## October 11, 2013

### Relative importance of transient, effective, and equilibrium sensitivities

Filed under: Uncategorized — troyca @ 8:11 pm

### Introduction

I have heard it mentioned that the transient sensitivity (or transient climate response, TCR) is more relevant to climate policy than equilibrium climate sensitivity, and wanted to see the degree to which this is true.  AR4 notes that:

Since external forcing is likely to continue to increase through the coming century, TCR may be more relevant to determining near-term climate change than ECS.

Also, see this very interesting paper by Otto et al., (2013) ERL.  In particular, I wanted to see the relative importance of different types of sensitivity (transient, "effective", and equilibrium) when determining the temperature anomaly in the year 2100 relative to 1850.  For a recap of these types of sensitivities, let’s go back to our simple energy balance model:

C(dT/dt) = F – ΔT*λ

Here, C represents the heat capacity of the system, T represents the surface temperature, F represents the forcing, and λ the strength of radiative restoration.  The TCR refers to the change in temperature in the 1% CO2 increase per year idealized scenario at the time when the concentration doubles, which occurs at 70 years (1.01^70 = 2.0).  Given the large heat sink that is the ocean, there will still be a residual imbalance at the top of the atmosphere after this 70 years.  This means that TCR depends not only on λ, but also on the heat uptake of things like the ocean, which could be represented here in the C term (although note that C varies over time as heat is captured by deeper layers of the ocean, which is why a one-box model is not great for simulating short and long-term transient responses).

For the equilibrium sensitivity, we also use the 2xCO2 scenario, but this time see how much the temperature changes after radiative equilibrium is reached at the top of atmosphere.  Now, in the idealized situation where λ is unchanging, we can calculate the temperature at equilibrium independent of the heat capacity of the system, as simply ΔT = F / λ.  It is this situation where we use a single-value of λ to calculate ΔT that the ΔT is referred to as "effective sensitivity".  Here, we’ll define λ_250 as the radiative restoration strength from 1850-2100, and ΔT = F_2xCO2 / λ_250 will be our "effective sensitivity".  This differs from ECS in that λ could theoretically change over subsequent centuries, as in Armour et al., 2012.  However, defined this way, ECS is irrelevant for this century’s warming, and such a discussion is more just academic (which is why the distinction between ECS and "effective sensitivity" has been minimized in the past).

So, in this way, I will technically be comparing the importance of TCR vs. effective sensitivity (EFS), although the latter is sometimes used synonymously with ECS.

### Method

Here, I will be employing the same two-layer model as in my last post.  Since EFS is determined by λ, it is easy to prescribe in this model.  However, the TCR depends not only on the EFS, but the heat transfer of the ocean as well.  To match the TCR to a target for a given EFS, I fix the "shallow" and "deep" layers at 90m and 1000m respectively, and use a brute force method (ugly, I know) to determine the rate of heat transfer between these layers that will result in this TCR.  From there, I have a model that simulates both the specified TCR and EFS, which I can then use to see the temperature rise from 1850 to 2100 using this model.

I have chosen TCRs of 1.1K, 1.4K, 1.8K, and 2.1K, and EFSs of 1.5K through 4.5K, based on what is feasible/possible for a given TCR.  Again, the adjusted forcings for the RCP scenarios come from Forster et al. (2013).

Script available here

### Results

This first graph is for the RCP6.0 scenario: As you can see, the relatively flat lines (small slope) indicates that given a specific TCR, the EFS has only a small effect on the temperature that might be expected in 2100.  On the other hand, the large amount of space between the different TCR lines, despite only small changes in the magnitude of TCR, indicates that two models can have the same EFS but produce very different magnitudes of warming by 2100 if their TCRs differ.

To quantify a bit more, the slope of the TCR-2.1 line is 0.16K per EFS, meaning that if the earth had a transient response of 2.1K, the difference between an EFS of 3.0 and an EFS of 4.0 would only produce an extra 0.16K in 2100K.  On the other hand, if we fixed the EFS at 3.0 and instead changed TCR, you can see that an increase between TCR of 1.4K and 2.1K (0.7K) produces a change of the same magnitude (~0.7K) in the expected temperature change by 2100, producing a ratio of 1.0 K per TCR.  A similar difference is found at 2.0 EFS when moving from 1.1K to 1.8K.  This would suggest that it is much more important to pin down the TCR (which has a large impact on this century’s warming), even if EFS remains uncertain, rather than trying to pin down EFS.  I should note, however, that for the low TCR scenario (1.1K), the slope of the line is ~0.34 K per EFS, which is double that at 2.1K.  This is because a low TCR suggests a lower heat capacity of the system, which in turn means a quicker pace to equilibrium, which means a greater importance of EFS.

For another look, here is the RCP4.5 scenario:

Here, the results are similar to the RCP6.0, although not quite as drastic.  For a given EFS (2.0 or 3.0), the change in 2100 warming is altered by about 0.75 K per TCR (rather than 1.0 K per TCR in the 6.0 scenario).  Part of this is because we only have ~3/4 of the forcing change (4.5 W/m^2 rather than 6.0 W/m^2), so obviously the warming in general by 2100 is decreased.  However, this alone does not explain why the slopes for the TCR-1.1 and TCR-2.1 have increased to 0.4 K / EFS and 0.2 K / EFS respectively.  For that, I suggest that the earlier stabilization of the 4.5 scenario forcing lends a slightly increased importance to the EFS, given the ~30 years it has to move towards that equilibrium prior to 2100.

### Conclusion

Clearly, TCR seems to be more important that EFS and (definitely more so than ECS) in determining the expected warming by 2100.  I tend to agree that it terms of policy, this suggests more focus should be placed on pinning down the TCR.

• 