The application of natural isotopes, stable as well as radioactive, has become a widespread tool for hydrological research, especially surface- and groundwater behaviour and exploration. By far the most common isotopes applied are those of the elements of hydrogen, oxygen and carbon, crucial in the water cycle. The concentration ratios of the stable isotopes in water vary, depending on the source of the water and natural processes such as evaporation and condensation. Radioactive isotopes may provide indications,depending on natural conditions, of the source of water and age, i.e. the time elapsed since infiltration. This is a textbook, explaining in a simple, but mathematically, physically and chemically correct form, the consequences of natural processes to stable isotope concentrations and radioactivities. After a broadly theoretical introduction, the elements of the water cycle are treated successively: Precipitation: globally, regionally and locally; Different forms of surface water: rivers, rivulets and small streams, lakes and stagnant waters, estuaries and the sea; Groundwater: infiltration and groundwater flow. The book is intended for students in the Earth Sciences, especially in Hydrology; trainees from developing countries; laboratory technicians and assistants; engineers involved in (geo)hydrological fieldwork and anyone who starts his work in natural abundances of stable or radioactive isotopes.

Table of Contents:
1 Atomic systematics and nuclear structure 1 1.1 Atomic structure and the periodic table of the elements 1 1.2 Structure of the atomic nucleus 2 1.3 Stable and radioactive isotopes 3 1.4 Mass and energy 4 2 Isotope fractionation 7 2.1 Isotope ratios and concentrations 7 2.2 Isotope fractionation 8 2.3 Kinetic, equilibrium and non-equilibrium isotope fractionation 9 2.3.1 Definitions 9 2.3.2 Isotope exchange 11 2.3.3 Relation between equilibrium and kinetic fractionation 12 2.4 Conclusions from theory 14 2.5 Fractionation by diffusion 15 2.6 Relation between atomic and molecular isotope ratios 16 2.7 Relation between fractionations for three isotopic molecules 17 2.8 Use of d values and isotope standards 18 2.9 Tracer concentration, amount of tracer 20 3 Isotope fractionation processes 23 3.1 Mixing of reservoirs with different isotopic composition 23 3.1.1 Mixing of reservoirs of the same compound 23 3.1.2 Mixing of reservoirs of different compounds 25 3.2 Isotopic changes in Rayleigh processes 25 3.2.1 Reservoir with one sink 26 3.2.2 Reservoir with two sinks 27 3.2.3 Reservoir with one source and one sink, as a function of time 29 3.2.4 Reservoir with one source and one sink, as a function of mass 32 3.2.5 Reservoir with two sources and sinks, with and without fractionation 32 4 Radioactive decay and production 35 4.1 Nuclear instability 35 4.2 Nuclear decay and radiation 35 4.2.1 Negatron (ß-) decay 36 4.2.2 Positron (ß+) decay 36 4.2.3 Electron capture (EC) 37 4.2.4 Alpha (a) decay 37 4.2.5 Branching decay 38 4.2.6 Spontaneous and induced fission, neutron emission 39 4.2.7 Radioactive decay series 39 4.2.8 Recoil by radioactive decay 40 4.3 Law of radioactive decay 41 4.3.1 Exponential decay 41 4.3.2 Half-life and mean life 42 4.3.3 Activity, specific activity and radionuclide concentration 43 4.3.4 Accumulation of stable daughter product 44 4.4 Nuclear reactions 45 4.4.1 Natural production 45 4.4.2 Anthropogenic releases of radionuclides 46 4.4.3 Radioactive growth 47 5 Natural abundance of the stable isotopes of C, O and H 49 5.1 Stable carbon isotopes 50 5.1.1 The natural abundance 50 5.1.2 Carbon isotope fractionations 51 5.1.3 Reporting 13C variations and the 13C standard 54 5.1.4 Survey of natural 13C variations 55 5.1.4.1 Atmospheric CO2 55 5.1.4.2 Seawater and marine carbonate 55 5.1.4.3 Vegetation and soil CO2 55 5.1.4.4 Fossil fuel 57 5.1.4.5. Global carbon cycle 57 5.1.4.6 Groundwater and river water 58 5.2 Stable oxygen isotopes 61 5.2.1 The natural abundance 61 5.2.2 Oxygen isotope fractionations 62 5.2.3 Reporting 18O variations and the18O standards 65 5.2.4 Survey of natural 18O variations 68 5.2.4.1 Seawater 69 5.2.4.2 Precipitation 69 5.2.4.3 Surface water 69 5.2.5 Climatic variations 70 5.3 Relation between 13C and 18O variations in H2O, HCO3- , and CO32- 72 5.4 Stable hydrogen isotopes 74 5.4.1 The natural abundance 74 5.4.2 Hydrogen isotope fractionations 74 5.4.3 Reporting 2H variations and the 2H standard 75 5.4.4 Survey of natural 2H variations 76 5.5 Relation between 2H and 18O variations in water 76 6 Natural abundance of the radioactive isotopes of C and H 81 6.1 The radioactive carbon isotope 81 6.1.1 Origin of 14C, decay and half-life 81 6.1.2 Reporting 14C variations and the 14C standard 82 6.1.3 Survey of natural 14C variations 85 6.1.3.1 Atmospheric CO2 85 6.1.3.2 Vegetation and soils 86 6.1.3.3 Seawater and marine carbonate 86 6.1.3.4 Groundwater 87 6.1.4 14C age determination 88 6.1.4.1 Dating terrestrial samples 88 6.1.4.2 Dating groundwater 90 6.2 Relation between 13C and 14C variations 91 6.3 The radioactive hydrogen isotope 93 6.3.1 Origin of 3H, decay and half-life 93 6.3.2 Reporting 3H activities and the 3H standard 93 6.3.3 Survey of natural 3H variations 94 6.4 Comparison of 3H and 14C variations 95 6.4.1 Relation between 3H and 14C in the atmosphere 95 6.4.2 Relation between 3H and 14C in groundwater 96 7 Isotopes in precipitation 99 7.1 18O and 2H in precipitation 99 7.1.1 Evaporation of seawater and the marine atmosphere 101 7.1.2 Formation of precipitation 101 7.1.2.1 Rayleigh depletion during precipitation 101 7.1.2.2 Relation between 18O/16O and 2H/1H in natural waters 104 7.1.3 Observed stable isotope effects in precipitation 105 7.1.3.1 The latitude / annual-temperature effect 106 7.1.3.2 Seasonal effect 108 7.1.3.3 Continental effect 111 7.1.3.4 Altitude effect 114 7.1.3.5 Amount effect 116 7.1.3.6 Interannual variations 117 7.1.3.7 Small-scale variations 118 7.1.3.7.1 Small-scale spatial variations 118 7.1.3.7.2 Small-scale temporal variations 119 7.2 3H in precipitation 119 7.2.1 Characteristics and distribution of 3H 119 7.2.2 Hydrological aspects 120 7.2.2.1 Long-term recovery of natural 3H levels 120 7.2.2.2 Seasonal variations in 3H 124 7.2.2.3 Geographical variations in 3H 124 7.2.2.4 Small-scale temporal 3H variations 124 8 Isotopes in surface water 127 8.1 Isotope fractionation during evaporation 127 8.1.1 Effective fractionation of 18O and 2H 127 8.1.2 Relation between isotopic and chemical composition 129 8.1.3 Relation between 18O and 2H by evaporation 130 8.1.4 Evaporation processes in nature 130 8.1.4.1 Evaporation of an isolated water body 130 8.1.4.2 Evaporation of a well-mixed water body with constant inflow and no outflow 131 8.1.4.3 Evaporation of a well-mixed water body with constant inflow and outflow 132 8.1.4.4 Evaporation of an isotopically inhomogeneous lake with a river inflow and with or without discharge 132 8.2 Observed 18O and 2H variations in surface water 134 8.2.1 18O and 2H in large rivers 134 8.2.2 18O and 2H in small rivers and streams 139 8.2.3 18O and 2H in the sea 142 8.2.4 18O and 2H in estuaries and coastal waters 143 8.2.5 18O and 2H in lakes 144 8.3 3H in surface water 146 8.3.1 3H in rivers and small streams 146 8.3.2 3H in the sea 149 8.3.3 3H in lakes 149 8.4 13C in surface water 149 8.4.1 The origin of inorganic carbon in natural waters 150 8.4.2 13C in rivers and small streams 150 8.4.3 13C in lakes 151 8.4.3.1 Chemical equilibration with atmospheric PCO2 152 8.4.3.2 Precipitation of calcium carbonate 152 8.4.3.3 CO2 consumption by biological activity 153 8.4.3.4 Isotopic exchange with atmospheric CO2 153 8.4.4 13C in the sea 153 8.4.5 13C in estuaries 154 8.5 14C in surface water 156 9 Isotopes in groundwater 159 9.1 18O in groundwater 159 9.1.1 Correlation between 18O of groundwater and precipitation 159 9.1.2 18O in saline water 160 9.2 2H in groundwater 162 9.3 3H in groundwater 162 9.3.1 Applications 162 9.3.2 3H in infiltration studies 162 9.3.2.1 Determination of the infiltration velocity with 3H 163 9.3.2.2 Determination of the infiltration rate with 3H 164 9.3.3 Dating groundwater with 3H 165 9.3.4 Absolute dating of groundwater with3H/3He 166 9.3.5 Infiltration versus upwelling 167 9.4 13C and 14C in groundwater 168 9.4.1 The origin of 13C and 14C in groundwater 169 9.4.1.1 Oxidation of organic matter in the upper soil 169 9.4.1.2 Atmospheric CO2 in rain water 169 9.4.1.3 Dissolution of silicate rock 170 9.4.1.4 Action of humic acid 170 9.4.1.5 Decomposition of organic matter in the saturated zone 170 9.4.1.6 Anaerobic decomposition of organic matter 170 9.4.1.7 Sulphate reduction 171 9.4.1.8 Ca - Na exchange 171 9.4.1.9 CO2 from volcanic activity 171 9.4.1.10 Exchange with the soil carbonate 171 9.4.1.10.1 Isotopic exchange 171 9.4.1.10.2 Dissolution-precipitation 172 9.4.2 The CO2 – CaCO3 concept 172 9.4.3 The closed dissolution system 173 9.4.3.1 The chemical dilution correction 173 9.4.3.2 The isotopic dilution correction 175 9.4.4 The open dissolution system 176 9.4.4.1 Isotopic exchange in the unsaturated zone 177 9.4.4.2 The dissolution-exchange model 177 9.4.4.3 The isotopic parameters 180 9.4.5 Isotopic changes in the aquifer 180 9.5 Relative 14C ages of groundwater 180 9.6 Dating groundwater with DOC 181 9.7 Relation between 14C and 3H in groundwater 181 APPENDICES I Water sampling and laboratory treatment 185 I.1 Water sampling and storage 185 I.1.1 Sampling bottles 185 I.1.2 General field practice 186 I.1.3 Precipitation 187 I.1.4 Surface water 187 I.1.5 Unsaturated zone water 188 I.1.6 Groundwater 188 I.1.7 Geothermal water 188 I.2 Laboratory treatment of water samples 188 I.2.1 The 18O/16O analysis of water 189 I.2.1.1 Equilibration with CO2 for mass spectrometric analysis 189 I.2.1.2 Other methods 190 I.2.2 The 2H/1H analysis of water 191 I.2.2.1 Reduction of H2O to H2 for mass spectrometric analysis 191 I.2.2.2 Other methods 191 I.2.3 The 3H analysis of water 192 I.2.3.1 Water purification 192 I.2.3.2 3H enrichment 193 I.2.3.3 Preparation of gas for PGC of 3H 194 I.2.4 The 14C analysis of dissolved inorganic carbon 194 I.2.4.1 In the field 194 I.2.4.2 In the laboratory 195 I.2.5 The 13C/12C analysis of dissolved inorganic carbon 195 II Measuring techniques 197 II.1 Mass spectrometry for stable isotopes 197 II.1.1 Physical principle 197 II.1.2 Reporting stable isotope abundance ratios 199 II.1.2.1 Measurement of 2H/1H in H2 200 II.1.2.2 Measurement of 15N/14N in N2 201 II.1.2.3 Measurement of 13C/12C and 18O/16O in CO2 201 II.1.2.3.1 Comparison with reference or standard 202 II.1.2.3.2 Isotopic corrections 202 II.1.2.4 Measurement of 18O/16O and 17O/16O in O2 203 II.2 Radiometry for radioactive isotopes 204 II.2.1 Gas counters 204 II.2.1.1 Ionisation chamber 205 II.2.1.2 Proportional counter 206 II.2.1.3 Geiger Müller counter 206 II.2.1.4 Counter operation 207 II.2.2 Liquid scintillation spectrometer 208 II.2.2.1 Physical principle 208 II.2.2.2 Counter operation 210 II.3 Mass spectrometry for low-abundance isotopes 210 II.3.1 Physical principle of AMS 210 II.3.2 Applications and (dis)advantages 212 II.4 Determination of 3H through mass spectrometric measurement of 3He 212 II.5 Reporting 14C activities and concentrations 214 II.5.1 The choice of variables 214 II.5.2 Special case 1: hydrology 215 II.5.3 Special case 2: oceanography 216 II.5.4 14C ages 217 II.5.5 Summary 218 III Chemistry of carbonic acid in water 219 III.1 Introduction 219 III.2 Carbonic acid equilibria 220 III.3 The equilibrium constants 222 III.3.1 Ideal solutions 223 III.3.2 Seawater 223 III.3.3 Brackish water 224 III.4 Carbonic acid concentrations 226 III.5 Examples for open and closed systems 227 III.5.1 Comparison of freshwater and seawater exposed to the atmosphere 228 III.5.1.1 For freshwater 229 III.5.1.2 For seawater 229 III.5.2 System open for CO2 escape and CaCO3 formation 229 III.5.2.1 Starting conditions 230 III.5.2.2 Escape of CO2 231 III.5.2.3 Precipitation of CaCO3 231 III.5.3 System exposed to CO2 in the presence of CaCO3 232 III.5.4 Closed system, mixing of freshwater and seawater 233 References and Selected Papers 237 Literature 243 IAEA Publications 245 Symbols, Units and Constants 249 Subject Index 253