Fig. 2: Vertical profiles of globally averaged ocean temperature and salinity in the last 400 years of the 500 years of piControl simulation (relative to the beginning of this 400 year time period). The last 400 years cover all simulations branched off since the first branch-off point is in year 150 of the piControl simulation, i.e. 350 years before the end of the piControl simulation (see Table 1).
In the last 100 years of the 500 year piControl simulation, which followed the 500 year spinup simulation, there are still imbalances in the top-of-atmosphere (TOA) and net surface radiation. Averaged over these 100 years the TOA radiation imbalance amounts to 0.34 W/m2 whereas the net surface energy flux consisting of radiation and turbulent heat fluxes amounts to 0.84 W/m2. Given that changes in the atmospheric energy content on this time scale are much smaller, the discrepancy implies an unphysical atmospheric energy non-conservation of about 0.5 W/m2. By using the delta approach in the evaluation of the climate change signal as briefly introduced in section 2.2, this non-conservation is cancelled out although one needs to keep in mind the non-linearity of the system.
The gradual energy loss of the ocean over the same time period, diagnosed from changes in the 3D ocean temperature (and sea-ice mass changes), corresponds to a global surface energy flux of -0.01 W/m2. The deviation from the atmospheric surface flux imbalance by 0.85 W/m2 cannot be explained by changes in the continental heat content, but points to further deviations from energy conservation that can be related to mismatching grids and coastlines between the model components, inconsistent treatment of temperature, precipitation and runoff (Mauritsen et al. 2012), or other inconsistencies. The atmosphere-related and the surface-related non-conserving energy terms partly compensate each other, resulting in an overall unphysical energy sink of -0.35 W/m2, and both of them are relatively constant over all simulations (when averaged over decades and longer; not shown).