  Using a Lagrangian framework, we discuss different conceptualizations of the
blockscale dispersion tensor. We distinguish effective and ensemble blockscale
dispersion, which measure the impact of subscale velocity fluctuations on
solute dispersion. Ensemble dispersion quantifies subscale velocity
fluctuations between realizations, which overestimates the actual velocity
variability. Effective dispersion on the other hand quantifies the actual
blockscale velocity variability and thus reflects the impact of subscale
velocity fluctuations on mixing and spreading. Based on these concepts, we
quantify the impact of subscale velocity fluctuations on solute particle
spreading and determine the governing equations for the coarse-grained
concentration distributions. We develop analytical and semi-analytical
expressions for the average and variance of the blockscale dispersion tensor in
3D flow fields as a function of the structural parameters characterizing the
subsurface. Our results illustrate the relevance of the blockscale, the initial
scale of the solute body and local-scale dispersion in controlling the
uncertainty of the plume's dispersive behavior. The analysis performed in this
work has implications in numerical modeling (i.e. grid design) and allows to
quantify the uncertainty of the blockscale dispersion tensor.
