Abstract
Two methods for generating representative realizations from Gaussian and lognormal random field models are studied in this paper, with term representative implying realizations efficiently spanning the range of possible attribute values corresponding to the multivariate (log)normal probability distribution. The first method, already established in the geostatistical literature, is multivariate Latin hypercube sampling, a form of stratified random sampling aiming at marginal stratification of simulated values for each variable involved under the constraint of reproducing a known covariance matrix. The second method, scarcely known in the geostatistical literature, is stratified likelihood sampling, in which representative realizations are generated by exploring in a systematic way the structure of the multivariate distribution function itself. The two sampling methods are employed for generating unconditional realizations of saturated hydraulic conductivity in a hydrogeological context via a synthetic case study involving physically-based simulation of flow and transport in a heterogeneous porous medium; their performance is evaluated for different sample sizes (number of realizations) in terms of the reproduction of ensemble statistics of hydraulic conductivity and solute concentration computed from a very large ensemble set generated via simple random sampling. The results show that both Latin hypercube and stratified likelihood sampling are more efficient than simple random sampling, in that overall they can reproduce to a similar extent statistics of the conductivity and concentration fields, yet with smaller sampling variability than the simple random sampling.
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Acknowledgements
This work is part of the project “Advances in Geostatistics for Environmental Characterization and Natural Resources Management,” implemented under the “Aristeia” Action of the “Operational Programme Education and Lifelong Learning,” and co-funded by the European Social Fund (ESF) and Greek National Resources. The authors would like to gratefully acknowledge the support of the guest editor Professor Jaime Gómez-Hernández to include this paper in the special issue, as well as the efforts of three anonymous reviewers, whose comments led to significant improvements in the originally submitted manuscript. The support of Stelios Liodakis from the Department of Geography at the University of the Aegean, Greece, in terms of fruitful discussions and administrative assistance for this project is also gratefully acknowledged.
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Kyriakidis, P., Gaganis, P. Efficient Simulation of (Log)Normal Random Fields for Hydrogeological Applications. Math Geosci 45, 531–556 (2013). https://doi.org/10.1007/s11004-013-9470-5
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DOI: https://doi.org/10.1007/s11004-013-9470-5