I haven’t really tackled anything specifically physicsy for a while so I thought I might comment on a recent post on Judith Curry’s blog that was pointed out to me by Very Tall Guy. It’s a guest post by Roger Pielke Sr called an alternative metric to assess global warming.
Roger seems to be suggesting that we should use ocean heat content (OHC) to assess global warming. I certainly agree as – I thought – do many others. If anything, I was under the impression that many were arguing that surface temperatures were a poor metric for assessing global warming. So, overall, the post is quite interesting. Roger does, however, say a few things that confuse me; for example
Stephens et al. (2012) reports a value of the global average radiative imbalance (which Stephens et al. calls the “surface imbalance”) as 0.70 Watts per meter squared, but with the uncertainty of 17 W m-2!
Stephens et al. (2012) do indeed suggest a surface radiative imbalance of 0.6 ± 17 Wm-2, but also show a top-of-atmosphere (TOA) imbalance of 0.6 ± 0.4 Wm-2. I would argue that the latter is what’s actually relevant to the climate system as a whole. I’ve never been quite sure why the uncertainty in the surface imbalance is so large, but I had assumed it had something to with the large variability in surface warming.
Roger also says,
It needs to be recognized that deep ocean heating is an unappreciated effective negative temperature feedback, at least in terms of how this heat can significantly influence other parts of the climate system on multi-decadal time scales. Nonetheless, we have retained this heating in our analysis.
I’m not quite sure what he means by this. I agree that the deep oceans can probably influence how the energy is distributed through the system and can play a role in variability, but am not sure why that’s a negative feedback.
Anyway, Roger’s basic argument seems to be that the standard equation
where ΔQ is the system heat uptake rate, ΔF is the change in radiative forcing, ΔT is the change in temperature and λ is essentially the climate sensitivity, is conceptually useful, but can be difficult to implement.
Roger seems to be arguing that we should be more explicit, and should instead use
The post then includes the following two figures
From the top figure one can work out that anthropogenic forcings have increase by ΔF = 1.72 Wm-2 since 1950. From the bottom, figure one can sum the 4 different feedbacks to get -1.21 Wm-2K-1. Surface temperatures have increase by around 0.6 K since 1950, so ΔFfeed = -1.21 x 0.6 = -0.73 Wm-2.
If you take those numbers and plug them into the second equation above, you get ΔQ = 1.72 – 0.73 = 0.99 Wm-2. So, this is somewhat bigger than the mean value in Stephens et al. (2012), but within the uncertainty range. The uncertainties in some of the quantities above are quite large; for example the change in radiative forcing is actually 1.72 ± 1.1 Wm-2 which, if included, would make the results consistent with the OHC measurements. There’s also been a small reduction in solar forcing since 1950, which isn’t included. So, it all seems about right to me. Quite impressive in some sense.
One thing I will add though is that, as far as I’m aware, the first equation above (which Roger seems to think is not ideal) is essentially the same as the one that Roger recommends. Consider the following :
where ΔW has units of flux per Kelvin, and ΔWnonTfeed is the flux per Kelvin for all feedbacks, bar those due to the change in temperature. Interestingly, using Roger’s own numbers, 1/λ = 1.21 Wm-2K-1, which gives λ = 0.82 K/Wm-2. Given that a doubling of CO2 produces a change in forcing of 3.7 Wm-2, this implies an equilibrium climate sensitivity of 0.82 x 3.7 = 3.1 K.
So, as far as I can tell, the form that Roger suggests using is essentially consistent with the form that most already use; you can estimate the feedbacks if one knows the change in temperature, the system heat uptake rate, and the change in anthropogenic/external forcings. If you want to check GCMs (which I think is part of what Roger is suggesting) you can take their feedbacks and use that to estimate the system heat uptake rate, which can then be compared with measurements. Alternatively, use the system heat uptake rate, the change in anthropogenic forcings and the change in temperature to estimate the feedbacks and then compare that with what GCMs suggest. Both seem essentially the same, to me at least.
However, I do agree with Roger that using OHC and other system heat uptake rates is a better way to assess global warming than using surface temperatures only. I am, however, slightly confused as to why he seems to be suggesting that this is somehow novel, as I suspect many others agree with him too. So, maybe I’m missing some subtlety here. If anyone can see something more to this than I have, feel free to let me know through the comments.