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2.1. Noble gas temperatures 2 Theory modeled and measured data. The quality of this matching is assessed by using the χ 2 method that weights the deviation between the measured and the predicted concentrations with the measurement accuracy σi: UA, PR and MR model χ 2 = � i � Ci,m − Cmodel �2 i σ2 i (2.12) The first model created to account for the presence of an excess air component was the unfractionated air model, or UA model. It is based on the assumption that enclosed air bubbles are completely dissolved in the water at or below the ground water table, leading to an atmospheric composition of the excess air component of the noble gas concentration without any signs of fractionation, as described by C UA i = Ci,eq + A · Ci,atm (2.13) where Ci,atm is the unfractioned excess air component and A is the fraction of air entrapped in the water volume, a scaling parameter of this model. Using Henry’s law (Equation 2.1), this relation is expressed as C UA i = Ci,eq(1 + A · Hi) (2.14) This basic assumption of complete dissolution did not prove to be realistic though, as Stute et al. [1995] showed excess air components in ground water to be enriched in the heavier noble gases. They introduced a modification of the UA model, called partial re-equilibration model, or PR model, assuming diffusive gas loss affecting the completely dissolved excess air component. The mass and temperature dependent diffusion coefficients of the individual noble gases [Jähne et al., 1987] would then account for the occurring fractionation. Inter-isotopic fractionation effects are not observed however [Peeters et al., 2003], on which the PR model’s applicability was criticized. Whether this effect should actually be expected at all to occur in a manner similar to internoble-gas fractionation has been questioned though [Bourg and Sposito, 2008]. The PR model can be expressed as [Aeschbach-Hertig et al., 2008]: � � � �� β C PR i = Ci,eq 1 + A · Hi · exp −FPR � Di DNe (2.15) where FPR is a parameter characterizing the amount of excess air loss, Di are the noble gas diffusion coefficients and 0.5 ≤ β ≤ 1 is a model parameter from gas transfer theory. Since this single step excess air intrusion and degassing leads to initial Ne excess amounts requiring unrealistic physical conditions in some studies [Kipfer et al., 2002] and failed to describe certain noble gas records [Ballentine and Hall, 1999], a variation of the PR model was introduced as the multi-step partial re-equilibration model, or MR model, by Kipfer et al. [2002]. The MR model assumes a physically more realistic occurrence of multiple (n) excess air intrusions and degassing steps, containing the PR model as the special case n = 1: � � � �� β C MR i = Ci,eq 1 + A · Hi · n� exp k=1 20 −k · FPR � Di DNe (2.16)
2 Theory 2.1. Noble gas temperatures Unfractionated excess air (UA) AEW & air air entrapment complete dissolution Oxygen depletion (OD) AEW & O2 depl. air air entrapment complete dissolution Partial re-equilibration (PR) AEW & air air entrapment complete dissolution di�usive gas loss Closed-system equilibration (CE) Multi-step partial re-equilibration (MR) AEW & air air entrapment partial dissolution, equilibration water-gas separation Figure 2.3: Schematic illustration of the mechanisms leading to excess air as proposed by some of the different presented models. Adapted from Wieser [2011]. 21
Page 1: Faculty of Physics and Astronomy He
Page 5: Measuring annual variation of soil
Page 8 and 9: CONTENTS CONTENTS 3.1 Setup of the
Page 11 and 12: Chapter 1 Introduction Understandin
Page 13: 1 Introduction Molins and Mayer [20
Page 16 and 17: 2.1. Noble gas temperatures 2 Theor
Page 24 and 25: 2.2. Physical processes and propert
Page 26 and 27: 2.2. Physical processes and propert
Page 28 and 29: 2.3. Soil atmosphere composition 2
Page 35 and 36: Chapter 3 Sampling sites and method
Page 37 and 38: 3 Sampling sites and methods 3.1. S
Page 43 and 44: Chapter 4 Measuring methods 4.1 Mas
Page 45 and 46: 4 Measuring methods 4.1. Mass spect
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Page 50 and 51: 5.2. Temperature profiles 5 Results
Page 52 and 53: 5.3. O2 and CO2 profiles 5 Results
Page 54 and 55: 5.4. Borehole sealing 5 Results 5.4
Page 56 and 57: 5.4. Borehole sealing 5 Results Fig
Page 58 and 59: 5.5. Noble gases 5 Results 8 days,
Page 60 and 61: 5.5. Noble gases 5 Results 5.5.3 So
Page 62 and 63: 5.5. Noble gases 5 Results 5.5.4 So
Page 64 and 65: 6 Discussion This rather extreme am
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Page 68 and 69: 6 Discussion Table 6.1: Synthetic d
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Chapter 7 Summary The results of th
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8 Outlook Considering the manifold
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A.1. Gas sample size A Calculations
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A.3. Fractionation-Values A Calcula
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Table B.3: Noble gas volume mixing
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Table B.5: Calculated values of rel
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Table B.8: Precipitation record of
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Table B.10: Complete dataset of nob
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Appendix C Additional plots and fig
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C Additional plots and figures Figu
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C Additional plots and figures �
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C Additional plots and figures O 2
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C Additional plots and figures 4 He
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C Additional plots and figures 20 N
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C Additional plots and figures 10 1
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Appendix D Datasheets 107
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D Datasheets LogTag TREX-8 Technica
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Bibliography [Aeschbach-Hertig 1994
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BIBLIOGRAPHY BIBLIOGRAPHY [Friedric
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BIBLIOGRAPHY BIBLIOGRAPHY [Riveros-
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Acknowledegment At the end of this
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