SIMULATION OF GROUND-WATER FLOW IN AN

UNCONFINED SAND AND GRAVEL AQUIFER AT 

MARATHON, CORTLAND COUNTY, NEW YORK

U.S. GEOLOGICAL SURVEY

Water-Resources Investigation Report 00-4026

Prepared in cooperation with

CORTLAND COUNTY SOIL AND 

WATER CONSERVATION DISTRICT
Simulation of Ground-water Flow in an Unconfined 

Sand and Gravel Aquifer at Marathon, Cortland 

County, New York

BY TODD S. MILLER

______________________________________________________________________

U.S. Geological Survey

Water-Resources Investigation Report 00-4026

Prepared in cooperation with

CORTLAND COUNTY SOIL and 

WATER CONSERVATION DISTRICT

Ithaca, New York

2000
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Acting Director

______________________________________________________________________________

For additional information write to: Copies of this report can be purchased from:

Subdistrict Chief U.S. Geological Survey

U.S. Geological Survey Branch of Information Services

30 Brown Road Box 25286

Ithaca, NY 14850 Denver, CO 80225-0286

ii
Contents iii

CONTENTS

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

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

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

Methods ............................................................................................................................................................. 2

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

Geology ................................................................................................................................................................................. 4

Hydrology.................................................................................................................................................................... 4

Sources of Recharge .................................................................................................................................................... 8

Ground-Water Discharge ............................................................................................................................................. 9

Surface-Water and Ground-Water Interaction ............................................................................................................. 9

Simulation of Ground-Water Flow ........................................................................................................................................ 13

Model Description and Design .................................................................................................................................... 13

Simplifying Assumptions .................................................................................................................................. 14

Model Grid ........................................................................................................................................................ 14

Boundary Conditions......................................................................................................................................... 16

Hydraulic Values................................................................................................................................................ 17

Model Calibration........................................................................................................................................................ 17

Model Sensitivity......................................................................................................................................................... 18

Model Application ....................................................................................................................................................... 19

Summary...................................................................................................................................................................... 23

References Cited.................................................................................................................................................................... 24

FIGURES

1. Map of study area at Marathon, Cortland County, N.Y. showing location of modeled area and lines of 

hydrogeologic sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2. Hydrogeologic sections A-A', B-B' and C-C' in modeled area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3. Maps showing drainage in the Tioughnioga River valley in Cortland County, N.Y.: A. During deglaciation. 

B. During pre-and postglaciation period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4. Map showing location of northernmost municipal pumping well, observation well with temperature probe, 

Tioughnioga River, and Hunts Creek at Marathon, N.Y.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5. Graph showing ground-water temperature and water level in observation well between municipal pumping 

well 452 and Tioughnioga River, Marathon, N.Y., August 1-7, 1997 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6. Graphs showing ground-water temperature and water level in observation well between municipal pumping 

well 452 and Tioughnioga River, Marathon, N.Y. A. July through September, 1997, B. October through 

December,1997, C. January through March, 1998, and D. April through June, 1998 . . . . . . . . . . . . . . . . . . . . . . . . . . 11

7. Schematic diagram of hydrologic settings where ground water discharges to the Tioughnioga River: 

A. Under non-pumping conditions. B. Where pumping by municipal well 452 intercepts ground water that would 

have flowed to Tioughnioga River and induces water to flow from the river to the well. . . . . . . . . . . . . . . . . . . . . . . . 13

8. Schematic diagram showing processes that affect exchange of water between Tioughnioga River and adjacent 

aquifer: When river stage rises from low level (1) to bankfull level (2) and is higher than adjacent water table, 

river water moves laterally into streambank. When the river overflows its banks (3), floodwaters seep 

downward to the water table.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

9. Diagram showing model representation of ground-water flow in the sand and gravel aquifer in the Marathon, 

N.Y.modeled area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

10. Map showing active cells and boundaries in aquifer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

11. Graphs showing results of sensitivity analyses for selected hydraulic properties in layer 1 of the unconfined sand 

and gravel aquifer at Marathon N.Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
iv Contents

12. Map showing simulated heads in the unconfined aquifer for average annual steady-state conditions with two 

simulated discharging wells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

13. Map showing areas contributing recharge to two simulated municipal pumping wells . . . . . . . . . . . . . . . . . . . . . . . . 22

TABLES

1. Streamflow losses from tributary streams to the unconfined aquifer in the Marathon, N.Y. modeled area, 

June 11, 1997 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2. Measured and simulated streamflow gains and losses in selected stream reaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3. Difference and root mean squared of the difference between measured and simulated heads at 7 wells in the 

unconfined aquifer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4. Steady-state water budget for the calibrated ground-water flow model with one simulated discharging well . . . . . . . 19

5. Water budget for the unconfined aquifer with two simulated discharging wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

CONVERSION FACTORS AND VERTICAL DATUM

Multiply By To Obtain

Length

inch (in.) 2.54 centimeter

foot (ft) 0.3048 meter

mile (mi) 1.609 kilometer

Area

square mile (mi2) 2.590 square kilometer

Flow

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

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

million gallons per day (Mgal/d) 3.785 cubic meters per day

gallons per minute (gal/min) 0.06309 liter per second 

foot per mile (ft/mi) 0.1894 meter per kilometer

Temperature

degrees Fahrenheit ( ̊F)  ̊C = 5/9 ( ̊F-32) degrees Celsius 

Specific Conductance

microsiemens per centimeter at 25 ̊ Celsius (μS/cm)

Vertical datum: 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.
Abstract 1

Simulation of Ground-water Flow in an Unconfined 

Sand and Gravel Aquifer at Marathon, Cortland 

County, New York

By Todd S. Miller

Abstract

The Village of Marathon, in Cortland 

County, N.Y., has three municipal wells that tap a 

relatively thin (25 to 40 feet thick) and narrow 

(less than 0.25 mile wide) unconfined sand and 

gravel aquifer in the Tioughnioga River valley. 

Only one of the wells is in use because water from 

one well has been contaminated by petroleum 

chemicals from a leaking storage tank, and water 

from the other well contains high concentrations 

of manganese. The operating well pumps about 

0.1 million gallons per day and supplies about 

1,000 people. 

A three-dimensional, finite-difference 

ground-water-flow model was used to 

(1) compute hydraulic heads in the aquifer under 

steady-state conditions, (2) develop a water 

budget, and (3) delineate the areas contributing 

recharge to two simulated wells that represent two 

of the municipal wellsone 57 feet east of the 

Tioughnioga River, the other 4,000 feet to the 

south and 75 feet from a man-made pond. The 

water budget for simulated long-term average, 

steady-state conditions with two simulated 

pumping wells indicates that the principal sources 

of recharge to the unconfined aquifer are 

unchanneled runoff and ground-water inflow from 

the uplands (41 percent of total recharge), 

precipitation that falls directly on the aquifer (34 

percent), and stream leakage (23 percent). Only 2 

percent of the recharge to the aquifer is from 

ground-water underflow into the northern end of 

the modeled area. Most of the simulated groundwater discharge from the modeled area 

(78 percent of total discharge) is to the 

Tioughnioga River; the rest discharges to the two 

simulated wells (19 percent) and as underflow at 

the southern end of the modeled area (3 percent).

Results of a particle-tracking analysis 

indicate that the aquifer contributing area of the 

northern (simulated) well is 0.10 mile wide and 

0.15 mile long and encompasses 0.015 square 

miles; the contributing area of the southern 

(simulated) well is 0.20 mile wide and 0.11 mile 

long and encompasses 0.022 square miles. The 

average traveltime of ground water from the 

valley wall to either simulated well is about 1.5 

years, calculated on the basis of an assumed 

aquifer porosity of 0.3. The flowpath analysis 

indicates that both contributing areas contain 

surface-water sources of rechargethe 

Tioughnioga River and Hunts Creek contribute 

water to the northern well, and a pond and a small 

tributary contribute water to the southern well. 

Ground-water temperature in an 

observation well between the Tioughnioga River 

and the municipal well fluctuated several degrees 

Fahrenheit in response to pumping of the 

municipal well. This temperature fluctuation, in 

conjunction with the pumping well causing a 

ground-water gradient from the Tioughnioga 

River to the pumping well (ground-water levels in 

the pumping well were generally greater than 3 ft 

lower than that of the Tioughnioga River), 

indicate that there is a hydraulic connection 

between the river and aquifer at this site.
2 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

INTRODUCTION

Aquifers are principal sources of water supply for 

many communities. Many municipal wells that tap 

these aquifers have been contaminated or are under 

threat of contamination because of the lack of 

knowledge of contributing areas that supply recharge 

to these wells. An important step in protecting 

municipal ground-water supplies from contamination 

is to identify the contributing areas to water-supply 

wells and the potential sources of chemical 

contaminants that are within the contributing area. 

Cortland County promotes implementing protection 

plans as the most cost-effective means of ensuring a 

safe drinking-water supply. The U.S. Environmental 

Protection Agency (1987) has recommended that 

municipalities adopt “Wellhead Protection” strategies 

to regulate land use in areas that contribute recharge to 

public-supply wells. The objectives of these strategies 

are to delineate the land-surface area from which 

water enters the ground-water system and flows to 

municipal wells, and to set regulations that minimize 

the possibility of contamination within these areas.

The Village of Marathon, in Cortland County, has 

three wells that tap a relatively thin (25- to 40-ft thick) 

and narrow (less than 0.25 mi wide) unconfined sand 

and gravel aquifer in the Tioughnioga River valley 

(fig. 1). In 1998, only one well (well 452, fig. 1) near 

the Tioughnioga River in the northern part of the 

village was used; the second well (well 450, fig. 1), 

also in that vicinity, has been abandoned because the 

water has been contaminated by petroleum chemicals. 

The third well (well 459, fig.1), near a pond in the 

southern part of the study area, is not used because the 

water contains high concentrations of manganese. The 

village is concerned about the quality of water in the 

Tioughnioga River because ground-water/surfacewater interaction is common in shallow water-table 

aquifers, and induced infiltration of surface water to 

the one remaining well is likely. Past flooding of the 

Tioughnioga River has also posed a threat of groundwater contamination of the municipal well. The 

village plans to have two wells (one for the principal 

supply and one for backup) and needs information on 

the aquifer to protect and manage the village supply, 

which serves about 1,000 people. 

During 1997-98, the U.S. Geological Survey 

(USGS), in cooperation with the Cortland County Soil 

and Water Conservation District, conducted an 

investigation of a part of the sand and gravel aquifer at 

Marathon to collect and compile data needed to 

delineate contributing areas to two hypothetical wells 

that represent the municipal supply wells. The study 

entailed a literature search, compilation of available 

hydrogeologic data, synoptic ground-water-level and 

streamflow measurements made during June 11-12, 

1997, continuous recording of ground-water levels 

and water temperature in an observation well between 

the Tioughnioga River and the municipal pumping 

well 452, and development of a finite-differenceground-water-flow model to simulate ground-water 

flow in the aquifer.

Purpose and Scope

 This report describes: (1) the hydrogeologic 

setting of the Marathon area, (2) the design of the 

ground-water flow model, and (3) the results of 

simulations made with the model. The report presents 

tables of the simulated inflows and outflows to the 

aquifer as computed for average, steady-state 

conditions, and includes maps showing the 

distribution of hydraulic head in the aquifer, and the 

contributing areas of the two municipal wells.

Methods

The three-dimensional, numerical-ground-water 

flow model MODFLOW, developed by the USGS 

(McDonald and Harbaugh, 1988), was used to 

simulate steady-state conditions in the aquifer and to 

compute ground-water levels and a water budget for 

the study area. The particle-tracking program 

MODPATH, also developed by the USGS (Pollock, 

1994), was used to delineate the areas that contribute 

recharge to two simulated wells that represent the 

municipal wells. Levels were run to (1) wells used to 

calibrate the model, (2) to the top and bottom of the 

pond in the southern part of the study area, and (3) in 

the channels of Tioughnioga River, Hunts Creek, and 

several other small streams. Depth soundings were 

made to obtain bottom elevation of the pond. Waterlevel and streambed-elevations measurements are 

accurate to a tenth of a foot where levels were run. 

Acknowledgments

Thanks are extended to Walter Ackley and Gary 

Lawrence (both former water supervisors for the 

Village of Marathon); and to Michael Root (current 
3

0

0 300 METERS

1,000 FEET

Flow

WELL AND WELL NUMBER

0.89

3.86

3.71

0.27

Study area

and modeled area

0.86

461

456

459

450

452

42° 27' NEW

YORK

Cortland

County

Cortland

Cortland County

0 5 MILES

0 5 KILOMETERS

Village of 

Marathon

model 

area

Tioughnioga River

W. Br. Tioughnioga R. valley

Village 

of Homer

Pond

Tributary A

TIOUGHNIOGA RIVER

Village of

Marathon

Tributary B

EXPLANATION

AQUIFER BOUNDARY

A

A/

B

B/

C

C/

A A/ LINE OF GEOLOGIC SECTION--

Sections shown in figure 2

451

453

86

455

78

462

457

459

456

0.20

454

STREAMFLOW-MEASUREMENT

SITE--Number is stream discharge,

in cubic feet per second

MUNICIPAL WELL AND WELL

NUMBER

0.20

Hunt's Creek

Flow

Base from U.S. Geological Survey, Marathon, N.Y., 1:24,000, 1994

76° 02' 30" 76° 01' 30"

42° 26'

Figure 1. Location of modeled area and lines of geologic sections at Marathon, Cortland County, N.Y. 

Introduction
4 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

water supervisor) for providing data and access to 

wells. Mr. Ackley knew much more about the aquifer 

than he gave himself credit for.

GEOLOGY

 The Marathon area is within the glaciated and 

dissected Allegheny Plateau, which consists of gently 

folded layers of shale with some siltstone, sandstone, 

and limestone that dip southward from 10 to 40 ft/mi. 

These rocks are part of the “Catskill Delta” complex 

(Woodrow and Sevon, 1985), which was deposited in 

marine seas during late Devonian time. These rocks 

were then uplifted above sea level millions of years 

later, then eroded to a nearly flat plain by the middle of 

the Cenozoic (Isachsen and others, 1991). They were 

again uplifted during Late Cenozoic time to form the 

Allegheny Plateau, which was subsequently dissected 

by streams and eroded by glaciers to form a smooth, 

hilly terrain. 

The entire region was glaciated several times 

during the Quaternary Period, which began 1.6 

million years ago and ended about 10,000 years ago 

(Isachsen and others, 1991). Some of the sediments 

that were eroded by the ice either became entrained 

in the glacier or were dragged along its bottom, 

where some of the material was ground up and later 

deposited as till on top of bedrock in most places. 

The till in the study area consists of poorly sorted 

clay, silt, sand, and stones that were compacted by 

the ice. Till and bedrock, which are much less 

permeable than sand and gravel, form the bottom of 

the overlying sand and gravel aquifer in the 

Tioughnioga River valley (fig. 2).

Alluvial and glaciofluvial deposits in the study 

area form a 25-to-40-ft thick sand and gravel aquifer 

(fig. 2, geologic sections A-A', B-B', and C-C' ). The 

upper part of the aquifer consists of recent alluvial 

deposits (flood-plain, fan, and channel sediments), and 

the lower parts may consist of glaciofluvial sediments 

such as kame and outwash deposits. The low areas 

adjacent to the Tioughnioga River have flood-plain 

deposits that consist of silt and fine sand and are only 

few feet thick and are unsaturated, except during 

extremely wet periods and floods. The fan and channel 

deposits consist of sand and gravel with various 

amounts of silt; the alluvial deposits also contain 

decaying organic matter. 

Kames form hummocky terraces along the lower 

flanks of the valley walls and probably extend below 

the alluvial deposits in the valley bottom; they consist 

of fair- to well-sorted silt, sand, and gravel that were 

deposited atop and next to glaciers and collapsed when 

the ice melted. Outwash is fluvial channel deposits 

deposited by meltwaters that flowed from the glacier 

southward through the Tioughnioga River valley when 

the glacier was north of Marathon. Outwash probably 

underlies the alluvial deposits in the valley and 

consists of well-sorted sand and gravel (fig. 2A). The 

outwash and kame deposits in the Marathon area 

typically contain many erratic clasts (rocks that are 

foreign to the Marathon area) that were transported by 

the glacier and meltwater from several tens of miles to 

the north, whereas the alluvial deposits tend to be 

mostly local shale and siltstone clasts that were eroded 

by upland streams and deposited in the valley, where 

they became reworked by the Tioughnioga River. 

 The Marathon area undergoes frequent flooding 

because the Tioughnioga River (about 115 ft wide) has 

a low stream gradient and occupies a relatively large 

part (8 to 13 percent) of a fairly narrow valley (900 to 

1,400 ft wide). Large streams that occupy relatively 

small valleys, or small streams that occupy relatively 

large valleys are known as misfit streams. The 

Tioughnioga river became a misfit stream because of 

glacial diversion of drainage. The valley at Marathon 

during preglacial time was on the south side of a 

nearby drainage divide (fig. 3B), and only a small, 

southward-flowing stream occupied the valley in the 

Marathon area. During the last glaciation, however, 

several streams near Cortland (about 15 mi north of 

Marathon) were diverted by the glacier from their 

preglacial course through the Fall Creek valley to the 

west (fig. 3B) and were rerouted to the south into its 

present course through the narrow valley now 

occupied by the Tioughnioga River. Most land 

development in the Tioughnioga River valley, from 

Cortland to Marathon, is on high ground, such as on 

alluvial fans and hillsides, because flooding is 

common in the valley.

HYDROLOGY

The upper part of the sand and gravel aquifer at 

Marathon consists of alluvial-fan and channel 

deposits, and the lower part probably consists of 

outwash and kame deposits (fig. 2). The overbank 

flood deposits are not part of the aquifer because they 

are only a few feet thick and are probably unsaturated 

most of the time. The top of the aquifer is the water 
5

VERTICAL EXAGGERATION X 20

DATUM IS SEA LEVEL

EXPLANATION

ALLUVIAL FLOOD-PLAIN DEPOSITS--silt, sand, 

and gravel. Area subject to overbank deposition 

during flooding

ALLUVIAL FAN DEPOSITS-- silty sand and gravel 

deposited along edges of valleys by upland streams

OUTWASH AND KAME DEPOSITS--generally wellsorted sand and gravel deposited by meltwater

TILL-- poorly sorted clay, silt, sand, and stones 

deposited by a glacier

SHALE AND SILTSTONE

WELL AND WELL NUMBER

POSITION OF WATER TABLE-- water levels 

measured June 12, 1997

DEVONIAN AGE

500 FEET

100 METERS

QUATERNARY AGE { { Qal

0

0

250

456

50

Qalf

Qt

Qsg

Dss

Qt

Qsg

FEET

1,050

AA

West

1,025

1,000

975

1,050

1,025

1,000

975

1,050

1,025

1,000

1,050

1,025

1,000

975

RailroadFront St.

Qalf

Qt

Tioughnioga River

BEND IN

SECTION

SECTION

C-C'

NYS Route 11

AA'

East

Qalf

454

78 455

462

Qt

Qsg

Dss

B

Railroad

Divers Crossing

Front St.

Tioughnioga River

Qt

SECTION

C-C'

459

456

Qal

457

NYS Route 11

Qalf

B'

Qt

975

Dss

Dss

Figure 2. Hydrogeologic sections A-A', B-B'and C-C' in modeled area, Marathon, N.Y. 

(Lines of section are shown in fig. 1)

Hydrology
6 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York EXPLANATION ALUVIAL FLOOD PLAIN AND CHANNEL DEPOSTS-- silt, sand, and gravel. Area subject to overbank deposition during flooding ALLUVIAL FAN DEPOSITS-- silty sand and gravel deposited along edges of valleys by upland streams GLACIOFLUVIAL DEPOSITS-- generally well-sorted sand and gravel deposited by meltwater TILL- poorly sorted clay, silt, sand, and 

QUATERNARY AGE stones deposited by a glacier

DEVONIAN

 AGESHALE AND SILTSTONE

{

{

453

WELL AND WELL NUMBER -number assigned by USGSWATER TABLE - water levels measured during June 12, 1997

450 86

SECTION

Hunts Creek

1,050

1,025

1,000

975

950

C

North 

Tioughnioga River

Levee

Qal

Qt

Municipal well

452 455

453

Vertical exaggeration X 20Datum is sea level

Dss

Qsg

Qal

Qt

A - A'

Dss Qal

Qalf

Qalf

Qsg

Qt

Figure 2. (continued) Hydrogeologic sections A-A', B-B', and C-C' in modeled area, Marathon, N.Y. (Lines of section are shown in 
7

1500

Messengerville

Base from U.S. Geological Survey,

1954, 1:250,000

PRESENT-DAY STREAM

SURFACE-WATER DIVIDE

CONTOUR INTERVAL 500 FEET

DATUM IS SEA LEVEL

Geology modified from 

Miller and others, 1998

Marathon

EXPLANATION

City of 

Cortland

Tioughnioga River

diverted southward

through preglacial 

divide

AQUIFER BOUNDARY

PREGLACIAL-DRAINAGE

COURSES- arrow indicates

direction of flow

Preglacial drainage

flowed southwestward

through Fall Creek valley

West Branch Tioughnioga River valley

OUTWASH.- Meltwater flowed

away from ice margins

Base from U.S. Geological Survey,

1954, 1:250,000

1500

1500

1500

1500

1000

1500

1500

1500

1500

1500

1000

0

0

5 MILES

5 KILOMETERS

CONTOUR INTERVAL 500 FEET

DATUM IS SEA LEVEL

From Miller and 

others, 1998

1500

1500

Marathon

Messengerville

Outwash drains 

southward through

Tioughnioga 

River valley

Tully

VALLEY HEADS ICE AND

MORAINES, hachures on 

ice side

City of 

Cortland

ONONDAGA CO

CORTLAND CO CAYUGA CO TOMPKINS CO

Fall Creek valley

East Branch Tioughnioga River valley

Tioughnioga River valley

Factory Brook valley

Trout Brook valley

A. DEGLACIATION PERIOD B. PRE- AND POSTGLACIAL PERIOD

Tully

ONONDAGA CO

CORTLAND CO CAYUGA CO TOMPKINS CO

Flow

Tioughnioga River

1500

1500

1500

1500

1000

1500

1500

1500

1500

1500

1000

1500

1500

1500

76°15' 76°10' 76°5'

42°45'

42 42°30' °30'

42°45'

76°15'

1500

1500

76°10' 76°5'

Figure 3. Drainage in the Tioughnioga River valley in Cortland County, N.Y.: A. During deglaciation. B. During pre-and 

postglaciation period. (Location is shown in fig. 1, inset map)

Hydrology
8 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

table, and the bottom is either the top of till or top of 

bedrock. The saturated thickness (the depth from the 

water table to the bottom of the aquifer) is typically 20 

to 30 ft. The aquifer is bounded laterally by the tillcovered bedrock hillsides. 

Sources of Recharge

The aquifer in the modeled area receives recharge 

from five sources: (1) precipitation that falls directly 

on the aquifer, (2) runoff (sheet flow over land surface) 

from unchanneled, till and bedrock hillsides that are 

adjacent to the sand and gravel deposits in the valley, 

(3) ground-water seepage from adjacent till deposits 

and bedrock, (4) stream leakage (natural leakage, and 

leakage induced by nearby pumping wells), and (5) 

southward inflow from the aquifer at the northern end 

of the modeled area. Part of the precipitation that falls 

on the aquifer is returned to the atmosphere by 

evapotranspiration; the remainder infiltrates to the 

water table. 

Rates of recharge from precipitation, as well as 

from other sources, vary seasonally. Most of the 

precipitation that falls during the nongrowing season 

(typically from mid-October through the end of April) 

infiltrates into the ground and recharges the aquifer, 

whereas most of the precipitation that falls during the 

growing season (May through September) is lost 

through evapotranspiration. Annual precipitation in 

the Marathon area is estimated to average about 40 in., 

slightly less than the 41.2 in. measured at the Cortland 

weather station during 1973-92 (National Oceanic and 

Atmospheric Administration, 1992), because the 

Marathon area receives slightly less lake-effect snow 

than Cortland. 

The average annual recharge to surficial sand and 

gravel aquifers in the northeastern United States is 

about equal to the long-term average annual stream 

runoff, which, for 30 years (1951-80) in southern 

Cortland County averaged about 22 in. (Lyford and 

Cohen, 1987). Therefore, the average volume of 

recharge that the aquifer receives from precipitation 

that falls directly on the aquifer is 47,700 ft3

/d, as 

calculated from an average annual recharge rate of 22 

in. (0.00502 ft/d) multiplied by the surface area of the 

aquifer (9,500,000 ft2

) in the modeled area. The 

average annual evapotranspiration is estimated to be 

18 in. (1.5 ft) and equals average annual precipitation 

(40 in.) minus average annual runoff (22 in).

Recharge to valley-fill aquifers from adjacent 

unchanneled hillsides includes surface runoff and 

lateral flow of ground water from the uplands; this 

water flows toward the valley and seeps into the 

aquifer along its edges. All precipitation that is not lost 

through evapotranspiration in the uplands adjacent to 

the aquifer is assumed to become either runoff or 

ground-water recharge that eventually flows into the 

valley and seeps into the aquifer.

The daily amount of recharge from runoff from 

adjacent unchanneled hillsides can be calculated by 

the following equation:

; (1)

where R = average annual rate of recharge 

from runoff from unchanneled 

hillsides, in ft3/d;

P = average annual precipitation of 

40 in. (3.4 ft);

ET = average annual 

evapotranspiration (1.5ft), as 

calculated from above;

DA= drainage area of hillside 

(12,425,000 ft2); and

t = 365 days.

Solution of the above equation indicates that the 

rate of recharge from runoff from unchanneled 

hillsides along the edges of the aquifer is 57,900 ft3

/d.

Tributaries to the Tioughnioga River that drain tilland-bedrock basins in the uplands are sources of 

aquifer recharge where they enter the main valley and 

flow over permeable sand and gravel deposits. The 

rate of recharge from these tributaries is controlled 

largely by the vertical hydraulic conductivity and 

thickness of the streambed, and by the hydraulic 

heads in the stream and aquifer. Rates of recharge 

from tributaries were estimated from the losses of 

water calculated from streamflow measurements 

made on most of the large tributaries in the study 

area on June 11, 1997, during a period judged to 

represent median annual flow conditions. Values 

are given in table 1. The median annual condition 

was defined as that when the flow duration at the 

stream gage in the Tioughnioga River at Cortland 

(station 01509000) was near 50 percent (285 ft3

/s) 

(Hornlein and others, 1997). 

R ( ) P ET – × DA

t = ------------------------------------
9

Table1. Losses of flows from tributary streams to the 

unconfined aquifer in the Marathon, N.Y. modeled area, 

June 11, 1997. 

[Values are in cubic feet per second; location of tributaries and 

streamflow-measurement sites are shown in fig. 1.]

Ground-Water Discharge

Water in the aquifer discharges into the 

Tioughnioga River, to the Village of Marathon’s 

municipal well, and as underflow out of the southern 

end of the study area. Ground water in most glaciated 

river valleys in the Northeast typically discharges to 

the main trunk stream. Water levels in most wells are 

higher than the surface of the Tioughnioga River, 

indicating that most ground water is discharging to the 

river. This is generally the condition except in the 

vicinity of the municipal pumping well, where 

ground-water levels are lower than the river during 

pumping periods.

Withdrawal of water from a shallow aquifer that 

is directly connected to a surface-water body affects 

the exchange of water between these two water 

bodies. Pumping water from the Marathon municipal 

well not only captures some of the ground water that 

would have discharged into the Tioughnioga River, it 

also induces some water from the river to flow into 

the aquifer.

Surface-Water and Ground-Water 

Interaction

Ground-water temperatures do not fluctuate as 

frequently, nor as widely or as rapidly, as do surfacewater temperatures. Therefore, the temperature of 

ground water and surface water at a given site can be 

used in conjunction with ground-water levels to 

indicate the degree of hydraulic connection between a 

stream and an adjacent aquifer. Water temperature at 

depths greater than 50 ft in coarse-grained aquifers in 

New England does not fluctuate but, rather, is near 

the mean annual air temperature of a region (47 oF in 

the Marathon area) if the vertical ground-water 

velocity is negligible (Lapham, 1989). Significant 

downward flow, such as near pumping wells, 

increases the depth to which ground-water 

temperature fluctuations are found. 

Ground-water temperature [sprobably] fluctuates 

near the municipal well in the northern part of the 

study area (well 452, fig. 1) because the well is 

screened at a shallow depth (22-28 ft below land 

surface), is only 57 ft east of the Tioughnioga River 

(fig. 4), and pumping is likely to induce the infiltration 

of surface-water. A temperature probe was installed 20 

ft below land surface in an observation well (screened 

from 20-25 ft below land surface) between the 

municipal well and the river19 ft west of the 

pumping well and 38 ft east of the Tioughnioga River 

(fig. 4)to verify this hydraulic connection. Small 

Tributary

Streamflow loss (-) 

between measurement 

site near valley wall and 

near mouth, during 

June 11, 1997

Hunts Creek -0.15

Tributary A -0.07

Tributary B -0.03

Estimated loss from other 

tributaries not measured

-0.05

Sum of tributary losses -0.30

Figure 4. Location of northernmost municipal pumping 

well (location is shown in fig. 1) and observation well 

with temperature probe in relation to Tioughnioga River 

and Hunts Creek at Marathon, N.Y.

TIOUGHNIOGA RIVER

Municipal pumping well

Observation well installed

with temperature probe 

Flow

Flow HUNTS CREEK

57 ft

38 ft

Not to scale

N

Hydrology
10 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

Water temperature in well

Water level in well

1,013

1,012

1,011

1,010

1,009

1,008

1,007

1,0062400 1200 2400 2400 1200 1200 2400 2400 1200 1200 2400 1200 2400 2400 1200

1 2 3 4 5 6 7

August 1997

WATER LEVEL, IN FEET ABOVE SEA LEVEL

68

65

60

55

50

45

40

38

WATER TEMPERATURE, DEGREES FAHRENHEIT

fluctuations in temperature would be expected even 

during nonpumping periods because the aquifer is thin 

in this area, whereas large fluctuations in temperature, 

which were found in the observation well and 

corresponded to the river-water temperature, indicate 

induced recharge from the river to the pumping well. 

Plots of ground-water temperature and water 

levels at this observation well during August 1-7, 1997 

are shown in figure 5; those from July 1997 through 

June 1998 are shown in figure 6. The ground-water 

temperature fluctuations correspond to the daily waterlevel drawdowns and recoveries caused by the 

pumping well, which is turned on and off two or three 

times a day. The temperature fluctuation in response to 

pumping indicates that the pumping well is inducing 

water from the Tioughnioga River in addition to 

capturing water from the aquifer’s shallow zone (fig. 

7), which undergoes warming and cooling in response 

to air temperature. Pumping of the municipal well 

typically causes a drawdown of about 3 ft below river 

stage in the observation well; this indicates that the 

hydraulic gradient slopes from the river to the well 

during pumping and water is induced from the river.

In summer, when surface water is warmer than 

ground water, the water temperature in the observation 

well rises when the municipal well is being pumped 

and falls when the well is turned off (fig. 5). The 

reverse is true in winter, when surface water is colder 

than ground water-the water temperature in the well 

falls when the well is being pumped and rises when 

the well is turned off. These relations do not 

necessarily hold during seasonal transitions when 

ground-water temperature lags about 1 month behind 

the seasonal trend of surface-water temperature. For 

example, surface water is warmest during July and 

August; whereas ground water is warmest during 

August and September (fig. 6A). Surface water is 

coldest during January and February; whereas ground 

water is coldest during February and March (fig. 6C). 

Ground-water temperatures in the observation 

well were found to “spike” according to the season 

and water temperature of the Tioughnioga River. The 

spikes occurred during (1) moderately high 

Figure 5. Ground-water temperature and water level in observation well between municipal pumping well 452 and Tioughnioga 

River, Marathon, N.Y., August 1-7, 1997. (Location shown in fig. 4.)
11

20 25 31 5 10 15 20 25 31 5 10 15 20 25 30

July August September

1997

1,006

1,013

1,007

1,008

1,009

1,010

1,011

1,012

WATER LEVEL, IN FEET ABOVE SEA LEVEL

38

68

40

45

50

55

60

65

WATER TEMPERATURE, IN DEGREES FAHRENHEIT

Water level

Water temperature

5 10 15 20 25 31 5 10 15 20 25 30 5 10 15 20 25 31

October November December

1997

1,006

1,013

1,007

1,008

1,009

1,010

1,011

1,012

ELEVATION, IN FEET ABOVE SEA LEVEL

44

66

46

48

50

52

54

56

58

60

62

64

WATER TEMPERATURE, IN DEGREES FAHRENHEIT

A.

B.

Figure 6. Ground-water temperature and water level in observation well between municipal pumping well 452 and 

Tioughnioga River, Marathon, N.Y.: A. July through September 1997. B. October through December 1997.

Hydrology
12 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

5 10 15 20 25 31 5 10 15 20 25 28 5 10 15 20 25 31

January February March

1998

1,006

1,013

1,007

1,008

1,009

1,010

1,011

1,012

WATER LEVEL, IN FEET ABOVE SEA LEVEL

38

68

40

45

50

55

60

65

WATER TEMPERATURE, IN DEGREES FAHRENHEIT

5 10 15 20 25 30 5 10 15 20 25 31 5 10 15 20 25 30

April May June

1998

1,006

1,013

1,007

1,008

1,009

1,010

1,011

1,012

WATER LEVEL, IN FEET ABOVE SEA LEVEL

40

58

42

44

46

48

50

52

54

56

WATER TEMPERATURE, IN DEGREES FAHRENHEIT

C.

D.

Figure 6. (continued). Ground-water temperature and water level in observation well between municipal pumping well 452 

and Tioughnioga River, Marathon, N.Y. C. January through March 1998. D. April through June 1998.
13

stormflows, when the river water rises to near bankfull 

stage and is higher than the adjacent ground-water 

levels and seeps into the streambanks; and (2) 

extremely high stormflows, such as that of early 

January 1998 (fig. 6C), when a large snowmelt caused 

the river to overflow its banks, and temporary flooding 

of the well area resulted in aquifer recharge with 

relatively cold surface water (fig. 8). This recharge 

caused rapid lowering of ground-water temperature in 

the observation well (fig. 6C).

SIMULATION OF GROUND-WATER FLOW

A three-dimensional numerical ground-water flow 

model, MODFLOW (McDonald and Harbaugh, 

1988), was used to compute (1) hydraulic heads 

(hereafter referred to as head) in the aquifer under 

steady-state conditions, and (2) the water budget for 

the modeled area. The output from MODFLOW was 

used in conjunction with a particle-tracking program, 

MODPATH (Pollock, 1994), to delineate the areas 

contributing recharge to two simulated wells 

representing the municipal wells, one near the 

Tioughnioga River in the northern part of the modeled 

area and the other near a pond in the southern part.

Model Description and Design

MODFLOW is a widely used code that is based on 

block-centered, finite-difference equations that 

simulate ground water flowing through a porous 

medium. MODFLOW views a three-dimensional 

system as a sequence of layers that may be designated 

as always confined, unconfined, or capable of being 

confined or unconfined.

Tioughnioga

River

Municipal

well 452

Land

Surface

A. Non-pumping conditions

Aquifer

Till or Shale

Water table

NOT TO SCALE

Water table

Tioughnioga

River

Land

Surface

B. Pumping conditions

Municipal

well 452

Aquifer

Till or Shale

NOT TO SCALE

EXPLANATION

1

3

2

SEQUENTIAL STREAM STAGES

BANKFULL STAGE streamwater flows into streambanks

FLOOD STAGE streamwater seeps down to water table

 in flooded area

Direction of ground-water flow

LOW STREAM STAGE (base-flow conditions)

Original water table

Stream

Aquifer

Land

Surface

1

2

3

-

-

Figure 7. Hydrologic settings where ground water 

discharges to the Tioughnioga River: A. Under nonpumping conditions. B. Where pumping by municipal 

well 452 intercepts ground water that would have flowed 

to Tioughnioga River and induces water to flow from river 

to well.

Figure 8. Processes that affect exchange of water between 

Tioughnioga River and adjacent aquifer: When river stage 

rises from low level (1) to bankfull level (2) and is higher than 

adjacent water table, river water moves laterally into 

streambank. When the river overflows its banks (3), 

floodwaters seep downward to the water table.

Simulation of Ground-Water Flow
14 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

Simplifying Assumptions

Five simplifying assumptions about the groundwater flow system were used for the simulations:

(1) Ground-water flow is horizontal within the 

model layers and vertical between layers. (The 

assumption that ground water moves only horizontally 

within layers applies reasonably well throughout the 

modeled area except near pumped wells and directly 

beneath recharge and discharge areas, where the 

vertical-flow component within layers may be 

appreciable.

(2) Recharge to the aquifer is areally uniform.

(3) The modeled aquifer can be divided into a 

finite number of square blocks or cells, each of which 

has uniform hydraulic properties. The water level 

calculated for the center of each block, termed the 

node, is assumed to be representative of water levels 

over that entire block.

(4) A simulated pumping well in a model cell is 

considered to be screened through the full saturated 

thickness of the cell. 

(5) Ground-water levels measured in seven wells 

on June 12, 1997 represent median annual conditions. 

Τhe median annual condition is defined as that when 

the flow-duration is near 50 percent (285 ft3

/s) as 

measured at the stream gaging station (01509000) on 

the Tioughnioga River at Cortland (Hornlein and 

others, 1997), 15 mi north of Marathon.

Model Grid

The model represents the unconfined aquifer as 

two layers (fig. 9), each 10 to 15 ft thick. The saturated 

thickness of these layers 1 and 2 was determined from 

results of test drilling by the Village of Marathon and 

by several consulting engineering companies for a 

variety of projects in the village. The two-layer 

representation provides adequate vertical resolution to 

simulate ground water that could flow beneath cells 

that represent streams (such cells are known as “weak 

sinks” because not all flow into the cell may be 

captured by the cell). All pumping wells are completed 

in the lower part of the aquifer and, therefore, are 

simulated as discharge from model layer 2.

The model grid has 45 rows and 165 columns and 

was superimposed on a map of the Marathon area (fig. 

10). The model contains a total of 14,850 cells (7,425 

cells for each layer), 7,606 cells are active (3,803 

active cells in each layer). A uniform cell size 

representing a 50-x 50-ft surface area was used. The 

model represents a 0.34 mi2 area. 

Layer 2

(Lower sand and gravel)

Layer 1

(Upper sand and gravel) Stream

Recharge from precipitation

No flow 

(till and bedrock)

Injection well

simulating recharge

from upland sources

No flow (till and bedrock)

No flow 

(till and bedrock)

EXPLANATION

Krv

SOUTHWEST NORTHEAST

Q

Q

Q

Kv

K v

Hydraulic conductance controlling flow between the 

aquifer and stream

Kv

Vertical hydraulic conductivity between layers 1 and 2

Q

Underflow into northern end of modeled area

Underflow out of the southern end of modeled area

Injection well

simulating recharge

from upland sources

Discharge 

from

Pumping 

well

r

out

in

out

in

Figure 9. Model representation of ground-water flow in the sand and gravel aquifer at Marathon, N.Y. 

(Location is shown in fig. 1.)
15

0

0 300 METERS

1000 FEET

42° 27'

42° 26'

76° 02' 30" 76° 01' 30"

Modeled area Active cell

Active cell simulating

stream or pond 

Active well simulating

recharge from uplands

and ground-water underflow 

Active cell simulating discharge

from a municipal well

Base from U.S. Geological Survey, Marathon, N.Y., 1994

EXPLANATION

Inactive cell area

Rows

40

165

Columns

30

60

1

10

20

45

1 10

20

30

40

50

160

70

90

80

100

110

120

130

140

150

Active well simulating discharge

as underflow in the south-east

end of modeled area

Active cell with well in which

water level was measured

and used to calibrate model

Figure 10. Active cells and boundaries in model of aquifer in Tioughnioga River valley at Marathon, N.Y. 

Simulation of Ground-Water Flow
16 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

Boundary Conditions

Several types of boundary conditions were 

specified in the model (figs. 9 and 10). Natural 

boundaries were used where possible, but arbitrary 

boundaries were used to limit the northern and 

southern extent of the model because the aquifer 

extends many miles beyond the modeled area. A 

specified-flux boundary was used to represent areal 

recharge from precipitation that falls directly on the 

aquifer. A specified-flux boundary, represented by 

recharge wells (injection wells), also was used along 

the valley walls to simulate recharge from surface 

runoff and ground-water seepage from bordering 

unchanneled uplands into the aquifer (layer 1). The 

drainage area of the unchanneled hillsides was 

delineated, and the recharge from these upland area 

was calculated from equation 1 (p. 8). The calculated 

recharge from the unchanneled upland area was then 

divided by the number of bordering active model cells 

to obtain the recharge rate for each of these cells.

The water withdrawn by the municipal supply 

well in the northern part of the aquifer was simulated 

as being pumped from layer 2 of the aquifer. 

Specified-flux boundaries, represented by wells, also 

were used to simulate ground-water flow into the 

northern boundary of the modeled area and out of the 

southern boundary of the modeled area. The flow into 

the northern end of the model was represented by 

recharge wells, whereas the flow out of the southern 

end was represented by discharge wells. The assigned 

flux in these boundary cells ranged from 100 to 300 

ft3

/d and was calculated from Darcy’s equation for 

one-dimensional flow in a prism of porous material:

; (2)

where Q = flow (ft3

/d)

K = hydraulic conductivity of the 

aquifer (ft/d);

A = cross-sectional area 

perpendicular to flow (ft2);

h2-h1 = head difference across the prism 

of flow (ft);

L = length of flow path (ft).

The following hydraulic values were used to 

calculate underflow (Q) out the Tioughnioga River 

valley: hydraulic conductivity (K), 100 ft/d, crosssectional area (A), 4,500 ft2, head difference (h2-h1) 

of 0.00033 to 0.00067 ft, and length (L) of 1 ft.

The River Package in MODFLOW was used to 

simulate flow of water between (1) the aquifer and the 

river and streams, and (2) the aquifer and the pond 

near the southern municipal well (well 459, fig. 1). 

The River Package was also used to simulate the 

recharge from upland tributaries that lose water where 

they flow over the aquifer. Streambed-conductance 

values in the River Package were adjusted until 

simulated losses were close to those losses measured 

in streams on July 11, 1997 (the period judged to 

represent median annual conditions and selected for 

steady-state simulation). 

Leakage between streams and aquifer, or 

stream and pond, depends on the head difference 

between the surface water and the water table and 

is adjusted according to a streambed-conductance 

term. The amount of leakage is computed by 

Darcy’s Law as follows:

, (3)

where Q = leakage to or from the aquifer 

through the streambed (ft3

/d);

Hs = head in the stream (ft);

Ha = head in the aquifer side of streambed (ft); and

Cstr= streambed conductance (ft2

/d), 

defined as the vertical hydraulic 

conductivity of the streambed, times 

the width of the stream reach, times 

its length, divided by the thickness 

of the streambed.

The pond and streams are in layer 1 of the model. 

Each stream cell was assigned values for the 

following: (1) layer, row, and column number, (2) 

average water-surface elevation, (3) streambed 

conductance, and (4) elevation of bottom and top of 

the streambed. A value of 5 ft/d was estimated for the 

vertical conductivity of the streambed, and a 

streambed thickness of 1.5 ft was used to compute 

streambed conductances. A streambed conductance of 

7,000 ft2

/d was used for the Tioughnioga River and 

pond, and values ranging from 800 to 1,900 ft2

/d were 

used for the small streams.

Q

KA h2 h1 ( ) –

L = -----------------------------

Q Cstr H

s

H

a = ( ) –
17

Hydraulic Values

 Transmissivity values were calculated from 

discharge and drawdown data that were collected by 

drillers at three aquifer-test sitesone in the northern 

part of the modeled area, one in the central part, and 

one in the southern part. Transmissivity was calculated 

from the following equation, which was derived from 

(Todd, 1980, eq. 4.70):

; (4)

where Q = well discharge (ft3/d),

s = drawdown (ft),

T = transmissivity (ft2/d),

t = time of pumping (d),

rw = well radius (ft), and

S = storage coefficient (dimensionless).

Transmissivity values calculated for the three 

aquifer-test sites in the north, central, and south parts 

of the modeled area were 1,900, 1,640, and 2,400 ft2

/d, 

respectively. The storage coefficient was assumed to 

be 0.1. The average horizontal hydraulic conductivity 

of layers 1 and 2 was estimated to be 88 ft/d, which 

was calculated by dividing the transmissivity values by 

the saturated thickness at each pumping test site, then 

averaging the three values. A value of 100 ft/d was 

finally used; this was based-on-trial and error 

calibration of the model.

The vertical hydraulic conductivity for layers 1 

and 2 was estimated to be 20 ft/d; this value was 

calculated by multiplying the horizontal hydraulic 

conductivity value of 100 ft/d by 0.2 to represent an 

assumed anisotropy of 1:5. Vertical hydraulic 

conductivity in stratified drift tends to be less than 

horizontal hydraulic conductivity because, at a small 

scale, the stratified drift contains many layers of 

sediment, some of which consist of plate-shaped 

particles that tend to settle horizontally and, thus, 

impede the vertical flow of ground water. 

Vertical leakance (Vcont) between most cells 

representing layers 1 and 2 was 1.1 ft/d. The vertical 

leakance was computed from the following equation 

(equation 51 of McDonald and Harbaugh, 1988, p. 5-

13) for two vertically adjacent geohydrologic units, 

each unit with its own value of hydraulic conductivity, 

and an average thicknesses of 20 ft for layer 1 and 15 

ft for layer 2.

; (5)

Where vk = thickness of the model layer k,

vk+1 = thickness of model layer k+1, 

kz i,j,k = vertical hydraulic conductivity of the 

upper layer in cell i,j,k,

kz i,j,k+1 = vertical hydraulic conductivity of the 

lower layer in cell i,j,k+1,

i = row number in model grid,

j = column number in model grid, and

k = layer number in model grid.

Model Calibration

The model was calibrated to flow measured in 

three small streams on June 11, 1997 and water levels 

measured in seven wells on June 12, 1997, a period 

judged to represent median annual conditions. The 

model was not calibrated to flows in the Tioughnioga 

River because the measurement error (typically 5 

percent) in large streams would be much greater than 

the gains or losses that would be expected to occur in 

each measured reach. For example, a measurement 

error of ± 13.2ft3

/s would be expected for June 11, 

1997, when streamflow in the Tioughnioga River was 

265 ft3

/s, but the model-generated gain of water from 

ground-water discharge into the Tioughnioga River in 

the modeled area was only 1.3 ft3

/d. 

The model was calibrated through a trial-and-error 

process. Calibration entailed running the model with 

initial estimates of input values and noting the 

differences between measured and simulated water 

levels and streamflows, and then adjusting the input 

values (within reasonably expected ranges) until the 

simulated water levels and streamflows were 

acceptably close to the measured values. Changes 

were made one at a time to the horizontal hydraulic 

conductivity, recharge rate, or the hydraulic 

conductance between aquifer and stream. Final 

horizontal hydraulic conductivity value for layers 1 

and 2 was 100 ft/d (the average hydraulic conductivity 

calculated from drawdown analyses during aquifer 

tests, as mentioned earlier, was 88 ft/d). Calibration 

was considered complete when the simulated 

T 2.3

4π

-------Q

s

--- 2.25 Tt

rw

2

S

log --------

–1

=

Vcontijk , , + 1 2⁄

1

vk ( ) ⁄ 2

kz ijk , ,

---------------- vk + 1 ( ) ⁄ 2

kzi jk , , + 1

+ -----------------------

= ----------------------------------------------

Simulation of Ground-Water Flow
18 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

streamflow losses were close to those measured (table 

2) and the root mean squared error of differences 

between simulated and measured water levels in the 

seven wells was 0.5 ft or less (table 3).

 The water budget for simulated long-term 

average, steady-state conditions with one simulated 

discharging well representing the municipal well 

pumping is given in table 4. The principal sources of 

recharge to the unconfined aquifer is from 

unchanneled runoff and ground-water inflow from the 

uplands (43 percent of total recharge); precipitation 

that falls directly on the aquifer (36 percent); stream 

leakage (19 percent), and ground-water underflow into 

the northern end of the modeled area (2 percent). Most 

ground-water discharge in the simulation was into the 

Tioughnioga River (87 percent of the total); the rest 

discharged to the simulated pumping well (10 percent) 

and out the southern end of the modeled area as 

underflow (3 percent). 

Model Sensitivity

A model-sensitivity analysis, wherein a single 

aquifer property or flux is varied while all other 

properties and fluxes are held constant, was conducted 

to identify the relative effect of adjustments of aquifer 

properties on simulated heads and stream-aquifer 

leakage. Future data-collection efforts can be directed 

to those aquifer properties to which the simulated 

heads were most sensitive. 

Recharge, horizontal hydraulic conductivity, 

vertical conductance between layers 1 and 2, and the 

vertical conductances between the aquifer and the 

streams were increased or decreased, one at a time, by 

multiplication factors within probable ranges; the 

effects of these adjustments on calculated heads at 

seven model cells representing the water-level 

measurement sites are plotted in figure 11. The 

smallest root mean square of the difference between 

Table 3. Difference and root mean square of the difference between measured and simulated heads at seven selected wells in 

the unconfined aquifer at Marathon, N.Y. 

[Values are observed head minus simulated head in layer 1, in feet. Well locations shown in fig. 1].

Location

Well no.

Model 

row

Model 

column

Measured head 

June 12, 1997

Head calculated 

by model

Difference 

between heads 

(X) X2

457 13 134 1008.2 1008.2 0.0 0.00

451 14 50 1007.2 1007.5 .3 .09

463 16 53 1007.3 1007.5 .2 .04

459 17 132 1002.7 1003.0 .3 .09

458 17 133 1003.1 1002.9 -.2 .04

455 18 79 1007.3 1007.8 .5 .25

461 21 129 1003.2 1003.7 .5 .25

Total .76

Root Mean Square 0.33

Table 2. Measured and simulated streamflow gains and 

losses in selected stream reaches near Marathon, N.Y.

[Values are in cubic feet per second. Negative numbers indicate losses. 

Locations are shown in fig. 1.]

Tributary stream

Measured

June 11, 

1997 Simulated

Hunts Creek -0.15 -0.15

Tributary A (near pond) -0.07 -0.07

Tributary B (west side of 

valley

-0.03 -0.03

Sum -0.25 -0.25
19

calculated and measured heads in the final, calibrated 

model (multiplication factor equal to 1 in fig. 11) was 

0.33 ft (table 3). All other multiplication factors 

resulted in root mean squared errors equal to or greater 

than 0.33 feet.

Results of the sensitivity analyses indicate that 

varying the recharge rate and horizontal hydraulic 

conductivity of layer 1 had relatively large effects on 

simulated heads (as much as 5 ft from the observed 

value), whereas varying the conductance between the 

aquifer and the streams, and the vertical conductance 

between layers 1 and 2, had little or no effect on 

simulated heads (fig. 11). Recharge was varied from 

0.5 to 1.5 times the average annual rate of 22 in/yr, 

horizontal hydraulic conductivity was varied from 0.2 

to 5 times the final value that was used in the model 

(100 ft/d), conductance between the aquifer and the 

streams was varied from 0.2 to 5 times the value used 

for the Tioughnioga River (7,000 ft/d) and the small 

streams (800 to 1,900 ft/d), and the vertical 

conductance between layers 1 and 2 was varied from 

0.1 to 10 times the values used for the final model.

Model Application

The Village of Marathon would like to have 

available two wells that are capable of meeting the 

water needs of the villageone main supply well and 

one backup well, and needs to know the recharge areas 

that supply water to the pumping wells. As mentioned 

earlier, only the well in the northern part of the study 

area is being used at present because water from the 

well near the pond in the southern part contains high 

concentrations of manganese. At the time of this study 

(1997-98), the village was considering either 

treatment of the water from the southern well to 

remove the manganese, or installing another well 

elsewhere. Delineations of the areas that contribute 

recharge to these wells would indicate where land-use 

restrictions are needed to protect the ground water 

from contamination. MODPATH was used to 

Table 4. Steady-state water budget for the calibrated model 

with one simulated discharging well 

 [Values are in cubic feet per day]

Budget component

Amount

(cubic 

feet per 

day)

Percent 

of total

A. Recharge to the aquifer

Precipitation on aquifer 47,580 36

Unchanneled runoff and 

ground-water inflow from 

uplands

57,490 43

Stream leakage 25,240 19

Ground-water inflow into 

northern end of modeled area

2,900 2

TOTAL 133,210 100

B. Discharge from aquifer

Municipal wells 13,100 10

Discharge from aquifer to 

surface water

115,610 87

Ground-water underflow out 

of southern end of modeled 

area

4,500 3

 TOTAL 133,210 100

Figure 11. Results of sensitivity analyses for selected 

hydraulic properties in layer 1 of the model of the 

unconfined sand and gravel aquifer at Marathon, N.Y. 

0.1 10 0.2 0.5 1 2 5

MULTIPLICATION FACTOR

2.4

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

ROOT MEAN SQUARE OF DIFFERENCE BETWEEN CALCULATED

 AND MEASURED HEAD IN THE UNCONFINED AQUIFER, IN FEET

Recharge

Horizontal hydraulic

conductivity

Hydraulic conductance

between aquifer and stream

Vertical conductance

between layers 1 and 2

Simulation of Ground-Water Flow
20 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

determine the aquifer contributing area to a pumped 

well (defined as the land-surface area within the valley 

in which water that infiltrates to the water table 

eventually flows to the pumping well) but the uplands 

that contribute surface runoff and ground-water flow 

to the adjacent aquifer contributing area are also part 

of the contributing area, however.

In the calibrated model, two simulated wells were 

used to represent the present municipal wells. Each 

well was simulated as discharging at a average daily 

rate of 13,100 ft3

/d (68 gal/min) which, individually, is 

the average amount of water now pumped daily 

(98,000 gal/d) by the village. The simulated wells are 

far enough apart (about 4,000 ft) that their drawdowns 

do not interfere with each other. The simulated water 

budget for long-term average, steady-state conditions, 

and with both municipal wells pumping at an average 

daily rate of 98,000 gal/d is given in table 5. The 

principal sources of aquifer recharge is from 

unchanneled runoff and ground-water inflow from the 

uplands (41 percent of total recharge); precipitation 

that falls directly on the aquifer (34 percent); stream 

leakage (23 percent), and ground-water underflow into 

the northern end of the modeled area (2 percent). Most 

ground-water discharge in the simulation was into the 

Tioughnioga River (78 percent of the total); the rest 

discharged to the two simulated pumping wells (19 

percent) and out the southern end of the modeled area 

as underflow (3 percent).

The calibrated model was used to compute heads 

in the aquifer (fig. 12) that would result during 

average-annual steady-state conditions with two 

simulated municipal wells pumping at their expected 

daily average rate. The lateral direction of groundwater flow is perpendicular to the potentiometric 

contours and is shown by several arrows in figure 12. 

Most ground water flows from the edges of the valley 

toward the Tioughnioga River, and some flows to the 

two wells; the rest leaves the southern end of the 

modeled area as underflow (fig. 12).

The particle-tracking program, MODPATH, was 

applied to the calibrated model to delineate the aquifer 

areas that contribute recharge to the two simulated 

pumping wells (fig. 13). The flowpath analysis 

indicates that, (1) the northern well’s contributing area 

is 0.10 mi wide and 0.15 mi long and covers an area of 

0.015 mi2

 within the valley, and (2) the southern well’s 

contributing area is 0.20 mi wide and 0.11mi long and 

covers an area of 0.022 mi2

 within the valley (fig. 13). 

The average traveltime for ground water to flow from 

the valley wall to either simulated pumping well is 

about 1.5 years, as estimated from an assumed aquifer 

porosity of 0.3. The flowpath analysis also indicates 

that the contributing areas of both wells contain 

surface-water bodiesreaches of the Tioughnioga 

River and Hunts Creek are within the contributing area 

of the northern well, and a reach of a small unnamed 

tributary and the northern part of the pond are within 

the contributing area of the southern well (fig. 13). 

Both wells are relatively close to these surface-water 

bodiesthe northern well is 57 ft east of the 

Tioughnioga River, and the southern well is 75 ft 

northeast of the pond and 90 ft south of the tributary 

stream; therefore, induced infiltration is likely. 

The uplands that contribute surface runoff and 

ground-water flow to the adjacent valley are also part 

of the contributing area to the pumped wells. The 

contributing areas beyond the valleys were not 

delineated by the model, but the upland contributing 

Table 5. Steady-state water budget with two simulated 

discharging wells

 [Values are in cubic feet per day]

Budget component

Amount

(cubic 

feet per 

day)

Percent 

of total

A. Recharge to the aquifer

Precipitation on aquifer 47,600 34

Unchanneled runoff and 

ground-water inflow from 

uplands

57,500 41

Stream leakage 32,800 23

Ground-water inflow into 

northern end of modeled area

2,900 2

TOTAL 140,800 100

B. Discharge from aquifer

Municipal wells 26,200 19

Discharge from aquifer to 

surface water

110,100 78

Ground-water underflow out 

of southern end of modeled 

area

4,500 3

TOTAL 140,800 100
21

EXPLANATION

AQUIFER BOUNDARY

1008 POTENTIOMETRIC CONTOUR--Shows

simulated head in layer 1 of aquifer. 

Contour interval 1 foot unless otherwise

noted. Datum is sea level

MUNICIPAL WELL

Base from U.S. Geological Survey, Marathon, N.Y., 1:24,000, 1994

Modeled area

Pond

Tioughnioga River

1000

1002

1002

1004

1006

1008

1008

1008

1010

1010

1010

1016

0

0 300 METERS

1000 FEET

42° 27'

76° 02' 30" 76° 01' 30"

42° 26'

Figure 12. Simulated heads in the unconfined aquifer at Marathon, N.Y., for average annual steady-state conditions 

with two simulated discharging wells. (Location is shown in fig. 1.)

Simulation of Ground-Water Flow
22 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

0

0 300 METERS

1,000 FEET

AREA CONTRIBUTING RECHARGE

TO SIMULATED PUMPING WELL 

EXPLANATION

AQUIFER BOUNDARY

Pond

Modeled area

TIOUGHNIOGA RIVER

Village of

Marathon

Hunt's Creek

GROUND-WATER FLOWPATH-- boxes

correspond to travel distance at half-year

intervals

SIMULATED PUMPING WELL

Flow

Base from U.S. Geological Survey, Marathon, N.Y., 1:24,000, 1994

42° 27'

76° 02' 30" 76° 01' 30"

42° 26'

Figure 13. Areas that contribute recharge to two simulated municipal pumping wells tapping the unconfined aquifer 

at Marathon, N.Y. (Location is shown in fig. 1.)
23

areas warrant consideration when the potential for 

aquifer contamination is evaluated. The upland 

contributing areas (not shown) would include: Hunts 

Creek basin and the unchanneled hillside adjacent to 

the valley-contributing area for the northern well, and 

the unnamed tributary’s upland basin and the 

unchanneled hillside adjacent to the valleycontributing area for the southern well.

About 31 percent of the water pumped by the 

simulated northern well (13,100 ft3

/d) was derived 

from the Tioughnioga River, 41 percent was from 

Hunts Creek, 16 percent from unchanneled runoff 

from adjacent hillsides, and 12 percent from 

precipitation that fell on the aquifer in the contributing 

area to the well. Increasing the simulated pumping rate 

resulted in an increase the amount of induced 

infiltration and in the percentage of pumped water that 

is derived from the Tioughnioga River; for example, at 

pumping rates of 38,400 ft3

/d (200 gal/min) and 

48,000 ft3

/d (250 gal/min), the percentage of pumped 

water derived from the river was 51 percent and 60 

percent, respectively.

SUMMARY

The Village of Marathon has three municipal wells 

that tap a relatively thin (typically 25-to 40-ft thick), 

narrow (less than 0.25 mi wide) unconfined sand and 

gravel aquifer in the Tioughnioga River valley. Only 

one of the wells was used by the village at the time of 

the investigation discussed in this report. The second 

well was abandoned as a result of contamination from 

a petroleum spill, and a third well, which is near a 

pond in the southern part of the study area, is not used 

because the water contains high concentrations of 

manganese. The village pumps about 0.1 Mgal/d and 

supplies about 1,000 people. 

The ground-water-temperature fluctuations in an 

observation well between the Tioughnioga River and a 

municipal pumping well correspond to the daily waterlevel drawdowns and recoveries caused by the 

pumping well, which is turned on and off two or three 

times a day. The temperature fluctuation in response to 

pumping indicates that the pumping well is inducing 

water from the Tioughnioga River, in addition to 

capturing water from the aquifer’s shallow zone, 

which undergoes warming and cooling in response to 

air-temperature changes. Pumping of the municipal 

well typically causes a drawdown of about 3 ft below 

river stage in the observation well; this indicates that 

the hydraulic gradient slopes from the river to the well 

during pumping and water is probably induced from 

the river. 

A three-dimensional, finite-difference-groundwater-flow model was used to (1) compute hydraulic 

heads in the aquifer under steady-state conditions, (2) 

develop a water budget, and (3) delineate the areas 

within the valley that contribute recharge to two 

simulated wells that represent two of the municipal 

wells. The contributing area of the contaminated well 

was not delineated because the well was abandoned. 

The simulated water budget for long-term average, 

steady-state conditions, and with both municipal wells 

pumping at an average daily rate of 68 gal/min (98,000 

gal/d), indicated that the principal sources of aquifer 

recharge is from unchanneled runoff and ground-water 

inflow from the uplands (41 percent of total recharge); 

precipitation that falls directly on the aquifer (34 

percent); stream leakage (23 percent), and groundwater underflow into the northern end of the modeled 

area (2 percent). Most ground-water discharge in the 

simulation was into the Tioughnioga River (78 percent 

of the total); the rest discharged to the two simulated 

pumping wells (19 percent) and out the southern end 

of the modeled area as underflow (3 percent). 

The flowpath analysis indicates that the northern 

well’s contributing area is 0.10 mi wide and 0.15 mi 

long and covers an area of 0.015 mi2 within the valley, 

and the southern well’s contributing area is 0.20 mi 

wide and 0.11mi long and covers an area of 0.022 mi2 

within the valley. The average traveltime of ground 

water from the valley wall to the pumping wells is 

about 1.5 years for both wells, as estimated from an 

assumed aquifer porosity of 0.3. The flowpath analysis 

indicates that surface water enters the contributing 

areas of both wells; the contributing area for the 

northern well contains a reach of the Tioughnioga 

River, and contributing area for the southernmost well 

contains part of a pond. Both wells are relatively close 

to these surface-water bodies; the northern well is 57 

ft east of the river and the southern well is 75 ft 

northeast of the pond; therefore induced infiltration 

can be expected.

Surface-water runoff and ground-water flow from 

uplands that drain to the adjacent contributing areas 

within the valley also enter the contributing area to the 

discharging wells, but the contributing areas beyond 

the valley were not delineated. 

Summary
24 Simulation of Ground-Water Flow in an Unconfined Sand and Gravel Aquifer at Marathon, Cortland County, New York

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