Prepared in cooperation with the City of Carrollton, Kentucky

Evaluation of the Groundwater-Flow Model for the 

Ohio River Alluvial Aquifer near Carrollton, Kentucky, 

Updated to Conditions in September 2010 

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2013–5032
Cover photo. Domestic well used for measuring groundwater levels near Carrollton, Kentucky 

(Michael D. Unthank, U.S. Geological Survey).
Evaluation of the Groundwater-Flow Model 

for the Ohio River Alluvial Aquifer near 

Carrollton, Kentucky, 

Updated to Conditions in September 2010 

By Michael D. Unthank

Prepared in cooperation with the City of Carrollton, Kentucky

Scientific Investigations Report 2013–5032

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: 2013

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Unthank, M.D., 2013, Evaluation of the groundwater-flow model for the Ohio River alluvial aquifer near Carrollton, 

Kentucky, updated to conditions in September 2010: U.S. Geological Survey Scientific Investigations Report 

2013–5032, 14 p.
iii

Contents

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

Introduction.....................................................................................................................................................1

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

Description of the Study Area ............................................................................................................2

Groundwater Hydrology.......................................................................................................................2

Description of the Model..............................................................................................................................2

Update of the Model to Conditions in September 2010 ...........................................................................6

Performance of the Updated Model...........................................................................................................6

Limitations, Potential Revisions, and New Data to Improve the Updated Model .............................12

Summary........................................................................................................................................................12

References Cited..........................................................................................................................................14

Figures

1. Map showing location of study area and extent of the Ohio River 

alluvial aquifer near Carrollton, Ky.............................................................................................3

2. Graph showing the Ohio River stage for October 2009 through September 2010 

at Markland Dam near Warsaw, Ky., U.S. Geological Survey (USGS) 

streamflow-gaging station 03277200 .........................................................................................4

3. Map showing the extent of finite-difference model grid near Carrollton, Ky.....................5

4. Map showing locations and amounts of groundwater 

pumpage near Carrollton, Ky. .....................................................................................................7

5. Map showing observation well network near Carrollton, Ky................................................8

6. Map showing simulated altitude of potentiometric surface of the 

alluvial aquifer near Carrollton, Ky., September 2010...........................................................11

7. Map showing difference between observed water levels and simulated water

 levels near Carrollton, Ky..........................................................................................................13

Tables

1. Groundwater withdrawals for public water-supply and industrialsupply wells, Carrollton, Ky., September 2010. ........................................................................6

2. Observed and simulated water levels and differences for observation 

wells near Carrollton, Ky..............................................................................................................9

3. Volumetric water budget comparison for 1995 model and 2010 model.............................10
iv

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in) 2.54 centimeter (cm)

inch (in) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2

) 2.590 square kilometer (km2) 

Volume

million gallons (Mgal) 3,785 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)

cubic foot per day (ft3

/d) 0.02832 cubic meter per day (m3/d)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3

/s)

Hydraulic conductivity

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

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in)

millimeter (mm) 0.03937 inch (in)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2

) 0.3861 square mile (mi2)

Hydraulic conductivity

meter per day (m/d) 3.281 foot per day (ft/d) 

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD 

of 1929)-a geodetic datum derived from a general adjustment of the first-order level nets of both the 

United States and Canada, formerly called Sea Level Datum of 1929.

Abbreviations

USGS U.S. Geological Survey

RMSE Root Mean Square Error
Evaluation of the Groundwater-Flow Model for the 

Ohio River Alluvial Aquifer near Carrollton, Kentucky, 

Updated to Conditions in September 2010 

By Michael D. Unthank 

Abstract 

 The Ohio River alluvial aquifer near Carrollton, Ky., 

is an important water resource for the cities of Carrollton 

and Ghent, as well as for several industries in the area. The 

groundwater of the aquifer is the primary source of drinking water in the region and a highly valued natural resource 

that attracts various water-dependent industries because of its 

quantity and quality. This report evaluates the performance 

of a numerical model of the groundwater-flow system in the 

Ohio River alluvial aquifer near Carrollton, Ky., published by 

the U.S. Geological Survey in 1999. The original model simulated conditions in November 1995 and was updated to simulate groundwater conditions estimated for September 2010. 

The files from the calibrated steady-state model 

of November 1995 conditions were imported into 

MODFLOW-2005 to update the model to conditions in 

September 2010. The model input files modified as part of 

this update were the well and recharge files. The design of 

the updated model and other input files are the same as the 

original model. The ability of the updated model to match 

hydrologic conditions for September 2010 was evaluated by 

comparing water levels measured in wells to those computed 

by the model. Water-level measurements were available for 

48 wells in September 2010. Overall, the updated model 

underestimated the water levels at 36 of the 48 measured 

wells. The average difference between measured water levels 

and model-computed water levels was 3.4 feet and the maximum difference was 10.9 feet. The root-mean-square error of 

the simulation was 4.45 for all 48 measured water levels. 

The updated steady-state model could be improved 

by introducing more accurate and site-specific estimates 

of selected field parameters, refined model geometry, and 

additional numerical methods. Collection of field data to 

better estimate hydraulic parameters, together with continued review of available data and information from area well 

operators, could provide the model with revised estimates of 

conductance values for the riverbed and valley wall, hydraulic conductivities for the model layer, and target water levels 

for future simulations. Additional model layers, a redesigned 

model grid, and revised boundary conditions could provide a 

better framework for more accurate simulations. Additional 

numerical methods would identify possible parameter estimates and determine parameter sensitivities.

Introduction

The Ohio River alluvial aquifer near Carrollton, Ky., is an 

important water resource for the cities of Carrollton and Ghent 

and several local industries. The aquifer is the primary source 

of drinking water in the region and a highly valued natural 

resource that attracts various water-dependent industries 

because of its quantity and quality. In 1999, the U.S. Geological Survey (USGS), in cooperation with the Carroll County 

Water-Supply Board, published the results of an investigation 

to characterize the hydrogeology of the Ohio River alluvial 

aquifer beneath Carrollton and the surrounding area. That 

investigation included the development of a groundwater-flow 

model that has been used to provide local water-resources 

managers with the information and simulation capabilities 

necessary to help manage and protect the area’s groundwater 

resources (Unthank, 1999). Since 1995, the groundwater-flow 

model has been used numerous times to study the possible 

effects of groundwater withdrawals from proposed new industries to the area and changes in withdrawals from groundwater 

users. However, an updated model for more recent (2010) 

conditions is not available to the public. 

In 2010, the USGS began a 2-year study of the groundwater resources in the Ohio River alluvial aquifer near Carrollton in cooperation with the City of Carrollton and a coalition 

of local water utilities and private industries. The principal 

objective of this study was to update the model to 2010 conditions. Because changes in withdrawals are the most significant 

changes to the modeled area and they are relatively small 

and not near the boundaries of the model, the original model 

should be appropriate to simulate these changes. The original 

calibrated steady-state model (Unthank, 1999) was updated 

and evaluated as part of this study to determine how well it 

simulated the period of steady-state conditions observed in 

September 2010. 
2

Evaluation of the Carrollton Groundwater-Flow Model, Updated to Conditions in September 2010

Purpose and Scope

This report evaluates the performance of an updated 

numerical model of the groundwater-flow system in the Ohio 

River alluvial aquifer near Carrollton, Ky., that originally 

simulated conditions in November 1995, in simulating groundwater conditions estimated for September 2010. An updated 

estimate of recharge to the groundwater-flow system from precipitation and revised groundwater discharges from production 

wells in the area were added to the original groundwater-flow 

model. The ability of the updated groundwater-flow model to 

match hydrologic conditions observed in September 2010 was 

evaluated by comparing measured water levels in a network of 

observation wells to those computed by the model. 

A numerical simulation model of the groundwater-flow 

system is a quick yet thorough tool that can be used as afor 

water-use and environmental-planning decisions. As new data 

and information become available, testing the performance of 

the model against those data will result in a better understanding of the model and the groundwater-flow system (Konikow 

and Bredehoeft, 1992). As the demands on groundwater 

resources of the study area continue to increase, the updated 

model can help water-resources managers to evaluate the 

effects on the groundwater-flow system from potential land 

development and industrial growth and expansion, changes in 

groundwater withdrawals, and long-term changes in precipitation and other forms of recharge.

Description of the Study Area

The study area spans parts of Carroll and Gallatin Counties in north central Kentucky (fig. 1). It consists of approximately 20 square miles (mi2

) of the Ohio River valley extending from the Kentucky River at Carrollton northeast to the 

Markland Locks and Dam near Warsaw, Ky. The study area 

is approximately 15 miles (mi) long and ranges in width from 

about 1.5 mi near Ghent to about 3 mi at Carrollton. The study 

area is bounded on the northwest by the Ohio River and on the 

southeast by steep bedrock valley walls. Land surface altitude 

in the study area ranges from 420 to 490 feet (ft) above sea 

level in the valley to slightly more than 800 ft above sea level 

atop the valley walls. Soils in the area are mostly silt and 

clay. Normal pool stage of the Ohio River and the Kentucky 

River in the study area is approximately 422 ft above sea level 

(fig. 2). Most of the area has been cleared for industrial use, 

but areas of agriculture are interspersed with institutional, 

recreational, and residential areas.

The population of Carrollton was 3,938 in 2010; 

Carroll County had a population of 10,811 while Gallatin 

County had a population of 8,589 (U.S. Census Bureau, 2010). 

The climate is temperate and the total precipitation from 

September 2009 through August 2010 was 40.66 inches (in) 

(National Oceanic and Atmospheric Administration Climate 

Summary available at http://www.wrcc.dri.edu/cgi-bin/

cliMAIN.pl?ky8446). The daily mean discharge of the Ohio 

River at Markland Dam (USGS station number 03277200) 

from September 2009 through August 2010 was 103,300 

cubic feet per second (ft3

/s), (http://waterdata.usgs.gov/

ky/nwis/annual/?search_site_no=03277200&agency_

cd=USGS&referred_module=sw&format=sites_selection_

links).

Groundwater Hydrology

Under natural conditions, regional groundwater flow 

in the alluvial aquifer is predominately horizontal, from 

the alluvium/bedrock boundary at the valley wall towards 

the Ohio River. This flow pattern is interrupted by cones of 

depression in the potentiometric surface formed in areas of 

large groundwater withdrawals. Water-level measurements and 

lithologic data indicate the alluvial aquifer to be unconfined 

(Unthank, 1999).

Recharge to the alluvial aquifer is from vertical infiltration of precipitation, flow from the valley wall, and infiltration 

from the Ohio River and smaller streams. Natural infiltration 

of water from the Ohio River to the alluvial aquifer may occur 

during periods of high river stage. Flood pulses originating 

from the Ohio River can reverse the groundwater gradients, 

thus recharging water back into the aquifer. Additional 

recharge to the alluvial aquifer occurs when pumping at 

groundwater production wells adjacent to the Ohio River and 

smaller streams lowers the water table below the stage of the 

streams, thus inducing recharge of surface water to the aquifer.

Discharge from the alluvial aquifer is by flow to the 

Ohio River and to pumped wells.

Description of the Model

The USGS developed a numerical flow model in 

1998 to simulate the groundwater-flow system of the Ohio 

River alluvial aquifer near Carrollton, Ky. (Unthank, 1999). 

The modular, finite-difference computer program MODFLOW 

(McDonald and Harbaugh, 1988) was used to construct 

a regional, two-dimensional, steady-state model of the 

groundwater-flow system in the alluvial aquifer. The model 

consisted of 1 layer, 36 rows, and 207 columns for a total of 

7,452 model grid cells with 5,237 active cells (fig. 3). Model 

grid-cell sizes varied from 200 ft by 200 ft in areas with wells 

and groundwater withdrawals to 1,000 ft by 1,500 ft for areas 

where data were sparse or near model boundaries.

Simulated recharge to the groundwater-flow system 

included infiltration of precipitation, subsurface flow from 

consolidated rocks along the valley wall, and seepage from 

streams. The amount of recharge from precipitation was 

estimated to be 12 percent of the total precipitation (42.05 in) 

for the 12-month period of December 1994 through November 

1995. Rorabaugh (1956) estimated the recharge to the alluvial 

aquifer in Louisville to be as much as 12 percent of the annual 

precipitation; this percentage of the annual precipitation was 
0 1 2 3 4 Miles0 1 2 3 4 Kilometers

Base from U.S. Geological SurveyMadison 1:100,000, 1990Falmouth 1:100,000, 1986Contour units are in meters

03277200

EXPLANATION

Ohio River Alluvial Aquifer

Study area

Gaging staton

85° 10'

85° 10'

85°

38° 40'

38° 40'

38° 45'

Figure 1. Location of study area and extent of the Ohio River alluvial aquifer near Carrollton, Ky.
4

Evaluation of the Carrollton Groundwater-Flow Model, Updated to Conditions in September 2010

Figure 2. Graph showing the Ohio River stage for October 2009 through September 2010 at 

Markland Dam near Warsaw, Ky., U.S. Geological Survey (USGS) streamflow-gaging station 03277200. 

assumed to be reasonable for the Carrollton area because 

the study areas are similar. Recharge from precipitation was 

distributed at a constant daily rate to all active model cells. 

The contact between the valley-fill alluvial deposits and the 

bedrock wall along the southeast edge of the study area was 

modeled as a head-dependent flux boundary with horizontal recharge available to the aquifer. Groundwater recharge 

from subsurface flow along the valley wall, estimated by 

the model using a head-dependent flux boundary, was about 

27,800 cubic feet per day (ft3

/d) per mile of boundary. An 

external boundary head of 600 ft above sea level was assumed 

for each cell. The conductance between the external source 

and the aquifer was estimated at 10 feet per day (ft/d) and held 

constant along the entire boundary. Seepage from streams was 

distributed to model cells representing each stream according 

to the rate determined for steady-state conditions specified by 

Unthank (1999). The total amount of recharge to the groundwater-flow system estimated under steady-state conditions of 

November 1995 was 3,034,800 ft3

/d.

A major hydrologic feature of the groundwater-flow 

system is the Ohio River. The river is hydraulically connected 

to the aquifer throughout the study area and can be both a 

source of recharge and point of discharge for the model. The 

river was simulated using the River Package in MODFLOW 

with the stage held at a constant 421 ft above sea level. The 

riverbed was held constant at 385 ft above sea level. The 

hydraulic conductivity of the riverbed was held at 0.65 ft/d 

based on estimates from Grubb (1975).

Other input parameters used for the simulation, but 

not varied, included the horizontal hydraulic conductivity 

of the alluvial deposits and the groundwater withdrawals. 

The horizontal hydraulic conductivity of the model 

layer was held at 350 ft/d; groundwater withdrawals 

were simulated for 29 wells with a total withdrawal of 

16.9 million gallons per day (Mgal/d). 

The bedrock beneath the alluvial deposits in the study 

area is comprised of shale and limestone and is not considered 

a source of water to the overlying alluvial aquifer. As such, 

the contact between the bedrock and the alluvial aquifer was 

modeled as a no-flow boundary.

Unthank (1999) compared observed and simulated 

water levels for 48 observation wells for the November 1995 

conditions. The simulated water levels compared closely to 

the observed water levels for most of the wells. The average 

absolute difference between the observed and simulated water 

levels for the 48 wells was 1.43 ft; the maximum difference 

was 4.43 ft. The root mean square error (RMSE) of the model 

simulation was 1.80.
85° 10'

85° 10'

38° 40'

38° 45'

Base from U.S. Geological SurveyMadison 1:100,000, 1990Falmouth 1:100,000, 1986

0 1 2 3 4 Miles0 1 2 3 4 Kilometers

85° 38° 40'

EXPLANATION

Model grid

Active cells

Figure 3. Extent of finite-difference model grid near Carrollton, Ky.
6

Evaluation of the Carrollton Groundwater-Flow Model, Updated to Conditions in September 2010

Update of the Model to Conditions in 

September 2010

Data files from the previous steady-state model (Unthank, 

1999) were imported into MODFLOW-2005 (Harbaugh, 

2005) to update the model to conditions in September 2010. 

MODFLOW-2005 is an updated version of MODFLOW 

(McDonald and Harbaugh, 1988). Well and recharge data files 

were modified as part of this update. The design of the updated 

model and other input files is the same as the original model. 

Discharge from pumping wells in the Carrollton area 

was estimated on a daily basis from records obtained from 

local well operators. Collectively, withdrawals from wells in 

the area during September 2010 were estimated to be about 

22.1 Mgal/d. The total number of operating wells was 31 

(fig. 4 and table 1). Pumping rates were assigned to model 

cells representing withdrawal wells; flows were distributed 

by well and were based on operator records. The total daily 

discharge from pumping wells in November 1995, used by the 

original model, was 16.9 Mgal/d and this value was assigned 

to 24 wells. Therefore, from 1995 to 2010, total daily discharge from pumping wells has increased by 5.2 Mgal/d; the 

number of pumping wells has increased by 7.

Daily recharge estimates from precipitation for the 

updated model were calculated as a percentage of the total 

precipitation for the 12-month period beginning in September 

2009 and ending in August 2010. The total precipitation for 

this period was 40.66 in as measured at the National Oceanic 

and Atmospheric Administration climate station at Markland 

Dam (Station 158446). This amount represents a 3.3-percent 

decrease in the amount of recharge available to the updated 

model compared to the original model input files.

The groundwater-flow system was conceptualized 

(Unthank, 1999) as a single-layer, steady-state model and 

remains so in the updated model. The hydraulic properties 

of the aquifer and the distribution of recharge were not 

changed in the updated model. The bedrock beneath the 

alluvial deposits was still considered a no-flow boundary in 

Table 1. Groundwater withdrawals for public water-supply and 

industrial-supply wells, Carrollton, Ky., September 2010.

[Mgal/d, million gallons per day]

Map 

number

Type of 

groundwater user

Number of 

wells

Withdrawals

(Mgal/d)

1 Public water supply 3 1.5

2 Industrial supply 4 2.5

3 Industrial supply 15 15.7

4 Industrial supply 2 0.5

5 Public water supply 4 1.7

6 Industrial supply 2 0.1

7 Industrial supply 1 0.1

the updated model. As in the original model, a general-head 

boundary was used to simulate conditions at the valley wall. 

The River Package in MODFLOW-2005 was used to simulate 

the groundwater-flow system’s boundary with the Ohio River 

and the groundwater/surface-water interactions. The altitude 

of the Ohio River stage was held at a constant 422 ft above sea 

level based on data from the USGS gaging station 03277200 

at Markland Locks and Dam for September 2010 (fig. 2).

Performance of the Updated Model

The ability of the updated model to simulate hydrologic 

conditions for September 2010 was evaluated by comparing water levels measured in wells to those estimated by the 

model. Hydrologic conditions at this time of the year are 

considered to be at or near steady-state conditions. Waterlevel measurements were available for 48 wells in September 

(fig. 5). Although many of the 48 wells are the same wells 

measured for the 1995 investigation, the two well networks are 

not the same. Table 2 is a comparison of the measured water 

levels in September 2010 to the simulated water levels.

Overall, the updated model underestimated the water 

levels at 36 of the 48 measured wells (table 2). The average 

absolute difference between observed water levels and simulated water levels was 3.4 ft, and the maximum difference was 

10.9 ft. The RMSE of the simulation was 4.45 for all 48 measured water levels. The original model produced an average 

difference in water levels of 1.43 ft, a maximum difference of 

4.43 ft and a RMSE of 1.80.

The total recharge to the groundwater-flow system simulated by the updated model was 3,259,976 ft3

. Infiltration from 

precipitation accounted for 18.4 percent of the total recharge; 

flow from the valley wall was approximately 21.3 percent. 

Induced flow from the Ohio River and other streams combined 

for the remaining 60.3 percent of the recharge. Discharge 

for the groundwater-flow system, by way of withdrawals 

from groundwater production wells, totaled 2,935,750 ft3 (90 

percent), and flow to the Ohio River and other streams totaled 

324,338 ft3

 (10 percent). Volumetric water budgets from the 

original and the updated models are listed in table 3.

Figure 6 shows the simulated altitude of the potentiometric surface for the alluvial aquifer estimated by the 2010 

model. As with the November 1995 results, cones of depression are present as the result of concentrated groundwater 

withdrawals in industrialized areas and public water-supply 

well fields. Outside of these production areas, the potentiometric surface shows a slight slope from the valley wall towards 

the Ohio River. Simulated water levels around the areas 

of concentrated groundwater withdrawals show the cones 

of depression in the potentiometric surface to extend well 

beneath the Ohio River. Although drawdowns in the potentiometric surface beneath the river are typically indicative of 

induced infiltration, additional field data are needed to confirm 

this condition and verify its extent.
85° 10'

85° 10'

85°

38° 40'

38° 40'

38° 45'

Base from U.S. Geological SurveyMadison 1:100,000, 1990Falmouth 1:100,000, 1986

6

5

4

3

2

1

Withdrawals, in million gallons/day

> 5.00.5 − 5.00.0 − 0.5

0 1 2 3 4 Miles0 1 2 3 4 Kilometers 

EXPLANATION

Ohio River Alluvial Aquifer

Study area

K

Figure 4. Locations and amounts of groundwater pumpage near Carrollton, Ky.
1

3

5

8 76

4

2 31

18

23

16 14

15

22

19

45

40

41

43 36

35

20

28

29

44 39 42 38

37

33

34

32

21

30

27

24

25

13

9 11

10 12 17

26

85° 10'

85° 10'

85°

38° 40'

38° 40'

38° 45'

Base from U.S. Geological SurveyMadison 1:100,000, 1990Falmouth 1:100,000, 1986

Observation Well, with identifier 34

0 1 2 3 4 Miles0 1 2 3 4 Kilometers 

EXPLANATION

K

Figure 5. Observation well network near Carrollton, Ky.
Performance of the Updated Model

9

Table 2. Observed and simulated water levels and differences for observation wells near Carrollton, Ky.—Continued

[Observation well locations are shown in figure 5. USGS, U.S. Geological Survey; ft, foot]

USGS local well 

number

Model cells Observed water level

(ft)

Simulated water 

level (ft)

Difference 

Model row Model column (ft)

1 35 6 426.4 422.6 3.8

2 19 7 423.6 421.3 2.3

3 20 12 423.8 420.9 2.9

4 14 10 419.8 419.9 -0.1

5 16 12 422.4 420.1 2.3

6 13 12 421.1 419.4 1.7

7 12 13 421.0 419.1 1.9

8 11 13 421.3 419.6 1.7

9 28 38 418.1 418.5 -0.4

10 22 37 414.7 417.9 -3.2

11 26 44 418.3 419.3 -1.0

12 23 41 417.8 417.6 0.2

13 21 59 420.4 421.5 -1.1

14 24 75 412.6 412.8 -0.2

15 23 76 414.2 411.6 2.6

16 27 81 408.7 399.9 8.8

17 21 77 410.6 411.3 -0.7

18 20 82 415.2 407.9 7.3

19 28 100 406.4 395.5 10.9

20 29 107 411.1 405.4 5.7

21 29 108 411.2 406.3 4.9

22 23 100 402.9 393.6 9.3

23 21 98 399.3 391.8 7.5

24 14 98 410.9 407.8 3.1

25 16 98 406.9 402.7 4.2

26 18 98 402.9 396.4 6.5

27 19 106 404.7 394.2 10.5

28 18 106 410.6 402.9 7.7

29 16 106 413.2 406.8 6.4

30 17 111 410.2 411.1 -0.9

31 21 120 420.2 415.9 4.3

32 16 135 425.1 421.5 3.6

33 16 146 426.6 422.0 4.6

34 11 147 425.0 422.0 3.0

35 17 155 423.9 421.2 2.7

36 13 154 422.2 420.8 1.4

37 16 158 423.2 421.4 1.8

38 10 166 420.7 422.4 -1.7

39 13 178 422.3 422.7 -0.4

40 24 189 427.6 423.0 4.6

41 20 186 424.3 422.9 1.4

42 13 183 422.6 422.6 0.0
10

Evaluation of the Carrollton Groundwater-Flow Model, Updated to Conditions in September 2010

Table 2. Observed and simulated water levels and differences for observation wells near Carrollton, Ky.—Continued

[Observation well locations are shown in figure 5. USGS, U.S. Geological Survey; ft, foot]

USGS local well 

number

Model cells Observed water level Simulated water Difference 

Model row Model column (ft) level (ft) (ft)

43 18 189 426.9 422.7 4.2

44 11 193 422.7 421.8 0.9

45 19 196 425.6 425.2 0.4

46 21 201 427.5 422.9 4.6

47 19 201 427.1 422.8 4.3

48 23 203 421.6 422.9 -1.3

Table 3. Volumetric water budget comparison for 1995 model and 2010 model.

[ft3, cubic feet]

Model input 1995 model (ft3) 2010 model (ft3)

Flow from the Ohio River 983,900 1,753,800

Flow from the bedrock valley wall 723,000 694,700

Recharge from precipitation and area streams 1,327,900 811,500

TOTAL 3,034,800 3,260,000

Model output

Discharge to withdrawal wells 2,511,400 2,935,800

Discharge to the Ohio River 520,800 324,300

TOTAL 3,032,200 3,260,100
0 1 2 3 4 Miles

0 1 2 3 4 Kilometers

EXPLANATION

K

85° 10'

85° 10'

85°

38° 40'

38° 40'

38° 45'

Base from U.S. Geological SurveyMadison 1:100,000, 1990Falmouth 1:100,000, 1986

Potentiometric surface, in feet above sea level

385 to 390390 to 394394 to 398398 to 402402 to 406406 to 410410 to 414414 to 418418 to 422422 to 426

Figure 6. Simulated altitude of potentiometric surface of the alluvial aquifer near Carrollton, Ky., September 2010.
12

Evaluation of the Carrollton Groundwater-Flow Model, Updated to Conditions in September 2010

Figure 7 shows the difference between the observed 

water levels and the simulated water levels for the 48 observation wells, indicated by graduated circles. Overall the observed 

water levels are higher than the simulated water levels, meaning the updated model is underpredicting the observed potentiometric surface. Water-level differences in 38 of 48 wells are 

less than 5 ft (table 2 and figure 7), and the greatest differences in water levels are found near the areas of concentrated 

groundwater withdrawals. Increasing the available recharge 

by increasing the percentage of precipitation infiltration, 

allowing more water to flow from the valley wall, assigning 

higher streambed conductance for the river, or combinations 

of all three can provide more water to the model. Additional 

measures, such as adjusting hydraulic conductivity values and 

resizing the model grid, may help to redistribute water in areas 

of concentrated groundwater withdrawals and reduce the difference in observed and measured water levels.

Limitations, Potential Revisions, and 

New Data to Improve the Updated 

Model

The limitations of the updated model are much the same 

as the limitations of the original model (Unthank, 1999). The 

detail and scale of the original model limits applications of 

this model as described in Unthank (1999). Relatively large 

changes in infiltration or pumping (approximately 25%) can 

be simulated with some accuracy, but detailed changes, such 

as rearranging withdrawals within a well field, may be limited 

by the scale of the model. 

The updated steady-state model of the groundwater-flow 

system of the Ohio River alluvial aquifer near Carrollton, 

Ky., could be further improved by making revisions based 

on data-collection activities designed to better quantify two 

critical sources of recharge to the flow system— flow from 

the bedrock valley wall and infiltration from the Ohio River. 

For the updated model, flow from the bedrock valley wall is 

configured as a general-head boundary. The quantity of flow 

across a general-head boundary is governed by water levels 

outside of the model area (external source) and the hydraulic conductance of the interface between the aquifer cell and 

the boundary (McDonald and Harbaugh, 1988). Identifying 

observation wells outside of the model boundary and conducting aquifer tests near the valley wall will provide data on the 

area’s external sources of water and the connectivity of these 

external sources to the aquifer. Similarly, the quantity of flow 

available to the aquifer from the induced infiltration of river 

water is characterized by how easily water moves from the 

river, through the riverbed, and into the alluvial deposits. Datacollection activities that can help characterize this connection 

and determine the amount of recharge available from the river 

include maintaining an observation well network to identify 

areas of induced infiltration, conducting floodwave analyses 

to calculate hydraulic conductivities and measuring infiltration 

rates directly with seepage meters. A series of potentiometric 

maps of the groundwater can be developed from water-level 

measurements taken from an observation well network and 

used to identify changing conditions in the aquifer and possible areas of drawdown in the river. Water-level measurements 

from temporary piezometers installed in the river can supplement the potentiometric surface mapping and help to delineate 

drawdowns beneath the river. Recording the aquifer’s response 

to flood events on the Ohio River and analyzing the movement 

of the floodwave is a direct means of calculating hydraulic 

conductivities near the river and characterizing the connection between the Ohio River and the aquifer. Lastly, seepage 

meters can measure the infiltration rates of the river water in 

areas of drawdown. The data can be used to calculate the vertical hydraulic conductivity of the riverbed. Collectively, these 

data-collection activities can provide the data and information 

to assess the amount of available recharge more accurately and 

determine the rates at which the recharge can be supplied to 

the model. 

Estimating the hydraulic conductivities assigned to the 

alluvial deposits could also improve the model representation of the groundwater-flow system. A generalized value 

of 350 ft/d was used as the hydraulic conductivity for the 

entire model layer in both the original and the updated model. 

Hydraulic-conductivity discretization for the model layer 

could be revised based on data and information available from 

field activities such as site assessments, installation and testing 

of new groundwater-production wells, and evaluation of existing production wells.

The accuracy of model simulations could improve by 

refining the model geometry and utilizing additional numerical 

methods. Additional model layers, finer model grid discretization, and revised boundary conditions are potential revisions to the model geometry that could improve the model’s 

performance. Likewise, model packages such as UCODE 

2005 (Poeter and others, 2005) and PEST (Doherty and Hunt, 

2010) could strengthen the model’s accuracy by performing 

sensitivity, calibration, and uncertainty analyses and parameter 

estimations respectively.

Summary

The Ohio River alluvial aquifer near Carrollton, Ky., is 

an important water resource for the cities of Carrollton and 

Ghent, as well as for several industries in the area. The aquifer 

is the primary source of drinking water in the region and a 

highly valued natural resource, attractive to various waterdependent industries because of its quantity and quality. In 

1998, the USGS completed an investigation to characterize 

the hydrogeology of the Ohio River alluvial aquifer beneath 

Carrollton and the surrounding area and provide local waterresources managers with the information and modeling 

capabilities necessary to help manage and protect the area’s 
85° 10'

85° 10'

85°

38° 40'

38° 40'

38° 45'

Base from U.S. Geological SurveyMadison 1:100,000, 1990Falmouth 1:100,000, 1986

Water level difference, in feet

-5 to -1-1 to 00 to 11 to 5> 5

0 1 2 3 4 Miles0 1 2 3 4 Kilometers

EXPLANATION

K

Figure 7. Difference between observed water levels and simulated water levels near Carrollton, Ky.
14

Evaluation of the Carrollton Groundwater-Flow Model, Updated to Conditions in September 2010

groundwater resources. Then in 2010, the USGS, in cooperation with the City of Carrollton and a coalition of local water 

utilities and private industries, began a 2-year study to update 

the modeling capabilities from the previous 1998 investigation. The original steady-state model has been updated and 

evaluated to determine how well it simulated the steadystate conditions of the groundwater-flow system observed in 

September 2010.

The files from the original steady-state model were 

imported into MODFLOW-2005 to update the model to conditions in September 2010. The main model input files modified as part of this update were the well and recharge files. 

Discharge from pumping wells was estimated on a daily basis. 

For September 2010, a total of 19.9 Mgal/d was pumped from 

31 wells. This represents an increase of 3 Mgal/d from the 

November 1995 simulation of 16.9 Mgal/d discharged from 

29 wells. The daily recharge from precipitation was decreased 

3.3 percent based on a 12-month total of 40.66 in for 2009 

through 2010, compared to 42.05 in for the 1995 simulation. 

The remainder of the input files and basic model design 

remained the same as the original model.

The ability of the model to match hydrologic conditions for September 2010 was evaluated by comparing water 

levels measured in wells to those computed by the model. 

Water-level measurements were available for 48 wells in 

September 2010— a time of the year when the groundwaterflow system is considered to be at or near steady-state conditions with stable stage conditions on the Ohio River and near 

constant withdrawals from area production wells. Differences 

in observed water levels compared to modeled water levels 

ranged from 0 to 10.9 ft with an average of 3.4 ft.

The updated steady-state model can be improved with 

more accurate and site-specific estimates of selected field 

parameters, refined model geometry, and additional numerical methods. Properly designed data collection activities and 

continued review of available data and information from area 

well operators would provide the model with revised estimates 

of conductance for the riverbed and valley wall, hydraulic 

conductivities for the aquifer, and model calibration targets 

for future simulations. Additional model layers, a redesigned 

model grid, and revised boundary conditions could provide 

a better framework for more accurate simulations. Additional numerical methods would identify possible parameter 

estimates and determine parameter sensitivities.

References Cited

Doherty, J.E., and Hunt, R.J., 2010, Approaches to highly 

parameterized inversion—A guide to using PEST for 

groundwater-model calibration: U.S. Geological Survey 

Scientific Investigations Report 2010–5169, 59 p.

Grubb, H.F., 1975, Simulated drawdown for selected well 

fields in the Ohio River alluvial aquifer: U.S. Geological 

Survey Water-Resources Investigations Report 74-2, 38 p.

Harbaugh, A.W., 2005, MODFLOW-2005, The U.S. Geological Survey modular ground-water model—the ground-water 

flow process: U.S. Geological Survey Techniques and Methods, book 6, ch. A–16, 264 p.

Konikow, L.F., and Bredehoeft, J.D., 1992, Ground-water 

models cannot be validated: Advances in Water Resources, 

vol. 15, no. 1, p. 75–83.

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, ch. A–1, 586 p. 

Poeter, E.P., Hill, M.C., Banta, E.R., Mehl, S., and Christensen, S., 2005, UCODE 2005 and six other computer 

codes for universal sensitivity analysis, calibration, and 

uncertainty evaluation constructed using JUPITER API: 

U.S. Geological Survey Techniques and Methods book 6, 

ch. A–11, 299 p.

Rorabaugh, M.I., 1956, Ground water in northeastern 

Louisville, Kentucky, with reference to induced infiltration: 

U.S. Geological Survey Water-Supply Paper 1360–B, 69 p.

Unthank, M.D., 1999, Hydrogeology and simulation of 

ground-water flow in the Ohio River alluvial aquifer near 

Carrollton, Kentucky: U.S. Geological Survey WaterResources Investigations Report 98–4215, 48 p.

U.S. Census Bureau, 2010, American FactFinder: accessed 

August 18, 2011, at http://factfinder2.census.gov/faces/nav/

jsf/pages/index.xhtml.

Unthank—Evaluation of the Groundwater-Flow Model for the Ohio River Alluvial Aquifer near Carrollton, Kentucky,—Scientific Investigations Report 2013–5032

Updated to Conditions in September 2010