Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields
- 172 Downloads
In earth and environmental sciences applications, uncertainty analysis regarding the outputs of models whose parameters are spatially varying (or spatially distributed) is often performed in a Monte Carlo framework. In this context, alternative realizations of the spatial distribution of model inputs, typically conditioned to reproduce attribute values at locations where measurements are obtained, are generated via geostatistical simulation using simple random (SR) sampling. The environmental model under consideration is then evaluated using each of these realizations as a plausible input, in order to construct a distribution of plausible model outputs for uncertainty analysis purposes. In hydrogeological investigations, for example, conditional simulations of saturated hydraulic conductivity are used as input to physically-based simulators of flow and transport to evaluate the associated uncertainty in the spatial distribution of solute concentration. Realistic uncertainty analysis via SR sampling, however, requires a large number of simulated attribute realizations for the model inputs in order to yield a representative distribution of model outputs; this often hinders the application of uncertainty analysis due to the computational expense of evaluating complex environmental models. Stratified sampling methods, including variants of Latin hypercube sampling, constitute more efficient sampling aternatives, often resulting in a more representative distribution of model outputs (e.g., solute concentration) with fewer model input realizations (e.g., hydraulic conductivity), thus reducing the computational cost of uncertainty analysis. The application of stratified and Latin hypercube sampling in a geostatistical simulation context, however, is not widespread, and, apart from a few exceptions, has been limited to the unconditional simulation case. This paper proposes methodological modifications for adopting existing methods for stratified sampling (including Latin hypercube sampling), employed to date in an unconditional geostatistical simulation context, for the purpose of efficient conditional simulation of Gaussian random fields. The proposed conditional simulation methods are compared to traditional geostatistical simulation, based on SR sampling, in the context of a hydrogeological flow and transport model via a synthetic case study. The results indicate that stratified sampling methods (including Latin hypercube sampling) are more efficient than SR, overall reproducing to a similar extent statistics of the conductivity (and subsequently concentration) fields, yet with smaller sampling variability. These findings suggest that the proposed efficient conditional sampling methods could contribute to the wider application of uncertainty analysis in spatially distributed environmental models using geostatistical simulation.
KeywordsGeostatistics Monte Carlo simulation Uncertainty analysis Hydrogeology
This work was funded as part of the research project with title (2269) “Advances in Geostatistics for Environmental Characterization and Natural Resources Management” (GEOSTATENV), implemented within the framework of the Action Aristeia I of the Operational Program “Education and Lifelong Learning” (Actions Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State.
- Alabert F (1987) The practice of fast conditional simulations through the LU decomposition of the covariance matrix. Math Geol 19(5):369–386Google Scholar
- Davis M (1987) Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Math Geol 19(2):91–98Google Scholar
- Helton JC, Johnson JD, Salaberry CJ, Storlie CB (2006) Survey of sampling based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf 91:1175–1209Google Scholar
- Kyriakidis P (2005) Sequential spatial simulation using latin hypercube sampling. In: Leuagthong O, Deutsch CV (eds) Geostatistics Banff 2004: 7th International Geostatistics Congress, Quantitative Geology and Geostatistics vol 14, Academic Publishers, Dordrecht, The Netherlands, pp 65–74Google Scholar
- McDonald M, Harbaugh A (1988) A modular three-dimensional finite difference ground-water flow model. Tech. Rep. Techniques of Water-Resources Investigations, Book 6: Modeling Techniques, US Geological SurveyGoogle Scholar
- McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245Google Scholar
- Sudicky E, Illman W, Goltz I, Adams J, McLaren R (2010) Heterogeneity in hydraulic conductivity and its role on the macroscale transport of a solute plume: from measurements to a practical application of stochastic flow and transport theory. Water Resour Res 46:W01508. https://doi.org/10.1029/2008WR007 CrossRefGoogle Scholar
- Switzer P (2000) Multiple simulation of spatial fields. In: Heuvelink GBM, Lemmens MJPM (eds) Proceedings of the 4th international symposium on spatial accuracy assessment in natural resources and environmental sciences, Coronet Books Inc., pp 629–635Google Scholar
- Zheng C (1990) MT3D, a modular three-dimensional transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems. Technical Report to the Kerr Environmental Research Laboratory, US Environmental Protection AgencyGoogle Scholar