For a multidimensional finite-size impulse input, analytical solutions to the conservation equation for concentration variance &sgr;2c are presented. Due to the dissipating action of local dispersion, at large times, &sgr;c is a decreasing fraction of the mean concentration. The Cape Cod bromide tracer exhibits this decrease. The larger the log conductivity microscale is, the slower is the action of local dispersion, and the slower is the predicted rate of decrease of the ratio of &sgr;c and the mean concentration (i.e., the coefficient of variation) with time, at large times, and vice versa. The coefficient of variation increases with distance from the center. A balance between the rates of production and dissipation of &sgr;2c relates it linearly to the squared gradients of the mean concentration field, away from the center of mass. For the zero local dispersion case, &sgr;c is an unboundedly growing multiple with time of the mean concentration. The longitudinal spatial second moment and macrodispersivities are insensitive to the inclusion/exclusion of local dispersion and therefore do not differentiate between the concentration fields for the two different cases. In contrast, the spatial-temporal evolution of &sgr;2c is singularly determined by the dissipating action of local dispersion. Measurements of local dispersivities need to be made along with a characterization of hydraulic conductivity variations to assess contaminant concentrations in aquifers. ¿ American Geophysical Union 1994