The receptivity of a two-dimensional boundary layer flow developing on a flat plate with a super-elliptical leading edge to incoming disturbances in the presence of a discrete roughness element (DRE) is studied by direct numerical simulation. The DRE is a truncated cylinder with height k and fixed diameter. Its height is varied to cover a parameter space defined by the ratio of the element height to the local boundary layer displacement thickness k/δ^∗ and the Reynolds number based on the element height, Re_{kk}. Under the conditions simulated, in the absence of externally-imposed disturbances, steady flows are recovered. Two sources of disturbances are then considered: a localized volumetric forcing analogous to a suction/blowing strip that introduces plane monochromatic Tollmien-Schlichting (T-S) waves upstream of the DRE, and synthetic isotropic free-stream turbulence (FST) imposed as an inlet condition upstream of the leading edge. Two different dimensionless temporal frequencies of the T-S waves, F = 90 × 10^(−6) (ω = 0.21) and F = 120 × 10^(−6) (ω = 0.29), two DRE heights, k = 0.3δ^∗ (Re_{kk} = 50) and k = 0.5δ^∗ (Re_{kk} = 138) and the turbulence intensities Tu = 0.03% and Tu = 0.3%, are combined in multiple test-cases and analysed through the amplification factor of the resulting disturbances.