WATER RESOURCES RESEARCH, VOL. 26, NO. 10, PAGES 2445-2453, OCTOBER 1990 Estimating Groundwater Exchange With Lakes 1. The Stable Isotope Mass Balance Method DAVID P. KRABBENHOFT Water Resources Division, U.S. Geological Survey, Madison, Wisconsin CARL J. BOWSER, MARY P. ANDERSON, AND JOHN W. VALLEY Department of Geology and Geophysics, University of Wisconsin-Madison Groundwater inflow and outflow contributions to the hydrologic budget of lakes can be determined using a stable isotope (180/160) mass balance method. Thestable isotope method provides a wayof integratingthe spatial and temporal complexitiesof the flow field around a lake, thereby offering an appealing alternative to the traditional time and labor intensive methods using seepagemeters and an extensive piezometer network. In this paper the method is applied to a lake in northern Wisconsin, demonstratingthat it can be successfully applied to lakes in the upper midwest where thousands of similar lakes exist. Inflow and outflow rates calculated for the Wisconsin lake using the isotope mass balance method are 29 and 54 cm/yr, respectively, which compare well to estimates, derived independently using a three-dimensional groundwater flow and solute transport model, of 20 and 50 cm/yr. Such a favorable comparison lends confidence to the use of the stable isotope method to estimate groundwater exchange with lakes. In addition, utilization of stable isotopes in studies of groundwater-lake systems lends insight into mixing processesoccurring in the unsaturated zone and in the aquifer surroundingthe lake and verifies assumedflow paths based on head measurementsin piezometers. INTRODUCTION The groundwater contribution to the hydrologic budget of a lake is difficult to quantify because heterogeneities, present in all aquifers, cause complicated patterns of groundwater flow around lakes. Traditional estimatesof groundwater-lake exchange are based on measurements from piezometers and require extensive piezometer networks to derive accurate estimates. To minimize the necessary number of piezome- ters, a technique that integrates all the complexities in the flow field and accounts for all the inflow and outflow is needed. This paper demonstrates that a mass balance method using stable isotopes is such a technique. Our study is presented in two parts that have the same objective: to determine groundwater inflow and outflow rates for lakes, with an application to a lake in northern Wisconsin.This paper describes the use of the stableisotope mass balance method. In the second paper [Krabbenhoft et al., this issue] the groundwater-lake exchange rates are estimated by calibration of a groundwater flow and solute transport model to a stable isotope plume downgradientfrom the lake. Traditionally, flow models alone have been used to estimate flow rates to lakes [e.g., McBride and Pfannkuch, 1975; Munter and Anderson, 1981]. Thus calibration of the solute transport submodelto the configurationof the isotope plume allows us to estimate flow rates more accurately. The isotope method and calibration of a solute transport model each represent independent ways of determining the ground- water component of a lake budget. When applied to the same groundwater-lake system, both methods yield similar re- sults. Each method alone represents an improvement over traditional methods of estimating the groundwater compo- This paper is not subject to U.S. copyright. Published in 1990 by the American Geophysical Union. Paper number 90WR01135. nent of a lake budget. Taken together the techniques are complementary and help establish confidence in the results. BACKGROUND Early efforts using stable isotopes for the study of lakes were described by Dincer [ 1968]. Later studies are reviewed by International Atomic Energy Agency [1979], Gat [1981], Gilath and Gonfiantini [ 1983], and Gonfiantini [ 1986]. Stable isotopes are useful in groundwater-lake studies because each of the components that contribute water to or remove water from a lake acquire different isotopic signatures, owing to fractionation processes. Thelight isotopic species of water, H•60, has a higher vapor pressure and diffusivity than the isotopically heavy species H•80 and HDO (where D is deuterium) and is preferentially removed from a lake during evaporation. The lake thereby becomesenriched in the heavy isotopic species of water. The degree of enrichment depends on climatic conditions, including average annual temperature, relative humidity, and precipitation and evaporation rates. Average annual precipitation and groundwater may ex- hibit different isotopic signaturesfor the following reasons. Some of the rain that falls on the land surface may evaporate before recharging the aquifer, leaving the residual water isotopically enriched [Turner et al., 1987]. Second, while all precipitation events contribute water directly to the lake, only larger events recharge the aquifer. This process is referred to as selective recharge. Thus the isotopic signature of average precipitation and groundwater should differ. Uptake by plant roots has also been suggested as a possible mechanism for fractionating average precipitation and groundwater. However, several studies demonstrate that this is not an important process [Zimmermann et al., 1967; White et al., 1985; Turner et al., 1987]. 2445