The spatial distribution of solute concentration in heterogeneous aquifers is extremely complex and variable over scales ranging from a few millimeters to kilometers. Obtaining a detailed spatial distribution of the concentration field is an elusive goal because of intrinsic technical limitations and budget constraints for site characterization. Therefore, local concentration predictions are highly uncertain and alternative measures of transport must be sought. In this paper, we propose to describe the spatial distribution of the concentrations of a nonreactive tracer plume by means of suitable spatial statistical transport measures, as an alternative to approaches relying only on the ensemble mean concentration. By assuming that the solute concentration is statistically distributed according to the Beta distribution model, we compare several models of concentration moments against numerical simulations and Cape Cod concentration data. These measures provide useful information which are: (i) representative of the overall transport process, (ii) less affected by uncertainty than the local probability density function and (iii) only marginally influenced by local features. The flexibility of the approach is shown by considering three different integral expressions for both the spatial mean and variance of concentration based on previous works. Aiming at a full statistical characterization, we illustrate how the Beta relative cumulative frequency distribution (obtained as a function of the spatial concentration) compares with the numerical cumulative frequencies. Our approach allows to estimate the probability of exceeding a given concentration threshold within the computational or observational domain, which could be used for sampling data campaigns, preliminary risk assessment and model refinement. Finally, our results highlight the importance of goal‐oriented model development.