A Bayesian Modeling Approach for Estimation of a ShapeFree Groundwater Age Distribution using Multiple Tracers
The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated. A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; ^{3}H, ^{3}He, ^{85}Kr, ^{39}Ar) and the La Selva Biological Station (CostaRica; SF _{ 6}, CFCs, ^{3}H, ^{4}He and ^{14}C), and compared to a number of mathematical forms.more »
 Authors:

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 The Catholic Univ. of America, Washington, DC (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Deltares, Utrecht (Netherlands); Geological Survey of the Netherlands, Utrecht (Netherlands); VU Univ., Amsterdam (Netherlands)
 Publication Date:
 Report Number(s):
 LLNLJRNL637575
Journal ID: ISSN 08832927
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Applied Geochemistry
 Additional Journal Information:
 Journal Volume: 50; Journal ID: ISSN 08832927
 Publisher:
 Elsevier
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 54 ENVIRONMENTAL SCIENCES
 OSTI Identifier:
 1237523
Massoudieh, Arash, Visser, Ate, Sharifi, Soroosh, and Broers, Hans Peter. A Bayesian Modeling Approach for Estimation of a ShapeFree Groundwater Age Distribution using Multiple Tracers. United States: N. p.,
Web. doi:10.1016/j.apgeochem.2013.10.004.
Massoudieh, Arash, Visser, Ate, Sharifi, Soroosh, & Broers, Hans Peter. A Bayesian Modeling Approach for Estimation of a ShapeFree Groundwater Age Distribution using Multiple Tracers. United States. doi:10.1016/j.apgeochem.2013.10.004.
Massoudieh, Arash, Visser, Ate, Sharifi, Soroosh, and Broers, Hans Peter. 2013.
"A Bayesian Modeling Approach for Estimation of a ShapeFree Groundwater Age Distribution using Multiple Tracers". United States.
doi:10.1016/j.apgeochem.2013.10.004. https://www.osti.gov/servlets/purl/1237523.
@article{osti_1237523,
title = {A Bayesian Modeling Approach for Estimation of a ShapeFree Groundwater Age Distribution using Multiple Tracers},
author = {Massoudieh, Arash and Visser, Ate and Sharifi, Soroosh and Broers, Hans Peter},
abstractNote = {The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated. A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (CostaRica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.},
doi = {10.1016/j.apgeochem.2013.10.004},
journal = {Applied Geochemistry},
number = ,
volume = 50,
place = {United States},
year = {2013},
month = {10}
}