I drafted up LI #1, which is mostly a re-post of the 'Case Study of a Climate Scientist Skeptic."  Except in the calculation this time, instead of trying to estimate the heat going into the oceans, I just used transient climate sensitivity, which I think is a better approach.  I'd also appreciate feedback on whether the tone of the intro is okay.

Lindzen Illusion #1: We Should Have Seen More Warming

Is that an expression? Very vivid imagery. But lest everyone be thinking about Jo Nova's buns, maybe you should just go with "lit a fire under the purportedly non-political global warming "skeptic" movement :-)

Well, they'll have to think about CM's buns as well - that should put them right off!

Well the expression is "lit a fire under his ass", but I didn't want to use that language :-)  But I can certainly take the buns out too.

Dana,

Not sure if you know, but Hansen has a new paper in the works in which he claims that the negative forcing from aerosols is -1.6 W m-2 +/- 0.3. Not sure whether or not this is helpful.  That sounds like a really high value to me, on par with CO2 forcing alone no?

I am a great lover of buns, but best to leave it out ;)  Not sure about making reference to 'doped up', maybe something more sophisticated is in order.

Thanks Alby.  I saw that paper but didn't get a chance to read it.  -1.6 W/m2 is definitely on the high side (about 0.4 W/m2 larger than the IPCC most likely value and almost as large as CO2, though that's now nearly 1.8 W/m2).  Certainly plausible though.  Maybe I'll run the numbers for that forcing as an alternative possibility.  Maybe use 1.8 W/m2 for CO2 and -1.6 W/m2 for aerosols.

I'll modify the language you mention a bit too :-)

Funny, using those values, the "expected" warming comes out to 0.8°C.  Suck on that, Lindzen!

Looks good to me.

Dana, you might find a basic error in my calculations again!

Equilibrium temperature change ΔT = λ*ΔF

λ = 0.8 K W^-1 m²

ΔF = GHGs – aerosols = 2.7 – 1.6 = 1.1 W m^-2

ΔT = 0.8*1.1 = 0.9 K

Transient temperature change ΔT = λ*ΔF

λ = 0.8 K W^-1 m²

ΔF = GHGs – aerosols – energy imbalance = 2.7 – 1.6 – 0.6 = 0.5 W m^-2

ΔT = 0.8*0.5 = 0.4 K

Turning the equation around to derive climate sensitivity:

λ = ΔT/ΔF

ΔT = 0.7 K

ΔF = 0.5 W m^-2

λ = 0.7/0.5 = 1.4 K W^-1 m² = 5.1 K per doubling of CO2

A couple things James.  In the first set of calculations, I'd suggest using more up-to-date GHG forcings, which brings it up to about 2.8 W/m2 and the net to 1.2 W/m2.  There's also the solar forcing if you want to be thorough, bringing it up above 1.3 W/m2, and ΔT to close to 1.1°C.

In the second set again I'd up the ΔF by about 0.2 to 0.25, so the ΔT becomes about 0.6 K.  That's a bit low, so it would suggest either the aerosol forcing or energy imbalance (or both) are slightly high.

In the third set ΔT = 0.8 K and ΔF = 0.73 W/m2, so λ = 1.1 = 4.1 K for 2xCO2.

You’re right, the GHG forcing should be 2.8 W m^-2 – I mistakenly rounded down instead of up. If anything I would think the energy imbalance is slightly low, because it’s being measured in a solar minimum and we don’t have good measurements of the deep oceans.

If I correct the GHG forcing and add in the solar forcing, I get 0.6°C. But I still don’t get the 0.8°C you use in your article. And a 4°C sensitivity seems like it’s worth mentioning.

But you also used a forcing of 1.5 W m^-2. Where did the extra 0.2 W m^-2 come from?

That’s still only 1.35. These equations are fascinating; ±0.1 here and there and you get quite different results.

Rearranging the equations to derive the energy imbalance…

Energy imbalance = ΔF_e – ΔF_t = ΔT_e/λ_e – ΔT_t/λ_e = 1.0/0.8 – 0.8/0.8 = 0.25 W m^-2

(sub e = equilibrium, sub t = transient)

…I get only 0.25 W m^-2, much smaller than observed.

Oh, I think the discrepancy is that I'm using the net IPCC forcing (1.6 W/m2 anthro plus 0.12 solar) whereas you're just using GHGs and aerosols, right?

Equilibrium temperature change: ΔT_e = λ_e*ΔF_e

λ_e = 0.8 K W^-1 m²

ΔF_e = 1.5 W m^-2

ΔT_e = 0.8*1.5 = 1.2 K

Transient temperature change using energy imbalance: ΔT_t = λ_e*ΔF_t

λ_e = 0.8 K W^-1 m²

ΔF_t = 1.5 – 0.6 = 0.9 W m^-2

ΔT_t = 0.8*0.9 = 0.7 K

Transient temperature change using transient climate sensitivity: ΔT_t = λ_t*ΔF_e

λ_t = 0.5 K W^-1 m²

ΔF_e = 1.5 W m^-2

ΔT_t = 0.5*1.3 = 0.7 K

Climate sensitivity using energy imbalance: λ_e = ΔT_t/ΔF_t

ΔT_t = 0.8 K

ΔF_t = 0.9 W m^-2

λ_e = 0.8/0.9 = 0.9 K W^-1 m² = 3.3 K for 2xCO2

Climate sensitivity using temperature change: λ_e = 1.5λ_t = 1.5ΔT_t/ΔF_e

ΔT_t = 0.8 K

ΔF_e = 1.5 W m^-2

λ_t = 0.8/1.5 = 0.5 K W^-1 m² = 2.0 K for 2xCO2

λ_e = 1.5λt = 3.0 K for 2xCO2

Yep, that looks about right.