 3,550 20 10 441339103232701 --

123 1 18 72 3,528 3,557 29 10 441338103233201 --

124 1 19 78 3,481 3,508 27 1 441337103225001 PDMT–1

125 1 19 80 3,414 3,487 73 10 441335103223202 --

126 1 19 80 3,414 3,487 73 10 441335103223201 --

127 1 19 81 3,457 3,483 26 10 441333103222801 --

128 1 19 75 3,454 3,531 77 10 441331103230701 --

129 2 19 69 3,547 3,690 143 10 441322103234202 --

130 2 19 69 3,581 3,669 88 10 441322103234201 --

131 1 20 78 3,489 3,497 8 10 441315103224001 --

132 1 21 78 3,458 3,492 34 10 441257103222501 --

133 1 26 109 3,268 3,278 10 10 441241103183401 --

134 1 25 89 3,414 3,418 4 10 441219103204801 --

135 1 24 79 3,495 3,499 4 10 441242103215701 --

136 1 24 79 3,477 3,499 22 10 441216103215801 --
72 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Table 20. Observed and simulated hydraulic head values for the Minnelusa hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Observed hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME)2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series 

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Observed 

hydraulic 

head

 (feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

 Difference 

between 

simlated 

and 

observed 

hydraulic 

head 

(feet)

Implied 

accuracy of 

hydraulic 

head

(feet)

Station 

identification 

number

Other 

identifier Layer Row Column

137 1 25 81 3,483 3,488 5 10 441210103215101 --

138 1 26 93 3,366 3,393 27 10 441212103201501 --

139 1 25 81 3,458 3,483 25 10 441211103213701 --

140 1 25 84 3,476 3,462 -14 10 441202103211301 --

141 1 26 90 3,449 3,412 -37 10 441318103221301 --

142 1 25 81 3,444 3,489 45 10 442137103213801 --

143 1 25 81 3,474 3,485 11 10 441202103213301 --

144 1 26 81 3,471 3,483 12 10 441200103213001 --

145 1 26 84 3,445 3,465 20 10 441157103213701 --

146 1 26 80 3,451 3,490 39 10 441220103214001 --

147 1 26 82 3,459 3,479 20 10 441151103213002 --

148 1 29 95 3,413 3,388 -25 10 441147103270001 --

149 2 27 80 3,415 3,581 166 10 441136103221301 --

150 1 27 81 3,460 3,485 25 10 441134103211601 --

151 1 29 91 3,418 3,416 -2 10 441131103200101 --

152 1 28 84 3,466 3,467 1 10 441130103205601 --

153 1 28 82 3,453 3,480 27 10 441119103210301 --

154 1 31 95 3,454 3,398 -56 10 441105103192001 --

155 1 30 86 3,413 3,462 49 10 441125103203001 --

156 1 30 83 3,403 3,482 79 10 441038103203001 --

157 1 31 83 3,423 3,479 56 10 441049103203701 --

158 1 31 84 3,423 3,474 51 10 441047103203301 --

159 2 31 82 3,496 3,588 92 10 441323103232301 --

160 1 31 83 3,438 3,477 39 10 441040103203201 --

161 1 31 83 3,492 3,476 -16 10 441038103203002 --

162 2 31 83 3,472 3,583 111 10 441037103203502 --

163 2 31 83 3,450 3,583 133 10 441037103203501 --

164 1 33 91 3,463 3,433 -30 10 441033103193001 --

165 1 32 88 3,443 3,449 6 10 441031103195201 --

166 1 32 85 3,487 3,464 -23 10 441024103201301 --

167 2 32 81 3,474 3,604 130 10 441023103204001 --

168 2 32 82 3,440 3,593 153 10 441023103203101 --

169 2 32 82 3,423 3,590 167 10 441023103203001 --

170 1 33 84 3,432 3,474 42 10 441007103201101 --

171 1 39 100 3,489 3,439 -50 10 440930103175201 --
Supplemental Information 73

Table 20. Observed and simulated hydraulic head values for the Minnelusa hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Observed hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME)2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series 

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Observed 

hydraulic 

head

 (feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

 Difference 

between 

simlated 

and 

observed 

hydraulic 

head 

(feet)

Implied 

accuracy of 

hydraulic 

head

(feet)

Station 

identification 

number

Other 

identifier Layer Row Column

172 1 37 87 3,447 3,460 13 10 440936103191801 Blackhawk 

Water Co. 

No. 3

173 1 42 106 3,416 3,402 -14 10 440919103170501 --

174 1 44 110 3,379 3,372 -7 10 440929103163501 --

175 1 45 110 3,392 3,379 -13 10 440916103163301 --

176 1 40 92 3,386 3,457 71 10 440907103183501 Blackhawk 

Water Co. 

No. 2

177 1 38 83 3,462 3,467 5 10 440908103193101 --

178 1 40 90 3,403 3,460 57 10 440901103184801 Blackhawk 

Water Co. 

No. 1

179 1 47 89 3,414 3,461 47 10 440829103183801 --

180 1 50 96 3,410 3,450 40 10 440826103174601 --

181 1 50 92 3,422 3,456 34 1 440818103180801 BLHK–1

182 1 50 91 3,449 3,457 8 10 440818103174701 --

183 1 59 104 3,313 3,430 117 10 440800103163001 --

184 1 60 93 3,409 3,450 41 10 440738103173901 --

185 1 60 93 3,412 3,450 38 10 440736103173701 --

186 1 63 90 3,434 3,453 19 10 440719103174801 --

187 1 79 107 3,400 3,385 -15 10 440636103152001 --

188 1 77 99 3,420 3,418 -2 10 440635103161801 --

189 1 82 102 3,383 3,399 16 10 440607103155901 --

190 1 77 85 3,419 3,445 26 10 440606103174701 --

191 1 77 86 3,419 3,442 23 10 440605103174701 --

192 1 77 84 3,421 3,445 24 10 440552103173401 --

193 1 77 85 3,427 3,443 16 10 440603103174501 --

194 1 82 95 3,336 3,412 76 10 440552103162301 --

195 1 79 85 3,414 3,441 27 10 440557103174401 --

196 1 79 84 3,449 3,443 -6 10 440556103174801 --

197 1 80 87 3,410 3,433 23 10 440542103172501 --

198 1 80 85 3,443 3,437 -6 10 440639103173701 --

199 1 81 85 3,438 3,434 -4 10 440545103173501 --

200 1 80 81 3,450 3,448 -2 1 440544103180001 CQ–1

201 1 81 84 3,444 3,437 -7 10 440544103174301 --
74 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Table 20. Observed and simulated hydraulic head values for the Minnelusa hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Observed hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME)2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series 

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Observed 

hydraulic 

head

 (feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

 Difference 

between 

simlated 

and 

observed 

hydraulic 

head 

(feet)

Implied 

accuracy of 

hydraulic 

head

(feet)

Station 

identification 

number

Other 

identifier Layer Row Column

202 1 82 85 3,468 3,434 -34 10 440544103173601 --

205 1 87 96 3,328 3,395 67 10 440538103161001 --

206 1 83 82 3,467 3,435 -32 10 440534103174801 --

207 1 85 87 3,450 3,421 -29 10 440534103171401 --

209 1 89 95 3,412 3,396 -16 1 440528103161001 CP

210 1 90 98 3,406 3,391 -15 10 440528103155201 --

211 1 82 74 3,471 3,442 -29 10 440521103184401 --

212 1 85 78 3,462 3,428 -34 10 440532103182001 --

213 1 92 94 3,403 3,393 -10 10 440514103161401 --

214 1 85 76 3,434 3,430 -4 10 450512103182101 --

215 2 83 65 3,406 3,478 72 10 440516103194001 WT–1

216 1 88 76 3,475 3,422 -53 10 440501103181501 --

217 1 88 77 3,450 3,419 -31 10 440459103181001 --

218 1 88 76 3,450 3,419 -31 10 440458103181101 --

219 1 97 95 3,396 3,383 -13 10 440452103155301 South Dakota 

ARNG

220 1 90 75 3,435 3,415 -20 10 440449103181501 --

221 1 90 75 3,415 3,414 -1 10 440446103181801 --

222 1 91 75 3,470 3,413 -57 10 440445103181601 --

223 1 101 92 3,392 3,375 -17 1 440430103160201 SP–1

224 1 95 74 3,400 3,399 -1 1 440423103180501 WCR–3

225 1 97 69 3,382 3,400 18 10 440403103183701 --

226 2 99 64 3,435 3,451 16 10 440347103190501 --

227 2 99 63 3,456 3,452 -4 10 440344103190801 --

228 1 104 75 3,360 3,373 13 10 440344103173701 --

229 1 106 75 3,360 3,369 9 1 440338103173301 CL–1

230 1 113 89 3,396 3,363 -33 10 440331103155101 --

231 1 106 70 3,395 3,384 -11 5 440326103180703 JS–1B

232 1 107 69 3,365 3,385 20 10 440321103181001 --

233 1 110 72 3,383 3,378 -5 1 440310103173801 CHLN–1

234 1 113 78 3,360 3,376 16 10 440309103170101 --

235 2 108 65 3,435 3,461 26 10 440308103183001 --

236 1 112 74 3,378 3,377 -1 10 440308103172501 --

237 1 121 97 3,353 3,325 -28 10 440308103144301 --

238 1 112 74 3,353 3,378 25 10 440336103165301 --
Supplemental Information 75

Table 20. Observed and simulated hydraulic head values for the Minnelusa hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Observed hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME)2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series 

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Observed 

hydraulic 

head

 (feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

 Difference 

between 

simlated 

and 

observed 

hydraulic 

head 

(feet)

Implied 

accuracy of 

hydraulic 

head

(feet)

Station 

identification 

number

Other 

identifier Layer Row Column

239 1 109 67 3,399 3,389 -10 10 440307103181501 --

240 1 114 78 3,364 3,377 13 10 440305103164501 --

241 1 115 78 3,370 3,377 7 10 440211103165601 --

242 1 115 78 3,350 3,378 28 10 440301103165701 --

243 1 114 76 3,380 3,378 -2 10 440300103170901 --

244 1 115 75 3,355 3,379 24 10 440257103171101 --

245 1 115 74 3,336 3,381 45 10 440252103172201 --

246 2 112 65 3,450 3,467 17 10 440249103182101 --

247 1 117 75 3,342 3,381 39 10 440247103165401 --

248 1 118 75 3,386 3,382 -4 10 440242103170801 --

249 1 121 82 3,374 3,378 4 10 440244103154102 --

250 1 126 92 3,351 3,341 -10 10 440236103145801 --

251 1 120 74 3,387 3,384 -3 10 440233103170501 --

252 1 123 81 3,381 3,381 0 5 440223103161701 Springbrook 

West Well 

No. 2

253 2 120 71 3,372 3,439 67 10 440224103172601 Carriage Hills 

No. 2

254 1 126 86 3,388 3,368 -20 5 440214103153501 Springbrook 

East Well

255 1 124 73 3,401 3,388 -13 10 440211103165201 --

256 1 125 76 3,409 3,387 -22 10 440211103164301 --

257 1 132 89 3,392 3,348 -44 10 440204103150001 --

258 1 134 93 3,390 3,335 -55 10 440203103143601 --

259 1 131 80 3,429 3,390 -39 5 440158103160401 Springbrook 

South 

No. 3

260 1 129 73 3,412 3,406 -6 1 440149103164901 Wildwood 

North

261 1 134 73 3,429 3,423 -6 5 440130103163401 Wildwood 

South

262 1 144 86 3,376 3,360 -16 10 440103103144801 --

263 1 145 82 3,456 3,396 -60 10 440059103154101 --

264 1 147 85 3,455 3,377 -78 10 440048103145001 --

265 1 141 63 3,475 3,485 10 10 440038103172601 --

266 1 145 70 3,459 3,469 10 10 440031103162701 --
76 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Table 20. Observed and simulated hydraulic head values for the Minnelusa hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Observed hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME)2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series 

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Observed 

hydraulic 

head

 (feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

 Difference 

between 

simlated 

and 

observed 

hydraulic 

head 

(feet)

Implied 

accuracy of 

hydraulic 

head

(feet)

Station 

identification 

number

Other 

identifier Layer Row Column

267 1 147 73 3,412 3,458 46 10 440028103160801 --

268 1 147 72 3,499 3,460 -39 10 440027103161001 --

269 1 146 69 3,494 3,478 -16 10 440022103163401 --

270 1 148 69 3,455 3,480 25 10 440007103165301 --

271 1 152 75 3,404 3,448 44 10 440010103154201 --

272 1 160 65 3,493 3,473 -20 1 435916103161802 RG–2

273 1 164 67 3,476 3,466 -10 10 435858103155701 --

274 1 175 62 3,539 3,449 -90 10 435803103160301 --

275 1 177 58 3,548 3,447 -101 10 445809103162201 --

276 1 183 75 3,547 3,414 -133 10 435720103141601 Hart Ranch 

No. 3

277 1 193 36 3,558 3,456 -102 10 435352103170801 --

278 2 196 27 3,527 3,514 -13 10 435325103171701 --

279 1 199 25 3,551 3,467 -84 10 435225103172801 --

280 1 203 17 3,536 3,504 -32 10 435119103175001 --
Supplemental Information 77

Table 21. Observed and simulated hydraulic head values for the Madison hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Estimated hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Estimated 

hydraulic 

head

(feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

Difference 

between 

simulated 

and observed 

hydraulic head 

(feet)

Implied 

accuracy 

of 

hydraulic 

head 

(feet)

Station 

identification 

number

Other

identifier Layer Row Column

1 3 1 70 3,621 3,684 63 1 441759103261202 TF–2

2 3 12 60 3,655 3,740 85 10 441500103253501 --

3 3 19 78 3,603 3,535 -68 1 441337103225002 PDMT–2

4 3 24 82 3,494 3,534 40 10 441220103213601 --

5 4 24 63 3,854 3,902 48 10 441157103234301 --

6 4 30 37 4,340 4,185 -155 10 440958103253401 --

7 4 30 39 4,280 4,160 -120 10 440934103252001 --

8 4 30 40 4,280 4,135 -145 10 440933103250701 --

9 3 40 92 3,511 3,480 -31 10 441636103183801 Black Hawk 

Water Co. 

No. 4

10 3 86 163 2,687 2,656 -31 10 440851103044801 Ellsworth 

AFB

11 3 37 57 3,895 3,839 -56 10 440828103222601 --

12 3 50 96 3,450 3,471 21 10 440826103174701 --

13 3 55 106 3,448 3,448 0 10 440823103162701 --

14 4 37 49 3,981 3,944 -37 10 440820103232601 --

15 3 39 57 3,808 3,813 5 1 440811103222201 DOTY

16 3 38 51 3,973 3,887 -86 10 440807103225801 --

17 3 38 50 3,976 3,900 -76 10 440804103230501 --

18 3 40 55 3,874 3,827 -47 10 440804103223001 --

19 3 40 56 3,774 3,809 35 10 440804103222701 --

21 4 39 51 3,913 3,873 -40 10 440758103225601 --

22 4 39 47 3,980 3,899 -81 10 440753103232401 --

23 3 42 56 3,772 3,784 12 10 440749103221501 --

24 4 42 53 3,876 3,815 -61 10 440744103223401 --

25 3 53 58 3,660 3,698 38 10 440658103213001 --

26 3 79 119 3,423 3,414 -9 10 440655103140501 RC–8

27 3 63 74 3,528 3,529 1 10 440650103193201 --

28 3 61 59 3,645 3,634 -11 10 440631103211201 --

29 3 67 73 3,536 3,521 -15 10 440630103192501 --

30 3 117 163 2,575 2,564 -11 10 440629103040901 City of Box 

Elder

31 3 81 105 3,481 3,415 -66 10 440622103152701 Coke Plant

32 3 84 105 3,444 3,408 -36 10 440612103152001 RC–10

33 3 80 81 3,451 3,454 3 1 440544103180002 CQ–2
78 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Table 21. Observed and simulated hydraulic head values for the Madison hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Estimated hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Estimated 

hydraulic 

head

(feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

Difference 

between 

simulated 

and observed 

hydraulic head 

(feet)

Implied 

accuracy 

of 

hydraulic 

head 

(feet)

Station 

identification 

number

Other

identifier Layer Row Column

34 3 70 55 3,646 3,581 -65 10 440540103211301 --

35 3 85 84 3,447 3,425 -22 10 440526103173001 RC–6

36 3 91 97 3,424 3,404 -20 10 440523103155701 BHPL

37 3 80 67 3,477 3,509 32 10 440518103193001 --

38 4 73 46 3,734 3,694 -40 10 440512103215701 --

39 4 73 45 3,764 3,716 -48 10 440508103220701 --

40 3 83 63 3,520 3,513 -7 10 440500103193601 WT–2

41 3 88 72 3,405 3,432 27 10 440453103184001 --

42 3 86 64 3,430 3,468 38 10 440446103193201 --

43 3 97 91 3,417 3,402 -15 10 440446103161701 LC

44 3 87 64 3,428 3,456 28 10 440441103193301 --

45 3 90 66 3,405 3,417 12 10 440432103191401 --

46 3 101 91 3,423 3,401 -22 1 440430103160202 SP–2

47 3 110 114 3,146 3,198 52 1 440427103131701 RC–7

48 3 99 62 3,418 3,416 -2 10 440337103191801 --

49 3 110 87 3,415 3,396 -19 10 440342103160701 RC–9

50 3 106 75 3,418 3,405 -13 1 440338103173302 CL–2

51 3 132 138 2,655 2,584 -71 10 440334103095601 Rapid Valley 

No. 4, 

RV–4

52 3 106 70 3,418 3,402 -16 1 440326103180702 JS–1A

53 3 110 73 3,418 3,406 -12 10 440310103173802 CHLN–3

54 3 107 63 3,417 3,415 -2 1 440308103184601 CLEGmdsn

55 3 110 69 3,419 3,405 -14 10 440308103180701 --
Supplemental Information 79

Table 21. Observed and simulated hydraulic head values for the Madison hydrogeologic unit in steady-state simulation.—Continued

[Observation name corresponds to site number in table 29 and plate 2 of Long and Putnam (2002). Estimated hydraulic head from Long and Putnam (2002). 

Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 

1/(SDME2) (Hill and others, 2000). Implied accuracy for sites with a single measurement was assigned a value of 10. Implied accuracy for sites with time-series

measurements was assigned a value of 1. Implied accuracy for sites with multiple measurements was assigned a value of 5. Other identifier used in Long and 

Putnam (2002). NGVD 29, National Geodetic Vertical Datum of 1929; --, none]

Observation 

name 

and 

site number

Model cell location

Estimated 

hydraulic 

head

(feet above 

NGVD 29)

Simulated 

hydraulic 

head

(feet above 

NGVD 29)

Difference 

between 

simulated 

and observed 

hydraulic head 

(feet)

Implied 

accuracy 

of 

hydraulic 

head 

(feet)

Station 

identification 

number

Other

identifier Layer Row Column

56 3 112 72 3,419 3,408 -11 10 440300103173501 CHLN–2

57 3 108 61 3,415 3,419 4 10 440247103192401 --

58 3 107 56 3,438 3,427 -11 10 440302103194601 --

59 3 110 57 3,434 3,426 -8 10 440247103191701 --

60 3 113 60 3,416 3,422 6 10 440238103185201 --

61 3 120 70 3,426 3,420 -6 10 440223103173201 Carriage 

Hills 

No. 1, CH

62 3 124 77 3,423 3,422 -1 10 440220103164001 RC–11

63 3 124 70 3,445 3,426 -19 10 440205103172001 --

64 3 137 62 3,475 3,463 -12 10 440054103173801 --

65 4 137 43 3,806 3,626 -180 10 440523103194201 --

66 3 146 58 3,531 3,543 12 10 440004103174001 HH

67 4 148 48 3,626 3,639 13 10 435937103184101 --

68 3 160 65 3,497 3,511 14 1 435916103161801 RG

69 4 156 49 3,594 3,617 23 10 435903103181301 --

70 4 157 44 3,580 3,639 59 10 435851103184201 --

71 3 170 77 3,498 3,476 -22 10 435851103143501 HR–2

72 3 176 55 3,488 3,514 26 10 435746103160601 --

73 3 187 84 3,498 3,375 -123 10 435718103130301 HR–1

74 3 183 38 3,515 3,552 37 10 435635103181401 PG

75 3 187 52 3,509 3,481 -28 10 435619103161901 --

76 3 189 38 3,530 3,509 -21 10 435518103173001 --

77 3 198 13 3,542 3,620 78 10 435227103185301 HWRD
80 Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, S. Dak.

Table 22. Supplemental interpolated hydraulic head values for the Minnelusa and Madison hydrogeologic units in steady-state 

simulation.—Continued

[Interpolated hydraulic head from estimated potentiometric contours in Long and Putnam (2002, plates 1 and 2). Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 1/(SDME)2

 (Hill and others, 2000). The SDME or 

implied accuracy for these supplemental sites was set at 10 feet. NGVD 29, National Geodetic Vertical Datum of 1929]

Observation 

name

Model cell location

Interpolated 

hydraulic head

(feet above 

NGVD 29)

Simulated 

hydraulic head

(feet above 

NGVD 29)

Difference 

between 

simulated and 

interpolated 

hydraulic head 

(feet)

Implied 

accuracy of 

hydraulic head 

(feet) Layer Row Column

Minnelusa hydrogeologic unit

801 1 17 162 3,020 3,001 -19 10

802 1 11 102 3,315 3,382 67 10

803 1 21 152 3,160 3,131 -29 10

804 1 34 128 3,266 3,197 -69 10

805 1 34 164 2,880 2,849 -31 10

806 1 69 156 3,070 3,010 -60 10

807 1 176 133 3,100 3,094 -6 10

808 1 193 163 2,780 2,816 36 10

809 1 193 139 3,130 3,043 -87 10

810 1 195 90 3,430 3,269 -161 10

811 1 122 126 3,150 3,184 34 10

812 1 76 161 2,900 2,890 -10 10

813 1 184 157 2,900 2,927 27 10

814 1 128 159 2,800 2,903 103 10

815 1 139 115 3,200 3,225 25 10

816 1 212 157 3,105 2,953 -152 10

817 1 104 124 3,200 3,227 27 10

818 1 127 154 2,900 3,006 106 10

819 1 122 142 3,000 3,093 93 10

820 1 162 141 3,000 3,063 63 10
Supplemental Information 81

Table 22. Supplemental interpolated hydraulic head values for the Minnelusa and Madison hydrogeologic units in steady-state 

simulation.—Continued

[Interpolated hydraulic head from estimated potentiometric contours in Long and Putnam (2002, plates 1 and 2). Implied accuracy is standard deviation of measurement error (SDME), which is used in the parameter estimation process to weight observations (weight = 1/(SDME)2

 (Hill and others, 2000). The SDME or 

implied accuracy for these supplemental sites was set at 10 feet. NGVD 29, National Geodetic Vertical Datum of 1929]

Observation 

name

Model cell location

Interpolated 

hydraulic head

(feet above 

NGVD 29)

Simulated 

hydraulic head

(feet above 

NGVD 29)

Difference 

between 

simulated and 

interpolated 

hydraulic head 

(feet)

Implied 

accuracy of 

hydraulic head 

(feet) Layer Row Column

Madison hydrogeologic unit

901 3 17 162 3,010 2,989 -21 10

902 3 11 102 3,300 3,399 99 10

903 3 21 152 3,100 3,126 26 10

904 3 34 128 3,200 3,208 8 10

905 3 34 164 2,880 2,792 -88 10

906 3 69 156 3,050 2,822 -228 10

907 3 176 133 2,900 2,854 -46 10

908 3 193 163 2,775 2,708 -67 10

909 3 193 139 3,090 2,973 -117 10

910 3 195 90 3,400 3,266 -134 10

911 3 122 126 2,910 2,914 4 10

912 3 76 161 2,880 2,724 -156 10

913 3 184 157 2,710 2,700 -10 10

914 3 128 159 2,570 2,588 18 10

915 3 139 115 3,020 3,038 18 10

916 3 212 157 3,100 2,897 -203 10

917 3 104 124 3,100 3,127 27 10

918 3 127 154 2,600 2,604 4 10

919 3 122 142 2,700 2,623 -77 10

920 3 162 141 2,700 2,648 -52 10
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1608 Mt. View Rd.

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(605) 394–3200

Or visit the South Dakota Water Science Center Web site at:

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Putnam and Long—Numerical Groundwater-Flow Model of the Minnelusa and Madison Hydrogeologic Units, Rapid City Area, South Dakota—SIR 2009–5205