Estimating Different Regimes in a Tracer Breakthrough Curve with Bayesian Statistics.
Abstract
Formally, all experimental scientists try to keep the conditions of the experiment in steady state or as close to steady state as possible in order to keep time, as a variable, out of the modeling picture. In practice, though, sometimes experiments do not go as wished, and the mathematical modelling of the data cannot ignore temporal changes in some of the physical parameters of the experiment. The authors have been working with a data set produced in an early experiment conducted at the Waste Isolation Pilot Plant site [Gonzales, 1984], and the presence of different physical conditions was admitted already in the original paper that presented those results. We propose using Bayesian statistics and the Reversible Jump Markov Chain Monte Carlo (RJMCMC) [Green, 1995] algorithm to find the number and duration of regimes that were present in the experiment. Our hypothesis is that for reasons particular to the experiment, the pumping in the extraction well diverged from a constant regime sometime during the experiment. We use a very simple 1dimensional transport model to explain the breakthrough curve for steadystate conditions, and the number and duration of different regimes is included as a free parameter to be inferred from the data. RJMCMC simulation provides an approximation to posterior probability distributions for the number of changepoints, time of ocurrence of these changes, and also probability distributions for the physical parameters that characterize each regime. We will also show that this problem can be seen as a variableselection problem, and that the method can be readily applied to other situations where variable selection is an ambition of the modelers. References: Gonzales D, Bentley C (1984). Field test for effective porosity and dispersivity in fractured dolomite: the WIPP, Southeastern New Mexico. In Groundwater Hydraulics, Rosenshein JS, Bennett GD (editors), Washington DC: American Geophysical Union, 207221. Green P (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711732.
 Publication:

AGU Fall Meeting Abstracts
 Pub Date:
 December 2007
 Bibcode:
 2007AGUFM.H23B1312M
 Keywords:

 1816 Estimation and forecasting;
 1832 Groundwater transport;
 1847 Modeling;
 1869 Stochastic hydrology;
 1873 Uncertainty assessment (3275)