5.15 Groundwater Dating and Residence-time Measurements F. M. Phillips New Mexico Tech, Socorro, NM, USA and M. C. Castro University of Michigan, Ann Arbor, USA

5.15.1 INTRODUCTION 452 5.15.2 NATURE OF GROUNDWATER FLOW SYSTEMS 452 5.15.2.1 Driving Forces 452 5.15.2.2 Topographic Control on Flow 453 5.15.2.3 Hydraulic Conductivity and Its Variability 453 5.15.2.4 Scales of Flow Systems 454 5.15.2.4.1 Vadose-zone scale 454 5.15.2.4.2 Local scale 454 5.15.2.4.3 Aquifer scale 455 5.15.2.4.4 Regional scale 455 5.15.2.5 Sources of Solutes at Various Scales 455 5.15.2.5.1 Meteoric (recharge) 455 5.15.2.5.2 Weathering 456 5.15.2.5.3 Diagenetic 456 5.15.2.5.4 Connate 456 5.15.2.5.5 “Basement waters” 456 5.15.3 SOLUTE TRANSPORT IN SUBSURFACE WATER 456 5.15.3.1 Fundamental Transport Processes 457 5.15.3.1.1 Advection 457 5.15.3.1.2 Diffusion 457 5.15.3.1.3 Dispersion 457 5.15.3.2 Advection–Dispersion Equation 458 5.15.3.3 Interaction between Hydrogeological Heterogeneity and Transport 458 5.15.3.3.1 Small-scale transport and effective dispersion 458 5.15.3.3.2 Large-scale transport and mixing 458 5.15.3.4 Groundwater Dating and the Concept of “Groundwater Age” 459 5.15.4 SUMMARY OF GROUNDWATER AGE TRACERS 460 5.15.4.1 Introduction 460 5.15.4.2 Radionuclides for Age Tracing of Subsurface Water 460 5.15.4.2.1 Argon-37 460 5.15.4.2.2 Sulfur-35 460 5.15.4.2.3 Krypton-85 461 5.15.4.2.4 Tritium 461 5.15.4.2.5 Silicon-32 463 5.15.4.2.6 Argon-39 463 5.15.4.2.7 Carbon-14 463 5.15.4.2.8 Krypton-81 464

451 452 Groundwater Dating and Residence-time Measurements

5.15.4.2.9 Chlorine-36 465 5.15.4.2.10 Iodine-129 465 5.15.4.3 Stable, Transient Tracers 466 5.15.4.3.1 Chlorofluorocarbons and sulfur hexafluoride 466 5.15.4.3.2 Atmospheric noble gases and stable isotopes 466 5.15.4.3.3 Nonatmospheric noble gases 467 5.15.5 LESSONS FROM APPLYING GEOCHEMICAL AGE TRACERS TO SUBSURFACE FLOW AND TRANSPORT 468 5.15.5.1 Introduction 468 5.15.5.2 Approaches 469 5.15.5.2.1 Direct groundwater age estimation 469 5.15.5.2.2 Modeling techniques: analytical versus numerical 470 5.15.5.2.3 Identification of sources and sinks of a particular tracer 471 5.15.5.2.4 Defining boundary conditions (modeling approach) 471 5.15.6 TRACERS AT THE REGIONAL SCALE 471 5.15.6.1 Introduction 471 5.15.6.2 Examples of Applications 472 5.15.6.2.1 Noble-gas isotopes—Paris Basin 472 5.15.6.2.2 Great Artesian Basin—noble-gas isotopes, 36Cl, and 81Kr 474 5.15.6.2.3 Implications at the regional scale 477 5.15.7 TRACERS AT THE AQUIFER SCALE 478 5.15.7.1 Introduction 478 5.15.7.2 Carrizo Aquifer 478 5.15.7.3 Implications at the Aquifer Scale 482 5.15.8 TRACERS AT THE LOCAL SCALE 483 5.15.8.1 Introduction 483 5.15.8.2 3H/ 3He, CFC-11, CFC-12, 85Kr—Delmarva Peninsula 483 5.15.8.3 Implications at the Local Scale 485 5.15.9 TRACERS IN VADOSE ZONES 486 5.15.10 CONCLUSIONS 490 REFERENCES 490

5.15.1 INTRODUCTION fluxes through subsurface systems are very difficult to measure. To some extent, subsurface fluxes can Water is the key to the geochemistry of the upper be estimated using methods based on the physics of crust and the surface of the Earth. Water interacts water flow (e.g., numerical modeling of flow extensively with minerals through hydrolysis, systems), but the very large variability of per- dissolution, precipitation, interface solute layers, meability imparts a high uncertainty to the results. etc., and is necessary for life, which directly and Fortunately, measurement of certain geochemical indirectly affects the chemistry of Earth systems. constituents in water can define residence times The local characterization of aqueous geochemical and fluxes in subsurface systems. This chapter will reactions is a natural and straightforward extension explore the geochemical means that are available of classical chemistry. However, neither the to help quantify subsurface fluxes, and will composition nor the evolution of the upper layers evaluate the implications of their application to a of the Earth can be explained by local-scale variety of specific systems. geochemistry. It is the open-system nature of geochemistry in this environment that provides most of its explanatory power, as well as its 5.15.2 NATURE OF GROUNDWATER intellectual challenge. The fundamental aspects of FLOW SYSTEMS near-surface geochemistry such as weathering 5.15.2.1 Driving Forces reactions, precipitation of sedimentary minerals, diagenesis, and metamorphic evolution all depend Water moves from areas of higher total fluid on transport of mass in and out of these systems. In energy to areas of lower energy. Kinetic energy, most cases, moving water is the transport agent. mechanical energy (e.g., compression), gravita- Geochemical constituents are transported by the tional potential, interfacial potential, and chemical circulation of the Earth’s three major near-surface potential can drive fluid flow. In general, velo- dynamic systems: the oceans, the atmosphere, and cities in the subsurface are low enough, so that continental water. This chapter deals with the third kinetic energy can be neglected. Water, therefore, of these, specifically with subsurface water. Sur- moves from areas of higher to ones of lower fluid face water is an important medium for transporting potential (Hubbert, 1940). In systems that are only geochemical constituents on a global scale, and is partially saturated with water (e.g., the vadose relatively easily accessed and quantified. In con- zone and oil and gas reservoirs), the combination trast, subsurface water is not easy to access, and of gravitational potential and interfacial potential Nature of Groundwater Flow Systems 453 (capillary action) serves to drive flow. In relatively law, has an extremely wide range in natural shallow (less than a few kilometers) saturated materials, extending over ,16 orders of magnitude groundwater systems, gravitational potential is (Freeze and Cherry, 1979; Manning and usually dominant. In deeper settings, additional Ingebritsen, 1999). Although, in any particular forces—such as compression due to compaction subsurface setting, the range will probably be much or tectonic movement, pressure generated by less, variations of five or more orders of magnitude chemical reactions, or chemical potentials deve- are common. To compound the difficulties of loped across semipermeable shales—may also be quantifying the behavior of fluids in such hetero- important (Neuzil, 1995, 2000; see Chapter 5.16). geneous systems, access to the subsurface is generally very limited and actual measurements of hydraulic conductivity are generally sparse. 5.15.2.2 Topographic Control on Flow Thus, although the physics of groundwater flow is The fundamentals of the major subsurface water well understood and amenable to quantitative cycle are straightforward. Water precipitates out of analysis, the great variability of properties and the atmosphere onto areas of relatively high the lack of constraints on their values render such topography. Some of this water infiltrates into the analyses, subject to great uncertainty. It is in this subsurface. Because it has greater gravitational perspective that the utility of geochemical tracers potential energy than water at lower elevations, it for water residence time can be appreciated. A flows downward, eventually re-emerging at the sequence of residence-time measurements along a surface either at the lowest elevation within the flow path essentially integrates the velocity history region, or at higher elevations where low- of the groundwater and thus provides a very permeability barriers force it to the surface. valuable constraint on the permeability structure. Topographically driven groundwater flow is The structure of the heterogeneity in hydraulic generally more important for geochemical pro- conductivity is typically complex. The fundamen- cesses than flow produced by the alternative tals of the geological controls on conductivity have mechanisms mentioned above. This is because been recognized for many years. For example, the circulation of meteoric water, driven ulti- Meinzer (1923) codified long-standing ideas of mately by solar energy, is a process that provides a high- and low-conductivity units termed “aquifers” continuous source of subsurface water that can and “aquitards.” However, continued research has carry large fluxes of solutes. Although other shown that these are considerable oversimplifica- driving forces, such as sediment compaction or tions of a typically very complex subsurface tectonic compression, may, for periods of time, permeability structure. An alternative view is to provide water velocities comparable to topogra- characterize the permeability structure as essen- phically driven flow at similar depths, the total tially fractal (Neuman, 1990, 1995); in other water flux is limited to the pore volume of the rock words, as the spatial scale of measurement undergoing compression. increases, the variability of hydraulic conductivity, One frequently underappreciated aspect of and the size of units of differing conductivity, also topographically driven flow is the pervasive extent increases in some proportional fashion, without of water circulation through the shallow crust. any apparent upper limit. Further refinement of Fairly subdued topography can drive appreciable these ideas would conceptualize hydraulic con- water flow to depths of several kilometers. ductivity as being characterized by nested scales of Under favorable circumstances, more significant variability, such that the increase in variability relief can produce circulation to depth below might be large for certain ranges of spatial scale 5km(Person and Baumgartner, 1995; Person and and small for others (Gelhar, 1993). For example, Garven, 1992). Permeability generally decreases consider an aquifer formed by deposition in the with depth (Manning and Ingebritsen, 1999), and valley of a meandering river, dominated by sand this is one factor that tends to limit groundwater channel deposits, but also containing many fine- fluxes at considerable depth. Another fairly grained overbank deposits. At a scale smaller than common limitation is provided by brines at that of a single channel or overbank unit, the depth; topographically driven freshwater is permeability might be relatively uniform, but as the generally unable to displace brines that are below sampling volume increases to incorporate bound- the discharge point of a groundwater basin ing units of contrasting lithology, the variability (see Chapter 5.17). would increase dramatically. However, further increase of the volume to incorporate many similar 5.15.2.3 Hydraulic Conductivity and units over the thickness of the entire aquifer would Its Variability result in little additional variability. This complex and hierarchical variation of The flow of groundwater and other subsurface hydraulic conductivity results in complex subsur- fluids is described by Darcy’s law (Darcy, 1856). face flow paths. It is not possible to incorporate Hydraulic conductivity, the constant in Darcy’s a complete and reliable description of actual 454 Groundwater Dating and Residence-time Measurements permeability structures in numerical models. are generally vertical (usually downward, but Although geochemical tracers cannot provide a upward in discharge areas and in many desert mapofthepermeabilityvariations,theycanprovide regions, and also seasonally upward in many important clues to the nature of the variations, and recharge areas). The scales of the flow systems they can help to discriminate between competing range from a few centimeters to as much as hypotheses. several hundred meters in deserts and mountai- nous karstic regions. Understanding downward 5.15.2.4 Scales of Flow Systems fluxes is of considerable importance because of the need to quantify groundwater recharge and to Both permeability distributions and topo- assess the potential for aquifer contamination. graphic variations can be considered as some However, this quantification is difficult because of form of hierarchical fractal process (Boufadel the nonlinear nature of the laws governing et al., 2000). The interaction of hierarchical unsaturated flow and the great degree of seasonal variability in both the main driving force and the variability in fluxes. main control on flow results in a nested, hierarchical system of flow regimes (Freeze and 5.15.2.4.2 Local scale Witherspoon, 1966, 1967; To´th, 1963). These are commonly classified as vadose-zone scale, local Local flow systems dominate groundwater scale, aquifer scale, and regional scale, going from circulation at shallow depths (down to as much as smallest to largest (Figure 1). 100 m) in humid regions (i.e., having significant diffuse areal recharge), unless the topography is 5.15.2.4.1 Vadose-zone scale very flat (To´th, 1963). Such systems vary from ,100 m to several kilometers in horizontal scale. It The vadose zone forms an essential, though is the discharge from such systems that supports frequently overlooked, component of the subsur- surface-water flow in streams and rivers under all face hydrologic system (Stephens, 1996). Fluxes but storm conditions. The primary control on

Figure 1 Illustration of the development of increasingly complex flow systems as topography becomes more complex. Contours of hydraulic head are indicated by dashed lines and groundwater flow lines by solid arrows. Scale is arbitrary, but might correspond to 100 km in the horizontal direction. In (a), smooth topography produces a regional-scale flow system. In (b) and (c) increasing local topography creates a mixture of intermediate and local-scale flow systems superimposed on the regional one (Freeze and Witherspoon, 1967) (reproduced by permission of American Geophysical Union from Water Resour. Res. 1967, 3, 623–634). Nature of Groundwater Flow Systems 455 groundwater flow in such systems is generally 5.15.2.5.1 Meteoric (recharge) considered to be topographic, with recharge at higher elevations (ridges or hills) and flow to Meteoric (atmospheric origin) waters that enter immediately adjacent streams or rivers (Buttle, the subsurface environment are not devoid of 1998). The water table generally represents a solutes, although they are generally quite dilute subdued replica of the topography. Such systems (E. K. Berner and R. A. Berner, 1996). They provide a large fraction of the groundwater supply contain ionic solutes, dissolved gases, and isotopic for drinking and other uses, and are particularly signatures that are derived from atmospheric susceptible to contamination. sources. The most important ionic solutes are generally of marine origin. These especially þ 2 22 include Na ,Cl , and SO4 . They also contain N2,O2, and CO2 from equilibration with the 5.15.2.4.3 Aquifer scale atmosphere, producing an oxidizing and weakly acidic solution. In areas having minimal soil– Many hydrogeologic investigations are carried out at the scale of the aquifer, a map-scale water or rock–water interaction after infiltration of precipitation, these characteristics of infiltrating geological unit capable of yielding significant þ 2þ 2 amounts of water. Aquifer scale may vary from a precipitation produce dilute Na or Ca –HCO3 subsurface waters. These constituents, particularly few kilometers to hundreds of kilometers. 2 Although aquifers may often span the horizontal Cl , which tends to act conservatively in ground- scale of the relevant flow system, they generally water, can under some circumstances be used to do not encompass the full vertical extent of the infer residence times. system. Although aquifer-scale studies often do In addition to these “ordinary” constituents, not provide a complete representation of the flow infiltrating meteoric waters may contain more system, they are very important because they exotic solutes that are particularly useful for focus on the units that provide most of the water tracing of water flow paths and residence times. supply, and for which the most data are available. Prominent among these are radionuclides pro- duced by the action of cosmic rays on the atmosphere. The most commonly employed are 3H, 14C, and 36Cl, but many others are described 5.15.2.4.4 Regional scale in this chapter. Another category of useful Many areas exhibit trends of elevation at the tracers is that produced by human activity, continental, or subcontinental scale (hundreds to whose atmospheric concentration histories are generally known. Those frequently employed for thousands of kilometers). Unless pervasive per- 3 14 36 meability barriers are present, the topographic subsurface tracing include H, C, and Cl gradients will drive deep circulation systems produced by atmospheric nuclear-weapons test- 85 129 over these continental scales (Figure 1)(Freeze, ing, Kr and I released from nuclear and Witherspoon, 1966; Person and Baumgartner, reactors, and chlorofluorocarbons and SF6 1995). Although both the depth and the quality of released by industrial and commercial users. water in such systems limit their human consump- Certain other “trace solutes” can be used to tion, they are critical for understanding the origins estimate residence times by virtue of temporal of diagenesis, many ore deposits, and petroleum fluctuations in input concentrations that can be reservoirs (Ingebritsen and Sanford, 1998). related to known fluctuations in environmental conditions. The trace molecular species of water 1 18 2 1 16 H2 O and H H O are introduced into the atmosphere by oceanic and continental evapo- 5.15.2.5 Sources of Solutes at Various Scales transpiration and are precipitated along with the 1 16 The chemical (and isotopic) composition of more common H2 O. The proportion of these subsurface water shows a fair degree of predict- rare isotopic species is governed by a variety of ability based on the hydrogeological environment environmental conditions, primarily by tempera- in which it is found (Drever, 1997). This ture (see Chapter 5.11). Similarly, the concen- predictability arises from distinctive geochemical trations of the atmospheric noble gases are reactions and sources of solutes that characterize temperature dependent. If fluctuations of tem- each of the flow-system scales described perature in the recharge area are known, then above. Although these are treated in more detail subsurface transport times can be inferred if elsewhere in the Treatise on Geochemistry, they corresponding spatial fluctuations can be are summarized below because they are an observed in the subsurface water. All of these integral part of the origin and interpretation tracers share the characteristic that can then be of geochemical indicators of residence time and used to estimate the time since entry into flow path. subsurface water systems. 456 Groundwater Dating and Residence-time Measurements 5.15.2.5.2 Weathering regional-scale groundwaters frequently acquire very high dissolved solids through interaction The chemical composition of most shallow with evaporites. Certain distinctive solutes intro- groundwater reflects that of atmospheric precipi- duced from the matrix along regional-scale flow tation, modified by additional solutes derived paths can be used for estimating residence times. from weathering. Weathering reactions generally These include certain isotopes of He, Ne, and Ar, result from the thermodynamic instability of and 129I. minerals formed in the deep subsurface (or the oceans) in the low-temperature, low-pressure, dilute, oxidizing, and acidic conditions typical of vadose zones and shallow groundwater. The 5.15.2.5.4 Connate solutes added to infiltrating precipitation through In addition to evaporites, groundwaters on these reactions vary greatly, depending on the regional flow paths frequently encounter connate mineralogy of the solid phase and the environ- waters, i.e., residual solutions retained in the mental conditions (Drever, 1997). Owing to the subsurface from the time that formations in slow kinetics of many weathering reactions the system were deposited in the ocean. These (particularly those involving aluminosilicate þ waters often show Na –Cl2 dominance (see reactions), solute concentrations can continue to Chapter 5.16). Such waters were previously increase and evolve over time (Rademacher et al., thought to have been largely swept out of 2001). These reactions lead to water at the sedimentary basins by circulation of meteoric vadose, local, and often aquifer scales that is water (Clayton et al., 1966), but this analysis more basic, less oxidizing, and more concentrated ignored the high density of these brines, which than precipitation, but still generally containing makes them very resistant to displacement by less than ,1,000 mg L21. Solutes introduced flowing dilute groundwater (Knauth and Beeunas, from these reactions are generally not used as 1986). Connate waters (or other saline formation residence-time tracers, but they can complicate waters) influence the composition of topographi- the use of atmospheric tracers that also have cally driven groundwater mainly by upward weathering sources (e.g., 14C and 32Si). diffusion of solutes. Because of their generally great age and immobility, they are not amenable to most groundwater dating methods, with the possible exception of 129I(Moran et al., 1995). 5.15.2.5.3 Diagenetic As the scale of flow systems increases from the local to the regional, groundwater moves to 5.15.2.5.5 “Basement waters” depths where pressures are much higher, tem- peratures higher, and redox conditions generally Highly saline water of distinctive isotopic more reducing. Under these conditions, waters composition is often found in environments of that have achieved near-equilibrium under vadose such depth and low permeability that flow rates or shallow aquifer environments begin to react must be extremely low or zero. These waters are þ again with the solid phases present. In some cases often characterized by Ca2 –Cl2 compositions these reactions simply take the form of recrys- and stable isotope composition “above” the tallization to higher P–T phases, but in others meteoric waterline (see Chapter 5.17). They solutes are dissolved at one point along a flow apparently result from water–rock equilibration path and precipitated at another point, producing over very long periods of time. Geochemically, cementation or mineralization of the rocks they have little influence on waters in active through which they are flowing. Increases of circulation systems, but mobile isotopes of the temperature, particularly, tend to produce total noble gases diffusing upward from this environ- solute concentrations that are higher than in ment can be a powerful tool for understanding the groundwaters in shallower flow systems. Anion flow systems into which they move. The noble-gas 2 concentration tends to evolve from HCO3 isotopes can also provide clues to the histories of dominance to Cl2 dominance along regional these nearly static waters. flow paths (Chebotarev, 1955); cation evolution is less predictable. One particularly important aspect of deep rock–water interaction is that 5.15.3 SOLUTE TRANSPORT IN highly soluble evaporite minerals (principally SUBSURFACE WATER halite) are uncommon near the surface of the Earth, because they have generally already been The objective of applying geochemical tracers dissolved by circulating meteoric water. Such to subsurface water systems is to understand their minerals are more common in the deep subsur- dynamics. The tracers themselves are solutes. In face where circulation rates are slow, and thus order to correctly understand the distribution of Solute Transport in Subsurface Water 457 the tracers, and to apply them to analyze the diffusion coefficient. For values of Pe less than ,1, system dynamics, a basic understanding of subsur- diffusion dominates, but above this value advection face transport processes is necessary. Transport of dominates (Perkins and Johnston, 1963). Appli- subsurface solutes can be ascribed to three cation of this equation to the various flow systems processes: advection, diffusion, and dispersion. described above indicates that for typical local or This section gives a brief introduction to these aquifer-scale systems, advection dominates deci- transport processes. More extensive treatments sively over diffusion. However, at the very slow can be found in Bredehoeft and Pinder (1973), flow velocities, characteristic of the deeper por- Domenico and Schwartz (1998),andPhillips tions of regional flow systems, diffusion may (1991). become dominant. Diffusion may also dominate in shallower flow systems where permeabilities are very low, such as clay-rich tills or shales, or in 5.15.3.1 Fundamental Transport Processes unusual circumstances where hydraulic gradients 5.15.3.1.1 Advection are negligible. In general, diffusion is an effective mechanism for redistributing solutes over short Advection is mechanical transport of solutes distances under most circumstances, but is a along with the bulk flux of the water. It is significant transport mechanism at aquifer or driven by the gradient in the total mechanical regional scales only when the time available for energy of the solution, just as the water flux is transport is also long. driven. For most circumstances, this means the gradient in gravitation potential energy. Advec- tive fluxes are simply the product of the 5.15.3.1.3 Dispersion water flux from Darcy’s law with the solute concentration: There is an additional mechanism of transport in flowing water termed dispersion. The dispersive Ja ¼ CK7h ¼ C q flux is given by where J is the advective solute flux, C the volume a J ¼ D7C concentration, K the hydraulic conductivity disp tensor, 7h the hydraulic head gradient, and q the where D is the dispersion coefficient tensor and is specific discharge. Advection transports all given by solutes at the same rate. 0 D ¼ aqs þ D d where a is the dispersivity tensor. Although the 5.15.3.1.2 Diffusion equation above appears to treat dispersion and Diffusion differs fundamentally from advection diffusion as separate and additive processes, they in that it is entropy driven, following the principle are, in fact, linked. An increased diffusion that solutes within a system will redistribute coefficient may appear to increase dispersion, themselves so as to maximize the entropy of the but will actually decrease it so long as the linear system. Diffusive transport is, therefore, governed velocity term in the equation is not very small. by concentration gradients: Dispersion is a mixing process that is actually driven by differential advection. Small-scale 0 Jd ¼ D d7C differences in velocity along different flow paths produce increasing variation in the concentration J D 0 where d is the diffusive flux, d the effective as a function of position. However, diffusion tends diffusion coefficient (accounting for the effects of to equalize concentrations between high- and low- 7C porosity and tortuosity), and the concentration velocity portions of the flow path and thus limits gradient. Since the concentration distributions of the amount of differential transport due to various solutes in a single system need not be mechanical dispersion. The additive diffusion identical, different solutes generally have different coefficient term on the right-hand side simply diffusive fluxes. ensures that concentration-gradient-driven trans- The relative importance of advection and port goes to the diffusive flux as the velocity goes diffusion is of fundamental significance for to zero. understanding solute transport in various settings. Dispersivity is treated as a tensor, because the This can be assessed using the Peclet number magnitude of velocity variations is greatest in q d the direction of flow and least transverse to the Pe ¼ s m D 0 direction (usually vertically transverse, if the flow d is horizontal). This means that, for equal concen- where qs is the average linear velocity of the water, tration gradients, the magnitude of the dispersive 0 dm the mean grain diameter, and D d the effective flux will also be greatest in the direction of 458 Groundwater Dating and Residence-time Measurements flow (longitudinal dispersion) and smallest described above. Small-scale variations in pore perpendicular to it (transverse dispersion). structure tend to spread solutes over limited distances. This spreading is then amplified as the solute-carrying groundwater encounters progres- sively larger-scale heterogeneities with increased 5.15.3.2 Advection–Dispersion Equation flow distance. The end result of these processes is In order to obtain a comprehensive description that at typical shallow groundwater velocities, of the transport of solutes in subsurface water, it is longitudinal dispersion is typically one or more necessary to consider all three transport mechan- orders of magnitude more effective in transporting isms. This can be accomplished by linking the three solutes than is diffusion. Furthermore, the effec- transport flux equations above through the continu- tiveness of the process increases as the transport ity equation, yielding the advection–dispersion scale increases. The amount of mixing and equation for steady-state flow: consequent spreading of concentration fronts is highly dependent on the local hydrogeology, X ›C D72C 2 q ·7C þ R ¼ which controls the permeability structure. Metho- s i dologies for moving from an understanding of the i ›t geological environment to the ability to predict where Ri are chemical or nuclear reac- the permeability structure, and from that ability to tions affecting the constituent modeled. The the prediction of dispersive behavior, have not advection–dispersion equation can be solved been achieved (Weissmann et al., 1999). analytically for simple boundary conditions, and such solutions have been used frequently in interpreting the distribution of age tracers (Sudicky and Frind, 1981; Zuber, 1986). However, numeri- 5.15.3.3.2 Large-scale transport and cal models provide a more flexible and realistic mixing means of implementing the advection–dispersion As the scale is increased from the aquifer to the equation for groundwater systems, which rarely regional, solute transport becomes even more correspond to the simplifications required for difficult to predict. At smaller scales a somewhat analytical solutions. homogeneous spatial distribution of high- and low-permeability facies can often be assumed. This leads to more uniform relative contributions 5.15.3.3 Interaction between Hydrogeological of advection and diffusion to total dispersion. Heterogeneity and Transport However, as the spatial scale increases, mixing processes extend over units that may have Section 5.15.2.3 above emphasized the high greatly differing distributions of high- and low- degree of heterogeneity of permeability that is permeability facies. For example, transport characteristic of most geological materials, and the processes in a sandstone aquifer may be domi- role of hierarchical scales of organization of the nated by advection, but in the adjoining shale permeability in determining average flow paths. aquitards, diffusion may dominate. The bound- These characteristics also play a critical role in the aries between units of differing transport charac- transport of solutes in the subsurface. The role they teristics are not necessarily abrupt or of simple play depends on the scale of the transport. geometry. Several approaches have been taken to dealing with solute transport in general, and transport of 5.15.3.3.1 Small-scale transport and geochemical dating tracers in particular, through effective dispersion these large-scale heterogeneous systems. The earliest approach was to assume such drastic Dispersion has often been treated as a constant contrasts that low-permeability units could be parameter, with values of the dispersivity on the treated as impermeable and impervious to diffu- order of centimeters (Perkins and Johnston, 1963). sion (Hanshaw and Back, 1974; Pearson and For typical shallow groundwater flow velocities, White, 1967). This is equivalent to treating the this places dispersive transport on the same order permeable units as a sealed tube. This conceptual as diffusion. However, extensive field tracer tests model is clearly an oversimplification, inasmuch have demonstrated that dispersion is much more as we know that cross-formational water fluxes are effective than these values would indicate and, common, and that diffusion coefficients of low- furthermore, that effective dispersivity tends to permeability units are not drastically smaller than increase with the scale of the tracer test (Gelhar, those of higher permeability units. The second of 1986; Schwartz, 1977; Sudicky and Frind, 1981). these shortcomings was acknowledged in models This behavior derives from the fundamentally that treated diffusion of tracers into adjacent quasifractal nature of hydraulic heterogeneity aquitards as a boundary condition for transport Solute Transport in Subsurface Water 459 equations (Sanford, 1997; Sudicky and Frind, complex interaction of irregular topographic 1981). Although an improvement, this conceptua- forcing with extremely heterogeneous distri- lization is also limited by the assumption that butions of permeability, groundwater flow paths transport in low-permeability units is diffusion are complex and difficult to predict, often resulting dominated (Phillips et al., 1990). In many cases in mixing on various scales. When large-scale advection may still dominate, and this carries advective mixing is combined with differential important implications for the spatial distribution transport of different species by diffusion and of radionuclide tracers or transient tracer pulses. dispersion, acting over a range of scales, the For example, diffusion will selectively move expectation of simple closed-system behavior for 14 2 H CO3 out of aquifers and into aquitards, parcels of groundwater is clearly naı¨ve. along the concentration gradient set up by 14C Geochemical species that can be used to gain decay within the aquitards, but will not induce any information on groundwater residence times are 2 net transport of stable HCO3 , thus mimicking the much better thought of as groundwater “age effects of radioactive decay on the 14C/C ratio. tracers” than they are as “dating methods.” In Advection, in contrast, will transport both species some cases (e.g., wells sampling local-scale flow at the same rate. systems in relatively homogeneous materials), Any truly comprehensive and accurate mathe- closed-system behavior may be approximated, matical description of large-scale solute transport and “dates” can be interpreted to reflect residence must incorporate both the effects of encountering time in a straightforward fashion. In general, progressively larger scales of hydraulic hetero- however, concentrations of age tracers should be geneity on differential advective transport and the viewed as data upon which inferences regarding progressive increase in the importance of diffu- the residence-time structure of the three- sion as larger volumes of low-permeability rock dimensional groundwater flow system can be are contacted. It must account for the three- based. Application of several tracers will gener- dimensional interaction between the hydraulic ally give much better constrained inferences than head field and the spatial configuration of those using only a single tracer (Castro et al., heterogeneities, and the effect of this interaction 2000; Mazor, 1976, 1990). Numerical transport on the fundamental advective and diffusive models offer by far the most flexible and transport mechanisms. The spatial distributions comprehensive approach to interpreting the tracer of permeability in any such model must have a data (Castro and Goblet, 2003; Dinc¸er and Davis, rigorous basis in hydrogeology. This is a 1984; Park et al., 2002). formidable undertaking, and we are far from Given the complex flow paths and mixing of accomplishing it. However, environmental geo- waters recharged at different times, even the chemical tracers provide one of the few realistic basic meaning of “groundwater age” can be approaches to obtaining data on solute transport ambiguous. Recently, several authors (Bethke at these scales, and thus represent a critical and Johnson, 2002a,b; Goode, 1996)have component to the solution of this fundamental addressed this problem by treating groundwater hydrological/geochemical problem. age as a parameter that accumulates in all water in a system by a linear buildup per unit mass per unit time, termed “age mass.” The “age” of the groundwater can then be rigorously defined by 5.15.3.4 Groundwater Dating and the Concept the accumulated age mass, equivalent to the of “Groundwater Age” average of the residence time of every water Suppose one holds an igneous rock specimen in molecule in the sample. Age mass is a completely which all of the mineral grains crystallized at very conservative quantity whose total does not nearly the same time, for which the crystallization vary with time in basins that have been at time was short compared to the period since hydraulic steady state for long periods. In such a solidification, and which has not experienced any system, the total age mass is simply “the total reheating or alteration since initial crystallization. water mass” £ “the average residence time” One could then measure some time-dependent (total mass divided by rate of recharge) £ “the property of the specimen (e.g., the amount of 40Ar age mass production rate” (1 kg age mass accumulated from the decay of 40K) and infer (kg water)21 yr21). a reasonably well-defined “crystallization age” for More traditional approaches to treating the age the rock. Unfortunately, an analogous set of of groundwater systems have tended to over- conditions is quite unlikely to hold rigorously emphasize the advective-dominated portions of for any sample bottle full of groundwater. As the system. The age mass approach forces previously emphasized by Davis and Bentley consideration of both advective and diffusive (1982), the dynamic nature of groundwater transport through the entire system. This is nicely systems renders such simplistic scenarios un- illustrated by the observation of Bethke and likely. This review has emphasized that, due to the Johnson (2002b) that the accumulation of age 460 Groundwater Dating and Residence-time Measurements mass in the water of an aquifer that is sandwiched (i) radionuclides of atmospheric origin that can be between two aquitards is, counter intuitively, used with the radiometric decay equation to “date” independent of the exchange rate with the water the time since recharge; (ii) stable constituents in the aquitards. The reason is that if the exchange originating with recharge that have known rate is high, longer residence-time water is rapidly patterns of age with time and can hence be used moved into the aquifer, but the average age of the to infer residence time; and (iii) constituents that water entering is not great (due to the rapid are added to groundwater in the subsurface at an exchange). Alternatively, if the exchange rate is approximately known rate, whose accumulation low, only small amounts of aquitard water enter, can thus be used to gain information on the but the average age of the aquitard water is great. residence time of the water. The average age of the water exiting the aquifer depends only on the total mass of water in the system and the total water flux through the system, not on the proportion of aquifer to aquitard, or the 5.15.4.2 Radionuclides for Age Tracing of transport characteristics of the two lithologies. Subsurface Water This approach to conceptualizing residence- 5.15.4.2.1 Argon-37 time distributions in groundwater systems has important practical implications for interpreting Among the unstable isotopes that have been age tracer measurements. For example, the pattern used as natural tracers in groundwater, 37Ar has of radiogenic helium concentration in the aquifer the shortest half-life (35 d; Lal and Peters, 1967; system described above would strongly resemble Loosli and Oeschger, 1969). Argon-37 is pro- that of the theoretical age mass distribution. duced by cosmic rays in the atmosphere. Since its Specifically, the concentration of helium would half-life is extremely short, most groundwaters increase much more rapidly with distance along have completely lost the atmospheric 37Ar signal the aquifer than a simple calculation based on the that was initially present in the recharge water. linear flow rate through the aquifer would Measured 37Ar in groundwater thus reflects the indicate. It would increase more rapidly because subsurface production rate of 37Ar and the helium would diffuse out of the aquitards into the transfer efficiency from rocks to groundwater. aquifer. If this additional source of helium is not The dominant source of subsurface 37Ar is accounted for, the velocity in the aquifer inferred through the following neutron reaction with from the helium distribution would be much 40Ca: 40Ca(n,a)37Ar. The neutron flux originates slower than the actual velocity. Similarly, a either directly from spontaneous fission of radionuclide tracer (such as 14Cor36Cl) would uranium or from (a,n) reactions within the matrix diffuse into the aquitard, along with the water, also rock. At present, 37Ar activities can be measured producing an incorrectly low apparent linear down to 100 mBq per liter (STP) of argon by gas velocity in the aquifer. proportional counting together with 39Ar (see Although a merely conceptual application of below). For comparison, atmospheric 37Ar the age mass approach can provide important activity is 50 mBq per liter (STP) of argon (Loosli insights into a simple system such as the one and Oeschger, 1969); activities as high as 0.2 Bq described above, its distribution in an actual per liter (STP) of argon have been measured in groundwater system is a complex function of groundwater in the Stripa granite, in Sweden advective and diffusive controls, like any other (Loosli et al., 1989). When used as a natural tracer solute. Thus, for actual applications the most of groundwater, 37Ar is used in combination with promising approach is to use numerical models to a number of other tracers (e.g., 39Ar, 85Kr, see calibrate the age mass distribution using results below) in order to provide more reliable estimates from a number of age tracers. Regardless of of groundwater residence times (Loosli et al., whether the goal of a study is to define 1989, 2000). groundwater velocity distributions, or to under- stand subsurface transport processes, the approach must be based on an understanding of the dynamics of the entire groundwater system. 5.15.4.2.2 Sulfur-35 Sulfur-35 is formed from the spallation of argon in the atmosphere. It has a half-life of 87 d (Lal and Peters, 1967). After oxidation to sulfate, it is 5.15.4 SUMMARY OF GROUNDWATER deposited on the land surface. Because of its AGE TRACERS relatively long residence time in the upper 5.15.4.1 Introduction atmosphere and its short half-life, specific activi- ties of 35S are low at the time of deposition. Due 35 22 Age tracers for groundwater and the vadose to the anionic form of SO4 it is relatively zone can be divided into three basic classes: conservative in soil water and groundwater and Summary of Groundwater Age Tracers 461 can be used to estimate residence times in shallow, 4,500 ^ 8 d (equivalent to 12.32 ^ 0.02 yr) rapidly circulating systems. It has seen limited (Lucas and Unterweger, 2000). Atmospherically application in hydrology because of its low produced tritium reacts rapidly to form tritiated specific activity in groundwater, requiring large water: 3HHO. Tritiated water is precipitated out of sample volumes, and the concomitant requirement the atmosphere together with ordinary water. The for low background sulfate sample waters tritium concentration in natural water is com- (Michel, 2000). monly expressed in Tritium Units (TU), where Most applications have mainly been to low- 1 TU is equal to one molecule of 3HHO per 1018 sulfate environments with rapid turnover, molecules of H2O. This is equivalent to a specific especially to studying the behavior of sulfate activity of 0.1181 Bq (kg water)21. during snowmelt (Michel et al., 2000). It has Tritium is commonly measured by two methods: proved useful in estimating storage time of b-counting or 3He ingrowth. Natural levels of groundwater contributing to stream flow, showing tritium are only marginally measurable by direct that even in apparently low-storage alpine systems, b-counting methods, but fortunately tritium is a preponderant fraction of the flow can be derived highly enriched over ordinary H in the H2 produced from groundwater with residence times of several by the electrolysis of water. b-Detection, either by years or more (Suecker et al., 1999). gas proportional counting or liquid scintillation counting, can then easily measure natural tritium (Taylor, 1981). A newer approach, with generally 5.15.4.2.3 Krypton-85 higher sensitivity, is to degass the water, then allow 3He to accumulate for up to a year, and measure the Anthropogenic 85Kr (half-life 10.76 yr) was first 3He using mass spectrometry (Clarke et al., 1976). released to the atmosphere in considerable The excellent properties of 3HHO as a tracer of amounts in the 1950s and 1960s by atmospheric water and the relative ease of measurement have nuclear-weapons testing. Today, it is continuously encouraged a very wide spectrum of applications produced through fission of uranium and pluto- of tritium to waters with a residence time of less nium and released to the atmosphere, mainly than 50 yr. during fuel rod reprocessing in nuclear power The average global production of tritium is plants. As shown in Figure 2(d), this artificially ,2,500 atom m22 s21 (Solomon and Cook, produced 85Kr has completely overwhelmed natu- 2000). The deposition rate of the tritium varies ral cosmogenic production of 85Kr, and has created with latitude, but it is also mixed with the bulk of a steady increase in the activity of this isotope in the precipitation originating from the ocean (which atmosphere, particularly in the northern hemi- has a very low tritium content), and thus the sphere (Weiss et al., 1992). The southern hemi- average tritium content of precipitation tends to sphere, without significant sources of this isotope, vary inversely with annual precipitation. Natural exhibits an average 85Kr activity 20% lower than tritium in precipitation varies from ,1TU in the northern hemisphere. Such variations need to oceanic high-precipitation regions to as high as be considered when interpreting 85Kr activities in 10 TU in arid inland areas. groundwater. Because 85Kr activities in ground- Since the 1950s natural tritium deposition has water are very low (1 L of water in equilibrium been swamped by the pulse of tritium released by with the atmosphere has a 85Kr activity of only atmospheric nuclear-weapons testing, followed by 8.6 mBq), analysis of this isotope is relatively other anthropogenic releases (Gat, 1980). Signifi- difficult (Fairbank et al., 1998; Rozanski and cant tritium was released by the fission and Florkowski, 1979; Smethie and Mathieu, 1986; thermonuclear devices tested in the mid-to-late Thonnard et al., 1997). Generally, 85Kr is 1950s, but it was the stratospheric thermonuclear- employed as a natural tracer in combination with weapons testing of the early 1960s that produced other isotopes and, particularly, with 3H, which has the peak pulse, as large as 5,000 TU in the mid- a similar half-life. Both tracers are used to estimate latitude northern hemisphere (Figure 2(a)). the age of rather young (#40 yr) waters. When Because most of the testing was in the northern dispersion is small in a particular groundwater hemisphere, southern hemisphere fallout was system, the age of groundwater can be estimated much less. This pulse has decayed in a quasi- directly from 85Kr activities (e.g., Ekwurzel et al., exponential fashion since that time and is now 1994; Smethie et al., 1992). beginning to approach natural levels. It has provided an invaluable transient tracer for shallow hydrological systems. 5.15.4.2.4 Tritium Application of tritium to hydrologic problems was first proposed by Libby (Bergmann and Tritium is produced in the atmosphere by Libby, 1957; Libby, 1953). Early applications cosmic-ray spallation of nitrogen (Lal and Peters, (Allison and Holmes, 1973; Carlston et al., 1960) 1967). Tritium decays to 3He with a half-life of focused on tracing the bomb-tritium pulse through 462 Groundwater Dating and Residence-time Measurements

Figure 2 Global environmental histories of hydrologic-cycle tracers that have been strongly affected by human activities: (a) tritium (data from measurements at Ottawa, Canada, by the International Atomic Energy Agency; http:// isohis.iaea.org/); (b) carbon-14 (data for 1955–1962 from Kalin (2000), data for 1963–1991 from Nydal et al. (1996)) http://cdiac.esd.ornl.gov/epubs/ndp/ndp057/ndp057.htm); (c) chlorine-36 (data from Synal et al. (1990); (d) krypton- 85 (data from Loosli et al., 2000); (e) chlorofluorocarbons (data for 1944–1978 from Plummer and Busenberg (2000); data for 1978–2003 from Cunnold et al. (1997); http://cdiac.esd.ornl.gov/ftp/ale_gage_Agage/); and (f) sulfur hexafluoride (data from Plummer and Busenberg, 2000). aquifers. This was soon extended to estimating important key to understanding matrix diffusion recharge by measuring tritium profiles through the of solutes in fractured media (Foster, 1975). vadose zone (Schmalz and Polzer, 1969; Vogel During the 1980s the bomb-tritium pulse in et al., 1974). Measurement of tritium profiles groundwater began to lose its definition. The through the English Chalk vadose zone proved an combined effects of decay and dispersion tended Summary of Groundwater Age Tracers 463 to reduce bomb-peak levels to values similar to behavior is produced in the vadose zone and that that of precipitation at that time. Fortunately, the 32Si may be useful for residence-time determi- limitations imposed by this loss of the tracer pulse nations in aquifers if the initial activity in the were countered by the introduction of the 3H/3He recharge area can be determined. However, until method (Tolstikhin and Kamensky, 1968). By this can be demonstrated, the applications of the measuring first the tritiogenic 3He and then the 3H isotope will remain limited. content by 3He ingrowth, both the initial 3H content and the time of decay can be calculated. The power of this approach for reconstructing residence times has been elegantly demonstrated 5.15.4.2.6 Argon-39 by Schlosser et al. (1988) and Solomon et al. In contrast to 37Ar, 39Ar in groundwater has its 3 3 (1992, 1993).The H/ He method has since origin in the atmosphere where it is produced by become a standard tool in the investigation of cosmic rays, and enters the water cycle as a the dynamics of shallow aquifers (Beyerle et al., fraction of the dissolved argon during ground- 1999; Ekwurzel et al., 1994; Puckett et al., 2002). water recharge. The activity of 39Ar in ground- 3 However, He is also produced by fission of water is extremely small, a fact that complicates uranium and nucleogenic processes in the subsur- its analysis (Loosli et al., 2000). Modern atmos- face, and corrections for these sources must pheric 39Ar activity is 16.7 mBq m23 of air sometimes be employed (Andrews and Kay, (Loosli, 1983). Two thousand liters of water in 1982a,b). equilibrium with the atmosphere at 20 8C have an 39Ar activity of only 1.2 mBq. When subsurface production of 39Ar (resulting from the reaction 39K(n,p)39Ar) can be neglected, this isotope with a 5.15.4.2.5 Silicon-32 half-life of 269 yr has been successfully used Silicon-32 is produced in the atmosphere by in combination with other tracers, in particular 14 cosmic-ray spallation of 40Ar (Lal et al., 1960). It with C to estimate groundwater ages in sedi- decays to 32P with a half-life of 140 ^ 6yr mentary basins (e.g., Andrews et al., 1984; (Morgenstern et al., 1996), although there is Purtschert, 1997). However, this procedure can some uncertainty regarding the exact value be complicated in crystalline terrains with (Nijampurkar et al., 1998). It is oxidized and high uranium and thorium contents and hence a 39 incorporated into precipitation as silicic acid. non-negligible subsurface production of Ar The global deposition rate is ,2 atom m22 s21 (Andrews et al., 1989; Lehmann et al., 1993). (Kharkar et al., 1966; Morgenstern et al., 1996; Nijampurkar et al., 1998). This produces activities 23 in natural water in the range of 2–20 mBq m 5.15.4.2.7 Carbon-14 (Morgenstern, 2000). Silicon-32 does not behave in a conservative fashion after it begins to move Carbon-14 is produced in the atmosphere by a through the subsurface. It reacts with silicate low-energy cosmic-ray neutron reaction with minerals, presumably by exchange, and 32Si nitrogen. It decays back to 14N with a half-life concentrations are markedly reduced during of 5,730 yr. The production rate is ,2 £ transport through the vadose zone (Fro¨hlich et al., 104 atom m22 s21, the highest of all cosmogenic 1987; Morgenstern et al., 1995). radionuclides. The rate is so high, because Silicon-32 is most sensitively measured using nitrogen is the most abundant element in the liquid scintillation counting. Silicon must be atmosphere and also has a very large thermal extracted from ,1m3 of water. The daughter neutron absorption cross-section. Radiocarbon 32P is allowed to grow into equilibrium over activity in the atmosphere is the result of several months, then is milked with complicated exchanges between terrestrial stable phosphorus for scintillation counting reservoirs (primarily vegetation), the ocean, and (Morgenstern, 2000). Very low counting back- the atmosphere. The combination of varying grounds are necessary. cosmic-ray fluxes (due to both varying solar and Silicon-32 has many attractive aspects for age terrestrial magnetic field modulations) and vary- tracing of groundwater. Its half-life makes it very ing exchange between reservoirs has caused the useful for filling the gap between 3H (12.3 yr) and atmospheric activity of radiocarbon to fluctuate by 14C (5,730 yr). It has a very small subsurface approximately a factor of 2 over the past production (Florkowski et al., 1988). However, 3 £ 104 yr (Bard, 1998). The current specific the disadvantage of unpredictable loss to the solid activity is 0.23 Bq (g C)21, rendering radiocarbon phase and analytical difficulties have limited the easily measurable by gas proportional or liquid number of its applications (Lal et al., 1970; scintillation counting, or by accelerator mass Nijampurkar et al., 1966). Morgenstern (2000) spectrometry (AMS). Radiocarbon measurements has proposed that most of the nonconservative are usually reported as “percent modern carbon,” 464 Groundwater Dating and Residence-time Measurements indicating the sample specific activity as a identifying the appropriate component of the DOC percentage of the 0.23 Bq (g C)21 modern for this application. atmospheric specific activity. In addition to the Radiocarbon is an indispensable tool in the age natural cosmogenic production of 14C, the isotope tracing of groundwater. Both its ease of use and its was also released in large amounts by atmospheric half-life make it the method of choice for many nuclear-weapons testing in the 1950s and 1960s investigations. However, results must always be (Figure 2(b)). approached with caution. The reliability of results Natural radiocarbon was first detected by Libby depends strongly on the complexity of the in the mid-1940s (Arnold and Libby, 1949; Libby, geochemistry. In some cases groundwater may 1946), but the first applications to subsurface show little evidence of chemical evolution after hydrology were not attempted for another decade recharge and measured radiocarbon activities can (Hanshaw et al., 1965; Mu¨nnich, 1957; Pearson, be accepted at face value. In other cases, the 1966). These early investigators discovered that isotopic composition of carbon may be strongly radiocarbon shows clear and systematic decreases altered by numerous surface reactions that are with flow distance that can be attributed to difficult to quantify, and interpretations may be radiodecay, but also exhibits the effects of speculative, at best. Interpretations must be carbonate mineral dissolution and precipitation evaluated on a case-by-case basis. reactions. Quantification of residence time is not possible without correction for additions of nonatmospheric carbon. Numerous approaches to this problem were attempted, including simple 5.15.4.2.8 Krypton-81 empirical measurements (Vogel, 1970), simplified 5 81 chemical equilibrium mass balance (Tamers, With a half-life of 2.29 £ 10 yr, Kr, still in its 1975), mass balance using d13C as an analogue “infancy” as a natural tracer, has had the potential for 14C(Ingerson and Pearson, 1964), and to be an excellent tool for dating old groundwater combined chemical/d13C mass balance (Fontes ever since it was first detected in the atmosphere and Garnier, 1979; Mook, 1980). (Loosli and Oeschger, 1969). In addition to its constant atmospheric concentration, anthropo- The correction methods cited above were 81 mainly intended to account for carbonate reactions genic and subsurface production of Kr have been shown to be negligible (e.g., Collon et al., in the vadose zone during recharge, although in 81 practice they have often been applied to reactions 2000; Lehmann et al., 1993). Nearly all Kr in groundwater results from the interaction of cosmic along the groundwater flow path as well. It is now rays with nuclei in the Earth’s atmosphere, in the general consensus that the preferred approach particular, through neutron capture by 80Kr and to treating the continuing reactions of dissolved spallation of heavier krypton isotopes. However, inorganic carbon during flow is geochemical mass its activity (0.11 nBq in water in equilibrium with transfer/equilibrium models (Kalin, 2000; Zhu the atmosphere) is lower than that of any other and Murphy, 2000). The most commonly tracer that has been used. The analytical challenge employed model is NETPATH (see Chapters to measure this isotope is, therefore, extreme. The 5.02 and 5.14; Plummer et al., 1991). This uses first measurements of 81Kr in groundwater were a backward-calculated solute mass balance, con- reported in the Milk River aquifer in Canada strained by simple equilibrium considerations, to (Lehmann et al., 1991; Thonnard et al., 1997), but calculate mass transfers of solutes from phase to an elaborate multistep enrichment procedure phase between two sample points. made it difficult to quantify the results, though The vast majority of groundwater radiocarbon an estimated groundwater age of 1.4 £ 105 yr was investigations have extracted the dissolved inor- obtained. A new measurement technique based on ganic carbon from the water for measurement. accelerator mass spectrometry (AMS) using However, dissolved organic carbon (DOC) has positive krypton ions coupled to a cyclotron was been sampled in a limited number of studies reported by Collon et al. (2000). In this study, 81Kr (Murphy et al., 1989; Purdy et al., 1992; Tullborg was measured in groundwater in the Great and Gustafsson, 1999). In principle, sampling Artesian Basin (GAB) in Australia and, for the DOC could avoid the complex geochemistry of first time, definite determinations of water resi- inorganic carbon. In reality, DOC consists of a dence times were made based on the atmospheric large number of organic species from various 81Kr/Kr ratio. Krypton dissolved in surface water sources (with different original 14C activities), of in contact with the atmosphere has an atmospheric varying chemical stability, and of varying reac- 81Kr/Kr ratio of (5.20 ^ 0.4) £ 10213. Observed tivity with the solid phase. Routine use of DOC for reductions of isotope ratios in groundwater groundwater age tracing may one day show were interpreted as being due to radioactive advantages over inorganic carbon, but this decay since recharge (Collon et al., 2000; will require considerable work separating and Lehmann et al., 2002b). Summary of Groundwater Age Tracers 465 5.15.4.2.9 Chlorine-36 mixing models may often provide useful approxi- mations of residence time (Bentley et al., 1986a; Chlorine-36 is produced in the atmosphere by Phillips, 2000), the best approach, as for all age cosmic-ray spallation of 40Ar (Lal and Peters, 36 tracing methods, is comprehensive simulation of 1967). It decays to Ar with a half-life of flow and transport for the entire groundwater ^ 301,000 4,000 yr (Bentley et al., 1986a). The system (Bethke and Johnson, 2002b; Castro and globally averaged production rate is between Goblet, 2003). 20 atom m22 s21 and 30 atom m22 s21 (Phillips, 36 In addition to the natural cosmogenic pro- 2000). Meteoric Cl then mixes with stable duction of 36Cl in the atmosphere, a very large oceanic chlorine in the atmosphere, diluting the 36 36 pulse of Cl was also introduced by the testing of Cl greatly near coastlines, but less inland. The thermonuclear weapons between 1954 and 1958 resultant specific activities of chlorine in atmos- (Bentley et al., 1982; Phillips, 2000; Zerle et al., pheric deposition range from less than 20 mBq 1997). This pulse had much less of a tail than the 21 21 (g Cl) to more than 1,000 mBq (g Cl) . These bomb radiocarbon and tritium pulses, because the specific activities are at the lower limits of the atmospheric residence time of chloride is shorter sensitivity of any form of decay counting, and (Figure 2(c)). Chlorine-36 can be applied to require large masses of chlorine that may be groundwater studies in a fashion analogous to difficult to obtain from dilute waters. Routine tritium, but has proved most useful in tracing 36 application of Cl to age tracing of groundwater is water movement through the vadose zone, possible only because of the high sensitivity and because, unlike tritium and radiocarbon, it is not much smaller sample size permitted by AMS volatile and thus does not disperse in the vapor (Elmore et al., 1979). Because an isotopic ratio is phase (Cook et al., 1994; Phillips et al., 1988; measured by mass spectrometry, the atomic ratio, Scanlon, 1992). atoms 36Cl per 1015 atoms Cl, is normally used in 36Cl studies instead of specific activity. Application of 36Cl to earth-science problems was attempted as early as the mid-1950s (Davis 5.15.4.2.10 Iodine-129 and Schaeffer, 1955), but little use was made of Iodine-129 has major sources in both surface and the method until the advent of AMS in 1979. Since subsurface environments. It is produced in the the analytical barrier was overcome, there have atmosphere by cosmic-ray spallation of xenon and been regular applications to long-residence-time in the subsurface by the spontaneous fission of aquifers around the world (mainly large sedimen- uranium. Iodine-129 of subsurface origin is tary basins). These include systems in Australia released to the surface environment through (Bentley et al., 1986b; Cresswell et al., 1999; volcanic emissions, groundwater discharge, and Torgersen et al., 1991), North America (Davis other fluxes. Due to its very long half-life, 15.7 Ma, et al., 2003; Nolte et al., 1991; Phillips et al., these sources are well mixed in the oceans and 1986; Purdy et al., 1996), Europe (Pearson et al., surface environment, producing a specific activity 1991; Zuber et al., 2000), Asia (Balderer and of ,5 mBq (g I)21 (equivalent to a 129I/I ratio of Synal, 1996; Cresswell et al., 2001), and Africa ,10212). Due to its low activity, the preferred (Kaufman et al., 1990). 129 36 detection method of IisAMS(Elmore et al., The major complications in using Cl to 1980). estimate the residence time of groundwater are Theverylonghalf-lifeof129Iraisesthe introduction of subsurface chloride and subsurface possibility of dating groundwater on timescales 36 production of Cl. High chloride concentrations greater than a million years (Fabryka-Martin et al., arising from connate waters, evaporite dissolution, 1985). For a few subsurface environments that or possibly rock–water interaction are common in approximate closed systems, including brines sedimentary basins and deep crystalline rocks. incorporated in salt domes (Fabryka-Martin et al., These may either diffuse upward or be advected 1985), and connate brine reservoirs (Fehn et al., into aquifers by cross-formational flow. In general, 1992; Moran et al., 1995), and iodine in oil (Liu this subsurface-source chloride is not 36Cl free, et al., 1997), this has proved successful. However, because 36Cl is produced at low levels (compared due to the complex subsurface geochemistry of to meteoric chloride) in the subsurface by absorp- iodine, subsurface fissionogenic production which tion by 35Cl of thermal neutrons produced by can be difficult to quantify, and the release of uranium and thorium series decay and uranium iodine from subsurface organic material, determi- fission (Lehmann et al., 1993; Phillips, 2000). The nation of the residence time of water in effects of radiodecay and of mixing with low 36Cl dynamic groundwater systems has generally not ratio subsurface chloride must be separated in order proved practicable (Fabryka-Martin, 2000; to evaluate residence times correctly. Park et al. Fabryka-Martin et al., 1991). (2002) have recently evaluated in detail the effects Iodine-129 has numerous anthropogenic of various mixing scenarios. Although simple sources. It was globally distributed by the 466 Groundwater Dating and Residence-time Measurements atmospheric nuclear-weapons testing of the 1950s (Thompson, 1976; Thompson et al., 1974), but and 1960s, and has continued to be released in was not widely employed until important proof- large amounts by nuclear technology, especially of-concept papers were published in the early nuclear fuel reprocessing (Wagner et al., 1996). 1990s (Bo¨hlke et al., 2002; Busenberg and As a result, environmental levels of the 129I/I ratio Plummer, 1991; Dunkle et al., 1993; Ekwurzel have increased to values in the range 10210 –1027. et al., 1994). Since that time the method has been This anthropogenic pulse can be used in a fashion widely used in shallow groundwater studies. It similar to bomb tritium. It has proved to be has found particular application in studies especially useful in identifying releases from tracing the source and fate of agricultural nuclear reprocessing plants and other nuclear contaminants (Bo¨hlke et al., 2002) and surface– facilities (Moran et al., 2002; Oktay et al., 2000; groundwater interaction (Beyerle et al., 1999). Rao and Fehn, 1999). Sulfur hexafluoride (SF6) is a nearly inert gas than has been widely used as a gas-phase electrical insulator. It has a very long atmospheric lifetime, and is detectable to very low levels by gas 5.15.4.3 Stable, Transient Tracers chromatography using the electron capture detec- tor. These characteristics render it useful for 5.15.4.3.1 Chlorofluorocarbons and sulfur estimating groundwater residence times in a hexafluoride fashion similar to CFCs, for the period from Several industrial chemicals have been created ,1970 to the early 2000s (Busenberg and that are highly volatile, resistant to degradation, Plummer, 2000). The major advantage over act conservatively in groundwater, are unusual or CFCs is that the atmospheric concentration of absent in the natural environment, and can be SF6 is continuing to increase monotonically detected at very low concentrations. If these (Figure 2(f)). One potential disadvantage is that compounds show a relatively regular increase in relatively high levels of apparently natural back- atmospheric concentration, then their concen- ground SF6 have been detected in areas of tration in shallow groundwater systems can be volcanic and igneous rock (Busenberg and correlated with the time of recharge of the water, Plummer, 2000). and residence times can be determined. One such class of compounds is the chloro- fluorocarbons (CFCs), halogenated alkanes that 5.15.4.3.2 Atmospheric noble gases and have been used in refrigeration and other indus- stable isotopes trial applications since the 1930s (Plummer and Busenberg, 2000). The atmospheric lifetimes of The solubility of ordinary atmospheric noble the common CFC compounds range from 50 yr to gases (neon, argon, krypton, and xenon) in water 100 yr. Their concentrations increased in a quasi- is temperature dependent (Benson, 1973). The exponential fashion from the 1950s through the stable isotope composition of precipitation (d2H, late 1980s (Figure 2(e)). Unfortunately, CFCs d18O) also depends on temperature. If variations catalyze reactions in the stratosphere that deplete in these constituents can be related to a known atmospheric ozone. This resulted in international history of temperature variation, then groundwater agreements to limit global CFC production residence times can be estimated (Stute and drastically. In response the rate of atmospheric Schlosser, 1993). CFC increase has leveled off and has started to This approach to residence-time estimation decrease. This complex concentration history has has been most commonly applied on two very resulted in a degree of ambiguity in residence- different timescales. The first is in utilizing the time estimates for water recharged since ,1990. annual temperature cycle. The second is the global The advantages of CFC dating are a lack of glacial–interglacial transition at ,15 ka. The sensitivity to dispersion and mixing, due to the approach of taking samples along a groundwater gradual and monotonic atmospheric concentration flow path and matching it to the seasonal recharge history (at least through the 1990s), and the virtual temperature signal generally works best when year-to-year dating sensitivity. The major com- applied to aquifer recharge from a surface-water plications of CFC dating are the time lag involved body (Beyerle et al., 1999; Sugisaki, 1961), in the diffusion of the atmospheric signal through because under conditions of general vertical re- vadose zones thicker than ,10 m, minor-to- charge the vadose zone damps much of the annual moderate sorption of some CFC species, and signal, and vertical mixing during water-table microbial degradation of some CFCs under fluctuations smoothes the annual signal. strongly reducing conditions (Plummer and The noble-gas concentration method has been Busenberg, 2000). applied to investigating the temperature history on Application of CFCs for groundwater the glacial–interglacial timescale around the studies was first explored in the early 1970s world (Stute and Schlosser, 1993). Although it Summary of Groundwater Age Tracers 467 is most commonly used in conjunction with (Gerling et al., 1971; Kunz and Schintlmeister, independent dating of the groundwater, the 1965; Mamyrin and Tolstikhin, 1984). Excesses of magnitude and timing of the noble-gas tempera- nucleogenic 3He in groundwater can result from ture signal are well enough established, so that, in situ production (i.e., produced in the reservoir when other dating means are not available or rock of the aquifer itself) and/or can be produced in successful, it can be used to define the position of deeper layers or deeper crust (external source). In water recharged during the climate transition the latter case, 3He must be transported to the upper (Blavoux et al., 1993; Clark et al., 1997; Zuber aquifers either through advection, dispersion, and/ et al., 2000). or diffusion. The concentration of 3He in ground- water will typically increase with distance from the recharge area and/or over time. In tectonically 5.15.4.3.3 Nonatmospheric noble gases active areas a mantle component of 3He may also be present (Oxburgh et al., 1986), reaching The following sections comprise a brief descrip- groundwater reservoirs either directly through tion of noble-gas isotopes (3He, 4He, 21Ne, and 40 igneous intrusions or through water transport Ar), where measured concentrations in ground- processes such as advection, dispersion, and waters were found to be in excess of solubility diffusion. equilibrium with the atmosphere (air-saturated In addition to the nucleogenic and mantle water (ASW)). Such excesses allow the use of component, tritiogenic 3He resulting from these isotopes as natural tracers of groundwater b-decay of natural (produced mainly in the upper flow (as opposed to those such as 20Ne, 22Ne, 36 38 atmosphere through the bombardment of Ar, and Ar that exhibit an atmospheric nitrogen by the flux of neutrons in cosmic contribution only). radiation) and bomb 3H (as a result of thermo- (i) Helium isotopes nuclear testing in the 1950s and 1960s) (see Section Helium-3. The concentration of 3He in ground- 5.15.4.2.4) can be present. This bomb-tritiogenic water frequently exceeds that of ASW values 3He component, when significant, is present in (cf. Section 5.15.4.3.2). These excesses can be up very young (tens of years), fast-flowing waters. to several orders of magnitude greater than the Helium-4. This isotope is also commonly found ASW concentration in old groundwater (e.g., in excess to ASW concentrations in groundwater; Castro et al., 1998a,b). They can derive from a excesses are typically higher in older than in number of 3He sources. Typically, with the younger groundwaters. Unlike 3He excesses, 4He exception of recharge areas and superficial result directly from radioactive decay of 235U, aquifers with fast-flowing (young) waters, the 238U, and 232Th. The radioactive decay of uranium main source of 3He over time is nucleogenic. and thorium series elements yields a-particles (2p, Nucleogenic production of 3He is the result of a 2n) that rapidly acquire two electrons, thus turning series of reactions (Andrews and Kay, 1982a,b; into stable 4He (2p, 2n, 2e2). Because production Lal, 1987; Mamyrin and Tolstikhin, 1984; of 4He is neither dependent on the nuclei of light Morrison and Pine, 1955): (a) spontaneous and elements nor on neutron flux, the radiogenic 4He neutron-induced fission of uranium isotopes and production rate in the crust tends to be greater and reaction of a-particles with the nuclei of light more homogeneous than the nucleogenic pro- elements give rise to a subsurface neutron flux; duction of 3He (Martel et al., 1990). As a result, (b) some of these neutrons reach epithermal the observed excesses of radiogenic 4He in energies and react with nuclei of the light isotope groundwater tend to be more uniform than those of lithium (6Li) to produce a-particles and tritium: of nucleogenic 3He. Assuming a homogeneous element distribution in the rocks, the radiogenic 6Lið3p;3n;3e2Þþn!að2p;2nÞþ3Hð1p;2n;1e2Þ production rate of 4He is given by 3 (c) H decays (half-life of 12.32 yr) by the Pð4HeÞ¼5:39 £ 10218½Uþ1:28 emission of b2 (decay of a neutron into a proton 3 218 21 21 and electron) to the stable isotope He: £ 10 ½Th mol grock yr

b2 3H!3He ð2p;1n;2e2Þ where [U] and [Th] are the concentrations of U and Th in the rock in ppm (Steiger and Ja¨ger, Reactions between the light isotopes of lithium 1977). Radiogenic 4He can be produced in situ or and epithermal neutrons yield almost all terrestrial have an origin external to the aquifer. nucleogenic 3He, including that found in excess of 3He/ 4He ratio. The measurement of the ASW in most groundwater reservoirs. Nucleogenic 3He/4He ratio (R) in groundwaters is particularly 3He can also be produced through 7Li reac- important, because it reflects the relative import- tions (7Li(a,3H)8Be; 3H(b2)3He; 7Li(g,3H) 4He, ance of crustal (radiogenic/nucleogenic) and 3H(b2) 3He), but the amount produced is negli- mantle helium sources. Typical crustal rock gible compared to that produced through 6Li 3He/4He production ratios have been estimated 468 Groundwater Dating and Residence-time Measurements to be 1 £ 1028 (Mamyrin and Tolstikhin, 1984). atmospheric 21Ne/22Ne ratio of 0.0290. A typical Other authors (e.g., Kennedy et al., 1984) crustal production 21Ne/22Ne ratio is 0.47 ^ 0.02 consider a wider range of typical crustal (Shukolyukov et al., 1973; Kennedy et al., 1990). : = : 21 production ratios, with 0 01 , R Ra , 0 1 The total present-day production rate of Ne has 3 4 : 26 (atmospheric He/ He ratio Ra ¼ 1 384 £ 10 ; been calculated for typical crustal rock by Clarke et al., 1976). Much higher 3He/4He values Bottomley et al. (1984) to be have been observed in the mantle; the most 21 225 225 common is 1.2 £ 1025 (Craig and Lupton, 1981). Pð NeÞ¼ð3:572£10 Þ½Uþ1:767£10 ½Th However, at specific sites such as Hawaii, mantle 3He/4He ratios can be up to a factor of 5 higher where [U] and [Th] are the concentrations of U than this common mid-ocean ridge basalt and Th in the rock in ppm. The values for (MORB) value (Alle`gre et al., 1983; Craig and isotopic composition and decay constants are taken from Steiger and Ja¨ger (1977). Lupton, 1976; Kyser and Rison, 1982; Rison and 21 Craig, 1983). A Ne mantle component has not been In order to use helium isotopes as natural identified in groundwaters. Its presence was tracers of groundwater flow and, in particular, in reported for the first time in 1991 in hydrocarbon order to estimate groundwater ages, it is neces- gas reservoirs within the Vienna Basin (Ballentine sary to separate different nonatmospheric helium and O’Nions, 1991). components for both isotopes. The major com- (iii) Argon-40 ponents are 3He and 4He from atmospheric Excess 40Ar, up to 35% of ASW, has also been equilibrium and from incorporation of “excess found in deep, old groundwaters in sedimentary air” (Heaton and Vogel, 1981; Weyhenmeyer basins (Castro et al., 1998b; Torgersen et al., et al., 2000), 3He and 4He of crustal origin (i.e., 1989). Radiogenic production of 40Ar through nucleogenic and radiogenic), 3He of mantle radioactive decay of 40K by electron capture is origin, and tritiogenic 3He. Methods for separa- responsible for these excesses. Eleven percent of ting these components have been described by 40K decay produces 40Ar; the remainder produces Stute et al. (1992b), Weise (1986), and Weise 40Ca by the emission of b2-particles (Faure, and Moser (1987). 1986).Thepresenceofaradiogenic40Ar component is easily identified and quantified by (ii) Neon-21 comparison with the 40Ar/36Ar atmospheric ratio Neon-21excesses relative to ASW concen- (295.5; Ozima and Podosek, 1983). The highest trations have also been observed in old ground- measured value of this ratio due to the presence of waters. However, the excesses are not comparable radiogenic 40Ar in groundwaters is 471.5. At to those observed for helium; they are only in the present, no resolvable mantle component has been order of a few to a few tens of percent. This excess identified. is attributed to the nucleogenic production of 21Ne Assuming a homogeneous element distribu- in crustal rocks. The reaction 18O(a,n)21Ne tion in the rocks, the radiogenic production rate accounts for 97% of the total nucleogenic of 40Ar is 21Ne. Magnesium accounts for the remaining 21 40 : 222 21 21 production of nucleogenic Ne via the Pð ArÞ¼1 73 £ 10 ½K mol grock yr reaction 24Mg(n, a)21Ne (Wetherill, 1954). where [K] is the concentration of K in rocks in Although only one study has reported the presence ppm, using current values of isotopic composition of nucleogenic 21Ne in groundwaters (Castro et al., and decay constants from Steiger and Ja¨ger (1977). 1998b), it is possible that, as more measurements In a manner similar to the helium and neon of 21Ne in old deep groundwaters become isotopes, 40Ar in groundwater reservoirs can result available, the presence of nucleogenic 21Ne will both from release of 40Ar from minerals forming prove to be more common in groundwater the aquifer and from production and release deeper reservoirs than is known at present. Numerous in the crust followed by upward transport. studies have reported considerable excesses of nucleogenic 21Ne in oil and gas fields (Ballentine and O’Nions, 1991; Ballentine et al., 1996; Hiyagon and Kennedy, 1992; Kennedy et al., 5.15.5 LESSONS FROM APPLYING 1985). There is a general consensus that noble GEOCHEMICAL AGE TRACERS gases found in these systems are transported to oil TO SUBSURFACE FLOW AND and gas reservoirs by groundwater. If so, similar TRANSPORT 21 Ne excesses should be expected in neighboring 5.15.5.1 Introduction groundwaters in amounts close to those in gas and oil fields. The most common and traditional tracers used The presence of nucleogenic 21Ne is gene- in groundwater studies in the last few decades rally identified through comparison with the (e.g., 3H, 14C, and 36Cl), as well as some relatively Lessons from Applying Geochemical Age Tracers 469 new and promising tracers for use in quantitative proper use. These sections will be followed by a groundwater dating (e.g., 32Si, 81Kr, and 4He), discussion of several case studies that represent have been discussed above. The practical appli- groundwater flow at different scales, ranging from cations and information to be gained from these regional to local, as well as within the vadose zone. environmental tracers are multiple and differ, depending on the tracers to be used and on the hydrogeological problem to be treated. Typically and depending on the scale of the study area (e.g., 5.15.5.2 Approaches regional versus local) as well as on the hydraulic 5.15.5.2.1 Direct groundwater age properties of the formation(s) (e.g., high versus estimation low to very low hydraulic conductivity), certain tracers will be better suited than others. Radio- This method is commonly used with radioiso- isotopes with short half-lives (e.g., 85Kr and 3H) tope tracers that undergo radioactive decay. The are suitable for dating young/fast-flowing waters tracer concentration will decrease over time (#40 yr). These radioisotopes are, therefore, ideal following an exponential decay law: for the study of aquifers with high hydraulic dN conductivities or, alternatively, to the study of ¼ 2lN dt recharge areas in regional aquifer systems (Schlosser et al., 1989; Solomon et al., 1993). where N is the number of atoms of the radioactive Tracers with intermediate half-lives (e.g., 14C and tracer, t the time elapsed since radioactive decay 36 Cl) are typically used to date submodern started at some initial time t0, and l is the decay (.1,000 yr) and old groundwaters up to 106 yr. constant of the tracer. Integrating this equation They are suited to the study of aquifers of yields intermediate hydraulic conductivity, i.e., study at NðtÞ¼N e2lt the aquifer scale and certain regional systems 0 (Jacobson et al., 1998; Pearson and White, 1967; where N0 is the initial number of radioactive tracer Phillips et al., 1986). In contrast, stable tracers atoms at time t ¼ 0: This equation can be such as 4He have no age limitations and can be rearranged and expressed in terms of time elapsed used within all age ranges; as a result, they are since decay started: particularly suited to the study of regional 1 Nt groundwater systems where very old waters may t ¼ 2 ln l N be present, as well as the study of groundwater 0 flow dynamics in aquitards where water can be If radioactive decay is the dominant process almost immobile (Andrews et al., 1985; Andrews causing reduction/change in tracer concentration, and Lee, 1979; Bethke et al., 1999; Castro et al., time t represents the “groundwater age” (Cook 1998a, 2000; Torgersen and Ivey, 1985). Silicon- and Bo¨hlke, 2000). It corresponds to the time that 32 potentially covers an age from a few tens of has elapsed since the water became isolated from years to 1,000 yr, a range that is problematic for the Earth’s atmosphere, i.e., the time elapsed since most tracers. recharge took place (Busenberg and Plummer, Two main approaches to derive information 1992; Davis and Bentley, 1982). One must be from such tracers in a groundwater system are cautious in interpreting such groundwater age possible: (i) independent and direct use of one estimates. Such ages may represent an “apparent” particular tracer by analyzing variations in its rather than the “real” groundwater age (Park et al., concentration in space and/or its evolution over 2002). A variety of processes may create these time and (ii) a more indirect use through incorpor- discrepancies. For example, 14C-determined ation of those tracers into analytical or numerical groundwater ages may be influenced by the transport models. Although both approaches allow introduction of inorganic “dead” carbon by the estimation of velocity fields, groundwater ages, dissolution of calcite or dolomite, resulting in recharge rates, and identification of mixing of apparent groundwater that are too old. Numerous different water bodies, the second approach will geochemical models have been developed to generally provide more complete information for a account for 14C mass transfer and its impact on particular groundwater flow systems, as it usually groundwater 14C concentration (e.g., Fontes and allows for a better representation of the real system Garnier, 1979; Mook, 1976; Pearson and White, (see below). In all cases, the use of a “multitracer” 1967; Plummer et al., 1991; Tamers, 1967). approach (i.e., the use of several tracers simul- Assumptions inherent in such geochemical taneously) provides more definitive answers models introduce new sources of uncertainty. compared to those based on only one single tracer. Some authors, therefore, prefer to the use the term In the following sections, we will briefly des- “model age” (Hinkle, 1996). Groundwater mix- cribe both approaches, their limitations and ing, diffusion, or dispersion may also give rise pitfalls, as well as information essential to their to erroneous age estimates. One way to identify 470 Groundwater Dating and Residence-time Measurements the effects of groundwater mixing when using 14C is important to view these groundwater ages with a ages is to use age constraints from the concen- critical eye. Accounting for multiple sources of tration of CFCs or tritium in tandem with the 4He within a complex hydrological system 14C data. requires the incorporation of data for the concen- Complications in the estimation of groundwater tration of this tracer into a transport model. ages are not unique to 14C. For example, diffusion Helium-4 can be used as a powerful quantitative can create major errors in estimated ages when dating tool for groundwater (Castro et al., 1998a). applying the 3H/3He method in areas where the groundwater velocity is less than ,0.01 m yr21. In such cases 3He will diffuse upwards, and little 5.15.5.2.2 Modeling techniques: analytical information regarding travel times will be pre- versus numerical 3 served in the He concentrations (Schlosser et al., As mentioned above, direct groundwater age 1989). Similar complications are inherent in the estimation methods may not be well suited for all use of other tracers as well (see, e.g., Phillips, study areas or with all groundwater tracers. Often, 2000; Sudicky and Frind, 1981; Varni and groundwater age estimates are more easily and Carrera, 1998). 4 correctly achieved through incorporation data for Some conservative tracers, such as He, have natural tracers in analytical and/or numerical also been used for the direct estimation of transport models. This is particularly true when groundwater ages (Andrews et al., 1982; multiple sources contribute to particular tracers, or Bottomley et al., 1984; Marine, 1979; Torgersen, 4 when an accurate hydrogeological representation 1980). The general concept of using He as a is needed for complex groundwater systems. dating tool is simple, and opposite to that of 4 Traditionally, the use of analytical models in radioactive tracers. As He is produced, minerals environmental tracer studies has been far more release it into groundwater. The longer the widespread than numerical models. There are a groundwater in contact with these minerals, the 4 number of reasons for this. Analytical models are greater the He accumulation in groundwater. If easier to use and manipulate than numerical ones; 4He release rates can be estimated (either through they require less hydrodynamic information direct measurement or through comparison of and/or field data; and the time required to build 3 4 He/ He ratios in waters and host rocks; e.g., a transport model is much less than for a Castro et al., 2000; Solomon et al., 1996); it numerical model. Multiple examples of such should be possible to estimate groundwater models can be found in the literature for residence times as the latter should be pro- various tracers: 3H, 4He, 14C, and 36Cl (e.g., 4 portional to He concentrations. However, these Castro et al., 2000; Nolte et al., 1991; Schlosser methods have systematically led to apparent et al., 1989; Solomon et al., 1996; Stute et al., inconsistencies in water ages calculated using 1992b; Torgersen and Ivey, 1985). Generally, other tracers. In particular, 4He methods typically these models are either applied to a single aquifer yield water ages that are much older than 14C ages, in porous or fractured media or to one particular sometimes by up to several orders of magnitude area within the aquifer such as recharge or (e.g., Andrews and Kay, 1982a; Andrews et al., discharge areas. 1982; Bottomley et al., 1984). Numerous authors The reliability of transport model results have observed that the 4He excesses in ground- depends on how well the model approximates water are generally larger than can be supported the field situation. They are limited in their ability by the steady-state release of 4He from the to incorporate complexities such as heterogeneity reservoir rocks to groundwater. Such 4He excesses in hydraulic properties and three-dimensional flow have been explained by the presence of an upward paths. In order to deal with more realistic flux originating mainly in the deep crust (Bethke situations, or when simulating transport of a tracer et al., 1999; Castro et al., 1998a,b, 2000; Marty at the regional scale (e.g., the scale of an entire et al., 1993; Stute et al., 1992b; Torgersen and sedimentary basin), it is necessary to solve Clarke, 1985; Torgersen and Ivey, 1985). Not the mathematical model approximately using considering the contribution of 4He from external numerical techniques. sources is probably the reason for many of the Many different kinds of transport models have discrepancies between ages estimated from 4He been developed, and have been extensively data and those estimated from other tracers described in the literature (Bethke et al., 1993; (Castro et al., 1998b). The presence of such an Bredehoeft and Pinder, 1973; Goblet, 1999; external flux invalidates the use of the 4He Konikow and Bredehoeft, 1978; Prickett et al., method, except in areas where in situ production 1981; Simunek et al., 1999). Although the is the only source of the observed excesses, or incorporation of environmental tracers in numeri- where its contribution can be determined pre- cal transport models is not new (see, e.g., Pearson cisely. Although important information can be et al., 1983), the effort has been made only gained from such direct age estimation methods, it recently to simulate the transport of these tracers, Tracers at the Regional Scale 471 in particular stable and conservative tracers such major importance near recharge areas, and of lesser as 3He, 4He, 21Ne, and 40Ar, at a regional scale importance in basin centers and in discharge areas (e.g., Bethke et al., 1999; Castro et al., 1998a; (Castro et al., 2000). Heterogeneities of hydraulic Zhao et al., 1998). In an attempt to reduce properties within a formation may also affect the uncertainties present in results obtained indepen- relative impact of a particular source or sink in dently through groundwater flow models, trans- different parts of the same system; it is, therefore, port models simulating the distribution of 14C and necessary to account fully for such variations. The 4He have been coupled with the latter to obtain use of numerical methods facilitates this task, as recharge rates and groundwater residence times variations may be imposed through boundary (Castro and Goblet, 2003; Zhu, 2000). conditions of the transport model (Bethke et al., Caution should also be used when estimating 1999; Castro et al., 1998a). hydraulic properties and groundwater ages through transport models. Although analytical and numerical models (in particular) allow for a 5.15.5.2.4 Defining boundary conditions much better representation of the geometry and (modeling approach) the heterogeneity of hydraulic properties of groundwater systems, a number of assumptions The imposition of proper boundary conditions is and simplifications still have to be made when another essential component of groundwater age imposing boundary conditions and hydraulic estimation when using a modeling approach. The parameters on the flow and transport domain. task is to account for the effects of areas outside the These assumptions give rise to sources of region of interest on the system being modeled uncertainty, resulting from (i) the inability to (de Marsily, 1986; Domenico and Schwartz, 1998). properly and fully describe the internal properties Three main types of boundary conditions can be and boundary conditions of a groundwater system considered in a transport model: (i) imposed and (ii) the lack of sufficient information for all concentrations within a particular region—such a of the parameters to be included in such boundary condition is independent of the ground- models (see, e.g., Konikow and Bredehoeft, water flow regime; (ii) imposed mass flux entering 1992; Maloszewski and Zuber, 1993). In this or exiting the system; and (iii) imposed sink or sense, estimated groundwater ages will also carry source terms for a tracer within the modeled an error/uncertainty that is difficult to assess. domain. When conducting simulations in transient Furthermore, numerical models with a large state, the imposition of an initial condition is re- number of adjustable parameters inherently pro- quired. Inappropriate model boundary conditions duce nonunique results. Confidence in model can lead to important differences between actual results can be increased through the use/simu- and simulated flow regimes and thus can lead to lation of multiple tracers within the same erroneous age estimate in real hydrological groundwater flow system and the use of coupled systems. water flow and transport models.

5.15.6 TRACERS AT THE REGIONAL 5.15.5.2.3 Identification of sources SCALE and sinks of a particular tracer 5.15.6.1 Introduction Independent of the method used, proper identi- This section deals with environmental tracers fication of all sources and sinks of a particular applied to regional systems, i.e., to the study of tracer is essential for estimating groundwater groundwater flow regimes in entire sedimentary residence times. If all important sources (e.g., systems. We will focus on studies employing internal production and external sources) and sinks numerical modeling that have been conducted in (e.g., radioactive decay) are not taken into account, two classical sedimentary basin-scale systems: the erroneous water ages will be obtained. For Paris Basin in France (Castro et al., 1998a,b) and example, exclusion of an external source of 4He the Great Artesian Basin (GAB) in Australia will lead to great discrepancies between 4He and (Bethke et al., 1999). These multi-layered aquifer 14C “ages.” Commonly, most tracers have multiple systems are ideal to illustrate the behavior of sources and sinks (e.g., Loosli et al., 2000; Phillips, conservative tracers such as noble gases and their 2000; Solomon, 2000; Solomon and Cook, 2000). relation to depth and recharge distance. The Paris Some sources have a dominant impact on tracer Basin study illustrates how a conservative tracer concentrations; others have only a minor or such as helium can be used as a quantitative dating negligible impact. Moreover, when considering tool through the use of coupled transport and an entire aquifer, one source may be dominant in groundwater flow models, and how a multitracer one part of the system and negligible in others. For approach (e.g., 3He, 4He, 21Ne, and 40Ar) can be example, in situ production of 3He and 4He is of used to identify dominant transport processes such 472 Groundwater Dating and Residence-time Measurements as advection, dispersion, and/or diffusion. Both a diameter of 600 km and maximum depth of studies illustrate the impact of external 4He fluxes 3,200 m. The system consists of seven major and hydraulic conductivities on 4He concen- aquifers (from top to bottom: Ypresian, Albian, trations. In addition, Bethke et al. (1999) have Neocomian, Portlandian, Lusitanian, Dogger, and demonstrated the impact of diffusion coefficients Trias) separated by low to very low hydraulic on aquitard concentrations. Applications of the conductivity aquitards (cf. Figures 3(a) and (b)). 81 36 129 direct dating method using Kr, Cl, and Iin Aquifers are recharged at outcrops to the east and the GAB are also presented (e.g., Bentley et al., southeast, and gravitational flow is toward the 1986b; Lehmann et al., 2002). These are an northwest. Concentrations and isotopic compo- important complement to numerical modeling sitions of helium, neon, and argon measured in studies. 3 3 five of these aquifers show excess He ( He)exc, 4 4 40 He ( He)exc,and Ar,aswellasvertical concentration gradients of these isotopes 5.15.6.2 Examples of Applications throughout the basin (Castro et al., 1998a,b). Water of the Dogger and the Trias formations also 5.15.6.2.1 Noble-gas isotopes—Paris 21 Basin has a Ne excess above ASW values (Figure 4). The dominant source of these excesses is radio- The Paris Basin, situated in northeastern and genic/nucleogenic production in the deep crust central France, is an intracratonic depression with underlying the basin. This external flux is

Figure 3 Simplified diagram of the Paris Basin: (a) locations of the sampled areas; central square—samples from the Paris region ( Meynier and Marty, 1990); (b) central square enlarged; and (c) simplified diagram of the main aquifers in the Paris Basin—arrows show exchanges of water (entering and leaving) between the aquifers (Castro et al., 1998b) (reproduced by permission of American Geophysical Union from Water Resour. Res. 1998, 34, 2443–2467). Tracers at the Regional Scale 473 responsible for the vertical concentration gradi- suggesting that 4He movement in aquitards is ents. In situ production in the basin appears to be a more independent of advection than 40Ar and thus minor source (13% at most) of these isotopes. is transported mostly by diffusion, whereas 40Ar is They are transported vertically throughout the primarily transported by advection (see discussion entire basin by advection, dispersion, and diffu- by Castro et al., 1998a). Neon-21 reflects an sion. The spatial and vertical variability through- intermediate situation. The behavior of this out the basin of the 4He/40Ar (0.69–70) and the isotope reflects differences in diffusion coeffi- 21Ne/40Ar ((8–23) £ 1027) ratios, as compared to cients in water and differences in vertical the crustal production ratios of 4 ^ 3and concentration gradients. Similar 4He/40Ar devia- 0.96 £ 1027, respectively, allow for identification tions have also been observed in the GAB of the dominant transport processes of each (Torgersen et al., 1989). Numerical simulations isotope through aquitards. An interesting feature of 4He transport in the Paris Basin allowed the of the 4He/40Ar ratio was observed in the Dogger, calculation of the advective, dispersive, and where it exhibits a great spatial variability. Values diffusive flux of 4He throughout the aquitards close to the crustal production ratio occur in water (cf. Figure 6). They confirmed that diffusion is the sampled near major faults (where transport by main transport mechanism of 4He through these advection is dominant), but much higher values formations, and that these fluxes decrease toward are observed away from faulted areas (Figure 5). the surface. This decrease is directly related to In the Trias, which is the deepest aquifer in direct a decrease in concentration gradient that is contact with the bedrock, all 4He/40Ar ratios related to dilution by recharge water carrying are similar to the crustal production ratio, atmospheric 4He. This dilution effect, as well as

3 4 21 22 Figure 4 Evolution (versus depth) of: (a) ( He)exc concentrations in the water; (b) ( He)exc; (c) ( Ne/ Ne) ratio; and (d) (40Ar/36Ar) ratio. The different aquifers are shown. All data are from Castro et al. (1998a) (solid squares) except those from the bedrock in figures 6(a) and (b) (Couy) (after Meynier and Marty, 1990), represented by solid triangles. The ASW value is given for (21Ne/22Ne) and (40Ar/36Ar) (Castro et al., 1998b) (reproduced by permission of American Geophysical Union from Water Resour. Res. 1998, 34, 2443–2467). 474 Groundwater Dating and Residence-time Measurements (Trias). These calculated turnover times were derived from modeling 4He concentrations in the Dogger aquifer (,105 yr for a corresponding thickness of 20 m). They agree with pure groundwater flow model results (Wei et al., 1990). However, these 4He groundwater ages are much shorter than those estimated from 4He data by Marty et al. (1993). This discrepancy is due to the neglect of diffusive transport of 4He by Marty et al. (1993). When vertical transport by diffusion is important, the amount of the tracer that moves upward into each aquifer is large compared to transport by advection only. Diffusive transport increases tracer concentrations, and thus leads to “apparent older” residence times if it is assumed that the tracer concentration is only proportional 4 40 Figure 5 Evolution of ( He/ Ar)rad ratio versus to groundwater age. Diffusion is particularly 40 36 Ae/ Ar in Dogger samples; the value of the Trias important in the deeper aquifers within a sedi- sample at Melleray is also given, together with the mentary basin. In shallow aquifers the opposite typical range of radiogenic crustal production values; can be true. Significant amounts of 3He and 4He the position of the mean value measured in oil (Pinti and Marty, 1995) is also shown (Castro et al., 1998b) can leave the system to the atmosphere by (reproduced by permission of American Geophysical diffusion. This leads to “apparent younger ages” Union from Water Resour. Res. 1998, 34, 2443–2467). (e.g., Castro et al., 1998a,b; Schlosser et al., 1989). Simulations of 3He, 4He, and 40Ar concentrations in the Paris Basin indicate that their crustal fluxes (in units of mol m22 yr21) are of 4.33 £ 10213, 4.0 £ 1026, and 2.52 £ 1027, respectively (Castro et al., 1998b). The estimated basin 4He flux is of the same order of magnitude as the estimated terrestrial crustal flux for this isotope (O’Nions and Oxburgh, 1983). This study also showed how 4He/40Ar ratios can help to determine low to very low hydraulic conduc- tivities. Based on the value of this ratio, an upper limit for the hydraulic conductivity of 10211 ms21 was determined for the Lias aquitard.

Figure 6 Calculated values of diffusive fd, advective 4 fC, and dispersive fD fluxes of He in each aquitard. 5.15.6.2.2 Great Artesian Basin—noble-gas Values are estimated on the same vertical line at the isotopes, 36Cl, and 81Kr center of the basin using 4He concentrations and vertical velocities obtained by fitting the model. Names on the The GAB, a multi-layered aquifer system with a x-axis indicate the aquitards between the named units. structure similar to that of the Paris Basin, is For example, Tr/Dog refers to the aquitards between the located in Australia between the Great Dividing Trias and Dogger aquifers (Castro et al., 1998a) (reproduced by permission of American Geophysical Range to the east and the Australian deserts to the Union from Water Resour. Res. 1998, 34, 2467–2484). west (Figure 8). The GAB occupies about one-fifth of the area of Australia and is one of the largest contiguous confined aquifer systems in the world. 4 the variation of the He concentration with re- The basin has a long history of investigations using charge distance and depth, can be clearly observed a variety of age tracing methods (Airey et al., 1979; in the calibrated two-dimensional transport model Calf and Habermehl, 1983). The basin was the site along cross-section A–E (Figures 3(a) and 7). of one of the first field tests of 36Cl behavior in Simulation of 4He transport in the basin regional-scale basin hydraulics, and 36Cl data coupled with a groundwater flow model allowed collection and interpretation has continued ever the estimation of hydraulic conductivities for since (Bentley et al., 1986b; Love et al., 2000; the different aquifers and, consequently, the Torgersen et al., 1991). In general, the data show estimation of groundwater residence times. Aver- the expected spatial variation: a relatively smooth, age turnover times for different aquifers are highly quasi-exponential decrease in 36Cl concentration variable, ranging from 8,700 yr for the shallowest and 36Cl/Cl ratio with flow distance (Figure 9). aquifer (Ypresian) to 30 Myr for the deepest The distribution of ages calculated in these Tracers at the Regional Scale 475

Figure 7 (a) Distribution of 4He concentration contours in mol m23. Contours for values of 1021,1022,1023,1024, and 1025 mol m23 are marked. Except for the curve for 1.1 £ 1021 mol m23 in the Trias, all other contours express constant concentration variations of 1 unit inside each order of magnitude. The measured value of each sample is given together with some contours whose values are close to the measured ones. In these cases, only the molar number is given; (b) measured 4He values plotted as a function of calculated values (Castro et al., 1998a) (reproduced by permission of American Geophysical Union from Water Resour. Res. 1998, 34, 2467–2484).

Figure 8 Distribution of 4He in groundwater from J-aquifer of the GAB. Contours and data points show 4He concentrations (1025 cm3 STP cm23) measured by Torgersen et al. (1992); contour lines are interpretive. Straight lines show flow paths A–A0,B–B0, and C–C0 (Bethke et al., 1999) (reproduced by permission of American Geophysical Union from J. Geophys. Res. 1999, 104, 12999–13010). 476 Groundwater Dating and Residence-time Measurements studies appears to be in general agreement with the Parallel to the collection of age tracing data understanding of flow in the basin developed using cosmogenic radionuclides, radiogenic sub- through physical hydrology. The main source of surface-produced noble gases have also been uncertainty has been discriminating changes in sampled (Torgersen and Clarke, 1985; Torgersen chloride concentration caused by time-variable et al., 1992, 1989), allowing an unusually detailed evapotranspiration in the recharge areas from intercomparison of results. Recently, Bethke et al. changes caused by diffusion of chloride out of (1999) have simulated 4He transport in ground- low-permeability strata, since these affect the age waters of the GAB, using the 36Cl results to help calculations differently (Andrews and Fontes, constrain the groundwater velocity field. Although 1993; Phillips, 2000; Torgersen and Phillips, (unlike the Paris Basin) 4He was not directly used 1993). to estimate groundwater residence times, the The 36Cl flow rate data were recently com- relationship between the groundwater flow regime pared with data from the newly advanced 81Kr in the GAB, transport of 4He within the basin, and method (Lehmann et al., 2002b). Although the resulting 4He distribution was examined. In this caution must be used when evaluating a new case, the water flow regime was considered method such as 81Kr, the correspondence of the “known,” and the groundwater flow model was residence-time estimates was generally good. initially built by deriving all hydraulic parameters Further, application of 81Kr may help to resolve from the literature. The groundwater flow model long-standing uncertainties in the groundwater results were used to simulate 4He transport. age distribution of the GAB. Bethke et al. (1999) simplified the hydrogeology of the GAB somewhat by using only four units, the J- and K-aquifers intercalated between two aqui- tards (Figure 10). However, these simplifications do not affect the response of 4He to variations in the external fluxes or hydraulic conductivities imposed on aquitards, or on assumed diffusion coefficients in these formations. The 4He concentrations in the J-aquifer in simulations by Bethke et al. (1999) were obtained from previous investigations (Torgersen and Clarke, 1985; Torgersen et al., 1992, 1989). These show 4He excesses with respect to the ASW that are larger in the center of the basin than at the margins (Figure 8). For water less than 5 £ 104 yr old, excesses were attributed to in situ production; for older waters (.105 yr), the domi- nant 4He source was attributed to crustal degassing. Torgersen and Clarke (1985) estimated the 4 Figure 9 Variation of the 36Cl concentration ratio with crustal He degassing flux in the GAB to be distance from the eastern margin of the GAB (Phillips, 5.12 £ 10218 mol cm22 s21. A number of previous 1993) (reproduced by permission of Elsevier from Appl. studies have reported average 4He continental Geochem. 1993, 8, 643–647). fluxes, ranging from 0.5 £ 10218 mol cm22 s21 to

Figure 10 Calculated model of helium transport for cross-section through GAB along flow line C–C0 in the central subbasin, from the Great Dividing Range to near Lake Eyre. Vertical exaggeration is ,100 times. Stratigraphic units, bottom to top, are J-aquifer, confining layers, K-aquifer, and overlying beds. Note logarithmic spacing of 4He contours (Bethke et al., 1999) (reproduced by permission of American Geophysical Union from J. Geophys. Res. 1999, 104, 12999–13010). Tracers at the Regional Scale 477 13 £ 10218 mol cm22 s21. The latter is a high increase in the hydraulic conductivity within estimate of the whole-crustal flux (see Torgersen aquifers leads to a decrease in 4He concentrations, et al., 1989). Radiogenic 40Ar excesses (compared owing to dilution by recharge water carrying to the ASW) were also observed, with 40Ar/36Ar atmospheric 4He. An increase in diffusion ratios up to 325.91 (Torgersen et al., 1989). As in coefficients within aquitards will have an opposite the Paris Basin, high deviations of the 4He/40Ar effect on upper aquifers, as more 4He will be ratio (up to 55) compared to the crustal production delivered not only through advection but also ratio also occur. In this case, differential release of through diffusion. Bethke et al. (1999) concluded 218 22 21 4He and 40Ar from rock to water, and a spatially and that a crustal flux of 3 £ 10 mol cm s best 4 temporally variable release of the two nuclides due explains the He concentrations in the GAB. This to tectonic stresses and igneous intrusions were value is about half of the production rate for the offered as explanations for these deviations. whole crust. Transport by diffusion was not considered by Torgersen et al. (1989). 5.15.6.2.3 Implications at the regional scale Hydrologic residence times estimated by Bethke et al. (1999) range from 1.5 £ 105 yr to 2 £ 106 yr, Simultaneous combination of a number of in the central portion of the basin (cross-section natural tracer concentrations (e.g., He, Ne, Ar, C–C0) based on the previous 36Cl studies, and also and 36Cl), isotopic ratios, and modeling of on physical hydrology. Here, groundwater flows to groundwater flow and mass transport within entire the west and southwest, and 4He concentrations, sedimentary systems leads to a tremendous calculated assuming a crustal flux to the J-aquifer improvement in knowledge of tracer behavior of 3 £ 10218 mol cm22 s21, increase to the south- and in the dynamics of these waters as a whole. east (Figure 10). The most notable outcome of their This understanding would not be possible without simulations was that a set of two-dimensional such a multitracer modeling approach in a system models, in which hydraulic conductivity was where extreme contrasts in hydraulic conductivity estimated based on 36Cl data, produced a reason- are present. For example, initial studies of noble able match to the general trends and irregularities gases in the Paris Basin concentrated on analyzing in the 4He distribution. These results support the the concentration of gases in one aquifer (Marty combined application of multiple tracers and et al., 1988). This approach did not indicate the numerical transport modeling as a key to under- external contribution of the noble gases (helium in standing the fluxes of water and geochemically particular). Noble gases were thought to be solely important solutes in the geological environment. the result of in situ production. Groundwater ages 4 were estimated based on in situ production rates, Results of sensitivity analyses show the He and the aquifer was thought to be a “closed,” concentrations at the top of the J-aquifer that nearly static system. Subsequent sampling at were predicted for differing fluxes of 4He into the multiple levels across the Paris Basin (at different base of the aquifer system (Figure 11). It is clear 4 depths and recharge distances) and isotopic that the He concentration at the top of the J-aquifer analysis revealed that the groundwater system is increases with higher crustal fluxes. By contrast, an very dynamic and interactive from a geochemical and hydrodynamic point of view. This dynamism is evident both at the scale of aquifers and aquitards within the system, and at the larger scale of the Earth’s continental crust. Indeed, the horizontal and vertical distribution of 4He/40Ar and 21Ne/40Ar within the deepest aquifers emphasize the importance of active, advective “crustal-scale” transport (Castro et al., 1998b). Concentrations and isotopic ratios also reveal combined upward movement via advection, dispersion, and diffusion of gases through succes- sive formations. The horizontal and vertical variations of 4He/40Ar and 21Ne/40Ar highlight a dominant upward diffusive transport of helium isotopes through low and very low permeability Figure 11 Variation in 4He concentration at top of J-aquifer along flow line C–C0as a function of basal 4He formations. This illustrates how such ratios flux. Bold line corresponds to Figure 10. Measured provide insight into the ranges of hydraulic values are from Torgersen and Clarke (1985) and conductivities within such formations, infor- Torgersen et al. (1992) (Bethke et al., 1999) (repro- mation that is unobtainable from independent duced by permission of American Geophysical Union hydrodynamic studies. For example, strongly from J. Geophys. Res. 1999, 104, 12999–13010). fractionated 4He/40Ar ratios indicate the 478 Groundwater Dating and Residence-time Measurements presence of underlying aquitards with hydraulic the Carrizo aquifer in Texas (Andrews and conductivities ,10211 ms21 or less. Combined Pearson, 1984; Castro and Goblet, 2003; Castro analyses of isotope ratios (actually, absence of et al., 2000; Pearson and White, 1967), and the fractionated isotope ratios) can identify areas Milk River aquifer in Ontario, Canada where advective transport dominates over diffu- (Andrews et al., 1991; Fro¨hlich et al., 1991; sion, as in areas where underlying formations Hendry and Schwartz, 1988; Nolte et al., 1991; exhibit relatively large vertical hydraulic conduc- Phillips et al., 1986; Schwartz and Muehlenbachs, tivities or where they are close to important faults. 1979). Here, we illustrate the use of natural tracers In contrast, strongly fractionated isotope ratios in the Carrizo aquifer, where the measured tracers indicate that diffusion is the dominant transport include 14C, 3He, 4He, atmospheric noble gases, process. and 36Cl. Confined aquifers such as the Carrizo are At the origin of these regional studies, there is ideal to observe, analyze, and discuss groundwater the question of the “age” of groundwaters and our mixing with surrounding formations. In addition, quest to “accurately determine groundwater ages.” while these two aquifers have been the object of Knowledge of the age of a groundwater implies: extensive study for several decades, our under- standing of tracer behavior in these systems is still . understanding of how a particular groundwater an ongoing process (Heaton et al., 1983). system functions; . all the hydrodynamic parameters in a particular system, with relative accuracy (e.g., distribution 5.15.7.2 Carrizo Aquifer of hydraulic head, hydraulic conductivity, and porosity); The Carrizo aquifer, a major groundwater . recharge (infiltration) rates; system, is part of a thick regressive sequence of . understanding of how our groundwater system fluvial, deltaic, and marine terrigenous units in the relates to the “outside world” through the Rio Grande Embayment area of South Texas imposition of boundary conditions represented along the northwestern margin of the Gulf Coast through numerical modeling; and Basin (Figure 12(a)). This aquifer has been . understanding and quantification of water flow particularly well studied for its content of and mass interactions taking place between environmental tracers in Atascosa and McMullen subsystems (aquifers and aquitards) within our Counties south of San Antonio (Andrews and major groundwater system of interest. Pearson, 1984; Castro and Goblet, 2003; Castro et al., 2000; Cowart, 1975; Cowart and Osmond, In one simple phrase, to be able to truly determine 1974; Pearson and White, 1967). It is overlain by the age of a single sample of groundwater implies the Recklaw formation that is composed of shales that we are able to understand precisely and fully with thin interbedded sands, and is underlain by the functioning of the system from both physical the Wilcox Group mainly composed of clay, and geochemical points of view. Such a goal has shale, and lenticular beds of sand (Figure 12(b)). not been accomplished. The combined regional Rainfall recharges the aquifer outcrop at the multitracer/modeling approach represents one northern part of Atascosa County, and ground- new important step in this (iterative) process. water flow is to the southeast. Discharge occurs by Perhaps more than at any other scale, regional upward cross-formational leakage driven by high studies exemplify the interdependence of geo- fluid pressure, as well as by fault-related per- chemical tracers and processes driving the meability pathways that are mainly present in the dynamics of groundwater, in that they integrate south of McMullen County. the long-term response of quasistatic formations The Carrizo was one of the earliest aquifers for (aquitards) with that of much more dynamic which 14C was employed as a tracer (Pearson and formations (aquifers). White, 1967). The results of the 14C measure- ments showed a consistent increase of age along flow paths. The early 14C results were checked about 30 years later using measurements of 5.15.7 TRACERS AT THE AQUIFER SCALE atmospheric noble-gas concentrations (Stute 5.15.7.1 Introduction et al., 1992a). These indicated that water recharged prior to a radiocarbon age of There are many examples in the literature where ,1.2 £ 104 yr was colder by ,5 8C than the a variety of tracers such as 37Ar, 39Ar, 36Cl, 14C, modern mean annual temperature. Although this 3He, and 4He have been used to date groundwater at age is ,30% younger than indicated by indepen- the aquifer scale. Notable examples include the Ojo dent chronology for the last glacial maximum, it Alamo aquifer in the San Juan Basin, New Mexico generally confirms the radiocarbon results. (Phillips et al., 1989; Stute et al., 1995), the Further confirmation comes from measurement Stampriet and Uitenhage aquifers in Southern of 36Cl in the same area (Bentley et al., 1986a). Africa (Heaton et al., 1983; Vogel et al., 1982), The water is too young to show much 36Cl decay. Tracers at the Aquifer Scale 479

Figure 12 Simplified diagram of the studied area and formations in southwestern Texas. (a) Geographical and tectonic context of the area of investigation within Texas (after Bebout et al., 1978; Hamlin, 1988). (b) Detailed area of investigation: latitude and longitude are indicated, as well as the location of cross-section A–A0 in which simulations of groundwater flow and mass transport were carried out; the locations of all 4He sampled sites in Atascosa and McMullen counties (cf. Castro et al., 2000) are also indicated as well as that of the wells for which hydraulic head measurements are used for calibration of the groundwater flow model, closed and open circles, respectively. (c) General schematic representation of cross-section in the area for the four studied formations: the Lower-Wilcox and lower part of the Upper-Wilcox formations undifferentiated, the Carrizo aquifer, the Recklaw formation, and the Queen-City aquifer (Castro and Goblet, 2003) (reproduced by permission of American Geophysical Union from Water Resour. Res. 2003, 39, 1172).

The 36Cl/Cl ratio in the region documenting the distance and 14C ages (e.g., Figure 13). Separation noble-gas paleotemperature decrease actually of helium components shows that ,99% of the 36 3 4 shows an increase in the Cl/Cl. Bentley et al. excess helium—( He)exc and ( He)exc—is of (1986a) explain this by comparison with the curve terrigenic origin due to the addition of nucleogenic of distance from the coastline, which varied as sea 3He and radiogenic 4He at a 3He/4He production level decreased during the glacial period. Chloride ratio of 7 £ 1028. From this, and through analyses concentration in precipitation decreases as with of 3He/4He ratios in groundwater and in reservoir increasing distance to the coast. The good rocks, it is apparent that most of the helium has an correspondence further supports the evidence for origin external to the aquifer, and that in situ distribution of flow velocities in the Carrizo. production makes a smaller and variable contri- This well-supported understanding of flow bution. Simulation and calibration of 4He transport velocities should aid in the interpretation of using a simple analytical model (Castro et al., the pattern of helium-isotope concentrations. 2000) illustrates the in situ contribution variations Helium-3 and helium-4 concentrations are in with recharge distance and with depth within the excess by up to one and two orders of magnitude aquifer (Figure 14). Modeling results (dashed line, compared to the ASW, respectively (Castro et al., Figure 14) show that in situ production can account 2000). Concentrations increase with recharge for 4He concentrations in the top of the aquifer if 480 Groundwater Dating and Residence-time Measurements

4 Figure 13 (a and b) Evolution of ( He)exc concentrations in the water as a function of recharge distance, depth, and calculated 14C ages, respectively, for the Carrizo aquifer (Castro et al., 2000) (reproduced by permission of Elsevier from Appl. Geochem. 2000, 15, 1137–1167).

10–4

10–5 12 13 18 z = 230 m 29 10–6 33 4 ) 14 –1 10–7 1 21 STP g 3 –8 6 10 z =0m (cm exc (4He) (cm3 STP g–1) He) –9 exc 4 10 ( 2, 22, 32 J = 3.6e–7, vo = 4, vf = 0.1, Z = 230 10–10 J = 3.6e–7, vo = 4, vf = 0.1, Z =0 J = 0, Pi only, vo = 4, vf = 0.1, Z = 230

10–11 020406080100 Recharge distance (km)

4 Figure 14 Calculated ( He)exc concentration curves for the bottom ðz ¼ 230 mÞ and for the top of the aquifer ðz ¼ 0mÞ (upper and lower plain line, respectively) as a function of the recharge distance for the Carrizo aquifer. The 4 4 measured ( He)exc concentration values are also shown as well as the He concentration curve resulting from in situ production only (dashed line) (Castro et al., 2000) (reproduced by permission of Elsevier from Appl. Geochem. 2000, 15, 1137–1167). the distance from the recharge area is #40 km. Castro et al. (1998a) (9 £ 1026 cm3 STP Similar to the Paris Basin (Section 5.15.6.2.1), this cm22 yr21). Using an average velocity calculated contribution decreases toward the discharge area from previous studies of 1.6 m yr21, tests of (,27%). At the bottom of the aquifer the in situ sensitivity to the 4He external flux were carried contribution represents no more than ,15% of out (e.g., Figures 15(a)–(e)). Some aspects of total 4He. these tests are worth noting: differences between The analytical model was calibrated with an bottom and top concentrations decrease with external flux to the bottom of the aquifer of decreasing flux. As the flux decreases, in situ 3.6 £ 1027 cm3 STP cm22 yr21. It is important to production becomes more important, 4He note that this flux represents only part of the local accumulation becomes independent of vertical integrated crustal production as a consequence of and horizontal position in the aquifer, and varies downstream 4He dilution in the deeper aquifer. mainly with time. For the smallest flux of Thus, this flux is smaller than the average crustal 3.59 £ 1029 cm3 STP cm22 yr21, 4He concen- flux calculated for the GAB by Torgersen and trations are similar in the top and bottom of the Clarke (1985) (3.62 £ 1026 cm3 STP cm22 yr21) aquifer as in situ production becomes almost or that calculated for the Paris Basin by entirely responsible for the 4He concentrations, Tracers at the Aquifer Scale 481

Figure 15 Model results for sensitivity tests of the 4He flux value for the Carrizo aquifer—(a–e): calculated 4 25 3 2 21 ( He)exc curves for five different orders of magnitude of the flux value, between 3.6 £ 10 cm STP cm yr and 3.6 £ 1029 cm3 STP cm2 yr21 and a constant velocity value of 1.61 m yr21. The calculated concentration curves for 4 the bottom ðz ¼ 230 mÞ and for the top ðz ¼ 0mÞ of the aquifer are represented. The measured ( He)exc concentration values in the aquifer are also shown (Castro et al., 2000) (reproduced by permission of Elsevier from Appl. Geochem. 2000, 15, 1137–1167). and the external flux is negligible. This illustrates finite element model with a more accurate the interplay between internal versus external representation of boundary conditions (i.e., a step sources of 4He. In the study by Castro et al. toward a comprehensive aquifer-system or even (2000), it was only possible to calibrate 4He basin-scale approach) has shown representation by concentrations by imposing an exponential a simple analytical model to be inadequate for this decrease in the groundwater velocities between system (Castro and Goblet, 2003). Although the recharge and discharge areas, with initial and finite element model has confirmed an exponential final velocities of 4.0 m yr21 and 0.1 m yr21, decrease in Carrizo velocities, the external flux respectively. value was one order of magnitude higher in the The analytical modeling of Castro et al. (2000) is analytical model than that obtained through typical of an aquifer-scale approach. Comparison numerical modeling. Advective groundwater ages of a more recent simulation of 4He transport using a estimated from numerical simulation of 4He 482 Groundwater Dating and Residence-time Measurements

Figure 16 Distribution of calculated advective water ages (kyr) in the system. Water age contours correspond to constant variations of 104 yr between 0 Myr and 0.1 Myr and variations of 105 yr for time periods varying between 0.1 Myr and 1 Myr, each one of these intervals being represented by a different color, from the youngest (dark blue) to the oldest (red), which corresponds to ages higher than 1Myr (Castro and Goblet, 2003) (reproduced by permission of American Geophysical Union from Water Resour. Res. 2003, 39, 1172). transport (Castro and Goblet, 2003) indicate an are: (i) an increase in concentration with increased increase in Carrizo water ages with distance from recharge distance and depth and (ii) the presence the recharge zone (Figure 16). Clearly, even with of two main crustal sources (radiogenic or multiple tracers, issues of model uniqueness nucleogenic), i.e., in situ production and an continue to affect interpretations. external flux with variable contributions depend- ing on the depositional context. This is general information that can now be considered to be well 5.15.7.3 Implications at the Aquifer Scale established, as it has been observed consistently in Perhaps more than studies at other scales, a variety of aquifer systems around the world in modeling of groundwater flow at the aquifer diverse sedimentary settings, as discussed above. If the external flux and in situ production of noble scale has revealed the utility of combining 4 atmospheric-source radioisotope or stable tracers gases in general, and He in particular, in a (e.g., 14C, atmospheric noble gases) with specific aquifer system are relatively constant, subsurface-sourced stable tracers. In comparison then the pattern of variation in concentration along to the regional scale, detailed knowledge of the one particular aquifer, such as a rapid versus a permeability structure is often needed. Indepen- slow increase in concentrations with increased dent information can often be obtained from recharge distance, will yield information on the hydraulic tests or from semiquantitative interpret- spatial variation of hydraulic parameters, and ation of aquifer properties based on hydrogeolo- those of hydraulic conductivity in particular. gical descriptions. Concentrations of natural At the aquifer scale, the most important tracers reveal not only the history of the tracer contribution of age tracers is probably reduction itself (e.g., its sources), but also the patterns of in the nonuniqueness of numerical models. Lack of water dynamics within a particular aquifer (e.g., uniqueness stems, among other things, from variation in water velocity is the horizontal inadequate knowledge of the distribution of direction). Some generalizations regarding pat- hydraulic properties within groundwater systems terns that are very commonly observed from the and from poor constraints on boundary conditions numerous studies of noble gases in aquifers in (Konikow and Bredehoeft, 1992; Maloszewski and sedimentary systems can now be drawn. These Zuber, 1993). Commonly, groundwater flow Tracers at the Local Scale 483 models are calibrated on measured hydraulic head 3H/3He, CFCs (CFC-11 and CFC-12), and 85Kr and/or hydraulic conductivity values. However, a can give insight into the dynamics of ground- good match does not prove the validity of the water flow systems and the major transport model, because the nonuniqueness of model processes that influence the concentration of solutions means that a good comparison can be different tracers. They also illustrate how the achieved with an inadequate or erroneous model. use of a multitracer approach using direct For example, in the case of the Carrizo aquifer, water dating methods at a local scale increases Castro and Goblet (2003) show that variations of confidence in estimated ages. hydraulic conductivity up to two orders of magnitude in the Carrizo aquifer and in the overlying confining layer lead to similar calculated 5.15.8.2 3H/3He, CFC-11, CFC-12, hydraulic heads. No clear-cut arguments are 85 available to validate one groundwater flow scena- Kr—Delmarva Peninsula rio over a different one. This is due, in part, to lack The Atlantic Coastal Plain of the Delmarva of information regarding recharge (infiltration) Peninsula in the East Coast of the US is composed rates in the study area. In contrast, when tested with 4 of Jurassic to Holocene sediments deposited a He transport conceptual model, all groundwater during a series of transgressions and regressions flow calibrated scenarios except one failed to 4 (Figure 17). It is covered by a highly permeable reproduce a coherent He transport behavior in the surficial Pleistocene aquifer that is directly system. This highlights the importance of contri- 4 recharged by local precipitation. Thirty-three butions of a tracer such as He for determining wells, some of which tap this formation, were which model most closely replicates natural used to sample 3H/3He (52 samples), CFCs conditions. Without the information provided by (282 samples), and 85Kr (four samples) (Dunkle this tracer, it would be very difficult to have a et al., 1993; Ekwurzel et al., 1994; Plummer et al., precise idea of the groundwater flow conditions of 1993; Reilly et al., 1994). this system, and, as a result, on the velocity In wells sampled at several levels, 3H and distribution of those waters as well as water age 3 ( He)tri concentrations, as well as apparent distribution. 3H/3He, CFC-11, and CFC-12 ages, increase significantly with depth below the water table (Figure 18). Moreover, most of the apparent CFC, 3H/3He, and 85Kr ages agree with each other to 5.15.8 TRACERS AT THE LOCAL SCALE within three years over the entire peninsula (e.g., 5.15.8.1 Introduction Figures 19(a) and (b)), indicating that these tracers behave fairly conservatively in this sandy uncon- There are numerous examples in the literature fined aquifer. Waters located in discharge areas in which environmental tracers have been applied such as those in well KE Be 170, where a mix of a at a local scale, both in porous media and in wide range of water ages intersects the well fractured crystalline rocks. Among these are screen, present large differences between CFC and studies in Liedern/Bocholt, Germany (Schlosser 3H/3He ages. This illustrates how ages based on et al., 1988, 1989), the Stripa Granite, Sweden different tracers can identify specific recharge (Andrews et al., 1989; Loosli et al., 1989), in versus discharge areas within a groundwater Sturgeon Falls, Ontario, Canada (Milton et al., system. 1997; Robertson and Cherry, 1989; Solomon Simulations using different dispersion values et al., 1993), the Delmarva Peninsula (Dunkle and an average vertical velocity of 1 m yr21 in a et al., 1993; Ekwurzel et al., 1994; Plummer, one-dimensional model (Ekwurzel et al., 1994) 1993), and in the Borden aquifer, Ontario showed that 3H/3He ages are more affected by (Smethie et al., 1992; Solomon et al., 1992). dispersion than CFC ages (Figure 20). This is Most of these studies were conducted in rela- because the abrupt concentration front presented tively surficial aquifers, and many focused on the by the peak-shaped 3H source function is subject application of the tritium/3He and CFC methods, to greater dispersion than the relatively gradual, which are well suited for young, fast-flowing monotonic CFC concentration increase (Figure 2). groundwater. Tracers such as 37Ar, 39Ar, 85Kr, Such dispersion would result in an apparent 36Cl, and 4He were also investigated. Helium-3 increase in 3H/3He ages in postbomb peak waters, confinement, dispersion, diffusion, sorption, and and in reduced apparent ages in prebomb peak microbial degradation are some of the processes waters. However, comparison of (3H þ 3He) that have been investigated by means of various concentrations with the 3H input function tracers. As an example, we focus on studies in the shows little smoothing, indicating that disper- Delmarva Peninsula (eastern seaboard of the US). sion has been negligible (Dunkle et al., 1993; These studies illustrate in a clear and elegant Ekwurzel et al., 1994). This inference is supported manner how a multitracer approach using by detailed numerical transport modeling 484 Groundwater Dating and Residence-time Measurements

Figure 17 Map of the Delmarva Peninsula, on the east coast of the US. Wells having the same series number (e.g., KE Be) are listed as the series number followed by a dash and well numbers listed in order of increasing depth within the boxes (Ekwurzel et al., 1994) (reproduced by permission of American Geophysical Union from Water Resour. Res. 1994, 30, 1693–1708). Tracers at the Local Scale 485

3 3 Figure 18 Depth profiles of tritium, H þ ( He)tri (tritium units), and apparent tracer ages from well nests Ph13 and Ph23 (Ekwurzel et al., 1994) (reproduced by permission of American Geophysical Union from Water Resour. Res. 1994, 30, 1693–1708).

Figure 19 (a) Apparent 3H/3He age compared toapparent CFC-11 and CFC-12 ages. Diagonal line is a 1 : 1 reference line. The vertical and horizontal reference lines are 26 yr age lines representing the bomb peak and a 2 yr lag for flow through the unsaturated zone. (b) Apparent CFC-11, CFC-12, 3H/3He, and 85Kr ages for Locust Grove wells sampled in November 1991 (Ekwurzel et al., 1994) (reproduced by permission of American Geophysical Union from Water Resour. Res. 1994, 30, 1693–1708).

(Reilly et al., 1994). The high correlation 5.15.8.3 Implications at the Local Scale observed between ages calculated using the three age tracers also supports this inference. Recharge The studies surveyed above, and those at other rates calculated from these different tracers are sites, provide a strong contrast to aquifer and also in good agreement (Ekwurzel et al., 1994). regional scale results. While the results of the 486 Groundwater Dating and Residence-time Measurements study areas is uncertain. Although age tracing techniques for local systems have clearly demon- strated their validity, have increased the general understanding of local flow systems, and have aided in the reconstruction and fate of contami- nants introduced into these systems, they have not yet reached their potential for elucidating funda- mental transport mechanisms in a variety of geological environments. There is much to be learned by future studies for this purpose.

5.15.9 TRACERS IN VADOSE ZONES Vadose zones are of great importance for both hydrological and geochemical reasons. Hydro- logically, they represent the portion of the Figure 20 Comparison of 3H/3He and CFC-12 ages from the Delmarva Peninsula, including effects of physical system where precipitation partitions dispersion. Average linear velocity of 1 m yr21 is the essential elements of the hydrological cycle: plotted with different dispersion coefficients and evapotranspirative return to the atmosphere, run- with a 1 : 1 reference line (Ekwurzel et al., 1994) off, and deep infiltration (i.e., aquifer recharge). (reproduced by permission of American Geophysical Quantification of the fluxes below the root zone is Union from Water Resour. Res. 1994, 30, 1693–1708). thus critical for both closing the water balance at the watershed scale and for analyzing ground- water resources. Geochemically, the vadose zone larger scale studies typically exhibit many constitutes the primary zone of interaction enigmatic features and major issues of nonunique- between earth materials and precipitation. Knowl- ness, most of the local-scale flow systems appear to edge of water fluxes through vadose zones is thus allow straightforward interpretations. Most of the a key to understanding the global solute balance, studies conducted at sites investigated previously as well as interactions of climate, geochemistry, or, by other approaches (Engesgaard et al., 1996; and tectonics on the continental scale. et al et al Reilly ., 1994; Shapiro ., 1999; Solomon Determination of water fluxes under unsatu- et al., 1992), hold few surprises. rated conditions by physical monitoring is often Several aspects of the results from local flow very difficult due to the effects of seasonal systems are noteworthy. One is the ease and fluctuations, problems of installing and maintain- reliability of estimating recharge rates by measure- 3 3 ing instrumentation, and the nonlinear nature of ment of vertical profiles of H/ He or CFCs in the variation of water potential and hydraulic recharge areas (Bo¨hlke and Denver, 1995; conductivity with water content. More direct Ekwurzel et al., 1994; Solomon et al., 1993). means of residence-time estimation by tracing Another is the apparently relatively minor level of solutes thus provide an important alternative to problems created by degassing of volatile tracers physical monitoring (Allison et al., 1994; Scanlon from the water table. Sampling near discharge et al., 1997). The majority of residence-time areas (principally streams), however, is somewhat tracers that rely on radiodecay for their time hazardous because of the mixing of deep, upward constant are volatile; therefore, most vadose-zone flow with shallow flow at the point of discharge. dating studies employ some form of signal tracing What is most surprising is the relative hom- rather than radioactive decay dating. ogeneity and the dominance of advective flow in Conceptually, vadose zones can be divided into most of the investigated systems. Where multiple two end-members: humid and arid. In humid tracers have been used, it is possible to estimate climates (or in irrigated areas), vadose zones are dispersivity independently. The longitudinal dis- generally thin (0–10 m), dynamic, and are 2 persivity values obtained for studies at the 10 – characterized by great variability in flow paths. 103 m flow scale have ranged from 0.1 m to 0 m Residence times vary from hours to a few years. In (Ekwurzel et al., 1994; Engesgaard et al., 1996; contrast, arid-region vadose zones are usually Reilly et al., 1994; Solomon et al., 1993; Szabo thick (10–1,000 m), with very small water fluxes, et al., 1996). These are significantly smaller than and a high degree of uniformity in flow paths. We many extrapolations would suggest (Gelhar, 1993; will give examples from very humid, subhumid Neuman, 1995). Whether these implications can (irrigated), and arid vadose-zone environments. be widely extended, or whether they result from Bonell et al. (1998) described the results of application of the tracing methods to a restricted detailed monitoring of soil water and runoff and hydrologically unusually homogeneous set of in tropical northeast Queensland, Australia. Tracers in Vadose Zones 487 Figure 21 shows the d2H variation of soil water as These are in response to heavy precipitation a function of depth during a three-month period in events having differing isotopic compositions. 1991. Each panel represents a nest of soil water Others (SC1 and SC2) show much variability samplers at different positions on a hillslope. with time in the upper soil horizons but little at Some sites (NC2, NC4, and SC3) show a depth, indicating an absence of continuous rapid large range in d2H throughout the depth profile. flow paths to greater than 1 m. Figure 22 shows

Figure 21 d2H values of soil water as a function of depth in vadose-zone profiles from small catchments near Babinda, Queensland, Australia. Numbers in symbol key refer to sampling dates during 1991. The climate is tropical and mean annual precipitation amounts to 4,000 mm (source Bonell et al., 1998). 488 Groundwater Dating and Residence-time Measurements

Figure 22 d2H of water from wells in the North Creek drainage (NCB) and South Creek drainage (SCA, SCB, SCC, and SCD) and stream water from North Creek (NBG) and South Creek (SBG) as a function of time during 1991. The drainages are near Babinda, Queensland, Australia (Bonell et al. (1998) (reproduced by permission of Elsevier from Isotope Tracers in Catchment Hydrology, pp. 334–347). d2H for well water samples over the same period, dispersion of clays when the original saline pore compared to stream water samples. The ground- water was displaced by dilute irrigation water. By water samples show a high degree of variability in matching the shapes of the annual pulses in both space and time, but not nearly as much as the transport simulations with those from the data, soil water. The stream-water depletion on day 47 they estimated an effective dispersion coefficient is in response to a major storm. The groundwater of 5 £ 10211 m2 s21, which, due to the uniformity response can be seen on day 52, but the of the loess, the low velocity, and the high volume groundwater has returned to near baseline by of immobile water, is mainly attributable to day 60. These data, therefore, indicate flow times diffusion rather than dispersion. for the vadose zone of ,5 d, but also show that Arid or desert vadose zones have been much less new recharge is mixing with a large reservoir of studied than those in humid climates. Geochemical shallow groundwater. Numerous studies have dating approaches have played an important role in shown that a short residence time, rapid response understanding their dynamics (Allison et al., and flow rates, and large temporal and spatial 1994). Walvoord et al. (2002a,b) have employed variability in fluxes are characteristic of tracer a combination of liquid–vapor flow modeling and transport in humid vadose zones (Kendall and modeling of chloride concentration profiles to McDonnell, 1998). demonstrate that pervasive upward total fluid Gvirtzman and Magaritz (1986) and Gvirtzman potential gradients below the root zone, caused et al. (1986) provide a good example of the power by desert vegetation, retain all water and solutes of geochemical tracers for understanding the that are deposited on the land surface (Figure 24). transport properties of semi-arid vadose zones. Measurements of numerous profiles within the The study was conducted beneath an irrigated southwestern US indicate that most desert vadose vineyard in the Negev Desert in Israel. The zones have been quantitatively retaining chloride vadose zone was ,11 m thick and composed of and other solutes since the end of the last glacial very uniform silt, which was deposited as loess. period at ,15 ka (Tyler et al., 1996). This amounts The vineyard received precipitation containing to a “dating” of the duration of a hydrological bomb and natural tritium during the winter regime. This history of the vadose-zone hydraulics months, amounting to 200 mm annual average. would be difficult or impossible to ascertain During the summer the vineyard was irrigated without the use of geochemical tracers. with ,650 mm yr21 of well water containing less The examples cited above illustrate the great than 1 TU. The authors used the alternating high- variability in soil–water movement and resultant and low-tritium inputs to trace 14 annual tritium geochemical processes in vadose zones. Humid cycles down to a depth of 8.75 m (Figure 23), for vadose zones are highly dynamic, with large water a mean velocity of 0.62 m yr21. They determined fluxes and great spatial and temporal variability of that the spreading of the annual pulses was largely those fluxes. Although variability is large at small due to exchange by diffusion with immobile time and space scales, mixing processes tend to regions within the loess that were created by rapidly average out these variations and their Tracers in Vadose Zones 489

Figure 23 Comparison of reconstructed irrigation water tritium input (left panel), immobile vadose-zone water tritium (center panel), and measured tritium (right panel), all as a function of depth. Study site is an irrigated vineyard in the Negev Desert, Israel (source Gvirtzman and Magaritz, 1986).

Figure 24 Simulated chloride concentrations as a function of depth, compared to measured data, for deep boreholes at the Nevada Test Site, USA. The simulations indicate that the upper 10–100 m of these vadose zones have been retaining all chloride deposited from the atmosphere onto the land surface for time periods from 9.5 ka to 110 ka (Walvoord et al., 2002a)(Walvoord, 2002) (reproduced by permission of American Geophysical Union from Water Resour. Res. 2002, 38, 1291). 490 Groundwater Dating and Residence-time Measurements effects on tracer concentrations. It is clear that these Alle`gre C. J., Staudacher T., Sarda P., and Kurz M. D. (1983) characteristics are very favorable for weathering Constraints on evolution of Earth’s mantle from rare gas systematics. Nature 303, 762–766. reactions, and that these are environments of high Allison G. B. and Holmes J. W. (1973) The environmental rates of chemical denudation. Less attention has tritium concentrations of underground water and its hydro- been devoted to how the small-scale heterogeneity logical interpretation. J. Hydrol. 19, 131–143. in flow paths and fluxes affects the chemical Allison G. B., Gee G. W., and Tyler S. W. (1994) Vadose-zone outcome of weathering averaged over the land- techniques for estimating groundwater recharge in arid and semiarid regions. Soil Sci. Soc. Am. J. 58, 6–14. scape (Bullen and Kendall, 1998). In contrast, Andrews J. N. and Fontes J.-C. (1993) Comment on “Chlorine desert landscapes exhibit a remarkable uniformity 36 dating of very old groundwater: 3. Further results on the of hydrologic regime, both in space and time Great Artesian Basin, Australia” by T. Torgerson et al. Water Resour. Res. 29, 1871–1874. (except in the vicinity of water courses or areas 234 238 where runoff is focused). Such vadose zones can be Andrews J. N. and Kay R. L. F. (1982a) U/ U activity ratios of dissolved uranium in groundwater from a Jurassic regarded as surfaces of “negative weathering”— limestone aquifer in England. Earth Planet. Sci. Lett. 57, there is no export of solutes and rather than being 139–151. depleted of mobile elements with time; they Andrews J. N. and Kay R. L. F. (1982b) Natural production of accumulate them from atmospheric deposition. tritium in permeable rocks. Nature 298, 361–363. Andrews J. N. and Lee D. J. (1979) Inert gases in groundwater from the Bunter Sandstone of England as indicators of age and paleoclimatic trends. J. Hydrol. 41, 233–252. 5.15.10 CONCLUSIONS Andrews J. N., Giles I. S., Kay R. L. F., Lee D. J., Osmond J. K., Cowart J. B., Fritz P., Barker J. F., and Gale J. (1982) During most of the second half of the twentieth Radioelements, radiogenic helium, and age relationships for groundwaters from the granites at Stripa, Sweden. Geochim. century, the emphasis in the study of subsurface Cosmochim. Acta 46, 1533–1543. water age tracers was on the development of new Andrews J. N., Balderer W., Bath A. H., Clausen H. B., Evans techniques and methodologies. This phase of the G. V., Florkowski T., Goldbrunner J. E., Ivanovich M., field has slowed greatly. Most tracers not in Loosli H. H., and Zojer H. (1984) Environmental isotope common use have at least been explored, and most studies in two aquifer systems: a comparison of ground water dating methods. In Isotope Hydrology 1983. IAEA, Vienna, are no longer used, because of major sampling and pp. 535–576. analytical difficulties. The only tracer that may be Andrews J. N., Goldbrunner J. E., Darling W. G., Hooker P. J., poised for a breakthrough in the near future is 81Kr Wilson G. B., Youngman M. J., Eichinger L., Rauert W., and (Collon et al., 2000; Lehmann et al., 2002b). The Stichler W. (1985) A radiochemical, hydrochemical, and inert geochemistry and the half-life of this dissolved gas study of groundwaters in the Molasse Basin of Upper Austria. Earth Planet. Sci. Lett. 73, 317–332. radionuclide render it sufficiently attractive for Andrews J. N., Davis S. N., Fabryka-Martin J., Fontes J.-C., regional and aquifer scale investigations in spite Lehmann B. E., Loosli H. H., Michelot L., Moser H., Smith of the difficulties in sampling and analysis. B., and Wolf M. (1989) The in-situ production of The new frontier in groundwater age tracers radioisotopes in rock matrices with particular reference to lies not in technique development, but rather the Stripa granite. Geochim. Cosmochim. Acta 53, 1803–1815. in interpretation within the hydrogeochemical Andrews J. N., Florkowski T., Lehmann B. E., and Loosli system. Until the 1990s, interpretation has tended H. H. 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