We investigate the transport of impurities that are interpreted as climate proxies and are soluble in the premelted liquid that separates ice grains in the polar ice sheets even at subfreezing temperatures. Spatial variations in the relative abundances of multiple impurity species lead to gradients in their intergranular concentrations, defined as the ratio of the mass of dissolved impurity to the mass of premelted liquid. We show how diffusion down these intergranular concentration gradients affects anomalies in the bulk concentrations, defined as the ratio of the impurity mass to the mass of a polycrystalline sample, which are measured in polar ice cores. To illustrate these processes, we show that two initially asynchronous, periodic signals evolve to become in-phase after a short time: similar behavior is evident in coastal Antarctica, where there is a migration of methane sulfonate (MSA-) from summer to winter peaks, and it becomes in-phase with the primary deposition of sea salt. Moreover, the approach allows us to examine how an initially constant bulk concentration profile is influenced by an abrupt change to the bulk concentration of a second component. The resulting profiles share features with those observed in the Eemian compositional record from the Greenland Ice Core Project (GRIP) ice core.