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The non‐local model of mixing based on internal wave breaking, IDEMIX, is implemented as an enhancement of a turbulent kinetic energy closure model in three non‐eddy resolving general circulation ocean models that differ in the discretization and choice of computational grids. In IDEMIX internal wave energy is generated by an energy flux resulting from near‐inertial waves induced by wind forcing at the surface, and at the bottom, by an energy flux that parameterizes the transfer of energy between baroclinic and barotropic tides. In all model simulations with IDEMIX, the mixing work is increased compared to the reference solutions without IDEMIX, reaching values in better agreement with finestructure observations. Furthermore, the horizontal structure of the mixing work is more realistic as a consequence of the heterogeneous forcing functions. All models with IDEMIX simulate deeper thermocline depths related to stronger shallow overturning cells in the Indo‐Pacific. In the North Atlantic, deeper mixed layers in simulations with IDEMIX are associated with an increased Atlantic overturning circulation and an increase of northward heat transports toward more realistic values. The response of the deep Indo‐Pacific overturning circulation and the weak bottom cell of the Atlantic to the inclusion of IDEMIX is incoherent between the models, suggesting that additional unidentified processes and numerical mixing may confound the analysis. Applying different tidal forcing functions leads to simulation differences that are small compared to differences between the different models or between simulations with IDEMIX and without IDEMIX. Plain Language Summary: Waves in the ocean interior play a fundamental role for ocean dynamics since they can carry energy over long distances and, once they break, lead to turbulent mixing. This turbulent mixing can cause dense water masses to rise from the deep ocean with a direct impact on large‐scale currents. The wave dynamics occur on spatial scales that cannot be resolved in global ocean or climate models. To account for these processes, we apply the new parameterization IDEMIX that describes internal wave generation, propagation, and mixing. Using three different ocean models with and without IDEMIX ensures that we can identify model‐specific effects of the parameterization and discriminate them from those independent of the model. We find that the simulated mixing patterns agree better with observations once IDEMIX is applied. Large‐scale currents and the vertical temperature distribution are substantially affected by the internal wave parameterization. Whether this leads to an improved agreement with observed currents and water mass properties depends on the specific model and on numerical effects. In most cases, simulations with IDEMIX are not very sensitive to details of how the internal wave model is driven by tidal energy input. Key Points: the IDEMIX closure for a consistent representation of internal wave‐induced mixing is evaluated in three state‐of‐the‐art ocean modelsonly in simulations with IDEMIX can the models reproduce the magnitude and spatial variability of the observed mixing workmost changes with IDEMIX can be attributed to stronger mixing, but some effects are confounded by other processes and numerical mixing [ABSTRACT FROM AUTHOR]

The anthropogenically-intensified greenhouse effect has caused a radiative imbalance at the top of the atmosphere during the industrial period. This, in turn, has led to an energy surplus in various components of the Earth system, with the ocean storing the largest part. The land contribution ranks second with the latest observational estimates based on borehole temperature profiles, which quantify the terrestrial energy surplus to be 6 % in the last five decades, whereas studies based on state-of-the-art climate models scale it down to 2 %. This underestimation stems from land surface models (LSMs) having a too shallow subsurface, which severely constrains the land heat uptake simulated by Earth System Models (ESMs). A forced simulation of the last 2000 years with the Max Planck Institute ESM (MPI-ESM) using a deep LSM captures 4 times more heat than the standard shallow MPI-ESM simulations in the historical period, well above the estimates provided by other ESMs. However, deepening the LSM does not remarkably affect the simulated surface temperature. It is shown that the heat stored during the historical period by an ESM using a deep LSM component can be accurately estimated by considering the surface temperatures simulated by the ESM using a shallow LSM and propagating them with a standalone forward model. This result is used to derive estimates of land heat uptake using all available observational datasets, reanalysis products, and state-of-the-art ESM experiments. This approach yields values of 10.5-16.0 ZJ for 1971-2018, slightly smaller than the latest borehole-based estimates (18.2 ZJ). [ABSTRACT FROM AUTHOR]