LINKING HIERARCHICAL STRATAL ARCHITECTURE TO PLUME SPREADING USING THE LAGRANGIAN-BASED APPROACH TO TRANSPORT MODELING

A Lagrangian-based model for particle displacement variance has been derived to correspond to a hierarchical covariance model recently determined for the Borden site. Previous work has shown that the sedimentary formation at the site of the natural gradient test is composed of a hierarchy of unit types. Units defined at a smaller scale (hierarchical level I) combine to form units at a larger scale (hierarchical level II). The covariance structure reflects the hierarchical stratal architecture by displaying two distinct integral scales, one corresponding to transitions across level I unit types and the other to transitions across level II unit types. These integral scales can be computed directly from the proportions, mean length, and variance in length of the level I unit types and level II unit types. The new dispersion model illustrates the relative contributions of the level I and level II unit types to plume spreading and allows for linking the particle displacement variance to the quantifiable physical attributes of the hierarchical stratal architecture.