Abstract. Diabatic transport schemes with hybrid zeta coordinates, which follow isentropes in the stratosphere, are known to greatly improve Lagrangian transport calculations compared to the kinematic approach. However, some Lagrangian transport calculations with a diabatic approach, such as the Chemical Lagrangian Transport Model of the Atmosphere (CLaMS), show low computational performance on modern high-performance computing (HPC) architectures. Here, we implemented and evaluated a new diabatic transport scheme in the Massive-Parallel Trajectory Calculations (MPTRAC) model. While MPTRAC effectively exploits modern HPC architectures, it was previously limited to kinematic trajectories on pressure coordinates. The extended modelling approach now enables the use of either kinematic or diabatic vertical velocities and the coupling of different MPTRAC modules based on pressure or hybrid zeta coordinates. The evaluation of the new transport scheme in MPTRAC shows that after 90-day forward calculations distributions of air parcels in the upper troposphere and lower stratosphere (UTLS) are almost identical for MPTRAC and CLaMS. No significant bias between the two Lagrangian models was found. Furthermore, after one day, internal uncertainties (e.g., due to interpolation or the numerical integration method) in the Lagrangian transport calculations are at least one order of magnitude smaller than external uncertainties (e.g., from reanalysis selection or downsampling of ERA5). Differences between trajectories using either CLaMS or MPTRAC are on the order of the combined internal uncertainties within MPTRAC. Since the largest systematic differences are caused by the reanalysis and the vertical velocity (diabatic vs. kinematic) the results support the development efforts for trajectory codes that can access the full resolution of ERA5 in combination with diabatic vertical velocities. This work is part of a larger effort to adapt Lagrangian transport in state-of-the-art models such as CLaMS and MPTRAC to current and future HPC architectures and exascale applications.