Analysis and modeling of solute transport dynamics by breakdown coefficients and random cascades

Abstract

The small‐scale variability and scaling properties of solute transport dynamics were investigated by laboratory experiments. Dye‐stained water was applied at a constant flux in a Plexiglas Hele‐Shaw cell filled with soil material, and the transport process was registered by digital photographs of the cell front, producing a very high resolution in both time (minutes) and space (millimeters). The experiments comprised different cell materials (uniform and natural sand) and different water fluxes. Scaling properties of vertically integrated dye mass distributions were analyzed and modeled using so‐called breakdown coefficients (BDCs), which represent the multiplicative weights in a microcanonical random cascade process. The pdfs of BDCs varied with scale, indicating self‐affine scaling, and were accurately approximated by beta distributions with a scaling parameter. Two versions of BDC‐based random cascade models were used to simulate mass distributions at different time steps. The results support the applicability of random cascade models to subsurface transport processes.