We test the use of a measure to diagnose a sub-mesoscale isopycnal diffusivity by determining the best match between observations of a tracer and simulations with varying small-scale diffusivities. Specifically, the robustness of a ‘roughness’ measure to discriminate between tracer fields experiencing different sub-mesoscale isopycnal diffusivities and advected by scaled altimetric velocity fields is investigated. We use the measure to compare numerical simulations of the tracer released at a depth of about 1.5 km in the Pacific sector of the Southern Ocean during the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES) field campaign with observations of the tracer taken on DIMES cruises. We find that simulations with an isopycnal diffusivity of ~20 m2s−1 best match observations in the Pacific sector of the ACC, rising to ~20-50 m2s−1 through Drake Passage, representing sub-mesoscale processes and any mesoscale processes unresolved by the advecting altimetry fields. The roughness measure is demonstrated to be a statistically robust way to estimate a small-scale diffusivity when measurements are relatively sparse in space and time, although it does not work if there are too few measurements overall. The planning of tracer measurements during a cruise in order to maximise the robustness of the roughness measure is also considered. It is found that the robustness is increased if the spatial resolution of tracer measurements is increased with the time since tracer release.