Context. This paper describes the modelling of gas and dust data acquired in the period August to October 2014 from the European Space Agency's Rosetta spacecraft when it was in close proximity to the nucleus of comet 67P/Churyumov-Gerasimenko. Aims. With our 3D gas and dust comae models this work attempts to test the hypothesis that cliff activity on comet 67P/Churyumov-Gerasimenko can solely account for the local gas density data observed by the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) and the dust brightnesses seen by the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) in the considered time span. Methods. The model uses a previously developed shape model of the nucleus. From this, the water sublimation rates and gas temperatures at the surface are computed. The gas expansion is modelled with a 3D Direct Simulation Monte Carlo algorithm. A dust drag algorithm is then used to compute dust volume number densities in the coma, which are then converted to brightnesses using Mie theory and a line-of-sight integration. Furthermore we have studied the impact of topographic re-radiation on the models. Results. We show that gas activity from only cliff areas produces a fit to the ROSINA/COPS data that is as statistically good as a purely insolation-driven model. In contrast, pure cliff activity does not reproduce the dust brightness observed by OSIRIS and can thus be ruled out. On the other hand, gas activity from the Hapi region in addition to cliff activity produces a statistically better fit to the ROSINA/COPS data than purely insolation-driven outgassing and also fits the OSIRIS observations rather well. We found that topographic re-radiation does not contribute significantly to the sublimation behaviour of H2O but plays an important role in how the gas flux interacts with the irregular shape of the nucleus. Conclusions. We demonstrate that fits to the observations are non-unique. We can conclude however that gas and dust activity from cliffs and the Hapi region are consistent with the ROSINA/COPS and OSIRIS data sets for the considered time span and are thus a plausible solution. Models with activity from low gravitational slopes alone provide a statistically inferior solution.