A Markov chain model for characterizing medium heterogeneity and sediment layering structure

Abstract

By leveraging use of "soft" data (e.g., initial moisture content, θi), 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 the vadose zone moisture movement at a field site, where the stratigraphy consists of imperfectly stratified soil layers. Soil heterogeneity is characterized via spatial variability of the geometry of soil textural classes. When the θi measurements, which carry signature about medium heterogeneity and stratigraphy, are not included in the TP/MC model, it is not possible to identify the horizontal TP. The θi measurements, when transformed into soil classes, are necessary in mapping the soil layering structure prevalent at the site. The soil hydraulic parameters for each soil class are treated deterministically and are estimated on the basis of core samples. To evaluate uncertainty in characterizing geometry of the soil classes, multiple conditional realizations of the soil classes are generated. A Monte Carlo simulation shows that the simulated mean moisture contents agree well with corresponding field observations. The observed splitting of the moisture plume in a coarse sand layer that is sandwiched between two fine-textured layers, the southeastward movement of the plume during the redistribution period, and the near-zero fluid flux below the bottom fine layer are adequately simulated. Spatial variability of the field-measured moisture content is sufficiently captured by the 95% confidence intervals calculated from the Monte Carlo simulations. Investigating the effect of data conditioning on the simulated results shows that a reduction of conditioning data does not necessarily deteriorate simulation results if other conditioning data exist within the mean length of the soil classes. The TP/MC method is flexible so that other types of site characterization data (e.g., geophysical data) can be incorporated as they become available. Copyright 2008 by the American Geophysical Union.