## 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 🙂

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, $Q$, is essentially given by

$Q = F - \lambda T$,

where $F$ is the change in forcing, $T$ is the change in temperature and $\lambda$ is the feedback factor. If there is a slowdown in surface warming ($dT/dt \Rightarrow 0$) 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 ($dQ/dt \sim dF/dt$ > 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.

Credit : Xie, Kosaka & Okumua (2015)

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.

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### 20 Responses to Energy budgets

1. JCH says:

Here’s why.

2. Roger Jones says:

This paper, like all the others, assumes that atmospheric warming driven by external forcing should be a linear process unless perturbed by some other process (e.g., natural variability).

“However, closure depends on invoking an unrealistically large increase in aerosol cooling during the so-called global warming hiatus since the late 1990s that was due partly to tropical Pacific Ocean cooling”

The assumption is implicit in this statement. It is true for the earth system, but not for the atmosphere, which is governed by nonlinear ocean-atmosphere interactions.

It seems that much of climate science of the moment is trying to thread a camel through the eye of a needle in order to defend the trend. It would be much better to admit that the atmospheric response to gradual forcing is seriously nonlinear and dispense with the camel stuff.

3. Roger,

It would be much better to admit that the atmospheric response to gradual forcing is seriously nonlinear and dispense with the camel stuff.

Possibly, although if I read Isaac Held’s stuff right, he’s suggesting that the non-linearity comes from the spatial structure of a response that is essentially linear.

4. Paul S says:

I think Brown et al. 2014 is a different angle on the same phenomenon. Their results come from unforced control runs.

Patrick Brown blogged it here: http://www.climate-lab-book.ac.uk/2014/toa-and-unforced-variability/

That seems to be down at the moment though – here’s a wayback: https://web.archive.org/web/20151105205447/http://www.climate-lab-book.ac.uk/2014/toa-and-unforced-variability/

For the observed uptake rate from Argo, reported global average figures up to about 2012 are very likely biased low by a substantial amount, e.g. http://www.ocean-sci.net/10/547/2014/os-10-547-2014.html (and on the flipside the large trend from 2012 is probably biased high due to the same coverage issue).

5. Paul S,
Thanks, I think I remember that now. There’s also Palmer & McNeall who seem to show something similar. There Figure 1 seems to show that 10-year internally-driven trends in surface temperature are typically positively correlated with the system heat uptake (although there is a lot of scatter) which – I think – is not what you’d expect if the basic energy balance equation was valid for internally-driven warming.

6. BBD says:

Paul S

Thanks for the link to von Shuckmann et al. My first reaction to reading the OP was on what evidence is it assumed that the rate of system heat uptake has not increased?

7. BBD says:

My (limited) understanding accords with what Patrick Brown wrote at CLB:

These model-based findings appear to contradict observations over the past 10-15 years. In particular, it has been suggested that we are currently in an unforced cooling situation analogous to that illustrated in Figure 2 (e.g., England et al., 2014; Trenberth and Fasullo, 2013). These findings suggest that we should expect this unforced cooling to be enhanced by the net energy imbalance at the TOA (i.e., there should have been a decrease in the rate of climate system heat uptake over this period). However, our best inventories of total climate system heat content have indicated that just the opposite has occurred (as T has been in an unforced cooling state, the rate of climate system heat uptake as increased; Trenberth and Fasullo, 2013; Balmaseda et al., 2013). This is not what the CMIP5 models typically do, but it does happen (~13% of the cooling decades investigated were associated with net positive climate system heat uptake). In these rare decades, changes in QBML flux are large enough to overcome the gain in climate system energy and cause T cooling. This does seem consistent with the recent finding that an increase in Pacific trade wind strength has increased the rate of heat storage below the mixed layer (QBML) to unprecedented levels (England et al., 2014).

8. BBD,

My first reaction to reading the OP was on what evidence is it assumed that the rate of system heat uptake has not increased?

If you look at the NOAA OHC data it doesn’t look like the rate changed much from the 1990s to the 2000s.

I’m slightly confused by this

These findings suggest that we should expect this unforced cooling to be enhanced by the net energy imbalance at the TOA (i.e., there should have been a decrease in the rate of climate system heat uptake over this period).

In a simple sense, if the temperature stops rising while we continue to increase anthropogenic forcings, then one might expect the rate of climate system heat uptake to increase. Isn’t that right? That it doesn’t seems to suggest some more complex interaction when the warming/cooling is internally-driven.

9. JCH says:

Missing heat per Trenberth:

1. sent back to outer space, which can easily happen while ACO2 is increasing
2. into the oceans, where the 2nd law saves libertarians because it cannot regroup and surge from the bottom to the top because deep can mean anything from 300 meters to the bottom of a trench
and:
3. temperature series were light (Karl), and possibly still are (me)

What else?

10. Paul S says:

if the temperature stops rising while we continue to increase anthropogenic forcings, then one might expect the rate of climate system heat uptake to increase. Isn’t that right?

If using a zero-dimensional model, yes. I think that expectation is what the QF – λTN curve shows in the figure.

But you’ve referenced Isaac Held talking about global feedback non-linearity coming from spatial feedback linearity. What would happen if internal variability optimally activated a spatial pattern which enhanced the global net feedback parameter temporarily?

11. What would happen if internal variability optimally activated a spatial pattern which enhanced the global net feedback parameter temporarily?

Yes, that’s what I thought was being suggested. I was mainly commenting on the quote that BBD provided that seemed to suggest that it was obvious that a temperature slowdown would decrease the rate of system heat uptake rate. I realise that it now looks like this is an outcome, but it’s not clear that it’s an obvious one unless you take the spatial distribution dependence into account (which is presumably not trivial).

12. Paul S says:

I don’t think Brown is suggesting it as an obvious outcome. He says what amounts to the opposite in the blog post:

It may seem counter-intuitive that the net flux at the TOA would enhance (rather than reduce) T change because the Stefan–Boltzmann law might lead us to expect that as T decreases (increases), the amount of outgoing longwave radiation emitted to space should decrease (increase) exponentially.

His simple explanation is:

In other words, it appears that changes in the climate system’s albedo are able to temporarily counteract the changes in outgoing longwave radiation and thus sustain the net TOA imbalance for a longer period of time than might be expected otherwise. We find that these changes in albedo appear to be associated with changes in the state of the Interdecadal Pacific Oscillation

13. Paul S,
Okay, sorry, I should have read that more closely. So, it’s essentially what he’s concluding, not what he thought should have been the case at the beginning?

14. BBD says:

ATTP

If you look at the NOAA OHC data it doesn’t look like the rate changed much from the 1990s to the 2000s.

What depth range are you looking at?

15. BBD says:

16. BBD,
Yes, but the rate through the 90s and 00s seems about the same, I think.

17. Paul S says:

ATTP,

Yeah, think that’s it.

JCH,

People tend to “miss” that Trenberth’s “missing heat” concerned an apparent discrepancy between two observing systems, not against modelling so much.

Not sure if this link will work but it’s from Trenberth et al. 2014 and shows global CERES TOA data against various ocean heat content global averages. His point particularly relates to the big bump in CERES 2008/09, not captured by ocean heat content measurements.

If the CERES data is correct the missing heat can’t have escaped to space and the surface and atmosphere don’t have enough heat capacity to explain the discrepancy. That leaves the oceans and perhaps the cryosphere-ocean link. Argo coverage gaps I think could explain some of the difference, with Indonesian, Arctic and Southern Ocean gaps standing out.

A general lack of coastal coverage may be relevant. There seems to be a degree of anti-correlation between global tide gauge trends and open ocean altimeter trends on short timescales (see Figure 2 in this paper), apparently related to ENSO shifts, suggestive of occasional coastal build up of ocean heat. This may not be captured by the largely open ocean-focused Argo network.

18. Paul S,
Thanks, that Trenberth link is very useful. I tried to explain that basic point to someone yesterday – invoking energy conservation – and was essentially called an idiot. Nice to have something specific to refer to, not that it will make any difference 🙂

19. CERES is probably not precise or accurate enough to make assessments from.
(uncertainty is much larger than any decade long trends ).

Largely that’s because reflections can vary in a number of directions so it’s not possible to know how much SW reflection varies.

The existing CERES show a cumulative Net of close to zero, but +/- a few W/m^2 could mean large imbalances either way.

20. JCH says:

Paul S – do you remember telling the Water Boiler that steric sea level rise may be underestimated because a pile of hot water was piled up in the Western Pacific… that was not being sampled by ARGO or satellites?

Is it here now?

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