This paper is an extension of the two-dimensional coupled Markov chain model developed by Elfeki and Dekking (2001) supplemented with extensive simulations. We focus on the development of various coupled Markov chains models: the so-called fully forward Markov chain, fully backward Markov chain and forward¿backward Markov chain models. We addressed many issues such as: sensitivity analysis of optimal sampling intervals in horizontal and lateral directions, directional dependency, use of Walther¿s law to describe lateral variability, effect of conditioning on number of boreholes on the model performance, stability of the Monte Carlo realizations, various implementation strategies, use of cross validation techniques to evaluate model performance and image division for statistically non-homogeneous deposits are addressed. The applications are made on three sites; two sites are located in the Netherlands, and the third is in the USA. The purpose of these applications is to show under which conditions the Markov models can be used, and to provide some guidelines for the practice. Entropy maps are good tools to indicate places where high uncertainty is present, so can be used for designing sampling networks to reduce uncertainty at these locations. Symmetric and diagonally dominant horizontal transition probabilities with proper sampling interval show plausible results (fits with geologists prediction) in terms of delineation of subsurface heterogeneous structures. Walther¿s law can be utilised with a proper sampling interval to account for the lateral variability. Keywords Markov chains - Walthers¿ law - conditional simulations - entropy - stochastic modelling - subsurface heterogeneity@en

Landfills represent a significant threat to groundwater contamination due to their nature of operation and their abundance. Monitoring well networks at these sites are of vital importance in detecting leakage plumes. This study presents a reliability assessment to estimate the performance of groundwater monitoring systems at landfill sites. A hypothetical problem is presented where the detection probability of several monitoring systems is compared. A Monte¿Carlo approach is used to incorporate uncertainties due to subsurface heterogeneity and the leak location. Hydraulic conductivity and leak location are considered as random variables with prescribed probability density functions. A finite difference groundwater model coupled with a random walk particle-tracking model simulates a contaminant plume released from the landfill for each Monte¿Carlo realization. The analysis shows that lateral dispersivity of the medium has a significant influence on the reliability of the monitoring system, since it is the primary parameter controlling the width of the contaminant plume. Furthermore the number and the location of the monitoring wells are dependent on the heterogeneity of the medium and size of the contaminant leak. It is concluded that the reliability of the common practice of three downgradient monitoring wells is inadequate from the point of view of prevention of groundwater contamination due to landfills. Keywords: Detection probability; Groundwater monitoring; Landfill; Contaminant plume; Monte¿Carlo analysis@en