Energy budgets

Stoat highlights an interesting paper that suggests that the rates of ancient climate change may be underestimate. I haven’t had a chance to really look at it, so if anyone has looked at it, and has any views, that would be interesting. I might suggest that you post any comments at Stoat, though, as I think he’s looking for them Image may be NSFW.
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This, however, gives me an opportunity to mention another paper that I found quite interesting. It’s by Xie, Kosaka, and Okumura, and is called Distinct energy budgets for anthropogenic and natural changes during global warming hiatus. The basic idea is that if you consider the basic energy balance formalism, then the system heat uptake rate, Image may be NSFW.
Clik here to view., is essentially given by

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Clik here to view.,

where Image may be NSFW.
Clik here to view. is the change in forcing, Image may be NSFW.
Clik here to view. is the change in temperature and Image may be NSFW.
Clik here to view. is the feedback factor. If there is a slowdown in surface warming (Image may be NSFW.
Clik here to view.) while we continue to increase anthropogenic forcings, then – if this equation applies – we’d expect to see an increase in the system heat uptake rate (Image may be NSFW.
Clik here to view. > 0). However, this isn’t really what we’ve seen in last decade, or so, when surface warming has been slower than expected.

What Xie, Kosaka & Okumura suggest is that the feedback response is different when the warming is internally-driven, compared to when it is externally forced. What they suggest is that when the temperature variation is internally-driven, the resulting spatial pattern produces a feedback response that leads to a top-of-the-atmosphere imbalance that is somewhat out of phase with the temperature variation.

This is illustrated in the figure below, which shows (in the left hand panel) the externally-forced temperature response (black line), the internally-driven temperature variation (green line) and the net temperature response (red line). The right-hand panel shows the change in system heat uptake rate due to the externally forced component only (black line), and what would be expected if the response to the internally-driven warming were the same as due to externally-driven warming (brown line). This shows that we’d expect – if the above equation applied – an increase in system heat uptake rate as the internal variability produced a temperature slowdown. The green line, however, shows a TOA response that is out-of-phase with the internally-driven temperature variation, and the red line shows how this influences the net system heat uptake rate, and might explain why the system heat uptake rate hasn’t increased during the surface warming slowdown.

I don’t really know if what they’re suggesting is plausible, or not. Given some of the discussion here, that the spatial pattern of the warming could influence the feedback response seems entirely reasonable. They also show that this out-of-phase response to internally-driven warming is consistent with what is seen in climate models.

That’s really all I was really going to say. I found it an interesting paper, as I had wondered why we weren’t see an increase in system heat uptake rate during the temperature slowdown, and the suggestion in the paper seems plausible. If anyone has any other views, though, feel free to make them in the comments. I should probably add that I’ve written this quite fast, and it’s getting late here, so apologies if I’ve made some kind if basic blunder in explaining this.