We examine three stochastic transport models of the Macrodispersion Experiment (MADE) site using high‐resolution conductivity fields derived from a new geostatistical interpretation of the flowmeter data. Evaluation of the spatial continuity of the hydraulic conductivity data revealed a hole effect structure indicating the occurrence of periodic structures, i.e., clustered lenses or facies. Alternatively, we examine geostatistical models based on indicator variables and found a similarity to bivariate Gaussian properties. Tritium transport was simulated in kriged fields and in random fields generated using different geostatistical models, at a grid spacing equal to the vertical support scale of the flowmeter measurements to explicitly represent small‐scale heterogeneity. Only those simulations obtained using the hole effect model resulted in a subset of realizations which reproduced the strong anomalous tracer spreading. Neglecting the hole effect structure of the spatial model in the Gaussian simulations resulted in a reduced tailing of the tracer, illustrating the importance of preferential flow on anomalous solute transport at the Columbus aquifer. Furthermore, we found that a multivariate Gaussian random function is adequate to model the spatial distribution of hydraulic conductivity at the MADE site, based on the results of the indicator transport simulations and the univariate and bivariate normality detected in the analysis of the flowmeter data. We conclude that, when small‐scale variability of hydraulic conductivity is correctly modeled at the flowmeter measurement support scale, the ADE is capable of reproducing the tracer spreading. Results suggest that the main contributor to the operational “memory function” used in previous successful mass transfer models is mostly a reflection of the suppressed spatial variation of hydraulic conductivity at the model scale.