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Markov Models and the Ensemble Kalman Filter for Estimation of Sorption Rates

Sandia journal manuscript; Not yet accepted for publication

Vugrin, Eric D.; Mckenna, Sean A.

Non-equilibrium sorption of contaminants in ground water systems is examined from the perspective of sorption rate estimation. A previously developed Markov transition probability model for solute transport is used in conjunction with a new conditional probability-based model of the sorption and desorption rates based on breakthrough curve data. Two models for prediction of spatially varying sorption and desorption rates along a one-dimensional streamline are developed. These models are a Markov model that utilizes conditional probabilities to determine the rates and an ensemble Kalman filter (EKF) applied to the conditional probability method. Both approaches rely on a previously developed Markov-model of mass transfer, and both models assimilate the observed concentration data into the rate estimation at each observation time. Initial values of the rates are perturbed from the true values to form ensembles of rates and the ability of both estimation approaches to recover the true rates is examined over three different sets of perturbations. The models accurately estimate the rates when the mean of the perturbations are zero, the unbiased case. Finally, for the cases containing some bias, addition of the ensemble Kalman filter is shown to improve accuracy of the rate estimation by as much as an order of magnitude.

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TYPE Journal Article YEAR 2007
OSTI

Hierarchical probabilistic regionalization of volcanism for Sengan region, Japan

Geotechnical and Geological Engineering

Kulatilake, Pinnaduwa H.S.W.; Park, Jinyong; Balasingam, Pirahas; Mckenna, Sean A.

A 1 km square regular grid system created on the Universal Transverse Mercator zone 54 projected coordinate system is used to work with volcanism related data for Sengan region. The following geologic variables were determined as the most important for identifying volcanism: geothermal gradient, groundwater temperature, heat discharge, groundwater pH value, presence of volcanic rocks and presence of hydrothermal alteration. Data available for each of these important geologic variables were used to perform directional variogram modeling and kriging to estimate geologic variable vectors at each of the 23949 centers of the chosen 1 km cell grid system. Cluster analysis was performed on the 23949 complete variable vectors to classify each center of 1 km cell into one of five different statistically homogeneous groups with respect to potential volcanism spanning from lowest possible volcanism to highest possible volcanism with increasing group number. A discriminant analysis incorporating Bayes' theorem was performed to construct maps showing the probability of group membership for each of the volcanism groups. The said maps showed good comparisons with the recorded locations of volcanism within the Sengan region. No volcanic data were found to exist in the group 1 region. The high probability areas within group 1 have the chance of being the no volcanism region. Entropy of classification is calculated to assess the uncertainty of the allocation process of each 1 km cell center location based on the calculated probabilities. The recorded volcanism data are also plotted on the entropy map to examine the uncertainty level of the estimations at the locations where volcanism exists. The volcanic data cell locations that are in the high volcanism regions (groups 4 and 5) showed relatively low mapping estimation uncertainty. On the other hand, the volcanic data cell locations that are in the low volcanism region (group 2) showed relatively high mapping estimation uncertainty. The volcanic data cell locations that are in the medium volcanism region (group 3) showed relatively moderate mapping estimation uncertainty. Areas of high uncertainty provide locations where additional site characterization resources can be spent most effectively. The new data collected can be added to the existing database to perform future regionalized mapping and reduce the uncertainty level of the existing estimations. © Springer Science+Business Media B.V. 2006.

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TYPE Conference YEAR 2007
ScopusOSTI
Results 126–150 of 191
Results 126–150 of 191