Analysis of the shallow groundwater flow system near Connetqout Brook, Long Island, New York

Jo~rnal of Hydrology, 107 (1989) 223-250

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El:~evier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

[2] ANALYSIS OF THE SHALLOW GROUNDWATER FLOW SYSTEM NEAR CONNETQUOT BROOK, LONG ISLAND, NEW YORK

K E I T H R. P R I N C E I, T H O M A S

E. R E I L L Y 2 and O. L E H N

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U.S. Geological Survey, M.S. 470, 345 Middlefield Road, Menlo Park, CA 94025 (U.S.A.) ~U.S. Geological Survey, M.S. 411, Nati[mal Center, Reston, VA 22095 (U.S.A.) 3U.S. Geological Survey, 5 Aerial Way, Syosset, N Y 11791 (U.S.A.) (Received June 14, 1988; accepted for publication J u n e 26, 1988)

ABSTRACT

Prince, K.R., Reilly, T.E. and Franke, O.L., 1989. Analysis of the shallow groundwater flow system near Connetquot Brook, Long Island, New York. J. Hydrol., 107: 223-250. Streamflow on Long Island is derived principally from shallow groundwater that fows above the deeper regional flow system. The movement of shallow groundwater was studied during 1975 82 at Connetquot Brook - an undisturbed stream in Connetquot River State Park - in south-central Long Island. The investigation encompassed: (1) field studies of streamflow, groundwater levels, and age of water as indicated by tritium concentrations, and (2) numerical simulation of the shallow flow system to evaluate the hydraulic factors that influence groundwater flow near and beneath the stream. Analysis of water-level data indicates that groundwater flow is essentially horizontal throughout the drainage basin except near and beneath the stream, where it moves upward diagonally and discharges to the stream. Water levels in wells driven directly into the streambed and in wells driven into the streambank at three sites were 1-2 ft higher than stream stage in the first 5 ft of penetration. Increases in head, which were detected to depths of 3ff ft beneath the streambed, indicate upward movement of water above that depth. Water samples from selected wells were analyzed for tritium concentration to determine the relative age of water to locate the bottom boundary of the shallow flow system, Tritium concentrations indicate that the lower boundary is from 45 to 100 ft below the water table. A two-dimensional cross-sectional flow model of the shallow flow system indicated that: (1) stream width and streambed hydraulic conductivity influence heads mostly within about 50ft of the stream; (2) the thickness of the shallow flow system influences heads more distant from the stream but has a negligible effect near the stream; and (3) the quantity of water entering the system as recharge from precipitation influences the heads throughout the area. Field measurements of hydraulic head indicate the shallow flow system to extend to about 30 ft below the stream channel. Results of th,z sensitivity analysis indicate that the thickness of the shallow system has a negligible effect on head distribution beneath the stream.

INTRODUCTION

Long Island, N.Y., is underlain by a southward-dipping sequence of unconsolidated gravel, sand, silt, and clay deposits that overlie Precambrian bedrock. This sequence forms the large groundwater reservoir that is the sole

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source of freshwater for the 3 million inhabitants of Nassau and Suffolk Counties (Fig. 1). Streams on Long Island are sustained principally by groundwater seepage; about 95% of the total streamflow under natural (predevelopment) conditions is derived from groundwater (Pluhowski and Kantrowitz, 1964). Although the flow of individual streams is relatively small, their combined base flow represents a significant percentage of the total freshwater outflow from the island's hydrologic system. In recent years, water managers and the public have become concerned that increasing withdrawals and loss of recharge, primarily through new sewer systems, may lower the water table and reduce streamflow throughout central Long Island, as predicted by Kimmel et al. (1977). The predicted lowering of the water table and reduction in streamflow may affect Long tsiand's wetlands and parks, where surface water is essential for recreation and wildlife habitat. Reduced streamflow will also increase bay salinity, which will adversely affect the island's shellfish industry. Thus, protection of the island's surface-water resources from depletion is essential. This study of the shallow groundwater flow system was conducted from 1975-82 in cooperation with Nassau County Department of Public Works, Suffolk County Department of Health Services, and Suffolk County Water Authority. It focused on the part of Connetquot Brook that flows through Connetquot River State Park, a limited-use preserve in Suffolk County (Fig. 1), because this area is isolated from the effects of urbanization - - an uncommon situation on Long Island. The study area encompasses 7.5 mi 2of the Connetquot Brook drainage area along a 5-mi reach of stream. Results of this study are applicable to othel- groundwater-fed streams in similar hydrogeologic settings.

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Purpose and scope Understanding the factors that influence the interaction between groundwater and 3urface water on Long Island is essential because, under natural conditions, stream base flow is a large part of the total discharge from the groundwater system. This report evaluates and describes factors that govern the flow of shallow groundwater near Connetquot Brook on Long Island, N.Y. It presents and interprets field data on shallow groundwater flow near and beneath the stream and describes results- 9f a sensitivity analysis with a numerical model.

Previous investigations Franke and Cohen (1972) first described the shallow groundwater flow systems associated with streams on Long Island and discussed the system boundaries. Franke and McClymonds (1972, p. F23) discussed the predominantly two-dimensional flow of the islahd's regional s:ystem and provided a generalized vertical section of the southern half of the island's groundwater reservoir. The vertical ~cction depicts the general pattern of grou~dwa:er flow and the relative size of the shallow groundwater system associated with streams in this area. (Fig. 2). Harbaugh and Getzen (1977) were the first to describe the three-dimens':onal nature of flow :n a shallow flow system. Prince (1980) discussed the shallow flow ' i g. 3). system further ~nd also depicted the system's three-dimensional nature .,F Both studies eiscussed and illustrated flow phenomena at the local scale and their interdependence with the regional flow system An important question suggested by Figs. 2 and 3 is the relation between

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shallow flow systems of differing depths and scales and the total groundwater flow system. Toth (1963) discussed concepts related to this question at some length and depicted the relative position of a series of small flow systems in a hypothetical cross section (Fig. 4). Harbaugh and Getzen (1977) modeled Long Island streams and their associated shallow flow systems on a regional-scale electric-analog model. Reilly et al. (1983, pp. 23-26) extended this work to include digital-numerical models. Pluhowski and Kantrowitz (1964, p. 50) reported measurable vertical gradients beneath the bed of a flowing stream. Prince (1980, p. 20) described a series of detailed head measurements near and beneath Connetquot Brook. Additional head measurements (as outlined in the section "Field Studies") and determination of the depth of the shallow flow system as indicated by water chemistry are discussed in detail in Prince et al. (1988). HYDROGEOLOGIC SETTING

Regiona! flow system Long Island is underl: in by a sequence of unconsolidated sedimentary deposits that rest on southward dipping bed, ock. The deposits overlying the bedrock surface have been classified in i:~:~three maj~r a q u i f e r s - the Lloyd aquifer (in the Lloyd Sand Member of the Cretaceous Raritan Formation),

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which overlies the bedrock surface; the Magothy aquifer (in the Cretaceous Matawan Group and Magothy Formation), which is separated from the Lloyd by the Raritan clay (in the clay member of the Raritan Formation); and the upper glacial (water-table) aquifer (in upper Pleistocene deposits), which overlies the Magothy and may be locally separated from it by confining units. The regional hydrogeology of Long Island is described in several reports including Cohen et al. (1968) and McClymonds a~.d Franke (1972). A detailed hydrogeologic description of the area surrounding Connetquot Brook is given in Pluhowski and Kantrowitz (1964) and Prince (1980). Long Island's groundwater system, under natural (undisturbed) conditions, is recharged solely by precipitation, which averages about 44 inches per year; recharge to the groundwater reservoir is estimated to be about half the precipitation, or 22 to 24 inch,~.s per year (Franke and McClymonds, 1972). Discharge from the groundwater reservoir under natural conditions occurs as: (1) seepage to streams; (2) evapotranspiration; and (3) subsurface discharge (underflow) to the surrounding saltwater bodies. Thc regional groundwater system can be visualized as flowing laterally north and south from the major groundwater divide (Fig. 1) and discharging to streams and to the south-shore bays, Long Island Sound, and the Atlantic Ocean. Groundwater in the deep, regional flow system is recharged by precipitation that falls upgradient of the shallow flow system boundary (Fig. 3). All water that enters a shallow flow system as precipitation either discharges as evapotranspiration or flows toward and eventually seeps into a stream channel, then discharges to tidewater. All streams on Long Island are fed by local shallow groundwater systems that flow above the regional flow system. The depth to which the shallow flow systems on Long Island extend is unknown, but Prince (1980) estimated that one associated with Connetquot Brook probably extends no deeper than 30ft below the water table and is therefore entirely within upper glacial aquifer, which in this area ranges from 50 to 150ft thick (Jensen and Soren, 1974).

Connetquot Brook drainage basin Connetquot Brook is about 37,000 ft long; its average discharge during 1944 --84 was 38.9 ft as-1. The topographic and groundwater drainage areas of the stream encompass 24mi 2 and approximately 28mi 2, respectively, but the boundaries of the two drainage areas differ significantly (Prince, 1980, Fig. 4). The stream-channel width ranges from a few feet to 80ft, and water depth ranges from a few inches to 3 ft or more in pools. Topographic relief in the Connetquot Brook drainage basin is about 200 ft.

Boundary conditions of the shallow groundwater system The following discussion of boundaries is valid for all shallow groundwater systems that feed streams. The top of the shallow system is the water table,

229

which fluctuates in response to intermittent recharge. During periods of recharge, the water table may be regarded as a flux boundary, whereas after an extended period without recharge, it functions as a stream-line surface where the groundwater flow lines are r3rallel to the water table. The lateral and bottom boundaries of the shallow flow system form a surface whose general configuration is depicted in Fig. 3. The local interstream divides and the upstream boundary of the shallow flow system (Fig. 3) represent the intersection of this surface with the water table. The approximate location of the local interstream divides can be estimated from the water-table contours on detailed water-table maps. The configuration of the upstream boundary of the shallow flow system is unknown, however, and may be more complicated than the nearly straight line indicated in Fig. 3. The shaI~e and position of this boundary are not fixed but shift in response to changes in recharge and discharge in: (1) the stream basin; (2) adjacent stream basins; and (3) the underlying regional flow system. These changes may cause the local interstream divides and upstream shallow flow-system boundaries to shift and may also affect the altitude of the bottom boundary. The discharge boundary of the shallow groundwater system during base flow is the streambed. The stream-surface altitude (stage) above the streambed is a direct measure of the head acting on the streambed boundary. This head at the streambed, in turn, is a function of position (head increases upstream) and time (changes in stream stage and discharge). On Long Island, fluctuations in stage during base flow are small, generally a few tenths of a foot at most locations. The streambed boundary under unstressed conditions is a "specifiedhead" boundary. One of the difficulties in analyzing the shallow flow systems is that only the altitude and position of the streambed remain fixed through time; the upper and lower boundaries of the shallow flow system shift continuously. The movement of these boundaries results in a nonlinear relationship between stress and the response of the shallow subsystem, as evidenced by seasonal changes in groundwater levels and streamflow. Another aspect of this nonlinear relationship between stress and system response is the fluctuation in length of the flowing part~ of the stream. Analysis of the shallow flow system requires use of simplifying assumptions that allow examination of the system under more ideal conditions. These assumptions are discussed further on. i

FIELD STUDIES OF THE SHALLOW GROUNDWATER FLOW SYSTEM

Field studies were conducted to obtain data on the dimensions and dynamics of the shallow groundwater flow system that drains to Connetquot Brook. The field data consisted of: (1) extensive groundwater level measurements, which were used to describe areal and vertical distribution of heads and evaluate flow paths; and (2) analyses of water samples for tritium concentration to determine the water's age, which was used to estimate travel times within the system and help delineate the boundary between the shallow flow system and the regional

230

flow system. A detailed description of the field studies is given in Prince et al. (1988).

Water-table configuration A network of 41 observation wells was installed along an undisturbed 950-ft reach of Connetquot Brook and its drainage basin, as shown in Figure 5. 09'30"

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Groundwater levels were measured periodically from J a n u a r y 1976 through September 1978; these measurements and well-completion data are given in Prince (1980). In addition, two water-table-contour maps were drawn, one for September 1977 (Fig. 5), the other for March 1978 (Prince, 1980). Comparison of the two maps shows that water levels in spring are significantly higher and gradients somewhat steeper than in the fall. As a result, the base flow of Connetquot Brook also is greatest in the spring and lowest in the fall. The regional water-table contours (Fig. 5) generally are perpendicular to the stream channel in the northern part of the basin and bend upstream as they approach the stream channel, as they do along most of Long Island's southshore streams: The channel of Connetquot Brock from the confluence of the unnamed tributary north of wells $57474 and S 57475 to gaging station 01306460 (Fig. 5) is unusual in t h a t it is essentially parallel to the upgradient water-table contours. This water-table configuration is useful as a basis for a cross-sectional model, as described further on. A notable characteristic of the water-table contours in Fig. 5 is their tendency to become more closely spaced with proximity to the stream. This may be attributed to two causes: (1) Cross-sectional areas perpendicular to the direction of flow decrease as flow lines converge toward the stream. In addition, the quantity of flow through successive downstream vertical sections increases as a result of a greater cumulative accretion of recharge toward the stream. Jacob (1943) showed how this resulted in the classic parabolic head profile in a one-dimensional system with evenly distributed recharge. (2) As pointed out by Rorabaugh (1960), significant head losses may occur near and particularly beneath partially penetrating s$~e~ms as a result of vertical head gradients, even in homogeneous aquifers. The lower hydraulic conductivity of the streambed sediments in comparison to aquifer material sJme distance from the stream tends to further increase head losses. These head losses and vertical flow components are not depicted on areal water-table maps, though. Field measurements and model results suggest that convergence of flow lines and recharge accreuon, described above, probably have a greater effect on heads t h a n vertical flow components beneath the stream. The closer spacing of water-table contours near the stream could not be verified from most regional water-table maps, however~ because the contour intervals on the maps are too ]arge and the control points too scattered. Wells at sites with more than one well were screened at differing depths to detect vertical differences in hydraulic head. At sites with three wells, one was screened near the water table, one at approximate|y 100ft below the water table, and one at an intermediate depth. At sites more than 50;t from the stream, a lack of measurable difference in simultaneous water-level measurements at differing depths indicated that groundwater flow ill the shallow flow system beyond the stream's immediate area of influence is essentially horizontal. Differences in water levels with depth were substantial directly

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beneath the stream and a few feet to either side of it, however, as described in the next section.

Groundwater levels and flow patterns near and beneath the stream Numerous groundwater-level measurements were made at three sites (A, B, C, Fig. 6) to obtain a detailed profile of head changes with depth. At all three sites (A, B, and C), one well was driven into the streambed and another along the streambank. At sites B and C, a third well was driven about 50 ft from the stream. A routine consisting of alternatively driving the well, pumping the well, and measuring the water level after it had returned to its static level during t h a t drilling interval was followed. Measurements were taken at 1-ft intervals where the head change was relatively large, and at 5-ft intervals where the head change was relatively small. Measured water levels from all three sites are plotted in relation to depth below the streambed surface in Fig. 7, The curves are similarly shaped at corresponding depths. In general, the largest increases in head with depth were at the streambed wells, followed closely by the streambank wells. At sites, A and B, the maximum head increase was about 1 ft, and at site C about 2 ft. Most of the head increase at sites A and B was within 5 ft below the streambed or, in the streambank wells, within 5 ft of the water table; at site C, the head increase occurred within l0 ft of the water table. Measurable increases in head beneath the streambed continued to a depth of about 30 ft, but water levels in the well about 50 ft from the streambank at sites B and C showed no change in head within a 40 ft depth. The sharp changes in slope of the individual curves in Fig. 7, which are drawn as a series of straight-line segments (labeled 1, 2, or 3), are assumed to result from: (1) differences in cross-sectional area as groundwater flow lines converge radially toward the streambed; and (2) local differences in vertical hydraulic conductivity due to vertical variations in the grain-size distribution of the sediments. A vertical section showing the water levels measured at site B is given in Fig. 8. These data, together with those in Fig. 7 for all three sites, indicate that water levels 50 ft from the streambank are virtually constant with depth. Thus: shallow groundwater flow at this distance from the stream is essentially horizontal. In the streambank and streambed wells, however, water levels increase with depth, but the increases beyond depths of 20 and 30 ff below the streambed were so small as to be within the error of m e a s u r e m e n t The depth below the streambed at which vertical (upward) gradients were no longer measurable is assumed to represent the local bottom of the shallow groundwater system that discharges to Connetquot Brook, and water below this depth is part of the deeper regional flow system.

Groundwater dating by tritium analysis Sixteen samples of groundwater and one sample o~~ stream water were

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EQUIPOTENTIAL LINEmApproximately located. Contour interval 0.2 foot

60

I

LOCAT!ON OF WELL SCREEN CENTER-Number is ground-water head in feet above sea level

/

/

/

/

/

\Wate,,aO,e

DISTANCE FROM STREAM CENTER, IN FEET

I

/

30

/

J

l

i /

/

/

I

20

~ +~7.00

-t- 26.95

+ 26.93

26.89

./

Streambankmeasurement

+ 26.73 " "(-.26.78 1 " ~ 26.82 + 26.84 + 26.86 -'f- 26.87

~-~ . . . . . .

Stream

Streambedmeasurement

26.46 . . . . 26.70

26.29

26.8~.--+-26.80

26.4 26.6

26~2

I"~

~, E

t

t

27.18

27.18

-L 27.18

+ 27.18

27.18 + 27.17 + 27.18 + 27,18

1

Measuremf.., site 47 feet f r o m stream

¢,O

10 10 10 10 10 4000 4000 4000 40OO 2500 2500 2500

$57478 $57479 $62237 $65595 $65598 $57468 $57469 $62234 $65599 $57466 $57467 $65597 Streamflowgaging station 013O6460

Dashes indicate no sample collected.

Lateral distance of sampling point from stream (ft)

Well number

-

-

-

-

7 0

12 8 25 25 73 28 7 12 -71 24 17

4 9 41 2 99 1 22 41 97 5 45 98 -

Altitude of center of well screen (ft ~ - : ~ sea ~evel)

Depth of center of well screen below water t~b~e (ft)

31.0 130.0

t}.l 0.9 0.3 0.2

32

<0.1 2.7 0.1 31.9 26.8 30.8 0.6 35.2 166.0 0.5

October 1978 January 1978

Tritium concentration (tritium units)

Tritium concentration in stream water and groundwater from selected wells near Connetquot Brook (well and site locations shown in Fig. 5)

TABLE 1

237

analyzed for tritium concentration by the U.S. Geological Survey Tritium Laboratory in Reston, Va., to help delineate the flow patterns and travel times in the shallow groundwater flow system near Connetquot Brook. Results are given in Table 1. Tritium values were corrected for decay to the collection date on the basis of a tritium half-life of 12.361 years (T.A. Wyerman, U.S. Geological Survey, written commun., 1979). Interpretation of tritium concentrations to establish the residence time of water is difficult because: (1) tritium-input rates vary through time; (2) evapotranspiration of precipitation; and (3) groundwater becomes mixed through hydrodynamic dispersion. Ferronsky and Polyakov (1982) discussed several models of hydrodynamic dispersion and their effects upon tritium concentrations in groundwater. For the purposes of this study, a less rigorous interpretation of the tritium data was judged sufficient. Samples of water having high concentrations of tritium, greater than 10 tritium units (hereafter T.U.), were assumed to contain mostly post-1952 water, and samples having low tritium concentrations (less than 1.0 T.U.) were ~ assumed to contain only pre-1952 water. (1952 marks the beginning of atmospheric testing of nuclear devices, which resulted in a marked increase in the tr.:tium concentration in precipitation.) Tritium concentrations in the 1-10 T.U. range probably indicate that a small quantity of post-1952 precipitation has mixed with a large quantity of pre-1952 water containing little or no tritium. The tritium data in Table 1 may be interpreted from the following assumptions: (1) a tritium half-life of 12.4 yr; (2) 1952 as the onset of increased tritium in precipitation; and (3) estimated pre-1952 tritium concentrations ~f about 8 T.U. for precipitation (Ferronsky and Polyakov, 1982). From these criteria, the data in Table 1 may be grouped into three tentative categories: (1) water having a concentration of 1.0 T.U. or less, which predates 1952 (well $57479 and October sampling at wells $57478, $62237, $65598, $65599, and $65597); (2) water having a concentration between 1.0 and 10.0 T.U., which contains a mixture of pre- and post-1952 water (well $65595); and (3) water having concentrations greater than 10.0 T.U., which entered the system after 1952. The velocity of shallow ground water in the area is useful in interpreting the data in Table 1. Average hydraulic-conductivity values for the upper glacial aquifer (McClymonds and Franke, ~972) and water-table gradients indicate the average velocity of shallow groundwater to be about 509 ft yr -~1. Thus, groundwater whose tritium concentration indicates an origin before 1952 must have entered the groundwater system 10,000-15,000 ft or more upg~adient from its present location. Tritium concentrations in wells 2500 and 4000ft from the stream ~iffered markedly with depth. Wells screened 95-100 ft below the water table contained less than 1 T.U., whereas those screened 40-45ft below the water table contained more than 25 T.U. This difference suggests that the boundary between the shallow and deeper flow systems at these distances from the stream is between these two depths. At both sites, water near the water tsble contained

238

more than 30 T.U., which is strongly indicative of water originating after 1952. Although all three shallower samples from the site 4000 ft from the stream had virtually uniform tritium concentrations with depth (26.8-31.9 T.U.), the well screened at an intermediate depth at the site 2500 f~ from the stream site (well $57467) had a significantly higher tritium concentration (166 T.U.) than the sample from $57466 (about 35 T.U.), the well screened near the water table. The high tritium concentration at intermediate depth suggests that this water is derived from precipitation that fell during the late 1950's and early- to mid1960's, when the tritium concentration of precipitation was at its maximum from atmospheric testing of atomic devices. These measurements also suggest that a "slug" of recharge from precipitation can retain its identity for at least 15 years in the shallow groundwater flow system without extensive vertical mixing. Tritium concentrations in all samples from the two sites 10 ft from the stream (Table 1) indicate that the water there either originated before 1952 or contained only small amounts of post-1952 water (well $57478 in J a n u a r y 1978, and well $65595). Because all shallow groundwater converges at the streambed (the discharge boundary of the shallow groundwater flow system), waters of differing ages were found close to one another in the streambed vicinity. The pattern and location of flow lines adjacent to the streambed do not remain fixed through time, however, because water-table fluctuations cause the local flow lines to shift, which causes mixing. The difference in tritium concentrations of the two samples from well $57478 (0.9 znd 0.1 T.U.) is attributed to such mixing. The single sample of stream water ¢collected during base flow) had a tritium concentration of 32 T.U. (Table 1), which was assumed to represent the average tritium concentration of local shallow groundwater at the time of sampling. Thus, the low values of tritium in well $57478, next to the stream, (0.1 and 0.9 T.U.) ~:ere unexpected because shallow groundwater adjacent to and feeding the stream during base flow would be expected to have about the same tritium concentration as the stream water itself. One explanation may be that a swamp that lies a few feet to the east and extends several thousand feet up and downstream discharges recent water into the stream, whereas water in the shallow streambank well probably originated upgradient of the swamp and is therefore older. MODEL STUDIES OF THE SHALLOW GROUNDWATER FLOW SYSTEM

A calibrated two-dimensional cross-sectional model of the study reach was developed, and a sensitivity analysis was done to evaluate the various parameters that control flcw within this system. Although the simulations pertain to the shallow flow system near the middle reach of Co~_~netquot Brooh: many of the conclusions regaMing the role of individual parameters wi.thin this shallow system could be applied to other stream systems on Long Island. Only two-dimensional, steady-state flow in the shallow system was simulated in this study because (]) the field data indicated vertical flow to be the critical factor in this system, and (2) the time and effort needed for a three-dimensional

239

transient-state model were beyond the project scope. The numerical simulations were carried out on a finite-difference modular format computer code developed by McDonald and Harbaugh (1984).

Description of model To eliminate the need to account fcr flow orthogona! to the vertical section, the model was constructed to coincide with a water-table flow line. Two simplifying assumptions that were made in the selection of this vertical section were that: (1) the shallow system could be represented as independent of the regional flow system; and (2) the vertical section through the shallow system, which followed a flow line defined by the water table, has no orthogonal flow beneath the water table. The first assumption is considered valid because, even though heads and flow within the shallow system are related to and dependent on the resional system, the two systems are separated by a flow line (flow surface in three dimensions). If the recharge and discharge boundaries of the shallow flow subsystem are accurately represented in the model, the bounding flow line at the bottom of the shallow flow system can be treated as a no-flow boundary. As long as the system is in equilibrium, the d~pth of this no-flow boundary will not move, and a model, therefore, could represent the shallow system independently. The second assumption considers the direction of horizontal flow to be the same at all depths within the shallow system. ThL¢. assumption allows the system to be represented by a two-dimensi,~nal modei that is defined along a stream line determined from a water-table map. To corroborate or refute this assumption with the available field data would be vh'~.~uallyimpossible; but, for the purposes of a sensitivity analysis under equilibrium conditions, this assumption is probably reasonable.

Boundary conditions The flow system and boundaries for the model cross section as conceptualized f,:~r this study are depicted in Fig. 9. The modeled groundwater system is assumerl to be in equilibrium, where inflow equals outflow with no change in s t o r a g e - that is, all model simulations are at steady state. If the natural flow system is in equilibrium, the flow-line boundaries at the interstream divide and between the shallow flow system and the regional flow system are stationary, and these boundaries can be simulate~l as no-flow boundaries. Field investigations have provided ~,~nesth~iate of the average thick~ce~ (m) of the shallow flow system and hence ~-,e depth of its botto,:~ boundary~ but the distance (1) to the interstream divide is uncertain. If the location of the interstream divide is known, the divide can be established as a no-flow boundary. If the model section is shorter than the distance from the stream center tc ,~.he true inter'stream divide, the quantity of water applied to the model as areal recharge will be less t h a n the quantity that enters the natural system. To

240 Lateral boundary I (interstream divide ~when Qin e~uals zero)

W _ ~

Free

iH::ddependentbou nda ry

surface

m,l K;

m

l

No flow boundary

EXPLANATION W= Recharge, ,n inr.n=~,par year W== Stream half-width, in feet Q,. ~ Specific flux, in feet squared per second ~-'=Oin K : ~ Vertical nyaraulic .,:onductivity, in feet per day K. = Horizun!al hyd:aul c conductivity, in feet per day K', = Streambed hyc~rat lic conductivity, in feet per da~/ ! rn = Shallow flow system thickness, in feet I m' : Streambed thickn~ss, in feet [ I =Distance from .~trf-am center to interstream divide, in feet J" Specified flux boundaw-..~. 1

Fig. 9. Schematic diagram of vertical model section through the shallow groundwater flow system associated with a stream and the assumed boundaries and parameters than govern flow.

simulate the flow system accurately, this additional quantity of water must be represented either by: (1) expanding the model grid such that the correct quantity of water enters the system by areal recharge; or (2) by introducing a specified-flux boundary (Qi,) to previde the proper quantity of inflow. Using Qin was selected as the more favorable alternative because it is more flexible. In an idealized aquifer system having straight, regularly spaced stream channels, groundwater flow is symmetric about the longitudinal axis of the streambed, and the groundwater flow lines from the two sides of each stream do not cross an imaginary vertical plane beneath the streambed center. Therefore, the model was designed to simulate flow on only one side of the s t r e a m - from the center of the stream to one interstream divide. The vertical boundary at the center of the stream was simulated as a no-flow boundary. The upper boundary of the model flow system, except for the stream, is a freely moving water table that receives uniform areal recharge (W). Simulating the upper boundary as a free surface is inherently correct, but uniform areal recharge is a simplification of the natural system. Uniform areal recharge ignores: (1) the intermittent nature and local variations of natural recharge; (2) losses by direct runoff to the stream; (3) flow in the unsaturated zone; and (4) fluctuations in evapotranspiration rate a s t h e depth to water changes locally and through time. Steady-state flow wa~ assumed in this study, however, because average natural recharge rates can satisfactorily simulate natural recharge. The discharge boundary at the stream is affected by streambed geometry, thickness, and permeability, and by hydraulic head difference between the strea.~ and the aquifer. The discharge boundary was simulated as a headdependent h~,akage boundar: i~r whicL ~he thickness, area, vertical hydraulic conductivity of the streambed, and the .~ead in the overlying stream are

241 Interstream

Stream center

divide

Streambank

llg w )-

2

5 4 ~ w

6

0

8 L_~_T2---_--_~

3

5 7

9

10

COLUMNS

11

12

13

14 0 0

10

20 5

30 10

..... -:Z

15 40

i- -----

..........................

131

50 FEET 15 METERS

Fig. 10. Finite-difference grid of model for simulation of the shallow flow system associated with a stream. Hachures over grid blocks 1-6 in layer 1 indicate streambed head-dependent leakage boundary.

specified. Thus, seepage through the streambed boundary is dependent upon the hydraulic gradient between the aquifer and the stream.

Model grid A variable-spaced, rectangular grid (Fig. 10) was used to represent the shallow flow systera as conceptualized from the field studies. The grid is a cross-sectional representation of the aquifer from the center of the stream to the initially assumed location of the interstream divide 6000 ft to the east. The initial thickness from the bottom of the shallow flow system to the streambed is assumed to be 30 ft. The thickness is divided into ten laye::s; the lower nine are 3 ft thick, ant2 ~;,e uppermost is 3 ft thick beneath the stream but elsewhere is dependent upon water-table altitude above the streambed (Fig. 10). The grid also is divided int~, 131 columns that are each 3ft wide beneath the stream (columns ~-6) but g :adually increase to 50 ft wide at a distance of 150 ft from the stream center. Frown t~ere to a point 6000 ft from the stream, the columns are 50ft wide. The streambed half-width was initially set at 18ft (Fig. 10).

Sensitivity tests Groundwater mg'rement in the shallow flow system is dependent upon several parameter~ whose values can be specified in the numerical modei. Not all parameters hay:.', equal effect of the head distribution or on the flow patterns in the model; large changes in some may have little effect, whereas small changes in others may have considerable influence. A systematic sensitivity analysis requires that pertinent parame~ezs be identified and the effect of changes in their niagnitude on wa~er leve:Is and flow patterns evaluated.

Shallow flow-system parameters Head in the shallow flow system can be defined as a functi,m of ten dimensional parameters (Fig. 9).

h = f(W~, m', ,~t, l, W, Kz, Kx, K'~, Q~)

242

where: h = head [L] ws = stream half-width [L] m" = streambed thickness [L] m = thickness of shallow flow system [L] 1 = distance from stream center to interstream divide [L] W = constant areal recharge [L T -1 ] = vertical hydraulic conductivity [L T -1 ] = horizontal hydraulic conductivity [L T- 1] K; = streambed hydraulic conductivity [L T] Q flow into system from right-side lateral boundary [L2T -~ ] f = some function in

--

For the purposes of sensitivity analysis, head (h) is a measure of system response to changes in other variables; W~, m', m, and 1 define the idealized configuration of the shallow system; W and Qi. define values of flux at two boundaries, and K x , K , ~ , and K~ define a distribution of hydraulic-conductivity values in the model cross section. TABLE 2 Values of dimensional p a r a m e t e r s and associated dimensionless p a r a m e t e r s investigated in sensitivity analysis Dimensional p a r a m e t e r s Name, symbol, and unit S t r e a m half-width (W~)

fit) Shallow system t h i c k n e s s (m) (ft) R e c h a r g e r a t e (W) (in y r - 1 )

Vertical hydraulic conductivity (Kz) (ftd -l)

Combined dimensionless p a r a m e t e r s

Values tested 9 18 27 18 30 39 16 20 24

65 6.5 .9.65

B o u n d a r y inflow (Qin) (ft2s - l )

0 2.0 4.0

Values tested

W~ll"

1.5 3.0 4.5 3.0 5.0 6.5 1.2 1.5

x

10 -3

x × x x

1.8

×

10 -3 10 -3 10 -5 10 -5 10 -5

roll W]Kb

Kz/Kx

300 30 3

Streambed vertical h y d r a u l i c conductivity (K~) ( f t d - ' )

Symbol

x 10 -3 x

10 -3

x

10 -3

1 1.0 x 10 -1 1.0 x 10 -~

×

10 -4

×

10 -4

"l = system length (ft). b K. = horizontal h y d r a u l i c c o n d u c t i v i t ] (ft d - 1).

K'~IK~

2.16 × 10 -1 2.16 × 10 -e 2.16 x 10 -a

Qm/Kxl

0 9.60 × 10 -6 1.92 × 10 -5

243

To simplify the process of analyzing tbe effects of these ten parameters upon the system, they were combined into eight dimensionless palameters through the 7r theorem (Bridgman, 1978, p. 40), as follows:

it W~ m' m W K z K z Qin 7 = f l' l' I'Kx'K,,'Kx'K,,I where hl.l is the dependent variable. Detailed systematic sensitivity tests were conducted on six of the remaining seven dimensionless parameters. (Streambed thickness, m'/1, was assumed to be a known constant derived from field measurements.) Values for each of the independent parameters were varied individually between anticipated extremes, and successive model runs were made to obtain head distributions resulting from each independent hydrologic condition. Only one parameter was changed at a time; all others were set at values used in an initial reference model run. Data from the twelve runs plus the reference run were evaluated by comparison of simulated with observed h]l values beneath the streambed and at the right-side lateral boundary near the watez" table. Values used for the reference model parameters were the best estimates obtained from McClymonds and Franke (1972), Cohen et al. (1968), the inve3tigations mentioned in the "Field Studies"section, and from field experience. Tb.e initial values used in the model were the median values tested for each parameter listed in Table 2. In all tests, head or stream-surface altitude at the head-dependent discharge boundary was zero; thus, all predic;i:ed model heads were referenced to this zero altitude.

Results of sensitivity tests The values of the six parameters that were investigated :~ the sensitivity analysis are shown in Table 2; plots of the resulting simulat d and measured h/l values beneath the stream are shown in Fig. 11, and those at the right-side lateral boundary are shown in Fig. 12. The sensitivity analysis for each of the six dimensionless parameters, which included changes in boundary conditions, was revealing. The pl~ts may be interpreted as being in one of two broad c a t e g o r i e s - those representing parameters to which heads ~h/l) are sensitive, and those to which h/1 is insensitive; results are summarized in Table 3. Insensitivity to a parameter is characterized by little or ~o change in h/l over the range of values tested, which is indicated by a horizontal or nearly horizontal line in Figs. 11 and 12. Correct interpretation of Figs. 11 and 12 requires an explanation of experimental bias. One value always lies on the observed h/l line in Fig. 11 (stream vicinity) because the choice of reference-model parameters was based on field measurements of ]head beneath the stream. The graphs for h/1 at the lateral boundary (Fig. 12)do not indicate this bias, however; all values of h/l in five of the six plots are below the observed h/1 values except for the Q~,/Kxl term, whose h/1 values plot both above and below the observed h/1 line (Fig. 12F). Table 3 and Figs. 11 and 12 indicate that h/l beneath the streambed is

244

i

I -F

'

I

'

L

'-[

A

3

,.H

I

l

---r

i

T

T ---~ . . . . T---~

I

B

2--

zx

OBSERVED DIMENSIONLESS HEAD

OBSERVED DIMENSIONLESS HEAD

z

W

1 -F,

I

t

i

1

.I___L

I

2

~

I

3

t

0

4

5

I

2

DIMENSIONLESS STREAM HALF-WIDTH ( Ws Ix 1 0 " )

-r--I

i

t

r

I

~---1

~---

I

I

i

( m l × 10-') 1 .... ~ .... ] I r

-----T-

c

3

,__

LI

I ....

3 4 5 6 DIMENSIONLESS SHALLOW FLOW SYSTEM THICKNESS

7

-l--r

D

3

~ A

~2

ZO-.. '~' DIMENSIONLESS HEAD

OBSERVED

z

r,,• -~', OBSERVED

DIMENSIONLESS HEAD ,,

~' j

O

o o

1

'!'

2

t _~-

3

4

0 I _ L_ i_. J. .....i ...._L__~J 0.0 0.2 0.4 0.6

.....

5

DIMENSIONLESS CONSTANT RECHARGE

T

( W K . , 10"") rr--T--

....

[. . . .

L_ L .i 0.8

. . . .

1.0

DIMENSIONLESS H~'DRAULIC CONDUCTIVITY

f-- T -

]- -._]

F

T

[

(K,K,) ~---T---T

T

T--~

15 (:3

121

i ,

fJ3~

"-

I

~,,o _j

t

v....

Z • 0" z ~

°i"

--

Z • 0"

I 5

/

I

OB,r::ERVED DIMENSIONLESS HEAD

t.p i

o

O B S E R V E DDIMENSIONLESS HEAD

" 0, 0 0

i 0" 05

~

', 0.10

i 0m' 5

~

i..~.~ 0. 20

DIMENSIONLESS STREAMEIED VERTICAL HYDRAULIC CONDUCTIVITY (K'~ K.) F i g . 11. Simulated and o b s e r v e d v a l u e s for a depth 4.5 ft beneath streambed.

of

o O.~5

: O

I 0.5

~

l I

~

~_ ' "5

,

L 2

! 2.5

DIMENSIONLESS RIGHT SIDE BOUNDARY INFLOW ( Q,,,K.I. 10-")

h/l in relation to dimensionless flow-system parameters

sensitive to the dimensionless parameters W~ll, W/Kx, K'~IK,~, and Qi, IK=I. At the lateral boundary, however, hi1 is sensitive to the dimensionless parameters m/l, W/K,,, and Qin/K,,l. The anisotrophy, Kz/K,,, has little effect on h/l at either

245 I

I

B

I

'

1

I

I

t

A

1

3~ OBSERVED DIMENSIONLESS HEAD ul

z 2--

W

T

1---

r

--!

r

I

3~ ¢3

OBSERVED DIMENSIONLESS HEAD

lad

-r m~

2~

Zx

zx

z

I

B

O~

I

Z

uu

1

0

, 0

I

I

,

1

,

I

2

L

3

'f,

I

0

4

5

2

DIMENSIONLESS STREAM HALF-WIDTH

( W=d× 10 ") I

I

'

I

I

'

'

l

1

J

J.

"!' I

~-_1

i _J

,

.....

I

I

7

I ....

D

3 t3

OBSERVED DIMENSIONLESS HEAD

=

3 4 5 6 DIMENSIONLESS SHALLOW FLOW SYSTEM THICKNESS

I

'

C

2

I

OBSERVED DIMENSIONLESS HEAD

m~

p

ZX

ZX

Z

Z

ill

o~-,

1

0

;

I

1

,

I

2

l

~

t_J

1 4

1 l ! J 1 L_I l 0.2 0.4 o.~ o., 1.0 O~MENS,ONLESSHYD~AUUCCONDUCT=WW

DIMENSIONLESS CONSTANT RECHARGE

( W/K,, 1

I

'

I

x

~0 ")

I

I

( K,,K.

i

I

1t

E Q

- -

-T

I

I -T---r---T- --T --T- --T-- 1

-t

F

£3

OBSERVED DIMENSIONLESS HEAD

I,M

J

°oo

5

!

"7"

I

03=-" 03 '

W~ .J Zx

Z×

_~

j-

,~,

"i'

u~

'f 0

OBSERVED DIMENSIONLESS HEAD

,

Z 2

1

--

C3

.... I

I 0.05

,

1

=

010

L

_L__A . . . . .

0.15

020

0.25

DIMENSIONLESS STREAMBED VERTICAL HYDRAULIC CONDUCTIVI~'Y

0

0.5

~

1.5

2

2.~

DIMENSIONLESS RIGHT SIDE BOUNDARY INF)OW

( O,. K./~

10 ")

(K'.,/K,)

Fig. 12. S i m u l a t e d and o b s e r v e d v a l u e s ot at t h e r i g h t . s i a e lateral b o u n d a r y .

h/i

in r e l a t i o n to d i m e n s i o n l e s s f l o w - s y s t e m p a r a m e t e r s

location. Of all the parameters examined, only W/K~ has a ,qignificant effect on h/i at both locations.

Simulation of the shallow flow system After the sensitivity analysis had been completed, the model was calibrated to simulate the shallow flow system near Connetquot Brook. Data used for

/

246 T ~,BLE 3 Sensitivity of head (h/l) b e n e a t h the streambed and at the right-side l a t e r a l b o u n d a r y to v a r i a t i o n s in dimensionless p a r a m e t e r s 1 ~imensionless rarameter

~¢/!~

(m/l) (W[K~) (K~/K~) (~ "~/K,,) (Qi~/Kx l )

Percent varied

100 70 40 990 990

2

P e r c e n t c h a n g e in h/l

Beneath

Near

streambed

Divide

1137 0 140 2 11013

9 151 ~37 6 71 x92

177

1Heads were sensitive to changes in this parameter. 2 ~-,m ranged e~,,~._._._._._n._. , ~n._._4_ . .n. . .× 10-4 ft 2 s-1., _percent c h a n g e is not applicable.

calibration included the water-table profile along vertical section A-A' from the September 1977 water-table map (Fig. 5); a field-measured potentiometric profile beneath the stream (Fig. 7B); and results of the sensitivity analyses. The September 1977 water levels were chosen because groundwater gradients, flow directions, and altitudes during that period were similar to those expected under average conditions and because long-term water-level records were unavailable. When the initial values for the model variables were chosen, streambed hydraulic conductivity (K'~) was adjusted to obtain a distribution of head values beneath the stream that were similar in gradient and magnitude to field data obtained earlier in the study. After a close match was achieved, the results were compared with the water-table profile drawn from the September 1977 water-table map (Fig. 5). The simulated water-table altitudes became increasingly too low with distance from the stream. The sensitivity graphs (Figs. II and 12) and data in Table 3 indicated that Qin/Kxl was the only dimensionless parameter that could be changed within acceptable limits that would increase the simulated h/1 values at the lateral boundary enough to equal the observed values. All other parameters either had little effect or would have to be changed to unrealistic values. The next step was to estimate a value of Qin that would yield an accurate result. Qi, at the lateral boundary was initially estimated directly from the sensitivity graph (Fig. 12F) and was adjusted further by trial and error until an acceptable h/1 value at the lateral boundary was obtained. However, the acceptable h/l value at the lateral boundary gave an incorrect h/1 beneath the stream; thus, further calibration was necessary. Table 3 indicates that h/l is sensitive to both Ws/l and K'~/Kx beneath the streambed but not at the lateral boundary. Because the selected stream width was already close to the measured field value, streambed conductivity, K~ was adjusted through trial

247

and error until the simulated h/l values beneath the stream were acceptably close to observed values while those at the lateral boundary remained essentially unchanged. When this was achieved, the model was considered calibrated. The final value used for K~ was 9.7ftd '; the final value for Q~, was 1.67 × 10-4ft2s -~. Values for all other parameters and boundary conditions remained the same as in the reference-model run for the sensitivity testing. The final calibrated value of Q~, is equivalent to areal recharge over a lateral distance of 3000ft. Thus, the 6000-ft length of the original model plus the addition of recharge from an equivalent length of 3000ft resulted in a total effective distance of 9000ft from the stream center to the interstream divide. Locating the interstream divide is uncertain, however, and the model studies indicated that the initial estimate of the distance from the stream to the divide was too low. The 9000-ft distance between the stream and the interstream divide obtained in model calibration is considered to be a reasonable approximation of field conditions at the location of the simulated cross section. Comparison of the simulated with the observed water-table profile for September 1977 (Fig. 5) shows a close match with only minor differences. Simulated groundwater seepage to the stream was also compared with seepage calculated from measurements made at two continuous-record gaging statio~ls and to a set of instantaneous measurements made above and below the modeled cross section. The simulated value was within 50% of the average seepage per unit stream length betweer, the continuous gages and within 15% of the value computed from nearby instantaneous measurements. These deviations can be attributed to: (1) lack of symmetry in Connetquot Brook's drainage basin; (2) use of field data from sites that are outside the modeled cross section; (3) fluctuations in natural )~'echarge during field measurements from the long-term average value used in the model; and (4) error in streamflow measurements. SUMMARY AND CONCLUSIONS

Several factors that control the movement of groundwater in a local shallow flow system on Long Island were investigated during 1975-82 at Connetquot Brook, a stream in central Long Island that is unaffected by urbanization. The first part of the study involved detailed field measurements of groundwater l e v e l s a n d collection of groundwater samples for tritium analysis to delineate the geometry of the shallow flow system. The second part consisted of sensitivity analyses of the factors that govern flow in the shallow system with a two-dimensional numerical r~lU(i~, - - 1 - 1 oi'a representative vertical cross section. During the field study, water levels were measured beneath and within a few feet of the stream channel to document head changes with depth and also were measured within a few thousand feet of the stream ¢o provide data for detailed . . . . . . . . . .,,,~ water-table maps. Wells were driven directly into the st .r,,,,~,-~ ---~ alongside the stream at three sites along the 5-mi stream reach studied, and head measurements were made at every 1-5 ft down to a 40-ft depth. In general, the

248

largest increases in head with depth were in the streambed wells, followed by the streambank wells. Water levels in streambed wells rose between 1 and 2 ft above stream level, and most of this increase was within the first 5 ft of penetration into the streambed. Head increases were noted to depths of about 30 ft beneath the streambed. Water-level measurements in two wells about 50 ft from the streambank showed no head increase within a depth of 40ft. Elsewhere in the drainage basin, comparison of water levels in wells screened near the water table with those in wells screened several tens of feet below showed no measurabledifferences; this similarity in heads with depth indicates essentially horizontal groundwater flow in the shallow flow system except within 50 ft of the stream. The head measurements just below and adjacent to the stream indicate the depth of the shallow flow system to be from 20 to 30 ft, but the data measured at greater distances from the stream were less definitive. The shallow flow system probably becomes somewhat thicker several thousand feet from the stream. These estimates are further corroborated by the distribution of tritium; water in the shallow flow system has higher tritium concentrations and is therefore younger than water in the deeper, regional flow system. Groundwater flow throughout the shallow system is predominantly horizontal except within a few feet of the stream, where flow lines bend upward toward the stream. The two-dimensional, cross-sectional, steady-state itow model was used to investigate the effects of several hydraulic and geometric factors that control flow in the shallow groundwater system. The shallow flow system was isolated from the regional system in the model by no-flow boundaries on the assumption that the shallow system and the deep regional groundwater flow system do not interact under steady-state conditions. In this study, the shallow system was divided into two parts - - one beneath the streambed and extending to a few feet from the stream channel, and the other extending from there to the interstream divide several thousand feet to the east. The factors that control flow in the shallow system were classified into three categories: (1) geometric parameters (stream width, streambed thickness, thickness of shallow flow system, and lateral extent of flow system); (2) permeability parameters (horizontal and vertical hydraulic conductivity of the shallow flow system and vertical streambed hydraulic conductivity); and (3) water-source parameters (areal recharge and inflow at the right-side lateral boundary). These dimensional parameters were combined into a series of dimensionless parameters to simplify analysis of model results. The model studies consisted of a sensitivity analysis to compare the effect of some of these parameters on calculated values of head in both the near-stream area and more distant parts of the shallow flow system. Results of the sensitivity analysis can be classified into three categories, depending on where model heads were sensitive: near the stream, at some distance (about 50 ft) from the stream, or both. Model heads in the near-stream area were sensitive to dimensionless parameters containing vertical hydraulic conductivity and width of the streambed; heads at some distance from the

249

stream were sensitive to dimensionless parameters containing the modeled thickness of the shallow flow system; and heads in both the near-stream and the more distant areas were sensitive to dimensionless parameters containing recharge, horizontal hydraulic conductivity, and the lateral-boundary flux term, which represents the additional recharge that would occur between the right-side lateral model boundary and the "true" interstream divide. Heads in the model were insensitive to the ratio between the vertical and horizontal hydraulic conductivity. The sensitivity analysis aided in the final calibration of a steady-state model of this system. The calibrated-model response compared well With heads measured in the field both near and away from the stream Results of the calibrated model runs support the original estimate that the shallow flow system is about 30 ft thick near the stream (as derived from field measurement and confirmed by analysis of tritium concentrations); they also suggest that the interstream divide is about 9000 ft east of the stream along the selected cross s~:ction. Sensitivity analyses suggest that flow in the shallow system is controlled mostly by recharge, but near the stream, it also is controlled by width and vertical hydraulic conductivity of the streambed. Near the interstream divide, flow is controlled by the thickness of the shallow flow system. ACKNOWLEDGEMENTS

The authors thank the Long Island State Park Commission for permitting access to Connetquot River State Park during the field investigations of 197582, and especially Park Superintendent Gilbert Bergen and his staff for their cooperation during the field operations. We also thank Theodore H. Wyerman of the U.S. Geological Survey in Reston, Va., for the tritium analyses reported herein. REFERENCES Bridgman, P.W., 1978. Dimensional Analysis: AMS Press, New York, N.Y., 113 pp. Cohen, P., Franke, O.L. and Foxworthy, B.L., 1968. An atlas of Long Island's water resources. N.Y. State Water Resour. Comm. Bull. 62, 117 pp. Ferronsky, V.I. and Polyakov, V.A., 1982. Environmental Isotopes in the Hydrosphere. Wiley, New Yol'k, N.Y., 466 pp. Franke, O.L. and Cohen, P., 1972. Regional rates of ground-water movement on Long Island, New York. U.S. Geol. Surv., Prof. Pap. 800-C: C271-277. Franke, O.L. and McClymonds, N.E., 1972. Summary of the hydrologic situation on Long Island, New York, as a guide to water-management alternatives. U.S. Geol. Surv., Prof. Pap. 627-F, 59 PP. Freeze, R.A. and Cherry, J.A., 1979. Groundwater. Prentice-Hall, Englewood Cliffs, N.J., 604 pp. Harbaugh, A.W. and Getzen, R.T., 1977. Stream simulation in an analog model of the groundwater system on Long Island, New York. U.S. Geol. Surv., Water.Resour. Invest. 77-58, 15 pp. Jacob, C.E., 1943. Correlation of groundwater levels and precipitation on Long Island, New York. Trans. Am. Geophys. Union, pp. 564-573. Jensen, H.M. and Soren, J., 1974. Hydrogeology of Suffolk County, Long Island, New York. U.S. Geol. Surv., Hydrol. Atlas HA-501, 2 sheets.

250 Kimmel, G.E., Ku, H.F.H., Harbaugh, A.W., Sulam, D.J. and Getzen, R.T., 1977. Analog model prediction of the hydrologic effects of sanitary sewerage in southeast Nassau and southwest Suffolk Counties, N e w York. Nassau County Dep. Public Works, Long Island Water Resour. Bull. 6, 25 pp. McClymonds, N.E. and Franke, O.L., 1972. Water-transmitting properties of aquifers on Long Island, New York. U.S. Geol. Surv., Prof. Pap. 627-E, 24 pp. McDonald, M.G. and Harbaugh, A.W., 1984. A modular three-dimensional finite-differencegroundwater flow model. U.S. Geol. Surv., Open-File Rep. 83-875, 528 pp. Pluhowski, E.J. and Kantrowitz, I.H.,1964. Hydrology of the Babylon-Islip area, Suffolk County, Long Island, N e w York. U.S. Geol. Surv., Water-Supply Pap. 1768, 119 pp. Prince, K.R., 1980.Preliminary investigationof a shallow groundwater flow system associated with Connetquot Brook, Long Island, New York, 1980. U.S. Geol. Surv. Water-Resour. Invest. 80-47, 37 pp. Prince, K.R., Franke, O.L. and Reilly,T.E., 1988. Quantitative assessment of the shallow groundwater flow system associated with Connetquot Brook, Long Island, N e w York. U.S. Geol. Surv., Water-Supply Pap. 2309. Reilly, T.E., Buxton, H.T., Franke, O.L. and Wait, R.L., 1983. Effects of sanitary sewers on ground-water levelsand streams in Nassau and Suffolk Counties, N e w York, Part 1-Geohydrology, modeling strategy, and regional evaluation. U.S, Geol. Surv., Water-Resour. Invest. 824045, 45 pp. Rorabaugh, M.I., 1960. Use of water levels in estimating aquifer constants in a finite aquifer. Int. Assoc. Sci. Hydrol., 52: 314-323. Toth, J.,1963, A theoretical analysis of groundwater flow in small drainage basins. J. Geophys. Res., 68 (16): 4795-4812.