One-dimensional advection–diffusion and advection–diffusion–dilution (or “leaky-pipe”) models have been widely used to interpret a variety of geophysical phenomena. For example, in the ocean these tools have been used to interpret the penetration and spreading of tracers such as Chlorofluorocarbons(CFCs) along the Deep Western boundary current (DWBC). Usually, the transport coefficients of such models are taken to be constant in time, thus assuming the transport to be in steady state. Here, we relax this assumption and calculate tracer-signal variability in two simple 1D models for the boundary current having low-amplitude time-varying coefficients. Given a background tracer gradient due, for example, to a steady-state source in a boundary region, the resulting tracer field exhibits fluctuations due to the transport acting on the gradients. We compare the transport-induced tracer fluctuations to propagated fluctuations occurring in steady-state models with a periodic source in the boundary region. Using coefficients fitted to DWBC tracer observations, we find that in the North Atlantic propagated tracer fluctuations are larger, while in the sub-tropics transport-induced fluctuations dominate. This contrasts a common view that subtropical and tropical DWBC fluctuations in tracers such as CFCs, temperature and salinity anomalies are propagated signals from the northern formation region. However, the predicted transport-induced fluctuations in these models are still smaller than the observed fluctuations.