We present some investigations into the current challenges encountered in eddy parameterisations for primitive equation (PE) ocean models. Using the finite-volume model FESOM2 and employing a dynamic correction method we investigate the causal relationships between the horizontal velocities, advected tracers and sea surface height. Considering different resolutions we are able to deduce that parameterisation of horizontal velocities only is ineffective on non-eddy resolving grids, while parameterisations of both tracers and velocities gives improvement on eddy-permitting grids. Furthermore, we present the theoretical aspects of applying two stochastic parameterisations to the primitive equations. These methods are Stochastic Advection by Lie Transport (SALT) and Stochastic Forcing by Lie Transport (SFLT). Initial investigations of these frameworks applied to FESOM2 are carried out, with some of the features of the resulting solutions examined. Finally, a study on the technical aspects of coarse graining shows the importance of rigour when projecting variables from a fine-grid to a coarse grid. This is of particular importance in PE models, in which vertical velocities are computed from the divergence of horizontal velocities. We derive general conditions for the preservation of divergence, curl, gradient and integrals and support our theoretical results with numerical simulations in FESOM2.