Noise is a persistent feature in seismic data and so poses challenges in extracting increased accuracy in seismic images and physical interpretation of the subsurface. A previous noise analysis on the passive seismic dataset collected on a permanent surface array at the Aquistore carbon storage site identified individual noise signals, broadly classified as stationary, pseudo non-stationary and non-stationary, providing a basis on which to build an appropriate spatial and temporal noise field model. We introduce a novel noise modelling method based on a statistical covariance modelling approach created through the modelling of individual noise signals. This modelling method provides a significantly more accurate characterisation of real seismic noise compared to noise models created using conventional methods. Furthermore, we have developed a workflow to incorporate realistic noise models within synthetic seismic datasets providing an opportunity to test and analyse detection and imaging algorithms under realistic noise conditions.