Environmental Isotopes in the Hydrological Cycle
Principles and Applications

VOLUME I:  INTRODUCTION - THEORY, METHODS, REVIEW
by Willem G Mook, Centre for Isotope Research, Groningen
Contributing Author
J.J.de Vries, Free University, Amsterdam

CONTENTS
1	THE GLOBAL CYCLE OF WATER		  1
	1.1	Introduction			  1
	1.2	The hydrosphere			  2
		1.2.1	Origin of water on earth		  2
		1.2.2	The hydro-tectonic cycle		  2
		1.2.3	Distribution of water over the various reservoirs	  4
	1.3	The global water budget		  6
	1.4	Components of the hydrological cycle	  7
		1.4.1	Evaporation		  7
		1.4.2	Precipitation and atmospheric circulation	  9
		1.4.3	Discharge from the continents	11
		1.4.4	Groundwater		13
		1.4.5	Continental water surplus and water use	16
	1.5	The hydrosphere and global change	16
		1.5.1	Climatic change		16
		1.5.2	The human factor		19
			1.5.2.1	Irrigation		21
			1.5.2.2	Wetland drainage	21
			1.5.2.3	Ground cover damage	21
			1.5.2.4	Deforestation		21
			1.5.2.5	Interbasin diversion	22
			1.5.2.6	Streamflow management	22
			1.5.2.7	Land use changes	22
	1.6	Isotopes in the hydrological cycle		23

2	ATOMIC SYSTEMATICS AND NUCLEAR STRUCTURE	25
	2.1	Atomic structure and periodic table of the elements	25
	2.2	Structure of the atomic nucleus		26
	2.3	Stable and radioactive isotopes		27
	2.4	Mass and energy			28

3	ABUNDANCE AND FRACTIONATION OF STABLE ISOTOPES	31
	3.1	Isotope ratios and concentrations		31
	3.2	Isotope fractionation			31
	3.3	Kinetic and equilibrium isotope fractionation	34
	3.4	Theoretical background of equilibrium fractionation	39
	3.5	Fractionation by diffusion		43
	3.6	Relation between atomic and molecular isotope ratios	44
	3.7	Relation between fractionations for three isotopic molecules	45

4	ABUNDANCE VARIATIONS BY NATURAL PROCESSES	49
	4.1	Use of d values and isotope references	49
	4.2	Tracer concentration, amount of tracer	52
	4.3	Mixing of reservoirs with different isotopic composition	53
		4.3.1	Mixing of reservoirs of the same compound	53
			4.3.1.1	Isotopic dilution analysis	55
		4.3.2	Mixing of reservoirs of different compounds	56
	4.4	Isotopic changes in Rayleigh processes	57
		4.4.1	Reservoir with one sink		57
		4.4.2	Reservoir with two sinks		60
		4.4.3	Reservoir with one source and one sink, as a function of time	61
		4.4.4	Reservoir with one source and one sink, as a function of mass	64
		4.4.5	Reservoir with two sources and sinks, with and without fractionation	64

5	RADIONUCLIDE DECAY AND PRODUCTION	67
	5.1	Nuclear instability			67
	5.2	Nuclear decay and radiation		68
		5.2.1	Negatron decay		68
		5.2.2	Positron decay		68
		5.2.3	Electron capture		69
		5.2.4	Alpha decay		69
		5.2.5	Spontaneous and induced fission, neutron emission	71
	5.3	Recoil by radioactive decay		71
	5.4	Nuclear reactions			72
		5.4.1	Natural production		72
		5.4.2	Anthropogenic releases of radionuclides	73

6	EQUATIONS OF RADIOACTIVE DECAY AND GROWTH	75
	6.1	Law of radioactive decay		75
	6.2	Half-life and mean life		77
	6.3	Activity, specific activity and radionuclide concentration	77
	6.4	Mixture of independent radioactivities	78
	6.5	Branching decay			78
	6.6	Radioactive decay series		79
		6.6.1	Secular equilibrium		81
		6.6.2	Transient equilibrium		82

		6.6.3	No-equilibrium		  83
	6.7	Accumulation of stable daughter product	  85
	6.8	Radioactive growth			  86

7	NATURAL ABUNDANCE OF THE STABLE ISOTOPES OF C, O AND H	  89
	7.1	Stable carbon isotopes		  90
		7.1.1	The natural abundance		  90
		7.1.2	Carbon isotope fractionations	  91
		7.1.3	Reporting 13C variations and the 13C standard	  96
		7.1.4	Survey of natural 13C variations	  96
			7.1.4.1	Atmospheric CO2	  96
			7.1.4.2	Seawater and marine carbonate	  98
			7.1.4.3	Vegetation and soil CO2	  98
			7.1.4.4	Fossil fuel		  98
			7.1.4.5.	Global carbon cycle	  99
			7.1.4.6	Groundwater and riverwater	100
	7.2	Stable oxygen isotopes		101
		7.2.1	The natural abundance		101
		7.2.2	Oxygen isotope fractionations	103
		7.2.3	Reporting 18O variations and the18O standards	107
		7.2.4	Survey of natural 18O variations	110
			7.2.4.1	Seawater		110
			7.2.4.2	Precipitation		110
			7.2.4.3	Surface water		113
		7.2.5	Climatic variations		113
	7.3	Relation between 13C and 18O variations in H2O, HCO3-, and CO32-	115
	7.4	Stable hydrogen isotopes		117
		7.4.1	The natural abundance		117
		7.4.2	Hydrogen isotope fractionations	117
		7.4.3	Reporting 2H variations and the 2H standard	118
		7.4.4	Survey of natural 2H variations	120
	7.5	Relation between 2H and 18O variations in water	120

8	NATURAL ABUNDANCE OF RADIOACTIVE ISOTOPES	125
	8.1	The radioactive carbon isotope		125
		8.1.1	Origin of 14C, decay and half-life	125
		8.1.2	Reporting 14C variations and the 14C standard	126
		8.1.3	Survey of natural 14C variations	129
			8.1.3.1	Atmospheric CO2	129
			8.1.3.2	Vegetation and soils	130
			8.1.3.3	Seawater and marine carbonate	130
			8.1.3.4	Groundwater		131
		8.1.4	14C age determination		132
		8.1.5	Dating groundwater		134
			8.1.5.1	Dating groundwater with DIC	134
				8.1.5.1.1	The origin of 14C in DIC	134
				8.1.5.1.2	The chemical/isotopic mass balance	135
				8.1.5.1.3	Isotopic exchange in an open system	136
			8.1.5.2	Dating groundwater with DOC	136
	8.2	Relation between 13C and 14C variations	137
	8.3	The radioactive hydrogen isotope		138
		8.3.1	Origin of 3H, decay and half-life	138
		8.3.2	Reporting 3H activities and the 3H standard	138
		8.3.3	Survey of natural 3H variations 	139
	8.4	Comparison of 3H and 14C variations	140
		8.4.1	Relation between 3H and 14C in the atmosphere	140
		8.4.2	Relation between 3H and 14C in groundwater	141

9	CHEMISTRY OF CARBONIC ACID IN WATER	143
	9.1	Introduction			143
	9.2	Carbonic acid equilibria		144
	9.3	The equilibrium constants		146
		9.3.1	Ideal solutions		147
		9.3.2	Seawater			148
		9.3.3	Brackish water		148
	9.4	Carbonic acid concentrations		155
	9.5	Examples for closed and open systems	156
		9.5.1	Comparison of freshwater and seawater exposed to the atmosphere	156
			9.5.1.1	For freshwater	157
			9.5.1.2	For seawater		158
		9.5.2	System open for CO2 escape and CaCO3 formation	159
			9.5.2.1	Starting conditions	159
			9.5.2.2	Escape of CO2	160
			9.5.2.3	Precipitation of CaCO3	161
		9.5.3	System exposed to CO2 in the presence of CaCO3	161
		9.5.4	Closed system, mixing of freshwater and seawater	163

10	WATER SAMPLING AND LABORATORY TREATMENT	167
	10.1	Water sampling and storage		167
		10.1.1	Sampling bottles		167
		10.1.2	General field practice		168
		10.1.3	Precipitation		168
		10.1.4	Surface water		169
		10.1.5	Unsaturated zone waters		169
		10.1.6	Groundwater		170
		10.1.7	Geothermal waters		170
	10.2	Laboratory treatment of water samples	170
		10.2.1	The 18O/16O analysis of water	171
			10.2.1.1	Equilibration with CO2 for mass spectrometric analysis	171
			10.2.1.2	Other methods	172
		10.2.2	The 2H/1H analysis of water	173
			10.2.2.1	Reduction of H2O to H2 for mass spectrometric analysis	173
			10.2.2.2	Other methods	173
		10.2.3	The 3H analysis of water		174
			10.2.3.1	Water purification	174
			10.2.3.2	3H enrichment	175
			10.2.3.3	Preparation of gas for PGC of 3H	175
		10.2.4	The 14C analysis of dissolved inorganic carbon	176
			10.2.4.1	In the field		176
			10.2.4.2	In the laboratory	177
		10.2.5	The 13C/12C analysis of dissolved inorganic carbon	177	

11	MEASURING TECHNIQUES	 		179
	11.1	Mass spectrometry for stable isotopes	179
		11.1.1	Physical principle		179
	11.2	Reporting stable isotope abundance ratios	181
		11.2.1	Measurement of 2H/1H in H2	182
		11.2.2	Measurement of 15N/14N in N2	183
		11.2.3	Measurement of 13C/12C and 18O/16O in CO2	184
			11.2.3.1	Comparison with machine reference	184
			11.2.3.2	Calibration		184
			11.2.3.3	Isotopic corrections	186
			11.2.3.4	18O correction for water-CO2 equilibration	188
			11.2.3.5	Normalisation	188
		11.2.4	Measurement of 18O/16O and 17O/16O in O2	190
	11.3	Radiometry for radioactive isotopes	191
		11.3.1	Gas counters		191
			11.3.1.1	Ionisation chamber	192
			11.3.1.2	Proportional counter	193
			11.3.1.3	Geiger Müller counter	193
			11.3.1.4	Counter operation	193
		11.3.2	Liquid scintillation spectrometer	195
			11.3.2.1	Physical principle	195
			11.3.2.2	Counter operation	196
	11.4	Mass spectrometry for low-abundance isotopes	197
		11.4.1	Principle and application of AMS	197
	11.5	Reporting 14C activities and concentrations	199
		11.5.1	The choice of variables		199
		11.5.2	The standardisation		201
			11.5.2.1	The question of isotope fractionation	201
			11.5.2.2	The question of radioactive decay	202
			11.5.2.3	Definition of the 14C standard activity	202
		11.5.3	Final definitions		203
		11.5.4	Special cases		204
			11.5.4.1	Hydrology		204
			11.5.4.2	Oceanography and atmospheric research	205
			11.5.4.3	Geochemistry		206
			11.5.4.4	Enhanced 14C radioactivity	208
			11.5.4.5	14C ages		211
		11.5.5	Summary			211

12	NATURAL ISOTOPES OF ELEMENTS OTHER THAN H, C, O	213
	12.1	Helium				214
		12.1.1	Origin and characteristics	215
		12.1.2	Experimental and technical aspects	215
		12.1.3	Sources of 3He		215
		12.1.4	Natural abundance		216
		12.1.5	Applications		216
			12.1.5.1	Principle of 3H/3He dating	216
			12.1.5.2	Mass spectrometric measurement of 3H through 3He	216
	12.2	Lithium				217
		12.2.1	Natural abundance		217
		12.2.2	Experimental and technical aspects	217
		12.2.3	Applications		217
	12.3	Beryllium			218
		12.3.1	Origin and characteristics	218
		12.3.2	Experimental and technical aspects	218
		12.3.3	Natural abundance		218
		12.3.4	Applications		219
	12.4	Boron				219
		12.4.1	Natural abundance		219
		12.4.2	Experimental and technical aspects	219
		12.4.3	Applications		219
	12.5	Nitrogen				220
		12.5.1	Experimental and technical aspects	220
		12.5.2	Natural abundance and isotope fractionation	220
		12.5.3	Applications		221
		12.5.4	18O/16O in nitrate		221
	12.6	Aluminium			222
		12.6.1	Origin and characteristics	222
		12.6.2	Experimental and technical aspects	222
		12.6.3	Natural abundance		222
		12.6.4	Applications		223
	12.7	Silicon				223
		12.7.1	Origin and characteristics	223
		12.7.2	Natural abundance		224
		12.7.3	Experimental and technical aspects	224
		12.7.4	Applications		224
	12.8	Sulphur				224 
		12.8.1	Experimental and technical aspects	225
		12.8.2	Natural abundance		226
		12.8.3	Applications		226
	12.9	Chlorine				226
		12.9.1	Radioactive 36Cl		226
			12.9.1.1	Origin and characteristics	226
			12.9.1.2	Experimental and technical aspects	227
			12.9.1.3	Abundance in nature	228
			12.9.1.4	Applications		228
				12.9.1.4.1	Dating old water	228
				12.9.1.4.2	Infiltration of young water	229
		12.9.2	Stable 35Cl and 37Cl		229
			12.9.2.1	Natural abundance and applications	229
			12.9.2.2	Experimental and technical aspects	229
	12.10	Argon				230
		12.10.1	Origin and characteristics	230
		12.10.2	Experimental and technical aspects	231
		12.10.3	Natural abundance		231
		12.10.4	Applications		231
	12.11	Krypton				231
		12.11.1	Origin and characteristics	231
		12.11.2	Experimental and technical aspects	232
		12.11.3	Natural abundance		233
		12.11.4	Applications		233
	12.12	Iodine				233
		12.12.1	Origin and characteristics	233
		12.12.2	Experimental and technical aspects	234
		12.12.3	Natural abundance		234
		12.12.4	Applications		234
	12.13	Decay series			235
	12.14	The uranium series			237
		12.14.1	238U/234U			237
		12.14.2	230Th - 234U dating		238
		12.14.3	226Ra and 222Rn		238
		12.14.4	210Pb			238
		12.14.5	Experimental and technical aspects	239
	12.15	The actinium series			239
	12.16	The thorium series			239

13	ERRORS, MEANS AND FITS			243
	13.1	Errors				243
	13.2	Precision and accuracy		243
		13.2.1	Definitions			243
		13.2.2	Significant figures and digits	244
		13.2.3	Uncertainties		245
	13.3	Instrumental uncertainties		246
		13.3.1	Mean values		246
		13.3.2	Distribution of data		246
		13.3.3	Standard deviation		248
			13.3.3.1	Precision of data	248
			13.3.3.2	Precision of the mean	249
	13.4	Statistical uncertainties		250
	13.5	Error propagation			251
		13.5.1	Standard deviation		251
		13.5.2	Weighted mean		252
	13.6	Least-squares fit			253
		13.6.1	Fit to a straight line		253
		13.6.2	Fit to non-linear curves		254
	13.7	Chi-square test			255


REFERENCES					257

LITERATURE					263

IAEA PUBLICATIONS				265

CONSTANTS					268					

SYMBOLS AND UNITS				269

SUBJECT INDEX				271