The transport of dissolved chemicals across a horizontal interface between surface water and a saturated porous medium, associated with an unstable density gradient across the interface, is studied experimentally. Particular attention is paid to the starting conditions (i.e. the rate at which the density difference increases), and to the effect of changes in the density difference once the convective flow pattern has been established. The goal is a general flux law for any time variation of the density difference. Three significant observations are discussed. First, greater masses added to the overlying water results in larger density instabilities that drive greater fluxes. Second, the rate of addition of the mass affects both the peak density gradient and the long-term flux across the interface. Slower rates of addition result in greater variability in the resulting flux. Third, throughout all experiments, the ratios of final fluxes for different masses are similar, regardless of addition time.