Using Cluster Analysis of Hydraulic Conductivity Realizations to Reduce Computational Time for Monte Carlo Simulations
Publication: Journal of Irrigation and Drainage Engineering
Volume 138, Issue 5
Abstract
Despite the conceptual simplicity of Monte Carlo-simulation methods in assessing uncertainty in hydrogeological systems, their use is limited by expensive computational requirements in terms of the large number of realizations that must be processed. Cluster analysis was applied in this paper to reduce the number of realizations to be processed by flow simulators while efficiently approximating flow-response statistics. Different clustering techniques were used to partition the ensemble of realizations into a few clusters that were significantly different from each other and had maximum intracluster similarity. The clustering step was achieved by using different similarity metrics. Then a subsample of the realizations was collected to represent the uncertainty in the whole ensemble. Two methods for collecting the subsample were investigated: the stratified sampling and centroid-based sampling. The performance of different clustering and sampling techniques was tested by evaluating the mismatch between the statistics of the ensemble response (the reference response) and the subsample response, which are estimated from the clusters. Results show that 25% of the realizations in the ensemble may be sufficient to estimate the uncertainty in the flow responses when a suitable clustering method and suitable similarity measures are used.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abonyi, J., and Feil, B. (2007). Cluster analysis for data mining and system identification, Birkhauser Verlag AG, Basel, Switzerland.
Anderberg, M. R. (1973). Cluster analysis for applications, Academic Press, New York.
Bakr, A. A., Gelhar, L. W., Gutjahr, A. L., and MacMillan, J. R. (1978). “Stochastic analysis of spatial variability in subsurface flows 1. Comparison of one- and three-dimensional flows.” Water Resour. Res.WRERAQ, 14(2), 263–271.
Dagan, G. (1982). “Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 1. Conditional simulation and the direct problem.” Water Resour. Res.WRERAQ, 18(4), 813–833,.
Deutsch, C. V. (2002). Geostatistical reservoir modeling, 1st Ed., Oxford University Press, Oxford, NY.
Everitt, B. S., Landau, S., and Leese, M. (2009). Cluster analysis, 4th Ed., Wiley, Chichester, U.K.
Freeze, R. A. (1975). “A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media.” Water Resour. Res.WRERAQ, 11(5), 725–741.
Gilbert, R. O. (1987). Statistical methods for environmental pollution monitoring, Wiley, Chichester, U.K.
Gómez-Hernández, J. J., and Carrera, J. (1994). “Using linear approximations to rank realizations in groundwater modeling: Application to worst case selection.” Water Resour. Res.WRERAQ, 30(7), 2065–2072,.
Gotovac, H., Cvetkovic, V., and Andricevic, R. (2009). “Flow and travel time statistics in highly heterogeneous porous media.” Water Resour. Res.WRERAQ, 45(7),. 〈http://www.agu.org/pubs/crossref/2009/2008WR007168.shtml〉.
Harbaugh, A. W., Banta, E. R., Hill, M. C, and McDonald, M. G. (2000). “MODFLOW-2000, The U.S. Geological Survey modular ground-water model-user guide to modularization concepts and the ground-water flow process.” Rep. No. 00-92, United States Geological Survey, Reston, VA.
Jones, B. (1997). MATLAB statistics toolbox: User’s guide, Version 5 [Computer software]. Natick, MA, The Math Works.
Kupfersberger, H., and Deutsch, C. V. (1999). “Ranking stochastic realizations for improved aquifer response uncertainty assessment.” J. Hydrol. (Amsterdam)JHYDA7, 223(1–2), 54–65.
Matern, B. (1986). Spatial variation, 2nd Ed., Springer-Verlag, New York.
Matheron, G. (1962). Traité de géostatistique appliquée, Editions Technip, Paris.
Rubin, Y. (2003). Applied stochastic hydrogeology, Oxford University Press, Oxford, NY.
Rubinstein, R. Y., and Kroese, D. P. (2007). Simulation and the Monte Carlo method, 2nd Ed., Wiley-Interscience, New York.
Smith, R. E, and Hebbert, R. H. B. (1979). “A Monte Carlo analysis of the hydrologic effects of spatial variability of infiltration.” Water Resour. Res., 15(2), 419–429.WRERAQ
Tang, D. H., and Pinder, G. F. (1977). “Simulation of groundwater flow and mass transport under uncertainty.” Adv. Water Resour.AWREDI, 1(1), 25–30,.
Yeh, T.-C. J. (1992). “Stochastic modelling of groundwater flow and solute transport in aquifers.” Hydrol. ProcessesHYPRE3, 6(4), 369–395.
Information & Authors
Information
Published In
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Dec 16, 2010
Accepted: Aug 31, 2011
Published online: Apr 16, 2012
Published in print: May 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.