We present an upscaled model to predict the plume evolution
in highly heterogeneous alluvial aquifers.
The model is parameterized exclusively by the
mean, variance and correlation length of the logarithm of hydraulic conductivity, porosity and the mean hydraulic
gradient. It can be conditioned on the tracer and conductivity data at the
injection region. The model predicts the evolution of the
longitudinal mass distribution observed at the MADE site, which is characterized
by strongly non-Gaussian plume shapes with a localized peak and pronounced
forward tail. The proposed model explains these features by the
conductivity heterogeneity at the injection region, and tracer propagation due to
a broad distribution of spatially persistent Eulerian flow speeds.