The coupled transport process through an integrated soil-groundwater system is quantified for kinetically sorbing solute that originates from a time dependent source at the soil surface and is transported by steady random velocity. The derived expressions of ensemble mean solute breakthrough at some arbitrary control plane normal to the mean flow direction involve probability density functions (pdfs) of advective solute travel time through the unsaturated and the saturated zone of the transport domain. A nonstationary travel time pdf is derived for the saturated zone, to account for possible effects of flow nonuniformity due to recharge of water from the unsaturated zone. Nonuniform mean flow in the saturated zone decreases the relative influence of spatial variability within that zone on the ensemble mean solute breakthrough curve. Factors such as the longitudinal extent of the solute source and the unsaturated zone variability become more important for the spreading of the expected solute breakthrough as the degree of flow nonuniformity in the saturated zone increases. This implies that possible far-field simplifications based on the assumption that the transport process in an integrated soil-groundwater system is dominated by the transport conditions in the saturated zone may not be valid in cases with significant groundwater recharge from the unsaturated zone. ¿ American Geophysical Union 1995