Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields

• Published in: Mathematical geosciences 2018-02, Vol.50 (2), p.127-146
• Main Authors: Liodakis, Stelios, Kyriakidis, Phaedon, Gaganis, Petros
• Format: Article
• Language: English
• Subjects: Case studies; Chemistry and Earth Sciences; Computer applications; Computer Science; Computer simulation; Conditioning; Cost analysis; Distribution; Earth; Earth and Environmental Science; Earth Sciences; Environment models; Environmental modeling; Environmental science; Fields; Fields (mathematics); Frameworks; Geology; Geostatistics; Geotechnical Engineering & Applied Earth Sciences; Hydraulic conductivity; Hydrogeological investigations; Hydrogeology; Hypercubes; Latin hypercube sampling; Monte Carlo simulation; Parameter uncertainty; Physics; Sampling; Sampling methods; Simulation; Simulators; Solutes; Spatial distribution; Special Issue; Statistical analysis; Statistical methods; Statistics for Engineering; Stratified sampling; Transport; Uncertainty; Uncertainty analysis; Yields
• ISSN: 1874-8961; 1874-8953
• DOI: 10.1007/s11004-017-9715-9

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, o