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Lindzen Illusion #1: We Should Have Seen More Warming

Posted on 22 April 2011 by dana1981

Australia has begun to discuss the possibility of implementing a carbon tax, and this seems to have lit a fire under the purportedly non-political global warming "skeptic" movement.  David Evans and Jo Nova have spoken at anti-carbon tax rallies, Chris Monckton wants to join them in an Australian speaking tour, and Aussie radio talk shows have even interviewed some prominent American climate "skeptics," including John Christy and Richard Lindzen.

Disappointingly, but perhaps predictably, both climate scientist "skeptics" used the opportunity for some serious Gish Galloping, as though they were in competition to see who could regurgitate more climate myths in his Australian radio interview.  As a consequence, we'll now be launching Lindzen Illusions to refute the myths of the latter, and adding to Christy Crocks to respond to those of the former.

In this first edition of Lindzen Illusions, we examine a rather old and stale myth; one which Lindzen has been making at minimum on an annual basis since 2002, and was making as early as 1989, despite the fact that it is flat-out rubbish.  Skeptical Science readers may recall that we have addressed this one before.  I am of course referring to "Earth hasn't warmed as much as expected."

"The models do say you should have seen 2-5 times more [warming] than you've already seen, you know, you have to then accept, if you believe the models, that you actually should have gotten far more warming than you've seen, but some mysterious process has cancelled part of it...if nothing else changed, adding the amount of CO2 that we have added thus far should account for maybe a quarter of what we have seen, we have added some other greenhouse gases, methane, fluorocarbons, freons, this sort of thing, and that should bring one to perhaps 0.5 C."

As we have already addressed this myth, the remainder of this post will be an updated version of the previous rebuttal (utilizing a slightly different approach to account for ocean thermal inertia, and looking at some more up-to-date numbers).  If Lindzen is going to regurgitate the same old long-debunked nonsense, we may as well replay the same old scientific piledriver of that myth!

Lindzen's argument hinges on ignoring two critical effects on the global surface temperature: the thermal inertia of the oceans, and the cooling effects of aerosols.

Thermal Inertia and Climate Sensitivity

Due to the fact that much of the Earth is covered in oceans, and it takes a long time to heat water, there is a lag before we see the full warming effects of an increase in atmospheric greenhouse gases (this is also known as "thermal inertia").  In fact, we know there remains unrealized warming from the greenhouse gases we've already emitted because there is a global energy imbalance.  The amount of unrealized warming is dependent upon the amount of CO2 in the atmosphere (or other radiative forcing causing the energy imbalance) and the thermal inertia of the oceans (which causes a lag before the warming is realized).  Lindzen does briefly acknowledge thermal inertia in a previous version of this myth, in testimony to the British Parliament:

"the observed warming is too small compared to what models suggest. Even the fact that the oceans' heat capacity leads to a delay in the response of the surface does not alter this conclusion."

Unfortunately, Lindzen does not substantiate this claim, or provide any references to support it.  However, the easiest way to incorporate this thermal lag is, rather than using the equilibrium climate sensitivity (ECS) to calculate the amount of global warming once the planet has reached equilibrium, using the transient climate sensitivity (TCS) to calcuate the transient climate response: how much the planet should have warmed right now in response to the CO2 we have emitted thus far.  The IPCC puts TCS between 1 and 3°C for a doubling of CO2, with a most likely value of 2°C.

Aerosols and Other Cooling Effects

Lindzen briefly addresses aerosols in another previous version of this argument:

"Modelers defend this situation...by arguing that aerosols have cancelled [sic] much of the warming (viz Schwartz et al, 2010)...However, a recent paper (Ramanathan, 2007) points out that aerosols can warm as well as cool"

In short, Lindzen's argument is that the radiative forcing from aerosols is highly uncertain with large error bars, and that they have both cooling (mainly by scattering sunlight and seeding clouds) and warming (mainly by black carbon darkening the Earth's surface and reducing its reflectivity) effects.  These points are both accurate. 

However, neglecting aerosols in calculating how much the planet should have warmed does not account for their uncertainty.  On the contrary, this is treating aerosols as if they have zero forcing with zero uncertainty.  It's true that aerosols have both cooling and warming effects, but which is larger?

In some of his many previous instances deploying this argument, Lindzen referred us to Ramanathan et al. (2007).  This study examined the warming effects of the Asian Brown Cloud and concluded that "atmospheric brown clouds enhanced lower atmospheric solar heating by about 50 per cent."  The study also noted that, consistent with Lindzen's claims about the aerosol forcing uncertainty, there is "at least a fourfold uncertainty in the aerosol forcing effect."  However, this study focused on the warming effects of black carbon, and did not compare them to the cooling effects of atmospheric aerosols.

Ramanathan and Carmichael (2008), on the other hand, examined both the warming and cooling effects of aerosols.   This study found that black carbon has a warming effect of approximately 0.9 W/m2, while aerosol cooling effects account for approximately -2.3 W/m2.  Thus Ramanathan and Carmichael find that the net radiative forcing from aerosols + black carbon is approximately -1.4 W/m2.  This is similar to the IPCC net aerosol  + black carbon forcing most likely value of -1.1 W/m2 (Figure 1). 

Figure 1:  Global average radiative forcing in 2005 (best estimates and 5 to 95% uncertainty ranges) with respect to 1750.  Source (IPCC AR4).

Note that Lindzen's assumed zero net aerosol + black carbon forcing is outside of this confidence range; therefore, neglecting its effect cannot be justified.  However, since the IPCC provides us with the 95% confidence range of the total net anthropogenic forcing in Figure 1, we can account for the uncertainties which concern Lindzen, and evaluate how much warming we "should have seen" by now.

Expected Forcing Effects on Temperature Thus Far

In fact, this is a simple calculation.  The IPCC 95% confidence range puts the total net anthropogenic forcing at 0.6 to 2.4 W/m2 (Figure 1).  A doubling of atmospheric CO2 corresponds to a radiative forcing of 3.7 W/m2, according to the IPCC.  Therefore, the net anthropogenic radiative forcing thus far is between approximately 16% and 65% of the forcing associated with a doubling of atmospheric CO2, with a most likely value of 45%. 

In order to be thorough, we can also include the natural radiative forcings.  Most have had approximately zero net effect since 1750, with the exception of the Sun, which has had a forcing of 0.06 to 0.30 W/m2 with a most likely value of 0.12 W/m2 over this period (Figure 1).  Therefore, net forcing since 1750 is approximately 0.66 to 2.7 W/m2, with a most likely value of 1.78 W/m2.  Thus the total net forcing thus far is between 18% and 73% of the forcing associated with a doubling of atmospheric CO2, with a most likely value of 48%.

What Does This Tell Us About Climate Sensitivity?

So far, global surface air temperatures have increased approximately 0.8°C  in response to these radiative forcings.  Since we're 18% to 73% of the way to the radiative forcing associated with a doubling of atmospheric CO2 (most likely value of 48%), the amount we should expect the planet to immediately warm once CO2 doubles (TCS) has a most likely value of 1.9°C, with a range of 1.1 to 4.4°C.  Although the upper bound is a bit high, this is very consistent with thr IPCC TCS of 1 to 3°C with a most likely value of 2°C.

The TCS is also approximately two-thirds of the ECS, which tells us that the warming we have seen so far is consistent with an equilibrium sensitivity of 1.6 to 6.6°C for a doubling of atmospheric CO2, with a most likely value of 2.9°C.  This is also broadly consistent with the IPCC ECS range of 1.5 to 4.5°C with a most likely value of 3°C.

How Much Warming Should We Have Seen?

We can also flip the calculation backwards and address Lindzen's central claim (how much warming should we have seen so far?), assuming the IPCC most likely TCS of 2°C for a doubling of atmospheric CO2 and using the numbers above.  In this case, we should have seen from 18% to 73% of 2°C, or about 0.36 to 1.46°C.   Clearly the amount of warming we have seen so far (0.8°C) is well within this range.  Additionally, the most likely amount of warming is 48% of 2°C, which is 0.96°C.  In other words, we have seen very close to the amount of warming that we "should have" seen, according to the IPCC.

We can also update the calculation with some more recent numbers.  For example, Hansen et al. have a new draft paper out which puts the aerosol forcing at -1.6 W/m2.  CO2 levels have continued to rise since the IPCC report, and the CO2 forcing is now 1.77 W/m2.  If we incorporate these figures, the most likely net forcing value becomes 1.5 W/m2, or 40% of the way to the doubled CO2 forcing.  Using these values, we would expect to have seen 0.8°C warming of surface temperatures to this point - precisely what has been observed.

Warming is Consistent with What We Expect

In short, contrary to Lindzen's claims, the amount of surface warming thus far (0.8°C) is consistent with what we "should have seen."  Moreover, this calculation puts the most likely climate sensitivity parameter value within the IPCC's stated range, whereas the much lower value claimed in Lindzen and Choi (2009) (less than 1°C for CO2 doubling) is very inconsistent even with our calculated ECS lower bound (1.6°C).  For additional discussion of the errors with Lindzen and Choi (2009), see here

When we actually account for thermal inertia and negative forcings, we find that the amount of warming we have seen is consistent with what the IPCC would expect, but inconsistent with Lindzen and Choi 2009.  Thus the correct conclusion is that if Lindzen is correct about low climate sensitivity, we should already have seen much less warming than we have seen thus far.

However, I'm not going to hold my breath waiting for Lindzen to retire this old jalopy of a myth.

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Comments 101 to 115 out of 115:

  1. Argus @99 & @89

    Perhaps you could further justify your statement

    I have great respect for Professor Lindzen; he is still an established atmospheric physicist and a famous professor of meteorology

    and explain why you feel it exempts Professor Lindzen from the serious scientific scrutiny in the OP ? I would also suggest that you take a moment to investigate the scientists Sir Cyril Burt and Gregor Mendel, both of whom (probably) transgressed in the production of their work. Wikipedia has good pages on both.

    Finally I would note that Lindzen does not have quite the same respect from other climate scientists as he does from you. From the proceedings linked @41 Sir John Houghton says of Lindzen (p18):

    but unfortunately he is not a man who does his homework. He does not read the rest of the literature; he quotes his own papers.
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  2. Hey, if it is "too early to say" that we should have seen more warming... and yet Lindzen already DID say that we should have seen more warming... then Argus clearly disagrees with Lindzen.

    Good on you chap. See, 'skeptics' don't always back each other no matter what nonsense one is putting out.
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  3. Ken L - you're equating two totally different concepts.
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  4. dana1981 #103

    If Lintzen is right, "we should have seen more warming", does that imply the current warming imbalance (+0.9W/sq.m) is reducing?

    Does anyone have later information on the summation of 2005 forcings shown at the top in Figure 1?
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  5. Can anyone quantify specifically how the amount of seasonal change the occurs in ocean water temperature corresponds to a 40 year delay between forcing and final response?

    No one, including Lindzen, disputes there is a delay, but it certainly can't be anywhere near 40 years. If it were, seasonal variability would not even occur. Heck, there would barely even be any difference between night and day with a decades long response time.
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  6. DB,

    My question is not answered there. How do you explain seasonal change with a 40 year delay?
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    Response:

    [DB] In addition to Riccardo's comment, seasonal variation is a consequence of the Earth's tilt, relative to it's plane of orbit around the sun, and intense heating of the sea surface in the regions at the equator. See illustration below:

    Earth's tilt relative to it's plane of orbit around the sun. Left-hand side=southern hemsiphere (austral) summer. Right-hand side= northern hemisphere (boreal) summer. Image courtesy of the Austalian Bureau of Meteorology 

    Thanks, Rob P!

  7. RW1
    "delay" doesn't mean that nothing happen in the meanwhile. The seasonal forcing is huge in comparison and the diurnal forcing is even larger. Still we see part of the effect. Should we be locked into a perennial winter or night it would be worse.
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  8. Riccardo (RE: 107),

    "RW1
    "delay" doesn't mean that nothing happen in the meanwhile."


    I never claimed or meant to imply that it doesn't. The point is an extremely large amount of temperature change occurs in each hemisphere in a very short period of time.

    "The seasonal forcing is huge in comparison and the diurnal forcing is even larger. Still we see part of the effect. Should we be locked into a perennial winter or night it would be worse."

    Of course, but how about a quantification showing it would take 40 years of a perennial winter or summer to reach equilibrium.

    There is roughly 5 C of change in average sea surface temperature occurring in each hemisphere every 6 months. This much change could not occur over this short a period of time if all or most of the whole mass of the ocean had to warm or cool by this much.

    As a result, it's doubtful the equilibrium response time to changes in forcing is much more than only few years with most of the response occurring in the first year.
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  9. Furthermore, what is the average sea surface temperature in the tropics? Since the tropics are roughly equivalent to perennial summer, this should give us an general idea of how much more change above 5 C is needed to occur at equilibrium. From this, we should be able estimate about how much longer it would take beyond 6 months.
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  10. RW1 - Seasonal variations don't penetrate deeply into the oceans, and they don't completely melt the Antarctica or Greenland ice caps, either. Only the upper 100 meters or so of ocean (the "well mixed" region where wind/wave turbulence has an effect) shows any significant response to seasonal variations.

    On the other hand, the average depth of the oceans is about 3800 meters. The ice caps contain well over 35*10^6 km^3 of ice (depending on who's doing the averaging). Those thermal masses are what will be affected over time by a change in the average temperature, as they respond much slower than the seasons do.

    Various people have looked at this, and the 40 year response for short term climate change is well established. Your "seasonal response" argument is ill-founded, and quite frankly I find it more than a little disingenuous.
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  11. RW1
    when you have a periodic forcing the amplitude of the response depends on the amplitude of the forcing (of course) and on the ratio of the period of the forcing and the response time of the system. You can do the calculations, they're pretty standard.

    "This much change could not occur over this short a period of time if all or most of the whole mass of the ocean had to warm or cool by this much."
    Indeed. The mixed layer depth is around 100 m. This is the relevant heat capacity which contribute to the response time. Beware that by changing the time scale you also change heat capacity and response time.

    "with most of the response occurring in the first year."
    A totally unsupported claim.
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  12. KR (RE: 110),

    "RW1 - Seasonal variations don't penetrate deeply into the oceans, and they don't completely melt the Antarctica or Greenland ice caps, either. Only the upper 100 meters or so of ocean (the "well mixed" region where wind/wave turbulence has an effect) shows any significant response to seasonal variations.

    On the other hand, the average depth of the oceans is about 3800 meters. The ice caps contain well over 35*10^6 km^3 of ice (depending on who's doing the averaging). Those thermal masses are what will be affected over time by a change in the average temperature, as they respond much slower than the seasons do."


    Most of the thermal mass is in the oceans (over 90%) - not in the ice caps. If seasonal variations from solar 'forcing' don't penetrate deep into the oceans, then there is no reason why 'GHG' forcing would either. Any GHG 'forcing' would be rolled in on top of seasonal solar 'forcing', and it would only a be a few extra milliwatts per year.

    Also, are you forgetting that the 2nd law says heat travels from warm to cold? Even if over the long term the heat penetrates deeper into the ocean, it's not going to make the surface any warmer. What matters is how quickly the surface water temperature can warm in response to a 'forcing'. I know of no reason why this would be any different for GHG 'forcing' than for seasonal solar 'forcing'.
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  13. Riccardo (RE: 111),

    "RW1
    when you have a periodic forcing the amplitude of the response depends on the amplitude of the forcing (of course) and on the ratio of the period of the forcing and the response time of the system. You can do the calculations, they're pretty standard."


    I presume you are referring to time constant calculations?
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  14. RW1 - "Any GHG 'forcing' would be rolled in on top of seasonal solar 'forcing', and it would only a be a few extra milliwatts per year."

    A few tenths of a watt, actually. And over time that constant offset will shift the centerpoint of ocean temperatures, with lows, highs, and averages shifting to a warmer point driven by the constant imbalance.

    "I know of no reason why this would be any different for GHG 'forcing' than for seasonal solar 'forcing'."

    Really, RW1? You know of no reason why a constant offset would cause a different response to a system with thermal inertia than a rapid variation with a constant average? If that is the case, I fear you will continue to have a great deal of difficulty understanding response times.

    Please read the 40 year response for short term climate change.
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  15. RW1
    yes, kind of. Applied to a climate system with a single characteristic time ts, you get a the response with amplitude proportional to 1/[1+(2*pi*ts/tf)**2] with tf period of the forcing.
    It's a crude model, but should give you the idea.
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