Environ. Sei. Technol. 1905, 19, 405-41 1
Use of Solute Tracers Released by Weathering To Estimate Groundwater Inflow to Seepage Lakes Robert E. Stauffer” Water Chemistry Laboratory, University of Wisconsin, Madison, Wisconsin 53706
The steady-state influx to seepage lakes can be estimated by using a solute mass balance, provided the excess of precipitation over evaporation is known for the lake surface. For lakes set in the dolomitic glacial drift of Wisconsin, Mg is an ideal groundwater tracer, both because it has the highest ratio of groundwater concentration to concentration in precipitation and because it behaves nearly conservatively in lakes set in semihumid climates. By use of the Mg mass balance, groundwater inflows were estimated for 10 natural lakes lacking surface inflows and set in pitted glacial outwash in central Wisconsin. The estimated inflows (range = 0.1-2.0 m year-’) accord with the lakes’ different geologic settings and with the lakes’ Si and Si/P ratios. The inflow estimates could be improved by better information on the precipitation excess and improved knowledge of the factors regulating Mg concentrations in local vs. regional groundwater flow systems.
Introduction Despite the interest and efforts of some early limnologists (1,2),the hydraulic and chemical relationships between groundwater and lakes remain poorly understood ( 3 , 4 ) . Many lakes throughout the formerly glaciated regions of upper Midwestern U.S.A. and south central Canada, and doline lakes set in karstic regions of Florida and Central America, lack distinct surface inflows and/or outflows. For these “seepage” lakes, and many other lakes with small drainage basins and only minor surface inflows, seepage is a major influence on lake geochemistry (including alkalinity buffering) and on lake trophic state. For this important class of small lakes, a better understanding of biogeochemistry awaits better information on lakegroundwater relations. In most lake studies the seepage inflow has been either neglected or crudely calculated as the residual in a hydraulic budget equation (3). Darcy’s equation is also used but requires detailed information on potentiometric gradients and the hydraulic conductivity of the local aquifer (4). In the hummocky terrain surrounding many glacial seepage lakes, the local head gradients can be seasonally unsteady (5),and point estimates of hydraulic conductivity are notoriously anisotropic and irregular. Even if the hydraulic features of the surrounding “drift” are well established, these may not apply to the fine-grained lake-bed seal laid down since the glacial retreat. Because of these practical problems in applying Darcy’s law, lake-bed seepage is sometimes measured directly by using seepage meters (6). Unfortunately, this approach is ineffective in estimating total groundwater inflow if groundwater enters partly through lakeside or subsurface springs. It is also ineffective for fractured hard rock basins or poorly consolidated organic sediments ( 4 ) . In this paper another approach is explored; e.g., what hydraulic inferences can be made about groundwater-lake interactions based on m a s balance studies of solute tracers *Address correspondence to this author at the Department of Geology, University of Maine a t Orono, Orono, ME 04469. 0013-936X/85/09 19-0405$01.50/0
mobilized into groundwater by soil and rock weathering? A set of mass balance equations is first identified which can be simultaneously solved to yield the inflow. Solutes are then evaluated for their potential as groundwater tracers. Following this theoretical development, the method is applied to the lake district in Central Wisconsin, thus illustrating the procedure’s practical potential and the sensitivity of the analytical solution to uncertainties in several key parameters.
Theoretical Considerations Mass Balance Equations. On the basis of the conservation of mass, the temperature-adjusted (7) lake volume at any time t is Vi(t)= Vl(t - 1) + Ao(P - E + Qi - Q, - D ) (1) where A, is lake surface area, and P, E, Qi, Q,, and D are the fluxes (m At-l) in direct precipitation, evaporation, groundwater inflow, seepage outflow, and surface discharge during the antecedent time interval, At = ( t - 1,t). If A, is a constant for small changes in lake surface elevation, or if corrections are applied accompanying changes in lake stage (often minor), lake stage is then hl(t) = hl(t - 1) + P - E + Qi - Q, - D (2) For stable climates and long enough At PI-E’+ QI’-QJ-D’=O (3) where here the primes denote steady-state fluxes. The temporal mass balance for a solute is M,(t) = Ml(t - 1) + PC, - EC, + QiCi - Q,C, - Dcd + F (4) where M l ( t ) is the mass storage (water column) of the designated solute expressed per unit A,, C,, ... Cd are the true mean concentrations during At in precipitation, evaporation, etc., and F represents a source-sink function (positive when into the lake water) for sediment-water exchanges, air-water interactions not directly linked to evaporation, radioactive decay, etc. If the solute is strictly conservative, F = 0. At steady state P’C,’ - E%,‘ Q[C[ - Q,‘CJ - D’cd’ F‘ = 0 (5) Rearrangement, of eq 2 yields Q, + D = X , Q, - Ah (6)
+
+
+
where X p = P - E denotes temporal “precipitation excess” on the lake surface. Because, to a very close approximation, c, = Cd for a suitable tracer (see later development), substihtion of eq 6 into eq 4 yields, on rearrangement AM + X,C, + EC, - PC, - AhC, - F Qi = (7) ci - c, For small seepage lakes changes in stage are easily measured by using automatic recorders that integrate out the effects of small amplitude surface seiches for time intervals as short as 12 h (5). The analogous equations for steady-state analysis are QJ+D’=Xpl+Q[ (8) and
0 1985 American Chemical Society
Environ. Sci. Technol., Vol. 19, No. 5, 1985 405
Qi‘ =
XplC,’
+ E’C,‘
- P’C,’
- F’
ci‘ - c,’
(9)
where X,,’ denotes the long-term precipitation excess for the lake surface. Solute Tracers. The above analysis shows that in order to estimate Qi or Q[ independently (not just net seepage, Qi - Q, or Q[-Q,’) eq 7 or 9 must be applied effectively to at least one solute. More generally, if n distinct source waters are to be independently estimated (set of Qi’s),a set of equations involving n solutes will have to be solved simultaneously. Even for n = 1, the analysis will be successful only for a solute satisfying certain conditions. In addition to the usual constraint that the solute can be easily and precisely analyzed, an optimal tracer should satisfy the following conditions: (1) C, = C,‘ = 0; (2) Ci >> C ,C( >> Cp’; (3) F = F’= 0; (4) variance Ci is minimum for tke groundwater system under study. For silicic acid (dissolved SiOJ and the common inorganic ions the first condition very nearly holds (negligible lake loss accompanying evaporation). However, the last three conditions are rarely simultaneously satisfied. Thus, a judicious evaluation of tradeoffs is required for each geologic setting of interest. Among the common anions, C1- is a tracer for “sea salt” (8) and, away from the sea coasts, linked to hydrothermal groundwaters (9,10) or the leaching of evaporites in areas of favorable sedimentary geology (11-13). Unlike portions of Michigan and New York State, however, Wisconsin is underlain at a relatively shallow depth by granitic basement rock and lacks halite in the overlying sedimentary layers (ref 14 and 15 p F23). In Wisconsin, elevated C1concentrations are mainly anthropogenic (street deicing, water softening, etc.). This ion is useful as a conservative contaminant tracer. Sulfate and nitrate are relatively abundant in Wisconsin precipitation and in precipitation elsewhere in the Midwest (16). Hence, condition 2 is violated. Furthermore, neither of these redox sensitive solutes behaves conservatively within the lake, its adjoining sediments, or the land drainage basin (17,18). Nor is alkalinity conservative, because of linkage both to calcite precipitation in calcareous lakes (19,20) and to the redox chemistries of Fe, Mn, S, and N (17,18). Among the cations, Na+ is linked geochemically with Cl(13),and environmental K concentrations vary irregularly in response to agricultural fertilization and seasonal demands of growing plants. In Wisconsin, neither ion offers potential as a general seepage tracer, but Na+ can substitute for Cl- as a contaminant tracer. Calcium and magnesium offer special promise as seepage tracers for lake basins set in thick calcareous glacial drift, or doline lake basins set in carbonate-rich areas of central Florida and Central America. Magnesium is also an obvious tracer in areas of ultramafic rock (13). In humid regions with abundant dolomite, Mg offers advantages over Ca as a tracer because, once in solution, it does not re-form a carbonate in lakes unless Mg/Ca > 2 (20). This geochemical distinction accounts for the very high CaO/MgO ratios in lake sediments of southeast Wisconsin (21, 22) and elsewhere (19,23). Because Mg behaves nearly conservatively within the lake water column, only a few measurements will suffice to estimate C,’ and Cd’ for individual study lakes. The Mg concentrations of groundwaters seeping into the lake, and lake water leaving the lake, will be nearly unaffected by their transits through recent sediments. Hence, C’, = Cd’. For temperate lakes in humid climates (X,’ > 0), with small littoral zones, medium Ca concentrations (525 mg 406
Envlron. Sci. Technol., Vol. 19, No. 5, 1985
L-l), low Ca/Mg atomic ratios (51.5), and low or moderate algal productivity, calcite formation will proceed slowly, if at all, in the upper water column during summer stratification (23). Even if calcite sparingly forms in the epilimnion of such a lake, much of it will redissolve in the undersaturated hypolimnion or in the surficial sediments prior to permanent burial (20,23). Thus, in lakes receiving only moderate amounts of Ca-rich groundwater, Ca will also act as a conservative element (F’ = 0). This class includes many “perchedn doline lakes in subtropical carbonate lithographies (e.g., Florida and Central America; cf. ref 24 and 25). It also includes seepage lakes in the Northern Highlands lake district of Wisconsin and similar regions ( I , 2). The major disadvantage of the common alkaline earths as groundwater tracers is that point estimates of Ci are potentially sensitive to both equilibrium and kinetic effects on carbonate dissolution. Holland (13) has stressed the importance of both temperature and Pco2on carbonate equilibria. In temperate climates the temperature of soil water percolating downward through the unsaturated zone varies widely as a function of season. Moreover, recharge to the water table occurs mainly as “piston flow” during the late fall-early spring when air temperatures are low (26). These cold waters dissolve calcite but, following some warming and retarded reaction with dolomite, become supersaturated with calcite (26). If significant recharge occurs during warm months, in response to above normal rainfall, the higher temperature during infiltration will result in lower Ca and Mg concentrations. The temporal and spatial factors influencing Pco2are even more important. High COz concentrations are associated with fertile, heavily cropped soils and poorly aerated peaty soils; low Pco, values are found in infertile sandy soils (13). Kinetics is also an important factor in carbonate geochemistry, particularly for dolomite dissolution (13,26). Along selected groundwater flow paths C[ may be dependent on the local abundance of carbonate minerals and hydraulic residence time. Thus, flow path is important in the segregated calcareous and overlying noncalcareous glacial drift found in Vilas County, northcentral Wisconsin ( I , 2). However in carbonate-rich lithographies reworked by glaciation, equilibrium with calcite is often attained within the upper unsaturated zone (26). In subtropical regions where surface soils have been intensively weathered, shallow groundwater flow paths lack carbonate exposure; the resulting waters are soft (24,25). The deeper penetrating regional flow nets intersect carbonate strata; hard waters result. Silicic acid is suitable as a tracer because C,’ is low ( 0, calcium and silica each enter into only one significant precipitation reaction (Ca2+ CaCO,; silicic acid biogenic opal). These reactions have received intensive study, and the analytical methodology for the dissolved and particulate phases is straightforward (19,36,37). Provided sufficient attention is paid to sediment focusing and to dissolution of opal and calcite in surficial sediments, it should be possible to estimate net sedimentary fluxes of both Si and Ca over seasonal and longer time intervals in seepage lakes. This objective has already been achieved for the calcite flux in Fayetteville Green Lake, NY (19). For doline lakes the groundwater influxes from the upper leached carbonatefree stratum, and the underlying carbonate-rich statra, may be separately estimable by using SiOz in conjunction with Ca (or Mg).
-
-
Methods Estimating X ’. Except for slightly lower precipitation (by -5 cm y e a d ) within the Lake Winnebago Lowland
MINNESOTA VILA ONEIDP.
WISCONSIN
YI”E*FoLII
WAUSHMA
WCHESTER
---- ------
.f
A,
\ t 3
100 Ln
WCIFORO
\
0
\
\
I
/
‘,\
‘\ \
ILLINOIS
\
I
e ‘
CHICAOD
L
s
*\‘\
/
Flgure 1. Location of study area. Late summer solute concentration profiles collected from stratified lakes in identified Wisconsin counties, in Minneapolis, and in Oakland Co., M I (not shown). Shallow seepage lakes in Portage Co. (not shown) lie just west of Waupaca Co. line. Seepage lakes in Adams Co.(not shown) lie just west of Marquette Co. line. Line A = approximate location of Magnesium Limestone cuesta; B = Niagara dolomite. Asterisk indicates location of study lakes in Northern Highlands (noncalcareous).
and along the west shore of Lake Michigan, the central Wisconsin lake region extending from 88’ to 90’ W longitude and between 43O and 44’30’ N latitude has a precipitation norm p’= 77.3 cm year-l (circumflexesdenote estimates), with a spatial coefficient of variation (c.v.) of only 2.7% (38). The 30-year norm at each site also has a C.V. -3%, e.g., equivalent to spatial variability in the region (cf. Figure 1). Expected annual evaporation from wind-exposed lakes ranges from 71 cm year1 for the NE corner of the rectangle to 75 cm year-l in the SW corner (ref 39 and 40, p 110). These estimates are also compatible with Ficke’s (41) detailed study of Pretty Lake, NE Indiana, and a detailed energy budget study of Lake Mendota, Madison, WI (R. Stauffer, unpublished results). Evaporation from small wind-sheltered seepage lakes is lower than for larger exposed lakes, but the downward shift (in %) is smaller than the percent reduction in over lake wind speed (42). Energy budget analysis indicates that a 25% reduction in wind speed will reduce evaporation by -lo%, because an upward shift in the surface equilibrium temperature causes increased sensible and long wave radiation losses. A 50% reduction in wind velocity causes -18% reduction in evaporation. Velocity reductions of 25-50% are to be expected for small forest-rimmed lakes (43, 44). When the above results are combined, X ’ = 13 f 3 cm year-l ( f l SD) for small seepage lakes near baupaca, WI. Because of its location SW of the other lakes, inconclusive evidence of slightly lower local P’, and much larger lake surface area (88 ha), &,’ is lower for Fish Lake (5 f 3 cm). Systematic bias in X ; is probably
