A long-term data set of Cl− concentrations in an artificial, leaking lake and in the underlying vadose zone was used to assess in situ vertical transport through a tertiary sandy deposit. Since the temporal resolution of the observed Cl− concentrations in the lake was relatively poor, a method was implemented to assess uncertainty on process identification as caused by a poor definition of the boundary condition. For this purpose we performed continuous stochastic simulations of Cl− concentrations in the lake conditioned to the discretely measured Cl− concentrations. This allows one to generate an ensemble of equiprobable time series of top boundary conditions. Each time series was subsequently used in an inverse convective–dispersive (CD) transport model based on the transfer function concept to identify the apparent transport properties of the unsaturated natural porous medium. For each simulation, one optimal parameter set in the least-square sense is then obtained, and the variance of the optimized parameters reflects the uncertainty due to the poor sampling frequency of Cl− in the lake. For the case study presented, we show that the variance component due to poor sampling of the top boundary condition is small for estimating the transport velocities. This component increases with the hydrodynamic dispersivity. However, for this latter parameter, the sampling variance component was still small compared with the total variability between dispersivity at different depths. Physical interpretation of variability and scale dependency of this latter parameter is studied in more detail in an accompanying paper.