A one-dimensional, fractional order, advection-dispersion equation accurately models the movement of the core of the tritium plume at the highly heterogeneous MADE site. An a priori estimate of the parameters in that equation, including the order of the fractional dispersion derivative, was based on the assumption that the observed power law (heavy) tail of the hydraulic conductivity (K) field would create a similarly distributed velocity field. Monte Carlo simulations were performed to test this hypothesis. Results from the Monte Carlo analysis show that heavy tailed K fields do give rise to heavy tailed velocity fields; however, the exponent of the power law (the tail parameter) describing these two distributions is not necessarily the same. The tail parameter that characterizes a velocity distribution is not solely dependent on the tail parameter that characterizes the K distribution. The K field must also have long-range dependence so that water may flow through relatively continuous high-K channels.