It is my understanding, that none of these details explain the divergence between AOGCMs and EBMs.

]]>CMIP 5 has calculated TCR and ECS for various models from 1%/yr experiments, from historic forcing experiments and from instantaneous 2X and 4X experiments. Comments from Nic indicate that the differences in TCR and ECS produced by these methods are minor and not related to their disagreement with EBMs. I don’t have a reference to prove this.

The relationship between ECS and TCR is doesn’t change with warming rate: The current radiative forcing is about 2.7 W/m2 and the current ocean heat uptake is about 0.7 W/m2, so the difference (2.0 W/m2) must be going to space because of the 1 K of warming we have experienced. So we are about 70% of the way to a new steady state.

Simple calculations show that a 1 W/m2 radiative imbalance is capable of warming the atmosphere plus a 50 m mixed layer of ocean at an initial rate of 0.2 K/yr, IF ALL THE HEAT REMAINS IN THE MIXED LAYER AND ATMOSPHERE. As the planet warms, however, a 1 W/m2 forcing becomes a smaller and smaller radiative imbalance at the TOA as the warmer planet radiates and reflects more heat to space. So warming will slow. Halfway to a new steady state, the imbalance will be 0.5 W/m2 and the warming rate will be 0.1 K/yr. The new steady state temperature depends on climate sensitivity. If ECS is low (1.8 K/doubling, EBM), the new steady state after a 1 W/m2 forcing will be 0.5 degK warmer and the warming rate will be cut in half in about 2 years. If ECS is high (3.6 K/doubling, typical AOGCM), the new steady state from a 1 W/m2 forcing will be 1 K warmer and the warming rate will be cut in half in about 4 years. In either case, the atmosphere and mixed layer can approach steady state within about a decade. So, on a decadal time scale, the atmosphere and mixed layer are nearly in a steady state with respect to a change in forcing. So, as best I can tell, it shouldn’t make too much difference to the mixed layer and atmosphere whether a 3.6 W/m2 forcing from 2XCO2 develops over 70 years, 35 years, or 140 years. A doubling over 7 or 14 years would be a very different story.

Of course, heat does get transported below the mixed layer. One might say the effective heat capacity of the ocean compartment in steady state with surface temperature grows with time. Doubling the depth of the mixed layer in the above calculation in the above calculation wouldn’t make a doubling over 70 years much different from a doubling over 140 years.

If this seems like a lot of hand waving (to some extent it does to me) the solution is to make a multi-compartment model. AOGCMs are multi-compartment models. They apparently get similar TCRs from historic and 1% pa experiments. Maybe the above handwaving provides a feeling for why this happens.

]]>In any case on the timeframes used for energy balance methods the increase in forcing is probably not too far from the way TCR is assessed using models. Thus these 2 ways of doing the calculation should be pretty close.

Model TCR I think is defined to be an approximation to how emissions have gone historically or might go in the future.

In any case the point frank makes is correct.

]]>They indeed do NOT take account of deviations from the 1%/year forcing in calculating TCR:

Both equations (1) and (2) assume constant linear feedbacks, and thatT is entirely externally forced . Otto et al. (2013) illustrated that the increase in total forcing over the last 70 years has approximated a linear ramp and constitutes most of the increase during the Instrumental period, implying that it is valid to estimate TCR using (2), provided that the final period is recent and the base period ends no later than about 1950.

It seems that deviations are not significant enough to make a material difference to the calculation – in principle they may be, but not in practice.

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