Linking Hierarchical Stratal Architecture to Plume Spreading in a Lagrangian-Based Transport Model

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In this article we present a new formulation of the Lagrangian-based model for macrodispersion of inert solutes. The formulation is based on a hierarchical expression of the spatial covariance of log permeability developed from recent findings at the well-studied Borden research site. The covariance expression represents a two-level hierarchy of stratal unit types with a corresponding hierarchy of permeability subpopulations. The covariance is a linear sum of terms corresponding to the probability of transitioning across stratal unit types of different scales, and these terms are directly related to quantifiable geometric attributes of the hierarchical stratal architecture at the Borden site. The new macrodispersion model is also a linear sum of terms, with different integral scales defined by the hierarchy of cross-transition probabilities and computed from the proportions and length statistics of the stratal unit types. The model allows the study of the contribution of each term to the composite particle displacement variance and thus the study of how the hierarchical stratal architecture influences plume spreading.