<p>Terrain following coordinates allow for better representation of physics at the sea-bed than traditional z-coordinates but result in numerical discretisation errors in the calculation of the horizontal pressure gradient (HPG) which manifest as spurious currents.&#160; As of NEMO r4.0.4, there were two HPG schemes available for use with terrain following coordinates, the traditional 2<sup>nd</sup> order sco scheme and the 3<sup>rd</sup> order prj scheme.&#160; The prj scheme, while highly accurate in the ocean interior, shows unphysical behaviour at the sea-bed for steeply sloping bathymetry.&#160; A task in the IMMERSE project was set up to identify, implement and test promising HPG schemes suitable for general vertical coordinates that are accurate, robust and physically consistent.&#160; As part of this task, the 3<sup>rd</sup>-order accurate density Jacobian scheme (djc) as proposed by Shchepetkin and McWilliams (2003) has now been implemented in the NEMO trunk (as a rewrite of the previously existing but non-operational djc scheme).&#160; Idealised testing has shown this scheme to be significantly more accurate than the sco scheme, and more robust than the prj scheme in coping with steeply sloping bathymetry.&#160; Initial results from applying the djc scheme in a challenging realistic configuration (the AMM7 with hybrid s-z-coordinates and non-uniform vertical discretisation) show a reduction in spurious currents with respect to the sco scheme.&#160; The prj scheme is highly sensitive to the rmax (maximum permitted slope) criterion.&#160; In cases where the bathymetry is so steep that a velocity-point may lie multiple levels below one of its neighbouring tracer-points, the nature of the prj near-bed HPG calculation leads to sudden spin-ups of spurious velocities which can exceed those of the djc scheme in the longer-term.&#160; Performance-wise, the djc scheme is 3 times slower than the sco scheme, but less expensive than the prj.&#160; Further work is planned to reduce the memory footprint.&#160; In addition to continued testing of the djc scheme, further work will look at alternative formulation (finite volume) HPG schemes, and high order variants.</p><p>This work is distributed under the Creative Commons Attribution 4.0 License. This licence does not affect the Crown copyright work, which is re-usable under the Open Government Licence (OGL). The Creative Commons Attribution 4.0 License and the OGL are interoperable and do not conflict with, reduce or limit each other.</p>