The enhanced greenhouse effect

This is really just an opportunity to write a little bit about science, and to advertise other people’s work. There are some who suggest that adding CO2 to the atmosphere can’t lead to warming because CO2 absorption is saturated. This is wrong for a couple of main reasons. One is very simply that it’s simply not true. Eli has a nice post (that partly motivated this post) that illustrates this. There’s also a Realclimate post (by Ray Pierrehumbert) that also shows this. It might be saturated in the middle of the absorption band, but it’s not saturated on the wings.

Another reason it is wrong is that even if it was saturated (which it’s not) adding CO2 would still lead to warming. This is explained in this Realclimate post, by Spencer Weart. Essentially, the presence of greenhouse gases prevents energy from being radiated directly from the surface to space; instead it’s radiated from within the atmosphere. In a simple sense, you can think of there being a layer in the atmosphere where the energy can be radiated directly to space. If you add more greenhouse gases (more CO2), then the layer from which the energy is radiated directly to space will move to a slightly higher altitude. This is because this extra CO2 will trap some of the energy being radiated from the original radiating layer.

However, the temperature of the atmosphere decreases with increasing altitude, and so moving the radiating layer to a higher altitude will reduce the outgoing energy flux. If we were in energy balance before adding the extra CO2, then we’ll now have more energy coming in than going out, and we’ll warm until we’re back in energy balance. Andrew Dessler has a nice video that explains some of the basic physics of the greenhouse effect and what happens as we add more CO2. Again, this post was partly motivated by seeing his video, so I can stop here, and hope that even if I didn’t explain this very clearly, the various posts to which I linked, and Andrew Dessler’s video, will clarify things.

Credits:
I should also add that I came across the Realclimate posts I mention above through this comment on Eli’s post.

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48 Responses to The enhanced greenhouse effect

1. Nick Stokes says:

“However, the temperature of the atmosphere decreases with increasing altitude, and so moving the radiating layer to a higher altitude will reduce the outgoing energy flux.”
There is a complementary effect too at near surface. What actually helps to keep us warm is down-welling IR (DWLWIR). With more GHG, this comes from lower, warmer altitude.

2. Clive Best says:

I disagree Nick. What you say would be true if radiation alone determined heat transport in the atmosphere.

3. Clive,
How does what you’ve presented contradict what Nick has said? Ultimately, the surface warms because it is receiving more energy (and warms to a new equilibrium). As I understand it, the DWLWIR does indeed increase. So, what are you actually suggesting?

4. Especially, as I think I also stressed the important of defining your terms 🙂

5. russellseitz says:

Watts’s response has been to ignore radiative transfer and return to the mythograpy of cosmic rays as the real deal in climate change :
https://vvattsupwiththat.blogspot.com/2017/05/do-cosmic-rays-cause-gish-gallup.html

6. Tom Curtis says:

Nick, the surface can warm either by an increase in down welling radiation or by a reduction in heat transport away from the surface by convection and/or evaporation/transpiration. With the introduction of an energy imbalance at the top of the troposphere due to increased greenhouse gases, that will result in a local warming at the top of the troposphere, which will result in a reduction of convection beneath it until. Overtime the adiabatic lapse rate will be restored, but for it to do so, the ground must have warmed as much as the upper troposphere. How much of the warming of the ground will be due to increased down welling radiation, or a temporary reduction in convection will partly depend on local conditions, and in any event will be irrelevant to the final gross outcome in terms of surface temperature which is governed by the TOA energy balance.

7. Tom,
Indeed, but I interpreted Nick’s comment as being what is happening once the surface has warmed. Unless I’m missing something (always possible) once the surface has warmed, this can only be sustained if there has been an increase in the the Downwelling Long-Wavelength (Infra-red) radiation.

8. Tom Curtis says:

attp, once the surface is warmed, it can also be sustained by a reduction in convection. All that is important is the energy balance. Nick may be talking about what actually happens in practice under most circumstances, in which case he is probably correct. Certainly the mechanism he describes is correct, and will be supplemented after some warming by additional DWLW radiation due to increased absolute humidity in most locations. Consequently, in practice, the mechanism he describes is a contributor to surface warming, and may be, in most circumstances the major contributor.

Indeed, I suspect in many circumstances convection will increase because the increase in DWLW radiation exceeds that needed to balance the temperature increase. But it is important to recognize that the warming would happen even if there was no DWLW radiation – that the energy balance at the TOA is sufficient cause for a surface warming because of the multiple means by which energy can be transported to and from the surface.

9. Tom,
Okay, thanks, I see what you mean. I agree that what is ultimately inortant is the energy balance and so surface warming could be sustained by reduced convection, but that – in most circumstances – there would be an increase in DWLWIR.

10. raypierre says:

The surface energy budget is mostly a sideshow. For the most part, the surface budget (which consists of radiation plus turbulent latent heat and sensible heat transfers) just acts to drag the surface temperature along with the low-level air temperature. Even so far as the downwelling IR goes, the main reason for the increase of downwelling IR is the increase of lower tropospheric temperature (mandated by combination of convection and top-of-atmosphere budget), not the direct effect of increased low-level opacity due to CO2. As the planet warms you do get a significant boost in lower level opacity from increasing boundary layer water vapor, but given that in most places the surface temperature is already close to the low level air temperature, this is not a major player, especially not over the oceans.

11. Ray,
Thanks for that clarification.

12. Clive Best says:

What I meant was that back radiation doesn’t by itself warm the surface. If that were the case then the surface would be far warmer – Pure radiative equilibrium. Convection maintains a lapse rate over a larger height. The effective radiation BB temperature remains 255K. The surface warms essentially because the tropopause is higher up.

13. Clive,
I don’t think that Nick was suggesting that back radiation – by itself – warmed the surface.

14. BBD says:

The surface warms essentially because the tropopause is higher up.

I hesitated before posting this as atmospheric physics is not my strong suit, but isn’t it more correct to say that the altitude of effective emission is raised? I mention this as for some time I thought that this *was* at the tropopause, but I was then told that no, it was not.

Clarification on this point would be welcome 🙂

15. BBD,
Yes, it is really that the altitude of effective emission is higher. However, I think that the combination of tropospheric warming, and stratospheric cooling does lead to the tropopause being higher up. However, that would more be the tropopause being higher because of the warming of the troposphere, than the surface warming because the tropopause is higher up.

16. BBD says:

17. JCH says:

Well, let’s hope the enhanced greenhouse effect works better than its explanations!

18. Tom Curtis says:

BBD, the altitude of effective emission to space is higher. The mean altitude of radiation to the ground is lower. I believe that, because there is far more water vapour at low altitude, and the atmosphere is far denser, the amount the later is lowered is substantially less than the former is raised.

19. Clive Best says:

This is what the altitude of effective emission height looks like for different atmospheric CO2 concentrations. These are centred on a narrow band of (quantum) emission lines centred on 15 microns. The rest of the earth’s emission spectrum is (to first order) unaffected.

The central lines are already saturated into the stratosphere where temperature increases with height. This means that for these lines IR emission actually increases with concentration – cooling the earth. However, the overall effect integrated over all lines is to reduce emission – warming the earth.

One of the Internet sources I like is the American Chemical Society web pages on this subject, which explains shows the effective temperature of outgoing IR from the top of the atmosphere as measured by satellites, and illustrates what is happening using a simplified model.
acs.org/content/acs/en/climatescience/atmosphericwarming.html

21. Bob Loblaw says:

Tom Curtis said: “BBD, the altitude of effective emission to space is higher. The mean altitude of radiation to the ground is lower. “

Two implications of this:

1) more IR from the surface also gets absorbed lower down, and

2) to get from the surface to space, by radiative transfer, IR has to go through more absorbed/emitted cycles.

For each absorbed/emitted cycle, only half gets re-emitted upwards, and half downwards, so the more times this happens the less efficient it is the upward transfer. Even if the atmosphere is “saturated” based on the idea that little goes from the surface to space in the first try, there is a huge difference between having to do it in two, or three, or four steps.

22. Tom Curtis says:

Bob Loblaw, yes the energy transfer by radiation becomes less efficient; but it is already less efficient than energy transfer by convection in the troposphere, which is whey the troposphere has an adiabatic lapse rate. Less efficient energy transfer by radiation will just mean more energy transfer by convection (and/or latent heat).

23. angech says:

Take your lumps and forcefully engage the public back.
“Nick Stokes says: May 28, 2017 at near surface. What actually helps to keep us warm is down-welling IR (DWLWIR). With more GHG, this comes from lower, warmer altitude.”
“Ultimately, the surface warms because it is receiving more energy (and warms to a new equilibrium)”.
Which puts more energy out at a higher altitude hence will increase the outgoing energy flux.

24. angech,

Which puts more energy out at a higher altitude hence will increase the outgoing energy flux.

Well, yes. If you add GHGs it reduces the outgoing energy flux, causing the system to warm until the surface temperature increases enough that the outgoing energy flux again (on average) balances the incoming energy flux. This is kind of a key point.

25. angech says:

” once the surface has warmed, this can only be sustained if there has been an increase in the the Downwelling Long-Wavelength (Infra-red) radiation.” Guaranteed by the effect of the CO2 increase.
Tom Curtis says: May 29, 2017
,” once the surface is warmed, it can also be sustained by a reduction in convection.”?
If the GHG increase was responsible for the warming why would there be any consequent reduction in convection? As you say.
” Indeed, in many circumstances convection will increase because [of] the increase in DWLW radiation.”
Which by necessity will reduce some of the effect of the CO2.This turbulence factor is presumably modeled in.

26. angech,
Lapse rate feedback (which is essentially evaporation from the surface and then the release of latent heat at a higher altitude) does indeed reduce warming. Also, if there were no convection and all of the energy were transported by radiation, surface warming would also be greater. All these factors are included, so I’m really not sure what you’re getting at.

27. Roger Jones says:

I don’t want to start an argument with raypierre but I don’t think this model is correct. Energy exchange at the ocean surface controls temperature. Heat take-up by the ocean is not energy limited (at least not in the current climate), but the current model of in situ atmospheric warming assumes it is. When statistical models testing secular trends and those testing for steps are compared, step-like change comes out on top. This is consistent with the ocean taking all the available heat from the atmosphere while maintaining steady-state ocean-atmosphere regimes. As the heat collects, the system becomes unstable and undergoes a regime shift, and parts of both the ocean and atmosphere undergo step-like warming. The western Pacific Warm Pool is the main heat engine for this process. Depending on the area of regime shift and emplacement of warmer water (maintaining higher air temperatures on ocean and adjacent land), these changes can be basin wide to global. The more energetic regime can then do the work to transport more heat energy to the top of the atmosphere and poles. During cooling phases, the opposite, step-like cooling, occurs and the ocean-atmosphere system does less work. This is standard complex system behaviour and is what Lorenz’s strange attractors do – maintain steady state conditions and trigger changes in state when they become unstable and flip.

So I don’t think the surface energy budget is a sideshow (it is on land, but that’s only 30% of the planet), I think it’s the main game. The ocean is the dog, the atmosphere the tail. Once the heat is emitted into the atmosphere, we then see atmospheric feedback processes respond.

If Earth didn’t have an ocean, we would probably not be having this exchange, because an atmosphere without a big storage mechanism to moderate its wild swings would make it very difficult for complex life to evolve.

28. JCH says:

There are three distinctly powerful surges in the evolution of the GMST during the 20th and the 21st centuries, and all three commenced with the ramp up of a positive PDO event: to ~ 1940; to ~1985, to 2017 and counting:

I am not saying the PDO caused them.

How much OHC was lost to the atmosphere during the recent El Niño? Look at OHC before the 14-16 EL Niño started versus OHC as of 3-31-2017.

29. Roger,
Okay, but surely the surface temperature (on average) is more constrained by the overall energy balance, than by energy released/taken up by the oceans. I’m not, however, arguing against the oceans playing a big role in surface temperature variability, though.

30. Roger Jones says:

ATTP,
I’m claiming that the atmosphere does not heat independently of the ocean (not enough to measure at least). The total annual flux for all greenhouse gases is 155 W m-2 (Schmidt et al. 2010). That all gets taken up in a stationary climate, no problems. The estimated additional AGW forcing 2003–14 was estimated to range between 1.6 to 1.75 W m-2 (Dieng et al. 2016). Uptake by the ocean was estimated as 0.625±0.115 during 1993–2008 and 0.51±0.12 during 2005–10 (Hansen et al. 2011), compared to 0.55 W m-2 1971–2010 (Rhein et al. 2013). The gap is top of the atmosphere loss and measurement issues. This compares to the estimate of the atmospheric contribution of 0.007 W m-2 1993–2008 based on calculations of warming and atmospheric mass and heat capacity (Hansen et al. 2011).

How does the memory of a trend equivalent to 0.007 W m-2 or even ten times that survive when ENSO events up to at least 100 times that and more than 200 for some (up to ~2 W m-2) just get pulled back into the ocean? This suggests that there is a cohort of anthropogenically-generated longwave radiation in the atmosphere that is not subject to the same rules as naturally-generated longwave radiation.

I’m a complete duffer at physics, I must admit, but cannot think of any situation where this can happen. In fact, all the work I’ve done in energy-balance hydroclimatology suggests the opposite is the case. The atmosphere generally, and the atmosphere above land does not warm independently of the ocean surface (see Lambert et al. 2011, but that’s my take on it). And the ocean surface is ruled by steady-state climate regimes.

Dieng, H. B., A. Cazenave, B. Meyssignac, and K. Schuckmann, 2016: Sea and land surface temperatures, ocean heat content, Earth’s energy imbalance and net radiative forcing over the last decade. EGU General Assembly Conference Abstracts, 7090.
Hansen, J., M. Sato, P. Kharecha, and K. v. Schuckmann, 2011: Earth’s energy imbalance and implications. Atmospheric Chemistry and Physics, 11, 13421-13449.
Lambert, F. H., M. J. Webb, and M. M. Joshi, 2011: The Relationship between Land–Ocean Surface Temperature Contrast and Radiative Forcing. Journal of Climate, 24, 3239-3256.
Rhein, M., and Coauthors, 2013: Observations: Ocean. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, T. F. Stocker, and Coauthors, Eds., Cambridge University Press, 255-316.
Schmidt, G. A., R. A. Ruedy, R. L. Miller, and A. A. Lacis, 2010: Attribution of the present-day total greenhouse effect. Journal of Geophysical Research: Atmospheres, 115, D20106.

31. JCH says:

Authors include Carl Wunsch…

ABSTRACT

15 A dynamically and data-consistent ocean state estimate during 1993-2010 is
16 analyzed for bidecadal changes in the mechanisms of heat exchange between
17 the upper and lower oceans. Many patterns of change are consistent with
18 prior studies. However, at various levels above 1800 m the global integral
19 of the change in ocean vertical heat flux involves the summation of positive
20 and negative regional contributions and is not statistically significant. The
21 non-significance of change in the global ocean vertical heat transport from
22 an ocean state estimate, “data” from which are of global coverage and are
23 regularly “sampled” spatially and temporally, raises the question whether an
24 adequate observational data base exists to assess changes in the upper ocean
25 heat content over the past few decades. Also, whereas the advective term
26 largely determines the spatial pattern of the change in ocean vertical heat
27 flux, its global integral is not significantly different from zero. In contrast,
28 the diffusive term, although regionally weak except in high-latitude oceans,
29 produces a statistically significant extra downward heat flux during the 00s.
30 This suggests that besides ocean advection, ocean mixing processes, includ-
31 ing isopycnal, diapycnal as well as convective mixing, are important for the
32 decadal variation of the heat exchange between upper and deep oceans as well.
33 Furthermore, our analyses indicate that focusing on any particular region in
34 explaining changes of the global ocean heat content could be misleading and
35 not necessarily correspond to changes in the global mean.

32. Roger Jones says:

JCH, if that is in response to anything I have posted could you please elaborate on your interpretation of what it is saying?

33. Roger,

I’m claiming that the atmosphere does not heat independently of the ocean (not enough to measure at least).

Yes, I agree with this, in the sense that they’re coupled. I don’t think the suggestion is that this isn’t the case. The suggestion is more – I think – that how much we ultimately warm is largely determined by the TOA imbalance. The oceans, of course, play a role in the rate at which the surface will warm and how the excess energy is partitioned between the different parts of the climate system, but doesn’t really play a big role in how much we will warm overall.

The estimated additional AGW forcing 2003–14 was estimated to range between 1.6 to 1.75 W m-2 (Dieng et al. 2016). Uptake by the ocean was estimated as 0.625±0.115 during 1993–2008 and 0.51±0.12 during 2005–10 (Hansen et al. 2011), compared to 0.55 W m-2 1971–2010 (Rhein et al. 2013).

Are these quite comparable? The former is the change in radiative forcing, but ignoring the – I think – Planck response. The latter is the essentially the system heat uptake rate which is really saying how out of balance we are after a change in forcing, plus feedbacks (including the Planck response).

Essentially,

$N(t) = \Delta F(t) - \lambda \Delta T(t),$

where $N(t)$ is the system heat uptake rate at time $t$, $\Delta F(t)$ is the change in external forcing, $\lambda$ is the net feedback response (including the Planck response), and $\Delta T(t)$ is the change in temperature. The relationship between $N(t)$ (the system heat uptake rate) and $\Delta F(t)$ depends on how quickly the feedbacks can act to return the system to energy balance.

34. Roger Jones says:

ATTP,
your response is a linearisation of what I was saying, which is not my point. Long-term warming follows a complex trend so these analytic solutions work very well. But that’s 50+ years stuff.

The gradually warming atmospheric signal is what I am taking aim at. If atmospheric warming does not follow a secular trend because it is being controlled by steady-state ocean-atmosphere regimes then raypierre’s response is valid for Venus but not Earth. I’m arguing against the phenomenon being seen as a secular trend produced by in situ atmospheric warming. If we have a staircase progression in climate change, then how we respond is very different to a smooth trend with variability imprinted upon it.

This has significant implications for the characterisation of climate risk and more broadly a general understanding of how climate works.

35. Roger,

If we have a staircase progression in climate change, then how we respond is very different to a smooth trend with variability imprinted upon it.

True, but presumably only for reasonably short timescales? The way we respond overall (i.e., aim to get emissions to zero) won’t be very different, but what we do on shorter timescales to adapt to the changes might be different.

This has significant implications for the characterisation of climate risk and more broadly a general understanding of how climate works.

Okay, but do we have a strong indication that it is more staircase-like than smooth + variability?

36. Roger Jones says:

Oh, and you can’t sort out the Planck response until you know where the energy has been partitioned.

37. Roger,

Oh, and you can’t sort out the Planck response until you know where the energy has been partitioned.

I don’t think the Planck response in W/m^2/K depends on this. However, how much of an actual response there is (i.e., the rate of surface warming) does. This was really all I was getting at in my earlier comment; how a change in forcing influences the time evolution of the system heat uptake rate depends on how fast the surface warms in response to that change. The oceans, of course, influence this, but don’t really influence how much we will warm overall (roughly speaking).

38. Roger Jones says:

“Okay, but do we have a strong indication that it is more staircase-like than smooth + variability?”

I understand that most of your focus is on mitigation policy, but the following things are relevant:
* sudden shifts cause big changes in extreme events and given that damages are logarithmic, this really matters for adaptation planning
* applied to mitigation policy it means you have underestimated risk (hark back to your recent post on climate economics – which many economists have not really got yet)
* people alive now, being born and who may be around soon, need the best advice they can get for decision making on human time scales. Strategic decision making needs to factor nonlinear change into decision making whether the main issue is climate change, health, economics or similar.

39. Roger Jones says:

“The oceans, of course, influence this, but don’t really influence how much we will warm overall (roughly speaking).”

Yes, but they influence how we will warm, and this is really important.

40. Roger,
Sure, I agree that if we are going to see sudden shifts then that has big implications for adaptation planning and would also mean that we’ve underestimated the risks with respect to mitigation policy. In fairness, some (including work by Ray and his colleagues) have tried to highlight possible non-linearities (not quite the same as you’re suggesting, though). My personal sense, though, is that it’s hard enough to get people to accept the risks associated with smooth, linear warming, let alone get them to accept the possibility that we could see sudden shifts into new regimes. This, however, is not me arguing against doing so, though.

41. Roger Jones says:

ATTP,
what would you say if I said I have no problem explaining this to the average punter but that the climate science community is especially resistant because it challenges ‘received wisdom’. An exception, my Australian colleagues are pretty supportive, but they know how much work has gone into making sure this isn’t just pissing in the wind.

42. Roger,
I have actually had the impression that you have had some trouble getting this accepted. I must admit that I have started reading it, but haven’t completely done so. I will endeavour to do so.

43. JCH says:

Roger Jones – in my own stumbling way I basically came to a similar conclusion as you before I read anything by you. There is just something about the way various scientists discuss the El Niño events venting ocean heat into the atmosphere that really bothers me because I do not think any significant OHC is actually leaving the oceans during the step ups.

I do not see how people can be so blasé when the mid-century hiatus, which was real and fits the PDO like a glove, which Curry and Tsonis absolutely believed was happening again with the recent “warming’ PAWS” – they predicted it lasting for as long as 2030s – is completely visible in Victor’s smoothed line and its apparent repeat, the PAWS, is completely invisible. The 30 years predicted doesn’t register at all. Not even a tiny blip.

We could be in the midst of a big step up in warming. It could be ending now; it may go on for years. If it continues, I suspect people are going to be very unhappy in general and very unhappy with climate scientists.

44. Roger Jones says:

JCH – I do see the ocean venting heat to the atmosphere triggered by ENSO. However, two things need to happen – one is the venting that puts the heat up there. The other is that large amounts of warmer water are emplaced at the ocean surface, maintaining warmer conditions where that occurs – this is commonly associated with decadal regime change. This may take one year but possibly several – there are people looking at that now. If there is no regime change, the heat gets drawn back into the ocean. So we see no shifts in El Nino events in 2002-3 or 2009-10 but do in 1997-98 and probably 2014-16 because the latter two were associated with regime change. The west Pacific warm pool collapses east across the Pacific – that has plenty of heat. This is surface-controlled warming.
Tsonis and Curry were too focused on the AMO, believing that the long cycle might dictate when the next shift occurred. This is too much of a mechanistic clockwork understanding. Under increasing forcing, there is no way the climate system can remain stable for that long. These steps come faster and closer together over time. Tsonis and his colleagues were right about these phenomena coming together in a lock-step motion but didn’t follow through to consider that they might actually be part of what drives warming.
I’ve been chasing step-like change since the early 1990s but only made these breakthroughs in the last couple of years. A colleague came in as a grad student and automated the detection test so we had access to a lot of obs and model data results. The other was that we had papers summarily dismissed by biased reviews based on statistical flim-flam. In pulling out all the stops we developed a physical narrative with the details described here. After publishing working papers last year we also were put in touch with a Russian group and a UK-European group doing similar work.
My take is that we are in a steady-state regime again that is globally about 0.3C warmer than 1997-2014. If the Interdecadal Pacific Oscillation is positive, it will be quite short-lived. Then we step up again.

45. [Mod: Apologies, I probably shouldn't have let your first comment through (which I now realise was on a different post). This comment is, unfortunately, both too confused and too certain to respond to, or to post. All I can suggest is that you spend a bit more time studying the basic greenhouse effect before asserting that it is wrong/has problems.]

46. JCH says:

RN Jones – thanks for that comment. It looks to me like a great deal of OHC was built up almost instantly during 2014 as ONI transitioned from negative to positive, and the eventual beginning of the EL Niño at the end of 2014. Then, as the El Niño event unfolded, OHC trended downward with wiggles (seasonal fluctuations), but it has snapped right back as ONI transitioned in last half of 2016 from La Niña to ENSO neutral. So OHC is suddenly back to the suddenly elevated spike that occurred in 2014. That is a lot of suddenness.

I do not think these two spikes can be just energy added to the oceans in those two short timespans – several months in 2014 and a few months in late 2016 and 1st 1/4 of 2017. A lot of it, I think, is water being transported from below 2000 meters to above 2000 meters, and then back down in the 16 La Niña, and back up as it faded to neutral ONI last 1/4 of 2016 and 1st 1/4 of 2017. For the time being, numbers on OHC below 2000 meters do not appear to be up to figuring this out.

With OHC where it is, I suspect a lot more surface warming by 2020. Time will tell, and not long to go.

47. rogerglewis says:

http://www.ecd.bnl.gov/steve/pubs/ObsDetClimSensy.pdf
“”1 63 For reasons having to do with stratospheric adjustment that occurs rapidly (months) following an
64 increase CO2, which has traditionally been used as a benchmark forcing in model studies of climate
65 sensitivity, the forcing pertinent to climate change and to determination of climate sensitivity has long
66 been considered to be the change in net absorbed radiation at the tropopause. Increasingly, however, it is
67 becoming recognized (e.g., Gregory and Forster, 2008) that the measure of forcing pertinent to the global
68 energy balance is the change in net radiation at the top of the atmosphere, again following such rapid