Chapter 14

Groundwater and Surface-Water Interactions in Riparian and Lake-Dominated Systems

John F. Walker and David P. Krabbenhoft

14.1 Introduction

This chapter presents an overview of the application of isotope tracers (primarily the isotopes of water) to further the understanding of hydrologic processes occurring in riparian areas contiguous with stream systems and in hydrologic systems dominated by lakes. The chapter begins with a discussion of the spatial distribution of lake-dominated systems and a general discussion of the dominant hydrological processes occurring in these systems. Next, a brief overview of previous research in this area is presented, which focuses on investigations of recharge processes in riparian areas and studies examining the hydrologic components of lake systems. A more detailed quantitative discussion of groundwater/lake interactions follows, including the application of stable isotopes for estimating groundwater/lake exchange and the development of an index-lake method for simplifying estimates of groundwater/lake exchange.

we present a case study describing qualitatively the current research being conducted forested catchment in northern Wisconsin. This work focuses on the use of multiple

.' :::~~~~:~u~tr:;a:~c:ers to examine hydrologic processes as the stream flows from the headwaters to ':_-- with a large lake. We conclude with suggestions for future directions in applying

stable-ISOI'op'e tracers to understanding hydrologic processes in riparian areas and lake­

~~~~~~::~~ systems, including the importance of spatial and temporal heterogeneity, the :11 of groundwater flow and reaction paths for understanding these complex systems,

the use of multiple isotopic tracers.

Importance of lake-dominated systems

and wetlands comprise a significant portion of the catchment land surface and cause noili!ications to the quantity and quality of water as it flows through a catchment. Lakes

nearly 8% of the surface area of Canada; in the United States, the total surface area of not been determined, and although it is certainly less than 8%, it is nonetheless an

mnort:antportion of the landscape for water supply, recreation, fisheries, and wildlife. Thus,

6,~!~J~:~t;l~1preserve these important landscape features, an improved understanding of their

;(.) processes is necessary.

Dominant hydrological processes

general hydrologic budget for a lake system (similar to the catchment water balance

468 Isotope Tracers in Catchment Hydrology

EXPLANATION

(14.1)

Surface~water flux

Evaporation (ET) Precipitation (P)

Surface Inflow (Sil

!J.V ~ p + S. + G. - ET - S - GI I 0 Ii

SoilEvaporation

Figure 14.1. Schematic diagram depicting components of the hydrologic budget for a lake system. ModifiedKrabbenhoft et al., 1994.

Discharge to lake (G)

Transpiration

===C>- Water flux involv'lng isotopicfractionation

-::z."", Water table

-... Water flux involving nofractionation

presented in Chapter 1) is shown schematically in Figure 14.1. The budget is statedmathematically as:

where !J.V is the change in storage, P is precipitation, Si is surface inflow, including anyoverland runoff, Gi is groundwater inflow, ET is evapotranspiration, So is surface outflow, andGo is groundwater outflow. In the regions where lakes are most abundant (northeasternnorth-central United States, low Arctic, Canadian Shield, and Atlantic provinces of Canada),the dominant budget components are precipitation, evapotranspiration, and groundwaterand outtlow. Due to the pervasive permeable soils, overland flows are generally smallnonexistent, and if tributary streams exist at all, the flows are small in comparisonprecipitation and evapotranspiration. Across the northern portion of North America, Sll()Wmc,]r

is the dominant precipitation event, and provides a substantial portion of the input to thedirectly and indirectly through recharge to the groundwater system.

Chapter 14: Groundwater and Suiface-Water Interactions... 469

Depending on the spatial and temporal distribution of hydraulic heads surrounding a lake,groundwaterllake systems can be described as one of the following types: (1) recharge systemswhere the lake surface is higher than the surrounding water table and where water flows to thegroundwater system; (2) flow-through systems, where the lake gains water from thegroundwater system in some parts of the lake and loses water to the groundwater system in

parts of the lake; and (3) discharge systems, where the lake level is lower than thesmIToundirlg water table and where water flows to the lake. Further classification of lakesrelates to their position within the regional groundwater-flow system. Terminal-lake systems

defined as lakes that function as the discharge point of the regional groundwater-flowFor terminal lakes, water is removed by evaporation and through surface outflow.

Previous Studies in Lake Systems

this section, previous studies applying stable isotopes to the characterization of hydrologicare examined, specifically for lake-dominated systems. Note that the fundamental

COilcepts of the use of isotopic tracers to separate flow components were presented in Chapterand will not be repeated here.

N;~~~~~;i~ researchers have applied isotopic tracers to estimate the components of thelJ budget for lake systems. The literature can be divided into three groups based on

general objectives and approach of the isotopic analysis. In the first group, isotopic andbalance analysis is used to explain the isotopic composition of the lake in general terms

inflow and outflow or mixing processes within the lake. In the second group, isotopicmass-balance analysis is used to estimate a particular term in the hydrologic budget,

lye,ic,rlly either groundwater inflow or outflow. In the third group, detailed analyses are useddescribe processes occurring in the hydrologic system.

the first group, several studies have used detailed isotopic samples within a lake alongassumptions about the isotopic content of various components of the hydrologic budget

"explain" the isotopic content of the lake and hence make general inferences about thehyclrollogic budget of the lake. For example, water samples along depth profiles in Lake

were analyzed for 3180 and compared to theoretical plots of steady-state lake isotopicversus relative humidity for assumed ranges of the isotopic content of air moisture and

ratio of evaporation to total input to the lake (Fontes et al., 1979a). Based on the observedof 3 180 and relative humidity, the authors concluded that there are relatively small netof lake water from the system. The authors indicated that further sampling of rain water

atmospheric vapor is needed to further refine the results, A similar approach applied toAsal found the most plausible model indicates a steady lake level and net loss through

~v"porat:ion ranging from 20·40% of the total inflow (Fontes et aJ., 1979b). Further refinementisotopic composition of atmospheric moisture is needed to give a better estimate of the

loss from the lake. Based on 3D and 0180 profiles in saline and fresh-water lakes inf\nltm·ctica and companion samples from surrounding glaciers, researchers used theoreticalsc"na~ic>s from an isotopic mixing model plotted as 3D versus 3180 to explain the isotopic

of the lakes (Matsubaya et al., 1979). The authors conclude that saline lakes near theare still receiving sea-water inflow, whereas other lakes in the region are isolated from

water--their isotopic content is controlled by the mixing of lake water with inflow frommelt water or precipitation.

14,3 Estimating Groundwater Exchange with Lakes

Isotope Tracers in Catchment Hydrology

The second group of papers use isotopic and hydrologic mass balances to solve for a particularterm in the hydrologic budget of a lake. In a seminal paper, the use of oD and 0180 wasdemonstrated to be effective in separating bulk inflow from bulk outflow for a lake's hydrologicbudget (Dincer, 1968). Likewise, Allison et aI. (1979) and Turner et al. (1984) used singleinflow and outflow terms and tritium data to quantify the hydrologic budget of two lakes inAustralia. Unfortunately, individual inflow and outflow terms were not distinguished from oneanother in these studies, limiting the practical application of the results. Zimmermann (1979)used aD samples collected over a 4-year period and isotopic mass balance to estimateevaporation and bulk inflow for two lakes; groundwater inflow was inferred as the differencebetween total inflow and precipitation. These researchers found that results based on 0180 wereless accurate than those based on aD because 0180 is more sensitive to relative errors in thekinetic separation term.

470

Groundwater components of water budgets for lakes commonly are calculated as the residof average precipitation and evaporation fluxes and changes in lake storage, leadingconsiderable uncertainty in calculated values (Winter, 1981). This type of budget calculationly provides an estimate for net groundwater flow because the calculation never separatestinflow and outflow components. Such budgets combine the net groundwater fraction (inflooutflow) of the lake budget with the errors associated with other components of the labudget. In many cases, these errors are comparable in magnitude to the individual groundwatflow components; relative en'ors greater than 100% are possible. For solute-loading estimaterrors of this magnitude are unacceptable and prevent further understandinggroundwater/lake systems.

The third group of studies use lake and adjacent groundwater samples to describe interactionbetween the groundwater system and the lake. For example, researchers used oD and 0180 toargue that Lake Chala was not a significant source of water to springs that were previouslythought to be in direct connection with the lake (Payne, 1970). In a similar investigation, aD,0180 and tritium samples were used to demonstrate that Lake Schwerin, Germany, loses somewater to the groundwater system, but that lake-derived groundwater does not enter a nearbylake (HUbner et aI., 1979). Based on rainfall, lake and groundwater samples near Lake Georgin New South Wales, investigators demonstrated that deep groundwater samples beneath tlake originated from distant recharge areas, whereas shallow samples beneath the lake exhibiteevidence of a mixing of lake water and deeper groundwater (Jacobson et al., 1991). Likewisprecipitation, lake and groundwater samples in four transects moving away from each "sideof the lake were collected near an artificial lake in Germany (Stichler and Moser, 1979). Tauthors found that flow directions could be deduced from the aD and 0180 content in the wellin relation to the lake content and local meteoric water line (LMWL), and that wells dowgradient of the lake showed seasonal patterns corresponding to seasonal lake water variationFinally, an investigation of Lake Barco in Florida, U.S.A. utilized samples from wetldcollectors, the lake, and nested piezometers beneath and adjacent to the lake to describe intetactions between the lake and groundwater system (Katz et aI., 1995). The authors were abletput together a detailed description of the complex flow patterns around the lake, and found tisotopic analyses provided insight into transient mounding beneath the lake that would not habeen discovered using synoptic water-level measurements and steady-state modeling.

Chapter 14: Groundwater and Surface- Water Interactions...

14.3.1 Stable-isotope mass-balance method

471

Equations presented in this section apply to groundwater/lake systems that are in hydrologicisotopic steady states and were published by Krabbenhoft et al. (1994). Equations that

de"cribe isotopic mass balances for nonsteady state systems and mathematical forms thatto the estimation of evaporation from lakes can be found in Chapters 5 and 7; Gilath

Gonfiantini, 1983; and Gonfiantini. 1986.

the purposes of this chapter, the isotope mass-balance method is applied to several seepagein northern Wisconsin, U.S.A. where streamflows and overland flows are insignificant.lakes are typical of the poorly integrated drainage of glaciated regions that are underlain

moderate to thick glacial deposits. Under these conditions, the hydrologic budget can besinlplifi"d to include only tenns for precipitation, evaporation, and groundwater. By restricting

analysis to lakes that are in isotopic steady state and by assuming that groundwater outflowisotopically the same as lake water, Krabbenhoft et al. (1990b) combined expressions for the

hy.ire,lo;gic budget and the isotopic mass balance to derive the" following expression for theh(lUn,d.,at,er-inl101N rate:

[P(OL - op) + E(OE - 0/)]

0G, - 0L(14.2)

Gi is the groundwater-inflow rate, BL is the isotopic composition of the lake, P is the

Pb~~~~:i::ii;:: rate, op is the isotopic composition of the precipitation, 0Gi is the isotopic9' of the groundwater inflow, E is the evaporation rate, and DE is the isotopicSOlmpositi()fi of the evaporate. In this expression, all of the tenns except the isotopicS6,mp,ositi()fi of the lake evaporate (OE) are directly measurable. The average isotopicS"Jmposition of the lake evaporate can be calculated from the relation formulated by Craig and

(1965):

(14.3)

0A is the isotopic composition of local atmospheric moisture, h is the relative humidity~9:nm,ali"ed to the surface temperature of the lake, a* is the equilibrium isotope fractionation

at the temperature of the air-water interface, e is the total fractionation factor, K is an¢moirical constant relating the kinetic fractionation factor and relative humidity, and all Dand

are in permil (%0).

;ip'lrkling Lake, a groundwater flow-through lake in northern Wisconsin (Figure 14.2), wasto test the isotope mass-balance method for estimating the groundwater component of ahydrologic budget. Both the isotope mass-balance method and a numerical groundwater­

fr~:nsp'ort model were used (Krabbenhoft et a!., 199Gb); rates calculated by the two methodscomparable. The major results of the isotope mass-balance study are summarized here.

WIsconsin

VILAS COUNTY

"...... 89°45'...... -. ......J

_._._._._._._._.---'.-.. 89°15'

-'·-'· ......l--'-----..,.

'-.-...., .........

46°15'~!

Isotope Tracers in Catchment Hydrology

Trout Lake

J ",Pallelle Lake

1 i4~O i Max Lake, Big Muskellunge Lake i" ---, Sparkling laketit,

I~'----j Little Rock Lake'. d • c~k'IL"kLake 1' ]

Van ereoa a e•Honeysl.lckle Lake '

! 1

1 !--------------------------------------", r------

~,foo;~~,~li~~~~I~~~~I;~!V·Y' L_. .i

In the mass-balance study, the isotopic composition of precipitation at Sparklingshown to vary sinusoidally, with nearly a 17%0 difference in 0 180 between summer prec·tation and the winter snowpack (-5 to -22%0, respectively; see Figure 14.3). The avervolume-weighted 0180 of precipitation was estimated to be -10.9%0. Several atmosphmoisture samples were collected during the ice-free periods. Analysis of these samples shothat local atmospheric moisture is 'in isotopic equilibrium with precipitation, except during Jand August, the wannest months. The disequilibrium during these 2 months is believed tthe result of water-vapor contributions from the many nearby lakes and (or) Lake SUlperiof,

Figure 14.2. Location of lakes sampled for groundwater-component investigations (Trout Lake was nm 'U'HP'~

Little Rock Lake was artificially divided and sampled as two separate lakes (North and South). Mc.difiedKrabbenhoft et al., 1994.

472

In the sandy outwash area of northern Wisconsin, high hydraulic conductivity promotesexchange of water between groundwater systems and lakes. Sparkling Lake occupitopographically low position in the local groundwater system; thus, it receives a consistent floof groundwater, which constitutes a substantial part of the lake's hydrologic budget. Taverage depth of the lake is 10m (lake volume/surface area), and the hydraulic residence ti(lake volume/total outflow rate) is relatively long (calculated to be about 10 years), Thecharacteristics of Sparkling Lake satisfy the assumptions for use of Equation 14.2 and increthe accuracy of groundwater-flow estimates.

Chapter 14: Groundwater and Suiface-Water Interactions... 473

o-5

Evaporation line

'I' Groundwater

o Precipitation

1> Sparkling Lake

-15 -10

0180, per mil

Local meteoricwater line

-20

0

-20

-40

-w

E• -80

'"c5~

-100

·120

-140

-160-25

14.3. Isotopic compositions (oD versus ( 180) of precipitation, groundwater, and Sparkling Lake water.from Krabbenhoft et aI., 1994.

Use of Equation 14.2, the isotopic information described above, and the average annual¢ipitation and evaporation rates (0.79 and 0.52 m/year, respectively), the average annuallllldwater inflow rate to Sparkling Lake was estimated to be 0.27 m/year (expressed as the~metric flow rate divided by the surface area of the lake). Because Sparkling Lake has no1a,:e-'wa·terinflows, the groundwater-outflow rate could be estimated as the residual in the

0180 composition of the lake water was virtually invariant during the 2-year samplingiod: the average 0180 value was -5.75%0, and the standard deviation was 0.1%0, which isghly equal to the analytical error expected for 0 180 determination. These values wereained from samples collected during semi-annual turnover periods when the lake wasrmally and chemically homogeneous. During maximum summer and winter thermal(i.tification, however, epiJimnetic waters were observed to be slightly fractionated; the

er 6180 value was -5.6%0, and the winter 3180 value was -5.9%0. The monthly isotopicposition (3180) of lake evaporate from Sparkling Lake was estimated by using Equation

,.3. Monthly evaporation-rate estimates were used to calculate the weighted average annualooflake evaporate (-16.9%ol_

bient groundwater in the Sparkling Lake area is isotopically homogeneous; average 0180,,11.5 ± 0.3%0. Downgradient from the lake, however, an easily identifiable plume ofapically enriched lake water provided substantiating evidence for assumed flow paths basedl1ydraulic-head measurements. The 0.6%0 difference between average precipitation andImdwater was attributed to the selective recharge of isotopically depleted spring snowmelt

I'l1pared to isotopically enriched summer precipitation.

Isotope Tracers in Catchment Hydrology474

The application of the index-lake method presented here is only for lakes that are in hydraand isotopic steady states. A lake's steady-state isotopic composition is determined by the 10term averages of c\, op, h, P, E, and water and air temperatures, which can vary greatly~

and seasonally and to some degree annually. Therefore, it is only proper to apply the indexmethod to lakes of similar hydraulic residence time, during which time the averages ofcontrolling factors are detennined.

The lake district of northern Wisconsin is a particularly appropriate area for applying the indlake method. This area contains more than 3,000 lakes situated in sandy, glacial outwash so(Frey, 1966; Attig, 1985). The region is topographically homogeneous, consisting of amosof similar low-relief watersheds that yield little or no overland runoff to lakes and streaTherefore, recharge on a regional scale should be relatively uniform, resulting in a groundwsystem with a unifonn isotopic composition; this uniformity is an underlying assumption ofindex-lake method.

The most difficult aspect of using stable isotopes for estimating hydrologic-budget components.of lakes is determining the evaporation rate (E) and the weighted average isotopic compositioof the lake evaporate (oe) (Webster et al., 1990). The isotopic composition of water vapor thaevaporates from the surface of a lake can be estimated by use of Equation 14.3. This expressioshows that the isotopic composition of lake evaporate is controlled by the interactions of th~

lake with the overlying atmosphere. Measurements of air and water temperatures, relativ~

humidity, and the isotopic composition of ambient atmospheric moisture are needed. Samplinof ambient atmospheric moisture is a tedious and time-consuming process and is rarely donWhen atmospheric-moisture measurements have been made, as they were at Sparkling Lak(yVebster et al., 1990), it is theoretically possible to extrapolate the results for use on nearblake systems and to assume that these lakes are affected by the same atmosphere. This kindQextrapolation is referred to as the "index-lake method" (Dincer, 1968; Gat, 1971); whereby thresults from a lake whose isotopic balance has been carefully determined are used to estimathydrologic-budget components of nearby lakes.

The isotopic composition of evaporating water bodies on plots of 0180 versus oDevaporation lines. The intersection of any evaporation line with the local meteoric water(LMWL) corresponds to the average composition of all water entering the lake. Geographiclustered lakes that meet the requirement of being in isotopic steady state should plot alonsame evaporation line, provided they are indeed affected by the same atmospheric condiand have about the same hydraulic-residence times. Groundwater-rich lakes should fallthe line closer to the meteoric water line, whereas groundwater-poor lakes containingh'evaporated water should plot farther from the IMWL. The isotopic compositions of foufl(see Figure 14.2 for lake locations) in northern Wisconsin that are within 10 km of eachand that have hydraulic residence times of about 10 years are plotted on Figure 14.4. Thlakes (Crystal, Pallette, Big Muskellunge, and Sparkling) are groundwater tlow-lhf(mgn

hydrologic budget, 0.50 m/year. These results were consistent with the results from adimensional groundwater-flow and solute-transport model of the Sparkling Lake system, fromwhich the groundwater-inflow and outflow rates were estimated to be 0.20 and 0.52respectively (Krabbenhoft et a!., 1990a).

14.3.2 Index-lake method

14: Groundwater and Suiface-Water Interactions... 475

(14.4)

EXPLANATION

III Sparkling Lake

• Big Muskellunge Lake

A Palletle Lake

• Crystal Lake

- IiG,

-20

-30

-40

E -50

Ii>C-

O -60"'

-70

-80

-90-15 -10 -5 0

0180, per mil

e 14.4. Isotopic compositions (oD versus ( 180) of four lakes in Vilas County, Wisconsin. The heavy linelocal meteoric water line based on data shown in Figure 14.3; the light line is the evaporation line determined't fit for the four lakes shown. Dashed lines represent specified ratios of G;lP calculated from Equation 14.4.fled from Krabbenhoft et al., 1994.

er the assumption of isotopic steady state and for the case where there are no surfaceows and outflows, the hydrologic budget and isotopic mass balance equations can bebined and solved for the groundwater outflow rate (G(}) relative to the evaporation rate (E),Hows:

no surface inflows or outflows; thus, they have the same hydrologic-budgetCOlm.,orlents (they receive water from precipitation and groundwater inflow and lose water toeVllporatlon and groundwater outflow). A best-fit evaporation line for these four lakes has an

2;::: 0.997 and intersects theLMWL at 0180= -11.0%0, a value close to the measured input­composition for the index lake (Sparkling Lake), -11.1 %0. This close agreement indicates

the hydrologic budgets of the lakes chosen for this application can be determined by theindex-laKe method.

Table 14.1. Comparison of groundwater-inflow rates (m/ycar) for several Wisconsin lakes.

isotope Tracers in Catchment Hydrology

Lake Isotope Solute methodmethod

Sparkling 0.29 0.24Big Muskellunge 0.15 0.14Pallette 0.10 0.13Crystal 0.Q7 0.03

In some situations, natural-solute tracers can be used in the same manner as stable-isottracers to estimate hydrologic-budget components for lakes (Stauffer, 1985). As dilute rechwaters from precipitation enter the aquifer, dissolution reactions result in net additioI1dissolved solids. In northern Wisconsin where glacial-outwash sediments are defided

Isotopic compositions of lakes whose hydraulic-residence times are relatively shortyears or less) vary seasonally (Gat, 1995). Seasonal response occurs whenever a signifimass of water of a different isotopic composition either is added to or removed from the IaSeasonal variations in P, E, Gj , Op, OM and 0E cause variations in 0L for isotopically nonsteastate systems. In northern Wisconsin, many shallow lakes are isotopically nonsteady stObserved 0 180 variations for several shallow lakes in northern Wisconsin are shown in Fi14.5; Sparkling Lake is shown for comparison. The isotopically-light value for each oftlakes represents an early spring water sample, whereas the enriched value represents lateThese data demonstrate the substantial seasonal variations in isotopic composition that tIl·arise in relatively shallow lakes when compared to isotopically invariant (deeper) lakes·s~

as Sparkling Lake. Attempts to apply the isotope mass-balance method for estimating au~.

groundwater exchange rates for these lakes would be challenging because detennination oftaverage annual 0L would be difficult. On the other hand, seasonal variations in the isbtqcompositions of lakes can provide valuable insight into processes (such as exchanges of Wwith atmosphere) that otherwise would be imperceptible in isotopically steady-state syste

If long-term averages of P and E for the index lake are assumed to be the same for those of theother lakes, groundwater outflow can be estimated by Equation 14.4, and the only remainingunknown in each lake's hydrologic budget, Gi• can be determined easily as the residual of thehydrologic budget. In the same manner, one can specify a groundwater-inflow rate and solveEquation 14.4 for 0L to estimate the steady-state isotopic composition of a lake. Specified ratiosof annual groundwater inflow to annual precipitation rates (Gi IP) that approximately bracketthe compositions of the three lakes and Sparkling Lake are plotted on the evaporation line inFigure 14.4. Groundwater-inflow rates for these lakes were estimated by use of Equation 14.2and are listed in Table 14.1. The accuracy of the estimates for Big Muskellunge, Pallette, andCrystal Lakes depends on the accuracy of the groundwater inflow estimate for Sparkling Lak(the index lake) and on the validity of the assumptions for the index-lake method. Theestimated error for groundwater inflow to Sparkling Lake is ± 7 em/year (Krabbenhoft et aI.,1990b), which then represents a minimum error for the estimates of the other lakes. Thereforefor lakes that receive relatively small amounts of estimated groundwater inflow, the relatierror associated with the estimate increases, and the utility of the index-lake method is reduce

476

Chapter i4: Groundwater and Suiface-Water interactions... 477

minerals, silicate hydrolysis is the dominant dissolution reaction (Kenoyer and1992; Bullen et aL, 1996). These reactions result in net additions of major cations

, Mg2+, Na+, and K+) and bicarbonate (HC03-) to water. Through this process, groundwaterdischalfge becomes the dominant source of cations and alkalinity for northern Wisconsin lakes(K"noyer and Anderson, 1989). Therefore, by measuring solute concentrations in precipitation,

and lake water, an expression for groundwater inflow can be derived that isanalogous to Equation 14.2:

(14.5)P(CL -Cp ) - E(CJ

CG; - CL

• • Honeysuckle (1.9 m)

• • Max (2.8 m)

• • Little Rock South (3.1 m)

• • Vandercook (3.5 m)

• • Little Rock North (3.9 m)

..... Sparkling (10m)

-6 -5 -4 -3 -2 -1 0

0"0, per mJl

14.5. Observed range of blRO values for five nonsteady-state lake systems and the steady-state SparklingThe mean depth of each lake is shown in parentheses. Modified from Krabbenhoft et aI., 1994.

solute tracers has one particular advantage over use of stable isotopes in that the solutentrations in lake evaporate are assumed to be equal to zero, This assumption means that

rs associated with estimating the isotopic composition of lake evaporate do not applyesolute tracer method. On the other hand, the chemistry of groundwater is often muchheterogeneous than the isotopic composition ofthe water (Krabbenhoft et aI., 1990b). In'on, contamination problems can be a concern for solutes at low concentrations, bute samples are unaffected by contamination. Thus, estimates of average isotopic cornpo­of a groundwater system are more accurate than are average chemical compositions.

the two methods have different degrees of appropriateness depending on the site.

Cp , CGi , and CL are the solute concentrations in precipitation, groundwater inflow, andlake, respectively. This relation is applicable only for systems that are compositionally in

state and where the solute acts conservatively within the lake.

Isotope Tracers in Catchment HydroLogy478

In this section preliminary research findings are presehted for an ongoing study in aforested catchment in northern Wisconsin. The research is being conducted under theof the Water, Energy, and Biogeochemical Budgets (WEBB) program, which is athe Global Climate Change research initiative of the U.S. Geological Survey. The studycoincides approximately with one of the Long Term Ecological Research (LTER) sitesby the United States National Science Foundation, the North Temperate Lakes LTER.brief description of the study area, the overall study design will be discussed. Next, anof the progression of the flow system will be presented, followed by a moreexamination of the data from three hillslope &ites. We conclude this section with lITLpllLCamconcerning use of isotopes to discern groundwater/surface-water interactions.

14,4 Wisconsin WEBB Case Study

Thousands of kettl~ lakes, fonned at the end of the last continental glaciation aboutyears ago, are concentrated in the Northern Highlands Lake District of north-centralThe lakes range in size from 0.1 to more than 1,500 hectares, in depth from 1 to 33 m, afertility from oligotrophic to eutrophic. Sparsely settled by humans, the lake district liestwo state forests that protect 80% of the land area and 60% of the lake frontage.have totally forested watersheds and no private frontage. The forest vegetation consistsmixture of coniferous and deciduous species.

where CLo is the solute concentration for a lake with no groundwater inflow. Substitution 0

values for northern Wisconsin (P =0.79 m, E =0.52 m, and Cp =0.2 mg CalL (Krabbenhofet aI., 1990b)) in Equation 14.6 yields a dissolved-calcium concentration of 0.7 mg/L. Thivalue is close to that of Houeysnckle Lake (0.6 mg CalL), a nearby lake that is known to havno groundwater inflow (William Rose, U.S. Geological Survey, oral commun., 1991). Thclose agreement between the calculated and the measured values also increases confidence'the values of P, E, and Cp used in the solute mass-balance method.

o PCpC =--

L P-E

Groundwater-inflow rates as calculated by the solute and isotope mass-balance methods(Equations 14.5 and 14.2, respectively) for several northern Wisconsin lakes are listed in Table14.1. Dissolved calcium was used as the solute tracer because it is the constituent whoseconcentration differs the most between groundwater and precipitation~the two inputcomponents to be separated by the solute mass-balance method. In addition, calcium is nearlyconservative in the soft water and moderately acidic to circum-neutral lakes of northernWisconsin. Results from the solute and isotope methods agree relatively well, except forCrystal Lake, where groundwater flow reversals are frequent. In this case, the isotope methodis unable to discern groundwater discharge, which is isotopically equivalent to the lake waterthat had previously recharged from the lake prior to the flow reversal. Equation 14.5 can be seequal to zero (Le., no groundwater inflow) and solved for CL, as follows:

14.4.1 Study area

Chapter 14: Groundwater and Surface-Water Interactions.. 479

14.6. Location of Wisconsin WEBB project and LTER study lakes.

--'-,"-"~:: 32' 30"

LTER study lakes

EXPLANATION

Surface-water basin boundary

Surface-water sub basin boundary

Streamflow-gaging station

Meteorological station

HHislope site

Transect sampling site, andnumber

•'.'"0

(.~90" €I SUperior

~o

89° 43'

Base Irom U.S. Geological Survey1:24.000; Boulder JunctilJll, 1981, Sayner, 19B2,While Sand Laka. 19B1. arnlWoodrul!, 1982

44°-

480 Isotope Tracers in Catchment Hydrology

Geologic features of the area are dominated by a sandy outwash plain consisting of 30-50 mof unconsolidated sand and coarser till overlying Precambrian igneous bedrock. The pre­dominant soils are thin, poorly developed forest soils with high organic content in the upperhorizon. The area is representative of the glacial lake districts common to the upper Midwestand Canada but has some individual characteristics that distinguish it from other nearby lakeareas. Among the most important of these features is the fact that the glacial drift is essentiallycarbonate free, with the result that the groundwater chemistry is almost entirely controlled bysilicate hydrolysis.

The seven study lakes of the LTER project (Figure 14.6) are within 10 km of each other, rangein elevation from 492 to 502 m a.s.!., and are exposed to almost identical climate. Meanmonthly temperatures are minimum in January, ranging from -17 to _6°C, and are maximuin August, ranging from +13 to +26 0c. Precipitation averages 76 em/year. The lakes are icefree about 7 months each year. The climate at the project site is affected by air masses from theNorth Pacific, the North Atlantic, the Gulf of Mexico, the Arctic, the High Plains, and the OhiqValley. Located about 70 km southeast of Lake Superior, and 200 km northwest LakeMichigan, the LTER site is also under strong climatic influence from the Great Lakes.

Most of the lakes in the area are seepage lakes-they have no surface-water inlets or outletsThus water budgets are dominated by direct precipitation, groundwater flow, anevapotranspiration. The seven LTER study lakes, five of which are seepage lakes, are an in thsame groundwater flow system (Figure 14.6). There are strong chemical gradients among thethat reflect increasing proportions of groundwater inputs. Those that are situated high on thlandscape, such as the two bog lakes and Crystal Lake, receive little groundwater flow and nstreamflow. Their ionic concentrations are low, with specific conductance ranging from 10-2JlS/cm. Other lakes that are low on the landscape, such as Trout Lake, are dominated bgroundwater and stream inputs, as reflected by greater specific conductance (70-90 JlS/cm

Several single-lake basin hydrogeologic studies recently conducted in the North Temper~

Lakes (NTL) area (Kenoyer, 1986; Marin, 1986; Krabbenhoft, 1988; Wentz and Rose, 198Krabbenhoft and Babiarz, 1992; Rose, 1993) have led to detailed descriptions of tgroundwater flow network around three of the LTER lakes (Sparkling Lake, Crystal Lake,Crystal Bog) and three non-LTER lakes in the area (Little Rock Lake, Pallette Lake, arrVandercook Lake). All of these studies concluded that the unconsolidated aquifere!hydraulically very conductive, providing for good connection between the aquifer and the lakBecause the precipitation readily percolates into the sandy soils of the region, surface-wa.runoff is negligible as a hydrologic input to the lakes.

14.4,2 Study design

One objective of the WEBB study is to examine processes at several spatial scales to explpossible predictive capabilities of scaling up from smaller to larger catchments. Therefsampling and data collection is being carried out at two spatial scales. The large-scale samp .is conducted at 10 discrete points on Allequash Creek and two tributaries from the headwato the confluence with Trout Lake (Figure 14.6; some sampling sites not shown for clar'Samples were collected in fall 1991 and monthly from May through October for 19921993. The samples were analyzed for major cations and anions, nutrients (total, ammonianitrate nitrogen, total phosphorus, and orthophosphorus), total organic and inorganic carb

481

-----

EXPLANATION

• Piezometer location

Dalalogger Bulk precipitationcollector

Recordingtensiomele

Schematic diagram depicting instrumentation and sampling points on hillslope sites at the Wisconsinresearch site.

t the smaller spatial scale, detailed monitoring sites have been installed on three hillslopestarting at the headwaters and ending at the outlet from Allequash Lake (Figure 14.6, sites 1,and 6). At each of the three sites, transects of nested piezometers were installed from near thep of the hiIlslope to the base of each hill. Additional nested sampling points extend from thelise of the hill to the other side of the stream, including a group of three well nests under thetieambed. Samples were collected from all the nested wells in the fall of 1992, and monthly

mJune 1993 through October 1993. The samples were analyzed for major cations and stable;$Otopes (D, 180, and 87Sr/86Sr); a subset of the well samples were analyzed for dissolved

ganic and inorganic carbon, pH, alkalinity, dissolved carbon gases (C02 and CH,J and nC.a sets of nested gravity and suction Iysimeters were used to sample the vadose zone. At each

e, bulk collectors are used to obtain precipitation and throughfall samples, which areyzed for stable isotopes (D, 180, and 87SrI6Sr). Associated with the small-scale sampling,

lltinuous records of instantaneous throughfall, stream discharge, water levels in the hillslopei~zometer nests, and tension in the vadose zone at six locations are collected. A general~ematic diagram depicting the instrumentation and groundwater-sampling sites for the

; slope sites is presented in Figure 14.7.

Chapter 14: Groundwater and Suiface-Water Interactions...

pH, alkalinity, and several stable isotopes (D, 180, 87Sr/86Sr, and BC). Associated with the large­scale sampling, a continuous record of discharge of all four streams tributary to Trout Lake isbeing collected at their confluence with Trout Lake and at the outlet from Trout Lake (Figure14.6). Additionally, samples were collected periodically from the other streams tributary to

rout Lake and at the outlet from Trout Lake (monthly from October 1991 through June 1993nd during six sampling trips per year).

Isotope Tracers in Catchment Hydrology

~40

Transect site~45 Local meteoric water line· 1

• 2~3

~50

• 4~5

6-7~55

E -•:0 ~60 ...~ • •6 •~ •

~65 • •• •~70 ••

• •~ •

~75 •

"0~12 ~11 ~10 ~9 ~8 ~7 ~6

0 180, per mil

Figure 14.8. Isotopic compositions (bD Versus bIRO) of samples collected along the Allequash Creekfrom October 1991 through February 1992. The local meteoric water line was established in a(Krabbenhoft et al., 1990a).

In many cases, use of additional isotopes can provide further information tounderstanding of a flow system. The stable-isotope pair 87Sr/86Sr can be used to discernsdifferences in the contact of water with different mineral matrices or the amount of contacfwith similar mineral matrices (Bullen et aI., 1996), thus further distinguishing the origingroundwater source water. In the case of the Allequash Creek catchment where theamineral composition is believed to be relatively homogeneous, slower flow ratescontact time result in a more radiogenic signal (enriched in 87Sr), whereas faster flow

As discussed previously, a plot of the isotopic composition (oD versus ( 180) can revealdifferences between meteoric sources of water and evaporative sources of water. For the caseat Allequash Creek, this amounts to a distinction between groundwater and more local surfacewater (Le., lake water). Results for stream-transect samples collected from October 1991through February 1992 are shown in Figure 14.8. As one moves from the headwaters (site I)to the confluence with Trout Lake (site 7), the flow system progresses from a more or lesshomogeneous meteoric source (groundwater and local recharge) to a mixture of groundwaprecipitation, and evaporated surface sources. The general trend for 0180 samples collectethrough time is the same (Figure 14.9a); stream water at the headwaters is close to the averaggroundwater composition for the area (-11%0), and the 5 180 composition becomes progressive1enriched along the transect, indicating evaporation along the stream course and mixing wiother evaporated waters.

14.4.3 Isotopic flow-system progression

482

483

Allequash Creek transect sampling results for (a) 0 180 and (b) 087SrfoSr. Results show the rangeat each transect site for samples collected from October 1991 through October 1992.

14: Groundwater and Suiface- Water Interactions...

e overall picture of the Allequash Creek flow system is a progression from a pureoundwater source to a mixture of relatively deep groundwater, relatively shallowundwater, and evaporative (surface) water. Further examination of the flow system comesm a detailed look at the isotopic compositions at a smaller spatial scale.

depleted 87Sr signal. The general trend for cPSr/86Sr samples collected through time at thetransect sites would indicate groundwater discharge from relatively long flow paths at

headwaters, inclusion of relatively shallow flow paths from sites 1 to 3, interception ofdistant flow paths to the lake (sites 4 and 5), and then a further progression toward mixingshallow flow paths from sites 6 to 7 (Figure 14.9b). Although the 6"Sr/86Sr results

relatively shallow and thus local flow paths, periodic sampling of the hills lopeiezometers shows values that are not sufficiently radiogenic to explain the water in the stream,hich indicates that the "shallow" flow paths are still quite distant from the stream and do not

dominantly originate as recharge on the adjacent hillslopes.

Figure 14.10. Cross section depicting shaded regions between isopleths of OIRO from piezometercollected at hills10pe site 3 during June 1993.

In this section, data collected during the spring of 1993 at each of the three detailed hillslopesites will be presented. The original sampling in the fall revealed several places whereadditional piezometers were needed to adequately define spatial trends. The piezometers wereinstalled the following spring, and all subsequent sampling was from the more complete set ofpiezometers.

8180 Values

II -5to-6

• -6to-7

-7 to-8

-8to-9

-9to-10

-10 to -11

-11 to -12

North

lsotope Tracers in Catchment Hydrology

. Piezometer location

1 __-=-=-=-=-=_-=_, Allequash Creek

-4 -'--------------------'-

o 0.5 1.0 1.5 2.0 metersI! I

Horizontal exaggeration x 2

South

E 2

~"0

~~ 0o.0os~ -1

-!lE.S -2c-.215 -3~W

The values of 0 180 collected from wells at the headwaters of Allequash Creek (hillslope site1) plot near the LMWL, clustering around the average composition of well-mixed groundwater(oD"-81%" 0 180"_11.3%,). The small degree of variation does not exhibit any spatial structurein the hillslope cross section. The isotopic composition (oD versus ( 180) of the piezometesamples shows the relatively homogeneous groundwater noted by Krabbeuhoft et al. (1990b)This is consistent with the general description presented earlier, with the headwaters receivinwell-mixed groundwater and the homogeneity in part due to relatively long flow paths.

A cross section with shading between isopleths of 0 180 for hillslope site 3 shows theof spatial variability (0 180 ranges from -5 to -11%0) present in a relatively confined areathe stream (Figure 14.10). Perhaps the most prominent feature is the presence of a "plume'water that is very enriched in 0 180 (values from -5 to -6%0). The near vertical orientation orcontours indicates that the source of enriched water is flowing upward from depth allcontributing more flow than the recharge water from the hillslope. The isotopic composi(oD versus 0 180) of the piezometer samples from hillslope site 3 indicates that the water i"plume" originates from an evaporative source (Figure 14.11a). The most likely source fotwater is Big Muskellunge Lake (average 0 180 composition of -4.5%,), which is nearly!away in another surface-water catchment (Figure 14.6). The average 0 180 composition 6

14.4.4 Isotopic complexity

484

i4: Groundwater and Surface-Water interactions... 485

-35

-40 (a)Local meteoric water line

-45 .....z-50 •• ••

E -55 •~

-60<1>"- •0' -65 •~

-70 •-75

-80

-85-12 -11 -10 -9 -8 -7 -6 -5 -4

8180, per mil

-35

-40 (b)Local meteoric water line

-45

-50

E -55~

,<1> -60 • ,a'"-a'

..-65 •

~ • •-70

-75 .'•-80 •-85

-12 -11 -10 -9 -8 -7 -6 -5 -4

8180, per mil

e 14.11. Isotopic compositions (oD versus OIRO) of samples collected from piezometers at hillslope site 3nd hillslope site 6 (b) during June 1993. The local meteoric water line was established in a previous studybbenhoft et aI., 1990a), and is extended to cover the range observed at all hillslope sites.

m (-9.5%0) would indicate that the stream either may receive water from a mixture ofy-derived groundwater and the plume of water from Big Muskellunge Lake or is simplyaporative evolution of water from the pond at the headwaters as it moves through the

ill system. Experiments to test these hypotheses are ongoing at the present time.

oss section with shading between isopleths of 0180 for hillslope site 6 is presented inre 14.12. Again there is a high degree of spatial variability presentin a relatively small areathe stream. The isopleths of 0 180 suggest local recharge water getting to the stream fromillslope, and perhaps a deeper source of water flowing toward the stream originating from

.Voi the southern bank. The -8%0 contour dipping away from the north side of the streamnel indicates that the stream probably is receiving groundwater on the southern side and

Figure 14.12. Cross section depicting shaded regions between isopleths of DlaO from piezometercollected at hillslope site 6 during June 1993.

8180 Values

II -510-6

I11III -6 to-7

-7 to-8

-8 to-9

-910-10

-10to-11

-11 to -12

North

Isotope Tracers in Catchment Hydrology

. Piezometer location

Allequash Creek

o 2 4 6 8 10meters-4 -'------------------'-

Vertical exaggeration x 4

I I

South2

E~

0;"0

ij.2l' 0o.Dro~ -1

"*E.~ -2

Co

'i\1 -3>mW

recharging water to the groundwater system on the north side of the creek. This interpretationis consistent with periodic head measurements made in selected piezometers in the vicinitythe creek. The isotopic composition (oD versus 0180) of groundwater samples from belowstream (Figure 14.11b) indicate that the water under the middle and north side of the streamderived from stream or lake recharge, which is consistent with the measured flow direction.Indeed, site 6 is directly downstream from Allequash Lake, hence the stream water willa high percentage of lake water.

In summary, the overall stream system appears to move from a well-mixed grclUnd,,'atedominated system at the headwaters to a flow system with complex flow directionssources. Midway through the stream system (site 3) the flows appear to come fromshallow and deep sources. At the outlet of the system shallow and deep sources alsocontribute to the stream, with the added complexity of groundwater recharge as wellcharge across the stream channel. The spatial variability of the observed groundwatervalues at the individual cross sections is verification of the complex nature of the flowThis combination of multiple isotope sampling from the lakes, the stream, and the gre.undwatsystem has provided a powerful tool to augment more traditional hydrologic apIJroaclles.

486

In this section, several observations are made based on the results of our case study.importance of spatial and temporal heterogeneity is discussed in the context of usingisotopes to distinguish components of the hydrologic budget. Next, the importance ofwater flow and reaction paths is discussed. Finally, a case is made for the use ofisotopes and other environmental tracers.

14.5 Concluding Remarks

Based on the results presented in Figures 14.10 and 14.12, it is clear that significant spatialheterogeneity of isotopic tracers exists (as shown in other hydrologic systems in Chapters 10,11 and 12). Even if one could derive a single representative value, use of a single concentrationto represent all groundwater would result in misleading conclusions. Under no circumstancescould one have inferred the complex pattern of flow and multiple sources present in thefiillslope/Allequash Creek system by just sampling the surface water. Thus, traditionalstreamflow separation techniques, with intensive stream sampling and limited groundwatersampling, may not have the appropriate sampling focus.

487

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H. and Gordon, L.T., 1965. Deuterium and Oxygen-I 8 variations in the oceans and the marine atmosphere.In: E. Tongiorgi (Ed), Stable Isotopes in Oceanographic Studies and Paleotemperatures, Spoleto.Consiglio Nazionale delle Riccrche, Pisa, Italy, pp. 9-130.T., 1968. The Use of Oxygen 18 and Deuterium Concentrations in the Water Balance of Lakes. WaterResour. Res., 4: 1289-1306.

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understanding of flow and reaction paths is increased by the use of multiple isotopiccers. In the example presented in Section 14.4, the natural isotopes of water (oD and ( 180)re used to identify sources of water, whereas a lithogenic isotope (o87Srfl6Sr) helped to

stinguish between flow-path depths, and can be used to elucidate reaction paths. While these'IN tools are powerful, traditional hydrologic monitoring is crucial for corroborating isotopic'nIts and for quantifying rates of surface water/grou~dwater interactions. Through a

bination of multiple isotopic tracers, intensive small-scale groundwater sampling, vadose-e sampling, precipitation sampling, and stream sampling, a more complete understanding

interactions between surface water and groundwater can be gained.

s is true in streamflow separation, a single groundwater term may not be appropriate forllssessing stream water quality. For studies attempting to understand the geochemical

teractions of surface water and groundwater, a more detailed analysis of flow paths iscessary. For the study presented in Section 14.4, there appear to be at least two distinctoundwater-flow sources contributing to the stream. These sources may have substantially

erent geochemical compositions. Likewise, the geocheJ11.ical evolution depends not only onflow paths but on the mineral composition of the matrix the water is flowing through, andamount of contact time with the minerals. Thus, techniques to examine reaction paths areessary for a more thorough understanding of the geochemical interactions.

Chapter 14: Groundwater and Surface- Water Interactions...

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Version: July 1998