Geological carbon storage is a promising solution to reduce the CO2 concentration in the atmosphere to ameliorate the effects of global warming from the greenhouse effect. Among feasible storage options, deep saline aquifers are believed to have the largest storage capacity for the gas collected from industrial processes. The first CO2 storage project at a commercial scale in a saline aquifer is in the Sleipner field of the Utsira storage formation in Norway. The long ongoing storage operation in the Sleipner field has been the subject of several past studies attempting to recreate the observed injected CO2 plume migration behaviour. History matching is a method to adjust the input parameters of the model in a way to minimise the mismatch between the simulated and the actual production data in reservoir engineering and applicable to carbon sequestration. Typical parameters adjusted in history matching are porosity, absolute and relative permeability data. In this study, we used an adjoint‐based optimisation tool and showed the importance of caprock morphology in finding an accurate plume match. Using a set of synthetic models, we initially minimised the mismatch between the observed and simulated CO2 plume outline by modifying the caprock topographical details. After testing the optimisation tool on the synthetic models, we applied the methodology to the Sleipner benchmark 2019 model and improved the plume match by locally adjusting caprock elevation within seismic detection limits. We subsequently improved the match by calibrating porosity, permeability, CO2 density and injection rate together in an experiment in which we calibrated all the parameters, including the caprock morphology, to find a better match. The results showed an improvement of around 8% (compared with the original model) in the plume match resulting from an average absolute elevation change of 3.23 m in the model while keeping the other parameters constant. Calibrating the porosity, permeability, CO2 density and injection rate resulted in a 5% improvement in the match, and once caprock morphology was included in the optimisation process, the match improvement increased by 16%. We changed the caprock elevation within a range lower than the seismic detection limit, and results showed that even a few metres variations in the elevation have significant impacts on the plume migration and trapping mechanism in the Sleipner model. The method presented in this work results in a better match than the original seismic data for the Sleipner model. © 2020 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons, Ltd.