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7 Hydrologic tracing

The most common measurement that hydrologistsmake pertains to the volumetric flow rate of waterin its various physical forms at different locationsand at different times – as liquid along streams, asrain or snow, as soil moisture in the soil profile,as groundwater in the subsurface, and as vapourin the atmosphere. The other important hydrologicparameter is the volume of the reservoir into whichthe water, in whatever form, flows in or flows out.As already mentioned in previous chapters, ma-jor objectives of various hydrologic measurementsare to: (i) generate hydrographs; (ii) develop waterbudgets; (iii) characterize flow paths; (iv) estimateresidence or storage time in the hydrologic reser-voir; (v) provide insight into hydrologic processesoperating at different spatial and temporal scales;and (vi) study interaction/transport across hydro-logic boundaries.

While transforming hydrologic measurements touseful information for resource management, sev-eral simplifying assumptions and process models,both empirical and physical, are used. Flow mea-surements are limited in temporal and spatial do-mains by practical considerations. This has con-strained the development of theories/models tosmall-scale catchments for short time scales. A ma-jor problem in hydrology, that still persists, is thescaling up of the inferences/results from small- tolarge-catchments and from short duration observa-tions to longer periods. This is because hydrologicprocesses and parameters vary on wide space-timescales, leading to highly complex, strongly nonlin-

ear catchment response due to strong interactionsand feedbacks between the various processes.

Water systems are also getting ever larger andmore complex and they are affected by complexpatterns of land use and other anthropogenic fac-tors. These developments require prediction, inspace and time, of functioning of hydrologic sys-tems and their impacts on future availability of wa-ter. Therefore, tools that track water movementwithin and across hydrologic reservoirs (i.e. hydro-logic tracers) and focus on hydrologic processesover a wide range of temporal- and spatial scalesare needed.

Water tracing techniques are useful, particularlydue to the fact that tracing of water enables di-rect insight into the dynamics of surface- and sub-surface water movement. As a result, tracer tech-niques provide useful tools to understand transportprocesses, phase changes (evaporation, condensa-tion, sublimation), and genesis of water massesand their quality. Tracer techniques are particu-larly useful in arid and semi-arid regions for quan-tifying groundwater flow and water movement inthe vadose zone. Tracer methods have become amajor tool for calibration and validation in catch-ment modelling and for identification and quan-tification of runoff generation processes. Tracertechniques can be extremely useful in assessmentof groundwater–surface water interactions, datingof groundwaters, quantifying water–rock interac-tions, and evaluating water resource vulnerabilityto various natural and anthropogenic factors.

Modern Hydrology and Sustainable Water Development S. K. Gupta

© 2011 S. K. Gupta. ISBN: 978-1-405-17124-3

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182 MODERN HYDROLOGY AND SUSTAINABLE WATER DEVELOPMENT

As shown subsequently, while advances are be-ing made in all tracer techniques, isotopic tracers,in particular, comprise a large and growing familyof hydrologic tracers.

7.1 Isotopes and radioactivity

Most elements found in nature consist of one ormore isotopes, which are atoms of the same ele-ment having the same number of protons but dif-ferent number of neutrons in their nucleus. As aresult, isotopes of an element have different atomicmasses. The mass number of an isotope is the sumof the number of protons and neutrons in its nu-cleus and is written as a superscript to the left ofthe element symbol. For example, amongst the hy-drogen isotopes, deuterium (denoted as D or 2H)has one neutron and one proton, whereas tritium(denoted as T or 3H) has one proton and two neu-trons. Isotope names are usually pronounced withthe name of the element first followed by its massnumber, as in ‘oxygen-18’ for 18O instead of ‘18-oxygen’. In many texts, especially older ones, themass number is shown to the right of the elementabbreviation, as in C-13 or C13 for 13C, pronouncedas ‘carbon-13’.

Radioactive isotopes are nuclides (isotope-specific atoms) that spontaneously disintegrateover time, with a characteristic half-life, to formother isotopes (radioactive or stable). During dis-integration, radioactive isotopes emit alpha (α)particles or beta (β) particles and sometimes alsogamma (γ ) rays. An alpha particle is a heliumnucleus that consists of two protons and two neu-trons. Beta particles are indistinguishable from elec-trons but with the difference that they originate inthe nucleus of a β emitting radioisotope. Gammarays are electromagnetic radiation of very shortwavelength. Typical gamma photon energies areseveral MeV . The half-life of a radioactive isotope(designated as t1/2) is the duration of time it takesfor half of the radioactive atoms in a sample todecay. The half-life of a given isotope remains in-variant; it does not depend on the number of atomsor how long they have been around or on the ex-ternal factors, such as temperature and other en-vironmental parameters. Therefore, decays occurat a faster rate when there are more numbers of

radioactive atoms and the decays are fewer whenthere are less numbers of atoms. In fact, the numberof disintegrating atoms of a radioactive substanceat a given time, t, is directly proportional to thenumber present in the substance at that time, thatis, dN/dt = Nλ . The half-life is invariant but thenumber of atoms remaining after each successivehalf-life gets smaller by one-half. The decay equa-tion (Eqn 7.1) expresses change in the concentra-tion (activity) of a radioactive nuclide over time:

At = A0 . e−λt (7.1)

where A0 is the initial activity of the parent nuclide,At is its activity after time ‘t’; λ is the radioactivedecay constant which equals ln(2/t1/2); with ln (x)defined as the natural logarithm (i.e. to the base ‘e’)of the variable ‘x’.

The activity of a radioactive substance is givenby the number of disintegrations per second of itsatoms. The original unit for measuring the amountof radioactivity was the curie (Ci) – defined to cor-respond to the number of disintegrations per sec-ond of one gram of radium-226 and more recentlydefined as:

1 curie = 3.7 × 1010 radioactive decays

per second [exactly].

In the International System of Units (SI), the curiehas been replaced by the becquerel (Bq), where:

1 becquerel = 1 radioactive decay per second

= 2.703 × 10−11 Ci.

Many of the units used in radioactivity are ex-pressed into smaller units or as multiples, usingstandard metric prefixes. Thus, a kilobecquerel(kBq) is 1000 becquerels, a nanogram is 10−9

gram, and a picocurie is 10−12 curie.The type and energy of the ionizing radiation

emitted are characteristic of the decaying radioiso-tope. Therefore, data on the emitted ionizing radia-tion, particularly its energy, yield qualitative as wellas quantitative information on the radioisotope. Anumber of techniques are used to measure the en-ergy of the emitted ionizing radiation, namely alphaspectrometry (for alpha particles), beta spectrom-etry (for beta particles), and gamma spectrometry(for gamma rays).

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HYDROLOGIC TRACING 183

In alpha spectrometry, the test sample isdeposited on a circular metal disk (∼25 mmdiameter) by electrolysis or by placing a drop ofsolution containing the radioactive substance tobe analysed, drying it to give a uniform coating,and placing it in contact with an ionizationdetector (e.g. silicon surface barrier detector) in anevacuated chamber. This is because the range ofα-particles in materials is small (1.12 cm for 2 MeValpha particles in air at 15◦C and 1 atm pressure).The electronics for counting of α-particles includesa pulse sorter (multi-channel analyser) and asso-ciated amplifiers and data readout devices. If thelayer formed on the disk is too thick, the lines ofthe spectrum get broadened. This is because someof the energy of the α-particles is lost during theirpassage through the layer of the active material. Analternative method is to use the internal liquid scin-tillation technique, in which the sample is mixedwith a scintillation cocktail and the emitted lightis then counted. The detector records the amountof light energy per radioactive decay event. Dueto imperfections of the liquid scintillation method,such as failure to detect all the emitted photons, itmay be difficult to count cloudy or coloured sam-ples. Furthermore, random quenching can reducethe number of photons generated per radioactivedecay. Therefore, it is possible to get a broadeningof the alpha energy spectra obtained through liquidscintillation. It is likely that the liquid scintillationspectra will be subject to a Gaussian broadeningrather than the distortion exhibited when the layerof an active material on a disk is too thick.

Geiger-Muller (G-M) counters, gas proportional,or scintillation counters with heavy shielding andappropriate electronics for data collection and anal-ysis are used for beta spectrometry, as in tritiumand radiocarbon measurements.

Gamma (γ ) spectrometry has been by far themost widely used method to measure the radioac-tivity. It is a powerful and useful measuring tech-nique to analyse radioisotopes in various kinds ofradioactive samples, because gamma rays exhibitdiscrete and unique energies that are intrinsic toeach radionuclide. Normally, a thallium-activatedsodium iodide [NaI (Tl)] scintillation detector ora solid-state germanium [Ge] detector is used todetermine the energy(ies) of the emitted ionizingradiation. The Ge semiconductor detector has a far

better energy resolution capability compared to theNaI (Tl) detector; hence most present-day gamma-spectrometry systems (used for radioactivity moni-toring, activation analysis, and research purposes)incorporate a Ge detector.

Stable isotopes are nuclides that do not undergoradioactive decay, even on geological timescales,though they may themselves be produced by thedecay of radioactive isotopes. Differences in iso-topic composition of a given element in differ-ent reservoirs in exchange with each other (e.g.components of the hydrologic cycle) arise becauseduring the process of exchange or phase changebetween different reservoirs (e.g. hydrologic pro-cesses), the heavier isotopes are somewhat sluggishcompared to their lighter counterparts and tend topreferentially stay with the denser phase. Such dif-ferences manifest themselves as isotope fraction-ation effects between reservoirs. The degree ofisotope fractionation thus is a measure of the ex-tent to which the hydrologic processes proceed.Isotopic compositions are normally expressed inδ–notation, as deviations of heavy to light isotopicratios relative to an international standard of knowncomposition, expressed as parts per thousand and(denoted as �), or per million. The δ values arecalculated as:

δ(in �) = (Rx/Rs − 1) × 1000 (7.2)

where Rx and Rs denote the ratio of heavy to lightisotope (e.g. 13C/12C, 18O/16O, or D/H) in the sam-ple and the standard, respectively.

7.2 Hydrologic tracers

Water is a universal solvent, which dissolves almosteverything that comes into contact with it, includ-ing atmospheric gases. Any substance that can beused for tracking water movement through a givenenvironment can be termed a hydrologic tracer.An ideal tracer behaves in the system exactly asthe traced material, at least as far as the parame-ters of interest are concerned. However, it shouldhave at least one characteristic property that dis-tinguishes it from the traced material. It should beconservative, that is, it should not have sourcesor sinks (decay, sorption, or precipitation) in thesystem. In practice, a substance which has known

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Fig. 7.1 Commonly used hydrologic tracers and theircharacteristics.

sources or sinks can also be regarded as a suitabletracer, if these can be properly accounted for, or iftheir influence is negligible in terms of the desiredaccuracy.

Hydrologists make use of both environmen-tal tracers (natural or anthropogenic compoundspresent in the environment) and injected tracers(e.g. dyes or chloride) that are introduced into awater body externally for studying its behaviour ina system. This basic grouping of commonly usedhydrologic tracers, based on their mode of intro-duction into a hydrologic system along with theirhalf-life (in case of radioactive isotopic tracers), isgiven in Fig. 7.1. Various hydrologic applications ofcommonly used elemental and isotopic tracers arelisted in Table 7.1.

7.2.1 Artificial tracers

Injected or artificially introduced tracers are usedto determine the direction and rate of groundwa-ter movement, the rate of river flow, and mixingcharacteristics of various water bodies.

In the case of an artificially injected tracer, theinput function is a sharp, well defined pulse with re-spect to time and location, mostly a delta-function.The output function is the measured concentration-time distribution of the tracer at the measuring orsampling location(s).

Some of the simple injected tracers are dyes andsalts (e.g. Rhodamine or common salt). These canbe used to measure the residence time of watersin a system. A known amount and concentrationof tracer can be added to a system and changesin water- fluorescence, electrical conductivity, orwater chemistry can be monitored at a given loca-tion by employing appropriate analytical methods.These methods may also be employed for ground-water tracing, but it should be noted that the sub-surface movement of water can also introduce saltsor the tracer can be adsorbed onto the aquifer ma-trix. Knowledge of the bedrock geology of thestudy site can, therefore, be helpful. While usingion chemistry to measure salt movement through asystem, it is important to ensure the conservative

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Table 7.1 Common hydrologic applications of various elemental and isotopic tracers.

Tracer Common hydrologic application

2H Tracing precipitation sources and estimating evaporation rates3H, 3He Dating young groundwaters4He Dating old groundwaters, engineering hydrology14C Groundwater dating and tracing of a variety of hydrologic processes15N, 34S Tracing the nitrogen source for surface- and groundwater, identifying source(s) of pollution18O Determining precipitation sources and evaporation rates. Can also record palaeoclimatic and

palaeohydrologic informationHe, Ne, Ar, Kr, Xe Estimate palaeo-recharge temperature32Si Tracing/estimating the groundwater recharge36Cl Dating very old groundwaters (∼1 Ma)Fe, Se Ascertaining redox condition of a given water body86Kr Dating recent groundwater recharge129I Constraining the groundwater age estimates and tracing groundwater flowsOs Heavy metal pollution tracing in the environment210Pb Identifying source(s) of lead pollution and determination of sedimentation rates222Rn Estimating groundwater discharge into surface water bodies and groundwater dating137Cs Estimating erosion and sedimentation rates

nature of the salt tracer, that is, the ion measuredat the outlet of the system is not prone to biologi-cal uptake or reactions with water or sediment thatwould cause it to drop out of the dissolved state.Chloride represents a useful tracer since it is rela-tively inert and not used by biota to any significantdegree. Nitrate is a poor tracer as it may be takenup by biota before it leaves the system.

In groundwater applications, hydrologists injecta tracer into a well (the injection well), and mon-itor nearby wells for the arrival of the tracer thatindicates movement of the groundwater from theinjection well to the monitoring/sampling well,thereby enabling determination of direction andrate of groundwater flow velocity. In rivers, mea-surement of the rate at which a river carries anintroduced tracer enables estimation of river dis-charge. In practice, an injected tracer substanceshould possess good solubility in water, physicaland chemical stability, and high resistance againstadsorption onto the surrounding substratum or thesuspended sediments. In addition, a tracer shouldbe detectable at low levels of concentration andshould be independent of temperature and pH ofwater. Furthermore, its natural background con-centration should be as low as possible. In addi-tion, questions such as whether the substance is

eco-friendly, available in the desired quantity, andis cost-effective, also play a role in its choice as anappropriate tracer.

Depending on the method of analysis, artificialtracers can be classified into four broad groups –chemical, radioactive, activable, and particulatetracers. Chemical tracers may be simple ionic com-pounds such as NaCl whose concentration can bedetermined by measuring conductivity or by ionselective electrodes, or metallic compounds suchas EDTA, which can be measured by atomic ab-sorption spectrometry. Although the number ofdifferent ions that may be used is large, cationsare usually lost from water by exchange. Organicdyes are frequently used but their major disadvan-tage is that they are not fully conservative and tendto be lost from water by adsorption, particularly onclays. Analysis is generally done by filter fluorome-ters or colorimeters, which are robust enough forfield use. Radioactive tracers are used extensivelyin water pollution studies because of high sensi-tivity of their detection that can be achieved and,with γ emitting tracers, the ability to be measuredaccurately in situ in the field. These tracers maybe obtained as labelled compounds such as triti-ated water (HTO) or from a soluble radioactive saltsuch as K82Br, which has been shown to be a very

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good water tracer with negligible adsorptive loss.The short half-life of 82Br (35.4 h) makes it highlyattractive for tracer tests extending over only a fewdays. Activable tracers are elements that are stablewhen used in field tests but are made radioactive foranalysis. A number of substances, notably the rareearths, may be used but their cumbersome analysisprocedure has not made them particularly attrac-tive for water tracing, although activation analysisis used for identifying pollutants. The same maybe said for particulate tracers. These may be plantspores or micro-organisms such as bacteria or bac-teriophages. An exception may be in the tracing ofsewage effluents in coastal waters, where the strainSerratia indica is used. Samples are collected, cul-tivated, and the organisms counted by microscopicexamination. Radioactive particulate tracers, onthe other hand, have many advantages of tracingthe movement of solids or salts through water, forexample, in sewage. Treated sewage sludge may becoated with a gold or silver amine complex to pro-vide a convenient tracer. However, surface labelledmaterials do not contain the tracer in proportion totheir mass but to their surface area, so that quan-titative errors may arise if the size distribution ofparticles in the sample is not taken into account.Artificial glass containing radioactive elements suchas 46Sc, powdered to match the size of the grainsin the sediment or silt being traced, however, doesnot have this disadvantage.

In recent years, gaseous tracer methods arealso being used for various applications. These in-clude dissolved inert gases used both as geochem-ically conservative tracers in groundwater systemsproviding structural information, flow paths, tran-sit times, and physical transport properties (Agar-wal et al. 2006; Kipfer et al. 2002; McNeill et al2001), as well as non-conservative, bulk partition-ing agents to determine re-aeration coefficients insurface streams (Mackinnon et al. 2002; Murphyet al. 2001). Gaseous tracers are also used for char-acterizing the presence and extent of non-aqueousphases in subsurface groundwater systems, for ex-ample, NAPLs at contaminated land sites (Mohrloket al. 2002). Noble gases as tracers are being par-ticularly investigated because of their low naturalbackground levels, high sensitivity of determina-tion (by GC-MS), and lack of any taste, odour,

colour, and toxicity problems. These propertiesrender noble gases as ‘environmentally-friendly’type of tracers to protect potable water (e.g. pub-lic) supplies under investigation. In addition, theydo not influence the intrinsic reactive processes oc-curring in the system being traced. For a detaileddescription of various applications and techniquesof using artificial tracers in hydrologic studies, ref-erence is made to Divine and McDonnell (2005)and Eilon et al. (1995).

7.2.2 Environmental tracers

Environmental tracers, of natural as well as an-thropogenic origin, are present in the environmentand there is no control in terms of their amount,location, and time of introduction into the envi-ronment but are nevertheless useful for hydrologicinvestigations. Variations, within and/or across hy-drologic reservoirs, in the composition of a largenumber of substances, elements, or their isotopes(Fig. 7.1) that dissolve in water or constitute thewater molecule itself, namely 2H (or D), 3H (or T )in the case of hydrogen, and 17O and 18O in case ofoxygen, are also used for hydrologic tracing. Thebroad objective is to obtain information on the hy-drologic system under investigation in terms of itscomponent reservoirs and the degree and rate ofexchange or mixing across the reservoir bound-aries or within the system itself. The informationon rates of hydrologic processes is obtained eitherthrough real-time monitoring or by making use ofradioactive isotopes, which due to their character-istic radioactive decay rates provide a measure oftime – just like a clock.

While using environmental tracers, the inputfunction depends on the temporal and spatial distri-bution of the tracer concentration in precipitationand on the recharge rate into the unsaturated zone,as well as on the physico-chemical and microbio-logical conditions during the tracer transport to thewater table. Therefore, determination of the inputfunction is one of the main problems in ascertainingthe validity of measurements of an environmentaltracer. The output function is the concentration-time distribution of the tracer at the measuring orsampling point(s).

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Table 7.2 Cosmogenic nuclide production rates and their inventories for radioisotopes of half-lives of more than 2 weeks.Based on Lal and Peters (1967).

Half- life (years) Production rate (cm2 sec)−1 Integrated inventory Globalunless stated inventory

Nuclide otherwise Troposphere Total (dpm/cm2) (atoms/cm2) (gm)

10Be 1.5 × 106 1.5 × 10−2 4.6 × 10−2 2.70 3.07 × 1012 2.6 × 108

26Al 7.1 × 105 3.8 × 10−5 1.4 × 10−4 8.40 × 10−3 4.52 × 109 1.0 × 106

36Cl 3.1 × 105 4.0 × 10−4 1.1x10−3 6.60 × 10−2 1.50 × 1010 4.6 × 106

81Kr 2.3 × 105 5.2 × 10−7 1.18 × 10−2 7.10 × 10−5 1.24 × 107 8.5 × 103

14C 5730 1.10 2.50 1.50 × 102 6.52 × 1011 7.7 × 107

39Ar 268 4.3 × 10−3 1.29 × 10−2 7.75 × 10−1 1.58 × 108 5.2 × 104

32Si ∼150 5.4 × 10−5 1.60 × 10−4 9.60 × 10−3 1.09 × 106 3.0 × 102

3H 12.3 8.4 × 10−2 2.50 × 10−1 1.50 × 101 1.40 × 108 3.6 × 103

22Na 2.6 2.4 × 10−5 8.60 × 10−5 5.16 × 10−3 1.02 × 104 1.935S 87 days 4.9 × 10−4 1.40 × 10−3 8.40 × 10−2 1.52 × 104 4.57Be 53 days 2.7 × 10−2 8.10 × 10−2 4.86 5.35 × 105 3.2 × 101

37Ar 35 days 2.8 × 10−4 8.30 × 10−4 4.98 × 10−2 3.62 × 103 1.133P 25.3 days 2.2 × 10−4 6.80 × 10−4 4.08 × 10−2 2.14 × 103 6.0 × 10−1

32P 14.3 days 2.7 × 10−4 8.10 × 10−4 4.86 × 10−2 1.44 × 103 3.9 × 10−1

A special class of environmental radioisotopes isof cosmogenic origin. These isotopes are producednaturally by cosmic radiation in the Earth’s atmo-sphere. Cosmic rays produce nine radio-nuclides ofhalf-lives ranging between 10 years and 1.5 Ma, and5 radio-nuclides, with half-lives ranging between2 weeks and 1 year (Table 7.2). These have beenused as tracers for measuring groundwater move-ment over time-scales ranging from a few weeksto millions of years. The various radio-nuclideslisted in Table 7.2 have been extensively studiedin the atmosphere, in wet precipitation, and inthe hydrosphere, and in some cases, for example10Be, in sediments (Lal 1999; Lal and Peters 1967).Their dispersion in different terrestrial reservoirsis controlled principally by two factors: theirchemical properties and half-lives (Lal and Peters1967). In the case of long-lived isotopes, it is nowpossible to measure their concentration using theAccelerator Mass Spectrometry (AMS), usuallyat levels of more than 106 atoms in a sample.AMS has been successfully used to measure manyisotopes for environment/hydrologic research.AMS detects charged ions that have been separatedbased on their mass. The main advantages of thistechnique are high precision, low detection limits,

and requirement of small quantities of sample.However, applicability of AMS is also limited bythe relative quantities required for the isotopes ofinterest (e.g. 32Si in silica).

Depending on the application, hydrologic tracerscan be classified into two broad categories, namelystudies involving: (i) movement of water, includ-ing its source identification, direction, and rate ofmovement and age; and (ii) hydrologic processes,including exchange across various reservoirs. In-jected tracers are mostly used for studying move-ment of water, whereas environmental tracers areused for both types of investigations.

Use of isotopes for transport, retardation, andresidence time distribution in groundwater hydrol-ogy is already well established (Mook 2000–2001).It is only during the last two decades that isotopetechniques have also been used for studying thehydro-geochemical response in catchment hydrol-ogy (Kendall and McDonnell 1998). Typically, iso-topes are used to: (i) determine the mechanismsand processes involved in generation of stream flowfrom various types of catchments; (ii) estimate res-idence time distribution of water within a catch-ment; (iii) determine the origin of stream flow com-ponents; (iv) calibrate or validate catchment stream

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flow models; (v) predict catchment responseto a given storm; and (vi) estimate hydrologicparameters of a catchment.

In the subsequent sections, the focus is onsome basic concepts related to environmentalisotope tracer hydrology for groundwater studies.Appropriate theoretical background informationon some individual tracer methods that have beenapplied in the North Gujarat regional aquifersystem is also given.

7.3 Tracers and groundwater movement

7.3.1 Groundwater age

Groundwater age is generally considered as the av-erage travel time for a water parcel from either thesurface or from the water table (point of recharge)to a given point in an aquifer. A schematic illus-tration of how a groundwater parcel ages as itflows along a streamline is shown in Fig. 7.2a.Groundwater dating (i.e. age estimation) involvesestimation of the groundwater age by one or moreavailable techniques. The term ‘residence time’ isoften used synonymously with ‘age’. Hence, theresidence time of groundwater is defined as theaverage travel time between the point of rechargeand the point of discharge, for example, to a riveror a lake or to any monitoring point in the ground-water zone. The tracer age estimate normally givesthe average age of a water sample. This is a goodapproximation in cases where the flow system is

simple, and can be approximated by a piston flowmodel (implying insignificant mixing and disper-sion during the course of flow). However, wheresignificant mixing and dispersion occur, for exam-ple, in long screens in water supply wells or ingroundwater bodies with a significant volume oflow permeability units (‘stagnant zones’) the esti-mated tracer model age may either underestimateor overestimate the actual mean age of the waterparcel (Bethke and Johnson 2002; Weissmann et al.2002). A sound knowledge of the geological settingand physical and chemical processes occurring inaquifers is, therefore, important for a proper in-terpretation and application of the environmentaltracers and estimated groundwater ages.

7.3.1.1 Groundwater age estimation

There are basically three different ways of esti-mating groundwater age at a groundwater wellor monitoring point: (1) by environmental tracers(Agarwal et al. 2006; Gupta 2001; Plummer et al.1993); (2) by groundwater flow modelling (Enges-gaard and Molson 1998; Gupta 2001); and (3) bya combination of both (Bauer et al. 2001; Trold-borg 2004). Approximate range (in years) of dat-ing employing commonly-used tracers is shown inFig. 7.2b.

It is usual to distinguish between young (mod-ern) groundwater and old groundwater. Younggroundwater is considered to be groundwaterrecharged to the aquifers since 1950 AD, whilethat recharged before 1950 is considered to be old

WaterTable Potentiometric

surface

Aquiclude

Confined Aquifer

Bedrock or next aquifer layer

(a)

Met

ho

d

104 Years101 102 103 105 106

3 3H/ He85Kr, CFC, SF6

39Ar14C

4 81He, Kr

(b)

Fig. 7.2 (a) Aging of groundwater along a flow line inan aquifer; (b) most commonly used environmentaltracers for groundwater age estimation and theiruseful dating ranges.

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36Cl3H

85Kr

CFC-12

SFx1

006

CFC-11

CFC-11314C

6000

4000

2000

01940 1960 1980 2000

600

400

200

0

5000

3000

1000

Year

1200

800

400

CF

C a

nd

SF

(p

ptv

), C

(p

mc)

6

14

Cl f

allo

ut

(ato

ms

m s

)-2

-1

Kr

(mB

q m

)85

-3

H (

TU

)3

Fig. 7.3 Concentration variation of severalenvironmental tracers in the atmosphereduring the period 1940–2000. These tracersare applied either as relative or absolutegroundwater dating tools. Redrawn from Clarkand Fritz (1997) and Hinsby et al. (2001). ©Geological Society of London.

groundwater (Cook and Bohlke 2000; Plummeret al. 1993).

7.3.1.1.1 Dating young groundwaters

During the past decade, several new environmen-tal tracers for dating of young groundwaters havebeen introduced. Especially tracers such as tritium(3H), CFCs, SF6, and 85Kr) are being increasingapplied for identification of modern water com-ponents possibly containing contaminants, and forgroundwater dating (Kipfer et al. 2002; Manninget al. 2005). Fig. 7.3 shows the varying atmo-spheric concentrations of the most common trac-ers for groundwater dating. The radionuclides 36Cl,3H, and 14C were introduced into the atmosphereby nuclear test explosions in the 1950s and early1960s, while 85Kr escapes into the atmosphere bythe processing of the fuel rods from nuclear powerplants. CFCs and SF6 are gases used in the industry,although the use of CFCs is now banned due totheir ozone depletion property. The tracers 85Kr,CFCs, and SF6 may be used for estimation of ab-solute ages, that is, under optimal conditions theycan estimate the year of recharge of a given wa-ter sample or the average residence time (i.e. age)of groundwater. The tracers 36Cl, 14C, and 3H arein this context considered as event markers (Cookand Bohlke 2000; Plummer et al. 1993), and mayonly be used for identification of human impactsor a relative age (e.g. recharged after 1960, 1990,etc.). However, 3H can be used together with itsdaughter nuclide 3He to estimate absolute ground-

water ages (Manning et al. 2005; Solomon andCook 2000).

7.3.1.1.2 Dating old groundwaters

Tracers, such as 39Ar,14C, 4He, and 81Kr, are usedfor dating groundwaters of pre-industrial age up toa million years old or more, in combination withgroundwater flow modelling (Agarwal et al. 2006;Lehmann and Purtschert 1997). In small catch-ments, with short distances between recharge anddischarge points, the groundwater used for drink-ing water supply is generally less than 1000 yearsold. However, in regional aquifer systems in largesedimentary basins, for example, Canada and Aus-tralia (Cresswell et al. 1999a; Frohlich et al. 1991;Lehmann and Purtschert 1997), France (Marty et al.1993), and India (Agarwal et al. 2006), groundwa-ter may be very old (>100 000 years). These areoften referred to as ‘very old groundwaters’ anddefined as groundwater without measurable 14C(Frohlich et al. 1991).

In the following, some of the commonly usedisotopic tracers used for groundwater dating arediscussed in some detail in terms of their produc-tion, introduction into the hydrologic cycle, mea-surement, and data interpretation.

7.3.1.2 Tritium

Hydrogen has three isotopes, two stable (1H and2H), and one radioactive (3H). The stable isotopesof hydrogen are considered together with stable

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isotopes of oxygen in Section 7.4. The radioac-tive isotope tritium (3H) can be used for datingvery young groundwaters (younger than 50 years).Natural tritium is produced in the stratosphereby interaction of the cosmic ray produced neu-trons with 14N according to the nuclear reaction147 N + 1

0n → 126C + 3

1 H . It combines with oxygento produce tritiated water (H3HO), which subse-quently enters the hydrologic cycle. Tritium de-cays to a rare, stable isotope of helium (3He) bybeta (β) emission with a half-life of 12.32 a (a de-notes for annum = year) (Lucas and Unterweger2000). Natural production of tritium in the atmo-sphere is very low. Lithogenic tritium is producedby bombardment of the lithium present in rocksby neutrons produced during the spontaneous fis-sion of uranium and thorium. This production islimited by the amount of lithium present in rocks.Tritium can also be produced from 10B throughneutron capture. In most cases, lithogenic produc-tion is negligible compared to other sources. Thelithogenic tritium enters the groundwater directly.The natural production of tritium has been supple-mented by anthropogenic production. Beginningin the 1950s, large amounts were produced fromthe atmospheric testing of thermonuclear bombs.Atmospheric concentrations of tritium decreasedafter 1963 (Fig. 7.3) as a result of the treaty banningabove-ground testing. However, anthropogenic tri-tium continues to be released from nuclear powerplants as a result of which present-day concentra-tions of tritium in the atmosphere have not re-turned to the pre-1950 natural concentrations. Thetritium levels , however, continue to gradually de-crease as it undergoes radioactive decay. All en-vironmental tritium, whether of cosmogenic or an-thropogenic origin, is rapidly incorporated into wa-ter molecules and becomes a part of the meteoricprecipitation to enter the hydrologic cycle.

Tritium concentrations are represented as abso-lute concentrations in tritium units (TU) and so noreference standard is required. One tritium unit isequal to one molecule of 3H per 1018 molecules of1H and has an activity of 0.118 Bq kg−1 (3.19 pCikg−1).

The large pulse of tritium that entered the hy-drologic cycle in the 1960s (Fig. 7.3) can be usedto establish the age of groundwater recharge re-

cently. High levels of tritium (>30 TU) indicatewater that was recharged during the late 1950sor early 1960s; moderate concentrations indicatemodern recharge; levels close to detection limit(∼1 TU) are likely to indicate sub-modern orpalaeo-groundwaters that have mixed with shal-low modern groundwaters (Clark and Fritz 1997).Bomb-produced tritium has also been used to studyrecharge of groundwater by tracing the movementof soil moisture through the vadose zone (Sukhijaand Rama 1973) and in shallow water table aquifers(Gupta 1983). Artificially injected tritium has alsobeen used for tracing soil moisture through thevadose zone (Datta et al. 1979). Environmental tri-tium can be used as a tracer in dating young ground-waters to help determine flow rates and directions,mean residence times, and hydraulic parameterssuch as conductivity, and can also be helpful in ob-serving preferential flow paths and in investigatingthe mixing of waters from different sources. Its use,however, is somewhat limited by a number of fac-tors, including uneven global distribution and localvariations due to continued nuclear releases. Someapproaches that may be used to counter the prob-lems using 3H in dating groundwaters include useof time series analysis to monitor the bomb spikefor 3H in an aquifer, to provide an indication of itsmean residence time.

Groundwater can also be dated quantitatively us-ing tritium and its daughter, 3He. Age is determinedby (Tolstikhin and Kamenskiy 1969):

τ = 1

λ. ln

(1 +

3 Hetri

3 H

)(7.3)

where λ is the decay constant of tritium (= ln2/12.32 = 0.05626 a−1); τ is the time since iso-lation of groundwater from the point of its contactwith the atmosphere and is the 3H -3He age; and3Hetri/3H is the concentration ratio of the two iso-topes, expressed in TU .

Dating by the 3H -3He method also presents prob-lems, since the total 3He in groundwater comesfrom a variety of sources: the atmosphere, 3H de-cay, subsurface nuclear reactions, and the Earth’smantle (Kipfer et al. 2002). The measured con-centration of 3He must be corrected for thesecontributing sources. 3He is also not a routinelysampled or measured isotope. Other concerns are

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fractionation of 3He if a gas phase is present andthe fact that the solubility of He is temperature de-pendent (Weiss 1971).

Tritium is measured by counting β decay eventsin a liquid scintillation counter (LSC). A 10 ml sam-ple aliquot is mixed with the scintillation com-pound that releases a photon when struck by aβ particle. Photomultiplier tubes in the counterconvert the photons to electrical pulses that arecounted over a period of several hours (muchsmaller counting time is required when using arti-ficial tritium due to its high concentration). Resultsare calculated by comparing the counts with thoseof calibrated standards and blanks. Increased pre-cision is achieved through concentration by elec-trolytic enrichment of 3H in water before counting,or by conversion to a suitable gas (CH4 or C3H8)for gas proportional counting.

7.3.1.3 Radiocarbon

Carbon has three isotopes, two stable (12C and 13C)and one radioactive (14C). Natural variation of thetwo stable isotopes of carbon can be useful for un-derstanding carbon sources and the carbon cycle inecosystems. W.F. Libby was awarded Nobel Prizein 1960 for his work concerning development of14C as a tool for archaeological dating. The half-lifeof 14C (= 5730 a) makes it useful for Late Quater-nary chronology. Even now it is used extensivelyto date groundwater (up to ∼40 ka), as well as fortracing hydrologic processes, such as groundwaterflow and ocean circulation.

Radiocarbon is formed in two different ways.Cosmogenically, 14C is produced by interaction ofcosmic ray produced neutrons with 14N accordingto the nuclear reaction14

7 N + 10n → 14

6C + 11 p . Sim-

ilar to tritium, a considerable amount of 14C wasadded to the atmosphere anthropogenically due tothe nuclear bomb tests in the 1950s and the useof nuclear power. Whichever way formed, 14C israpidly oxidized to 14CO2, which enters the Earth’splant and animal life cycle through photosynthesisand the food chain. The rapidity of the dispersalof 14C into the atmosphere has been demonstratedby measurements of radioactive carbon producedfrom thermonuclear bomb testing. 14C also entersthe Earth’s oceans through exchange across the

ocean surface–atmosphere boundary and as dis-solved carbonate through terrestrial water influx.Plants and animals that utilize carbon in the biolog-ical food chain take up 14C during their life times.They exist in equilibrium with 14C production andits radioactive decay rates in the atmosphere. Thus,the 14C concentration in active carbon pools in ex-change with the atmosphere stays the same over aperiod of time. This is referred to as ‘modern car-bon’ 14C concentration and corresponds to A0 inEqn 7.1. The activity of modern carbon is definedas 95% of the 14C activity in 1950 of the NBS ox-alic acid standard. This is close to the activity ofwood grown in 1890 in a fossil-CO2-free environ-ment and equals 13.56 dpm g−1 carbon. All 14Cmeasurements are referred to as percent moderncarbon (pmC). As soon as a plant or animal dies,it ceases the metabolic function of carbon uptake;there is no replenishment of radioactive carbon butradioactive decay continues.

The solid carbon method for 14C isotope count-ing, originally developed by Libby and his collab-orators, was replaced by gas counting methods inthe 1950s. Liquid scintillation counting, utilizingbenzene, acetylene, ethanol, methanol, etc., wasdeveloped around the same time. Today, the vastmajority of radiocarbon laboratories utilize thesetwo methods for radiocarbon dating. A recent de-velopment of major interest is the development ofthe Accelerator Mass Spectrometry (AMS) method,in which all the 14C atoms can be counted directly,rather than only those decaying during the count-ing interval allotted for each analysis, as in gas orliquid scintillation counting methods. The main ad-vantages of the AMS technique are high precisionand low detection limits.

7.3.1.3.1 Radiocarbon dating of groundwater

Radiocarbon dating of groundwater is based onmeasuring the loss of amount of parent radionu-clide (14C) in a given sample. This assumes twokey features of the system. The first is that the ini-tial concentration of the parent is known and hasremained constant in the past. The second is thatthe system is closed to subsequent gains or losses ofthe parent 14C, except through radioactive decay.But, the very process of incorporating radiocarbon

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into groundwater by dissolution of plant root respi-ration and decay-derived carbon dioxide (with 100pmC) in the presence of old/radioactively dead (∼0pmC) lime/dolomite in the soil zone, strongly dilutethe initial 14C activity in total dissolved inorganiccarbon (TDIC), according to the principal chemicalreactions:

CaCO3 + H2O + CO2 ⇔ Ca2+ + 2HCO−3 (7.4)

CaMg(CO3)2 + 2H2O + 2CO2 ⇔ Ca2+

+Mg2+ + 4HC O−3 (7.5)

This causes an artificial ‘aging’ of groundwater bydilution of 14C when using Eqn 7.1. Subsequentevolution of the carbonate system can also lead tosome changes in the 14C activity of groundwater.Unravelling the relevant processes and distinguish-ing 14C decay from 14C dilution is an engaging geo-chemical problem.

There are several models that aim to estimatethe contribution of soil carbonates to the TDIC andestimate the applicable value of A0. This is doneeither through a stoichiometric approach for thevarious chemical reactions involving carbon or byestimating dilution of active carbon using an iso-tope mixing approach based on the 13C content ofeach species involved, or a combination of the twoapproaches. Various methods for estimating A0 canbe found in Mook (1976) and Fontes and Garnier(1979). The error due to incorrect estimation of A0,however, is < t1/2 of 14C, except in a special caseof carbonate aquifers where continuous exchangebetween TDIC and the aquifer matrix may reduceA0 to <50 pmC. Since most of the chemical and iso-tope exchange occurs in the unsaturated soil zoneduring the process of groundwater recharge, andbetween TDIC and the soil CO2, the A0 in severalgroundwaters has been found to be 85 ± 5 pmC(Vogel 1967, 1970).

In the North Gujarat-Cambay study reported sub-sequently (Chapter 13), the theoretical value of A0

(after equilibrium between soil CO2, soil carbon-ate (at 14C = 0 pmC; δ13C = 0 �), and infiltratingwater) is estimated using the following equation(Munnich 1957, 1968):

A0 = δ13CTDIC

δ13Csoil − ε100 (7.6)

where δ13CTDIC is the δ13C value of the groundwaterTDIC; δ13Csoil is the δ13C of soil CO2 (∼ –22 �); andε is equilibrium fractionation between the soil CO2

and the TDIC of groundwater (∼ –9 �). The δ13Cvalues are computed using Eqn 7.2 with Pee DeeBelemnite (PDB) limestone as the standard refer-ence material. The model of Eqn 7.6 is used takinginto account that application of any other modelwould give radiocarbon ages differing by < ± 2ka. Also because in regional aquifers the differencein groundwater ages between any two locations,after the confinement of the groundwater in theaquifer becomes effective, is virtually independentof the applicable value of A0.

For 14C dating, about 100 litres of groundwateris piped directly into a collapsible high-density PVCbag through a narrow opening. The PVC bag is keptin the folded condition in a stand designed specif-ically for this purpose and assembled from its pre-fabricated parts at the site (Fig. 7.4a). The PVC bagunfolds only when the groundwater fills it. Beforepiping in the groundwater, a few pellets of NaOH(∼10g) are added to the PVC bag to raise the solu-tion pH to >10 for immobilizing the dissolved CO2

in the form of CO32− and its eventual precipitation

as barium carbonate. At pH >10.3 most of the dis-solved CO2 is in the form of CO3

2−, since at thispH, activity of HCO3

− drops and activity of CO32−

rises rapidly (Drever 1997).Depending upon the alkalinity and sulphate con-

centration of groundwater samples (measured inthe field), a pre-determined amount of barium chlo-ride (BaCl2) is then added to the ‘groundwater-NaOH’ solution to ensure complete precipitationof dissolved carbonates (Clark and Fritz 1997). Fol-lowing vigorous stirring, the mixture is left undis-turbed for precipitates to settle in the conical baseof the PVC bag (Fig. 7.4a). It usually takes 4 to 5hours for the precipitates to settle. After decant-ing the supernatant liquid, precipitates are trans-ferred to glass bottles (Fig. 7.4b) and sealed. Care istaken to prevent/minimize sample exchange withatmospheric CO2 during the entire extraction pro-cedure.

On reacting with orthophosphoric acid, the bar-ium carbonate precipitate liberates CO2. The lib-erated CO2 is first converted to acetylene andthen trimerized into benzene (C6H6) and the 14C

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Fig. 7.4 (a) Photograph of a speciallydesigned foldable stand with a conicalaluminium base, which holds a high densityPVC bag filled with 100 litres of watersample. The supernatant water is decantedby piercing the bag after the carbonateprecipitates settle in the conical base of thebag; (b) Carbonate precipitates aretransferred from the PVC bag into a 1.2-litresoda-lime glass bottle without exposure tothe atmosphere. See also Plate 7.4.

activity in the benzene counted by liquid scintil-lation spectroscopy (Gupta and Polach 1985). Asmall aliquot of the sample CO2 is sealed in glassampoules for δ13C measurement, using a stable iso-tope ratio mass-spectrometer (SIRM).

When using AMS for 14C measurement, onlyabout a litre of water sample sealed in a glass bottleis collected in the field and all subsequent process-ing of the sample is carried out in the laboratory.

7.3.1.4 Silicon-32

Silicon-32 (32Si) is a cosmogenic isotope producedin the atmosphere by spallation of Argon-40. With ahalf-life of ∼150 years, 32Si is ideally suited to pro-vide chronology in the range 50–1000 years. Be-cause the nuclide is produced in the atmosphere,the highest activity per unit volume of water isfound in fresh precipitation. The concentration insoil is several orders of magnitude higher. This isdue to accumulation of 32Si from exchange be-tween dissolved silica in the infiltrating water andsilica adsorbed onto the soil sediments.

Detection of natural 32Si is, however, difficultdue to the extremely low levels of concentrationand isotopic ratios. When using AMS, for measure-ment of silicon, the ratio of 32Si /28Si must exceed10−15 (Morgenstern et al. 2000). It is possible to sat-isfy this condition for precipitation samples. How-ever, for groundwater and soil samples where 28Si

is abundant, the ratio is �10−15 (Morgenstern et al.2000). Therefore, scintillation counting is the pre-ferred method for analysing 32Si in groundwatersand soils.

In order to determine the activity of 32Si by de-cay counting, the activity of the daughter product,32P, is measured. 32P, rather than 32Si, is selectedfor analysis because of its shorter half-life (14.3 dvs. ∼150 a of 32Si) and the higher energy of itsbeta decay (Emax = 1.7 MeV vs. 0.22 MeV of 32Si).To relate the activities of the parent and daughter,a secular equilibrium must be achieved (Fig. 7.5).This occurs when the ratio of the activity of the par-ent and the daughter remains constant with time.At this point, the ratio of the isotope abundances isequal to the ratio of their decay constants (λ) thatare known. Therefore, if the activity of the daughter(A32P) is measured when secular equilibrium hasbeen established, the activity of the parent (A32Si)can be calculated from:

A32Si = A32 P ∗(λ32 P/λ32Si) (7.7)

Elaborate chemical processing of a water samplefor 32Si measurement involves several steps, suchas: (i) addition of silica carrier; (ii) co-precipitationof ferric hydroxide and silica; (iii) purification ofprecipitated silica; (iv) allowing sufficient timefor 32Si to come into secular equilibrium with32P; (v) addition of carrier phosphate; (vi) precip-itation of ammonium molybdophosphate (AMP);

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Fig. 7.5 (a) Activity of 32Si in various waters and soil; (b) Activity of 32Si in a sample is measured by counting decay events ofthe daughter product 32P after about two months when secular equilibrium has been established between the activities ofthe parent and daughter isotopes.

(vii) precipitation of ammonium magnesium phos-phate; (viii) ignition of the phosphate at 1000◦C;(ix) separation of phosphorus from silica; and fi-nally (x) decay counting of 32P.

32Si is has been found as a useful tracer for thestudy of ocean circulation (Lal et al. 1976), studyof atmospheric circulation involving exchange pro-cesses between stratosphere and troposphere (Lal1999), understanding groundwater flow (Guptaet al. 1981; Nijampurkar et al. 1966), and datingof marine siliceous biota (Brzezinski et al. 2003).

7.4 Stable isotopes of oxygen and hydrogen

Amongst various isotopes used as tracers in hydrol-ogy, stable isotopes of oxygen (18O) and hydrogen(2H or D) are the most important. Being an integralpart of the water molecule, these are ideally suitedto trace the movement of water throughout thehydrologic cycle. Some basic information on theseisotopes is given in Table 7.3.

In hydrologic parlance, the two isotopes are alsoreferred to as water isotopes. Importance and ap-plications of water isotopes to hydrologic studieshave been discussed at length and demonstrated inseveral parts of the world (Araguas-Araguas et al.1998; Clark and Fritz 1997; Dincer et al. 1974; Gatand Matsui 1991). Several Indian case studies have

also been reported over the last few decades (Bhat-tacharya et al. 2003, 1985; Das et al. 1988; Dattaet al. 1994, 1996, 1991; Deshpande et al. 2003; Kr-ishnamurthy and Bhattacharya 1991; Kumar et al.1982; Navada et al. 1993; Navada and Rao 1991;Shivanna et al. 2004; Sukhija et al. 1998; Yadav1997) and in recent years by Gupta and Deshpande(2003b, 2005a, b, c) and Gupta et al. (2005b).

Isotopic compositions are expressed inδ–notation calculated as in Eqn 7.2 with SMOW(Standard Mean Ocean Water; Craig, 1961b) orthe equivalent VSMOW (Gonfiantini 1978) as areference standard.

Isotopic fractionation occurs mainly by equilib-rium isotopic exchange reactions and kinetic pro-cesses. Equilibrium exchange reactions involve re-distribution of the isotopes between the productsand reactants (or the two phases during phase

Table 7.3 Natural abundance of oxygen and hydrogenisotopes (compiled from the CRC Handbook).

Name (Symbol) Oxygen (O) Hydrogen (H)

Atomic number 8 1Atomic mass 15.9994 g/mol 1.00794 g/mol

Stable isotopes 16O (99.76%) 1H (99.985%)(Naturalabundance)

⎧⎨⎩ 17O (0.038%)

18O (0.21%)

2H (0.015%)

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change) in contact with each other. As a ‘ruleof thumb’, amongst different phases of the samecompound (e.g. H2O), the denser the material, themore it tends to be enriched in the heavier isotopes(D and 18O).

In systems that are not in equilibrium, forwardand backward reaction rates are not identical, andisotope reactions become unidirectional, for exam-ple, when reaction products are physically isolatedfrom the reactants. Such reactions are called ki-netic. A third type of reaction, where fractiona-tion of isotopes occurs, is the diffusion of atomsor molecules across a concentration gradient. Thiscan be diffusion in another medium or diffusionof a gas into a vacuum. In this case, fractionationarises from the difference in diffusive velocities ofisotopic molecular species.

Isotope fractionation is expressed by a frac-tionation factor, α, which is the ratio of theisotope ratios for the reactant and the product(α = Rreactant/Rproduct). For example, in the water→vapour system, the fractionation factor is given by:

α18O(water→vapour) =(

18O/16O)

water(18O/16O

)vapour

(7.8)

Craig (1961b) showed that despite great complex-ity in different components of the hydrologic cycle,δ18O and δD in fresh waters correlate on a globalscale. Craig’s Global Meteoric Water Line (GMWL)

defines the relationship between δ18O and δD inglobal precipitation as:

δD = 8 × δ18O + 10 (�SMOW) (7.9)

This equation indicates that the isotopic compo-sition of meteoric waters behaves in a fairly pre-dictable manner. The GMWL is the average of manylocal or regional meteoric water lines, which maysomewhat differ from each other due to varying cli-matic and geographic parameters. A local meteoricwater line (LMWL) can differ from GMWL in bothslope as well as the intercept on the deuteriumaxis. Nonetheless, GMWL provides a reference forinterpreting hydrologic processes and provenanceof different water masses at a given place.

To improve precision of the Craig’s GMWL,Rozanski et al. (1993) compiled isotope data inprecipitation from 219 stations of the IAEA/WMOoperated Global Network for Isotopes in Precipita-tion (GNIP). This refined relationship between 18Oand D in global precipitation (Fig. 7.6) is given by:

δD = 8.17(±0.07) × δ18O

+11.27(±0.65) (�VSMOW) (7.10)

The evolution of δ18O and δD values of mete-oric waters begins with evaporation from oceans,where the rate of evaporation controls thewater−vapour exchange and hence the degree ofisotopic equilibrium. Higher rates of evaporationimpart a kinetic or non-equilibrium isotope effect

Fig. 7.6 The linear regression line between δ18O andδD of global precipitation samples. Data areweighted average annual mean values forprecipitation monitored at 219 stations of theIAEA/WMO global network. Redrawn from Rozanskiet al. (1993). © American Geophysical Union.

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Fig. 7.7 (a) Model for non-equilibrium evaporation over a water body. Relative fluxes of water across mixed water column↔ boundary layer ↔ mixed open air column through transition zone are shown by arrows. ‘Kinetic’ isotope fraction,namely, depletion of heavy isotopes in the overlying air column and enrichment in the water is caused by differences in therate of diffusion of 18O to 16O and 2H to 1H. (b) Because soil water taken up by plant roots is quantitatively released by leavesto the atmosphere, transpiration, unlike evaporation, is a non-fractionating process. Both (a) and (b) redrawn from Clark andFritz (1997). © Geological Society of London.

to the vapour. Kinetic effects are influenced by sur-face temperature, wind speed (shear at water sur-face), salinity, and most importantly humidity. Forlower values of humidity, evaporation becomes anincreasingly non-equilibrium process.

The most accepted model for non-equilibriumevaporation from a water body involves diffusionof water vapour across a hypothetical boundarylayer (bl) with a thickness of a couple of micronsabove the air–liquid water interface (Fig. 7.7a). Theboundary layer has virtually 100% water saturation.This layer is in isotopic equilibrium with the under-lying water column. Between the boundary layerand the mixed atmosphere above is a transitionzone through which water vapour is transported inboth directions by molecular diffusion. It is withinthe transition zone that non-equilibrium fractiona-tion arises as a result of diffusivity of 1H2

16O in airbeing greater than that of 2H1H16O or H2

18O. Theadditional isotopic enrichment (�ε) of evaporatingwater due to kinetic fractionation at relative humid-ity (h; fractional) is approximated by the follow-

ing two empirical relationships (Gonfiantini 1986)that ignore all other controlling factors excepthumidity:

�ε18Obl−v = 14.2 × (1 − h)� (7.11)

�ε2 Hbl−v = 12.5 × (1 − h)� (7.12)

It is seen from these equations that the relativemagnitude of kinetic fractionation for oxygen iso-topes is significantly higher than that for hydrogenisotopes. The total enrichment between the wa-ter column and open air is the sum of the enrich-ment factor for equilibrium water vapour exchange(εl→v) and the kinetic factor (�εbl-v). For 18O, thiswould be:

δ18Ol − δ18Ov = ε18Ol→bl + �ε18Obl→v (7.13)

Because the boundary layer is at 100% saturation,ε18Ol→bl corresponds to equilibrium fractionationin water→vapour system. This calculation repre-sents enrichment of water with respect to vapour.The depletion in vapour with respect to waterresults in negative isotopic enrichment. Under

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conditions of 100% relative humidity (h = 1), thevapour is in isotopic equilibrium with sea water(�ε18Obl-v = 0). When relative humidity is low (e.g.h = 0.5), the vapour is strongly depleted in 18Ocompared to D. The global atmospheric vapour isformed with an average relative humidity around85% (h = 0.85). This is why the Craig’s GMWL hasa deuterium intercept of 10 �.

Thus, formation of atmospheric vapour massesis a non-equilibrium process due to humidity beinglower than its saturation value. However, the re-verse process, that is, condensation to form cloudsand precipitation, takes place in an intimate mix-ture of vapour and water droplets with near sat-uration humidity so that equilibrium fractionationbetween vapour and water is easily achieved. Asa result, isotopic evolution of precipitation dur-ing rainout is largely controlled by temperature.Because of this, the slope of GMWL (equal to8) is largely in agreement with that given bythe ratio of equilibrium fractionation factors forD and 18O:

S ≈ 103lnαDv→l

103lnα18Ov→l= 8.2 at 25oC (7.14)

However, slopes of various LMWLs vary from 9.2to 8.0 for commonly encountered range of temper-ature between 0 and 30◦C. It is thus seen that therelationship between 18O and D in meteoric waters

arises from a combination of the non-equilibriumfractionation from the ocean surface (at ∼85% rela-tive humidity) and equilibrium condensation fromthe vapour mass. However, during rainout, fur-ther partitioning of 18O and D between differentregions is governed by the Rayleigh distillationequation.

As an air mass moves from its vapour source areaover continents along a trajectory, it progressivelycools and loses its water content through the rain-out process. During rainout, 18O and D in vapourand the condensing phases (rain or snow) withinthe cloud get partitioned through equilibrium frac-tionation. But along the trajectory, as each episodeof rainout removes some of the vapour mass, theheavier isotopes from the vapour are preferentiallyremoved compared to the lighter ones, so that re-maining vapour becomes progressively depleted in18O and D. Each rainout event gives isotopicallyenriched rain (or snow) with respect to its con-tributing parent vapour. It, however, gets depletedwith respect to the preceding rainout spell becausethe vapour from which it was formed is isotopicallydepleted with respect to the vapour of the earlierrainout event (Fig. 7.8). One can model the isotopesystematics during a rainout process according tothe Rayleigh distillation equation as:

Rv = Rv0 f (α−1) (7.15)

Cloud

Sea

Cloud

Heavy

Light

Light Vapour

Light rain dropsEvap.

Equator Temperate PoleLat.~ 0

δδ

DO

18

-ve

Latitude Effect

Cloud

Cloud

Heavy

LightAltitude Effect

Alt

itu

de

High

Low

Fig. 7.8 Rainout of vapour leads to progressiveheavy isotope depletion in successive rainoutevents away from the vapour source. Thisprocess, together with decrease in condensationtemperature, explains the latitudinal and thealtitudinal decrease in δ-values observed in globalprecipitation data.

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Since Rl / Rv = α = Rl0 / Rv0, this equation canalso be written in terms of liquid water, i.e.:

Rl = Rl0 f (α−1) (7.16)

In the above equation, Rv0 is the initial isotoperatio (18O /16O or D/H) of vapour in the cloudand Rv the ratio after a given proportion of thevapour has rained out to yield the precipitationwith the isotopic ratio, Rl, from liquid equilibriumvalue (Rl0) corresponding to Rv0. The residual frac-tion in the vapour reservoir is denoted by f . Thefactor α denotes the equilibrium water→vapourfractionation factor at the prevailing in-situ cloudtemperature.

Along the trajectory, when part of the rainedout vapour is returned to the atmosphere throughevapotranspiration, the Rayleigh law, however, isnot applicable. The downwind effect of evapotran-spiration flux on the isotopic composition of at-mospheric vapour and precipitation depends ondetails of the evapotranspiration process. Transpi-ration returns precipitated water essentially unfrac-tionated back to the atmosphere, despite the com-plex fractionation in leaf water (Forstel 1982; Zim-mermann et al. 1967). This is because of quantita-tive transfer of soil water taken up by the roots tothe atmosphere (Fig. 7.7b).

Thus transpiration, by returning vapour masswith isotopic composition RV (= Rl/α) in the down-wind direction, in a way restores both the vapourmass and the heavy isotope depletion caused bythe rainout in such a way that the subsequent rain-out event is not depleted as much as it would havebeen without the transpiration flux. Under suchcircumstances, the change in isotopic compositionalong the air mass trajectory is only due to the frac-tion, fnet, representing the net loss of water fromthe air mass, rather than being a measure of thetotal amount of rainout. This causes apparent re-duction in the downwind isotopic gradient. Theevaporated water, on the other hand, is usually de-pleted in heavy species relative to that of transpiredvapour (i.e. <RV), thus restoring the vapour massto the downwind cloud but depleting its heavy iso-tope composition. This causes apparent increase inthe downwind isotopic gradient.

The isotopic imprints of evaporation are alsorecorded in the form of a parameter ‘d-excess’

in the evaporating water body, the evaporatedvapour, and the precipitation originating from anadmixture of atmospheric vapour and the evap-orated flux. Since the kinetic fractionation for18O is more than that for D, as seen from Eqn7.11 and Eqn 7.12, the relative enrichment of theresidual water for an evaporating water body ishigher for 18O than for D. Correspondingly, forthe resulting vapour, the depletion is more for18O than for D. The extent to which 18O is frac-tionated more compared to D can be representedby a parameter ‘d-excess’, defined by Dansgaard(1964) as:

d − excess = d = δD − 8 × δ18O(�) (7.17)

The d-excess, as defined above, represents the δDexcess over 8 times δ18O for any water body orvapour. Since magnitude of equilibrium fraction-ation for D is about 8 times that for 18O, anyvalue of δD in vapour in excess of 8 times δ18Ois indicative of the effect of kinetic fractionationdue to evaporation. As already mentioned, the in-tercept (∼10�) of GMWL also signifies the ki-netic fractionation during evaporation but the dif-ference between intercept and d-excess is thatthe intercept of a meteoric or any other waterline is valid for an entire dataset, whereas the d-excess parameter can be calculated even for a sin-gle water sample whose δD and δ18O values areknown.

As evaporation proceeds, because of the rela-tively higher enrichment of 18O in the residual wa-ter, the d-excess of the evaporating water body de-creases and that of the resulting vapour increases.Therefore, if the original water was meteoric in ori-gin, the residual water not only becomes enrichedin heavier isotopes but also shows progressivelylower d-excess values as evaporation proceeds, thatis, its position on the δ18O–δD plot will lie belowthe LMWL. The resulting vapour on the other handshows the opposite effect. Furthermore, since con-densation and consequently rainout is an equilib-rium process (with slope ∼ 8), it does not signif-icantly alter the d-excess. Thus d-excess providesan additional handle to identify vapours of differ-ent histories and their mixing. Due to the effectof evaporation, most meteoric and subsurface pro-cesses shift the (δ18O–δD) signatures of water to a

P1: SFK/UKS P2: SFK



position below the LMWL. It is rare to find precipi-tation or groundwaters that plot above the LMWL,that is, show higher d-excess. However, in low-humidity regions, re-evaporation of precipitationfrom local surface waters and/or soil water/watertable creates vapour masses with isotopic contentthat plots above the LMWL. If such vapours arere-condensed significantly before mixing with thelarger tropospheric reservoir, the resulting rainwa-ter will also plot above LMWL (Clark and Fritz1997), along a condensation line with a slope ofabout 8. It is, however, important to recall that re-cycling of water back to the atmosphere in the formof vapour from soil moisture by plant transpirationis a non-fractionating process and, therefore, doesnot affect the d-excess either of soil water or of theatmospheric moisture.

A small fraction of rain percolates down throughthe soil layer and eventually becomes groundwa-ter. For many groundwaters, their isotopic compo-sition has been shown to equal the mean weightedannual composition of precipitation (Bhattacharyaet al. 1985; Douglas 1997; Hamid et al. 1989;Krishnamurthy and Bhattacharya 1991; Rank et al.1992). However, significant deviations from pre-cipitation values are also found in several cases.Such deviations from local precipitation are morepronounced in arid regions due to extensive evap-oration from the unsaturated zone or evaporativelosses even from the water table (Allison et al.1984; Dincer et al. 1974). Considering that only asmall fraction of precipitation actually reaches thewater table in most situations, the meteoric signalin groundwater can get significantly modified. Iso-tope variations in precipitation get attenuated andseasonal influences in recharge are reflected in thefreshly recharged groundwater. This bifurcation ofthe hydrologic cycle between precipitation and sur-face water on the one hand and groundwater onthe other ends where groundwater discharges andrejoins surface runoff in streams and rivers. Thusenvironmental isotopes, with their ability to char-acteristically label hydrologic components depend-ing on the extent of the hydrologic process, playa significant role in quantifying the relative contri-bution of groundwater to stream flow and in un-derstanding the hydrologic processes operating ina catchment.

7.5 Dissolved noble gases

Atmospheric gases enter the meteoric water cycleby gas partitioning during air–water exchange withthe atmosphere in accordance with their solubilitygoverned by respective Henry coefficients. There-fore, ubiquitous presence of atmospheric gases inthe meteoric water cycle in solubility equilibriumdefines a natural baseline. As a result, in most cases,the gas abundance in water can be understoodas a binary mixture of two distinct gas compo-nents – a well-constrained atmospheric solubilityequilibrium component and a residual componentthat may either be of atmospheric (e.g. trappedair bubbles) or non-atmospheric origin (e.g. radio-genic or terrigenic noble gases). Nitrogen (N2),oxygen (O2), and carbon dioxide (CO2) are reac-tive gases and participate in many biogeochemicalreactions which, depending on the particular reac-tion and the prevailing condition, also act as theirsources and sinks, thereby causing additional vari-ations in their concentration in waters of meteoricorigin. On the other hand, noble gases, being inert,are conservative. Their low abundance also makesthem an ideal tracer of many hydrologic processes.

As gas exchange phenomena proceed fairlyrapidly, with controlling gas transfer velocities ofthe order of 10−5 m s−1 (Schwarzenbach et al.2003), the surface waters of open water bodies areexpected to have noble gases in equilibrium withthe atmosphere at the prevailing physical condi-tions. This is supported by experimental evidence(Aeschbach-Hertig et al. 1999; Craig and Weiss1971) and holds for all atmospheric gases that haveno additional sources or sinks and hence can beconsidered as bio-geochemically conservative.

Gas partitioning at the free air–water interfacecan be reasonably well described by Henry’s law,according to which concentrations in the twophases are directly proportional to each other:

cia / ciw = ki

(T , c jw, . . . . . .

) ≈ ki (T , S) (7.18)

where cia and ciw denote the concentrations of gasi, in ‘air’ and ‘water’ phases, respectively, underthe atmospheric solubility equilibrium condition.In this form, Henry coefficient (ki) is inverse of the‘solubility of a gas in water’. Poorly soluble gases

P1: SFK/UKS P2: SFK



Fig. 7.9 Variation of gas solubility (in termsof Henry coefficient/ constant) in water withtemperature of equilibration. Note thelogarithmic scale for ordinate axis. The unitof Henry coefficient is the ratio lgas/lwater.Data Source: Ar - (Weiss, 1970); He, Ne -(Weiss, 1971); Kr - (Weiss and Kyser, 1978),Xe - (Clever, 1979); CFCs - (Warner andWeiss, 1985); SF6 - (Bullister et al., 2002).Redrawn from Aeschbach-Hertig (personalCommunication).

have large values of ki, whereas highly soluble gaseshave low values of ki.

Atmospherically derived noble gases make upthe largest and most important contribution to thenoble gas abundance in meteoric waters. The gasspecific Henry coefficient can often be assumedto depend only on temperature and salinity of thewater so that equilibrium concentrations of noblegases implicitly carry information on the physicalproperties of the water during gas exchange at theair–water interface, that is, air pressure, tempera-ture, and salinity of the exchanging water mass.

The dependence of noble gas solubility equilib-rium on the physical conditions during gas ex-change, in particular the sensitivity of the Henrycoefficient to temperature (Fig. 7.9), has beensuccessfully used in groundwater studies to re-construct the soil temperature prevailing at thetime of groundwater recharge. If an aquifer con-tains groundwater that was recharged duringdifferent climatic conditions in the past, noblegas concentrations provide information about thepast temperature (Andrews and Lee 1979; Mazor1972). This approach has been applied to recon-struct the prevailing continental temperature ofthe Pleistocene–Holocene transition in the tropics(Stute et al. 1995a; Weyhenmeyer et al. 2000), aswell as in mid-latitudes (Aeschbach-Hertig et al.2002; Beyerle et al. 1998; Stute et al. 1995b; Stuteand Schlosser 2000).

The experimental part of studying the dissolvedconservative gases in water can be divided into foursteps: (i) sample collection, storage and transporta-

tion to the laboratory; (ii) gas extraction from thewater sample; (iii) purification and separation ofthe extracted gases; and (iv) quantitative chromato-graphic (for CFCs and SF6) or mass spectrometric(for noble gases) analysis.

Depending on the dissolved gas species of in-terest, their physical properties vis-a-vis their per-meation through and interaction with the materialof the container in which the collected sample isstored for transportation and ultimate laboratoryanalyses, special field procedures and protocolshave been devised. The main aim of each such pro-cedure is to ensure that no loss of the dissolved gasand interaction with the atmosphere or with thematerial of the container occurs during collectionand storage of the water sample.

For detailed discussion of methods for noblegas analysis in waters (and other terrestrial fluids),the reader is referred to Bayer et al. (1989), Bey-erle et al. (2000), Clarke et al. (1976), Groning(1994), Ludin et al. (1997), Rudolph (1981) andStute (1989).

The various CFC species (CFC-12, CFC-11, andCFC-113) and SF6 are measured in the laboratoryusing a purge-and-trap gas chromatography proce-dure with an electron capture detector (ECD). Fora detailed description, reference is made to Busen-berg and Plummer (2000) and Plummer and Busen-berg (2000).

7.5.1 Dissolved helium

Helium (4He) is the second most abundant elementin the universe after hydrogen, constituting 23% of

P1: SFK/UKS P2: SFK



its elemental mass. It is the second lightest elementin the Periodic Table after hydrogen. It is a colour-less, odourless, non-toxic, and virtually inert mono-atomic gas. Although there are eight known iso-topes of helium, only two isotopes, namely 4He (2protons and 2 neutrons) and 3He (2 protons and 1neutron), are stable. The remaining six isotopes areradioactive and extremely short-lived. The isotopicabundance of helium, however, varies greatly, de-pending on its origin. On the Earth, helium is pro-duced by radioactive decay of heavy elements suchas uranium and thorium. The alpha particles pro-duced during radioactive alpha decay are actuallyfully ionized 4He nuclei. In the 238U , 235U , and232Th series, the decay chains yield 8, 7, and 6atoms of 4He, respectively (Fig. 7.10). Helium thusproduced is released from grains by etching, disso-lution, and fracturing and by alpha recoil and thenexpelled into the atmosphere by diffusion and tem-perature variations. Helium is produced in rocksand soils within the Earth and eventually escapesto outer space from the atmosphere due to its in-ertness and low mass. Its concentration, therefore,shows a gradient decreasing towards the groundsurface–atmosphere interface. In the Earth’s atmo-sphere, the concentration of helium is approxi-mately 5.3 parts per million (ppm) by volume.

Water in solubility equilibrium with the atmo-sphere usually shows low concentrations of heliumbecause of its low solubility (∼1%) and low atmo-spheric concentration (Fig. 7.9). In groundwaters,however, dissolved helium can be high due to itsradioactive production and release from earth ma-terials. Since its diffusivity in water is low (7.78 ×10−5 cm2s−1 at 25◦C; CRC, 1980), it gets trapped ingroundwater and collects additional radiogenic he-lium from the aquifer matrix while moving throughit until the groundwater comes in contact with theatmosphere. This provides a basis for groundwaterdating by the helium method, knowing the heliumproduction rate in the aquifer matrix from its ura-nium and thorium content (Castro et al. 2000; Clarket al. 1998; Frohlich and Gellermann 1987; Mazorand Bosch 1992; Torgersen 1980). Presence of frac-tures and fissures, particularly in hard rocks, pro-vides preferential pathways for migration of radio-genic helium from the interconnected pore spacesbetween the subsurface grains. Therefore, depend-

Neutron Number

124 128 132 136 140 144

124 128 132 136 140 144

Ato

mic

Nu

mb

erA

tom

ic N

um

ber

80

84

88

92

234

Po

At

Rn

Pb

Bi

Po

Tl

Pb

Bi

Po

HgTl

Pb

α - decayβ - decay

238U Decay Series

238

U

Th

234

Pa234

U

230

Th

226

Ra

Rn

222

218218

218

214214

214

210210

210

210

206206

206

124 128 132 136 140 144

Th

Pa

Ac

Th

Ra

At

Rn

At

Bi

Po

Pb

Bi

Po

Tl

Pb

Fr

235U Decay Series


80

84

88

92 U

235

231

231

227

227

223

223

219

219215

215

215

211

211211

207

207

Ato

mic

Nu

mb

er

80

84

88

92

Th

Ac

RaRa

Rn

Po

Pb

Bi

Po

Tl

Pb

Th

232Th Decay Series


232

228

228

228

224

220

216

212212

212

208

208

Fig. 7.10 Radioactive decay chains of Uranium andThorium. The number below the box with element code ismass number (= Atomic number + Neutron number). Notethat 8, 7, and 6 α-particles (the helium nuclei) are producedin the decay chains of 238U , 235U , and 232Th, respectively.222Rn is produced in the decay chain of 238U . Redrawnfrom Faure (1986). © John Wiley & Sons Inc.

ing on the collection volume of a particular fractureor fissure, helium concentration in the groundwa-ter residing in the fracture zone can be significantlyhigher compared to its production from the rockvolume in contact with groundwater. This formsthe basis of delineating the deep subsurface struc-tural zones (Filippo et al. 1999; Gulec et al. 2002;Gupta and Deshpande 2003a; Kulongoski et al.2003, 2005; Minissale et al. 2000).

Furthermore, during and just before occur-rence of an earthquake, enhancement of helium

P1: SFK/UKS P2: SFK



concentration in some groundwaters has been no-ticed (Barsukov et al. 1984; Rao et al. 1994; Reimer1984). This is possibly due to rock dilation andfracturing during incipient fault movements thatform a basis for using helium monitoring as a toolfor earthquake prediction. The important point tonote is that the entire radiogenic helium may notbe released from the rock matrix in the normalcourse, giving a release factor of less than unity.When the groundwater has dissolved helium in ex-cess of the atmospheric equilibration value, it isreferred to as having a ‘helium anomaly’ or ‘ex-cess helium’. Groundwaters may have ‘excess he-lium’ due to other factors as well, such as: (i) oc-currence of uranium mineralization within a par-ticular aquifer zone or in its vicinity, forming abasis for radioactive mineral exploration (Reimer1976); and (ii) occurrence of a natural gas reser-voir below the aquifer system which can havehigh concentration of helium, forming a basis forpetroleum exploration using helium surveys (Jonesand Drozd 1983; Weismann 1980). In addition, de-pending on the physical nature of the capillaryfringe zone overlying the saturated zone, air bub-bles can be entrapped and transported into thesaturated zone. Air bubbles can also be entrappedby rapid rise of the water table due to occasionalheavy rainfall spells in semi-arid regions. Entrap-ment and subsequent dissolution of such air bub-bles into groundwater introduces excess air andconsequently all its components including helium.This contributes additional helium to groundwaterover and above its atmospheric equilibration value(Andrews et al. 1985; Heaton 1981; Heaton andVogel 1981).

Helium permeates readily through many materi-als and for this reason it is important to carefullychoose the containers in which groundwater sam-ples intended for a post-collection helium analysisat a later time are to be stored. The most appropri-ate material for such containers is oxygen-free highconductivity (OFHC) copper tubing in which sam-ples for helium analyses are sealed by crimping atboth the ends (Craig and Lupton 1976; Lupton et al.1977). Gupta and Deshpande (2003a) showed thatloss of dissolved helium from thick-walled soda-lime glass bottles, with bromobutyl synthetic rub-ber stoppers manufactured according to guidelines

of US Pharmacopoeia Standard II (USP Std-II) andsecured by additional triple aluminium caps fixedby a hand-held crimping tool, was less than 0.15 %per day.

7.5.1.1 4He dating method

The helium-4 dating method for groundwater isbased on estimating the amount and rate of ac-cumulation of in-situ produced radiogenic 4He ingroundwater (Andrews and Lee 1979; Stute et al.1992). If secular equilibrium and release of all the4He atoms produced in the interstitial water are as-sumed, groundwater ages can be calculated fromthe annual 4He production rate estimated as below(Torgersen 1980):

J′He = 0.2355 × 10−12 U ∗ (7.19)

where

U ∗ = [U ] {1 + 0.123 ([T h]/[U ] − 4)} (7.20)

J ′He = production rate of 4He (in cm3STP g−1 rock

a−1); [U] and [Th] are concentrations (in ppm) ofU and Th, respectively, in the rock/sediment.

Accumulation rate (AC′He) of 4He

in cm3STP cm−3water a−1 is, therefore, given by:

AC′He = J

′He.ρ.He.(1 − n)/n (7.21)

where He = helium release factor; ρ = rock den-sity (g cm−3); and n = rock porosity.

If helium measurements are made on equili-brated headspace air samples, the dissolved he-lium concentrations (cm3STP cm−3water) wouldbe in terms of Air Equilibration Units (AEU), whichexpresses the dissolved helium concentration interms of the corresponding equilibrium dry gasphase mixing ratio at 1 atmosphere pressure at25◦C. As a result, water in equilibrium with aircontaining 5.3 ppmv helium is assigned the dis-solved concentration of 5.3 ppmAEU . Water ofmeteoric origin has a minimum helium concentra-tion (4Heeq) of 5.3 ppmAEU , acquired due to itsequilibration with the atmosphere during the fallof raindrops. Excess helium (4Heex) represents theadditional helium acquired by groundwater eitherfrom in-situ produced radiogenic 4He and/or othersubsurface sources.

P1: SFK/UKS P2: SFK



Using a dimensionless Henry coefficient (Hx)of 105.7 for helium at 25◦C (Weiss 1971), 5.3ppmAEU corresponds to a moist air equilibriumconcentration of 4.45 × 10−8 cm3 STP He cm−3

water. Therefore:

AC He = AC′He.106. HX.

(T/T 0

).P0/(P0 − e)

(7.22)

where AC He = accumulation rate of 4He inppmAEU a−1; T0 = 273.15◦ K; P0 = 1 atm; ande = saturation water vapour pressure (0.031 atm)at 25◦C, Hx = 105.7.

For an average [U] = 1 ppm for alluvial sedimen-tary formations and [Th]/[U] = 4 (Ivanovich 1992),n = 20 %; He = 1; ρ = 2.6 g cm−3, an in-situ 4Heaccumulation rate (AC He ) of 2.59 × 10−4 ppmAEUa−1 is obtained. Therefore, from the measured he-lium concentration of the sample (4Hes), the age,t, of groundwater can be obtained by using:

t = 4 Heex / AC He (7.23)

where 4Heex is obtained by subtracting 4Heeq (=5.3 ppmAEU at 25◦C and 1 atmosphere pressure)from the measured concentration in groundwatersample (4Hes).

The above formula, however, ignores ‘excess air’helium (4Heea) due to super-saturation of atmo-spheric air as the groundwater infiltrates throughthe unsaturated zone. Various models have beenproposed for estimating this component in ground-water (Aeschbach-Hertig et al. 2000; Kulongoskiet al. 2003) based on measurement of other dis-solved noble gases. However, from other studies(Holocher et al. 2002), it appears that 4Heea canbe up to 10 to 30% of 4Heeq. Therefore, if it is ig-nored, there may be an apparent over-estimation ofgroundwater ages to the extent of about 6 ka.

Furthermore, (4Hes) can contain other terrigenichelium components (Stute et al. 1992) that cancause overestimation of groundwater age. Theseterrigenic components are: (i) flux from an externalsource, for example, deep mantle or crust, adjacentaquifers, etc. (Torgersen and Clarke 1985); and (ii)release of geologically stored 4He from young sedi-ments (Solomon et al. 1996). Depending upon thegeological setting, particularly in regions of activetectonism and/or hydrothermal circulation, contri-

bution of these sources may exceed the in-situ pro-duction by several orders of magnitude (Gupta andDeshpande 2003a). Additional measurements/data(e.g. 3He/4He ratio, and other noble gases) are re-quired to resolve these components. For recent re-views on terrigenic helium, reference is made toBallentine and Burnard (2002) and Castro et al.(2000). However, in many cases it seems possibleto rule out major contributions from terrigenic Hesources, since the helium flux may be shielded byunderlying aquifers that flush the helium out ofthe system before it migrates across them (Castroet al. 2000; Torgersen and Clarke 1985). Accord-ing to Andrews and Lee (1979), with the exceptionof a few localized sites and for very old ground-waters, ‘excess He’ in groundwater occurs due toin-situ production and is, therefore, often used forquantitative age estimations within the aquifer ifthe U and Th concentrations of the aquifer ma-terial are known. But in case there is evidenceof deep crustal 4He flux (J0) entering the aquifer,the Eqn 7.23 becomes modified thus (Kulongoskiet al. 2003):

t = 4 HeE x/[(J0/nZ0ρw)

+AC He]/8.39 • 10−9 (7.24)

where Z0 is the depth (m) at which the 4He fluxenters the aquifer; and ρw is the density of water(1 g cm−3).

7.5.2 Dissolved radon

Radon (Rn) is a chemically inert radioactive noblegas formed by disintegration of Ra (radium) in thedecay chains of uranium and thorium (Fig. 7.10).There are 20 known radioactive isotopes of Radonbut it does not have any stable isotope. Amongst itsisotopes, 222Rn, formed by decay of 226Ra (in the238U decay series; Fig. 7.10), has the longest half-life of 3.8235 days, decaying to 218Po (polonium)by emitting an α–particle.

Natural radon concentration in the Earth’s atmo-sphere is very low (1 in 1021 molecules of air) dueto its radioactive decay, though it has been shownto accumulate in the air if there is a meteorologicalinversion. The natural waters in equilibrium with

P1: SFK/UKS P2: SFK



the atmosphere have low concentration of approx-imately 7 × 10−4dpm l−1 (Gupta et al. 2002).

Groundwaters can have higher concentration of222Rn due to its subsurface production. Due to itsdiffusion into the atmosphere, the radon content inthe unsaturated zone, similar to other inert gases, islower than that in the saturated zone. The mobilityof radon in groundwaters is to some extent linkedto its parent radium, which is particle- and salinity-sensitive (Krishnaswami et al. 1991).

As with helium, faults and fractures in the crustact as preferential pathways for migration of radon.Unlike helium that can go on accumulating in stag-nant or confined groundwaters (Gupta et al. 2002),radon is expected to be in steady state between pro-duction, decay, and mobilization from the rock–soilmatrix. The steady state conditions may not prevailduring and for a short time following any distur-bance, such as an earthquake. Similar to heliumanomalies, radon anomalies have also been used asseismic precursors (Shapiro 1981; Virk et al. 2001),for delineation of active fracture zones (Reddy et al.2006), radioactive mineral exploration (Jones andDrozd 1983; Weismann 1980), and for groundwa-ter dating using helium/radon ratios (Agarwal et al.2006; Gupta et al. 2002). In the last applicationmentioned above, due to the fact that both theradiogenic gases are produced from the decay of238U , their ratio is independent of uranium con-centration in the rock matrix (Torgersen 1980).

Radon is one of the heaviest gases at room tem-peratures and can accumulate in buildings and indrinking water and may cause lung cancer (BEIR1999). Therefore, it is considered to be a healthhazard. It is probably the most significant contami-nant of indoor air quality worldwide.

For 222Rn measurements, in view of its short half-life, water samples need to be measured withina short period after collection. There are severalmethods, but γ -spectroscopy provides a conve-nient tool by counting 609 keV gamma rays pro-duced by the decay of its short-lived daughter 214Biusing a high purity germanium (HPGe) gamma rayspectrometer. A repeat counting after a period ofmore than three weeks gives a measure of 222Rnsupported by 226Ra in the groundwater. Activityvalues are decay corrected to take into account thestorage time since collection.

7.5.2.1 4He/222Rn dating method

Since both 4He and 222Rn in groundwater, beingproduced by the α decay of U and/or Th in theaquifer material, have a common origin, their si-multaneous measurement in groundwater can alsobe utilized for calculating its age (Torgersen 1980).

As in the case of 4He, the 222Rn accumulationrate (ACRn) in cm3STP cm−3water a−1 is givenby:

AC Rn = J′Rn.ρ.Rn.(1 − n)/n (7.25)

where:

J′Rn = 1.45 × 10−14 [U ] (7.26)

and J ′Rn = production rate of 222Rn in cm3STP

g−1rock a−1 and [U] = concentration (in ppm)of U in the rock/sediment.

Thus, from the accumulation rate ratio of 4Heand 222Rn (= ACHe/ACRn), the age of groundwatercan be calculated as follows:

Age(t) = (Rn He)(AC Rn/AC He

) (C4/A222

)(7.27)

where Rn/He is the release factor ratio for radonand helium from the aquifer material to groundwa-ter; C4 is concentration (atom l−1) of 44He; andA222 is activity (disintegration l−1 a−1) of 222Rn ingroundwater. From Eqn 7.19 to Eqn. 7.21 and Eqn7.25 to Eqn 7.27, it is seen that 4He/222Rn ages areindependent of porosity, density, and U concen-tration, but do require measurement of [Th]/[U] inthe aquifer material. The ratio Rn/He dependsupon grain size and recoil path length of both222Rn (∼0.05 µm) and 4He (30–100 µm) (Andrews1977). Release of 222Rn by α–recoil from the outersurface (∼0.05 µm) of a grain (∼2–3 mm) has beenestimated to be ∼0.005% (Krishnaswami and Sei-demann 1988). In addition to α–recoil, both 222Rnand 4He can diffuse out of rocks/minerals through anetwork of 100–200A

◦nanopores present through-

out the rock or grain body (Rama and Moore 1984).Radon release factors (Rn) ranging from 0.01–0.2have been indicated from laboratory experimentsfor granites and common rock-forming minerals(Krishnaswami and Seidemann 1988). On the otherhand, Torgersen and Clarke (1985), in agreementwith numerous other authors, have shown that

P1: SFK/UKS P2: SFK



the most likely value of He ≈1. Converting C4

(atm l−1) to CHe (ppmAEU) units and A222 (disin-tegrations l−1 a−1) to A’222 (dpm l−1) units, Eqn7.27 can be rewritten as:

Age(t) = 4.3 × 108.(Rn/He)

.(AC Rn/AC He).C He/A′222 (7.28)

Here, 1 ppmAEU 4He concentration correspondsto 2.26 × 1014 atoms of 4He l−1 of water. An-other implicit assumption in the 4He/222Rn datingmethod is that both 4He and 222Rn originate fromthe same set of parent grains/rocks and their mobi-lization in groundwater is similarly affected.

Andrews et al. (1982) used the following one-dimensional equation for calculating diffusive trans-port of 222Rn in granites:

Cx = C0 exp(−√

λ/D.X) (7.29)

where C0 and Cx are concentrations of 222Rn froman arbitrary point taken at x = 0 and x = x,respectively; D = diffusion coefficient in water(∼10−5 cm2 s−1); and λ = decay constant for 222Rn.They calculated that Cx/C0 = 0.35 at a distanceequal to one diffusion length X = (D/λ)1/2 (=2.18 cm). Therefore, even at high 222Rn activity, itsdiffusion beyond a few metres distance is not possi-ble. The average radon diffusion co-efficient in soilswith low moisture content and composed of siltyand clayey sand is even lower, ∼2 × 10−6 cm2 s−1

(Nazaroff et al. 1988). Thus, 222Rn measurementsof groundwater depend essentially on the U con-centration in the pumped aquifer horizons in thevicinity of the sampled tube well.

Therefore, for groundwaters that may have acomponent external to the aquifer, the measured222Rn, because of its short half-life (t1/2 = 3.825 d),is indicative of its local mobilization; whereas 4He,being stable, may be mobilized from the entire flow-path. In such cases, the resulting 4He/222Rn ages forgroundwater samples having high ‘excess He’ maybe over estimated.

7.5.3 Chemical tracers

Application of injected chemical tracers to streamflow gauging (see Section 2.6.1.4) and of environ-mental chemical tracers to study sea water intru-

sion (see Section 6.6) has already been mentioned.A wide range of chemically conservative solutescan be found in different reservoirs and transferof water taking place in recharge/discharge zoneswithin the catchment system can be studied bymeasuring them. Solutes, such as chloride, sul-phate, silica, or bromide, have been used for hy-drograph separation (Hooper and Shoemaker 1986;Kobayashi et al. 1990; Pinder and Jones 1969; Rob-son and Neal 1990) and as tracers to infer waterpathways and response times of the catchment toa given storm (Espeby 1990; Jardine et al. 1989;Kennedy et al. 1984). The basic premise of ap-plicability of chemical tracers to evaluating hydro-logic processes is that the tracers, artificial as wellas environmental, imprint their signature on thesource waters similar to isotopes. The interpreta-tion of such chemical data requires care in that thecatchment is a major source of some constituents,such as base cations and silica, and the atmosphereis a major source of anions, such as sulphate andchloride, and each may change within a catch-ment. For example, sulphate budgets may balancein highly acidic catchments, whereas chloride bud-gets may not balance in the short term due to in-teraction with vegetation (Harriman et al. 1990;Peters 1991).

7.5.3.1 Fluoride

In an aqueous solution, the element fluorine(F) commonly occurs as the fluoride ion (F−).In groundwaters, fluoride is one of the mostimportant environmental pollutants resultingfrom natural and/or anthropogenic factors. Purefluorine (F2) is a corrosive pale yellow gas that isa powerful oxidizing agent. It is the most reactiveand electro-negative of all the elements and readilyforms compounds with most other elementsincluding noble gases.

The ill effects of excessive fluorine-fluoride in-gestion on human health have been extensivelystudied (Gupta and Deshpande 1998; Luke 1997;WHO 1970, 1984; Zero et al. 1992). The occur-rence and development of endemic fluorosis hasits roots in the high fluoride content in water, air,and soil of which water is perhaps the major con-tributor. The Bureau of Indian Standards (BIS 1990)

P1: SFK/UKS P2: SFK



recommends the permissible limit of fluoride indrinking water as 1 part per million (ppm), whichis lower then the WHO (1984) drinking water limitof 1.5 ppm. Gupta and Deshpande (1998) have de-scribed the hazardous effects on human and cattlehealth from excessive fluoride in the NGC regionof Gujarat, where it was observed that ingestionof excessive fluoride has adverse effects on hu-man teeth and bones (known as dental and skeletalfluorosis).

The normal fluoride content in the atmosphericair is reported as between 0.01 and 0.4 µg m−3.However, in industrial areas, it is known to rangefrom 5 to 111 µg m−3 (Bowen 1966). Averagefluoride content of precipitation varies from al-most nil to 0.089 mg l−1 with as high a value as1 mg l−1 (Gmelin 1959; Sugawara 1967) in indus-trial areas. The fluoride content of rivers also variesgreatly, depending on the fluoride content of efflu-ent discharges of groundwater feeding the streamand on the amount of precipitation and runoff.The fluoride content in surface waters is generallyhigher during dry periods due to its evaporativeconcentration (Deshmukh et al. 1995 a, b). Themean concentration of fluoride in ocean watersranges from 0.03 to 1.35 mg l−1 and is found toincrease with depth in many cases (Bewers 1971;Riley 1965). The groundwaters, particularly in thearid and semi-arid regions throughout the globe,are known to have high fluoride concentration(Handa 1977).

The fluoride content of groundwater greatly de-pends on the type of soil/rocks/aquifer it comesinto contact with. There are more than 150fluorine-bearing minerals in the form of silicates,halides, and phosphates (Strunz 1970; Wedepohl1974). Fluorite (CaF2) is the most widely dis-tributed fluorine bearing mineral in Nature, whilefluorapatite (Ca5F(PO4)3) is a common member ofthe immiscible phase generated during early differ-entiation of mafic and ultramafic magmas formingapatite-magnetite rocks. In advanced stages of dif-ferentiation, fluorine is enriched into the residuumand, therefore, rocks such as granitoids or peg-matites have a high content of apatite resulting inaverage fluorine content of up to 2.97% (by weight)in these rocks. In sedimentary rocks, in addition tofluorite and fluorapatite in the clastic component,

clay-sized minerals such as micas (muscovite, bi-otite, phlogopite, zinnwaldite, and lepidolite) andclay minerals (montmorillonite, illite, and kaolinite)have a high content of fluorine due to replacementof OH– by F– or due to admixture of skeletal de-bris in which hydroxyl bonds are replaced by flu-orine in the hydroxy-apatite structure (Carpenter1969). Out of the total fluorine content of the clay-sized particles, 80–90% is hosted in the micaceousminerals and the remainder is associated with clayminerals (Koritnig 1951).

The fluorine content of soils depends mainly onthe rocks from which they are derived and the cli-matic regime in which the soil is formed. How-ever, in warm and humid climates, decomposi-tion of organic remains can be the main sourceof fluorine. The average fluorine content in thesoil ranges between 90 and 980 ppm (Fleischerand Robinson 1963). The leaching of fluoridefrom soils and the aquifer matrix into groundwa-ter involves adsorption-desorption and dissolution-precipitation processes. Since the solubility of flu-orite and fluorapatite is very low in natural wa-ters (Deshmukh et al. 1995b), it is dissolved slowlyby the circulating water through leaching. Fluo-ride from mica is leached out rapidly. However,on account of the ionic strength of complex form-ing ions, solubility of fluorite can be drasticallymodified. Calcium and sulphate ions significantlylower the fluorite solubility in natural waters, oftencausing precipitation of fluorite (Deshmukh et al.1993; Handa 1977; Perel’man 1977). Distribution ofCa and F in groundwater is, therefore, antipathic(Deshmukh et al. 1995b; Dev Burman et al. 1995;Handa 1977; Srivastava et al. 1995). Fluorine fromthe clay minerals is readily desorbed in an alkalineenvironment. Fluoride to hydroxyl ion exchange inclay minerals depends upon the concentration offluoride ion and pH of the circulating water (Hub-ner 1969). Thus, solubility of fluorine-bearing min-erals is governed by various parameters such as pH,alkalinity, ionic strength, calcium, and sulphate ionconcentration, etc.

It is seen from the global map of endemicfluorosis affected areas (Fig. 7.11a) that mostof the fluoride affected regions are in arid tosemi-arid climatic zones (Fig. 7.11b). In India,fluoride-rich groundwaters are found in arid

P1: SFK/UKS P2: SFK



(b)

Hyper Arid

Arid Dry Sub HumidSemi Arid

(a)

Fig. 7.11 (a) Global distribution of areas affectedby endemic fluorosis. Redrawn fromhttp://www.unicef.org/programme/wes/info/fl map.gif. (b) Geographicaldistribution of arid and semi-arid regions. Redrawnfrom www.wateryear2003.org/en/ev.php-URL ID=5137. It may be noted that mostfluoride-affected areas are located in the arid andsemi-arid regions. See also Plate 7.11.

regions, especially in Rajasthan, Gujarat, and inte-rior parts of the southern peninsula characterizedby episodic rainfall separated by extended dry peri-ods (Agrawal et al. 1997; Jacks et al. 1993; Vasavada1998). Fluoride excess is also reported from thearid climatic regions in North China (Yong and Hua1991).

The fluoride content of thermal springs canincrease with temperature due to increasedrock–water interaction at elevated temperature(Chandrasekharam and Antu 1995) and/or scav-enging from the large volume of rock duringhydrothermal circulation (Gupta and Deshpande2003a; Minissale et al. 2000), but this is not ob-served as a rule. There are thermal springs with aconcentration of fluoride as low as <0.15 mg l−1

and as high as 55.4 mg l−1 (Gmelin 1959; Sugawara1967).

7.6 Models for interpretation ofgroundwater age

In an aquifer system, an ensemble of watermolecules arriving at a particular location withinit comprises molecules that spend various timedurations between their recharge and arrival. Theconcept of groundwater dating involves estimatingthe average time spent in the aquifer by the watermolecules before reaching a given location. Thus,the age of groundwater at a given location is the av-erage time spent by water molecules in the aquifersince the time of recharge until their arrival at thelocation. Depending on the conceptual mathemati-cal model employed to describe the aquifer system,age can give additional information on the system.The common conceptual models in use for inter-pretation of the groundwater age estimates are:

P1: SFK/UKS P2: SFK



(i) Piston Flow Model (PFM); (ii) Well-Mixed Reser-voir Model (WMRM); and (iii) Dispersion-AdvectionModel (DAM).

Piston Flow Model (PFM) is the most com-monly used groundwater flow model for estimatinggroundwater age. It assumes that as groundwatermoves away from the recharge area, all the flowlines have the same velocity and that hydrodynamicdispersion as well as molecular diffusion of watermolecules is negligible. Thus, water moves fromthe recharge area as if a parcel is being pushed bya piston with the mean velocity of groundwater.This implies that a radio tracer that appears at thesampling point at a given time, t, has entered thesystem at the time instant (t − T ), and from thatmoment its concentration decreases only due to ra-dioactive decay during the time span, T , spent inthe aquifer. Therefore:

Cout (t) = Cin (t − T ) .exp(−λT ) (7.30)

The term C represents the tracer concentration (oractivity) of water with the suffix representing theappropriate location. Eqn 7.30 describes a dynamicsystem and is mathematically equivalent to describ-ing the concentration of a radioisotope in a staticwater parcel isolated since its recharge, whereby:

Ct = C0.exp(−λt) (7.31)

Here, t is the radiometric age of the water thatcorresponds to the age, T , of the dynamic system.If x is the distance from the recharge boundary,T = x/u can be used to estimate the flow rate (u)of groundwater in the aquifer:

Ct = C0exp(−λx/u) (7.32)

Unlike the PFM, if it is assumed that the rechargeflux completely mixes with the entire volume ofthe reservoir before its outflow, one gets anotherextreme situation and the model is known as theWell Mixed Reservoir (WMR) model. In applyingthis model to an aquifer system, it is assumed thatthe well-mixed reservoir comprises the entire vol-ume between the recharge area and the samplingpoint. Under this condition for a radiotracer:

Ct = C0/(1 + λt) (7.33)

In Eqn 7.33, λ is the radioactive decay constant andτ is the ratio of the reservoir volume to the input

flux to the reservoir and represents the estimatedmixing time (or the mean residence time) of waterbetween the recharge area and the sampling loca-tion. It is seen that τ , as estimated from the tracerdata, actually represents a dynamic parameter – themixing time:

τ = 1

λ

(C0

Ct− 1

)(7.34)

The phenomenon of mixing accompanying themovement of water molecules through porous me-dia can also be described by a diffusion-advectionequation in which the diffusion coefficient is re-placed by a dispersion coefficient (Gupta 2001;Scheidegger 1961). For a radiotracer, the one-dimensional continuity equation in the groundwa-ter flow system may be written as:

∂C

∂t= ∂

(D∂C /∂t − uC

)∂x

+ W1 − W2 (7.35)

In the above equation, D is the diffusion coefficientof the tracer, and as in the case of PMF, x is thedistance from the recharge boundary, u is the bulkflow velocity, and W 1 and W 2 are the rates of the in-troduction and removal of the tracer, respectively.With further assumptions of u and D not being afunction of x and in the case of steady state (i.e.∂C/∂t = 0), the above equation reduces to:

D∂2C

∂x2− u

∂C

∂x+ W1 − W2 = 0 (7.36)

In the case of radioactive tracers, the term W 2

includes, in addition to radioactive decay, loss oftracer due to non-radioactive processes (e.g. ad-sorption on the aquifer matrix). Considering theloss of tracer by radioactive decay alone and forW 1 = 0, the above equation can be rewritten as:

D∂2C

∂x2− u

∂C

∂x− C = 0 (7.37)

This equation for D = 0, and the boundary condi-tion C = C0 at x = 0, give the solution for the pistonflow (Eqn 7.32).

In the case of finite dispersion, the solution of(Eqn 7.37) for the boundary conditions C = C0

at x = 0 and C = 0 at ∞, is given by Gupta

P1: SFK/UKS P2: SFK



et al. (1981):

C /C0= exp

[xu

2D

{1 −

(1 + 4λD/u2

)1/2}]

(7.38)

The tracer concentration decreases exponentiallywith distance, similar to PFM (Eqn 7.32). There-fore, a simplistic application of the PFM would givean apparent velocity:

ua = u

2

{1 −

(1 + 4λD/u2

)1/2}

(7.39)

There are several other mathematical models inuse that conceptualize the flow of groundwaterin aquifer systems differently, depending on spe-cific aquifer geometry and flow paths. But for aconfined aquifer with a well-defined recharge area,the above models are commonly used to interpretthe environmental isotopic data and to determinethe groundwater age evolution from recharge todischarge regions of the aquifer. This, however,is a challenging task for hydro-geochemists, be-cause sampling locations are often randomly dis-tributed over the area where water from the aquiferis pumped at various depths or where springs bringwater to the surface. Several environmental trac-ers (including radionuclides) find application in de-termining magnitude and direction of groundwaterflow, hydro-geological parameters of the aquifer,and age of groundwater (Andrews et al. 1989;Cserepes and Lenkey 1999).

7.6.1 Dual radiotracer dating

It is readily seen from Eqn 7.38 and Eqn 7.39 that asimplistic application of PFM would lead to consid-erable overestimation of flow velocity in highly dis-persive groundwater flow systems (D/(xu) >> 1).For a given value of the dispersion coefficient, thedifference between the real and the apparent ve-locities becomes more pronounced for the smallerhalf-life tracer. For real velocity approaching zero,a minimum apparent flow velocity equal to (λD)1/2

is obtained.For a confined aquifer, assuming W 1 = W 2 = 0,

Eqn 7.38 shows that a plot of ln(C/C0) versus xu/D

is a straight line, whose slope is a function of the pa-rameter D/u2. However, the value of abscissa (i.e.xu/D) in a given field situation will not be knowna priori. Therefore, it is not possible to estimateboth parameters D and u when using only one ra-diotracer. However, in the case of two radiotracers‘1’ and ‘2’, the ratio of their relative concentrationsis obtained from Eqn 7.38 as:

ln(C/C0

)1

= 1 − (1 + 4λ1 D / u2

)1/2

1 − (1 + 4λ2 D / u2

)1/2 ln(C/C0

)2

(7.40)

which is a straight line on a log-log plot, the slope ofwhich is a function of parameter D/u2 (Fig. 7.12).The distance from the recharge boundary (charac-terized by C/C0 = 1 for both tracers) to any pointin the plotting field is a linear measure of the di-mensionless parameter, xu/D. Thus knowing x (i.e.distance of the sampling well from the rechargeboundary), both u and D can be estimated.

7.6.1.1 General case: semi-confined aquifer

The steady state continuity equation for the generalcase of a semi-confined aquifer, taking into accountthe variation of u (due to leakage influx and out-flux) along the aquifer and with other simplifyingassumptions as for Eqn 7.35, can be written as:

Dd2C

dx2= d(uC )

dx+ pC0 − EC − λC − qC = 0

(7.41)

The term p represents the rate of leakage influxof relatively young water (activity ≈ C0) from theoverlying unconfined aquifers and the term, q, rep-resents the leakage out flux (activity = C) from theaquifer. With reference to Eqn 7.35, pC0 = W 1 and(E + λ + q)C = W 2. If p is assumed constant, thendu/dx = constant, or zero implying q = constantor zero. If we further assume that the aquifer is ex-tensive enough so that tracer activity at dischargeboundary is not controlled by the leakage flux (i.e.dC/dx = 0), the solution (Gupta et al. 1981) of Eqn7.41 is:

C = β1 exp(m1x) + β2 exp(m2x) + pC0/K

(7.42)

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100

10-110-2

10-3

10-4

10-5

1.0

0.9

0.8

0.7

0.6

0.5

0.4

Silicon-32 (C/C )0

Carb

on

-14 (C/C

)0

PISTON FLOW MODEL

D/u= 100 yrs

2

200

500

1,000

2,00

05,

000

10,0

00Fig. 7.12 Expected variation ofconcentrations of 32Si and 14C in aconfined aquifer. The distance of ‘dots’from C/C0 = 1 for both tracers(corresponding to recharge boundary inthe field) along each line corresponds tointeger value of xu/D at intervals of 5 forD/u2 = 100 and 200 years, and 1 for othervalues of D/u2. Redrawn from Gupta et al.(1981). © American Geophysical Union.

withK = λ + E + p

m1 = u{

1 + (1 + 4K D/u2

)1/2}

/ 2D

m2 = u{

1 − (1 + 4K D/u2

)1/2}

/ 2D

β1 =(m2/m1

)C0

(1 − p/K

)exp {(m2 − m1) L }[

1 − (m2/m1

)exp {(m2 − m1) L }]

β2 = C0

(1 − p/K

)[1 − (

m2/m1

)exp {(m2 − m1) L }]

where L is the lateral extent of the aquifer. In thelimit L → ∞ and since m1 > m2, β1 ≈ 0 and β2 ≈C0 (1 − p/K). In this case, Eqn 7.42 becomes:C /C0

= exp (mx) + {p/(p + λ} {1 − exp (mx)}(7.43)

where

m =u0+(p−q)x−[{u0+(p−q) x}2+4 (λ+ p) D]1/2

2 D

(7.44)

For the particular case p = q; du/dx = 0, the u isconstant and m becomes independent of x and isgiven by:

m = u [1 − { 1 + 4 (λ + p) D/u2}1/2]

2 D(7.45)

It is easy to see that for p �= 0, the tracer concentra-tion given by Eqn 7.43 approaches an asymptoticvalue:

(C/C0

)asym

= p/(p + λ

)(7.46)

independent of eddy diffusivity, D. From Eqn 7.43and Eqn 7.46, it is easy to see that the asymptoticvalue is reached first for the smaller half-life traceras one moves away from the recharge boundaryalong the length of the aquifer. In a real field situ-ation, unless the tracer half-life is compatible withaquifer dimensions, it may not be possible to ob-serve the asymptotic value of the tracer concentra-tion to enable estimation of the value of p.

Gupta et al. (1981) outlined a graphical pro-cedure using Eqn 7.43 employing simultaneousmeasurements of two radiotracers to estimate theaquifer parameters of interest. It is seen (Fig. 7.13)from the log-log plot of activity ratios, C/C0, oftwo tracers 32Si and 14C for p �= 0, that thestraight line behaviour observed in p = 0 is sig-nificantly altered and the lines bend towards thelarger half-life tracer axis. Concentration of theshorter-lived tracer reaches an asymptotic valuefirst; eventually terminal values are reached forboth the tracers. In principle, if the sampling isextensive, one should first estimate D and u fromthe straight line part of the curve near the origin,

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Silicon-32 (C/C )0

Carb

on

-14 (C/C

)0

10-110-210-310-4 100

1.00.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

PISTON FLOW MODEL

P=

1x10

-5

5x10

-5

1x10

-4

2x10

-4

D/u = 1,000 a2

Open wells, GujaratTubewells, GujaratTubewells, Rajasthan

Fig. 7.13 32Si and 14C concentrations ingroundwaters of Gujarat and Rajasthan,indicating significant contribution fromleakage of relatively young water into theaquifer system, particularly in Rajasthan.Redrawn from Gupta et al. (1981). ©American Geophysical Union.

as can be done from Fig. 7.12 and using Eqn 7.40.Having estimated both D and u, the value of pcan be estimated from an appropriate curve, as inFig. 7.13. This diagram has some data points fromthe available 32Si and 14C measurements on ground-waters in Gujarat and Rajasthan taken from Nijam-purkar (1974). Because of relatively few data pointsand large scatter, it is not possible to quantita-tively estimate the various groundwater parametersfrom this data. However, significant leakage of rela-tively young groundwater is indicated, particularlyin the case of samples from Rajasthan. Gupta (2001)used these concepts of dual radiotracer dating withdata on 14C and 36Cl generated by Cresswell et al.(1999a, b) from Central Australia.

7.7 Tracers for estimation of groundwaterrecharge

Groundwater recharge may be defined as ‘thedownward flow of water reaching the water table,contributing to the groundwater reservoir’ (Lerneret al. 1990). There are two main types of recharge:direct (vertical infiltration of precipitation whereit falls on the ground) and indirect (infiltration fol-lowing runoff). It is generally believed that in tem-perate climates most recharge is direct, whereasin arid regions most recharge occurs from surfacerunoff. However, this distinction does not alwayshold true: there are some situations in temperate

regions where indirect recharge dominates, mostnotably in karst areas, where recharge occurs fromlosing rivers and via swallow holes and other solu-tion features. Without underestimating the signifi-cance of indirect recharge, the emphasis here is ondirect recharge.

Groundwater recharge can be estimated usingboth environmental and injected tracers. Lerneret al. (1990) separated the methods into signa-ture methods and throughput methods. In the sig-nature method, a parcel of water containing thetracer is tracked and dated. Throughput methods,on the other hand, involve a mass balance of tracer,comparing the concentration in precipitation withthe concentration in soil water or sometimes withthe concentrations below the water table. Pistonflow is generally assumed in most tracer studies.However, tracers can be used to investigate flowprocesses, including the occurrence of preferen-tial pathways.

Throughput tracer studies may involve both thesaturated and the unsaturated zones. Recharge es-timates based on the use of environmental tracers(i.e. C1− and 3H) in the saturated zone, give long-term (>1 year) averages and an areally-integratedvalue, which is difficult to obtain using soil physicsmethods. Regional recharge rates are required forresource planning. Studies based on monitoring oftracers in unsaturated profiles usually yield point(area <0.1 m2) recharge values. Thus the technique

P1: SFK/UKS P2: SFK



could be developed to measure spatial variabilityand to ascertain the effects of various factors onrecharge.

7.7.1 Environmental chloride method

The most successful non-isotopic environmentaltracer in hydrologic studies is chloride, which is de-posited from the atmosphere both as dry and wetprecipitation transported by winds. Chloride hasbeen used for estimating areal recharge based on itsconcentration in the saturated zone (Eriksson andKunakasen 1969; Kitching et al. 1980), and local-ized recharge by considering its depth distributionin soil water (Allison and Hughes 1978; Kitchinget al. 1980; Peck et al. 1981; Sharma and Hughes1985). From the depth distribution of chloride con-centration of soil water (C) and its volumetric watercontent (θ), time-averaged vertical water flux (qw)can be computed using a steady state water andsolute flow model, i.e.:

qw = 1

C

(Js + Ds θ

∂C

∂z

)(7.47)

where Js is the average chloride input to the sys-tem (= P Cp, with Cp as the time-averaged chlorideconcentration of the long-term average annual rain-fall P); Ds is the diffusion-dispersion coefficient ofthe solute; and ∂C /∂z is the slope of the observedchloride concentration with respect to depth. Thecomputed vertical water flux below the root zonedepth of the local vegetation is interpreted as theaverage recharge rate to the groundwater.

Chloride concentrations of groundwater fromsaturated zone have also been used to estimate theratio of annual recharge to total groundwater stor-age. In this case, the groundwater recharge is givenby the ratio of chloride deposition (mg m−2 a−1)and its concentration (mg m−3) in groundwater.

Complications may arise in interpreting chloridedata, for example, when water movement throughthe profile deviates significantly from vertical, orwhen water flow through the profile is not steadyand uniform. Even in relatively uniform, sandy pro-files, about 50% of annual recharge may occur viamovement of water through preferred pathways,bypassing the soil matrix (Sharma and Hughes1985; Sukhija et al. 2003). In some forested lat-eritic profiles with clayey subsoil, recharge through

macro-pores amounts to more than 95% (Peck et al.1981) of the total infiltration at the given site. Sev-eral aspects of interpretation of the observed chlo-ride profiles still remain unresolved.

7.7.2 Environmental tritium method

Tritium, generated by atmospheric nuclear tests,is the most common environmental isotope usedin recharge studies (Smith et al. 1970). Localizedrecharge rates have been estimated from distribu-tion of tritium in the unsaturated part of the profile(Sukhija and Rama 1973) and found to agree withother estimates, such as from the chloride methodand injected tritium method.

When using the environmental tritium method,to begin with the tritium input function from pre-cipitation is estimated, as shown in Fig. 7.14a.In this case study (from Ahmedabad, India) tri-tium concentration measurement data for theperiod 1962–1970 was available. For the pe-riod 1952–1962, the input function was extrapo-lated from correlation with Ottawa (Canada) data(Sukhija and Rama 1973). The bomb tritium peakfor 1953–1964 is clearly seen. The total tritium fall-out (TU × cm) is given by:

T =∑

Ai . Pi (7.48)

whereT = total tritium fallout (TU × cm);Ai = tritium concentration (TU) of precipi-

tation in month (or year), i;Pi = precipitation amount (cm) in month

(or year), i.The summation is carried out for the period 1952

(onset of thermonuclear era) to the time of carryingout the investigation (November 1967 or Novem-ber 1969 in the two cases shown in Fig. 7.14a).

Similarly for percolation function:

t =∑

aj . mj (7.49)

wheret = total amount of tritium (TU × cm)

present in the soil column;aj = tritium content (TU) of the soil

segment j;mj = Moisture content (cm) of the soil

segment j.

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Fig. 7.14 (a) An example of the application of bomb-produced environmental tritium for groundwater recharge estimationusing soil moisture tracing in North Gujarat, India. Redrawn from Sukhija et al. (2003). (b) An example of the application ofinjected tritium as tracer for soil moisture movement and groundwater recharge estimation at a site near Ahmedabad,Gujarat, India. Redrawn from Bhandari et al. (1986). The peak of various tritium profiles is seen to move seasonallyupward/downward in tandem with soil moisture movement, but from one rainy season to the next a net downwardmovement in response to groundwater recharge can be clearly seen. Both types of measurements also indicate that rainfall ofa given year takes a couple of years of transport through the unsaturated soil zone before reaching the water table. Redrawnfrom Sukhija et al. (2003). © Springer.

Since ‘T ’ equals total fallout of tritium at the siteand ‘t’ equals the amount percolated (net amountafter evapotranspiration and runoff losses are takeninto account), t/T represents the fraction of rainfallthat goes to recharge the groundwater. Therefore,recharge, as a percentage of precipitation by theintegral method, is given by:

r (%) = t/T • 100 Tritium Integral Method

(7.50)

The tritium peak method aims to locate the positionof 1963 precipitation in the soil profile, assuminga layered movement of soil moisture (piston flow).The recharge is computed by estimating the totalsoil moisture above the peak position and assign-ing the same to precipitation since 1963 up to the

time of investigation (November 1967 or Novem-ber 1969 in Fig. 7.14a). Thus:

r (%) = S/P • 100 Tritium Peak Method (7.51)

whereS = Soil moisture content (in cm) in the column

from surface to the depth of tritium peak;P = Precipitation since 1963 up to the time of

investigation.Overall, recharge rates computed by the tritium

peak method represent an average of relativelysmall duration (5–7 years), while the tritium inte-gral method gives recharge averaged over longerduration (15–20 years), though the results are likelyto be biased towards years with higher tritium con-tent in precipitation.

P1: SFK/UKS P2: SFK



The environmental tritium peak methods havebeen successfully applied throughout the world,and in many different climates (Scanlon et al.2006). In low-rainfall, arid conditions, infiltratingrainwater moves intermittently and remains in theunsaturated zone for decades. In moister climateswhere infiltration is high, artificial tritium can be in-jected as a tracer to determine the rate of recharge.This method is applicable for estimating piston flowrecharge anywhere, provided layered movement ofsoil moisture can be reasonably assumed.

7.7.3 Tritium injection method

While estimating recharge using tritium injection,tritiated water is generally injected as a slug involv-ing a set of 5 to 10 injections at a properly selectedsite to form a layer below the root zone of thelocal vegetation (depth: 60–80 cm) before com-mencement of the rainy season, and soil profilesare sampled during the post-rainfall dry period upto depths of 2 to 6 m. At each site, several suchsets of close-by injections are made for repeat sam-pling for a period of 1 to 3 years after the injec-tions are done. An example of one such study isshown in Fig. 7.14b. Interesting observations re-garding soil moisture movement in arid and semi-arid regions can be made from this diagram: (i) thetracer peak in the soil moisture gradually broadenswith time due to diffusion/dispersion and move-ment; and (ii) there is a net downward layeredmovement of tracer over the full year cycle. Theupward layered movement during the dry period isalso clearly discerniable. Therefore, recharge esti-mates from tritium injection methods are likely toshow higher variability depending on climatic con-ditions prevailing at the site during the time periodbetween injection and sampling. To obviate someof these problems, tritium injection stations weresampled over a period of two to three consecutiveyears during 1977–1979.

Datta et al. (1980b) conceptualised the unsatu-rated transport of moisture as pulses of infiltratingsheet through a series of interconnected expand-able mixing cells sub-dividing the soil profile. Inresponse to infiltration, each hypothetical soilcell expands to hold soil moisture up to its fieldcapacity and drains any excess water downwards

under the influence of gravity to the soil celldirectly below, making the recharge pulse movedownwards towards the water table. By applyingthe mass balance equation successively to each hy-pothetical mixing cell subdividing the soil profileat discrete time intervals, the process of dispersionand mixing leading to broadening of the tracerpeak (Fig. 7.14b) is mathematically approximatedand closely reproduces the field data. A closecorrelation was found to exist between the rainfalland estimated number of recharge pulses from thefield data (Datta et al. 1980b).

Tritium concentrations in the saturated zonehave been used to estimate the ratio of an-nual recharge to total groundwater storage in theaquifer. From the fact that evaporation is accompa-nied by isotope enrichment, depth distributions of18O and 2H have been used to estimate recharge,particularly in areas where direct evaporation is amajor component of total vapour-transpiration (Al-lison and Hughes 1978; Sharma and Hughes 1985).

7.8 Tutorial

Ex 7.1 The figure below (Fig. 7.15) shows a saltwave recorded during a slug-injection measure-ment experiment in a mountainous stream. Thevolume of injected solution was 6.35 l. This vol-ume resulted from mixing 1 kg of salt with 6 l ofwater (total solution volume 6.36 l), followed byextracting 10 ml of injection solution for use in thecalibration procedure. The stream EC data were

00

5

10

60

20

15

25

30

120 180 240Time (s)

EC

(S

.cm

)µ

797S.cmµ

Fig. 7.15

P1: SFK/UKS P2: SFK



logged at 1 second intervals, and the calibrationconstant was 2.99 × 10−6 cm/µS.Solution:

Q = V

k.�t.[EC (t) − ECbg

]

= 6.35 × 10−3 m3(2.99 × 10−6 cm/µS

)(1s)

(797 µS/cm

)= 2.66m3.s−1

Ex 7.2 Protactinium-231 is a radioactive isotope,decaying into the daughter isotope Actinium-227with a half-life of 32 760 years. What type of decaydoes protactinium-231 undergo?

Ex 7.3 If a particular confined groundwater con-tains 3% of the original activity of carbon-14 in therecharge area, what would be its approximate age?

Ex 7.4 In a 1-day-old sample of radioactive zinc(71m30 Zn ) with a half-life of 3.97 hours, how much

of the original zinc has decayed?

Ex 7.5 What is the total number of radioactiveatoms present in 1 gram of each of the followingsubstances:

Ex 7.6 Using the following chart identify theisotope best suited to examine date an artefactfrom the early Bronze Age in Egypt, around theyear 3000 BC?

Ex 7.7 Abundance ratio of 2H/1H and 18O/16O inVSMOW are 1.5575 × 10−4 and 2.0672 × 10−2,respectively. Determine abundance ratios of 2H/1Hand 18O/16O in water samples with δ18O and δDvalues as: (–10, –70), (0, 11), (5, 62), (–22, –135).Calculate d-excess for these water samples.

[Hint: Use Eqn 7.2 and Eqn 7.17]

Ex 7. 8 The average δ18O of the base flow wa-ter of a high mountain stream was estimatedas –10 �, and δ18O of the snowpack meltwaterwas estimated as –16 �. During a particular meltseason, the δ18O of the stream water monitored atfour different times was –11, –13, –13.5, and –12�. Calculate the proportion of the snowmelt com-ponent in the total stream flow water at the timeinstants of the four measurements.

[Hint: Use two-component mixingmodel with base flow as one and snowpack as theother component]

Table 7.4

Cosmogenic Nuclides

Nuclide Symbol Half-life Source Natural Activity

Carbon-14 14C 5730 a Cosmic-ray interactions, 14N(n, p)14C 6 pCi g−1 (0.22 Bq g−1) in organicmaterial

Hydrogen-3(Tritium)

3H 12.3 a Cosmic-ray interactions with N and O,spallation from cosmic-rays, 6Li(n,alpha)3H

0.032 pCi kg−1 (1.2 × 10−3 Bq kg−1)

Beryllium-7 7Be 53.28 days Cosmic-ray interactions with N and O 0.27 pCi kg−1 (0.01 Bq kg−1)

Table 7.5

Isotope

Parent DaughterHalf-life ofparent (a)

Effective datingrange (a)

Uranium-235 Lead-207 710 million >10 millionPotassium-10 Argon-49 1.3 billion 10 000 to 3 billionCarbon-14 Nitrogen-14 5730 Up to 50 000

P1: SFK/UKS P2: SFK



Ex 7.9 The groundwater samples up gradient froma lake clearly showed meteoric origin, as their iso-topic composition was similar to that of rainfall(Fig. 7.16). Water samples from two in-lake wellshad isotopic compositions similar to meteoric wa-ter and plotted along the meteoric water line, in-dicating that groundwater inflow occurs at thesesites. The isotopic compositions of groundwaterdown-gradient from the lake had enriched valuesrelative to meteoric water and plotted along a mix-ing line described by the expression, δD = 4.6 ×

δ18O − 1.3. The mixing line connects the isotopiccomposition of the surface water and groundwaterend members, for example, evaporated lake waterand groundwater up-gradient from the lake. Inter-section of the GMWL and the mixing line is at (–3.5,–17.5) and represents the average isotopic compo-sition of groundwater. Use isotope mass-balancecalculations, using δ18O and δD, to estimate thefraction of lake water contribution at each well lo-cation.

Fsw denotes fraction of lake water mixing with ground water

Well No.

δ18O(‰)

δD(‰)

Fsw

(δ 18O)Fsw

(δD)

W-80 0.95 2.50 0.63 0.59

W-20 –2.25 –11.0 0.18 0.19

W-40 –1.00 –5.55 0.35 0.35

W-60 –0.45 –2.00 0.43 0.46

Lake 3.60 16.5 1.0 1.0

Fig. 7.16

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