a digital simulation of the glacial-aquifer … ... 4. map showing location and potentiometric...
TRANSCRIPT
A DIGITAL SIMULATION OF THE GLACIAL-AQUIFER SYSTEM
IN SANBORN AND PARTS OF BEADLE, MINER, HANSON,
DAVISON, AND JERAULD COUNTIES, SOUTH DAKOTA
By Patrick J. Emmons
U.S. GEOLOGICAL SURVEY
Water-Resources Investigations Report 87-4082
Prepared in cooperation with the SOUTH DAKOTA
DEPARTMENT OF WATER AND NATURAL RESOURCES
and SANBORN COUNTY
Huron, South Dakota 1988
DEPARTMENT OF THE INTERIOR
DONALD PAUL MODEL, Secretary
U.S. GEOLOGICAL SURVEY
Dallas L. Peck, Director
For additional information write to:
District Chief U.S. Geological Survey Rm. 317, Federal Bldg. 200 4th St. SW Huron, SD 57350
Copies of this report can be purchased from:
U.S. Geological Survey Books and Open-File Reports Federal Center, Bldg. 810 Box 25425 Denver, CO 80225-0425
CONTENTSPage
Abstract ................................... 1Introduction ............................... 2Geologic setting ............................. 4Hydrologic setting ............................ 8Simulation of flow in the ground-water system .............. 21
Simplifying assumptions ....................... 21The digital model .......................... 23Model data ............................. 23
Dimensions of the finite-difference grid ............ 23Altitude of the top of the aquifer ............... 23Altitude of the bottom of the aquifer ............. 25Hydraulic conductivity of the aquifer ............. 25Storage in the aquifer ..................... 25Recharge to the aquifer .................... 30Evapotranspiration from the aquifer .............. 30Pumpage from the aquifer .................... 31River leakage from the aquifer ................. 31
Calibration and application of the ground-water-flow model ........ 36Steady-state simulation ....................... 36Transient simulation ........................ 38
1973-83 simulation period ................... 401976 monthly simulation period ................. 48
Model sensitivity ............................ 52Summary and conclusions ......................... 54Selected references ........................... 57
111
ILLUSTRATIONSPage
Figure 1. Map showing location of the study area and majorphysiographic divisions in eastern South Dakota ....... 3
2. Schematic diagram showing site-numbering system ....... 53. Map showing bedrock geology ................. 74. Map showing location and potentiometric surface
of the aquifers in the glacial outwash ............ 95. Geohydrologic section showing the relation
between glacial aquifers and confining beds ......... 106. Map showing thickness of the glacial-aquifer system ..... 137. Map showing thickness of confining bed overlying
the glacial-aquifer system .................. 148. Bar chart showing annual precipitation and departure
from normal at Huron, Forestburg, and Mitchell ........ 169. Hydrographs of water-level changes in wells completed
in the glacial-aquifer system ................ 1710-17. Map showing:
10. Finite-difference grid blocks and model boundariesused to define the glacial-aquifer system ........ 22
11. Altitude of the top of the glacial-aquifer system .... 2412. Altitude of the bottom of the glacial-aquifer system . . 2613. Average hydraulic conductivity for each grid block ... 2814. Average recharge for each grid block .......... 3215. Average evapotranspiration for each grid block ..... 3416. Simulated prepumping potentiometric surface ....... 3917. Simulated 1983 potentiometric surface .......... 43
18. Hydrographs showing comparison of simulated andobserved annual potentiometric heads ............. 45
19. Map showing drawdown between the simulated predevelopment steady-state potentiometric surface and the simulated 1983 transient potentiometric surface ............ 46
20. Map showing simulated potentiometric surface, August 1976 . . 5021. Hydrographs showing comparison of simulated and
observed monthly potentiometric heads, 1976 ......... 51
iv
TABLES
Page
Table 1. Thickness, storage coefficient, and hydraulic conductivityof the glacial aquifers .................... 11
2. Recharge to the glacial aquifers ............... 183. Monthly pan evaporation and estimated potential
evapotranspiration ...................... 194. Ground-water use in the James River basin and
the study area ........................ 205. Relation between grain size and hydraulic conductivity .... 276. 1976 monthly ground-water withdrawal from the study area ... 317. Comparison between simulated and observed
potentiometric heads ..................... 378. Simulated water budget under steady-state conditions ..... 409. Average annual precipitation and estimated recharge ...... 41
10. Estimated annual pan evaporation and estimatedpotential evapotranspiration ................. 42
11. Annual simulated water budgets, 1973-83 ............ 4712. Average monthly precipitation and recharge for 1976 ...... 4913. Estimated monthly evapotranspiration for 1976 ......... 4914. Monthly simulated water budgets, 1976 ............. 5315. Model sensitivity to changes in recharge,
evapotranspiration, and hydraulic conductivity ........ 55
CONVERSION FACTORS
For readers who may prefer to use metric (International System) units rather than inch-pound units, the conversion facto-rs for the terms in this report are listed below i
Multiply inch-pound unit
acreacre-foot per day (acre-ft/d)acre-foot per year (acre-ft/yr)cubic foot per second (ftVs)foot (ft)foot per day (ft/d)gallon per minute (gal/min)inchinch per year (in/yr)mile (mi)
0.4047,233,233
0.028320.30480.30480.06308
25.425.4
1 .609
To obtai,n metric^ un^t> +
hectarecubic meter per yearcubic meter per yearcubic meter per secondmetermeter per dayliter per secondmillimetermillimeter per yearkilometer
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 "Mean Sea Level of 1929."
A DIGITAL SIMULATION OF THE GLACIAL-AQUIFER SYSTEM
IN SANBORN AND PARTS OF BEADLE, MINER, HANSON,
DAVISON, AND JERAULD COUNTIES, SOUTH DAKOTA
By Patrick J. Emmons
ABSTRACT
The drought in South Dakota from 1974-76 and the near-drought conditions in 1980-81 have resulted in increased demands on the ground-water resources within many of the irrigated areas of the James River basin in eastern South Dakota. These increases in demand for irrigation water from the glacial- aquifer system and continued requests to the State of South Dakota for addi tional irrigation well permits have created a need for a systematic water- management program to avoid overdevelopment of this system in the James River basin.
The aquifer system which can be unconfined at shallow depths and confined at greater depths in the same section has a thickness ranging from less than 10 feet to greater than 200 feet and an average hydraulic conductivity of 316 feet per day. Calculated storage coefficients of the aquifer system range from 0.00039 to 0.000017 and specific yield values are as great as 0.28. Calculated recharge rates to the unconfined aquifer range from 0.9 to 3.4 inches per year and to the confined aquifer, 0.24 to 0.72 inch per year. Evapotranspiration, which accounts for most of the natural discharge from the aquifer, was estimated to be as great as 36.2 inches per year in some locations.
An equally spaced grid containing 56 rows and 52 columns was used to simulate the glacial-aquifer system. The steady-state simulation was cali brated using water-level data collected before significant ground-water development (before 1973). The aquifer was also simulated in 11 annual transient stress periods from 1973 through 1983 and in 12 monthly transient stress periods for 1976.
The simulated predevelopment potentiometric heads were compared to average water levels from 32 observation wells to check the accuracy of the simulated potentiometric surface. The average arithmetic difference between the simulated and observed water levels was 1.68 feet and the average absolute difference was 4.38 feet. The nonpumping steady-state simulated water budget indicates that recharge from precipitation accounts for 97.1 percent of the water entering the aquifer and evapotranspiration accounts for 98.2 percent of the water leaving the aquifer. The sensitivity analysis of the steady-state model indicates that the model is most sensitive to reductions in recharge and least sensitive to changes in hydraulic conductivity.
In the annual transient simulation, recharge, evapotranspiration, and pumpage were adjusted annually. The maximum annual recharge varied from
1
0.10 inch in 1976 to 8.1M inches in 1977. The potential annual evapotran- spiration varied from 29.9 inches in 1982 to M8.9 inches in 1976. Withdrawals from the glacial-aquifer system increased 2.6 times between 1975 and 1976. Since 1976, the pumpage has fluctuated annually in both distribution and quantity, however, the maximum annual withdrawals have not increased significantly since 1976. The average annual arithmetic difference between the simulated and observed water levels ranged from -3.88 feet in 197 1* to 2.23 feet in 1982; the average absolute difference ranged from M.70 feet in 1973 to 11.70 feet in 1982. The annual transient simulated water budget varies considerably as a result of changes in recharge and evapotranspiration.
In the 1976 monthly transient simulation, the maximum annual recharge rate of 0.10 inch was distributed over the months of March, April, and September. The potential monthly evapotranspiration rate ranged from 12.50 inches in August to 0.00 inch during the winter when the ground was frozen. The average arithmetic and absolute differences between the simulated and observed potentiometric heads for each of the 12 monthly simulation periods were calculated. The average arithmetic difference ranged from -1.25 feet in November to 2.68 feet in July. The average absolute difference ranged from 3.82 feet in October to 6.88 feet in July. The simulated monthly water budgets varied considerably as a result of changes in the monthly evapotranspiration, storage, and pumpage.
INTRODUCTION
The drought in South Dakota from 197^-76 and the near-drought conditions in 1980-81 have resulted in increased demands on the ground-water resources within many of the irrigated agricultural areas of the James River basin in eastern South Dakota. Between 1972 and 1980, the total quantity of ground- water irrigation from the glacial-aquifer system in the James River basin increased from M,999 acre-ft/yr (South Dakota Water Resources Commission, 1973) to 35,M22 acre-ft/yr (South Dakota Dept. of Water and Natural Resources, 1981), an increase of greater than 600 percent. These increases in demand for irrigation water from the glacial-aquifer system and continued requests to the State of South Dakota for additional irrigation well permits have created a need for a systematic water-management program to avoid overdevelopment of these aquifers in the James River basin.
In 1979, the South Dakota Department of Water and Natural Resources and Sanborn County entered into a cooperative agreement with the U.S. Geological Survey to define the flow system of the glacial-aquifer system in part of the James River basin (fig. 1). The study area has been divided into a northern part and a southern part. An appraisal of the northern part of the aquifer system in Spink and northern Beadle Counties has been completed (Kuiper, 198M).
The purpose of this study was to describe the flow system of the glacial aquifers in the southern part of the James River basin by using a digital flow model. More specifically, the study will better define the glacial aquifer boundaries; determine the aquifer thickness, direction of ground-water movement, and hydrologic properties of the glacial-aquifer system; and identify areas of ground-water recharge and discharge and determine rates of natural recharge and discharge. This report presents the results of the
100° . - - I _ T
} \\ ICAMPBELLJ MC i i.^_.^j v
ED MUND S j /\y / I / / ' r\ ri i I / / I / iin - '-T -T - 1-4 '.: /
-SkUiGSBURYj BROOKINGS 1
k © I
STUDY AREA OF KUIPER (1984)
STUDY AREA OF THIS REPORT
PHYSIOGRAPHIC BOUNDARY
GREAT PLAINS PROVINCE
MISSOURI RIVER TRENCH
COTEAU DU MISSOURI
CENTRAL LOWLANDS PROVINCE
JAMES RIVER LOWLANDS
LAKE DAKOTA PLAIN
JAMES RIVER HIGHLANDS
COTEAU DES PRARIES
MINNESOTA RIVER-RED RIVER LOWLANDS
Figure 1. Location of the study area and major physiographic divisions in eastern South Dakota.
investigation of the glacial aquifer in the southern part of the James River basin using a two-dimensional ground-flow model and describes the design and calibration of that model.
The scope of this investigation included the collation, examination, and synthesis of aquifer-test data, several thousand well and test hole logs, water-level measurements, pumpage data, and other miscellaneous geohydrologic data.
The aquifer-test data provided site-specific information on the aquifer's characteristics, such as hydraulic conductivity and storage coefficient. Koglin, Stack-Goodman, and Ambroson (1981) and Schroeder (1982) have compiled well and test-hole data for Beadle and Miner Counties, respectively. Well and test-hole data for Kingsbury, Me Cook, Hanson, Davison, Aurora, Jerauld, and Sanborn Counties were obtained from the South Dakota Geological Survey, U.S. Geological Survey, U.S. Bureau of Reclamation, private drillers, and other miscellaneous sources. The well and test-hole data provided detailed informa tion on the extent, thickness, and composition of the aquifers and confining beds. Water-level data which were obtained from the South Dakota Department of Water and Natural Resources provided historical water-level data and allowed for the determination of long-term water-level changes. The South Dakota Department of Water and Natural Resources also provided the pumpage data. This data was used to determine the magnitude of the stress being applied to the aquifer system as a result of pumpage.
Where existing data were inadequate, the South Dakota Geological Survey drilled five additional test wells. All these data were used to develop a digital flow model of the aquifer system. The aquifer system was simulated by using the U.S. Geological Survey's modular, three-dimensional, finite- difference, ground-water flow model program developed by McDonald and Harbaugh (1984).
Wells and test holes used in this report are numbered according to the Federal land-survey system of eastern South Dakota (fig. 2).
GEOLOGIC SETTING
During the Pleistocene Epoch, continental glaciation from the north and east covered eastern South Dakota, depositing a blanket of glacial drift over the eroded preglacial bedrock surface. Glaciation radically altered the topography by partially filling major valleys and entirely obliterating many small valleys, forcing the cutting of new valleys and forming massive end moraines. The overall effect of glaciation has been to reduce the local topo graphic relief. One of the greatest changes caused by the glaciers was the rearrangement of the surface drainage. Before glaciation, the main streams flowed toward the east. As a result of glaciation, the drainage in eastern South Dakota is now predominately southward (Flint, 1955).
The James basin is a lowland of low to moderate relief that trends north- south between the Coteau du Missouri and the Coteau des Prairies highlands, which are of glacial origin (fig. 1). The basin is 50 to 75 mi wide and approximately 250 mi long in South Dakota. The James River, which occupies the central axis of the basin, drains the basin to the south (Flint, 1955).
I09N6IW3600DD
/
'o «*^
Figure 2.--Site-numbering system. The well number consists of township followed by "N," range followed by "W," and section number, followed by a maximum of four uppercase letters ^that indicate, respectively, the 160-, 40-, 10-, and 2^-acre tract in which the well is located. These letters are assigned in a counterclockwise direction beginning with "A" in the northeast quarter. A serial number following the last letter is used to distinguish between wells in the same tract. Thus, well 109N61W36DDDD is the well recorded in the SE£ of the SE^ of the SE* of the SE£ of section 36 in township 109 north and range 61 west of the 5th meridian and baseline system.
Most of the surficial deposits in the study area are the result of glaciation and are collectively called drift, which is any material deposited by or from a glacier. Drift can be subdivided into two major types, till and outwash, which differ greatly in both physical and hydrologic characteristics. Till, which was deposited directly from or by glacial ice, is a heterogeneous mixture of silt, sand, gravel, and boulders in a clay matrix. Outwash, which was deposited from or by meltwater streams on top of the ice or beyond the margin of the active glacial ice, consists primarily of layers of clayey or silty sand and sandy gravel, interbedded with layers of sandy or gravelly silt or clay. Beds of well-sorted sand and gravel are contained in the outwash but are generally small and discontinuous (Howells and Stephens, 1968).
The drift may be covered by deposits of alluvium along streams and rivers and locally, the drift may be covered by windblown sand and silt. The alluvium consists of poorly sorted, poorly stratified, thin, discontinuous layers of material that ranges in size from clay to boulders. Alluvium under lying the James River flood plain is as much as 25 ft thick and generally contains a much higher proportion of silt than does the alluvium elsewhere in the study area (Howells and Stephens, 1968).
The bedrock units directly underlying the drift in the study area in descending order are the Cretaceous Pierre Shale, Niobrara Formation, and Carlile Shale, and the Precambrian Sioux Quartzite (fig. 3). The Pierre Shale consists of a light to dark-gray fissile bentonitic clay-shale. Hedges (1968) reports that the Pierre Shale in Beadle County contains marly zones and chalky beds. Also, thin limestone beds, concretions, and bentonite stringers may be present. In the study area, the shale ranges from 0 to 600 ft in thickness.
The Niobrara Formation is predominantly a light- to dark-gray speckled marl with some chalk and shaly beds. The marl contains shells of Foraminifera (one-celled organisms) which give the marl a distinctive white speckled appearance. The formation ranges from 0 to 110 ft in thickness.
The Carlile Shale directly underlies the drift only in the southeast and a small area in the south-central part of the study area. The Carlile Shale consists mostly of light-gray to black shale containing silty and sandy zones. The thickness of the shale ranges from 0 to 312 ft. The Codell Sandstone Member is situated at or near the top of the Carlile Shale. A light-blue to black shale zone may separate the Codell Sandstone Member from the overlying Niobrara Formation. The Codell is a brown, fine- to medium-grained, moderately cemented sandstone. Thin shale layers in the Codell are common. The Codell Sandstone Member ranges from 0 to 120 ft in thickness.
The Sioux Quartzite underlies the drift only in. the southeastern part of the study area. The Sioux Quartzite is a hard, massive, pink siliceous ortho- quartzite which is horizontally bedded, cross-bedded, and jointed. Thickness of the quartzite in the study area is unknown (Hedges, 1968).
98° 30'
44°30' I 12 N.
T.I II
N.
T.I 10 N.
T. 109
T,!08 ft
I 107N.
Ii03 R
R.65W, R.64W. R.63W, R.6! W. R.60W. R.59W, R.58W, R.57W, R.56W.
EXPLANATION
Kp PIERRE SHALE
Kn NIOBRARA FORMATION
Kc CARLILE SHALE
p-6 SIOUX QUARTZITE
024 SMILES Geology by Hedges and others, 1981t r t, ,4 i 024 6 KILOMETERS
Figure 3. Bedrock geology.
7
HYDROLOGIC SETTING
Ground water is a major source of water in the James River basin. In the unconsolidated surficial deposits, only the more sandy and gravelly glacial outwash deposits yield significant quantities of as much as 1 ,000 gal/min of water to wells. The remaining unconsolidated surficial deposits generally are either too clayey and silty or are too thin to serve as major sources of water except in very localized situations.
The recharge, movement, and discharge of water in the outwash aquifers are controlled by the lithology and stratigraphy of the surficial deposits and the underlying bedrock units. The till and the layers of silt and clay within the outwash deposits act to confine the outwash aquifers. The Niobrara Formation and the Codell Sandstone Member of the Carlile Shale may provide significant quantities of water to wells; however, these bedrock aquifers generally are isolated to some extent from the overlying outwash aquifers by till, clay and silt layers within the outwash deposits or shale units, or both. The Pierre Shale, Carlile Shale, and the Sioux Quartzite generally yield little or no water to wells and are considered to be confining beds.
The complex hydrologic system which exists in the glacial outwash has been subdivided into four aquifers in the study area (fig. 4). They are the Floyd, Warren, Tulare, and Bad-Cheyenne aquifers. According to Hedges and others (1981), the aquifer boundaries are based on one or more of the following criteria:
a) A thinning or constriction of the aquifer.b) A facies change from high to low permeability of the aquifer
material.c) A change from unconfined to confined conditions or vice versa.d) A ground-water divide.e) A ground-water discharge point such as a stream or lake.
The study area encompasses most of the Warren and Floyd aquifers and only a small part of the Tulare and Bad-Cheyenne aquifers. Most of the Tulare aquifer is located to the north and west in Spink and Hand Counties, respectively. The Bad-Cheyenne aquifer extends northwest into Hand and Hyde Counties.
The four glacial outwash aquifers generally are separated from each other by till confining beds and may be internally confined by till and thin clay and silt outwash layers (fig. 5). However, the till, and clay and silt outwash layers generally allow some flow to occur between and within aquifers.
Table 1 indicates that there is generally more variation of hydraulic conductivity within the aquifer than among the four aquifers. The hydraulic conductivity of the Warren aquifer ranges from 160 to 670 ft/d with an average of 410 ft/d. Hydraulic conductivity of the Floyd aquifer ranges from 37 to 589 ft/d with an average of 260 ft/d and.hydraulic conductivity of the Tulare aquifer ranges from 20 to 1,430 ft/d with an average of 270 ft/d. There is no hydraulic conductivity data available for the Bad-Cheyenne aquifer.
98° 30'
44°304- T,I 12 N.
T.! If
N,
Ii 10 N.
T,109 N.
T.108
N.
T.107 N.
T.106
N.
T.105 N.
I!04 N.
T,103
N.
R.65W, R.64W. R.63W. R.62W. R.61 W. R.60W, R.59W. R.58W. R.57W. R.56W.
024 6 MILES I , »-, H i024 6 KILOMETERS
EXPLANATION
F FLOYD AQUIFERW WARREN AQUIFERT TULARE AQUIFER
BC BAD-CHEYENNE AQUIFER
( APPROXIMATE LIMITS OF AQUIFER___A' LINE OF GEOHYDROLOGIC SECTION SHOWN ON FIGURE 5-BOO POTENTIOMETRIC CONTOUR--Shows altitude of potentiometric
surface in May, I 980. Contour interval 20 feet. Datum is sea level
LOCATION OF HYDROGRAPHS SHOWN ON FIGURE 9
Geohydrology by Hedges Ond others, 1981
Figure JJ. Location and potentiometric surface of the aquifers in the glacial outwash.
AR
. 6
5
W.I
I R. 60 W.
| R. 59 W.
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6
KIL
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Sa
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(s
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cl
ay,
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w
ith
san
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or s
htl
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Figure
5. Geohydrologic se
ctio
n showing
the
relation between
glacia
l aq
uife
rs an
d co
nfin
ing
beds.
Table 1. Thickness, storage coefficient, and hydraulicconductivity of the glacial aquifers
Location
109N63W34ACAB110N60W11BBD110N61W06ACDD2111N59W06BBBB2112N59W31CCCD1112N59W32DDDD2113N62W05DDBB1113N62W18BCAD11 1 3N62W22ABBA2113N62W22ABBA4113N62W34CDCC2113N62W36DCDB1
115N66218DCCC115N66220DABD115N66W20DADB4115N66W20DACA115N66W20DABD3115N67W19CABB2115N67W19CABB3115N68W23BBAB
108N63W20ABCC
108N61W17AACC
114N63W24CBAA1114N63W26ACAA1
Aquifer
WarrenFloydFloydFloydFloydFloydTulareTulareTulareTulareTulareTulare
TulareTulareTulareTulareTulareTulareTulareTulare
Floyd
Warren
Warren
TulareTulare
Aquifer Storage thickness coefficient (feet) (dimensionless)
Beadle County
855524334040504243434930
2 Hand County
7130308040535319
3 Hanson County4-87
(mean = 38,median = 32)
" Jerauld County
70
^anborn County
42
*Spink County
6560
--0.04.00035.00017.00017.00039
.00027.00034.00033.00044.00039
.0135
.15
.28
.14
.00038
.00016
.00016
.00052
--
.0001
.000017
"
Hydraulic conductivity (feet per day)
6708016045038023047090
260260140210
8111611695
21713913920
37-589(mean = 255,median = 245)
402
160
1,430560
Howells and Stephens, 1968. 2 From Koch, 1980a.3 From Hansen, 1983; Aquifer thickness and hydraulic conductivity were calcu lated from transmissivity and thickness of the Floyd aquifer at 31 test holes, "From Hamilton, 1985.
11
Because all of the aquifers are in outwash deposits with similar hydraulic conductivities and are hydraulically connected by zones of material with lower hydraulic conductivity, the aquifers are treated as a single glacial-aquifer system rather than individual aquifers in this report.
A reliable delineation of the glacial-aquifer system is difficult to obtain due to the glacial processes that deposited the glacial outwash. The system is comprised of a series of connected and disconnected lenses, fingers, stringers, and channels of sand and gravel separated by layers of clay and silt outwash and till (fig. 5). The thickness of the sand and gravel layers in the aquifer system as well as other hydrologic characteristics vary greatly over short distances. For example, in the southeastern corner of T. 111 N., R. 63 W., Sec. 22, the aquifer consisted of 13 ft of gravel and 14 ft of sand. In section 23, approximately 0.25 mi east, the aquifer is composed of 63 ft of sand in one test hole and 30 ft of sand and 22 ft of gravel in another test hole. As a result of the extreme variations in thickness and composition, individual aquifer units often can be traced for only short distances or not at all. The composite gla-cial-aquifer system thickness ranges from less than 10 ft to greater than 200 ft (Howells and Stephens, 1968). The average thickness of the aquifer ranges from 4 to 144 ft and averages 56 ft in thickness (fig. 6). More than 1,000 drillers' logs were used to estimate the thickness. The aquifer top is defined as the uppermost occurrence of sand and gravel below the till where present. If no till is present, the aquifer top is land surface. The bottom of the aquifer is defined as the top of the bedrock or the bottom of the lowermost sand and gravel. The average aquifer thickness also includes all silt and clay layers in the aquifer zone. Lateral boundaries for the aquifer system were placed where the average sand and gravel thickness was less than about 5 ft.
The average thickness of the confining bed ranges from 4 to 170 ft and averages 49 ft (fig. 7). The thickness was estimated from the drillers' logs. The confining bed thickness was calculated as the thickness of all the clay and silt between land surface and the top of the aquifer. The confining bed controls, in part, the quantity of water which can recharge the aquifer and also the quantity of water available for evapotranspiration.
The hydraulic conductivity of the glacial-aquifer system, calculated from aquifer tests in the study area, ranges from 80 to 670 ft/d with an average of 316 ft/d (table 1). If the 31 hydraulic conductivity values estimated from test-hole data from Hanson County south of the study area are included, the average hydraulic conductivity decreases to 267 ft/d.
Water in the glacial-aquifer system occurs under unconfined water-table conditions and confined or artesian conditions. Due to the complexity of the aquifer system, an aquifer can be confined and unconfined in the same area. The value of the storage coefficient derived from an aquifer test is an indication of whether the aquifer is confined or unconfined in the vicinity of the test. The storage coefficient of most confined aquifers ranges from about 0.00001 to 0.001. The storage coefficient in an unconfined aquifer, often referred to as specific yield, generally ranges from 0.1 to 0.3. With one exception, the storage coefficients calculated from aquifer tests in the study area range from 0.00039 to 0.000017, indicating the aquifer system is artesian in these areas. One storage value, 0.04, indicates transitional conditions
12
1234 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
Aquifer model boundary
Aquifer model boundary
50 LINE OF EQUAL THICKNESS OF AQUIFER Contour interval 25 feet
56
R.65W. R.64W. R.56W.
24 6 KILOMETERS
Figure 6. Thickness of the glacial-aquifer system,
13
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
Aquifer model boundary
Aquifer model boundary |
50 LINE OF EQUAL THICKNESS OF CONFINING BED--Contour interval 25 feet
56
R.65W. R.56W.
2 4 6 KILOMETERS
Figure 7. Thickness of confining bed overlying the glacial-aquifer system,
between confined and unconfined. No specific yield values indicating unconfined conditions were calculated in the study area. Specific yield values as large as 0.28, however, were calculated from aquifer tests in Hand County located west of the study area.
Recharge to the glacial-aquifer system occurs as infiltration of precipitation and snowmelt directly into the aquifer or through the overlying confining bed. The thickness of the clay and silt in the overlying till and alluvium (fig. 7) controls the rate at which the underlying aquifer system can be recharged. Recharge occurs rapidly where there are permeable sediments overlying the aquifer. When the clay and silt are sufficiently thick (generally greater than 40 ft), there is probably little or no recharge by infiltration to the underlying aquifer. To a lesser extent, the aquifer in the study area also receives water as underflow from the west and as leakage from the lateral till boundaries.
The relationship between precipitation and recharge can be observed by comparing precipitation data and hydrographs for selected wells. For example, between 1968 and 1973i precipitation was generally at or above normal (fig. 8). Examination of the hydrographs (fig. 9) indicates a general water- level rise over the same period of time. Hedges and others (1983) calculated recharge rates to the Floyd and Warren aquifers from observation-well data and by flow net analysis. They also report results of recharge rates estimated from computer model analyses of the Tulare aquifer (table 2). The recharge rates to the unconfined parts of the glacial-aquifer system range from 0.9 to 3.4 in/yr and in the confined parts of the aquifer range from 0.24 to 0.72 in/yr.
Ground water flows downgradient perpendicular to the potentiometric contours as shown in figure 4. Although some long-term water-level declines have occurred as indicated by the hydrographs (fig. 9), the general direction of ground-water movement has remained the same. The direction of ground-water movement in the glacial-aquifer system in the study area is generally eastward or southeastward, west of the James River and westward or northwestward east of the James River. However, there is no or a very poor hydraulic connection between the aquifer system and the James River. Benson (1983, p. 47) states, "...there is probably no significant interchange between the James River and the underlying aquifers in Beadle County." According to Steece and Howells (1965), little natural surface discharge occurs from the glacial-aquifer system in Sanborn County. There is some discharge from the aquifer to Dry Run Creek and to the James River in Hanson and Davison Counties (Benson, 1983; Hansen, 1983); however, most of this discharge is south of the study area. A small amount of water may leak from the aquifer in the lateral low hydraulic conductivity till layers and into the underlying bedrock.
Evapotranspiration accounts for most of the natural discharge from the aquifer system. The potential evapotranspiration in the study area is estimated to be 72 to 74 percent of the pan evaporation or about 36.2 in/yr (Farnsworth and others, 1982). The potential evapotranspiration of an area can be estimated from pan-evaporation data (table 3). According to Farnsworth and Thompson (1982), the monthly estimated pan evaporation at Huron computed from meteorological measurements between January 1956 and December 1970 using a form of the Penman Equation are as follows:
15
91
DEPARTURE FROM NORMAL, IN INCHES
PRECIPITATION, IN INCHES
OQ C
CD
00
I
oH"
a a> a
£c0)
crc
OQ
a3H-ri- O & CD
U1O^
IOO CO
o>
o roa» oo o ro ^. a» o» o ro
a»
a»
//////I
xxxx) /s//.
ZZJ
VsVSJ.
106N58W07BCCC1 J£U
1316
13121308
1304
j 1300W 1296
Fj 1292_J 1288
<r; 1284ttj 1280^0 1276
H 1272
> 1268
OQ 1264
- -~ yy^^^ ^-^~ * - - ;-----------
1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983
107N62W35AAAB1320
1316
1312
130613041300
12961292
128812841280
1276
1272
12681264
1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983
110N60W20AAAC1320
13161312
1308
130413001296
12921288
1284
128012761272
12681264
GO
Om E-
&H
g
J
w >w_]K wt_l<^
1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983
111N63W24DDDD1320
131613121308
1304
1300129612921288
12841280
1276127212681264
1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983
Figure 9. Water-level changes in wells completed in the glacial-aquifer system,
17
Table 2. Recharge to the glacial aquifers
[From: Hedges and others, 1983]
Aquifer
Units in inches per year
From computermodel analysis
Fromobservation well data
From flow net analysis
Floyd aquifer: East James
Buried-unconfined (part) Buried-confined
Pearl Creek:Buried-confined (all)
Tulare aquifer: East James
Buried-unconfined (part) Hitchcock
Buried-unconfined (part) Western Spink
HandBuried-unconfined (part)
Warren aquifer: Morris Creek
Buried-confined
Warren aquifer: (continued) West James
Buried-unconfined (part) Buried-confined
0.38 to 1.52 (best fit) 0.76
0.41 to 1.66 (best fit) 0.83
0.41 to 1.66 (best fit) 0.83
3.4
.9
2.5
2.0
3.4
3.0
0.30
,72
,24
,35
35
Table 3. Monthly pan evaporation and estimated potential evapotranspiration
Mean monthly Mean monthly potential"pan evaporation" evapotranspiration 1
Month (inches) (inches)
JanuaryFebruaryMarchAprilMayJuneJulyAugustSeptemberOctoberNovemberDecember
0.69.83
2.154.456.267.688.897.684.963.521 .60.84
0.50.61
1.573.254.575.616.495.613.622.571.17.61
Annual 49.55 36.18
*The mean monthly pan evaporation multiplied by 0.73,
The estimated potential evapotranspiration is from wet soil or other moist natural surfaces. The potential evapotranspiration from the glacial- aquifer system is reduced by the depth to water in the aquifer and by the confining bed overlying the "aquifer. As the depth to water in the aquifer increases, the amount of water for evapotranspiration decreases. There is probably very little water removed by evapotranspiration where the aquifer potentiometric surface is greater than 10 to 15 ft below land surface. A till confining bed overlying the aquifer can decrease the quantity of water avail able for potential evapotranspiration from the aquifer even though the potentiometric surface may be less than 15 ft below land surface.
Ground water is used for irrigation, municipal, industrial, farm, ranch, and domestic use. However, most of the water withdrawn from the glacial- aquifer system is used for irrigation. Withdrawals other than irrigation generally hav£ little effect on the aquifer system. Permitted ground-water withdrawal rates in the study area have increased from 136 ftVs in 1973 to 499 ftVs in 1981, a 267 percent increase in 8 years (table 4). The actual ground-water withdrawal rate for irrigation has increased from 2.66 to 12.45 ftVs. The effects of the continued increase in the withdrawal of ground water are shown on the hydrographs (fig. 9). The hydrographs indicate that possible long-term water-level declines are beginning to occur in some areas as the result of the continuing increase in ground-water withdrawals.
19
Tabl
e 4.
Gro
und-
wate
r us
e in
th
e Ja
mes
Rive
r? ba
sin
and
the
stud
y ar
ea
Year
Proj
ecte
d ac
reag
e th
at wa
sir
riga
ted
with
grou
nd wa
ter
in the
Jame
s River
basi
n1
(acr
es)
Aver
age
dept
h of
ground-water
applied
in the
Jame
s Ri
ver
basin
1 (inches)
Permitted
grou
nd
water
acre
age
in
the
stud
y ar
ea
(acr
es)
Perm
itte
d ground-
wate
r withdrawal
in the
stud
y ar
ea
(cub
ic feet
per
seco
nd)
Grou
nd-w
ater
withdrawal in
the
study
area
(cub
ic fe
et
per
seco
nd)
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
14,463.87
9,18
1.32
13,479.39
13,6
61 .64
16,793.85
34,4
59.8
449
,237
.02
53,0
44.9
960
,045
.60
69,240.91
71 ,37
0.36
74,991.95
60,5
69.1
1
12.5 8.3
13.2
13.0
12.7
16.0
12.1
710.15
7.76
10.5
112.52
8.78
9.18
12
,287
.69,
997.
110
,222
.215
,819
.825
,562
.828,304.2
36,042.2
39,5
59.9
43,767.9
Not
calcualted
Not
calculated
135.64
109.96
119.
02190.60
285.92
311 .48
402.
54445.65
499.21
Not
calculated
Not
calculated
2.
663.
375.33
14.1
015
.64
11.73
8.47
9.79
16.52
29.5
212
.45
Sout
h Dakota De
part
ment
of
Water
and
Natural
Resources
irrigation qu
esti
onna
ire
information (written
commun., 19
70-8
3).
Withdrawal da
ta not
available fo
r 19
82.
Withdrawal wa
s estimated using
1983
pumpage
and
comparing
prec
ipit
atio
n data fo
r 1981-83.
SIMULATION OF FLOW IN THE GROUND-WATER SYSTEM
S impli fy ing Assumpt ions
Ground-water flow within an aquifer system is governed by a complex series of interrelated hydrologic processes. A number of simplifying assumptions make it possible to describe these hydrologic processes and allow the aquifer system to be represented mathematically. The simplifying assumptions may not exactly represent the hydrologic processes, but should include the basic assumptions and logic governing these processes.
The simplifying assumptions for simulation of the glacial-aquifer system are:
1. The aquifer consists of one layer. The top of the aquifer is defined as the first occurrence of sand or gravel below the till confining bed or land surface if the confining bed is not present. The bottom of the aquifer is defined as the bottom of the lowest sand or gravel layer or the top of the bedrock. The aquifer includes all of the deposits between these vertical limits.
2. The overlying confining bed allows recharge to infiltrate downward to the aquifer and ground water to migrate upward through the till when the confining bed is less than about 45 ft thick.
3. The clay and silt or bedrock below the aquifer is an impermeable lower boundary of the aquifer system.
4. All lateral boundaries of the aquifer system are impermeable or no- flow boundaries. At 12 internal locations, the potentiometric heads are held constant or are specified-head boundaries.
5. The James River is hydraulically isolated from the aquifer system by the confining bed except at 2 river-head boundary locations (fig. 10). At these 2 locations, water discharges from the aquifer to the river.
6. All flow in the aquifer is horizontal and in the overlying confining bed, vertical. Storage occurs only in the aquifer. The confining bed yields no water to wells.
7. The principal source of recharge to the aquifer system is precipita tion. The thickness of the overlying confining bed (fig. 7) controls the rate at which the aquifer system can be recharged. The greater the confining bed thickness, the lower the recharge rate.
8. Discharge from the aquifer occurs as evapotranspiration, pumpage, and at the specif ied-head boundary. The primary method of discharge is evapotranspiration. Upward leakage of water from the aquifer to the zone where evapotranspiration can occur is controlled by the thickness of the overlying confining bed. The greater the thickness of the confining bed, the lower the rate at which evapotranspiration can occur.
21
12.3
4
6
8
0
2
4
6
6
0
2
>4
>6
28
JO
52
54
56
58_^
K3
\Z
14
16
(8
>0
>2
54
56
2 3 4 6 8 10 12 14 16 18 20 22
I
24 26 28 30
AA
32 34 36
38 40 42 44
46
48 50 52
T. -112
N.
T.1 1 1
N.
T.1 10
N.
T.
N.
T. i n Q
N.
T. 107
N.
T. i /-* cN.
T. 105
N.
T. 1 04
N.
T. 103
N.
R.65W. R.64W. R.63W. R.62W. R.6 I W. R.60W. R.59W. R.58W. R.57W. R.56W.
EXPLANATION
NO-FLOW BOUNDARY
SPECIFIED-HEAD BOUNDARY
A RIVER-HEAD BOUNDARY
0246 MILES
024 6 KILOMETERS
Figure 10.--Finite-difference grid blocks and model boundaries used to define the glacial-aquifer system.
22
The Digital Model
A mathematical model of an aquifer system is the application of mathema tical equations describing ground-water flow and certain simplifying assumptions to a concept of the flow system. A digital-computer model or simply a digital model is a mathematical model that uses a digital computer to obtain approximate solutions to the partial differential equations of ground- water flow. The digital model used in this study is the U.S. Geological Survey modular three-dimensional finite-difference ground-water flow model of McDonald and Harbaugh (1984).
The model uses finite-difference methods to obtain approximate solutions to partial-differential equations of ground-water flow. The modeling area was subdivided into a series of finite-difference grid blocks in which the aquifer properties are assumed to be constant (fig. 10). The continuous derivatives of the partial differential equation of ground-water flow are replaced by the finite-difference approximations at the center (node) of each of the grid blocks. The result is a series of finite-difference equations that were solved with the slice-successive overrelaxation (SSOR) numerical technique.
Model Data
A ground-water flow model is constructed by entering a value for the hydrologic components that define the system at each finite-difference node. The value assigned to the node is considered to be representative of the entire grid block. The following is a list of components used in the model of the glacial-aquifer system:
1. Dimensions of the finite-difference grid.2. Altitude of the top of the aquifer.3. Altitude of the bottom of the aquifer.4. Hydraulic conductivity of the aquifer.5. Storage of the aquifer.6. Recharge to the aquifer.7. Evapotranspiration from the aquifer.8. Pumpage from the aquifer.9. River leakage from the aquifer.
Dimensions of the Finite-Difference Grid
A finite-difference grid is required so the geohydrologic data can be put in a form to be entered and manipulated by the computer-model program. The equally spaced finite-difference grid selected to represent the model area has 56 rows and 52 columns. The grid blocks are 1 mi or 5,280 ft on a side. Each grid block, shown in figure 10, overlies a 640-acre section.
Altitude of the Top of the Aquifer
The altitude of the top of the aquifer (fig. 11) is the top of the first sand or gravel layer below the overlying till confining bed. Where the till is not present, the altitude of the aquifer top is land surface.
23
98°30 1234 6 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52
1240 ALTITUDE OF TOP OF AQUIFER Contour interval 40 feet. Datum is sea level
56
R.65W. R.64W. R.63W. R.62W. R.6I W. R.60W.
4 6 MILES
R.59W. R.58W. R.57W. R.56W.
024 6 KILOMETERS
Figure 11. Altitude of the top of the glacial-aquifer system.
24
Altitude of the Bottom of the Aquifer
The altitude of the bottom of the aquifer is the bottom of the lowermost sand and gravel layer (fig. 12).
Hydraulic Conductivity of the Aquifer
The hydraulic conductivity, a measure of the ability of the aquifer to transmit water, varies greatly over short distances due to the variability of the glacial deposits. All of the test-hole and drillers' logs were examined and an average composite log for each section was developed. Using the average composite logs for each section of land and the hydraulic conductivity values (table 5), an average composite aquifer hydraulic conductivity was calculated for each section of land (fig. 13). The relationship between hydraulic conductivity and grain size was varied to achieve the best overall model results. The assignment of the average composite hydraulic conductivity for each section is based on the assumption that aquifer materials are uniformly variable and the test-hole and drillers' logs adequately depict the range of the types and thicknesses of aquifer materials in each section.
The hydraulic conductivity of the aquifer system is generally much less than assigned by Koch (1980b) to the alluvial-mantled outwash deposits of the Big Sioux aquifer, located east of the James River basin in South Dakota (table 5). The hydraulic conductivities of the outwash deposits in the glacial-aquifer system are less because they contain much more silt and clay.
The average composite hydraulic conductivities for each section of land range from 11 to 320 ft/d (fig. 13). These average composite hydraulic conductivities are less than the hydraulic conductivities calculated from aquifer tests (table 1). This is expected as the aquifer tests are site specific and generally are conducted in areas where the aquifer has greater hydraulic conductivity and thickness.
As a result of the averaging process for hydraulic conductivity, the ground-water-flow model will approximate the glacial-aquifer system on a regional scale, but locally, deviations may occur.
Storage in the Aquifer
With one exception, storage coefficients calculated from aquifer tests in the study area range from 0.00039 to 0.00001? (table 1), indicating artesian conditions exist at these locations in the glacial-aquifer system. The exception, a storage value of 0.04, most likely indicates a transition between confined and unconfined conditions. Specific yield values as high as 0.28 were calculated from aquifer tests in the glacial-aquifer system west of the study area.
A storage coefficient of 0.0003 was used in the ground-water flow model to represent the glacial-aquifer system in a grid block where the average potentiometric head was higher than the average altitude of the top of the aquifer (artesian conditions). A specific yield of 0.15 was assigned when the average potentiometric head in the section was lower than the average altitude of the top of the aquifer for the same section (water-table conditions).
25
98°30'
1234 698°
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 4O 42 44 46 48 50 52
ALTITUDE OF BOTTOM OF AQUIFER Contour interval 40 feet. Datum is sea level
56
R.65W.
T.103
N.
R.56W.
4 6 KILOMETERS
Figure 12. Altitude of the bottom of the glacial-aquifer system.
26
Table 5. Relation be
twee
n gr
ain
size
and
hydraulic
conductivity
ro
-o
Grain
size
Clay or
si
ltSa
nd,
very fine
Sand
, fi
neSa
nd,
fine to me
dium
Sand
, me
dium
Sand
, fi
ne to
coarse
Sand,
medium to
coar
seSand,
coar
seSand an
d gr
avel
Sand
, coarse,
and
grav
elGr
avel
Rang
e of
hydraulic
cond
ucti
viti
esin
gl
acia
l drift
1(f
eet
per
day)
<20
10-80
70-1
4070-400
130-
400
70-6
0013
0-80
0
400-
1 ,0
0040
0-1 ,2
0040
0-1 ,400
800-2,000
Hydraulic
cond
ucti
vity
assigned to
Big
Siou
xaq
uife
r1
(feet
per
day)
10 40 70 200
270
300
400
540
600
670
800
Hydraulic
conductivities us
ed in th
is model
(feet
per
day)
Mode
lro
w 1-8
12 -- -- -- 150 -- 170 -- 190
Mode
lro
w 9-
13 6 -- -- -- 75 -- -- 85 -- 95
Mode
l Mo
del
row
14-1
5 ro
w 16-18
15
6 -- __ __ 188
75__ __
212
85__
238
95
Model
row
19-5
6
22 -- -- --281
319
356
'Fro
m Ko
ch,
1980
b.
rv>
oo
ow
i 2
4°3
0'-
4
CO
LUM
N
98
°30
' 9
8°
1 2
i, 4
6
8 1
0
12
14
16
18
2
0
22
2
4
26
2
8
30
" "I
58L_
r -
. 66
i 66
| 59
J116
|77
' 32
31
r
. 52
71
76
51
r~ -i
1 22
51
18
29
52
'
i1
15
32
20 1
1 19
~
"~
. '
15 21
,18
Li
25
23 1
31
17
51
35
253
215
16
13
12
13
11
15
137
57
18
53
66
76
1371
|
65
91
77
50
61
131
|121
22
5 11
0 78
75
15
7
|118
170
91
61
61
88
1220
16
3 11
2 59
61
82
' 68
65
15
1 10
5 12
9 99
115
120
121
136
157
151
239
107
123
121
87
237
.211
207
118
151
121
203
1112
17
1 15
7 22
0 20
2 17
3
I [1
85
202
95
110
' 10
36
29
~
~ "
"
52
56
50
51
11
51
56
119
117
141
13
19
11
37
27
10
19
15
90
57
39
32
52
53
68
98
66
77
82
78
11
58
58
77
90
76
65
58
81
90
112
100
67
18
27
33
15
37
18
19
26
17
10
15
26
19
27
17
32
53
25
28
31
32
26
39
18
26
10
32
26
11
50
19
61
79
66
117
10
51
18
51
67
56
72
70
56
53
11
52
73
61
69
65
11
18
37
31
27
26
29
16
12
32
22
16
21
10
58
73
31
11
50 -3
5
69
67
62
58
51
38
103
95
65
13
35
18
17
31
30
20
18
11
51
10
32
32
21
16
17
18
15
18
38
15
12
13
19
31
23
25
19
19
29
23
13
13
92
116
117
101
19
96
.111
99
76
67
55
80
67
63
12
38
38
36
23
30
29
21
12
11
113
110
110
133
112
77
195
107
111
112
121
103
112
185
112
202
118
110
88
153
176
206
131
136
91
109
180
189
167
150
169
121
139
166
100
91
115
189
159
128
100
58
275
215
161
162
131
97
283
237
180
117
117
103
229
229
291
115
123
19
135
119
120
111
109
36
59
67
12
50
11
37
29
15
- 32
33
39
25
112
109
103
115
121
91
85
117
89
91
102
96
100
59
67
79
99
95
91
58
72
92
103
85
130
90
77
79
92
101
109
91
77
133
97
91
61
68
91
137
130
119
116
113
137
117
67
102
105
101
121
83
53
68
98
57
61
11
19
38
HO
1H
Hi
35
H3
50
1 1
11
13
. |1
23
L -i
r J
56
68
61 L
j
31
39
81
77
27
52
27
95
125
108
85
59
31
97
66
116
121
92
38
50
13
127
137
79
10
30
28
52
58
23
38
11
18
18
21
30
60
37
11
20
16
31
27
35
15
25
31
35
26
26
22
12
13
13
29
22
33
50
12
38
22
22
36
28
16
30
32
27
103
11
61
86
61
112
6H
H9
19
76
91
90
15
18
31
39
28
20
23
31
26
25
30
35
22
35
25
27
29
11
87
87
95
85
115
106
109
66
76
80
101
85
103
61
87
32
12
67
71
67
91
36
53
53
107
135
102
77
123
126
96
111
91
99
123
83
111
121
98
153
161
115
111
118
157
228
275
231
1HH
15
7 19
1 22
0 26
2 26
3
108
135
171
229
202
202
98
81
90
191
151
201
135
131
139
77
I85
11
1 12
1 83
.
105
63
51
61 (
_
32
3
4
36
3
8
40
4
2
44
4
6
48
5
0
52
1
__
_J
9*I
97
63
61
101
65
67
60
91
106
90
76
82
29
77
79
81
121
101
31
60
101
115
72
108
37
55
110
69
11
75
15
36
51
17
19
17
15
35
36
17
17
36
21
31
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Recharge to the Aquifer
The areal distribution of recharge to the aquifer was based on analyses of precipitation data (fig. 8) and on the thickness of the confining bed overlying the aquifer (fig. 7). The areal distribution of recharge to the aquifer was tested and refined as part of the steady-state simulation process. It was determined that the maximum available recharge to the aquifer was 7.0 in/yr and occurred only where the average thickness of the confining bed in the section overlying the aquifer was less than 10 ft. With average confining bed thicknesses between 10 and 45 ft, the rate of recharge to the aquifer decreased linearly to 0.0 in/yr. No recharge occurs when the average confining bed thickness in the section exceeds 45 ft. Figure 14 shows the percentage of available recharge that reaches the aquifer. Because an empirical relationship was developed between recharge and thickness of the confining bed overlying the aquifer, the values should not be considered absolute. The values are hydrologically reasonable and provide the best overall model results.
Evapotranspiration from the Aquifer
The areal distribution of evapotranspiration from the aquifer is controlled by the potential evapotranspiration (table 3). the thickness of the confining bed overlying the aquifer (fig. 7), and the depth of the potentiometrie head below land surface. The areal distribution of potential evapotranspiration from the aquifer in each section was tested and refined as part of the steady-state simulation process. The best overall model results were obtained when the potential steady-state evapotranspiration rate was 36.0 in/yr. The potential evapotranspiration rate can occur only where no confining bed is present above the aquifer. Even though the potentiometric head in the aquifer may be close to land surface, the confining bed will restrict upward movement of water and reduce the potential evapotranspiration rate. Therefore, when the average confining bed thickness is between 0 and 45 ft, the potential evapotranspiration rate decreases linearly from 36.0 to 0.15 in/yr. The potential evapotranspiration remains constant at 0.15 in/yr for confining bed thicknesses greater than 45 ft. Figure 15 shows the percentage of the potential evapotranspiration available from the aquifer.
The evapotranspiration from the aquifer is controlled also by the depth of the aquifers' potentiometric surface below land surface. Evapotranspira tion did not occur when the potentiometric heads are greater than 15 ft below land surface. Because an empirical relationship was developed between potential evapotranspiration rate from the aquifer, thickness of the confining bed overlying the aquifer, and depth of the potentiometric head below land surface, does not mean these values should be considered absolute, but only that they are reasonable hydrologically and provide the best overall model results.
30
Pumpage from the Aquifer
Ground-water withdrawal data are required to simulate the glacial-aquifer system. Pumpage data were collected for the period 1973 through 1983. Before 1973, the aquifer was in steady-state or equilibrium conditions. That is, although the water levels in the aquifer system may have declined during the summer months due to reduced recharge, increased evapotranspirat ion or pumpage, the water levels generally recovered to approximately the same or equilibrium levels during the winter or early spring months. Because the aquifer system was in equilibrium before 1973. pumpage was not included in the pre-1973 steady-state simulation.
Beginning in about 1973, ground-water withdrawals (table 4) had increased in some parts of the aquifer to the point that the aquifer did not fully recover before the next pumping season. To simulate the period from 1973 through 1983, the annual pumpage by section was included in the annual transient simulation. Examination of precipitation data (fig. 8) indicates that 1974 through 1976 was a period of below normal precipitation with 1976 being the driest. To simulate 1976, monthly pumpage by section was included in the 1976 monthly transient simulation (table 6).
Table 6. 1976 monthly ground-wa.ter withdrawal from the study area
Pumpage l Month (cubic feet per second)
January 1.59February 1 .59March 1.59April .00May 19.85June 40.50July 48.99August 45.64September 15.34October .00November 1 .59December 1 .59
Dakota Department of Water and Natural Resources (written commun.).
River Leakage from the Aquifer
Where the glacial-aquifer system is hydraulically connected to the James River, the river may contribute water to or drain water from the aquifer, depending on the head gradient. Hansen (1983) indicates that the river is hydraulically connected to the aquifer in a small part of the study area in Davison County; the locations of these river grid blocks are shown in figure 10 as river-head boundaries.
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ES
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. 58 W
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.
Figure
14. Average recharge for
each
grid block.
oo -tr
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T. 107
N. T. 106
N. T. 105
N. T. 104
N. T. 103
N.
R. 65 W.
R. 64 W.
R. 63 W.
R. 62 W.
R. 61
W.
0
R. 60 W.
6 MILES
R. 59 W.
R. 58 W.
R. 57 W.
R. 56 W.
i '
AKILOMETERS
Figu
re 15. Average evapotranspiration for
each
gr
id bl
ock.
CALIBRATION AND APPLICATION OF THE GROUND-WATER-FLOW MODEL
Model calibration is the process by which input data are adjusted so the model will adequately simulate historical potentiometric heads and flows. The initial equilibrium conditions were simulated by entering average recharge and evapotranspiration, and by setting the storage in the aquifer to zero. This is referred to as the steady-state or equilibrium simulation. The simulated steady-state potentiometric heads were compared to the observed annual average pre-1973 potentiometric heads to assess the accuracy of the steady-state simulation. The transient simulation includes storage and time-dependent recharge, evapotranspiration, and pumpage. Again, the simulated transient potentiometric heads were compared to observed potentiometric heads.
Calibration involves varying the values of hydraulic conductivity, recharge, evapotranspiration, and storage to bring simulated potentiometric heads closer to the observed potentiometric heads. The parameters were varied within reasonable hydrologic limits. Calibration was completed when a "best fit" between the simulated and observed potentiometric heads was obtained.
Table 7 gives an indication of how well the model duplicated observed potentiometric heads. The smaller the average difference between the simulated and observed potentiometric heads, the better the model represents the glacial-aquifer system. However, because of the uneven areal distribution of the data, the degree to which the model duplicates observed potentiometric heads can only be assessed where sufficient water-level data exist.
There are several means by which errors can be introduced into the analysis. The complexity of the aquifer can result in seemingly unusual water levels. In addition, nearby pumping can result in observed water levels which do not reflect natural conditions. Inaccurate measurement or recording of water levels can result in additional errors. Errors in the model formula tion, estimation of the hydrologic parameters, and the lateral differences between well location and node center in the model will also produce differences between the simulated and the observed potentiometric heads. The table reflects the best composite set of average arithmetic and absolute differences obtained between the simulated and observed potentiometric heads for the steady-state simulation, the 1976 monthly, and 1973-83 transient simulations.
Steady-State Simulation
The steady-state simulation provides information on the hydrologic condi tions in the glacial-aquifer system before significant ground-water develop ment; no storage terms or pumpage are included in the simulation.
The ground-water withdrawals in the study area before 1976 were much less than the withdrawals after 1976 (table 4). Before 1973 the aquifer generally was in equilibrium with water levels nearly recovering to prepumping levels during the nonirrigated fall, winter, and spring seasons (fig. 9). Precipitation in the study area was significantly less than normal from 1974 through 1976 (fig. 8). As a result of the drought, large and continued increases in ground-water withdrawals began in 1976. Therefore, the steady- state simulation represents average conditions for the glacial-aquifer system before 1973.
36
Table 7. Comparison
betw
een
simulated
and
obse
rved
po
tent
iome
tric
heads
Average
arit
hmet
ic
difference be
twee
n Mo
del
simu
late
d an
d obse
rved
si
mula
tion
pote
ntio
metr
ic he
ads
1(feet)
Average
absolute
diff
eren
ce be
twee
nsimulated
and
obse
rved
potentiometric he
ads2
(fee
t)
Maxi
mum
positive
difference be
twee
nsimulated
and
observed
pote
ntio
metr
ic heads*
(fee
t)
Maximum
negative
diff
eren
ce be
twee
nsimulated
and
obse
rved
potentiometric he
ads"
(feet)
Number of
observation
wells
with observed
potentiometric
heads
Ste
ad
y-s
tate
Tra
nsie
nt
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
Jan
ua
ry
1976
Fe
bru
ary
19
76M
arch
19
76A
pril
1976
May
19
76Ju
ne
1976
July
19
76A
ug
ust
19
76S
epte
mbe
r 19
76O
ctober
1976
Nov
embe
r 19
76D
ecem
ber
1976
1.6
8
-1.2
7-3
.88
-1.5
2-3
.10
-.49
-.9
9.7
5-.
21
.75
2.2
3.5
4 -.
93
-.6
3 .17
2.68
1.45
1.4
2.7
9-1
.24
1.55
4.3
8
4.5
76.6
54.7
05.9
85.2
66.3
29.1
89.8
610.3
911.7
01
1.4
6 5.3
65.2
8 5.7
46.8
85.8
55.7
43.8
24.2
94.
11
16.2
2
14.3
912
.91
13.8
917
.65
15.5
82
4.3
24
3.8
044.4
646.7
544.2
04
1.9
1
14
.89
14.6
2 9.5
314.1
21
7.6
29-
341
0.5
98.7
317.6
8
8.3
2
10
.35
15.4
711.5
718.0
22
7.4
73
4.4
54
5.3
84
5.6
445.8
34
6.0
04
7.1
8 13.8
416.0
5 14.5
51
4.6
21
4.7
614.8
815.0
51
4.6
41
1.9
8
32 32 32 32 50 60 74 no
114
114
122
120 0 17 32 0 0 15 16 35 13 24 14 31
'Pos
itive
numb
er in
dica
tes
simu
late
d he
ad was
higher th
an th
e observed head;
nega
tive
numb
er indicates
simulated
head
was
lowe
rth
an th
e ob
serv
ed head.
2The
abso
lute
va
lue
of a
number is th
e number wi
thou
t it
s associated si
gn.
For
exam
ple, th
e ab
solu
te value
of 2
and
-2 are
the
same
.'P
osit
ive
difference wh
en simulated
head
is greater
than
ob
serv
ed wa
ter
leve
l.
"Negative
difference wh
en si
mula
ted
head is less th
an observed wa
ter
leve
l.
There are water-level data from 32 observation wells completed in the aquifer system for the period before 1973 (fig. 16). The observed potentio- metric heads are used to check the accuracy of the simulated potentiometric surface. The average arithmetic difference between the predevelopment simu lated and observed water levels was 1.68 ft and the average absolute difference was 4.38 ft (table 7). The difference between simulated and observed heads was more than 10 ft at three locations. The simulated head was 15.28 ft higher than the average observed water level in the observation well located in grid block: row 5, column 22, 16.22 ft higher in row 20, column 27, and 13.37 ft in row 30, column 35 (fig. 16).
The reasons for the discrepancies are unknown but may be due to the complexity of the glacial-aquifer system. These observation wells may be partly isolated from the surrounding aquifer by till or clay and silt outwash, and therefore, water levels from these wells may not represent the regional potentiometric surface. Also due to the simplifying assumptions in the model and the size of the finite-difference grid, the simulated steady-state heads will contain inaccuracies. However, the model is one of the best means of improving and evaluating our understanding of the aquifer system and of testing the sensitivity of the model to changes in selected aquifer properties.
The highest potentiometric heads are located on the eastern and western boundaries of the model area and the lowest heads are near the James River which runs approximately through the center of the area simulated (fig. 16). Ground water flows from higher to lower potentiometric head and perpendicular to the potentiometric contours. The flow west of the James River is eastward toward the river and east of the James River the flow is westward or northwestward. Previous studies have indicated that the James River gains little water from the underlying glacial-aquifer system. The steady-state simulation shows that evapotranspiration can reasonably remove enough water from the aquifer to approximate the predevelopment potentiometric surface.
Recharge from precipitation was 97.1 percent of the predevelopment inflow to the aquifer (table 8). The average annual recharge to each active model grid block was 0.96 inch. This value is in the range of aquifer recharge calculated from observation-well data, flow-net analyses, and values used in other computer models (table 2). Evapotranspiration accounts for 98.2 percent of the outflow from the predevelopment steady-state aquifer. The average evapotranspiration from each active model grid block was 0.97 in/yr.
Transient Simulation
The transient simulation includes pumpage from and storage in the aquifer system. The transient or pumping simulation includes 11 consecutive pumping periods between 1973 and 1983 (table 4) and 12 monthly pumping periods in 1976 (table 6). The starting potentiometric heads in the 1973 transient simulation are the heads generated by the steady-state simulation. Subsequent annual simulations used the potentiometric heads generated by the preceeding simula tion. The starting potentiometric heads in the 1976 monthly transient simulation were those generated by the 1975 annual transient simulation. Subsequent monthly simulations used potentiometric heads generated by the preceeding monthly simulation.
38
1234
98°30'
6| 898°
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52
Aquifer model boundary
? f 5r d \r?
Aquifer model boundary i
1275 POTENTIOMETRIC CONTOUR Shows altitude of water level. Contour interval 25 feet. Datum is sea level
LOCATION OF OBSERVATION WELL NODE
LOCATION OF OBSERVATION WELL NODE WHERE SIMULATED AND OBSERVED POTENTIOMETRIC HEADS DIFFER BY MORE THAN 10 FEET
56
R.65W R.56W.
2 4 6 KILOMETERS
Figure 16. Simulated prepumping potentiometric surface.
39
Table 8. Simulated water budget under steady-state conditions
Flow rates incubic feet
Budget component per second Percent
INFLOW
Recharge to the aquifer from precipitation 101.42 97.1 Inflow at specified-head boundaries 3.06 _2_._9
Total inflow 104.48 100.0
OUTFLOW
Evapotranspiration from the aquifer 102.85Discharge from the aquifer to the stream 1.36Outflow at specified-head boundaries .51
Total outflow 104.73 100.0
The following sections briefly compare the simulations with the known hydrology at the end of 11 annual and 12 monthly periods. The most recent (1983) annual simulation and the August 1976 monthly simulation will be compared in more detail.
1973-83 Simulation Period
Water levels in the aquifer system were at or near their highest levels at the end of 1972 and the beginning of 1973 (fig. 9). In the spring of 1973, the water levels began to decline due primarily to a substantial decrease in precipitation in the study area (fig. 8). This drought which lasted through 1976 created a large increase in the demand for ground water for irrigation (tables 4 and 6).
Recharge to and evapotranspiration from the glacial-aquifer system are difficult to estimate accurately. They are controlled by a number of complex, interrelated variables which are not fully understood and cannot be accurately measured. The recharge and evapotranspiration rates used in the transient simulations were estimated based on only three of these variables: precipita tion, pan evaporation, and thickness of the confining bed overlying the aquifer system.
Maximum annual recharge to the aquifer system was estimated from the average annual precipitation recorded at Huron, Forestburg, and Mitchell (table 9). The maximum annual recharge ranged from 0.10 inch in 1976 to 8.14 inches in 1977 which correspond to the driest and wettest years. The percentage of the maximum available annual recharge which actually infiltrates is controlled by the thickness of the confining bed overlying the glacial- aquifer system (fig. 14).
40
Table 9. Average annual precipitation and estimated recharge
Year
19731974197519761977197819791980198119821983
Average annualprecipitation forHuron, Forestburg,
and Mitchell 1(inches)
21.5313.3018.9112.5526.8218.3522.4715.7417.7926.6920.39
Averageannual
departure 2(inches)
-1 .50-9.73-4.12
-10.483.79
-4.68-.56
-7.29-5.243.66
-2.64
Maximum annualrecharge tothe glacial
aquifer system3(inches)
6.62.45
4.66.10
8.144.247.002.283.828.105.77
*Data from the U.S. Department of Commerce, 1973-83.2Departure from 23.03 inches per year, the average annual precipitation forHuron, Forestburg, and Mitchell, from 1968 through 1972. Data from the U.S.Department of Commerce, 1968-72. Calculated from the following table:
Departure (inches) Recharge calculation
0.00.0 to -1.00<-1.00 to -10.00<-10.00
7.00 inches + (0.30 x departure)7.00 inches7.00 inches - [(departure - 1.00 inch) x 0.75]0.10 inches
41
Table 10. Estimated annual pan evaporation and estimated potential evapotranspiration
Annual pan Annual potentialevaporation 1 evapotranspiration 2
Year (inches) (inches)
5148496752494250514146
37.235.035.848.938.035.030.736.537.229.933.6
19731974197519761977197819791980198119821983
Average 49.6 36.2
Estimated using data from the U.S. Department of Commerce, 1973-83. Calculated as 0.73 times the annual evaporation.
The evapotranspiration rate from the aquifer also is difficult to esti mate. The estimate of the annual potential evapotranspiration is calculated as 73 percent of the estimated total annual pan evaporation (table 10). The estimated total annual pan evaporation varied from 41 inches in 1982 to 67 inches in 1976 with an average of 49.6 inches. Annual potential evapotran spiration varied from 29.9 inches in 1982 to 48.9 inches in 1976 with an average of 36.2 inches. Figure 15 shows the percentage of the potential available evapotranspiration which can be withdrawn from the aquifer system.
The acreage permitted to be irrigated with ground water in the James River basin before 1973 was small (table 4). However, as a result of the 1974-76 drought, the quantity of permitted acreage increased dramatically after 1975. Ground-water withdrawals in the study area prior to 1976 were small. In 1976, withdrawals were 2.6 times the withdrawal in 1975. Since 1976, the ground-water withdrawals in the study area have fluctuated annually in both distribution and quantity; however, the maximum annual withdrawals have not increased significantly since the large increase in 1976. The location of each grid block in which pumping occurred in 1983 is shown in figure 17.
The average arithmetic difference between the simulated and observed water levels for the eleven annual calibration periods ranged from -3.88 ft in 1974 to 2.23 ft in 1982 (table 7). The average absolute difference ranged from 4.57 ft in 1973 to 11.70 ft in 1982. The average arithmetic difference between the simulated and observed water levels for 1983 was 0.54 ft and the average absolute difference was 11.46 ft. The maximum positive difference
42
1234 6 8 10 12 14 16 18 20 22 24 26 28 30 I 32 34 36 38 40 42 44 46 48
Aquifer model boundary
Aquifer model boundary i
EXPLANATION
-1275 POTENTIOMETRIC CONTOUR Shows altitude of water level. Contour interval 25 feet. Datum is sea level
O LOCATION OF OBSERVATION WELL NODE
p LOCATION OF PUMPING NODE
L" J_ 5 A J 1
r i
I I
1 ! QI
R.65W. R.64W. R.63W. R.62W. R.6IW. R.60W. R.59W. R.58W. R.57W.
024 6 MILES
R.56W.
024 6 KILOMETERS
Figure 17. Simulated 1983 potentiometric surface.
between the simulated and observed water levels was 41.91 ft in the observation well located in grid block row 52, column 42, and the maximum negative difference was 47.18 ft in the observation well located in grid block row 54, column 50 (fig. 17). The relatively large 1983 maximum positive and negative differences are probably a result of the complexity of the glacial- aquifer system and the model's inability to simulate the aquifer on a scale small enough to adequately represent this complexity. The model does, however, adequately simulate the glacial-aquifer system on a one-square-mile scale.
Figure 18 shows four hydrographs of measured water levels from observa tion wells in the study area and the simulated potentiometric heads for the corresponding grid block in which the observation wells are located. The four hydrographs indicate that there is generally good agreement between the simu lated and observed potentiometric heads and demonstrates the ability of the transient simulation to simulate the aquifers' responses to changes in annual recharge, evapotranspiration, and pumping.
The highest simulated 1983 potentiometric heads are located along the eastern and western boundaries of the model area and the lowest heads are found along the James River (fig. 17). The potentiometric heads range from greater than 1 ,400 ft above sea level along the west boundary of the model to less than 1,250 ft above sea level along the James River. The direction of ground-water flow generally is eastward, west of the James River and westward or northwestward, east of the James River. Configuration of the potentio metric surface and direction of ground-water flow are similar to those of the predevelopment conditions (fig. 16).
Comparison of the simulated predevelopment steady-state and 1983 poten tiometric heads indicates that the heads have declined more than 25 ft (fig. 19). Although drawdowns of more than 25 ft have occurred, the conver sion from confined to unconfined conditions will result in a significant reduction in this drawdown rate. When the head declines in a confined aquifer, water in storage is released from the expansion of water and from the compression of the aquifer. Where the aquifer is unconfined, the predominant source of water is from gravity drainage of the sediments through which the decline in the water table occurs. In an unconfined aquifer, the volume of water derived from expansion of water and compression of the aquifer is negligible (Heath, 1983).
A hydrologic budget equates accretions to the water supply to depletions of the water supply. A budget equation states that inflow minus outflow equals change in storage. A general equation of the hydrologic budget for the glacial-aquifer system may be written:
precipitation + inflow at boundaries + discharge from ground-water storage = evapotranspiration + outflow at boundaries + recharge to ground-water storage + pumpage.
44
OQ
C
-J
0>
WA
TER
LEV
EL,
IN F
EE
T A
BO
VE
SEA
LEV
ELW
ATE
R LE
VEL
, IN
FE
ET
AB
OV
E SE
A L
EVEL
OO
O
O
3 o 0) CL
O cr
w 0)
2: CT)
CO
^ ro 4^ a
a
a
a
o 2: 05
O ro
o
2!
en
ro
CO en ro
o en en CD ro
o
o
o
0) a. o
o O 0) 0) CL w
34 68 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
Aquifer model boundary
Aquifer model boundary
10 LINE OF EQUAL DRAWDOWN Contour interval 5 feet
R.65W. R.64W. R.63W. R.62W. R.6I W. R.60W. R.59W. R.58W. R.57W. R.56W.
024 6 MILES
024 6 KILOMETERS
Figure 19. Drawdown between the simulated predevelopment steady-state potentiometric surface and the simulated 1983 transient potentiometric surface.
Table
11.
Annu
al simulated
wate
r budgets, 1973
-83
-Cr
1973
19
74
1975
19
76
1977
19
78
1979
1980
1981
1982
1983
Sour
ces
of wa
ter
(acc
reti
ons)
(cub
ic fe
et per
second)
Rech
arge
fr
om
106.09
12.74
88.5
8 3.
62
132.
14
75.98
110.
72
50.6
6 75.99
131.
42
101.
31
prec
ipit
atio
n
Rech
arge
fr
om sp
ecif
ied-
2.
82
3.07
2.93
3,
.21
2.89
3.
00
2.8*
7 3.08
3.04
2.
83
2.94
he
ad bounda
ries
Disc
harg
e fr
om storage
3-09
42
.33
4.12
55.60
2.43
5.44
1.14
19.88
8.88
1.84
3.86
Tota
l 11
2.00
58.14
95.63
62.4
3 13
7.46
84.42
114.
73
73.6
2 87
.91
136.09
108.11
Cons
umpt
ion
of wa
ter
(depletions)
(cub
ic feet pe
r second)
Evap
otra
nspiration
106.61
52.9
1 81
.37
46.5
5 91
.48
69.7
3 88
.24
61.7
4 69.02
99.8
0 89
.48
from a
quif
er
Pumpage
2.66
3.37
5.33
14.10
15.64
11.73
8.47
9.79
16.06
9.39
12.32
Disc
harg
e fr
om th
e 1.
71
1.69
1.47
1.
64
1.56
1.
30
1.47
1.66
1.59
1.38
1.44
aquifer
to the
stre
am
Disc
harg
e from specified-
.62
.60
.60
.55
.58
.58
.59
.57
.56
.58
.57
head
boundaries
Rec
harg
e to
st
ora
ge
.58
.00
7.0
3
.00
28.1
2 1.
36
15.8
5 .3
3 1.
00
24.7
0 4.3
6
Tota
l 11
2.18
58
.57
95.8
0 62
.84
137.
38
84.7
0 11
4.62
74
.09
88.2
3 13
5.85
10
8.17
The water budgets for the 11 transient simulation periods vary consider ably as a result of changes in the annual recharge from precipitation and discharge from evapotranspiration (table 11). The recharge rate from precipi tation was very small in 1974 and 1976 compared with the other annual simula tions. The reduced recharge resulted in decreased potentiometric heads in the aquifer, thereby causing reduced evapotranspiration rates and an increase in the discharge of water from storage.
The 1983 simulated water budget (table 11) indicates recharge from precipitation is the major budget component, contributing approximately 94 percent of the inflow. Specified-head boundaries account for 2.7 percent of the inflow. Quantitatively, recharge from precipitation and inflow from specif ied-head boundaries are about the same as the predevelopment steady- state water budget (table 8). The major difference between the predevelopment and 1983 simulated water inflows is storage. In 1983 inflow from storage accounted for 3.86 ft 3 /s or 3.6 percent of the accretions. In 1983 evapotranspiration accounted for 89.48 ftVs and the specified-head boundaries accounted for 0.57 ftVs of the depletions from the aquifer compared to 105.82 and 0.70 ftVs, respectively in the predevelopment steady-state simulation (table 8). Pumpage accounted for 12.32 ftVs and recharge to storage 4.36 ftVs in the 1983 depletions.
1976 Monthly Simulation Period
The last and driest year in the 1974-76 drought was 1976. Monthly model runs for 1976 were chosen to determine how well the transient simulation could simulate a year when estimated maximum recharge was very small and potential evapotranspiration was calculated to be the greatest of the 11 annual simulation periods.
The maximum recharge rates to the aquifer for each month in 1976 are shown in table 12. The average annual maximum recharge rate of 0.10 inch (table 9) was distributed in March and April which accounts for recharge due to snowmelt in the spring, and in September when the average annual departure was 0.20 inch above normal due to rain storms. The percentage of the maximum available monthly recharge which can actually reach the aquifer is controlled by the average thickness of the confining bed in each grid block overlying the glacial-aquifer system (fig. 14).
The monthly evapotranspiration for 1976 (table 13) was estimated using Department of Commerce data (1976) and the relationships presented by Farnsworth and Thompson (1982) and Farnsworth, Thompson, and Peck (1982) for estimating evapotranspiration from pan evaporation data. The calculated potential evapotranspiration rate ranges from 12.5 inches in August to 0.0 inch in the winter months when the ground is frozen. Figure 15 shows the percentage of the potential monthly evapotranspiration which can be withdrawn from the glacial-aquifer system.
Figure 20 shows the simulated potentiometric surface at the end of August 1976 and the location of each grid block in which ground-water withdrawal occurred. August was selected because it was the month when the potentiometric heads were the lowest, as indicated by the hydrographs in figure 21. The summer months of June, July, and August had the greatest ground-water withdrawal rates (table 6).
48
Table 12.--Average monthly precipitation and recharge for 1976
Month
JanuaryFebruaryMarchAprilMayJuneJulyAugustSeptemberOctoberNovemberDecember
Average monthlyprecipitation forHuron, Forestburg,
and Mitchell 1(inches)
0.44.60.86
1.791.012.321.57.46
2.17.98.03.33
Averagemonthlydeparture 1(inches)
+0.02-.09-.29-.43
-1.97-1.48-1 .00-1 .98+ .20-.66-.73-.23
Maximum monthlyrecharge tothe glacial
aquifer system(inches)
__
0.05.02
.03 "
*Data from the U.S. Department of Commerce, 1976.
Table 13.--Estimated monthly evapotranspiration for 1976
Month Maximum evapotranspiration(inches)
JanuaryFebruaryMarchAprilMayJuneJulyAugustSeptemberOctoberNovemberDecember
0.0.0
2.54.57.08.512.012.52.5.5.0.0
Total 50.0
49
1234 61 8 10 12 14 16 18 20 22 24 26 28 30 I 32 34 36 38 40 42 44 46 48
Aquifer model boundary
Aquifer model boundary i
1275 POTENTIOMETRIC CONTOUR--Shows altitude of water level. Contour interval 25 feet. Datum is sea level
O LOCATION OF OBSERVATION WELL NODE
p LOCATION OF PUMPING NODE
R.65W. R.64W. R.63W. R.62W. R.6I W. R.60W. R.59W. R.58W. R.57W. R.56W.
024 SMILES I i 'i i 1 i 'i i 1 ' ' 024 6 KILOMETERS
Figure 20. Simulated potentiometric surface, August 1976.
50
C -s CD ro i i o
o B
WA
TER
LEV
EL,
IN F
EE
T A
BO
VE
SEA
LEV
EL
S5 CD
C
O DJ
^
O
O o
o
WA
TER
LEV
EL,
IN F
EE
T A
BO
VE
SEA
LEV
EL
CD o o
o CD
CO en td
o CD
00 td
o
o
o
ct
CD
O. o
cr
w CD <: CD a 3
o
\
a
o ct CD
3 ct !-
o
3 CD
ct
\
CD
0) a
w vo
q
CT
>
The average arithmetic difference between the simulated and observed water levels for the 12 monthly simulation periods ranged from -1.24 ft in November to 2.68 ft in July. The average absolute difference ranged from 3.82 ft in October to 6.88 ft in July (table 7). In August, the average arithmetic difference between the computed and measured water levels was 1.45 ft and the average absolute difference was 5.85 ft. The maximum positive difference between the simulated and observed water levels in August was 17.62 ft in the observation well located in grid block row 35, column 21, and the maximum negative difference was 14.76 ft in the observation well located in grid block row 15, column 30 (fig. 20). The average arithmetic and absolute differences between the computed and measured water levels (table 7) and the hydrographs (fig. 21) demonstrate the ability of the monthly transient simulations to very approximately replicate the aquifers' response in 1976 to monthly changes in pumping, recharge, and evapotranspiration.
The configuration of the August 1976 potentiometric surface (fig. 20) is similar to the predevelopment potentiometric surface (fig. 16) and the 1983 simulated potentiometric surface (fig. 17) except that the heads are, in general, lower. The August potentiometric heads range from greater than 1,400 ft above sea level along the west boundary of the model to less than 1,250 ft above sea level along the James River. The direction of ground-water flow generally is eastward, west of the James River and westward or northwestward east of the James.
A simulated water budget equating monthly accretions and depletions of the water supply for 1976 is shown in table 14. The water budget for the 12 monthly simulation periods varies considerably as a result of changes in the monthly evapotranspiration, storage, and pumpage. The primary source of water in 1976 was from storage. Recharge from precipitation and leakage across the model boundaries, represented by specified-head nodes, generally supplied less than 10 percent of the water. The major losses of water were pumpage and evapotranspiration during the months of Hay through August. In the fall and winter months, most of the water discharged from storage went back into storage elsewhere in the model.
MODEL SENSITIVITY
The confidence in the model's response needs to be based on a subjective appraisal of the analogy between the glacial-aquifer system and the model. A significant part of this analogy is the assumption that the aquifer characteristics have the same or similar characteristics assumed in the model. Because the aquifer characteristics are not known with certainty, the sensitivity of the model to each of several selected characteristics was tested.
The sensitivity of the model was tested by changing the values assigned for recharge, evapotranspiration, and hydraulic conductivity. The extent to which these variations affect the simulated response is a qualitative measure of the sensitivity of the model to uncertainty in that aquifer characteristic. Thus, if the variation produces a minor change in the predicted response, the model is not sensitive to that aquifer characteristic.
52
Tabl
e 14. Monthly
simulated
water
budgets, 1976
uo
Rech
arge
fr
om p
reci
pita
tion
Recharge fr
om specified-
head boundaries
Discha
rge
from
st
orag
e
Total
Janu
ary
0.00
2.57
26.30
28.87
February
0.00
2.57
2M.12
26.69
Marc
h April
0 2 25 28
Sources
of
(cub
ic
.72
0,29
.67
2.7M
.22
26.08
.61
'29.11
Consumption
Evapot
rans
pira
tion
fr
om
aquifer
Pump
age
Disc
harge
from th
e aquifer
to the
stre
am
Disc
harg
e fr
om sp
ecif
ied-
head boundaries
Rechar
ge to st
orag
e
Tota
l
.00
1.57
1.93 .66
21.3
9
28.5
5
.00
1.57
1.86 .68
22.1
9
26.30
10 1 1 IM 28
(cubic
.M9
16.80
.57
.00
.72
1.51
.69
.69
.10
10.20
.57
29.20
May
June
July
August
September
October
November
Dece
mber
wate
r (accretions)
feet pe
r
0.00
2.81
MM. 28
47.09
of water
feet per
21.88
19. M9
1.5M .69
3.57
M7.1
7
seco
nd)
0.00
0.
00
2.85
2.
92
64.90
77.10
67.75
80.0
2
(dep
leti
ons)
second)
23.76
28.62
MO. 03
M8
.M5
1.76
2.
00
.66
.65
1.73
.3^
67.9
1 80.06
0.00
2.93
73-87
76.80
29.06
MM.7M
2.13 .65
.20
76.78
0.143
2.70
38.06
Ml. 19
8. MM
15.15
2.0M .67
1M.67
MO. 97
0.00
2.61
25.9
8
28.5
9
1.99 .00
1.97 .68
23.57
28.2
1
0.00
2.59
2M.1
7
26.76
.00
1.57
1.91 .69
22.20
26.37
0.00
2.5M
22.69
25.2
3
.00
1.57
1.86 .70
20.85
2M.98
Sensitivity of the simulated steady-state condition is described by comparing the standard steady-state simulation (the one described thus far in the report) with an alternative simulation (one in which an aquifer characteristic had an alternative value).
Table 15 shows the sensitivity of the steady-state simulation to changes in recharge, evapotranspiration, and hydraulic conductivity. The areal distribution of the percentage of maximum recharge and potential evapotranspiration in each grid block was not changed. Also the areal distribution of the hydraulic conductivity was not changed.
The steady-state simulation is most sensitive to changes in recharge. A 25-percent reduction in the maximum recharge rate from 7.00 to 5.25 in/yr resulted in the average arithmetic difference decreasing 2.99 ft. Also the maximum positive and negative differences changed 1.77 and 3.57 ft, respec tively. Increasing the recharge rate 25 percent from 7.00 to 8.75 in/yr produced somewhat smaller changes in the average arithmetic difference and in the maximum positive and negative differences. The average absolute difference was slightly higher.
The effects of decreasing the potential steady-state evapotranspiration rate from 36.0 to 27 in/yr produced a 1.01-ft increase in the average arithmetic difference and a 0.31-ft difference in the average absolute difference from the standard steady-state simulation. An increase in the evapotranspiration rate to 45 in/yr resulted in the average arithmetic difference decreasing 1.96 ft and the average absolute difference decreasing 0.69 ft.
The steady-state simulation is relatively insensitive to changes in hydraulic conductivity. In general, a 50-percent change in hydraulic conductivity produced less change in the average arithmetic and absolute differences than a 25-percent change in recharge or evapotranspiration. This sensitivity analysis indicates that the accuracy of the recharge and evapotranspiration used in the model is more important than the accuracy of the hydraulic conductivity.
SUMMARY AND CONCLUSIONS
During the Pleistocene Epoch, continental glaciation from the north and east covered eastern South Dakota and deposited a blanket of glacial drift (till and outwash) over the preglacial bedrock surface. The more sandy and gravelly outwash deposits can yield significant quantities of water to wells. The till and other unconsolidated surficial deposits serve primarily as confining beds. The bedrock directly underlying the drift generally yields little or no water to wells or is hydraulically separated from the overlying outwash by till or other silt and clay deposits.
The complex hydrologic system which exists in the glacial outwash has been subdivided into four aquifers in the study area. However, the aquifers have similar hydraulic conductivities and are hydraulically connected by zones of lower hydraulic conductivity; therefore, the aquifers have been treated as one glacial-aquifer system, rather than individual aquifers in this report.
Tabl
e 15. Model
sensitivity
to ch
ange
s in
recharge,
evapotranspiration,
and
hydraulic
conductivity
Average
arit
hmet
ic
difference between
Model
simu
late
d an
d observed
simu
lati
on
wate
r levels
1 (f
eet)
Aver
age
abso
lute
difference be
twee
nsimulated
and
obse
rved
water
levels
2(f
eet)
Maximum
posi
tive
diff
eren
ce be
twee
nsi
mula
ted
and
obse
rved
water
levels
3(f
eet)
Maxi
mum
negative
diff
eren
ce be
twee
nsimulated
and
observed
water
leve
ls'*
(fee
t)
Number of
obse
rvat
ion
well
swith ob
serv
edwa
ter
leve
ls
Stan
dard
st
eady
- 1.
68
state
model
Steady-sta
te model
-1-3
1 with maximum
recharge
redu
ced
25 percent
Stea
dy-state mo
del
2.56
with maximum
recharge
incr
ease
d 25
percent
Steady-state model
2.69
with
ma
ximum
evapot
ranspiration
reduced
25 percent
Stea
dy-s
tate model
-.28
with
maximum
evapot
rans
pira
tion
in
crea
sed
25 percent
Steady-state model
2.09
wi
th h
ydra
ulic
conduc
tivity
reduce
d 50
percent
Stea
dy-s
tate model
-.03
with hy
draulic
conduc
tivi
ty
increase
d 50
pe
rcen
t
1.38
1.37
1.11
1.69
3.69
1.16
1.05
16.2
2
17
.15
17.9
5
15
.15
17.1
5
15.1
5
8.32
11.89
6.89
5.89
10.89
7.89
8.89
32 32 32 32 32 32 32
Positive numbers
indicate si
mulated
head
was
higher than th
e observed head;
negative nu
mber
s indicate simulated
head
wa
s lo
wer
than th
e observed head.
2The ab
solu
te va
lue
of a
numb
er is
th
e number wi
thou
t it
s associated si
gn.
For
exampl
e, th
e ab
solu
te value
of 2
and
-2 are
the
same
.'P
osit
ive
difference when simulated
head
is greater
than
ob
serv
ed wa
ter
leve
l.
"Negative
diff
eren
ce when simulated
head
is less th
an observed water
leve
l.
Thickness of the glacial-aquifer system ranges from less than 10 feet to greater than 200 feet. The lateral boundaries were placed where the aquifer thickness was less than about 5 feet. In the study area, the hydraulic conductivity ranged from 80 to 670 feet per day with an average of 316 feet per day. Because of the complexity of the glacial-aquifer system, the aquifer can be both confined and unconfined. The storage coefficients calculated from aquifer tests in the study area generally ranged from 0.00039 to 0.0000.17. Specific yield values as large as 0.28 were calculated for the aquifer west of the study area. Recharge to the glacial-aquifer system occurs as infiltration of precipitation and snowmelt directly into the aquifer or through the overlying till confining bed. Calculated recharge rates to the unconfined aquifer ranged from 0.9 to 3.4 inches per year and to the confined parts ranged from 0.24 to 0.72 inch per year. Evapotranspiration accounts for most of the natural discharge from the glacial-aquifer system. The average potential evapotranspiration estimated from pan evaporation is 36.2 inches per year. Little natural discharge from the aquifer system to the James River occurs in the study area. The direction of water movement in the glacial- aquifer system generally is eastward or southeastward, west of the James River and westward or northwestward, east of the James River.
In order to simulate ground-water flow within an aquifer system, a number of simplifying assumptions must be made. The simplifying assumptions for the glacial-aquifer system are: (1) The aquifer consists of one layer, (2) the overlying confining bed controls recharge to and discharge from the aquifer, (3) the silt and clay or bedrock is the lower impermeable boundary of the aquifer, (4) all lateral boundaries exhibit no flow except for 12 specified- head nodes, (5) the James River is hydraulically isolated from the aquifer except at 2 river nodes, (6) most recharge is by precipitation, and (7) most discharge is by evapotranspiration.
A grid that contains -56 rows and 52 columns of equally spaced blocks, each 1 mile wide and 1 mile long, was used to simulate the glacial-aquifer system. The aquifer was simulated prior to significant ground-water development (pre-1973) under steady-state conditions. The aquifer also was simulated in 11 annual pumping periods from 1973 through 1983 and in 12 monthly pumping periods for 1976.
The steady-state simulation represents the glacial-aquifer system prior to 1973i when the aquifer system generally was in equilibrium; that is, water levels recovered to near-prepumping levels during the nonirrigation season. The maximum available recharge to the aquifer was 7.0 inches per year and occurred only where the average thickness of the confining bed was less than 10 feet. With an average confining bed thickness between 10 and 45 feet, the rate of recharge to the aquifer decreased linearly to" 0.0 inch per year. The potential evapotranspiration rate was 36.0 inches per year and can occur only where no confining bed is present above the aquifer. When the average confining bed thickness is between 0 and 45 feet, the potential evapotranspiration rate decreases linearly from 36.0 to 0.15 inches per year. The steady-state simulated water budget indicates that recharge from precipitation accounts for 97.1 percent of the water that enters the aquifer or 0.96 inch per year per active grid block, and evapotranspiration accounts for 98.2 percent of the water that leaves the aquifer or 0.97 inch per year per active grid block.
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Eleven consecutive annual pumping periods from 1973 through 1983 were simulated. In 1973, water levels began to decline because of a decrease in recharge, which lasted through 1976 and because of an increase in pumping of ground water for irrigation. Recharge, evapotranspiration, and pumpage were adjusted annually. The maximum annual recharge varied from 0.10 inch in 1976 to 8.14 inches in 1977. The potential annual evapotranspiration varied from 29.9 inches in 1982 to 48.9 inches in 1976. Withdrawals from the glacial- aquifer system in 1976 were 2.6 times those in 1975. Since 1976, the pumpage has fluctuated annually in both distribution and quantity, however, the maximum annual withdrawals have not increased significantly. The annual water budget from the transient simulations varies considerably as a result of changes in recharge and evapotranspiration.
For 1976, 12 consecutive monthly pumping periods were simulated. The maximum annual recharge rate of 0.10 inch was distributed over March, April, and September. The potential monthly evapotranspiration rate ranged from 12.50 inches in August to 0.00 inch during the winter months when the ground was frozen. The simulated monthly water budgets varied considerably as a result of changes in evapotranspiration, storage, and pumpage.
Since the model is based on a number of simplifying assumptions, it cannot represent exactly the hydrologic processes in the aquifer system. The confidence in the model's response needs to be based on an objective appraisal of the analogy between the glacial-aquifer system and the model. Because the aquifer characteristics are not known with certainty, the sensitivity of the steady-state simulation to changes in recharge, evapotranspiration, and hydraulic conductivity were tested. The sensitivity analysis indicates that the model is most sensitive to reductions in recharge and least sensitive to changes in hydraulic conductivity. Since the model was insensitive to hydraulic conductivity, and recharge and discharge were widely distributed, a large range of combinations of recharge and evapotranspiration could give an equally good fit to the measured water levels. Hqwever, the values of recharge and evapotranspiration used in the model are considered to be reasonable estimates. The model is one of the best means of evaluating and improving our understanding of the aquifer system and of testing the sensitivity of various aquifer properties in the study area.
SELECTED REFERENCES
Bardwell, Lawrence, 1984, Water quality of South Dakota's glacial aquifers: South Dakota Department of Water and Natural Resources, 52 p.
Benson, R.D., 1983, A preliminary assessment of the hydrologic characteristics of the James River in South Dakota: U.S. Geological Survey Water- Resources Investigations Report 83-4077, 114 p.
Driessen, J.L., 1980, Soil survey of Sanborn County: U.S. Department of Agriculture Soil Conservation Service, 191 p.
Dyman, T.S., and Barari, Assad, 1976, Ground-water investigation for the city of Wolsey: South Dakota Geological Survey Special Report 63, 19 p.
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Farnsworth, R.K., and Thompson, E.S., 1982, Mean, monthly, seasonal, and annual pan evaporation for the United States: National Oceanic and Atmospheric Administration Technical Report NWS 34, 82 p.
Farnsworth, R.K., Thompson, E.S., and Peck, E.L., 1982, Evaporation atlas for the contiguous 48 United States: National Oceanic and Atmospheric Administration Technical Report NWS 33 , 26 P.
Flint, R.F., 1955, Pleistocene geology of eastern South Dakota: U.S. Geological Survey Professional Paper 262, 173 p.
Hamilton, L.J., 1980, Major aquifers in Aurora and Jerauld Counties, South Dakota: South Dakota Geological Survey Information Pamphlet No. 23, 5 p.
1985, Water resources of Aurora and Jerauld Counties, South Dakota: U.S. Geological Survey Water-Resources Investigations Report 84-4030, 58 p.
Hansen, D.S., 1983, Water resources of Hanson and Davison Counties, South Dakota: U.S. Geological Survey Water-Resources Investigations Report 83-4108, 55 p.
Heath, R.C., 1983, Basic ground-water hydrology: U.S. Geological Survey Water-Supply Paper 2220, 84 p.
Hedges, L.S., 1968, Geology and water resources of Beadle County, South Dakota, part 1, geology: South Dakota Geological Survey Bulletin 18, 66 p.
Hedges, L.S., Alien, Johnette, and Holly, D.E., 1983, Evaluation of ground- water resources, eastern South Dakota and the upper Big Sioux River South Dakota and Iowa; Task 7, ground water recharge: South Dakota Geological Survey, 56 p.
Hedges, L.S., Burch, S.L., lies, D.L., Barari, R.A., and Schoon, R.A., 1981, Evaluation of ground-water resources eastern South Dakota and upper Big Sioux River, South Dakota and Iowa: South Dakota Geological Survey.
Heil, D.M., 1979, Soil survey of Beadle County, South Dakota: U.S. Department of Agriculture Soil Conservation Service, 169 p.
Howells, L.W., and Stephens, J.C., 1968, Geology and water resources of Beadle County South Dakota, part II, water resources: South Dakota Geological Survey Bulletin 18, 63 p.
lies, D.L. , 1979a, Ground-water study for the city of Huron: South Dakota Geological Survey Open-File Report No. 24-UR, 37 p.
1979b, Sanitary landfill investigations for the city of Huron: South Dakota Geological Survey Open-File Report No. 26-UR, 30 p.
Koch, N.C., 1980a, Geology and water resources of Hand and Hyde Counties, South Dakota, part II, water resources: South Dakota Geological Survey Bulletin 28, 46 p.
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1980b, Appraisal of the water resources of the Big Sioux aquifer, Brookings, Deuel, and Hamlin Counties, South Dakota: U.S. Geological Survey Water-Resources Investigations 80-100, 46 p.
Koch, N.C., and McGarvie, S.D., 1988, Water resources of Miner County, South Dakota: U.S. Geological Survey Water-Resources Investigations Report 86-4035, 37 p.
Koglin, E.N., Stack-Goodman, Kathleen, and Ambroson, J.R. , 1981, Test hole logs and well logs of Beadle County, volumes 1 and 2: South Dakota Geological Survey Open-File Report No. 4-CS, 1,21? p.
Kuiper, L.K., 1984, Appraisal of the water resources of the eastern part of the Tulare aquifer, Beadle, Hand, and Spink Counties, South Dakota: U.S. Geological Survey Water-Resources Investigations Report 84-4078, 52 p.
McDonald, M.G., and Harbaugh, A.W., 1984, A modular three-dimensional finite- difference ground-water flow model: U.S. Geological Survey Open-File Report 83-875, 528 p.
McGarvie, S.D., 1983, Major aquifers in Miner County, South Dakota: South Dakota Geological Survey Information Pamphlet no. 20, 10 p.
Norris, S.E., 1962, Permeability of glacial till: U.S. Geological Survey Research 1962, p. E150-E150.
Schoon, R.A., 1971, Geology and hydrology of the Dakota Formation in South Dakota: South Dakota Geological Survey Report of Investigations No. 104, 55 p.
Schroeder, Wayne, 1982, Test hole logs and well logs of Miner County: South Dakota Geological Survey Open-File Report No. 5-CS, 719 p.
Spuhler, Walter, Lytle, W.F., and Moe, Dennis, 1971, Climate of South Dakota: South Dakota State University Agricultural Experiment Station Bulletin 582, 5 p.
Steece, F.V., and Howells, L.W., 1965, Geology and ground water supplies in Sanborn County, South Dakota: South Dakota Geological Survey Bulletin 17, 182 p.
- - 1969, Geology and ground water supplies in Sanborn County South Dakota, part II, ground water basic data: South Dakota Geological Survey Bulletin 17, 200 p.
Walker, I.R., 1961, Shallow outwash deposits in the Huron-Wolsey area Beadle County, South Dakota: South Dakota Geological Survey Report of Investigations No. 91 , 44 p.
U.S. Army Corps of Engineers, 1951, Time lag and soil permeability in ground- water observations: U.S. Army Corps of Engineers Bulletin No. 36, 50 p.
U.S. Department of Commerce, 1956-83, Climatological data for South Dakota (issued annually).
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