VTG: Technically you are correct that TCR is the temperature change (dT) after doubling CO2 (dF) over 70 years (1% pa) averaged over two decades. As I just discussed, there isn’t much difference if the rate differs from 1% pa. And the proper name for ECS from an EBM is “effective ECS”, because slow feedbacks (changes in surface albedo, ice caps, vegetation, and outgassing of CO2 with warming) may not reach steady state within a 70-year 1% pa experiment. In abrupt 2X and 4X CO2 experiments, dF is plotted against dT and the “line” extrapolated to dF = 0 to obtain ECS and to dT = 0 to obtain the effective radiative forcing. In practice, there is often a bend in the “line” around 20 years.

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

]]>VTG wrote: “OK, so I went back to look at the Lewis and Curry paper. They indeed do NOT take account of deviations from the 1%/year forcing in calculating TCR”.

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.

]]>Curry has a new post reviewing recent papers on ocean heat uptake that reviews some of the recent papers. As usual in climate science there are a rather broad range of results.

]]>See this comment and link on linearity of response

]]>On second thought VTG you have a point. There is a difference between very long term response and short term response. Energy balance methods all make the linearity assumption and there is a huge literature on the subject.

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.

]]>Of course vtg you missed the point. For small changes in Erf the exact path of the change shouldn’t matter too much and the response will be linear. All simple forcing/ feedback analyses make some assumption like this. Climate models should show this behavior too if they aren’t Fundamental flawed.

]]>OK, so I went back to look at the Lewis and Curry paper.

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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