The question whether, apart from a vertical redistribution of OHC, more heat is sequestered in the deep ocean in a hiatus period is important, giving its implications for the energy balance of the planet. The Earth’s response to changes in radiative forcing can be explained by a simple energy balance model16. This model predicts that a reduced energy imbalance arises when external forcing causes a hiatus, while an increased imbalance arises when it is due to internal climate dynamics. The forced response is described by

$${\rm{Q}}={\rm{\lambda }}\,{\rm{\Delta }}{\rm{T}}+{\rm{N}}$$ (1)

where Q is the net radiative forcing, λ ΔT is the change in net radiation due to a temperature change ΔT, λ is the climate feedback parameter and N is the TOA net downward radiation, which equals OHU. In this simple model OHU is related to ΔT through ocean heat uptake efficiency, κ:

$${\rm{N}}={\rm{\kappa }}\,{\rm{\Delta }}{\rm{T}},$$ (2)

such that

$${\rm{Q}}=({\rm{\lambda }}+{\rm{\kappa }})\,{\rm{\Delta }}{\rm{T}}$$ (3)

It then becomes evident that N is a constant fraction of Q. If the radiative forcing Q decreases, the TOA radiative imbalance, N, and net OHU also decrease.

Alternatively, a hiatus can be forced by internal climate dynamics. In that case, during the hiatus Q keeps increasing while ΔT stalls. The increased radiative forcing during the hiatus period ΔQ then has to be balanced by in an increased ΔN;

$${\rm{\Delta }}{\rm{Q}}={\rm{\Delta }}{\rm{N}},$$ (4)

Alternatively a perturbation can be added to the forced response balance of Eq. 1, that compensates the radiatively forced temperature increase:

$$0={{\rm{\lambda }}}_{{\rm{N}}}\,{{\rm{T}}}_{{\rm{N}}}+{{\rm{N}}}_{{\rm{N}}},$$ (5)

where the subscript N denotes a natural fluctuation. Then it becomes clear that if T N is negative (the negative of ΔT during a hiatus period), N N has to be positive, i.e. the OHU and the TOA radiation imbalance become larger. This is the opposite relation between temperature variation and variation in N than in case of a radiatively forced hiatus. Such an opposite reaction in N also implies that Eq. 2 cannot hold for natural fluctuations, as Eq. 2 predicts a positive correlation between N and temperature fluctuations. As a result, the OHU efficiency κ has to change and has to become larger for a hiatus period and smaller for a positive natural temperature fluctuation. This can be explained by the fact that κ is essentially a diffusivity parameter, but that natural changes in OHU efficiency could be brought about by changes in deep convection and overturning circulation17,18, which are not well captured by a relation like Eq. 2.

Such anti-correlation between OHU, or N and GSMT has not been demonstrated to exist, neither in climate models, nor in observations. The implication then would be that the forcing-feedback-response energy balance model does not hold for dynamical fluctuations. This is especially puzzling as this model has recently been extended to account for (slow) changes in λ and κ that occur when the radiative forcing no longer increases and the planetary system approaches equilibrium19,20. If the transient behaviour in λ and κ is accounted for, an efficacy parameter, ε, can be defined, and the total temperature response can be split into a response to radiative forcing and a response to OHU forcing with the response to the latter forcing being larger by the factor ε19. This extended radiative-forcing-response model does not allow for decoupling of GMST variations from OHU variations, as it explicitly recognizes that all other forcing than radiative forcing must be moderated by OHU.

The lack of evidence for such a relation, both in observational studies14,21 and in analyses of unforced model simulations22,23, lead to the conjecture that the warming hiatus was a pure surface phenomenon due to a vertical redistribution of OHC only. Some support, however, for a relation between OHU/N and GMST has been found. For instance, the ORAS reanalysis of OHC shows a steep acceleration in OHC from year 2000 to 2010 relative to the decade before24, implying increased OHU during the hiatus period. Other OHC-data products, however, do not show such an acceleration11. A recent analysis claimed that reliable estimates of OHC since 1960 can now be made25. There still remains the issue that a reliable estimate of the relation between OHU and GMST is elusive as the length of the observational record is insufficient to separate different signals at different timescales. For this reason, analysing the relation in CMIP5 models is valuable.

Recent analyses of the relation between N at the TOA and GMST in climate models found a complex lead-lag relation between N and GMST at decadal timescales, peaking when GMST was leading with negative correlation, but with positive correlation when N was leading by more than a year26. Here, this analysis is extended by examining natural fluctuations between GMST and OHU, and by using forced simulations in which this relation might be affected by the forced response. By decomposing OHU in its various components, improved insight in the various feedbacks acting on OHU-forced temperature variations can be obtained, further elucidating the role of water vapour feedbacks (latent and sensible heat flux), Planck feedback (longwave radiation), and cloud and ice-albedo feedbacks (shortwave radiation). To isolate natural fluctuations in forced scenario runs performed by climate models, only single-model ensembles are considered from which the ensemble mean (forced) response is subtracted. It should be stressed that in this set-up only the mechanisms of how hiatus and surge events arise in climate models can be assessed and that the results do not need to be representative for the recent hiatus period. In particular, it was assessed that climate models have strong biases in simulating the ocean energy change associated with the El Niño-Southern Oscillation (ENSO), and that the subsequent area-averaged tropical Pacific OHC variability is greatly underestimated27. Nevertheless, understanding how hiatus events arise in climate models yields observable metrics that can verify/falsify whether the models behave in a similar way as the real world, and the qualitative relation between OHU and GMST could still be correct, despite biases like weaker GMST variance as observed, and as a result, weaker and less simulated hiatus periods than observed, and too weak OHU variations associated with ENSO.