A Markov Chain Model for Characterizing Medium Heterogeneity and Sediment Layering Structure

Accurate simulation of flow and contaminant transport in heterogeneous media is often hampered by difficulty in characterizing medium heterogeneity, in particular, heterogeneity in the lateral direction such as horizontal variability of sediment layering structure that is prevalent in sedimentary environments. Leveraged by using “soft” data, this study applies the transition probability (TP) based Markov chain (MC) model to sediment textural classes for characterizing the medium heterogeneity and sediment layering structure. The TP/MC method is evaluated by simulating vadose zone moisture movement at the field site, where the stratigraphy consists of imperfectly stratified layers. Soil heterogeneity is characterized by describing spatial variability of geometry of soil textural classes. Identifying the horizontal TP is not possible without incorporating the initial moisture content (θi) measurements, which carry signature about site heterogeneity and stratigraphy. The θi measurements, when transitioned into soil classes, are indispensable for depicting the sediment layering structure prevalent at the site. Multiple conditional realizations of the soil classes are generated to represent uncertainty in characterizing geometry of the soil classes. A Monte Carlo (MC) simulation shows that the simulated mean moisture contents agree well with corresponding field observations, whose spatial variability is sufficiently captured by the 95% confidence intervals calculated from the MC simulations. This is achieved by treating soil hydraulic parameters of each soil class deterministically and estimating them from core samples. Investigating effect of data conditioning on the simulated results shows that reducing conditioning data does not necessarily deteriorate simulation results, if the reduced data are within the mean length of other conditioning data. The TP/MC method for site characterization is flexible so that additional measurements of various types (e.g., geophysical data) can be incorporated as they become available.